Intelligent and Fuzzy Systems: Digital Acceleration and The New Normal - Proceedings of the INFUS 2022 Conference, Volume 1 (Lecture Notes in Networks and Systems, 504) 3031091728, 9783031091728

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Lecture Notes in Networks and Systems 504

Cengiz Kahraman · A. Cagri Tolga · Sezi Cevik Onar · Selcuk Cebi · Basar Oztaysi · Irem Ucal Sari   Editors

Intelligent and Fuzzy Systems Digital Acceleration and The New Normal - Proceedings of the INFUS 2022 Conference, Volume 1

Lecture Notes in Networks and Systems Volume 504

Series Editor Janusz Kacprzyk, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland Advisory Editors Fernando Gomide, Department of Computer Engineering and Automation—DCA, School of Electrical and Computer Engineering—FEEC, University of Campinas— UNICAMP, São Paulo, Brazil Okyay Kaynak, Department of Electrical and Electronic Engineering, Bogazici University, Istanbul, Turkey Derong Liu, Department of Electrical and Computer Engineering, University of Illinois at Chicago, Chicago, USA Institute of Automation, Chinese Academy of Sciences, Beijing, China Witold Pedrycz, Department of Electrical and Computer Engineering, University of Alberta, Alberta, Canada Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland Marios M. Polycarpou, Department of Electrical and Computer Engineering, KIOS Research Center for Intelligent Systems and Networks, University of Cyprus, Nicosia, Cyprus Imre J. Rudas, Óbuda University, Budapest, Hungary Jun Wang, Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong

The series “Lecture Notes in Networks and Systems” publishes the latest developments in Networks and Systems—quickly, informally and with high quality. Original research reported in proceedings and post-proceedings represents the core of LNNS. Volumes published in LNNS embrace all aspects and subfields of, as well as new challenges in, Networks and Systems. The series contains proceedings and edited volumes in systems and networks, spanning the areas of Cyber-Physical Systems, Autonomous Systems, Sensor Networks, Control Systems, Energy Systems, Automotive Systems, Biological Systems, Vehicular Networking and Connected Vehicles, Aerospace Systems, Automation, Manufacturing, Smart Grids, Nonlinear Systems, Power Systems, Robotics, Social Systems, Economic Systems and other. Of particular value to both the contributors and the readership are the short publication timeframe and the world-wide distribution and exposure which enable both a wide and rapid dissemination of research output. The series covers the theory, applications, and perspectives on the state of the art and future developments relevant to systems and networks, decision making, control, complex processes and related areas, as embedded in the fields of interdisciplinary and applied sciences, engineering, computer science, physics, economics, social, and life sciences, as well as the paradigms and methodologies behind them. Indexed by SCOPUS, INSPEC, WTI Frankfurt eG, zbMATH, SCImago. All books published in the series are submitted for consideration in Web of Science. For proposals from Asia please contact Aninda Bose ([email protected]).

More information about this series at https://link.springer.com/bookseries/15179

Cengiz Kahraman A. Cagri Tolga Sezi Cevik Onar Selcuk Cebi Basar Oztaysi Irem Ucal Sari •

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Editors

Intelligent and Fuzzy Systems Digital Acceleration and The New Normal Proceedings of the INFUS 2022 Conference, Volume 1

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Editors Cengiz Kahraman Department of Industrial Engineering Istanbul Technical University Istanbul, Turkey

A. Cagri Tolga Department of Industrial Engineering Galatasaray University Istanbul, Turkey

Sezi Cevik Onar Department of Industrial Engineering Istanbul Technical University Istanbul, Turkey

Selcuk Cebi Department of Industrial Engineering Yildiz Technical University Istanbul, Turkey

Basar Oztaysi Department of Industrial Engineering Istanbul Technical University Istanbul, Turkey

Irem Ucal Sari Department of Industrial Engineering Istanbul Technical University Istanbul, Turkey

ISSN 2367-3370 ISSN 2367-3389 (electronic) Lecture Notes in Networks and Systems ISBN 978-3-031-09172-8 ISBN 978-3-031-09173-5 (eBook) https://doi.org/10.1007/978-3-031-09173-5 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

INFUS is an acronym for intelligent and fuzzy systems. It is a well-established international research forum to advance the foundations and applications of intelligent and fuzzy systems, computational intelligence, and soft computing for applied research in general and for complex engineering and decision support systems. The principal mission of INFUS is to construct a bridge between fuzzy and intelligence systems and real complex systems via joint research between universities and international research institutions, encouraging interdisciplinary research and bringing multidiscipline researchers together. INFUS 2019 was an on-site conference organized in Istanbul, Turkey. INFUS 2020 and INFUS 2021 conferences were organized as online conferences because of pandemic conditions. INFUS 2022 conference is organized as both online and on-site conference this year. The theme of INFUS 2022 conference this year is digital transformation and the new normal. Digital transformation plays a vital role in the sustainability of the organization, and it is a long-term investment. As the world continues to fight the devastating impact of the coronavirus pandemic, the need for digital transformation has become more necessary than ever. While companies will undoubtedly face significant challenges in the digital transformation process, it has become a must for managers to accelerate the digital transformation of operations. The new normal is the state to which economies, societies, etc. settle following a crisis that is the coronavirus pandemic in our case. The post-COVID-19 era brought us to a new normal that will accelerate digital transformation in many areas such as digital economy, digital finance, digital government, digital health, and digital education. To prepare for a digital “new normal” and maintain a leadership position among competitors, both manufacturing and service companies need to initiate a robust digital transformation. Digitizing an industrial company is a challenging process, which involves rethinking established structures, processes, and steering mechanisms. INFUS 2022 aims to bring together the latest theoretical and practical intelligent and fuzzy studies on digital transformation, digital acceleration, and the new normal, to present it to the participants and to create a discussion environment.

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Researchers from more than 20 countries such as Turkey, Russia, China, Iran, Poland, India, Azerbaijan, Bulgaria, Spain, Ukraine, Pakistan, South Korea, UK, Indonesia, USA, Vietnam, Finland, Romania, France, Uzbekistan, Italy, and Austria contributed to INFUS 2022. Our invited speakers this year are Prof. Krassimir Atanassov, Prof. Vicenc Torra, Prof. Janusz Kacprzyk, Prof. Ahmet Fahri Özok, Prof. Ajith Abraham, Prof. Okyay Kaynak, Prof. Habib Zaidi, and Prof. Vilem Novak. It is an honor to include their speeches in our conference program. We appreciate their voluntary contributions to INFUS 2022, and we hope to see them at INFUS conferences for many years. This year, the number of submitted papers became 364. After the review process, about 46% of these papers have been rejected. More than 50% of the accepted papers are from other countries outside Turkey. We again thank all the representatives of their countries for selecting INFUS 2022 as an international scientific arena. We also thank the anonymous reviewers for their hard works in selecting high-quality papers of INFUS 2022. Each of the organizing committee members provided invaluable contributions to INFUS 2022. INFUS conferences would be impossible without their efforts. We hope meeting all of our participants next year in Turkey at a face-to-face conference. We would like to thank our publisher Springer Publishing Company, Series editor Prof. Janusz Kacprzyk, Interdisciplinary and Applied Sciences and Engineering and Editorial Director Thomas Ditzinger, last but not least, Project Coordinator Viradasarani Natarajan for their supportive, patient, and helpful roles during the preparation of this book. Cengiz Kahraman A. Cagri Tolga Selcuk Cebi Basar Oztaysi Sezi Cevik Onar Irem Ucal Sari

Organization

Program Committee Chairs Kahraman, Cengiz Cevik Onar, Sezi Oztaysi, Basar Tolga, Çağrı Ucal Sari, Irem Çebi, Selçuk

ITU, Industrial Engineering Department, Istanbul, Turkey Istanbul Technical University, Istanbul, Turkey İstanbul Technical University, Istanbul, Turkey Galatasaray University, Department of Industrial Engineering, Istanbul, Turkey Istanbul Technical University, Industrial Engineering, Istanbul, Turkey Yildiz Technical University, Industrial Engineering, İstanbul, Turkey

Program Committee Members Alkan, Nurşah

Aydin, Serhat Boltürk, Eda Dogan, Onur Haktanır Aktaş, Elif Ilbahar, Esra Kahraman, Cengiz

Istanbul Technical University, Department of Industrial Engineering, Maçka, Beşiktaş, Turkey National Defence University, Industrial Engineering Department, Istanbul, Turkey Istanbul Settlement and Custody Bank Inc.-Takasbank, İstanbul, Turkey Izmir Bakircay University, Department of Industrial Engineering, İzmir, Turkey Altinbas University, Industrial Engineering, Istanbul, Turkey Yildiz Technical University, Industrial Engineering Department, İstanbul, Turkey ITU, Industrial Engineering Department, Istanbul, Turkey

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Karaşan, Ali Kutlu Gündoğdu, Fatma Otay, Irem Cevik Onar, Sezi Oztaysi, Basar Seker, Sukran Senvar, Ozlem Tolga, Çağrı Ucal Sari, Irem Çebi, Selçuk Çoban, Veysel

Organization

Yildiz Technical University, Istanbul, Turkey National Defence University, Industrial Engineering Department, Istanbul, Turkey Istanbul Bilgi University, Istanbul, Turkey Istanbul Technical University, Istanbul, Turkey İstanbul Technical University, Istanbul, Turkey Yildiz Technical University, Istanbul, Turkey Marmara University, Department of Industrial Engineering, Istanbul, Turkey Galatasaray University, Department of Industrial Engineering, Istanbul, Turkey Istanbul Technical University, Industrial Engineering, Istanbul, Turkey Yildiz Technical University, Industrial Engineering, İstanbul, Turkey Bilecik Seyh Edebali University, Bilecik, Turkey

Contents

Ordinary Fuzzy Sets Fuzzy Static and Dynamic De Novo Type Approaches to Optimal System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Janusz Kacprzyk

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Non-additive Measures, Set Distances and Cost Functions on Sets: A Fréchet-Nikodym-Aronszajn Distance and Cost Function . . . . . . . . . . Vicenç Torra

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Ergonomics, Human Performance, and Fuzzy Logic . . . . . . . . . . . . . . . Ahmet Fahri Özok

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Systematic Mapping Study of Fuzzy Risk Indicators for Pedestrians . . . Maroua Razzouqi, Azedine Boulmakoul, Ghyzlane Cherradi, Lamia Karim, Adil El Bouziri, and Ahmed Lbath

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Dealing with Nonmonotonic Criteria in Decision-Making Problems Using Fuzzy Normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bartłomiej Kizielewicz, Jakub Więckowski, Bartosz Paradowski, and Wojciech Sałabun

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Feasibility Analysis of Automated Vertical Farming in Istanbul Using Fuzzy Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Osman Pakirdasi and A. Cagri Tolga

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How Mining and Summarizing Information on Time Series Can Be Formed Using Fuzzy Modeling Methods . . . . . . . . . . . . . . . . . . . . . . . . Vilém Novák

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Fuzzy-Chaotic Variant of the Multiverse Optimizer Algorithm in Benchmark Function Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . Lucio Amézquita, Oscar Castillo, and Prometeo Cortes-Antonio

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Classification of Non-pharmaceutical Anti-COVID Interventions Based on Novel FTOPSIS-Sort Models . . . . . . . . . . . . . . . . . . . . . . . . . Alexander Radaev, Elif Haktanir, Boris Yatsalo, and Cengiz Kahraman

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A Hybrid Fuzzy Rule-Based Polyhedral Separation Approach: Medical Diagnosis Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Halil İbrahim Ayaz and Bilal Ervural

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Fuzzy Pedestrian’s Risk Perception and Notification in Fuzzy Neighborhoods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Azedine Boulmakoul, Souhail El Kaissi, and Ahmed Lbath

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The Approximate Method for Solving Second-Order Fuzzy Boundary Value Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nurain Zulaikha Husin, Muhammad Zaini Ahmad, and Mohd Kamalrulzaman Md Akhir Deployment of Software Agents and Application of Fuzzy Controller on the UWB Localization Based Mobile Robots . . . . . . . . . . . . . . . . . . . Burak Karaduman, Baris Tekin Tezel, and Moharram Challenger

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Real-Time Distributed System for Pedestrian Assistance Using Fuzzy Logic: Application and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 Azedine Boulmakoul, Kaoutar Bella, and Ahmed Lbath Fuzzy Clustering Based Association Rule Mining: A Case Study on Ecommerce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 Başar Öztayşi, Pelin Yurdadön, and Sezi Çevik Onar A Novel Fuzzy Clustering-Based Task Allocation Method for Location and Routing of Multi Robots in the Response Phase of Disasters . . . . . . 119 Abdullah Osman and Tarık Küçükdeniz The Method of Ranking Business Processes on Weaknesses Based on the Theory of Fuzzy Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 Alekperov Ramiz Assessment of the Effectiveness of Marketing Activities of Commercial Enterprises Using the Theory of Fuzzy Sets . . . . . . . . . . . . . . . . . . . . . . 135 Alekperov Ramiz and Salahli Vuqar Sparse Weighted Multi-view Possibilistic C-Means Clustering with L1 Regularization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 Josephine Bernadette Benjamin, Shazia Parveen, and Miin-Shen Yang Picture Fuzzy Simple Additive Weighting Method for Food Presentations Scoring of Gastronomy Students . . . . . . . . . . . . . . . . . . . 151 Fatma Yaşlı and Sema Ekincek

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A Proposed Methodology for Risk Classification Using Fuzzy Group Decision Making and Fuzzy C-Means . . . . . . . . . . . . . . . . . . . . . . . . . . 160 Fatih Yiğit and İlknur Dönmez Prediction of the Annual Yield of Citrus Growth in the Guzelyurt District Using Fuzzy Inference Systems . . . . . . . . . . . . . . . . . . . . . . . . . 168 Filiz Al-Shanableh Parallel Machine Scheduling with Fuzzy Processing Times and Sequence Dependent Setup Times: An Application in a Textile Company . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 Gülce Çini, Ayhan Özgür Toy, and Önder Bulut Integrated Warehouse Layout Planning with Fuzzy C-Means Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 Tarık Küçükdeniz and Özlen Erkal Sönmez Planning and Scheduling Scheme Based on Fuzzy Finite State Machine Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 Margarita Knyazeva, Alexander Bozhenyuk, and Stanislav Belyakov Electric Vehicle Selection by Using Fuzzy SMART . . . . . . . . . . . . . . . . 200 Basar Oztaysi, Cengiz Kahraman, and Sezi Cevik Onar Fuzzy Periodic Patterns from Super-Market Datasets . . . . . . . . . . . . . . 208 Fokrul A. Mazarbhuiya, Limainla Kichu, and M. Y. AlZahrani A Supervised Approach to Community Detection Problem: How to Improve Louvain Algorithm by Considering Fuzzy Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 María Barroso, Daniel Gómez, and Inmaculada Gutiérrez Hierarchical Fuzzy Inference System for Diabetes Mellitus Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 Daud Mohamad and Aisya Irdina Hissamudin Danger Level Ranking of Possible Dam Failures in Turkey by Grey Relational Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 Halid Akdemir and Cihan Bayindir An Adaptive Fuzzy Assisted Fault Identification Observer for Bearing Using AE Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 Farzin Piltan and Jong-Myon Kim Using Fuzzy Set Based Model for Pharmaceutical Supply Chain Risks Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 Irem Yalcinkaya and Selcuk Cebi A New Fuzzy Based Risk Assessment Approach for the Analysis of Occupational Risks in Manufacturing Sector . . . . . . . . . . . . . . . . . . . 261 Selcuk Cebi and Merve Karamustafa

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Fuzzy Predictor of Daily Average Water Consumption Per Capita for Turkey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 Halid Akdemir and Cihan Bayindir Distributed No-Wait Flow Shop with Fuzzy Environment . . . . . . . . . . . 279 Ramazan Başar, Kadir Büyüközkan, and Orhan Engin Fuzzy Based Weighted, Arithmetic Optimization Algorithm (AOA) for Cash Management Optimization on Automatic Teller Machines (ATM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 Ali Tunç and Sakir Taşdemir Site Selection of Grid-Connected Photovoltaic Power Plants with Fuzzy Hybrid Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 Veysel Çoban and Sezi Çevik Onar Classification of Provinces in Turkey in Terms of Health Indicators with Fuzzy Clustering Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 Aslı Dolu and Ümit Kuvvetli The Facility Location Problem with Fuzzy Parameters . . . . . . . . . . . . . 311 Gamze Erdem, A. Özgür Toy, and Adalet Öner Fuzzy Network Data Envelopment Analysis in the Evaluation of Project Success Across the Project Life Cycle . . . . . . . . . . . . . . . . . . 319 Dorota Kuchta and Agata Klaus-Rosińska Solving Matrix Games Involving the Level (glower, g upper) Interval Valued Pentagonal Fuzzy Payoffs: Signed Distance Ranking Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328 V. Kamal Nasir and A. Jamal Barakath A Literature Review on Supplier Selection Problem and Fuzzy Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 Mert Paldrak, Gamze Erdem, Melis Tan Tacoğlu, Simge Güçlükol, and Efthimia Staiou Fuzzy C-Means Clustering of Ships Passing Through Turkish Straits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352 Cengiz Vefa Ekici, Ozcan Arslan, and Ulku Ozturk Applying Fuzzy Decision Tree Method for Hypertension Classification in Adolescent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360 Hizir Sofyan, Elfayani Elfayani, Azalya Rahmatika, Marzuki Marzuki, and Irvanizam Irvanizam Action Selection Based on Fuzzy AHP-Based TOPSIS Method in Fuzzy FMEA-Based Risk Assessment: A Case Study . . . . . . . . . . . . . 369 Murat Oturakçı and Aziz Kemal Konyalıoğlu

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Forecasting Crop Yields Based on Fuzzy Analysis of the Dynamics of Remote Sensing Multispectral Data . . . . . . . . . . . . . . . . . . . . . . . . . . 378 Elchin Aliyev and Fuad Salmanov Supplier Selection After Pandemic in SMEs Using Fuzzy Best Worst Method and Fuzzy WASPAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 Irem Ucal Sari, Arda Pesek, and Kami Bozukyan Fuzzy TODIM for ELICIT Information . . . . . . . . . . . . . . . . . . . . . . . . 396 Álvaro Labella, Diego García-Zamora, Rosa M. Rodríguez, and Luis Martínez A Novel MCDM Method Based on Possibility Mean and Its Application to Water Resource Management Problem Under Bipolar Fuzzy Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405 Totan Garai, George Biswas, and Uttaran Santra Fuzzy TOPSIS and Goal Programming Approaches to Multi Objective Facility Location Problem for Emergency Goods and Services Distribution and Bornova/Izmir Case Study . . . . . . . . . . . 413 Mert Paldrak, Simge Güçlükol, Mahmut Ali Gökçe, and Melis Tan Tacoğlu Determination of Competencies with Fuzzy Multi-criteria Decision Making Methods for Determining the Development Program for Analyst Position in a Participation Bank . . . . . . . . . . . . . . . . . . . . . 425 İbrahim Yel, Ahmet Sarucan, and Mehmet Emin Baysal Z-Fuzzy Numbers Using Fuzzy Z - Numbers When Processing Flexible Queries . . . . . . . . 435 Ramiz Alekperov Comparative Analysis of Expert Evaluation Criteria Under Z-Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445 Olga Poleshchuk Creation of a Group Expert Criterion for Evaluating the State of a Plant Species Under Z-Information . . . . . . . . . . . . . . . . . . . . . . . . . 452 Olga Poleshchuk Data Envelopment Analysis with Z-Numbers – An Application to Project Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460 Dorota Kuchta and Barbara Gładysz Picture Fuzzy Sets Risk Analysis of Digital Transformation with an Integrated Picture Fuzzy QFD and FMEA Methodology . . . . . . . . . . . . . . . . . . . . 471 Elif Haktanır

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ARAS Method in Picture Fuzzy Environment for the Selection of Catering Firm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481 Nihan Tirmikcioglu Working Environment Selection After Pandemic Using Picture Fuzzy Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489 Mustafa Bal and Irem Ucal Sari Cloud Service Provider Selection Using Interval-Valued Picture Fuzzy TOPSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498 Cengiz Kahraman, Sezi Cevik Onar, and Basar Oztaysi Picture Fuzzy Benefit/Cost Analysis in Digital Transformation for an IT Firm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508 Eda Boltürk Intuitionistic Fuzzy Sets On the Temporal Intuitionistic Fuzzy Sets . . . . . . . . . . . . . . . . . . . . . . . 519 Krassimir T. Atanassov Intuitionistic Fuzzy Generalized Net Model of the Humanoid Service Robot Functionalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 529 Simeon Ribagin, Sotir Sotirov, Evdokia Sotirova, Iasen Hristozov, and Krassimir Atanassov The Initial Value Problem of Intuitionistic Fuzzy Differential Equations and the Economic Growth Models . . . . . . . . . . . . . . . . . . . . 537 Nguyen Dinh Phu, Nguyen Nhut Hung, and Le Thi Ngoc Quynh Second Order Intuitionistic Fuzzy Time Series Forecasting Model via Crispification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556 Nik Muhammad Farhan Hakim Nik Badrul Alam and Nazirah Ramli Internally Stable Set in Intuitionistic Fuzzy Graph . . . . . . . . . . . . . . . . 566 Cengiz Kahraman, Alexander Bozhenyuk, and Margarita Knyazeva Investigation of Employer Attractiveness from an University Students Perspective by Application of Intuitionistic Fuzzy Assessments . . . . . . . 573 Milen Todorov, Gergana Avramova-Todorova, and Sotir Sotirov Digital Interpretation of Movie Sales Revenue Through Intuitionistic Fuzzy Analysis of Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 581 Velichka Traneva and Stoyan Tranev Circular Intuitionistic Fuzzy Analytic Hierarchy Process for Remote Working Assessment in Covid-19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 589 Esra Çakır and Mehmet Ali Taş

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Weighting ESG Criteria of Banks by Using Interval Valued Intuitionistic Fuzzy Best Worst Method . . . . . . . . . . . . . . . . . . . . . . . . . 598 Burcu Simsek Yagli, Nuri Ozgur Dogan, and Ibrahim Yagli Watson Crick Intuitionistic Fuzzy Automata . . . . . . . . . . . . . . . . . . . . . 606 N. Jansirani, N. Vijayaraghavan, and V. R. Dare Generalized Net Model of a Serial Composition of Services with Intuitionistic Fuzzy Estimations of Uncertainty . . . . . . . . . . . . . . . 616 Velin Andonov, Stoyan Poryazov, and Emiliya Saranova Intuitionistic Fuzzy Estimations of Uncertainty of a Parallel Composition of Services . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624 Stoyan Poryazov, Velin Andonov, and Emiliya Saranova Intuitionistic Fuzzy Model for Franchisee Selection . . . . . . . . . . . . . . . . 632 Velichka Traneva and Stoyan Tranev Software Selection for IT Industry Using Complex q-Rung Orthopair Fuzzy MCDM Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 641 D. Ajay, J. Aldring, and T. S. Jaganath Internet of Things Fermatean Fuzzy CRITIC Testing Procedure for New Normal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 649 Mehmet Kabak, Serhat Aydın, and Ahmet Aktaş IoT Platform Selection Using Interval Valued Intuitionistic Fuzzy TOPSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656 Sezi Çevik Onar, Cengiz Kahraman, and Başar Öztayşi A Hybrid Algorithm for Multilayer Perceptron Design with Intuitionistic Fuzzy Logic Using Malignant Melanoma Disease Data . . . 665 Sotir Sotirov, Yaroslava Petrova, Hristo Bozov, and Evdokia Sotirova Generalized Net Model of Balanced Iterative Reducing and Clustering Using Hierarchies (Birch) with Intuitionistic Fuzzy Evaluations . . . . . . . 673 Veselina Bureva, Petar Petrov, and Stanislav Popov Software Utility of One-Way Intuitionistic Fuzzy ANOVA . . . . . . . . . . . 681 Velichka Traneva, Deyan Mavrov, and Stoyan Tranev Spherical Fuzzy Sets Analyzing Critical Criteria of Spaceport Site Selection Based on Spherical Fuzzy AHP Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693 Melike İlhan, Fatma Kutlu Gündoğdu, and Ali Karaşan Fuzzy Analytic Hierarchy Process Using Spherical Z-Numbers: Supplier Selection Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 702 Nurşah Alkan and Cengiz Kahraman

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A Multi-attribute Decision Making Method for the Evaluation of Software Enterprise Based on T-Spherical Fuzzy Dombi Aggregation Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 714 Kifayat Ullah, Zunaira Gul, Harish Garg, and Tahir Mahmood A Decision Support System for Rheumatoid Arthritis (RA) Treatment Selection and Factor Prioritization by Using Spherical Fuzzy Sets . . . . . 723 Rana Ezgi Köse, Neriman Rençber, Tuğçe Beldek, and Aziz Kemal Konyalıoğlu Neuro-Fuzzy Systems Active Power Control of a Natural Gas/Fuel Oil Turbine Power Plant with Adaptive Neuro-Fuzzy Inference System-Based on Modern Controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 735 Rahma Tabakh, Hasan Tiryaki, and Nevra Bayhan ANFIS-Based Determination of pH Level of Liquid Raw Materials with Image Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 744 Batuhan Atasoy, Kadim Tasdemir, Mahmut Durmus, Ezgi Demir, Fatih Gucluer, and Emre Tosun Recurrent Neural Network Controller for Linear and Nonlinear Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 752 Saeid Sheikhmemari Prediction of the Spatiotemporal Dynamics of von Kármán Vortices by ANFIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 761 Cihan Bayindir and Halid Akdemir Two-Stage Rail Defect Classification Based on Fuzzy Measure and Convolutional Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . 769 Ilhan Aydın and Erhan Akın Optimal Gene Selection and Classification of Microarray Data Using Fuzzy Min-Max Neural Network with LASSO . . . . . . . . . . . . . . . . . . . . 777 Yashpal Singh and Seba Susan Interval Type-3 Fuzzy Aggregators for Ensembles of Neural Networks in Time Series Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 785 Oscar Castillo, Martha Pulido, and Patricia Melin Brain Signal Classification Using Self-tuning Assisted Fuzzy Structure Uncertain Indirect Observer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794 Shahnaz TayebiHaghighi, Young-Doo Lee, and Insoo Koo Estimating Return Rate of Blockchain Financial Product by ANFIS-PSO Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 802 Şule Öztürk Birim, Filiz Erataş Sönmez, and Yağmur Sağlam Liman

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Intelligence Intelligent Fuzzy Clinical Decision Support System to Predict the Coimbra Breast Cancer Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . 813 Y. F. Hernández-Julio, H. Muñoz-Hernández, L. A. Díaz-Pertuz, M. Prieto-Guevara, N. S. Arrieta-Hernández, N. A. Figueroa-Mendoza, M. Aviles-Román, and W. Nieto-Bernal Evaluation of Artificial Intelligence Applications in Aviation Maintenance, Repair and Overhaul Industry via MCDM Methods . . . . 822 Metin Emin Aslan and A. Cagri Tolga Rethinking Customer Analytics: The Impact of Artificial Intelligence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 831 Ali Pişirgen, Abdulkadir Hızıroğlu, and Onur Doğan Mixing Population-Based Metaheuristics: An Approach Based on a Distributed-Queue for the Optimal Design of Fuzzy Controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 839 Alejandra Mancilla, Oscar Castillo, and Mario García Valdez Fuzzy Subsets Theory-Based Imprecision Modeling Using Ontology and Applied to Risk Estimation in Project Intelligent Management . . . . 847 Larbi Abdelmadjid and Malki Mimoun Personalized Literature Selection System Based on the Nearest Neighbor Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 856 Hubert Zarzycki and Oskar Skubisz A Meta-heuristic Approach to the Single Machine Scheduling Problem with Periodic Maintenance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 864 Kadir Büyüközkan, Mehmet Emin Baysal, Cahit Yalçın, and Ahmet Sarucan The Intelligent System for Interactive Analysis and Forecasting of Graph Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 870 Vadim Moshkin, Nadezhda Yarushkina, and Irina Moshkina Classification of Concrete Surface Damage Using Artificial Intelligence Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 879 Ching-Lung Fan Extraction of Delay Parameters of Fluid Flows by Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 887 Cihan Bayindir and Onur Üstüner Optimal Control and Dynamic Stability of Power Injection Based on Fuzzy Intelligent Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 895 Yousif I. Al Mashhadany, Gozde Ulutagay, and Baraa Jalil Abdulelah

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Optimization of Moving Averages as Trend Indicators of a Stock Market Asset with Particle Swarm Optimization Algorithm . . . . . . . . . 905 Francisco Solano López Rodríguez and José Manuel Zurita López Intelligent Valid Inequalities for No-Wait Permutation Flowshop Scheduling Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 914 Damla Yüksel, Levent Kandiller, and Mehmet Fatih Taşgetiren An Intelligent Smartphone-Based ADAS . . . . . . . . . . . . . . . . . . . . . . . . 923 Manolo Dulva Hina, Assia Soukane, and Amar Ramdane-Cherif Selectivity: The Essence of Natural and Artificial Intelligence . . . . . . . . 932 Yinsheng Zhang An Intelligent Understanding of the Post-COVID-19 Uncertainty: Provided Guidelines and Strategies for Resilient Supply Chain Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 941 Fariba Farid and Yaser Donyatalab Intelligent Supply Chains Through Implementation of Digital Twins . . . 957 Oray Kulaç, Banu Y. Ekren, and A. Özgür Toy Evaluation of Control and Management System Performance for the Complex Objects Under Uncertainty . . . . . . . . . . . . . . . . . . . . . 965 Olesiya Kosenko, Stanislav Belyakov, Alexander Bozhenyuk, and Margarita Knyazeva A Price Sensitivity Based Intelligent Pricing System for Global E-commerce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 974 Pelin Yurdadön, Başar Öztayşi, and Egemen Berki Çimen Intelligent Approach Based on Group Method of Data Handling to Predict Economic Growth Through Entrepreneurship and Innovativeness with Time Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 982 Özlem Şenvar and Melis Zeren Intelligent Word Embedding Methods to Support Project Proposal Grouping for Project Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 990 Meltem Yontar Aksoy, Mehmet Fatih Amasyali, and Seda Yanık Comparative Study of the Firefly Algorithm and the Whale Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 999 Hubert Zarzycki A Novel Multiswarm Firefly Algorithm: An Application for Plant Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1007 Nebojsa Bacanin, Miodrag Zivkovic, Marko Sarac, Aleksandar Petrovic, Ivana Strumberger, Milos Antonijevic, Andrija Petrovic, and K. Venkatachalam Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1017

Ordinary Fuzzy Sets

Fuzzy Static and Dynamic De Novo Type Approaches to Optimal System Design Janusz Kacprzyk(B) Systems Research Institute, Polish Academy of Sciences, Ul. Newelska 6, 01-447 Warsaw, Poland [email protected]

Optimization is a powerful and omnipresent paradigm to design, develop, rationalize, improve, and even optimize, all kind of problems, processes, and systems. It concerns issues and problems the very essence of which boil down to a quest for some rationality, with respect to properties or behavior, that can be conceptualized or represented as some sort of the maximization (or minimization) of a utility or valuation function which stand for an evaluation of performance. Such a performance function to be maximized (or minimized) and some constraints, which are both functions of some variables that are selected to characterize the problem considered, is a very convenient form of how to effectively and efficiently present the very objective of the system concerned and its behavior. The above mentioned optimization based approach has been booming for decades, with very many strong theoretical and algorithmic results, and has shown its usefulness for solving a multitude of practical problems. However, the very essence of virtually all these problems has been the optimal allocation of fixed or limited resources in a given system. In many practical problems, however, the essence is not only the optimal allocation of fixed resources in a given, fixed and specified system but rather a deeper task of an (optimal) design of the particular system. For instance, if we take into account as an illustration a regional agriculture modeling problem (cf. [10]) in which, briefly speaking, there are constraints related to the use of fertilizers and watering (irrigation). Then, in the traditional optimization type approach, we just have as the right hand sides of the two respective constraints the limits (possibly in financial terms) of what is available separately for the fertilizers and watering. However, in practice very often the very essence of the problem is different, that is, some funds (e.g. governmental, regional, etc.) are available and we should additionally, in the course of optimization, distribute these funds into parts devoted to, in our simple example, the fertilizers and watering, in

J. Kacprzyk, Fellow, IEEE, IET, EurAI, IFIP, IFSA, AAIA, SMIA, Full member, Polish Academy of Sciences, Member, Academia Europaea, Member, European Academy of Sciences and Arts, Member, European Academy of Sciences, Member, International Academy for Systems and Cybernetic Sciences (IASCYS), Foreign member, Bulgarian Academy of Sciences, Foreign member, Finnish Society of Sciences and Letters, Foreign member, Royal Flemish Academy of Belgium for Sciences and the Arts (KVAB), Foreign member, Spanish Royal Academy of Economic and Financial Sciences (RACEF), Foreign member, Lithuanian Academy of Sciences, Foreign member, Mational Academy of Sciences of Ukraine © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 3–6, 2022. https://doi.org/10.1007/978-3-031-09173-5_1

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addition to the traditional optimization. Of course, this all can involve multiple objectives, too. The above philosophy of an optimal system design, termed de novo programming has been introduced by Zeleny [20], first for single objective problems (cf. [20, 21]) and then extended for multiobjective problems (cf. [22, 23]). This approach has attracted much attention in the optimization, operations research, systems analysis, etc. communities, and has been applied to solve many practical problems. In a rich literature on the de novo programming, one can cite, for instance, the following evelopments: new general de novo programming problems with the maximization and minimization type objectives (GDNPP), cf. [Li and Lee [12, 13], Chen and Hsieh [6], Umarusman [19], Chakraborty and Bhattacharya [3, 4]), to just mention a few. What concerns the applications, Miao et al. [14] have proposed an interval-fuzzy de novo programming method for planning water resource systems under uncertainty, Saeedi et al. [15] has shown an application to determine the capacity in a closed-loop supply chain network with a queueing system, Sarjono et al. [16] have shown an application for production planning optimization at an Indonesian ceramics company, Chen [5] has proposed an application in integrated circuit (IC) design, Sharah and KhaliliDamghani [18] have proposed an application in gas supply chain, Zhang, Huang and Zhang [24] have proposed an application for water resources systems planning’, etc. There is a long tradition of using fuzzy logic and fuzzy optimization in the de novo programming. Just to mention a few, one can cite here: Chen and Hsieh [6] who have introduced a new approach to the solution of multi-stage GDNPP using fuzzy dynamic programming (cf. Kacprzyk [9]), Chakraborty and Bhattacharya [3, 4] who have proposed a new method for the solution of GDNPP in one step under fuzzy environment using the Zimmermann [25]’s fuzzy linear programming approach, Ghorbani et al. [7] proposed the use of a fuzzy goal programming approach, Chakraborty et al. [4] introduced the concept of duality, Sen [17] showed how the concept of a penalty function can be employed, Sharahi and Khalili-Damghani [18] showed the use of type 2 fuzzy sets, etc. A good source of information is the recent paper by Banik and Bhattacharya [1]. For our purposes, an important direction is the use of the de novo programming approach in a dynamic setting in which the sustainable regional agricultural development model operates [10, 11]. The best known paper is presumably here Chen and Hsieh [6] who introduced a new de novo type model using fuzzy dynamic programming in the sense of Bellman and Zadeh [2] and Kacprzyk [8, 9]. We will basically follow the line of reasoning of Chen and Hsieh [6] but will add another important dimension related to the temporal distribution of funds ove the planning horizon which is clearly subject to the effect of discounting, that is, the funds to be determined for earlier development planning stages are more valuable than those for the later stages. This is both in the sense of the face value, that is, expressed directly in monetary terms, and also indirectly, in terms of some value to various stakeholders, for instance the inhabitants whose preference is claarly a possibly fast attainment of some socio-economic objectives and it is obvious that more funds at earlier stages can have a positive effect on the attainment of these objectives (cf. Kacprzyk et al. [11]). Moreover, we add to the traditional de novo fuzzy dynamic programming model the condition of the so-called stability (cf. Kacprzyk and Straszak, [10], Kacprzyk et al., [11]) which

Fuzzy Static and Dynamic De Novo Type Approaches to Optimal System Design

5

boils down the limitation on the variability of crucial agricultural regional development indicators and funds to be spent over the planning horizon. The above synergistic combination of both traditional de novo programming approaches and new elements, mostly in the context of dynamic oprtimization, related to discounting and stability, may be a powerful tool for solving a multitude of problem. In the paper an application for sustainable regional agriculture planning is shown.

References 1. Banik, S., Bhattacharya, D.: One-step approach for solving general multi-objective De Novo programming problem involving fuzzy parameters. Hacettepe J. Math. Stat. 48(6), 1824–1837 (2019). https://doi.org/10.15672/HJMS.2019.659 2. Bellman R.E., Zadeh L.A.: Decision making in a fuzzy environment, Management Science 17(4), B 141–B 164 (1970) 3. Chakraborty, S., Bhattacharya, D.: A new approach for solution of multi-stage and multiobjective decision-making problem using de novo programming, European J. Scientific Res. 79(3), 393–417, (2012) ISSN 1450-216X 4. Chakraborty, S., Bhattacharya, D.: Optimal system design under multi-objective decision making using de-novo concept: a new approach. Int. J. Comput. Appl. 63(12), 0975–8887 (2013) 5. Chen, J.K.: Adopting de novo programming approach on IC design service firms resources integration. Math. Probl. Eng. 2014, 1–13 (2014) 6. Chen, Y.-W., Hsieh, H.-E.: Fuzzy multi-stage de-novo programming problem. Appl. Math. Comput. 181(2), 1139–1147 (2006) 7. Ghorbani, M., Arabzad, S.M., Tavakkoli-Moghaddam, R.: A multi-objective fuzzy goal programming model for reverse supply chain design. Int. J. Oper. Res. 19(2), 141–153 (2014) 8. Kacprzyk, J.: Multistage Decision Making under Fuzziness. Verlag TÜV Rheinland, Cologne (1983) 9. Kacprzyk, J.: Multistage Fuzzy Control: A Model-Based Approach to Control and DecisionMaking. Wiley, Chichester (1997) 10. Kacprzyk, J., Straszak, A.: Determination of stable trajectories for integrated regional development using fuzzy decision models. IEEE Trans. Syst., Man Cybern. Vol. SMC 14, 310-313 (1984) 11. Kacprzyk, J., Kondratenko, Y.P., Merigó, J.M., Hormazabal, J.H., Sirbiladze, G., GilLafuente, A.M.: A status quo biased multistage decision model for regional agricultural socioeconomic planning under fuzzy information. In: Kondratenko, Y., Chikrii, A., Gubarev, V., Kacprzyk, J. (eds) Advanced Control Techniques in Complex Engineering Systems: Theory and Applications. Studies in Systems, Decision and Control, vol 203. Springer, Cham, pp. 201–226 (2019) https://doi.org/10.1007/978-3-030-21927-7_10 12. Li, R.J., Lee, E.S.: Fuzzy approaches to multi-criteria de novo programs. J. Math. Anal. Appl. 153(1), 97–111 (1990) 13. Li, R.J., Lee, E.S.: Multi-criteria de novo programming with fuzzy parameters. Comput. Math. Appl. 19(5), 13–20 (1990) 14. Miao, D.Y., Huang, W.W., Li, Y.P., Yang, Z.F.: Planning water resources systems under uncertainty using an interval-fuzzy de novo programming method. J. Environ. Inform. 24(1), 11–23 (2014) 15. Saeedi, S., Mohammadi, M., Torabi, S.: A de novo programming approach for a robust closedloop supply chain network design under uncertainty: an m/m/1 queueing model. Int. J. Ind. Eng. Comput. 6(2), 211–228 (2015)

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16. Sarjono, H., Salim, M.L., Suprapto, A.T.: Production planning optimization using de novo programming at Ceramics Company in Indonesia. OIDA Int. J. Sustainable Dev. 8(11), 57–62 (2015) 17. Sen, S.: A multi-objective interval goal programming method using penalty function. Int. J. Oper. Res. 27(1–2), 232–251 (2016) 18. Sharahi, J.S., Khalili-Damghani, K.: Fuzzy type-II De-Novo programming for resource allocation and target setting in network data envelopment analysis: A natural gas supply chain. Expert Syst. with Appl. 117, 312–329 (2019) 19. Umarusman, N.: Min-max goal programming approach for solving multi-objective de novo programming problems. Int. J. Oper. Res. 10(2), 92–99 (2013) 20. Zeleny, M.: A case study in multi-objective design: de novo programming. In: Nijkamp, P., Spronk, J. (Eds.): Multiple Criteria Analysis: Operational Methods, pp.37–52. Gower Publishing Co., Hampshire (1981a) 21. Zeleny, M.: On the squandering of resources and profits via linear programming. Interfaces 11(5), 101–107 (1981) 22. Zeleny, M.: Optimal system design with multiple criteria: de-novo programming approach. Eng. Cost Prod. Econ. 10(2), 89–94 (1986) 23. Zeleny, M.: Optimizing given systems vs. designing optimal systems: the de novo programming approach. Int. J. General Syst. 17(4), 295–307 (1990) 24. Zhang, G.H., Huang, Y.M., Zhang, X.D.: Inexact de novo programming for water resources systems planning. Eur. J. Oper. Res. 199(2), 531–541 (2009) 25. Zimmermann, H.J.: Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst. 1(1), 45–55 (1978)

Non-additive Measures, Set Distances and Cost Functions on Sets: A Fr´ echet-Nikodym-Aronszajn Distance and Cost Function Vicen¸c Torra(B) Department of Computing Sciences, Ume˚ a University, Ume˚ a, Sweden [email protected]

Abstract. Fuzzy measures are set functions that are monotonic with respect to the set inclusion. They are also called non-additive measures, monotonic games, and capacities. Cost functions, as the ones used in the optimal transport problem, are typically functions between pairs of elements of, in general, two different sets. In some particular problems, they can be functions that take two elements from the same set. In this case, it is usual that the cost from one element to itself is zero and between different elements is not zero. Other properties can vary, but it is not uncommon that the cost function satisfies the axioms of a distance when applied to two elements of the same set. In this paper we discuss a related problem. In particular, we consider the problem of defining cost functions for power sets. This type of functions are required in extensions of some operations in which fuzzy measures take a role. Then, we define a Fr´echet-Nikodym-Aronszajn-like distance using fuzzy measures and prove some properties. Keywords: Set functions Cost functions

1

· Non-additive measures · Fuzzy measues ·

Introduction

Michio Sugeno defined in his PhD dissertation in 1974 [10] fuzzy measures (see also his previous works [8,9]), and proposed the integral now known as Sugeno integral to integrate a function with respect to such measure. The same concept has appeared in other areas. For example, when Gustave Choquet introduced in 1954 [1] the integral now known as the Choquet integral used non-additive measures with the name capacities. In game theory, these measures are known as monotonic games. They are also known, in general, as non-additive measures. Fuzzy measures have become a basic concept in aggregation, as they are the way to express background knowledge on the information sources. That is, when This study was partially funded by the Wallenberg AI, Autonomous Systems and Software Program (WASP) funded by the Knut and Alice Wallenberg Foundation. c The Author(s), under exclusive license to Springer Nature Switzerland AG 2022  C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 7–15, 2022. https://doi.org/10.1007/978-3-031-09173-5_2

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we have data to be aggregated associated to the reference set X, fuzzy measures allow us to evaluate the importance of sets A ⊂ X. While for additive measures the importance of a set is the addition of the importance of the elements in the set, this is not the case when the measure is not additive. Additive measures and, in particular, probability measures on X can be defined in terms of a function on X. E.g., a probability distribution. This is not possible for non-additive measures. We need to define the measure on the power set of X when X is a finite set, or on, e.g., a σ-algebra on X when X is not finite. In this paper we discuss a problem that can be seen as related. The one of cost functions. Given a reference set X, a cost function is a function c : X × X → R+ . In this paper we consider the problem of defining them on the power set of X. That is, c : 2X × 2X → R+ . We discuss these functions and we propose a cost function that is a generalization of the Fr´echet-NikodymAronszajn distance. We prove conditions of being the cost function a distance, and discuss a generalization of a distance by reformulating the triangle inequality. The structure of the paper is as follows. In Sect. 2 we review some concepts we need later. Then, in Sect. 3 we introduce costs functions on subsets of X. The paper finishes with some research directions for future work.

2

Preliminaries

In this section we review fuzzy measures and cost functions. We begin with fuzzy measures. For details on fuzzy measures we refer the reader to [3,11,12]. 2.1

Fuzzy Measures

A fuzzy measure is a generalization of an additive measure in which the additivity condition is dropped and it is replaced by a monotonicity condition. More precisely, a set function is defined as follows. We review the definition for finite sets. Definition 1. [10] Let X be a reference set. Then, a set function μ : 2X → [0, 1] is a fuzzy measure if the following holds: (i) μ(∅) = 0 (ii) μ(X) = 1, and (iii) μ(A) ≤ μ(B) if A ⊂ B. The first two conditions are the boundary conditions, and the third one is the monotonicity condition. Fuzzy measures that satisfy the second conditions are also known as normalized fuzzy measures. This second condition is sometimes dropped. Then, the measure is not normalized. A fuzzy measure is subadditive when for all A, B such that A ∩ B = ∅ we have that μ(A ∪ B) ≤ μ(A) + μ(B). In contrast, we have that a measure is superadditive when for all such sets μ(A ∪ B) ≥ μ(A) + μ(B).

Non-additive Measures, Set Distances and Cost Functions on Sets

2.2

9

Cost Functions and Distances

Cost functions [7] are defined, in general, as functions on the product of two different reference sets X and Y . So, they are applied to pairs (x, y) for x ∈ X and y ∈ Y . The value is positive. So, cost functions are such that c : X ×Y → R+ . When X = Y , then, it is usual to require c(x, x) = 0 and symmetry (i.e., c(x, y) = c(y, x)). In addition to these two properties, it is usual to require that c is a metric and, thus, it also satisfies the triangle inequality. For example, when X is the real line, the Euclidean distance c(x, x ) = |x − x | and the square of the Euclidean distance c(x, x ) = (x − x )2 have been used. As a summary, we include the definition of a cost function in terms of these three properties. Definition 2. Given a reference set X, a function c : X × X → R+ is a cost function if – c(x, x) = 0, – c(x, y) = c(y, x), and – c(x, z) ≤ c(x, y) + c(y, z). Note that these are the properties of a pseudometric. That is, the properties of a metric (or distance) except the identity of indiscernibles (i.e., we have c(x, x) = 0 but we may have other elements x = y such that c(x, y) = 0.

3

Cost Functions for Sets

Let us consider cost functions for sets when the two sets under consideration coincide. That is, c : X × X → R+ . In this case we can define the cost function in terms of a distance for sets. The literature offers several alternatives for distances on sets. See e.g. [2,5,6]. Following [2] we distinguish three families of distances. The first two ones assume a distance d on X and extend it into sets of elements from X. The third one is the measure metrics and it is based on the existence of an (additive) measure on X. We review the first two here. There are variations of these distances but we will review the most usual ones. See e.g., [2] for these variations. The third one is given in the next section. – The ordinary distance between two sets: d(A, B) =

inf

a∈A,b∈B

d(a, b).

– The Hausdorff distance between two sets:   h(A, B) = max supa∈A inf d(a, b), supb∈B inf d(a, b) . b∈B

a∈A

10

V. Torra

The first distance is known to be the shortest distance between A and B. This is illustrated in Fig. 1 (left). When A ⊆ B the distance will be zero. In contrast, the Hausdorff distance is about the largest move to have an element in A to be in B (or the reversal). In this case, when A is a subset of B, distance is, in general, not zero. This is illustrated in Fig. 1 (right). In terms of cost functions, the ordinary distance between two sets has peculiar properties. If we consider c(A, B) as the cost of transferring some quantity from A to B, we will have that the cost will be always zero when there is a common element between A and B. We can call these elements conveyors.

Fig. 1. Representation of ordinary distance (left) and Hausdorff distance (right).

Observe that for a finite reference set X, if we consider the cost between all pairs of subsets of X we will have several of them that have cost zero because of this property. In contrast, this situation does not occur in the Hausdorff distance. The distance between A and B for A ⊂ B is in general not zero. Nevertheless, if d(1, 2) = 1 then both d({2}, {1}) = 1 and d({1, 2}, {1}) = 1. So, from the point of view of costs the two alternatives are not distinguishable. We review in the next section a metric based on measures. 3.1

Measure Metrics and Measure Cost

Symmetric difference between two sets A and B corresponds to the following two equivalent expressions A B = (A \ B) ∪ (B \ A) = (A ∪ B) \ (A ∩ B). This symmetric difference has been used to define a distance or metric that appears in the literature under different names. They include, at least, [4] (p. 25) Symmetric difference metric, Fr´echet-Nikodym-Aronszayn distance, and Measure metric. The definition is based on a measure on X. Definition 3. Let X be a reference set, and μ be an additive measure on X. Then, the Fr´echet-Nikodym-Aronszayn distance is defined as d(A, B) = μ(A B).

Non-additive Measures, Set Distances and Cost Functions on Sets

11

We can easily observe that for μ(A) = |A| (i.e., the cardinality of A), the distance has connections with the Jaccard distance (i.e., 1 − J(A, B)) where J(A, B) is the Jaccard index (also known as the intersection over the union [13]), through the Steinhaus distance (see [4] p.25 for details). This is a well known metric. Let us prove as the proof will give us some insights for later in the paper. To prove that the expression above is a metric we need to prove the triangle inequality. That is, d(E, F ) ≤ d(E, G) + d(G, F ) for all E, F, G subsets of G. This can be proven graphically considering the three sets and their intersections as shown in Fig. 2. The triangle inequality corresponds to prove that d(E, F ) ≤ d(E, G) + d(G, F ), that, taking into account the figure corresponds to the measure of the following regions: (1) μ({1, 2, 4, 5}) ≤ μ({1, 6, 3, 4}) + μ({6, 5, 2, 3}), which, for an additivity measure μ corresponds to: μ({1, 4}) + μ({2, 5}) ≤ μ({1, 4}) + μ({6, 3}) + μ({5, 2}) + μ({6, 3}). Naturally, this holds, and the inequality is proven.

G 3

E

2 1

7 6

4 5

F

Fig. 2. Representation of three sets E, F , and G and their intersections to prove the triangle inequality.

We can easily extend this definition to the case of non-additive measures. The definition is given below. We use the term cost instead of distance because, in general, triangle inequality does not hold, as we see later. Definition 4. Let X be a reference set, and μ be a non-additive measure on X. Then, the Fr´echet-Nikodym-Aronszayn cost function is defined as c(A, B) = μ(A B).

12

V. Torra

The following is, of course, trivial, as fuzzy measures generalize additive measures. Lemma 1. The Fr´echet-Nikodym-Aronszayn cost function generalizes the Fr´echet-Nikodym-Aronszayn distance. It is easy to see that if A = B then the cost function is zero. Naturally, it is also symmetric. Let us consider the triangle inequality. Proposition 1. Let X be a reference set, μ be a non-additive measure, and c be a cost function as in Definition 4. Then, if the measure is subadditive c satisfies the triangle inequality. Proof. Our proof is also graphical and based on Fig. 2. Again, our goal is to prove that the triangle equation (Eq. 1) holds. Graphically: μ({1, 2, 4, 5}) ≤ μ({1, 6, 3, 4}) + μ({6, 5, 2, 3}). Let us observe that if μ is subadditive then μ({1, 2, 4, 5}) ≤ μ({1, 4}) + μ({2, 5}) and naturally by monotonicity we have that μ({1, 4}) ≤ μ({1, 6, 3, 4}) μ({2, 5}) ≤ μ({6, 5, 2, 3}) Combining the last three equations we obtain Eq. 1: μ({1, 2, 4, 5}) ≤ μ({1, 4})+μ({2, 5}) ≤ μ({1, 6, 3, 4})+μ({2, 5}) ≤ μ({6, 5, 2, 3}). Therefore, the proposition is proven.



In fact, the triangle inequality is only true for subadditive measures. Observe that Eq. 1 can be rewritten (using A1 = {1, 4}, A2 = {2, 5}, and B∗ = {6, 3}) as μ(A1 ∪ A2 ) ≤ μ(A1 ∪ B∗) + μ(A2 ∪ B∗)

(2)

for pairwise disjoint A1 , A2 , B∗. As this needs to hold for all pairwise disjoint sets, it needs to hold for B∗ = ∅. For such B∗, the condition corresponds to subadditivity. Then, if the measure is subadditive, the equation will also hold for any other B∗. As the triangle inequality implies subadditivity, and in Proposition 1 we proved the reversal, the following holds. Proposition 2. The Fr´echet-Nikodym-Aronszajn cost function satisfies the triangle inequality if and only if the fuzzy measure is subadditive.

Non-additive Measures, Set Distances and Cost Functions on Sets

3.2

13

Why Triangle Inequality for All?

The axiom for triangle inequality in Definition 2 is for all x, y, and z. Then, we are extending this axiom for all sets E, F , and G in Fig. 2. Is this necessary? Are really all possible sets G necessary? If we look again to the usual case, when we consider x, y, and z we naturally consider x, y, and z to be different points, and, if they coincide, we have some distances equal to zero and nothing happens (i.e., the inequality is satisfied as equality). In the case of sets, this is not the case. E, F , and G can be partially the same, but not exactly the same. In this case, the inequality fails. So, let us revise the axiom above requiring that it holds for G with at least some element outside E and F . Formally, G ∩ ¬E = ∅ and G ∩ ¬F = ∅. That is, let us consider the following alternative axiom. Definition 5. We call the restricted triangle inequality for sets the following axiom: d(E, F ) ≤ d(E, G) + d(G, F ) for all E, F, G ⊂ X such that G ∩ ¬E = ∅ and G ∩ ¬F = ∅. Then, observe that taking into account the restricted triangle inequality, Eq. 2 is not for all sets B∗ but, instead, B∗ needs to have at least one element in subset 3 of Fig. 2. In this case, the superadditive fuzzy measure described in the following example satisfies the restricted triangle inequality. Example 1. Let us consider a finite set X and a non-additive measure μ defined as follows: μ(A) = |A| + (|A| − 1) · α for a given positive larger than zero α (i.e., α > 0). Then, it is very easy to see that the measure is superadditive because given two sets A1 and A2 with empty intersections A1 ∩ A2 = ∅. μ(A1 ∪ A2 ) = |A1 | + |A2 | + (|A1 | + |A2 | − 1) · α = |A1 | + |A2 | + (|A1 | + |A2 |) · α − α ≥ μ(A1 ) + μ(A2 ) = |A1 | + (|A1 | − 1) · α + |A2 | + (|A2 | − 1) · α = |A1 | + |A2 | + (|A1 | + |A2 |) · α − 2α We can prove that the cost function defined using this measure satisfies the restricted triangle inequality. This is seen observing that Eq. 2 corresponds (using Fig. 2 and the fact that G has non empty intersection to ¬E and ¬F ) to: μ({1, 4} ∪ {2, 5}) ≤ μ({1, 4} ∪ {6, 3}) + μ({2, 5} ∪ {6, 3}). which can be seen in the form μ(A1 ∪ A2 ) ≤ μ(A1 ∪ B∗) + μ(A2 ∪ B∗) with a non empty B∗ in region 3 (and possibly also in 6). In other words, we know for sure that |B ∗ | needs to be at least one. The definition of the measure states that the last equation correspond to the following inequality: |A1 |+|A2 |+(|A1 |+|A2 |−1)·α ≤ |A1 |+|B∗|+(|A1 |+|B∗|−1)·α+|A2 |+|B∗|+(|A2 |+|B∗|−1)·α.

14

V. Torra

Which can be reduced after to some simplifications to: 0 ≤ |B ∗ | + |B ∗ | · α + |B ∗ | + (|B ∗ | − 1) · α, = 2|B ∗ | + 2|B ∗ |α − α which for |B ∗ | ≥ 1 is clearly true for any α > 0. Nevertheless, not all superadditive measures satisfy this axiom. It is enough to consider the equation above with regions 2 and 4 empty, and the following (partially defined) measure: μ({1}) = μ({5}) = μ({3, 6}) = 1, μ({1, 5}) = 10, μ({1, 6, 3}) = 3, μ({6, 5, 3}) = 3 which is superadditive but that does not imply: μ({1, 5}) ≤ μ({1, 6, 3}) + μ({6, 5, 3}). Therefore, as an interim conclusion, we have shown that the Fr´echetNikodym-Aronszajn cost function is only a distance for subadditive fuzzy measures. Nevertheless, when we use the axiom of restricted triangle inequality, we have other measures (including some superadditive ones) that are compliant with the axiom.

4

Conclusions and Future Work

In this paper we have considered cost functions for pairs of sets on a finite reference set. We have discussed three families of distances as cost functions on sets, including one based on fuzzy measures. We have introduced the axiom of restricted triangle inequality. We plan to further study these distances and cost functions, and, in particular, the cost functions that satisfy the restricted triangle inequality. Another research direction is to study the extension of the Steinhaus distance by means of using fuzzy measures.

References 1. Choquet, G.: Theory of capacities. Ann. Inst. Fourier 5, 131–295 (1953/1954) 2. Conci, A., Kubrusly, C.: Distances between sets - a survey. Adv. Math. Sci. Appl. 26, 1–18 (2017) 3. Denneberg, D.: Non Additive Measure and Integral. Kluwer Academic Publishers (1994) 4. Deza, E., Deza, M.-M.: Diccionary of distances. Elsevier (2006) 5. Fujita, O.: Metric based on average distance between sets, Japan. J. Indust. Appl. Math. 30, 1–19 (2013) 6. Horadan, K.J., Nyblom, M.A.: Distances between sets based on set commonality. Discret. Appl. Math. 167, 310–314 (2014) 7. Santambrogio, F.: Optimal Transport for Applied Mathematicians. PNDETA, vol. 87. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20828-2 8. Sugeno, M.: Fuzzy measures and fuzzy integrals (in Japanese). Trans. Soc. Instrum. Control Eng. 8, 2 (1972)

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9. Sugeno, M.: Constructing fuzzy measures and grading similarity of patterns by fuzzy integrals (in Japanese). Trans. Soc. Instrum. Control Eng. 9(3), 361-368 (1973) 10. Sugeno, M.: Theory of Fuzzy Integrals and its Applications, Ph. D. Dissertation, Tokyo Institute of Technology, Tokyo, Japan (1974) 11. Torra, V., Narukawa, Y., Sugeno, M., (eds.): Non-additive measures: theory and applications. Springer (2013). https://doi.org/10.1007/978-3-319-03155-2 12. Torra, V., Narukawa, Y.: Modeling decisions: information fusion and aggregation operators. Springer (2007). https://doi.org/10.1007/978-3-540-68791-7 13. https://medium.com/nodeflux/distance-iou-loss-an-improvement-of-iou-basedloss-for-object-detection-bounding-box-regression-4cbdd23d8660

Ergonomics, Human Performance, and Fuzzy Logic Ahmet Fahri Özok(B) Industrial Engineering Department, Istanbul Okan University, Tuzla Campus, Akfırat, 34959 ˙Istanbul, Turkey [email protected]

Abstract. In scientific applications, we use ergonomic principles initially on the design of human-machine interfaces and in product design. The ergonomic design of the physical and psycho-social environment of Man-Machine Systems is also very important as they affect human performance. But in any case, we have to consider what human being pays if we ignore scientific principles to apply in every kind of Man-Machine System design. If we can group the complexity of interrelationships among different parameters in this type of system it gives us the opportunity to use fuzzy logic. For different kinds of human performance problems fuzzy logic seems to be very flexible to solve them. Keywords: Ergonomics · Human performance · Fuzzy logic · Human-machine interface · Man-machine system

1 Ergonomics and Human Performance Ergonomics, as an engineering science, had its meaning in the late 1940s. International Ergonomics Association (IEA) has defined ergonomics as follows: “Ergonomics is the scientific discipline concerned with the fundamental understanding of interactions among humans and other elements of a system and the application of appropriate methods, theory, and data to improve human well-being and overall system performance.” If we study socio-technical systems, it is not enough the emphasize optimizing the common area between individual operators and their immediate physical and psycho-social environment. The main aim of ergonomics is to apply scientific knowledge about human capabilities, physical and mental limitations, and other important parameters to the design of technical devices, operator controls, Anthropometric dimensions, and physical and social environments. Another important point in system design is to enhance occupational health and safety, comfort conditions, productivity, and efficiency. Work System includes micro and macro ergonomic systems. Recent socio-technical system developments make it possible to take into consideration for product design and design of Work Stations, advanced technology, demographic changement, cultural factors, and worldwide competition. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 16–18, 2022. https://doi.org/10.1007/978-3-031-09173-5_3

Ergonomics, Human Performance, and Fuzzy Logic

17

Ergonomics is an interdisciplinary science that deals with the interaction of human beings with all kinds of objects they use. We know that there is a direct relation between system performance and the efficiency of human effort. From applied psychological studies, we also know that people achieve more if they are properly motivated. All ManMachine system designers must study all parameters of the physical and socio-technical work environments that motivate people, such as illumination, vibration, noise, and humidity in comfort intervals, meaningful and satisfactory work, and opportunity for social status advancement. Briefly, anatomical, physiological, psychological, physical and all other environmental factors influence human performance.

2 Different Fuzzy Models in Ergonomics According to general System Theory, all systems are more than the simple sum of their individual parts. In an ergonomic system, all system elements are interrelated. If any element changes, it affects also other parts. If all elements work with each other harmonically, the total performance effects will be more than the simple sum of the elements would indicate. Because of this reason we have to make full harmonization of each element of the socio-technical system to achieve work system effectiveness. For an effective Work System design, we should be human-centered. It means the personal subsystem is a joint component with the technological subsystem. We always have to take into consideration the general principles of participative management and we should allow for extensive worker participation throughout the design process. The allocation process determines which partial tasks should be done by humans. In many cases making micro ergonomics improvements, application projects yield positive results, and then comes macro ergonomics change to the work system in a short period. At a macro level, we must consider the whole organization and then improve all socio-technical elements. Communication, coordination, and control functions are very important at a macro level. The performance of human beings in Man-Machine Systems is an essential part of System Performance. Because of the need to establish human performance factors we use different approaches: Biomechanics, Work physiology, psychophysics, and psycho-sociology are some of them. Fuzzy Models make it possible to accommodate the dynamic nature of human performance. At this point, the most important factor is performance measure identification. In the fuzzy literature, human performance reliability is defined as the conditional probability that human performance is greater or smaller than for a given critical limit [3]. Because of the multivariate character of human performance, Fuzzy Model is much more appropriate. Performance can be estimated using linguistic descriptions of human performance regarding the performance measures. These measures in crisp values are mapped into the universe of discourse by normalization. As a second step, the normalized values can be converted to corresponding fuzzy values by fuzzification. In general, the more fuzzy sets defined, the more accurate the output of the fuzzy estimator. But we have to be aware at the same time that as the number of subsets increases, more time is needed for computation. Therefore, in practice, there is a trade-off between timeliness and accuracy [4]. A general review of human performance literature shows that many approaches are based on highly questionable assumptions about human behavior [1].

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3 Conclusions Fuzzy mathematics can represent and use vague information [2]. It can be used to model the Man-Machine system that is difficult to define precisely in deterministic or probabilistic models. Fuzzy Models include vagueness but at the same time our subjectivity. This subjectivity subconsciously includes many parameters. It makes it possible to manipulate imprecise decision-making problems. Because in many cases our decision problems are too complex, the parameters are accurate, unclear, and verbally defined. In fuzzy logic processing, we have three steps: fuzzification, fuzzy inference, and defuzzification. Most complex problems can be proceeded by this way and give better results if we use it properly. “Fuzzy modelling of load heaviness”, “The effects of preloading on the estimation of the heaviness of lifted weights as determined by the application of fuzzy set method”, and “An application of fuzzy set theory for prediction of contributing factors to work strain from handling tasks” are some titles from fuzzy model applications.

References 1. Baziuk, P.A., Rivera, S.S., Leod, J.N.: Fuzzy Human Reliability Analysis: Applications and Contributions Review. Advances in Fuzzy Systems, Article ID 4612086, 9. Hindawi Publishing Corporation (2016) 2. Özok, A.F.: Fuzzy set theory and social sciences. In: Kahraman, C., Cebi, S., Çevik Onar, S., Öztay¸sı, B., Tolga, C., Uçal Sari, I. (eds.) INFUS 2021, vol. 197, pp. 182–184. Springer Verlag (2021) 3. Kahraman, C., Gülbay M., Kabak, O.: Applications of Fuzzy Sets in Industrial Engineering: A Topical Classification. In: Kahraman, C. (Ed.), vol. 201, pp. 1–55, Springer Verlag (2006) https://doi.org/10.1007/3-540-33517-X_1 4. Kolarik, W.J., Woldstad, J.C., Lu, S., Lu, H.: Human performance reliability. On-line assessment using fuzzy logic, IIE Trans. 36, 457–467 (2006)

Systematic Mapping Study of Fuzzy Risk Indicators for Pedestrians Maroua Razzouqi1(B) , Azedine Boulmakoul1 , Ghyzlane Cherradi1 Lamia Karim2 , Adil El Bouziri1 , and Ahmed Lbath3

,

1 Computer Science Department, FSTM, II University of Casablanca, Hassan Casablanca,

Morocco [email protected] 2 ENSAB, Hassan 1st University, Settat, Morocco 3 LIG/MRIM, CNRS, University Grenoble Alpes, Saint-Martin-d’Hères, France [email protected]

Abstract. In order to study the most frequently occurring traffic events, measures have been developed. These measures, known as risk indicators, facilitate the analysis of accidents in order to predict them and to take the necessary precautions before they occur. In this article, we study the risk for the most vulnerable user, the pedestrian. And we focus on fuzzy indicators being more relevant, and closer to reality because the risk is not a discrete event that can be modeled using traditional Boolean logic. A systematic mapping study was conducted in this paper, filtering the research works published between 2012 and 2022. The papers under consideration were chosen after extensive research in well-known digital libraries such as PubMed, Scopus, Google Scholar, ArXiv, IEEE Xplore, and the ACM Digital Library. Then we compare the various approaches that have been used. We also investigate the applicability of those fuzzy risk indicators to pedestrians, their reliability and validity, as well as their ability to predict the severity of accidents. Keywords: Road safety · Fuzzy logic · Risk indicators · Pedestrians’ safety

1 Introduction Every traffic event involving two or more road users in close proximity is dangerous. These occurrences are distinguished by the frequency and severity with which they occur. The two latter measures are linked in such a way that the frequency of extremely severe but infrequent events can be calculated based on the known frequency of less severe but more frequent events. As a function of the initial conditions and the avoidance actions defined by these conditions, one can calculate the probability of an accident occurring This work was partially funded by Ministry of Equipment, Transport, Logistics and Water − Kingdom of Morocco, The National Road Safety Agency (NARSA) and National Center for Scientific and Technical Research (CNRST). Road Safety Research Program# An intelligent reactive abductive system and intuitionist fuzzy logical reasoning for dangerousness of driver-pedestrians interactions analysis: Development of new pedestrians’ exposure to risk of road accident measures. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 19–26, 2022. https://doi.org/10.1007/978-3-031-09173-5_4

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as a result of a traffic event. If this probability exceeds zero, the event is classified as critical [1]. A risk indicator should ideally reflect both of the above-mentioned aspects in order to accurately estimate the risk of collision [2]. This means that critical events are identified by estimating the severity of the initial conditions or their proximity to the crash and then evaluating the effectiveness of any potential avoidance action taken by the road users involved based on the initial conditions. Finally, these variables are added together to produce a final estimate of the crash risk in a specific traffic event. According to the study’s findings, different indicators and their combinations can reflect various aspects of any traffic event. However, it does not appear that there is a single indicator that covers all of the bases. A wide range of human activities involves some degree of numerical inaccuracy. This is due to a lack of knowledge or specific features about the actor’s state and/or environment that would allow one to act correctly in accordance with intellectual, moral, or even aesthetic ideals. This imprecision characterizes one’s understanding of a given situation and is caused by a lack of information. Fuzzy set theory is a natural modeling tool for this type of situation. Because real numbers are used to represent precise numerical quantities, it stands to reason that “fuzzy real numbers” can be used to represent imprecise or ambiguous quantities. Zadeh introduced the concept of a fuzzy set in 1964, describing the mathematics of fuzzy set theory and, by extension, fuzzy modeling. Traditional knowledge representation systems are incapable of expressing fuzzy concepts. As a result, logic-based and classical probability-based techniques are insufficient for dealing with knowledge representation. Because such knowledge is lexically imprecise and emphatic by nature, it necessitates a suitable framework for dealing with knowledge representation. Zadeh’s theory attempts to address this issue by utilizing opportunity distribution, or fuzzy intervals. On the interval of real numbers [0,1], the values “True” and “False” were proposed to be operated by Zadeh [3]. To our knowledge, no systematic mapping or review focusing on fuzzy risk indicators for pedestrians has been conducted to date. This paper presents a systematic mapping study, filtering research works on fuzzy risk indicators for pedestrians published between 2012 and 2022. The purpose of this study is to define the various methods used and compare their applicability, validity, and ability to predict the severity of accidents. Outline of the Paper. In the following sections of this paper, we begin with a presentation of the research methodology used in this study in Sect. 2. Then, in Sect. 3, we present the various results discovered as a result of the question mapping. Finally, we present a summary of our findings.

2 Research Methodology This section describes the methodology used to create this Systematic Mapping Study (SMS) following the guidelines given by Peterson et al. [4, 5]. The primary goal of an SMS is to provide a structure for the various types of published research reports and results by categorizing them. As a result, it provides a map of its discoveries. It frequently requires less effort while providing a clearer picture. There are five critical steps in our systematic mapping study’s process: (1) the definition of mapping questions,

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21

(2) the search for relevant articles, (3) article selection, (4) data extraction, and (5) data mapping. Each stage of the process has a conclusion. 2.1 Mapping Questions We identified six mapping questions (MQs) based on the study’s focus. Table 1 presents each mapping question with its motivation. Table 1 Mapping study questions. ID

Mapping Question

Main Motivation

MQ1 When were these studies conducted and To identify the publication trends on how has the frequency changed over time? pedestrians’ fuzzy risk indicators over time MQ2 Which publication channels are the main target for this research topic?

To discover where pedestrians’ fuzzy risk indicators can be found

MQ3 What type of research is published?

To explore the different types of research conducted in this subject

MQ4 What are the applied methods on the selected papers?

To discover the applied methods to assess the risk for pedestrians

MQ5 What’s the level of reliability and validity of those methods?

To explore the level of reliability and validity of each of these methods

MQ6 Which indicators predict the severity of accidents?

To identify the indicators that can predict the severity of an accident

2.2 Search Strategy In order to find the studies that will help us address the mapping questions, we defined a search string that we used on six well-known scientific digital libraries: PubMed, Scopus, Google Scholar, ArXiv, IEEE Xplore, and the ACM Digital Library. We conducted an automatic search, for the period: from 2012 to 2022, in the engine of each of these digital libraries using the following search string: “Fuzzy AND (risk OR safety) AND (indicator* OR index* OR measure* OR exposure) AND pedestrian*” 2.3 Study Selection The selection process focused on determining the articles most relevant to the SMS’s goal. First, based on the title and abstract, each paper is classified as “included,” “excluded,” or “uncertain” based on the inclusion and exclusion criteria in Table 2. Then, papers labeled as “uncertain” are classified after screening the introduction and conclusion. In cases where the introduction and conclusion aren’t enough to decide whether the paper should be included or not, a full-text screening is a solution.

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M. Razzouqi et al. Table 2 Inclusion and exclusion criteria.

Inclusion

Exclusion

1. Studies presenting fuzzy risk indicators for pedestrians 2. Studies using risk indicators to assess the behavior of a pedestrian during a vehicle-pedestrian interaction using fuzzy logic 3. Studies using risk indicators to predict the risk of collisions/accidents using fuzzy logic 4. Studies that were published in the time from 2012 to 2022

1. Studies not written in English 2. Studies that were only available in the form of abstracts or Powerpoint slides 3. Studies that are duplicates of other studies 4.Studies presenting summaries of conferences/editorials or guidelines/templates for conducting mapping studies

2.4 Data Extraction Strategy and Synthesis Method The data extraction step’s goal is to collect all data relevant and important to answer the MQs raised in this study. The data extraction form used to collect all of the information from the selected studies is shown in Table 3. Table 3 Data extraction form. Data item

MQ

Study ID Article Title Authors names Publication Year

MQ1

Publication Channel

MQ2

Research Type

MQ3

Applied Method

MQ4

Reliability

MQ5

Validity

MQ5

Severity

MQ6

3 Results and Discussion Figure 1 presents an overview of the study selection process. This section discusses the results of Table 1’s mapping questions (MQs) based on the 29 selected papers [6–34].

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Fig. 1. Study selection flowchart.

3.1 MQ1: When was this research conducted and how has the frequency changed over Time? Figure 2 depicts the annual distribution of papers published from 2012 to 2022. After examining the distribution of papers over time, we found that the trends of publications are characterized by discontinuity. In fact, no papers were published in 2015. This figure, also, revealed that research interest in this topic is increasing over time.

Fig. 2. Frequency of the studies over time.

Fig. 3. Types of publications.

3.2 MQ2: Which Publication Channels are the Main Target for this Research Topic? Three channels of publication were identified: journal, conference, and a book chapter. Over 55 percent (16 papers) of the 29 selected studies were published in journals, 44 percent (13 papers) were presented at conferences, and 3 percent (one paper) came from a book chapter. The distribution of the selected studies across the publication sources is shown in Fig. 3. It’s worth mentioning that each of those sources was only used once. 3.3 MQ3: What Type of Research is Published? Figure 4 shows that almost all of the selected studies are methodological. In fact, those studies attempt to devise, test or improve new research methods in order to assess the risk of collisions that may occur during vehicle-pedestrian interactions.

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Fig. 4. Research types.

3.4 MQ4: What are the Applied Methods on the Selected Papers? Figure 5 shows that most of the studies (10 papers) applied fuzzy clustering analysis. For the remaining papers, five studies suggested an improvement of risk indicators, three used the fuzzy analytical hierarchy process, and other methods.

Fig. 5. The applied methods.

Fig. 6. Levels of reliability, validity, and severity prediction.

3.5 MQ5 &MQ6: What’s the Level of Reliability and Validity of Those Methods? and Which Indicators Predict the Severity of Accidents? Figure 6 shows that all of the methods applied in the selected studies are qualified as reliable to pedestrians, most of them are valid, but very few can predict the severity of the risk.

4 Conclusion This paper was written as an SMS to investigate the fuzzy risk indicators for pedestrians. We began by conducting an automatic search in six digital libraries using a specific research string, which generated 9980 papers. We obtained 29 selected papers after performing the study selection, which we used to answer 6 MQs. The following are the key findings of these MQs: There has been a surge in interest in the subject in recent years. The chosen papers were published in a wide range of venues. Several methods were used in the selected studies, but the fuzzy clustering analysis combined with classical risk indicators was the most commonly used. All of the methods used in the selected studies are considered reliable to pedestrians, and the majority of them are valid, but only a few of them can predict the severity of the risk. In terms of future research, more emphasis should be placed on the enhancement of fuzzy risk indicators, with a focus on the ability to calculate and predict the severity of the risk.

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Dealing with Nonmonotonic Criteria in Decision-Making Problems Using Fuzzy Normalization Bartłomiej Kizielewicz1 , Jakub Więckowski1 , Bartosz Paradowski1 , and Wojciech Sałabun1,2(B) 1 Research Team on Intelligent Decision Support Systems, Department of Artificial Intelligence and Applied Mathematics, Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin, ul. Żołnierska 49, 71-210 Szczecin, Poland 2 National Institute of Telecommunications, Szachowa 1, 04-894 Warsaw, Poland [email protected]

Abstract. The modeling of the decision-making process frequently has many simplifications. One of such typical actions is the assumption that we have in the decisional problem only monotonic criteria. However, in many cases, it is contradictory to reality. Therefore, the proper normalization of nonmonotonic (and strongly nonlinear) criteria should be applied more and more often. We, therefore, take up the challenge of showing an easy way to normalize strongly nonlinear criteria that have a nonmonotonic character. The proposed normalization must be well fitted with expert knowledge. As the main contribution, we propose to use fuzzy normalization based on Triangular Fuzzy Numbers (TFNs) and the TOPSIS technique. First, we present the idea of our proposed approach. Then we show short study cases that demonstrate the differences between results obtained using our approach and the assumption about monotonic criteria. Finally, we analyze our ranking result using similarity coefficients and present future research directions.

Keywords: TOPSIS

1

· Fuzzy normalization · Fuzzy logic

Introduction

Fuzzy logic is widely used in multi-criteria decision-making problems. It is an effective approach for modeling uncertain data. Its popularity is mainly due to its ease of application and flexibility of usage in many areas [2]. Many studies have repeatedly verified the effectiveness of multi-criteria models involving fuzzy logic assumptions. Furthermore, it shows the relevance of this problem in the complex analysis of decision-making options. The assumptions of MCDA methods often include an initial operation to transform the input data. One such operation is the normalization of the decision matrix. It allows the decision matrix to operate in a specified space x ∈ [0, 1] c The Author(s), under exclusive license to Springer Nature Switzerland AG 2022  C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 27–35, 2022. https://doi.org/10.1007/978-3-031-09173-5_5

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regardless of the discrepancy of the initial data. Most problems incorporate linear characteristics that define the preferred values of the criteria for performing data normalization. It is a direct way of describing the significance of parameters. However, many areas require a non-linear characterization. It allows the problem to be described in such a way as to indicate more than one extreme of the function [5]. A real-world example might be represented by a client considering residential units, pointing to the requirements that the flat should be located on the first or top floor of the building [4]. It shows that the preferred values are directed in two opposite directions. Modeling this situation is possible using a non-linear approach. Current approaches concerning data normalization involve several different techniques. The literature review indicates that the most popular way to perform the data normalization is the linear approach [3]. It is used in the various area combining the different MCDA methods. There are also some cases where a nonlinear, more specifically logarithmic normalization method, has been investigated in game theory [11]. However, one can see a lack of solutions using non-linear data normalization methods in the context of multi-criteria problems. It creates a significant gap that needs to be filled. In this paper, we propose a method to combine the assumptions of fuzzy logic in the context of non-linear data normalization using MCDA methods. For this purpose, we used fuzzy normalization based on the Triangular Fuzzy Numbers (TFNs) and the TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) method to evaluate alternatives. We used a theoretical problem with a randomly generated decision matrix as a computational example to show the effectiveness of the proposed approach. The study aims to fill the gaps related to the unexploited potential of fuzzy logic in data normalization. The introduction of a new approach to data normalization will allow the nonlinear preferences of the decision-maker to be shaped, which will translate into increased usefulness of the models. The rest of the paper is organized as follows. In Sect. 2, we present the preliminaries concerning fuzzy logic, fuzzy normalization, and the TOPSIS method. Section 3 shows the study case, where the theoretical multi-criteria problem was used regarding the non-linear data normalization. Finally, in Sect. 4, we present the conclusions drawn from the research.

2 2.1

Preliminaries Fuzzy Logic

The Fuzzy Logic is a tool introduced to deal with uncertainty [6]. It allows dealing with uncertain data in many fields, e.g., computer vision, decision support systems, or regression problems [7]. Due to their growing importance in multicriteria decision-making, many different approaches based on fuzzy logic have been developed, i.e., Intuitionistic fuzzy sets (IFS) [1], Pythagorean fuzzy sets (PFS) [10], or Hesitant fuzzy sets (HFS) [9]. Furthermore, the assumptions of fuzzy logic allow increasing the usability of the designed models. Additionally,

Nonmonotonic Criteria in Decision-Making Problems

29

to provide basic knowledge about the described assumptions, we present below selected arithmetic operations [5]. Definition 1 (The fuzzy set and the membership function). The characteristic function μA of a crisp set A ⊆ X assigns a value of either 0 or 1 to each member of X, as well as the crisp sets only allow a full membership (μA (x) = 1) or no membership at all (μA (x) = 0). This function can be generalized to a function μA˜ so that the value assigned to the element of the universal set X falls within a specified range, i.e. μA˜ : X → [0, 1]. The assigned value indicates the degree of membership of the element in the set A. The function μA˜ is called a membership function and the set A˜ = (x, μA˜ (x)), where x ∈ X, defined by μA˜ (x) for each x ∈ X is called a fuzzy set. ˜ Definition 2 (The triangular fuzzy number (TFN)). A fuzzy set A, defined on the universal set of real numbers , is told to be a triangular fuzzy ˜ m, b) if its membership function has the following form (1): number A(a, ⎧ 0 x≤a ⎪ ⎪ ⎪ x−a ⎪ ⎨ m−a a ≤ x ≤ m x=m (1) μA˜ (x, a, m, b) = 1 ⎪ b−x ⎪ m ≤ x ≤ b ⎪ ⎪ b−m ⎩ 0 x≥b and the following characteristics (2), (3): x1 , x2 ∈ [a, b] ∧ x2 > x1 ⇒ μA˜ (x2 ) > μA˜ (x1 )

(2)

x1 , x2 ∈ [b, c] ∧ x2 > x1 ⇒ μA˜ (x2 ) > μA˜ (x1 )

(3)

Definition 3 (The support of a TFN). The support of a TFN A˜ is defined as a crisp subset of the A˜ set in which all elements have a non-zero membership value in the A˜ set (4): ˜ = {x : μ ˜ (x) > 0} = [a, b] S(A) A

(4)

Definition 4 (The core of a TFN). The core of a TFN A˜ is a singleton (one-element fuzzy set) with the membership value equal to 1 (5): ˜ = {x : μ ˜ (x) = 1} = m C(A) A

(5)

Definition 5 (The fuzzy rule). The single fuzzy rule can be based on the Modus Ponens tautology. The reasoning process uses the IF − T HEN, OR and AN D logical connectives. Definition 6 (The rule base). The rule base consists of logical rules determining the causal relationships existing in the system between the input and output fuzzy sets.

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Definition 7 (The S-norm operator (sum)). The S-norm operator is a S function modelling the OR intersection operation of two or more fuzzy numbers, ˜ In this paper, only the ordinary product of real numbers is used e.g. A˜ and B. as the S-norm operator (6): μA∪ ˜ B ˜ (x) = μA ˜ (x) + μB ˜ (x) − μA ˜ (x) · μB ˜ (x) 2.2

(6)

Fuzzy Normalization

Although there are many data normalization techniques, they cannot reflect the decision maker’s preferences in the decision-making process. Therefore, we propose a fuzzy normalization (FN) technique based on fuzzy numbers to determine the decision maker’s preference for given criteria against the fuzzy numbers specified for them. We can represent the whole process of fuzzy normalization technique as follows: Step 1. Define a decision matrix of dimension n × m, where n is the number of alternatives, and m is the number of criteria (7). ⎡ ⎤ x11 x12 . . . x1 m ⎢ x21 x22 . . . x2 m ⎥ ⎥ (7) xij = ⎢ ⎣... ... ... ... ⎦ xn1 xn2 . . . xnm Step 2. For each criterion, determine the fuzzy numbers denoting its monotonicity. In this case, we will use the triangular fuzzy numbers defined by T F N = (α, m, β). Step 3. Normalize each value for a given criterion using the membership function for the specified triangular numbers of fuzzy criteria according to the Eq. (1). When there is more than one number of fuzzy numbers for a given criterion, their aggregation should be used with the S-norm operator defined by the Eq. (6). 2.3

TOPSIS

The TOPSIS Method (Technique for Order Preference by Similarity to an Ideal Solution) was developed for solving decision problems [8]. The main assumption of this method is to perform calculations of the distance to the ideal solutions. Then, based on this, the preference of the alternatives is provided. The main steps’ formal notation of the TOPSIS method should be presented as follows. Step 1. Normalization of the defined decision matrix (8): Profit:rij =

xij −minj (xij ) maxj (xij )−minj (xij ) Cost:rij

i = 1, . . . , n

=

max xj (xij )−xij max xj (xij )−minj (xij )

(8)

j = 1, . . . , J

Step 2. Calculation of a weighted normalized decision matrix (9): vij = wi · rij ,

i = 1, . . . , n

j = 1, . . . , J

(9)

Nonmonotonic Criteria in Decision-Making Problems

31

Step 3. Identification of the Positive and Negative Ideal Solutions for a defined decision-making problem (10):   A∗ = {v1∗ , . . . , vn∗ }= maxj vij | i ∈ I P  , minj vij | i ∈ I C  (10) A− = v1− , . . . , vn− = minj vij | i ∈ I P , maxj vij | i ∈ I C where I P stands for profit type criteria and I C for cost type. Step 4. Calculation of the Positive and Negative Distances using the ndimensional Euclidean distance with Eq. (11):  n 2 (v − vi∗ ) , j = 1, . . . , J Dj∗ =  i=1 ij (11)  n − 2 , j = 1, . . . , J Dj− = i=1 vij − vi Step 5. Calculation of the relative closeness to the Ideal Solution (12): Cj∗ =

3

(

Dj− ∗ Dj +Dj−

)

,

j = 1, . . . , J

(12)

Study Case

Simplifying data modeling in decision-making is often applied using monotonic criteria. Linear models are particularly popular. However, they are not a reliable representation of expert knowledge. New solutions should be tested to ensure correct data normalization based on non-linear criteria, thus verifying their performance. In this study, we attempted to perform fuzzy normalization with Triangular Fuzzy Numbers (TFNs) and the TOPSIS method. Providing a comprehensive analysis of the results involved generating different assessment function spaces. In addition, it allowed us to examine the behavior of the results when modeling different non-linear expert preferences. We presented three spaces representing expert preference functions. These are shown in Fig. 1. Each space was described by TFNs defined on the intervals x ∈ [0, 1]. We also outlined the formula used to describe the theoretical problem surface for each space. The theoretical problem of applying fuzzy normalization to a multi-criteria decision problem was performed considering two criteria C1 and C2 . Table 1 presents the results for the preference function (a) from Fig. 1. The overview includes the reference ranking, the Fuzzy Normalization TOPSIS (FNTOPSIS), and the conventional TOPSIS method. The triangular fuzzy number T F N (0, 1, 1) was used for both criteria to normalize the data using the fuzzy normalization method. It is worth pointing out that the obtained ranking of the alternatives for both methods is similar to the reference ranking. It is due to the characteristics of the preference function, which is highly similar to a linear course. It causes that both ranking calculation approaches give a high correlation of results.

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Fig. 1. Surfaces determined for the theoretical multi-criteria decision problems.

Table 1. Obtained results regarding the problem spaces defined as (a). Ai

C1

A1

0.80456 0.04230

C2

6

6

7

A2

0.93356 0.00527

4

5

5

A3

0.95864 0.60967

1

1

1

A4

0.95541 0.49531

2

2

2

A5

0.53133 0.00603 10

10

10

A6

0.31843 0.44457

9

9

8

A7

0.66354 0.11624

8

7

9

A8

0.33902 0.79168

5

4

4

A9

0.02687 0.73428

7

8

6

A10 0.92733 0.30126

3

3

3

Reference FN-TOPSIS TOPSIS

Nonmonotonic Criteria in Decision-Making Problems

33

The positional rankings corresponding to the results obtained for the preference function (b) from Fig. 1 are shown in Table 2. The triangular fuzzy number T F N (0, 0.5, 1) was used for fuzzy normalization for both criteria. Compared to the previous example, the characteristics of the function flow are different. Thus, the results obtained with FN-TOPSIS and TOPSIS are significantly divergent. The ranking of FN-TOPSIS is almost identical to the reference ranking, except for two positions. In contrast, TOPSIS provided ratings almost opposite. Table 2. Obtained results regarding the problem spaces defined as (b). Ai

C1

A1

0.15167 0.67212

C2

Reference FN-TOPSIS TOPSIS 5

5

8

A2

0.98961 0.99241 10

10

1

A3

0.98313 0.04826

9

9

5

A4

0.43541 0.31595

3

3

9

A5

0.36277 0.38048

1

2

10

A6

0.11577 0.92904

8

8

6

A7

0.69195 0.48506

2

1

4

A8

0.79649 0.84151

6

6

2

A9

0.99328 0.25357

7

7

3

A10 0.22667 0.63209

4

4

7

Last Table 3 presents result obtained by use of function (c). For fuzzy normalization, triangular fuzzy numbers used: for criterion C1 T F N (0, 0, 0.5) and T F N (0.5, 1, 1) used, for criterion C2 T F N (0, 0.5, 1) used. In this case, we can see that the original TOPSIS placed an alternative in the first place, whereas reference and FN-TOPSIS placed it in tenth place. This case proves how different the results from original TOPSIS can differ depending on a specific function. Table 3. Obtained results regarding the problem spaces defined as (d). Ai

C1

C2

Reference FN-TOPSIS TOPSIS

A1

0.76762 0.15923

7

7

7

A2

0.58924 0.87987

8

8

2

A3

0.71847 0.58289

5

4

3

A4

0.26155 0.42846

3

3

9

A5

0.84002 0.48892

2

2

4

A6

0.15379 0.49456

1

1

8

A7

0.30975 0.23841

6

6

10

A8

0.66910 0.96516 10

10

1

A9

0.33584 0.90780

9

9

5

A10 0.77386 0.33474

4

5

6

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The obtained results show that when the problem space is close to linear, the TOPSIS and FN-TOPSIS methods guarantee a strong correlation of results. When the expert’s preference characteristics are transformed to non-linear, the FN-TOPSIS method provides results consistent with the reference rankings, while the TOPSIS method does not meet this expectation. The proposed approach is widely applicable in practical problems where the expert’s preferences are nonmonotonic.

4

Conclusions

The evolving ways of solving multi-criteria decision-making problems cause the need to discover different possibilities for obtaining the most appropriate results. For this purpose, we presented the possibility of using fuzzy normalization together with the TOPSIS method, which allows a better expression of preferences for a given criterion. As can be seen from the study, the use of fuzzy normalization functions for non-monotonic problems often yields completely different results than those obtained using TOPSIS alone. With reference rankings, the FN-TOPSIS rankings overlap almost completely, whereas with standard TOPSIS the results deviate significantly. This shows how important a non-monotonic approach is for some problems. In future work, it is worth considering checking the performance of fuzzy normalization using other MCDA methods, additionally, it is worth checking if it would be possible to create better non-monotonic functions for normalization.

References 1. Atanassov, K.: Intuitionistic fuzzy sets. Int. J. Bioautomation 20, 1 (2016) 2. Djenadic, S., Tanasijevic, M., Jovancic, P., Ignjatovic, D., Petrovic, D., Bugaric, U.: Risk evaluation: brief review and innovation model based on fuzzy logic and MCDM. Mathematics 10(5), 811 (2022) 3. Jahan, A., Edwards, K.L.: A state-of-the-art survey on the influence of normalization techniques in ranking: improving the materials selection process in engineering design. Materials Design 1980–2015(65), 335–342 (2015) 4. Kizielewicz, B., Bączkiewicz, A.: Comparison of fuzzy TOPSIS, fuzzy VIKOR, fuzzy WASPAS and fuzzy MMOORA methods in the housing selection problem. Procedia Comput. Sci. 192, 4578–4591 (2021) 5. Kizielewicz, B., Sałabun, W.: A new approach to identifying a multi-criteria decision model based on stochastic optimization techniques. Symmetry 12(9), 1551 (2020) 6. van Krieken, E., Acar, E., van Harmelen, F.: Analyzing differentiable fuzzy logic operators. Artif. Intell. 302, 103602 (2022) 7. Schwartz, D.G., Klir, G.J., Lewis, H., Ezawa, Y.: Applications of fuzzy sets and approximate reasoning. Proc. IEEE 82(4), 482–498 (1994) 8. Shekhovtsov, A., Sałabun, W.: A comparative case study of the VIKOR and TOPSIS rankings similarity. Procedia Comput. Sci. 176, 3730–3740 (2020)

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9. Torra, V.: Hesitant fuzzy sets. Int. J. Intell. Syst. 25(6), 529–539 (2010) 10. Yager, R.R., Abbasov, A.M.: Pythagorean membership grades, complex numbers, and decision making. Int. J. Intell. Syst. 28(5), 436–452 (2013) 11. Zavadskas, E.K., Turskis, Z.: A new logarithmic normalization method in games theory. Informatica 19(2), 303–314 (2008)

Feasibility Analysis of Automated Vertical Farming in Istanbul Using Fuzzy Logic Osman Pakirdasi and A. Cagri Tolga(B) Galatasaray University, Istanbul 34357, Turkey [email protected], [email protected]

Abstract. Because of growing population, degradation of arable lands and the adverse effects of climate change, food security becomes an issue of concern, which tends scientists and entrepreneurs to find out more sustainable and effective food production methods. Automated Vertical Farms are just one example. Global vertical farming was valued nearly USD 1.9 billion at 2018. In this paper, we will conduct a case study for Istanbul, where cultivable land is scarce, so local production is limited and demand for leafy greens depends on imports from other parts of Turkey. We will examine the profitability of automated vertical farming considering investment costs, operational and sales income. However, the expenditures and incomes are not stable because of the inflation rate. Therefore, to overcome these problems we use fuzzy logic, the expected inflation rates, which is given in probabilities, is taken from market participants survey made by Turkish Central Bank. We use inflation rate as a trapezoidal fuzzy number and get fuzzy result. The results show that because of high investment and operating costs, investing vertical farms are more profitable if top quality, high-priced products can be cultivated. Keywords: Automated vertical farming · Fuzzy logic · Engineering economics

1 Introduction The Worlds’ population is increasing. The United Nation estimates an increase of the Worlds’ population nearly ten percent by 2030 and slightly more than twenty-five percent by 2050 to 9.7 billion [1]. Growing population also increases the demand for food. To eliminate the hunger, food production would be increased by 60% at 2050 [2]. Increasing food production can be achieved by expanding arable land. However, studies show that worlds’ farmland is degraded because of the natural processes or human originated causes such as desertification, salinization, compaction, or encroachment of invasive species [3]. The one third of worlds’ farmland is estimated to be degraded from moderate to high [4]. Twenty percent of global greenhouse gases emission which is the main cause of climate change is produced by agricultural processes [5]. Climate change adversely effects the food production by droughts, floods, and temperature fluctuations especially agricultural production [6]. Also, conventional agricultural production depends on water, seventy percent of annual water consumption is used in agriculture [7]. However, because © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 36–43, 2022. https://doi.org/10.1007/978-3-031-09173-5_6

Feasibility Analysis of Automated Vertical Farming in Istanbul

37

of climate changes and excessive water usage water resources are in danger which would limit the agricultural production in the future [8]. In 2016, more than twenty percent of fruits and vegetables were lost from harvest to retail, which means the food waste in retail and consumption level did not include [9]. The United Nation also estimates that two-thirds of World population would live in urban areas by 2050 [10]. Thus, storage and transportation need of agricultural products from farmlands to urban areas will also increase, which will increase the energy consumption and the risk of food lost. Because of the drawbacks of conventional agricultural practices, some other farming practices have been studied to promote sustainability [11]. Indoor Vertical Farming in Urban areas is an applied method which is not affected by climate change, desertification, water scarcity or transportation loses. As recent studies show that, Turkey is under a serious desertification risk, 12.7% of lands in Turkey are in low-risk group, 53.2% are in moderate, and 25.5% are in highrisk group [12]. Also, with increasing petroleum and fertilizer prices transportation and cultivation costs are increased which effect market prices of leafy greens and other vegetables. Thus, more sustainable, and efficient farming practices are necessary, also for Turkey, to maintain production and to reduce the market prices. Thus, in this paper we examine the profitability of automated vertical farming operated in Istanbul, which is the most crowded city of Turkey, and the leafy greens are imported from other cities of Turkey. With the databases searches we made; we can say that this will be the first feasibility analysis for Vertical Farms operating in Turkey. This paper is organized as follows. In Sect. 2 literature review is given. Section 3 introduces methods and materials. In Sect. 4 results are presented with discussion, last part is Sect. 5 which is conclusion.

2 Literature Review Vertical farming is an alternative agricultural method in which soilless farming systems such as hydroponic, aeroponic, or aquaponics are used. It is not a new concept, in 1915 a book named Vertical Farming was written by Gilbert Ellis Bailey. However, vertical farming is gaining its fame recently, nevertheless, the global vertical farming market was valued at USD 1.922 billion in 2018 and USD 951.1 million of this market is in North America [13]. Vertical farming provides greater yields from a square meter of space by vertically stacking plant growing layers with far less water usage at about one tenth of that is used in conventional methods [14]. Furthermore, in some vertical farming practices with a distillation system, water can be reused, and this reduces water usage to one tenth of common vertical farming practices [15]. Vertical farms can be operated in indoor environment, in which, production systems can be controlled automatically such as lighting, climatization and irrigation so that, they called as Plant Factories [16]. Also, plant factories reduce excessive use of pesticides and herbicides because of indoor environment [17]. These Plant factories, Indoor Vertical Farms, are just called as Vertical farms in this paper. Because Vertical Farms can be sited in urban areas, the transportation and storage costs are reduced [15]. Also, controlled environment enables high and uniform production year-round [18].

38

O. Pakirdasi and A. C. Tolga

Beside the benefits, investment cost per square meter of vertical farm ten times higher than that of a high-tech greenhouse [19]. Also, in contrast with greenhouses operating costs per square meter in vertical farms can be five times higher [19]. Especially for too hot or too cold regions, in-stead of farming in greenhouses, growing in an indoor closed system would yield a higher energy efficiency [14]. Despite the debate over pros and cons, the number of vertical farms is increasing in USA, Japan, Canada, and Europe. Some examples of vertical farming companies around the world are, Plenty (Jeff Bezos and Walmart are the known investors) (San Francisco, CA, USA), VertiCrop (Vancouver, BC, Canada), Green Sense Farms (Shenzhen, China), Lufa Farms (Montreal, QC, Canada), Nuvege (Kyoto, Japan), PlantLab (Den Bosch, Holland), Green Spirit Farms (Michigan, USA), Sky Greens (Singapore), Ikea (Sweden) and the numbers are increasing rapidly [15, 19]. As, the market value of vertical farms are increasing, feasibility analysis for vertical farms in different countries are made. In this paper, we analyze economic feasibility of vertical farms in Istanbul with the theoretical data used in previous papers.

3 Methods and the Assumptions The vertical farms operated in different countries are expected to have the same or similar inputs and outputs, if the indoor conditions like humidity, temperature, photosynthetically active radiation, and plant spacings are set same [18]. However, the worth of inputs and outputs are different for all countries. In this paper, we used quantities of required inputs and possible outputs per square meter given in literature to calculate economic feasibility of vertical farms in Istanbul. Basically, there are two types of costs, investment, and operation costs. Investment costs are construction which is in our case interior isolation of building walls and ceiling, and growth platforms for plants, and equipment which are air conditioning, LED lighting, irrigation system, sensors and controlling unit. Operation costs are electricity, labor, rent, water, and others such as fertilizer, CO2, and seed. For vertical farms to reach a higher thermal resistance with a R value 13, 5 cm polystyrene foam blocks are used [18]. Ceiling and the side walls must be isolated which leads to 440 square meter of isolation area. By 2022, the insulation price including material and labor for a square meter is 150 Turkish Liras. Growth platforms are the important part of the vertical farms. There are some different models used for vertical farming around the globe. However, the higher material, installation, and transportation costs and the taxes, make them unaffordable. In this paper we calculate cost for constructing a growth platform with PVC pipes and iron bars. Only 60% of space can be used for production, 40% of space is used for spaces between growth platforms and for seedling, planting, harvesting, and packaging areas. Nevertheless, with four stacking layers total cultivation area is 480 square meters for 200 square meters of total space. Growth platform constructed with iron bars and PVC planting pipes costs three thousand and five hundred Turkish Liras (Table 1). As vertical farms have a good insulation, the system is independent of weather. However, cooling the vertical farms is important because artificial lights produce heat. As an air conditioner, air cooled chiller with Fan coil is assumed to be used [18].

Feasibility Analysis of Automated Vertical Farming in Istanbul

39

Table 1. General assumptions Unit Building Width/Length/Height

10/20/4

m

Stacking Layers/Cultivable area

4 / 480

piece / m2

Insulation

150

TL/m2

Growth Platform

3.500

TL

Air Conditioner1

6.0000

TL

Led Light2

2.850

TL

Distribution of Electricity, and Connections

250.000

TL

Pump3

8.000

TL

Distribution pipes with valves and fittings

6.000

TL

Other Equipment

10.000

TL

Plant; Butterhead Lettuce Yield/year

504

Heads/m2 /year

Artificial light is the only light source for plants to photosynthesis in vertical farms and it is assumed 190 watts of led lighting is mounted in a square meter of cultivation area [18]. The unit cost of Led lights is assumed 15 Turkish Liras per watt [20]. In vertical farms nutrient water is pumped to the plants. So, irrigation system with an adequate pump is also must for vertical farms. The cost of water distribution system including distribution pipes, valves, and fittings is assumed 6.000 Turkish Liras. Sensors and controlling unit are necessary to automatically control the system. Temperature, humidity, CO2 , pressure, pH, and EC sensors are all used in system and IoT based controlling programs nowadays are available for free. The main operating cost of vertical farms are electricity. Especially, artificial lights consume most of the electricity. The total electric consumption to produce one kg dry weight is given 280 kWhe for United Arab Emirates, and 247 kWhe for Netherlands by Luuk Graamans [18]. In UAE the energy consumption is higher because energy needed for cooling is higher. For our study, we take 260 kWhe electric consumption to produce one kg dry weight, because Istanbul has a similar climate with Netherlands in comparison with UAE. Employing a worker, beside from the owner, is crucial, also for small scaled vertical farms, because the process is continuous for 365 days per year. For vertical farming, warehouses or industrial plants can be used instead of apartments because of high electric usage. To calculate rent of a square meter we used Endeksa which gives statistics about real estate market. Warehouse and industrial plants’ monthly rent per square meter is 53 Turkish Liras [21] (Table 2, 3). 1 Frigotek FMC-3 Chiller and Alda AFC-20 Fancoil suitable for 200 square meters. 2 Philips GreenPower LED toplighting. 3 Etna EILR4 40–160/0,55 in-line pump suitable for 200 square meters.

40

O. Pakirdasi and A. C. Tolga Table 2. Total Capital Expense (COPEX) Unit Insulation

66.000,00

TL

Growth Platform

700.000,00

TL

Air Conditioner

60.000,00

TL

Led Ligting and Wiring

1.600.000,00 TL

Pump

8.000,00

TL

Distribution Pipes with Valves 6.000,00 and Fittings

TL

Equipment

10.000,00

TL

Total

2.450.000,00 TL

Table 3. Total Operational Expenditures (OPEX) Unit Labor

90.000,00

TL/year

Rent

156.000,00

TL/year

Electricity

1.920.000,00

TL/year

Water

1.080,00

TL/year

Others

120.000,00

TL/year

Total

2.287.080,00

TL/year

The output of the system is 504 heads of Butterhead Lettuce from a square meter of cultivation area for a year [18]. The economic evaluation tools that are used for feasibility analysis are: Net Present Value (NPV); under the net present value method, all expected cash flows are discounted to today’s date, which is generally the start of the project’s life. NPV =

n  t=1

Rt (1 + i)t

(1)

where Rt is the cash flow at the end of period t, i is the effective interest rate per period and the t is the number of time periods. Internal Rate of Return (IRR); in the IRR method the IRR is a discount rate that makes Net Present Value of all cash flows equals to zero. 0 = NPV =

T  t=1

Ct − C0 (1 + IRR)t

(2)

Feasibility Analysis of Automated Vertical Farming in Istanbul

41

where IRR is the internal rate of return, C t is the net cash inflow during the period t, C 0 is the total initial investment and t is the number of time periods. For fuzzy calculations, simple operations with trapezoidal fuzzy numbers are used.

Membership degree

1.5 1 0.5 0 0.15

0.18

0.21

0.24

0.27

0.3

0.33

0.36

0.39

Fig. 1. Trapezoidal fuzzy inflation rate membership diagram

We use two different scenarios, in first scenario, we assume the products are top quality and sold from the highest price, for second scenario, we assume the products are sold from the lowest price in the wholesale market. The lowest and the highest wholesale prices taken from Istanbul Metropolitan Municipality website [22]. For calculating NPV, we use real interest rate instead of effective interest rate, because we accept the annual cash flows same for every year without considering inflation. As the real interest rate depends on expected inflation rate, which we took from market participant survey of Turkish Central Bank [23]. The expected inflation rate is a bar diagram where rates are given with probabilities. To simplify calculations, we assume the diagram is trapezoidal, so we get a trapezoidal fuzzy number (Fig. 1) which is accepted as inflation rate. Thus, we calculate Fuzzy NPV as a result.

4 Result and Discussion In our model, total yield per year is 241920 heads of Butterhead Lettuce. As the real interest rate is calculated as a fuzzy number which is (−0,16; −0,14; −0,06; −0,03) our production cost per head is calculated as a fuzzy number (10,28; 10,15; 9,85; 9,79). With all the assumptions we made and under the negative real interest rates, the production cost of a head lettuce would be between 9,79 and 10,28 TL. With a sale price of 10 TL the NPV would be in between 844 thousand TL lost and 1.5 million TL gain, and with a sale price of 15 TL the NPV is between 13.8 million and 37.7 million TL. Also, calculated IRR is −10% for the first scenario so, real interest rates higher than −10% makes the project infeasible. In contrast, IRR is calculated 54% for the second scenario, which indicates real interest rate lower than %54 makes the project profitable. Both calculations show the effect of sale prices on NPV. For these reasons, features such as, weight, diameter, color, and taste of Lettuce, cultivated in Vertical Farms, must be compared with market products to assess its market price beforehand. In Turkey, leafy greens whole sales prices are low in contrast with, Japan, Canada, Europe, and United States where vertical farms are commercially feasible. A comparative

42

O. Pakirdasi and A. C. Tolga

study made for feasibility of Vertical Farms in Brazil versus in USA, shows that Brazil market is not feasible for vertical farms, where wholesale price of lettuce is 1,5 TL with a production cost of 8,5 TL versus wholesale price of 26 TL with a pro-duction cost of 15 TL in USA [24]. In another paper Quebec, Canada was studied and cost per head was calculated 11 TL where wholesale price was 18 TL [25] (Table 4). Table 4. Cash Flow Analyses for Butterhead Lettuce Vertical Farm SC1-L

SC2-H

Inflation Rate ~

(0,18; 0,21; 0,33; 0,36)

(0,18; 0,21; 0,33; 0,36)

Unit

Real Interest Rate ~

(−0,16; −0,14; −0,06; −0,03)

(−0,16; −0,14; −0,06; −0,03)

Annual Income

2.419.200,00

3.628.800,00

TL

Annual OPEX

2.287.080,00

2.287.080,00

TL

Price/Head

10

15

TL

Cost/Head ~

(10,28; 10,15; 9,85; 9,79)

(10,28; 10,15; 9,85; 9,79)

TL

Total Investment

2.450.000,00

2.450.000,00

TL

Policy Rate

14

14

TL

NPV4 ~

(−844; -588; 948; 1.504)

(13.849; 16.445; 32.034; 37.686)

TL

Payback Period

(15; 12,5; 8,5; 7,5)

(2; 1,5; 1,5; 1,5)

Years

Project IRR

−10%

54%

Also, led lighting used in our base paper written by Graamans, is higher than other papers. In our model 190 W/m2 per cultivation area is expected to use however in Quebec, Canada research 120 W/m2 is used. They reach 52 kg/m2 fresh weight of Lettuce, where Luuk Graamans expects 71 kg/m2 fresh weight. The Canadian papers’ expected yield is lower but also, they have lower investment cost and consume less electricity.

5 Conclusion The aim of this study was to examine profitability of Vertical Farms in Istanbul, Turkey with the data previously given in literature. The production cost of a head lettuce is calculated approximately equal to minimum sale price of a head lettuce in wholesale market, which reveals that production cost of a head lettuce produced in vertical farms higher than conventionally produced ones because of high investment and operational costs. The feasibility of the system depends on the quality of the products. If the products’ quality meets the market demand with high priced ones, system becomes profitable otherwise the system is not a good option for entrepreneurs. Therefore, there must be made more work to decrease investment and operating costs or to find alternative markets with higher prices such as e-commerce sites, hotels, and the restaurants. This study is a starting point. For future studies, we will work with different varieties such as herbs and other leafy greens, also, we will analyze alternate production system with off-season 4 Results are divided by 1000.

Feasibility Analysis of Automated Vertical Farming in Istanbul

43

products with higher sale price. Also, we will examine the feasibility under different light intensities which effects both investment and operational costs. So that, we will try to find more sustainable and more profitable management methods also, by using MCDM methods.

References 1. United Nations, Department of Economic and Social Affairs. World population predicted to reach 9.7 billion by 2050 (2015) 2. FAO: Global Agriculture towards 2050, How to Feed the World 2050. Rome (2009) 3. Gibbs, H.K., Salmon, J.M.: Mapping the world’s degraded lands. Appl. Geogr. 57, 12–21 (2015) 4. FAO and ITPS: Status of the World’s Soil Resources. Rome (2015) 5. FAO. The share of agriculture in total greenhouse gas emissions. Rome (2021) 6. Parker, L., Bourgoin, C., Martinez-Valle, A., Läderach, P.: Vulnerability of the agricultural sector to climate change. PLoS ONE 14(3), e0213641 (2019) 7. FAO: The future of food and agriculture: Trends and challenges. Rome (2017) 8. United Nations, UN World Water Development Report (2022) 9. FAO. Moving forward on food loss and waste reduction. Rome (2019) 10. United Nations, Department of Economic and Social Affairs, World Urbanization Prospects, The 2018 Revision 11. FAO. The future of food and agriculture – Alternative pathways to 2050. Rome (2018) 12. Turkes, M., et al.: Desertification vulnerability and risk assessment for Turkey via an Analytical Hierarchy Process model. Land Degradation & Development. 31 (2019) 13. PR Newswire. The North American vertical farming market was valued at USD 959.1 million in 2018. PR Newswire US. June 24 (2019) 14. Van Gerrewey, T., Boon, N., Geelen, D.: Vertical farming: the only way is up? Agronomy 12(1), 2 (2022) 15. Al-Kodmany, K.: The vertical farm: A review of developments and implications for the vertical city. Buildings 8(2), 24 (2018) 16. Toyoki, K., Genhua, N., Michiko, T.: Plant Factory, An Indoor Vertical Farming System for Efficient Quality Food Production, Elsevier, US (2015) 17. Kurt, B., Bruce, T.: Future food-production systems: vertical farming and controlledenvironment agriculture, sustainability: science. Practice and Policy 13(1), 13–26 (2017) 18. Graamans, L., Esteban, B., Andy, D., Ilias, T., Cecilia, S.: Plant factories versus greenhouses: Comparison of resource use efficiency. Agric. Syst. 160, 31–43 (2018) 19. Butturini, M., Marcelis, L.F.M.: Vertical farming in Europe: present status and outlook. 2nd edn. Academic Press – Elsevier (2019) 20. Avgoustaki, D.D., Xydis, G.: Indoor vertical farming in the urban nexus context: business growth and resource savings. Sustainability 12(5):1965 (2020) 21. Endeksa Homepage www.endeksa.com Accessed 14 Mar 2022 22. Istanbul wholesale prices, tarim.ibb.istanbul/hal-mudurlugu/hal-fiyatlari.html Accessed 10 Mar 2022 23. TCMB market participant survey https://www.tcmb.gov.tr/wps/wcm/connect/TR/TCMB+ TR/Main+Menu/Istatistikler/Egilim+Anketleri/Piyasa+Katilimcilari+Anketi/ Accessed 14 Mar 2022 24. Trimbo, A.: Economic sustainability of indoor vertical farming in Sao Paulo. Diss (2019) 25. Eaves, J., Eaves, S.: Comparing the Profitability of a Greenhouse to a Vertical Farm in Quebec. Canadian J. Agricultural Econ. 66 (2017)

How Mining and Summarizing Information on Time Series Can Be Formed Using Fuzzy Modeling Methods Vil´em Nov´ak(B) Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, 30. dubna 22, 701 03 Ostrava 1, Czech Republic [email protected] http://ifm.osu.cz/ Abstract. In this paper we provide an overview of fuzzy modeling methods applied to time series processing. The basic methods are Fuzzy Transform (F-transform) and selected methods of Fuzzy Natural Logic (FNL). We address classical tasks such as estimation of trend and its prediction, and also methods for mining information from time series. We provide information that can hardly be obtained using statistics. Namely, we automatically form an explanation of the forecast in natural language, provide comments to the slope of time series in an imprecisely specified area, detect possible structural breaks, “bull and bear” phases of financial time series, measure of similarity between time series and provide automatic summarization of knowledge about time series expressed in natural language. Keywords: Fuzzy natural logic · Fuzzy transform · Time series · Mining information · Bull and bear phases · Evaluative linguistic expressions

1

Introduction

In this paper, we focus on processing of time series using fuzzy modeling methods. We will demonstrate that they are able not only to compete with the classical statistical methods but additionally they can provide information unreachable by the latter. Besides classical tasks such as estimation of trend and its prediction, our methods automatically generate explanation in natural language of how the prediction was obtained. Furthermore, we can also automatically form comments to the slope of time series in an imprecisely specified area. This is further used for detection of structural breaks and “bull and bear phases” (this is important for financial time series). An interesting task provided by our methods is The work was supported from ERDF/ESF by the project “Centre for the development of Artificial Intelligence Methods for the Automotive Industry of the region” No. CZ.02.1.01/0.0/0.0/17-049/0008414. c The Author(s), under exclusive license to Springer Nature Switzerland AG 2022  C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 44–52, 2022. https://doi.org/10.1007/978-3-031-09173-5_7

Mining and Summarizing Information on Time Series

45

also automatic summarization of knowledge about time series expressed in natural language. The summarization is realized using the theory of general (fuzzy) quantifiers, e.g. “most, many, a lot of, a few”, etc. The knowledge concerns either single time series (detection and characterization of monotonous segments, future trend, and summarizing information on them), or we can also generate summarizing information on a multitude of time series. It is important to emphasize, however, that our goal is not to beat statistical methods but rather to extend the power of time series processing methods and benefit from the mutual synergy of both worlds. The primary theoretical method used in our applications is Fuzzy Transform (F-transform) completed by selected methods of Fuzzy Natural Logic (FNL). A detailed description of these techniques including various applications can be found in the book [21] and in many papers. It is important to note that our methods are robust and extremely fast because the time complexity of the Ftransform is linear. This paper is structured as follows. In Sect. 2, we introduce the basic concepts of fuzzy transform and fuzzy natural logic. In Sect. 3 we introduce time series, its decomposition into components, application of the F-transform to it and mention basic principles of forecasting. In Sect. 4 we overview the main kinds of information that can be mined from time series using fuzzy modeling methods.

2

Preliminaries

Recall that by a fuzzy set A on the universe U , we understand a function A : U → [0, 1].1 We often write A ⊂ U or A ∈ F (U ) where F (U ) is the set of all ∼ fuzzy sets on U . 2.1

Fuzzy Transform

This is a universal technique introduced by I. Perfilieva in [22,24] that has applications in many areas. Its fundamental idea is to transform a real bounded continuous function f : [a, b] → [c, d], where [a, b], [c, d] ⊂ R, to a finite vector of components and then transform it back. The principle concept is that of a fuzzy partition of [a, b] which consists of a finite set of fuzzy sets Ah = {A0 , . . . , An }, n ≥ 2, defined over the set of nodes a = c0 , . . . , cn = b such that ck+1 = ck + h where h > 0. The direct F-transform. Since F-transform is widely known and presented in many papers and books, we will remind only the basic concepts needed in this paper. Based on the given fuzzy partition Ah , the (n+1)-tuple Fm [f ] = (F0m [f ], . . ., m Fn [f ]) is called m-th degree direct fuzzy transform of f where Fkm [f ](x) = βk0 [f ] + βk1 [f ](x − ck ) + · · · + βkm [f ](x − ck )2 , 1

k = 0, . . . , n. (1)

The interval [0, 1] is a set of truth values where 0 means falsity, 1 truth and the other values express partial truth. This interval can be replaced by a suitable bounded lattice.

46

V. Nov´ ak

The inverse F-transform is fˆhm (x) =

n 

Fkm [f ] · Ak (x),

x ∈ [a, b].

(2)

k=0

It can be proved that fˆhm approximates the original function f with arbitrary precision (depending on h). We can set the parameters so that the approximating function fˆhm has desired properties. The computational complexity of the Ftransform is linear. The following holds (see [24]): βk0 [f ] = f (ck ) + O(h2 ), βk1 [f ]



2

= f (ck ) + O(h ),

βk2 [f ] =

(3) (4)



f (ck ) + O(h2 ). 2

(5)

Hence, each coefficient βkj provides a weighted average of values as well as of first and second derivatives of the function f over the area characterized by the fuzzy set Ak ∈ Ah .2 2.2

Fuzzy Natural Logic

This is a class of special formal theories of mathematical fuzzy logic whose goal is to model the reasoning of people based on using natural language. The main theory is that of evaluative linguistic expressions (see [14,21]) that are expressions of natural language such as small, medium, big, very short, more or less deep, quite roughly strong, extremely high, etc. Various kinds of applications of FNL require a special function of local perception 3 A = LPerc(x, w) (6) which assigns a proper evaluative expression A to the value x ∈ w where w = [vL , vs ] ∪ [vS , vr ] is a context. To determine it, we must first specify, what does it mean “extreme (utmost) value”. There are two such values: the smallest value vL , and the largest one vR . Both are completed by a typically medium value vS .4 2 3

4

In fact, the F-transform provides weighted average of arbitrary derivative but in time series processing we need only the first and second ones. Such a function is implemented in the experimental software LFL Controller and LFL Forecaster (see http://irafm.osu.cz/en/c100 0) developed in the Institute for Research and Applications of Fuzzy Modeling of the University of Ostrava, Czech Republic. The authors are Vil´em Nov´ ak, Anton´ın Dvoˇr´ ak and Viktor Pavliska. The results demonstrated in this paper were obtained using the mentioned software. For example, the context for height of trees in Europe can be vL = 1 m, vR = 50 m and vS = 20 m.

Mining and Summarizing Information on Time Series

47

The theory of evaluative expressions is applied in a formal theory of fuzzy/linguistic IF-THEN rules and approximate reasoning [17,20,21]. The basic concept is that of a linguistic description R1 = IF X is A1 THEN Y is B1 , ............................. Rm = IF X is Am THEN Y is Bm

(7)

where “X is Aj ”, “Y is Bj ”, j = 1, . . . , m are evaluative linguistic predications (for example, “trend is very steep, difference is small, trend-cycle is stagnating”, etc.). The linguistic description can be learned from data. Finding a proper conclusion on the basis of linguistic description done using a special reasoning method of Perception-based Logical Deduction (PbLD). It acts locally so that it mimics the way how people make their reasoning on the basis of linguistic information.

3

Time Series

Let T = {1, . . . , p} be a set of natural numbers interpreted as time moments. A time series is a set X = {X(t, ω) | t ∈ T, ω ∈ Ω} where X(t, ω) = TC (t) + S(t) + R(t, ω),

t ∈ T, ω ∈ Ω.

(8)

The TC (t) is a trend-cycle that can be further decomposed into trend and cycle, i.e., TC (t) = Tr (t) + C(t). The S(t) is a seasonal component that is a mixture of r periodic functions r  Pj eiλj t (9) S(t) = j=1

where λ1 , . . . , λr are frequencies and Pj , j = 1, . . . , r are constants. We assume that R is a random noise, i.e., a stationary stochastic process with the mean E(R(t, ω)) = 0 and variance Var(R(t, ω)) < σ, t ∈ T. If we fix ω ∈ Ω then the time series becomes a real (or complex) valued function X = {X(t) | t ∈ T}. Let us choose h > 0, form a fuzzy partition Ah , and apply the F-transform to X. Then the inverse F-transform of X w.r.t. Ah is ˆ h (t) = TC ˆ h (t) + Sˆh (t) + R ˆ h (t), X

t ∈ T.

(10)

It can be proved that setting h = dT for some d and a proper periodicity T , the F-transform removes part or the whole of the seasonal component S and reduces the noise R. The inverse F-transform (10) enables us to estimate the trend or trend-cycle: ˆh TC hT C ≈ X TC

and

ˆh Tr hT ≈ X T

48

V. Nov´ ak

where hT C is set according to a periodicity T chosen from the middle of the list of found periodicities, and hT from the longest ones. Forecasting of time series is accomplished in two phases: first we forecast m [X] and from them using the inverse Ffuture components Fnm [X], . . ., Fn+k−1 transform we obtain forecasted trend or trend cycle. The forecast of the components is realized on the basis of the learned linguistic description using the PbLD method developed in FLN (for the details see [21]). The other components (cyclic or seasonal) are forecasted using other methods, for example classical ARIMA or neural networks. Then the forecast of the whole time series is obtained by summing predictions of TC and S. The learned linguistic description explains in natural language the way, how the forecast was obtained.

4

Mining Information from Time Series

In [5], a concise overview of methods for mining information from time series is given. However, the author in his paper did not consider methods of fuzzy modeling. We are convinced, however, that they can offer many interesting results in the area of mining information from data of any kind (and thus, of course, also from time series). Besides others, they can generate sentences of natural language characterizing various features occurring in time series. 4.1

Evaluation of Local Trend in Natural Language

A convenient tool for evaluation of the slope of time series is the F1 -transform since it makes it possible to estimate the average slope (tangent) over an imprecisely determined area, and using methods of FNL, it can be characterized in natural language. Example of such evaluation of time series from Fig. 1 is the following: Trend in the interval [60, 80] is “a little decreasing”. Global trend of the whole time series is “very little decreasing”. It is important to emphasize that the evaluation is based on the values of the time series, not on the estimated trend-cycle! Moreover, as one can certainly agree, the slope is not immediately recognizable from the graph even by eyes. A related task is to find the largest interval with a specific monotonous trend (e.g., slightly decreasing; cf. [19]). This task is important for the investment where we want to detect “bull and bear” phases of financial time series (cf. [13]). There are two ways how such interval can be identified: directly from data or indirectly from the estimated trend-cycle. Example of the identification of monotonous intervals in the time series from Fig. 1 is in Table 1. The found intervals are in the figure marked below the graph.

Mining and Summarizing Information on Time Series

49

Fig. 1. Artificial time series with marked real trend-cycle (dotted line) and its estimation using the inverse F-transform (solid line). Below the graph are outlined intervals due to Table 1: based on the data (up), and on the estimated trend cycle (down). Above the graphs are marked the bull and bear phases that were identified using our method.

4.2

Other Applications

On the basis of our theories, we also addressed the following problems: (a) Identification of structural breaks that are sudden, considerable changes in the ordinary course of the time series X. In statistics, methods suggested to solve this task are, e.g., [2,3,25]. In [16], we suggested a method for their detection which is similar to finding intervals of monotonous described above. We check the slope of time series within two subsequent intervals determined by two adjacent fuzzy sets Ai , Ai+1 ∈ Ah for a particular fuzzy partition Ah with sufficiently short h. Examples demonstrating our method are presented, e.g., in [26]. Let us remark that we also developed a method for detection of structural breaks in time series volatility. Table 1. Identified intervals with monotonous trend of time series from Fig. 1 and the linguistic evaluation of their slope From data

From trend-cycle

Identified interval

Linguistic evaluation

Identified interval

Linguistic evaluation

[1, 21]

Hugely increasing

[1, 20]

Hugely increasing

[21, 48]

Clearly decreasing

[20, 31]

Clearly decreasing

[48, 53]

Clearly increasing

[31, 36]

Stagnating

[53, 58]

A little increasing

[36, 47]

Clearly decreasing

[58, 69]

Clearly increasing

[47, 52]

Stagnating

[69, 80]

Clearly decreasing

[52, 69]

Clearly increasing

[69, 80]

Clearly decreasing

50

V. Nov´ ak

(b) In [18], we suggested an index of similarity of two time series. It is based on the application of the F-transform. Unlike other known indexes that are based on the values of time series (cf., e.g., [6,9]) our similarity index considers also distances between average values of tangents in the corresponding areas. We argue that it better captures the idea of similarity of time series. We have suggested also another index in [10]. (c) Automatic summarization of knowledge about time series. This task is addressed by several authors (see, e.g., [1,7,8,11,27]). The fuzzy natural logic suggests a sophisticated formal theory of intermediate quantifiers (see [4,12,15]) that are expressions of natural language such as most, many, a lot of, a few, several, etc. A typical example of such summarizing statement is: The trend in the first quarter of the year is in most tracked time series slightly increasing. (d) Perceptually important points are points where the time series essentially changes its course (cf. [5]). Clearly, we cannot expect that they are isolated time points but rather certain imprecisely determined areas. A suitable method is based on the higher-degree F-transform because it makes it possible to estimate the first and second derivatives in a vaguely specified area. Another method based on construction of a special Laplacian with kernels producing fuzzy partition is suggested in [23].

5

Conclusion

In this paper, we gave an overview of a few non-statistical methods for analyzing and forecasting time series, and mining information from them expressed in sentences of natural language. The theoretical background of our methods are the theory of fuzzy transform and theories of fuzzy natural logic.

References 1. Castillo-Ortega, R., Mar´ın, N., S´ anchez, D.: A fuzzy approach to the linguistic summarization of time series. Multiple-Valued Logic Soft Comput. 17(2–3), 157– 182 (2011) 2. De Wachter, S., Tzavalis, D.: Detection of structural breaks in linear dynamic panel data models. Comput. Stat. Data Anal. 56(11), 3020–3034 (2012) 3. Doerr, B., Fischer, P., Hilbert, A., Witt, C.: Detecting structural breaks in time series via genetic algorithms. Soft. Comput. 21(16), 4707–4720 (2016). https:// doi.org/10.1007/s00500-016-2079-0 4. Dvoˇr´ ak, A., Holˇcapek, M.: L-fuzzy quantifiers of the type 1 determined by measures. Fuzzy Sets Syst. 160, 3425–3452 (2009) 5. Fu, T.C.: A review on time series data mining. Eng. Appl. Artif. Intell. 24, 164–181 (2011)

Mining and Summarizing Information on Time Series

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6. Goldin, D.Q., Kanellakis, P.C.: On similarity queries for time-series data: constraint specification and implementation. In: Montanari, U., Rossi, F. (eds.) CP 1995. LNCS, vol. 976, pp. 137–153. Springer, Heidelberg (1995). https://doi.org/10.1007/ 3-540-60299-2 9 7. Kacprzyk, J., Wilbik, A., Zadro˙zny, S.: Linguistic summarization of time series using a fuzzy quantifier driven aggregation. Fuzzy Sets Syst. 159, 1485–1499 (2008) 8. Kacprzyk, J., Wilbik, A., Zadro˙zny, S.: An approach to the linguistic summarization of time series using a fuzzy quantifier driven aggregation. Int. J. Intell. Syst. 25, 411–439 (2010) 9. Mantegna, R.N., Stanley, H.E.: Introduction to Econophysics: Correlations and Complexity in Finance. Cambridge University Press, Cambridge (1999) 10. Mirshahi, S., Nov´ ak, V.: A fuzzy method for evaluating similar behaviour between assets. Soft. Comput. 25, 7813–7823 (2021) 11. Moyse, G., Lesot, M.: Linguistic summaries of locally periodic time series. Fuzzy Sets Syst. 285, 94–117 (2016) 12. Murinov´ a, P., Nov´ ak, V.: The structure of generalized intermediate syllogisms. Fuzzy Sets Syst. 247, 18–37 (2014) 13. Nguyen, L., Mirshahi, S., Nov´ ak, V.: Trend-cycle estimation using fuzzy transform and its application for identifying of bull and bear phases in markets. Intell. Syst. Account. Finance Manage. 27, 111–124 (2020). https://doi.org/10.1002/isaf.1473 14. Nov´ ak, V.: A comprehensive theory of trichotomous evaluative linguistic expressions. Fuzzy Sets Syst. 159(22), 2939–2969 (2008) 15. Nov´ ak, V.: A formal theory of intermediate quantifiers. Fuzzy Sets Syst. 159(10), 1229–1246 (2008) 16. Nov´ ak, V.: Detection of structural breaks in time series using fuzzy techniques. Int. J. Fuzzy Logic Intell. Syst. 18(1), 1–12 (2018) 17. Nov´ ak, V., Lehmke, S.: Logical structure of fuzzy IF-THEN rules. Fuzzy Sets Syst. 157, 2003–2029 (2006) 18. Nov´ ak, V., Mirshahi, S.: On the similarity and dependence of time series. MDPI Math. 9(5), 550–563 (2021). https://doi.org/10.3390/math9050550, http://www. mdpi.com/2227-7390/9/5/550 19. Nov´ ak, V., Pavliska, V.: Time series: how unusual local behavior can be recognized using fuzzy modeling methods. In: Kreinovich, V. (ed.) Statistical and Fuzzy Approaches to Data Processing, with Applications to Econometrics and Other Areas. SCI, vol. 892, pp. 157–177. Springer, Cham (2021). https://doi.org/10.1007/ 978-3-030-45619-1 13 20. Nov´ ak, V., Perfilieva, I.: On the semantics of perception-based fuzzy logic deduction. Int. J. Intell. Syst. 19, 1007–1031 (2004) 21. Nov´ ak, V., Perfilieva, I., Dvoˇr´ ak, A.: Insight into Fuzzy Modeling. Wiley, Hoboken (2016) 22. Perfilieva, I.: Fuzzy transforms: theory and applications. Fuzzy Sets Syst. 157, 993–1023 (2006) 23. Perfilieva, I., Adamczyk, D.: Features as keypoints and how fuzzy transforms retrieve them. In: Rojas, I., Joya, G., Catal` a, A. (eds.) IWANN 2021. LNCS, vol. 12862, pp. 14–27. Springer, Cham (2021). https://doi.org/10.1007/978-3-03085099-9 2 24. Perfilieva, I., Daˇ nkov´ a, M., Bede, B.: Towards a higher degree F-transform. Fuzzy Sets Syst. 180, 3–19 (2011) 25. Preuss, P., Puchstein, R., Detter, H.: Detection of multiple structural breaks in multivariate time series. J. Am. Stat. Assoc. 110, 654–668 (2015)

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26. Truong, P., Nov´ ak, V.: An improved forecasting and detection of structural breaks in time series using fuzzy techniques. In: Rojas, I. (ed.) Contribution to Statistics. Springer, Cham (2022) 27. Wilbik, A., Dijkman, R.M.: On the generation of useful linguistic summaries of sequences. In: 2016 IEEE International Conference on Fuzzy Systems, pp. 555–562 (2016)

Fuzzy-Chaotic Variant of the Multiverse Optimizer Algorithm in Benchmark Function Optimization Lucio Amézquita , Oscar Castillo(B)

, and Prometeo Cortes-Antonio

Tijuana Institute of Technology, Tijuana, México {lucio.amezquita19,prometeo.cortes}@tectijuana.edu.mx, [email protected]

Abstract. In this work we present a new variation of the Multiverse Optimizer using Fuzzy logic and chaos theory (FCMVO) for optimization of benchmark mathematical functions. Over this study, we present some variations in Mamdani and Sugeno approximations in conjunction with some of the most used chaotic maps in the literature; like the Logistic map, Chebyshev map and Gauss map. By using chaos theory, we are substituting some of the random parameters for the MVO algorithm, and Fuzzy logic is used for dynamic parameter adaptation to substitute some equations of the MVO algorithm. The main tests for the variations presented are done with 13 benchmark mathematical functions, where we compare the original MVO in these functions, the comparison against a Chaotic MVO with 10 different chaotic maps, and the Fuzzy-Chaotic MVO with the same functions, so we can observe the improvement. In this study, we have the objective to determine if the combination of Fuzzy Logic and Chaos theory have significant improvement over the original MVO or its single variations, so we can proceed to further testing over control problems. Keywords: Multi-verse optimizer · Fuzzy logic · Optimization · Dynamic parameter · Mamdani · Sugeno · FCMVO · Chaotic maps · Chaos theory · Benchmark

1 Introduction In recent times, we have observed numerous uses of computational intelligence techniques, and, as a part of these techniques, we have Fuzzy Logic proposed by Zadeh. The use of fuzzy controllers is increasingly common in recent control system applications [1, 2], this occurs mostly, because fuzzy logic [3] can resemble on human reasoning, making it easier to understand. Other computational techniques widely used are the optimization algorithms [4], that are part of metaheuristics; their objective is to find the optimal result for a specific problem. When an optimization algorithm is used with a control problem, it can be used to find the best setup for the parameters of the problem, just to mention one of the many uses. These metaheuristics have inspirations over natural behavior or artificial behavior. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 53–63, 2022. https://doi.org/10.1007/978-3-031-09173-5_8

54

L. Amézquita et al.

One of the metaheuristics used in previous works [5–8] has been the Multiverse Optimizer (MVO), that uses some concepts of cosmology; the main uses where to optimize benchmark mathematical functions, system identification analysis and multiple control problems, where we concluded that, the MVO algorithm can be competitive against other optimization algorithms. Over the tests done and the adjustments in the algorithm, we designed a Fuzzy Logic MVO variant called FMVO, where we used fuzzy logic for dynamic parameter adaptation to obtain good results in the cases. In this paper we have the objective to observe the benefits of using Chaotic Maps alongside with Fuzzy Logic in the MVO algorithm, so we can then implement over more complex problems. This paper is organized as follows: Sect. 2 has a brief description of the MVO algorithm and some variations on the state of the art, Sect. 3 describes Chaos theory and some of the chaotic maps to use in the variation presented of the MVO algorithm, Sect. 4 has the results for the benchmark testing and Sect. 5 presents the conclusions to this work.

2 Multi-verse Optimizer and Literature Review of Variants The optimization algorithms are widely used computational techniques to find the best result for a specific problem, over these algorithms we can find the Multi-Verse Optimizer (MVO) proposed by Seyedali Mirjalili [9], which has inspiration over cosmology. Its solutions are represented by Universes and these interact between them with white and black holes, exchanging some elements of the universes to elevate the inflation rate, that represent the fitness of the solution. This optimization algorithm has received some adaptations after its appearance in 2015, where these works tried to solve the problem of stagnation in local optimal results, this by implementing some of the most used improvements for nature-inspired algorithms. Some of the improvements are achieved by using Levy flights [10] by improving the search ability of MVO; also to improve the behavior some works used chaotic maps [11], the use of neural networks [12], and quantum theory [13]. These variations of the MVO algorithm have made similar adequations to the algorithm, where they implement them in the main equation of the algorithm presented in (1), j that represents the wormhole. In this equation we have that xi indicates the jth parameter of the ith universe, TDR and WEP are Travel Distance Rate and Wormhole Existence Probability, Xj indicates the jth parameter of the best universe so far, lbj shows the lower limit of the jth variable, ubj is the upper limit of the jth variable and r2 , r3 , r4 are random numbers between [0, 1]. From here, the parameter that is replaced is r4 by the respective adequation in the cited works. ⎧    ⎪ ⎨ Xj + TDR × ubj − lbj  × r4 + lbj  r3 < 0.5 r < WEP 2 j Xj − TDR × ubj − lbj × r4 + lbj r3 ≥ 0.5 xi = (1) ⎪ j ⎩ xi r2 ≥ WEP

Fuzzy-Chaotic Variant of the Multiverse Optimizer Algorithm

55

3 Chaos Theory and Fuzzy Logic Implementation In this work we are going to describe a new variation of the MVO algorithm that uses Chaotic Maps and Fuzzy Logic (that has not been previously presented) to bring a better behavior of the algorithm, and find better solutions over benchmark mathematical functions. The implementation of Chaos theory resides on the use of one of the 10 chaotic maps [14] to replace a random value in one of the equations in MVO algorithm. In (2) the MVO algorithm presents an exchange of the solution in the algorithm, j where xi is the jth parameter of the ith solution, Ui represents the ith universe or solution, j xk indicates the jth parameter of the kth in a selection, NI (Ui ) is the normalized inflation rate of the solution and r1 is a random number in [0, 1]; here is where we replace the r1 value for a value generated by a chaotic map. j xk r1 < NI (Ui ) j xi = (2) j xi r1 ≥ NI (Ui ) Another implementation over the MVO algorithm resides in the Wormhole existence probability WEP and Travel Distance Rate TDR, represented by (3) and (4); here we designed a fuzzy inference system that replaces the equations and behave in similar way as the values obtained in the original algorithm. Here we designed Mamdani and Sugeno fuzzy inference systems. In Fig. 1 we can observe the inputs and surface of the Sugeno FIS for WEP, and in Fig. 2 for TDR. WEP surface

input Lightyears in1mf1

1

in1mf2

in1mf3

1

0.9 0.8 0.7 0.6 output

Degree of membership

0.8

0.4

0.6 0.5

0.2

0.4 0.3

0 0.2 0

0.2

0.4

0.6

0.8

1

0

0.2

0.4

0.6

0.8

1

Fig. 1. Input and surface for WEP of the Sugeno fuzzy system

WEP = min + l × TDR = 1 −

max − min L l 1/p L1/p

 (3) (4)

In the inputs of both systems we can observe, in the membership functions, that we are using generalized bell, as for the output we are using constant functions for each input membership function, giving us in the WEP system, 3 fuzzy rules, and for the TDR

56

L. Amézquita et al. TDR surface

input Lightyears

1

in1mfin1mf3in1mf4 1 2 2 in1mf14 in1mf5in1mf6in1mf7in1mf8in1mfi9 n1mf1in01mf1in11mf1in1mf13

1

n1mf17 in 1mf16 5

0.8

0.6

0.6 output

Degree of membership

0.8

0.4

0.4

0.2 0.2 0 0 0

0.2

0.4

0.6

0.8

1

0

0.2

0.4

0.6

1

0.8

Fig. 2. Input and surface for TDR of the Sugeno fuzzy system

system a total of 16 fuzzy rules. With these fuzzy inference systems [15–17], we are substituting the WEP and TDR equations of the MVO algorithm, so that the algorithm can handle uncertainty in different application cases.

4 Test and Results In this new variation of the algorithm called Fuzzy-Chaotic Multi-Verse Optimizer (FCMVO) we are using two Fuzzy inference systems to adapt WEP and TDR, as well as the use of a Chaotic map to generate a parameter. The tests are done with 13 benchmark mathematical functions that are used in the works of the original MVO and previous works of the algorithm [5, 7, 9]. We did perform 30 tests in our comparisons with 50 universes or solutions and 500 iterations; the comparisons are done with 5, 50 and 100 dimensions for each function; as for other parameters, they are dynamically adapted by the algorithm. In the first results we are comparing the original MVO algorithm with a Chaotic MVO, using only chaos maps to compare which map can work better with the algorithm. For the results, we used a Z-test with a 95% of confidence to compare results between the original MVO and the Chaotic version using 10 different chaos maps, that are: Chebyshev, Circle, Gauss, Iterative, Logistic, Piecewise, Sine, Singer, Sinusoidal and Tent maps. This can be observed in Table 1 for 50 dimensions. Table 1. Test results in 50 dimensions comparing MVO with Chaotic variant using Singer, Sinusoidal and Gauss chaos maps Algorithm

MVO

Function

Average

SD

Average

MVO Singer SD

z

Average

MVO Sinusoidal SD

z

Average

MVO Gauss SD

z

F1

1.04E +

2.12E +

9.76E +

2.06E +

−1.17

9.64E +

2.14E +

−1.38

8.80E +

2.23E +

−2.85

01

00

00

00

00

00

00

00

F2

4.29E + 02

1.40E + 03

2.44E + 02

3.53E + 02

−0.70

5.02E + 02

2.02E + 03

0.16

3.41E + 00

1.20E + 00

−1.66

F3

5.87E + 03

1.42E + 03

6.09E + 03

1.50E + 03

0.59

6.55E + 03

1.41E + 03

1.88

5.01E + 03

1.66E + 03

−2.15

(continued)

Fuzzy-Chaotic Variant of the Multiverse Optimizer Algorithm

57

Table 1. (continued) Algorithm

MVO

Function

Average

SD

Average

MVO Singer SD

z

Average

MVO Sinusoidal SD

z

Average

MVO Gauss SD

z

F4

1.66E + 01

6.53E + 00

1.89E + 01

6.96E + 00

1.28

2.06E + 01

6.68E + 00

2.31

9.23E + 00

2.06E + 00

−5.93

F5

6.64E + 02

6.96E + 02

7.11E + 02

4.91E + 02

0.30

8.66E + 02

8.40E + 02

1.01

1.01E + 03

1.05E + 03

1.49

F6

1.06E +

2.71E +

9.79E +

1.88E +

−1.30

9.90E +

2.58E +

−1.00

9.76E +

3.06E +

−1.09

01

00

00

00

00

00

00

00

F7

1.19E-01

4.03E-02

1.21E-01

3.33E-02

0.16

1.20E-01

4.00E-02

0.08

9.64E-02

2.91E-02

−2.51

F8

1.25E + 04

8.00E + 02

1.22E + 04

8.66E + 02

−1.36

1.22E + 04

7.96E + 02

−1.37

1.28E + 04

1.01E + 03

1.43

F9

2.54E +

4.94E +

2.76E +

3.54E +

1.96

2.85E +

5.21E +

2.39

2.33E +

4.87E +

−1.68

02

01

02

01

02

01

02

01

F10

3.49E + 00

3.08E + 00

4.07E + 00

4.28E + 00

0.61

4.08E + 00

4.30E + 00

0.61

3.15E + 00

5.99E-01

−0.59

F11

1.09E + 00

1.82E-02

1.08E + 00

1.71E-02

−1.38

1.09E + 00

1.79E-02

−0.59

1.09E + 00

2.07E-02

−0.05

F12

6.57E + 00

2.64E + 00

5.88E + 00

1.87E + 00

−1.17

5.85E + 00

2.39E + 00

−1.10

4.93E + 00

2.34E + 00

−2.54

F13

9.08E +

1.34E +

8.27E +

1.16E +

−0.25

8.84E +

1.31E +

−0.07

2.90E +

2.61E +

−2.48

00

01

00

01

00

01

00

00

From the performed tests, we only presented 3 of the 10 chaotic maps that were used, also, we only presented the case with 50 dimensions, similar tests were done with 5 and 100 dimensions. However, because of the length of this paper, we could not present all the results of the Chebyshev, Circle, Iterative, Logistic, Piecewise, Sine and Tent chaos maps in 5, 50 and 100 dimensions. An overall analysis of the results pointed out that, the chaotic map with the best overall performance was the Gauss map, and this is because each map has a different behavior when it generates the values for parameter r1 . In the next case, we used the Fuzzy variants of the MVO algorithm without using chaotic maps, calling it FMVO, which is used in Mamdani and Sugeno Fuzzy inference systems. This comparison can be observed in Table 2, which is done with 50 dimensions. Table 2. Test results in 50 dimensions comparing MVO with Fuzzy variants Algorithm

MVO

F-MVO Mamdani

F-MVO Sugeno

Function

Average

SD

Average

SD

z

Average

SD

z

F1

1.04E + 01

2.12E + 00

4.22E + 00

1.54E + 00

−12.94

1.41E + 00

2.26E-01

−23.13

F2

4.29E + 02

1.40E + 03

1.84E + 02

3.50E + 02

−0.93

5.23E + 03

1.91E + 04

1.37

(continued)

58

L. Amézquita et al. Table 2. (continued)

Algorithm

MVO

Function

Average

SD

F-MVO Mamdani Average

SD

z

F-MVO Sugeno Average

SD

z

F3

5.87E + 03

1.42E + 03

4.46E + 03

1.32E + 03

−3.98

2.26E + 03

4.86E + 02

−13.20

F4

1.66E + 01

6.53E + 00

1.69E + 01

7.05E + 00

0.14

1.94E + 01

6.19E + 00

1.65

F5

6.64E + 02

6.96E + 02

5.02E + 02

5.32E + 02

−1.01

5.20E + 02

7.26E + 02

−0.79

F6

1.06E + 01

2.71E + 00

4.05E + 00

1.38E + 00

−11.75

1.44E + 00

2.77E-01

−18.37

F7

1.19E-01

4.03E-02

7.71E-02

2.46E-02

−4.88

6.70E-02

2.47E-02

−6.05

F8

1.25E + 04

8.00E + 02

1.26E + 04

9.34E + 02

0.85

1.24E + 04

9.12E + 02

−0.46

F9

2.54E + 02

4.94E + 01

2.91E + 02

4.74E + 01

2.99

2.83E + 02

5.49E + 01

2.13

F10

3.49E + 00

3.08E + 00

8.15E + 00

8.24E + 00

2.90

4.83E + 00

6.50E + 00

1.02

F11

1.09E + 00

1.82E-02

1.00E + 00

6.84E-02

−6.71

8.01E-01

5.89E-02

−25.72

F12

6.57E + 00

2.64E + 00

4.77E + 00

1.64E + 00

−3.16

5.21E + 00

1.73E + 00

−2.35

F13

9.08E + 00

1.34E + 01

1.95E + 00

2.01E + 00

−2.88

3.67E-01

1.65E-01

−3.56

As we can observe, the Fuzzy variants of MVO can outperform in some cases the original MVO algorithm in the same initial setup, on this we can conclude that the fuzzy inference systems can give us better results on benchmark mathematical functions. Moving forward, we can make the combination of chaotic maps and fuzzy logic, so the tests done in the FCMVO can be observed in Tables 3, 4. With the obtained results, we can observe that the Fuzzy-Chaotic variant of MVO could perform better than the original algorithm in most benchmark mathematical functions and, also, over its variants with only chaotic map or fuzzy logic, making this variant a good choice in this particular chaotic map. Analyzing the results with other chaotic maps, we found that the algorithm could not even perform equally as the original MVO algorithm, even with fuzzy logic being implemented, but in the combination of a certain chaotic map, such as the Gauss map, this combination could outperform the original algorithm and the fuzzy variant in numerous cases.

FCMVO Mamdani Gauss

SD

1.57E + 00

1.77E + 00

6.82E + 02

4.13E + 00

5.30E + 02

1.74E + 00

1.93E-02

9.38E + 02

3.64E + 01

6.95E + 00

1.00E-01

1.48E + 00

5.09E-01

Average

4.04E + 00

3.16E + 00

3.09E + 03

1.21E + 01

4.93E + 02

3.81E + 00

7.51E-02

1.25E + 04

2.44E + 02

5.79E + 00

9.75E-01

3.80E + 00

1.13E + 00

Algorithm

Function

F1

F2

F3

F4

F5

F6

F7

F8

F9

F10

F11

F12

F13

9.08E + 00

1.34E + 01

2.64E + 00

1.82E-02

1.09E + 00

6.57E + 00

3.08E + 00

4.94E + 01

8.00E + 02

4.03E-02

2.71E + 00

6.96E + 02

6.53E + 00

1.42E + 03

1.40E + 03

2.12E + 00

SD

3.49E + 00

2.54E + 02

1.25E + 04

1.19E-01

1.06E + 01

6.64E + 02

1.66E + 01

5.87E + 03

4.29E + 02

1.04E + 01

Average

MVO

MVO Gauss

−3.25

−5.01

−6.16

1.66

−0.85

2.90E + 00

4.93E + 00

1.09E + 00

3.15E + 00

2.33E + 02

1.28E + 04

9.64E-02

0.11

9.76E + 00

−5.41

1.01E + 03

9.23E + 00

5.01E + 03

3.41E + 00

8.80E + 00

Average

−11.51

−1.07

−3.23

−9.68

−1.66

−13.20

z

2.61E + 00

2.34E + 00

2.07E-02

5.99E-01

4.87E + 01

1.01E + 03

2.91E-02

3.06E + 00

1.05E + 03

2.06E + 00

1.66E + 03

1.20E + 00

2.23E + 00

SD

−3.65

−2.24

−6.12

2.07

1.06

−1.24

−3.34

−9.26

−2.40

3.39

−5.88

−0.65

−9.53

z

1.95E + 00

4.77E + 00

1.00E + 00

8.15E + 00

2.91E + 02

1.26E + 04

7.71E-02

4.05E + 00

5.02E + 02

1.69E + 01

4.46E + 03

1.84E + 02

4.22E + 00

Average

2.01E + 00

1.64E + 00

6.84E-02

8.24E + 00

4.74E + 01

9.34E + 02

2.46E-02

1.38E + 00

5.32E + 02

7.05E + 00

1.32E + 03

3.50E + 02

1.54E + 00

SD

FMVO Mamdani

−2.17

−2.43

−1.26

−1.20

−4.30

−0.69

−0.36

−0.61

−0.06

−3.23

−5.08

−2.83

−0.44

z

Table 3. Test results in 50 dimensions for FCMVO Mamdani with Gauss map comparing with original MVO, MVO with Gauss map and FMVO Mamdani variants Fuzzy-Chaotic Variant of the Multiverse Optimizer Algorithm 59

2.73E-01

2.21E + 00

4.57E + 02

6.35E + 00

4.34E + 02

3.36E-01

1.81E-02

8.51E + 02

4.50E + 01

8.61E + 00

6.88E-02

1.16E + 00

2.32E + 00

1.80E + 03

1.44E + 01

3.62E + 02

1.45E + 00

6.17E-02

1.22E + 04

2.95E + 02

1.04E + 01

7.94E-01

3.72E + 00

4.34E-01

F1

F2

F3

F4

F5

F6

F7

F8

F9

F10

F11

F12

F13

3.40E-01

SD

Average

1.39E + 00

Function

FCMVO Sugeno Gauss

Algorithm

2.64E + 00 1.34E + 01

9.08E + 00

1.82E-02

1.09E + 00

6.57E + 00

3.08E + 00

4.94E + 01

8.00E + 02

4.03E-02

2.71E + 00

6.96E + 02

6.53E + 00

1.42E + 03

1.40E + 03

2.12E + 00

SD

3.49E + 00

2.54E + 02

1.25E + 04

1.19E-01

1.06E + 01

6.64E + 02

1.66E + 01

5.87E + 03

4.29E + 02

1.04E + 01

Average

MVO

−3.53

−5.41

−22.77

4.12

3.40

2.90E + 00

4.93E + 00

1.09E + 00

3.15E + 00

2.33E + 02

1.28E + 04

9.64E-02

−7.13 −1.26

9.76E + 00

1.01E + 03

9.23E + 00

5.01E + 03

3.41E + 00

8.80E + 00

Average

−18.30

−2.02

−1.37

−14.97

−1.67

−23.11

z

MVO Gauss

2.61E + 00

2.34E + 00

2.07E-02

5.99E-01

4.87E + 01

1.01E + 03

2.91E-02

3.06E + 00

1.05E + 03

2.06E + 00

1.66E + 03

1.20E + 00

2.23E + 00

SD

−5.13

−2.54

−22.54

4.58

5.19

−2.51

−5.54

−14.77

−3.12

4.22

−10.23

−2.38

−18.02

z

3.67E-01

5.21E + 00

8.01E-01

4.83E + 00

2.83E + 02

1.24E + 04

6.70E-02

1.44E + 00

5.20E + 02

1.94E + 01

2.26E + 03

5.23E + 03

1.41E + 00

Average

FMVO Sugeno

1.65E-01

1.73E + 00

5.89E-02

6.50E + 00

5.49E + 01

9.12E + 02

2.47E-02

2.77E-01

7.26E + 02

6.19E + 00

4.86E + 02

1.91E + 04

2.26E-01

SD

0.96

−3.94

−0.40

2.81

0.99

−0.73

−0.94

0.17

−1.02

−3.08

−3.76

−1.50

−0.23

z

Table 4. Test results in 50 dimensions for FCMVO Sugeno with Gauss map compared with the original MVO, MVO with Gauss map and FMVO Sugeno variants

60 L. Amézquita et al.

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61

5 Conclusions In this work we presented some variants of the Multiverse Optimizer using Fuzzy Logic and Chaotic Maps, resulting on a variant called Fuzzy-Chaotic Multi-Verse Optimizer (FCMVO), which could perform better in benchmark mathematical functions. We wanted to experiment in more ways than only using fuzzy logic for WEP and TDR, so we combined in part of the original algorithm, the use of chaotic maps [18], so we could have a better behavior, than using random numbers. Over the test results, we compared with similar tests in previous works of MVO [5, 6] over benchmark mathematical functions, and also, in new tests using chaotic maps and Fuzzy logic. For these results, we could observe a better behavior in the MVO algorithm, mainly with Fuzzy logic [1, 19], outperforming in most functions the original algorithm. We found in the results that, the Gauss map aided the MVO algorithm to obtain better results in comparison with other chaotic maps, even in combination with Fuzzy Logic, surpassing the original MVO in multiple cases, bringing us a starting point for future studies. With this study, we can conclude that the FCMVO algorithm can be better than the original MVO and the Fuzzy variant of MVO, this by the aid of chaotic maps in most of the functions we have tested, this by substituting the randomness of the MVO algorithm and by dynamically adapting WEP and TDR. This work has opened a path to test more with type-2 fuzzy logic [16, 17, 20, 21] and developing more adaptions over the random values of some parameters in the original MVO. As for future research we can use Fuzzy Logic and Chaotic maps in more cases of study. The main contribution in this work is to analyze the improvements of the MVO algorithm with multiple techniques, such as fuzzy logic and chaos theory, to propose better variants of the algorithm.

References 1. Cuevas, F., Castillo, O., Cortes, P.: Towards a control strategy based on Type-2 fuzzy logic for an autonomous mobile robot. In: Castillo, O., Melin, P. (eds.) Hybrid Intelligent Systems in Control, Pattern Recognition and Medicine. SCI, vol. 827, pp. 301–314. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-34135-0_21 2. Amador-Angulo, L., Castillo, O.: Optimal design of fuzzy logic systems through a chicken search optimization algorithm applied to a benchmark problem. In: Melin, P., Castillo, O., Kacprzyk, J. (eds.) Recent Advances of Hybrid Intelligent Systems Based on Soft Computing. SCI, vol. 915, pp. 229–247. Springer, Cham (2021). https://doi.org/10.1007/978-3-03058728-4_14 3. Zadeh, L.A.: Fuzzy algorithms. Inf. Control. 12, 94–102 (1968). https://doi.org/10.1016/ S0019-9958(68)90211-8 4. Aljarah, I., et al.: A robust multi-objective feature selection model based on local neighborhood multi-verse optimization. IEEE Access. 9, 100009–100028 (2021). https://doi.org/10.1109/ ACCESS.2021.3097206 5. Amézquita, L., Castillo, O., Soria, J., Cortes-Antonio, P.: A fuzzy variant of the multi-verse optimizer for optimal design of fuzzy controllers. In: Kahraman, C., Cebi, S., Cevik Onar, S., Oztaysi, B., Tolga, A.C., Sari, I.U. (eds.) INFUS 2021. LNNS, vol. 307, pp. 537–545. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-85626-7_63

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6. Amézquita, L., Castillo, O., Soria, J., Cortes-Antonio, P.: Optimal design of fuzzy controllers using the multiverse optimizer. In: Abraham, A., Hanne, T., Castillo, O., Gandhi, N., Nogueira Rios, T., Hong, T.-P. (eds.) HIS 2020. AISC, vol. 1375, pp. 289–298. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-73050-5_29 7. Amézquita, L., Castillo, O., Soria, J., Cortes-Antonio, P.: Optimization of membership function parameters for fuzzy controllers in cruise control problem using the multi-verse optimizer. In: Castillo, O., Melin, P. (eds.) Fuzzy Logic Hybrid Extensions of Neural and Optimization Algorithms: Theory and Applications. SCI, vol. 940, pp. 15–40. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-68776-2_2 8. Amézquita, L., Castillo, O., Soria, J., Cortes-Antonio, P.: A novel study of the multi-verse optimizer and its applications on multiple areas of computer science. In: Melin, P., Castillo, O., Kacprzyk, J. (eds.) Recent Advances of Hybrid Intelligent Systems Based on Soft Computing. SCI, vol. 915, pp. 133–144. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-587 28-4_7 9. Mirjalili, S., Mirjalili, S.M., Hatamlou, A.: Multi-Verse Optimizer: a nature-inspired algorithm for global optimization. Neural Comput. Appl. 27(2), 495–513 (2015). https://doi.org/10. 1007/s00521-015-1870-7 10. Hu, C., Li, Z., Zhou, T., Zhu, A., Xu, C.: A multi-verse optimizer with levy flights for numerical optimization and its application in test scheduling for network-on-chip. PLoS ONE 11, 1–22 (2016). https://doi.org/10.1371/journal.pone.0167341 11. Ewees, A.A., El Aziz, M.A., Hassanien, A.E.: Chaotic multi-verse optimizer-based feature selection. Neural Comput. Appl. 31(4), 991–1006 (2017). https://doi.org/10.1007/s00521017-3131-4 12. Dao, T.K., Yu, J., Nguyen, T.T., Ngo, T.G.: A hybrid improved MVO and FNN for identifying collected data failure in cluster heads in WSN. IEEE Access. 8, 124311–124322 (2020). https://doi.org/10.1109/ACCESS.2020.3005247 13. Sayed, G.I., Darwish, A., Hassanien, A.E.: Quantum multiverse optimization algorithm for optimization problems. Neural Comput. Appl. 31(7), 2763–2780 (2017). https://doi.org/10. 1007/s00521-017-3228-9 14. Saremi, S., Mirjalili, S., Lewis, A.: Biogeography-based optimisation with chaos. Neural Comput. Appl. 25(5), 1077–1097 (2014). https://doi.org/10.1007/s00521-014-1597-x 15. Bernal, E., Lagunes, M.L., Castillo, O., Soria, J., Valdez, F.: Optimization of Type-2 fuzzy logic controller design using the GSO and FA algorithms. Int. J. Fuzzy Syst. 23(1), 42–57 (2020). https://doi.org/10.1007/s40815-020-00976-w 16. Castillo, O., Ochoa, P., Soria, J.: Fuzzy logic systems. In: Differential Evolution Algorithm with Type-2 Fuzzy Logic for Dynamic Parameter Adaptation with Application to Intelligent Control. SAST, pp. 5–8. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-621 33-9_2 17. Lagunes, M.L., Castillo, O., Valdez, F., Soria, J.: Comparison of fuzzy controller optimization with dynamic parameter adjustment based on of Type-1 and Type-2 fuzzy logic. In: Castillo, O., Melin, P. (eds.) Hybrid Intelligent Systems in Control, Pattern Recognition and Medicine. SCI, vol. 827, pp. 47–56. Springer, Cham (2020). https://doi.org/10.1007/978-3030-34135-0_4 18. Ewees, A.A., Elaziz, M.A.: Performance analysis of chaotic multi-verse harris hawks optimization: a case study on solving engineering problems. Eng. Appl. Artif. Intell. 88, 103370 (2020). https://doi.org/10.1016/J.ENGAPPAI.2019.103370 19. Bernal, E., Castillo, O., Soria, J., Valdez, F.: Type-2 fuzzy logic for dynamic parameter adaptation in the imperialist competitive algorithm. In: Castillo, O., Melin, P. (eds.) Hybrid Intelligent Systems in Control, Pattern Recognition and Medicine. SCI, vol. 827, pp. 109–118. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-34135-0_9

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20. Castro, J.R., Sanchez, M.A., Gonzalez, C.I., Melin, P., Castillo, O.: A New Method for Parameterization of General Type-2 Fuzzy Sets. 10, 31–57 (2018) https://doi.org/10.1080/ 16168658.2018.1509519 21. Ontiveros-Robles, E., Melin, P., Castillo, O.: Comparative analysis of noise robustness of type 2 fuzzy logic controllers. In: Kybernetika, vol. 54, no. 1. Institute of Information Theory and Automation of The Czech Academy of Sciences, pp. 175–201, (2018) https://doi.org/10. 14736/kyb-2018-1-0175

Classification of Non-pharmaceutical Anti-COVID Interventions Based on Novel FTOPSIS-Sort Models Alexander Radaev1(B) , Elif Haktanir2,3 , Boris Yatsalo4 , and Cengiz Kahraman5 1

Institute of Atomic Energy of the National Research Nuclear University MEPHI (IATE MEPHI), Obninsk, Russian Federation [email protected] 2 Department of Industrial Engineering, Istanbul Technical University, 34367 Besiktas Istanbul, Turkey [email protected] 3 Department of Industrial Engineering, Altinbas University, 34217 Bagcilar Istanbul, Turkey 4 Institute of Cybernetic Intelligent Systems of the National Research Nuclear University MEPHI (MEPHI), Moscow, Russian Federation 5 Department of Industrial Engineering, Istanbul Technical University, 34367 Besiktas Istanbul, Turkey [email protected] Abstract. Assigning alternatives to predefined ordered categories under multicriteria conditions is the essence of multi-criteria sorting problematic. The family of fuzzy multi-criteria sorting models with the common name FTOPSIS-Sort are introduced based on the fuzzy extension of Multi-Criteria Decision Analysis (MCDA) ordinary method TOPSIS with the use of different approaches to assess functions of fuzzy numbers and different fuzzy ranking methods. The features of adjusting Fuzzy TOPSIS (FTOPSIS) models to sorting problematic are presented. The developed FTOPSIS-Sort models are implemented for multi-criteria sorting of non-pharmaceutical interventions against COVID-19. Keywords: Fuzzy MCDA · Fuzzy numbers Fuzzy TOPSIS · Fuzzy multicriteria sorting

1

· Fuzzy ranking methods ·

Introduction

The three main problems within Multi-Criteria Decision Analysis (MCDA) are choice, ranking, and sorting alternatives. Sorting methods are designed to assign alternatives to one of the predefined ordered classes [21]. As a rule, a multicriteria sorting method (MCDA-Sort) is a modification of an existing MCDA method, which is used for ranking alternatives. The most common MCDA-Sort methods are ELECTRE-TRI, UTADIS, ELECTRE TRI-C, and FlowSort [2]. For decision making in fuzzy environment fuzzy extensions of ordinary MCDA c The Author(s), under exclusive license to Springer Nature Switzerland AG 2022  C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 64–72, 2022. https://doi.org/10.1007/978-3-031-09173-5_9

Family of FTOPSIS-Sort Models

65

sorting methods are implemented with the use of fuzzy numbers (FNs) or/and linguistic variables. In this paper, the ordinary/classical fuzzy sets by Zadeh are considered. Any FMCDA model implies implementation of an approach to assess functions of fuzzy quantities (FNs) along with the use of a fuzzy ranking method. The extension of real function to function of FNs is based on the extension principle [16]. However, the implementation of the extension principle is ineffective even for assessing simple functions of FNs. For determining functions of FNs, the following main approaches are used in the literature: approximate assessing functions based on the basic type of FNs: triangular FNs (TrFNs) or/and Trapezoidal FNs (TpFNs), Standard Fuzzy Arithmetic (SFA) and Transformation Methods (TMs) [5]. The use of approximate computing based on the basic type of FNs is generally accepted approach within FMCDA. There exist several dozens of fuzzy ranking methods used within FMCDA models. In this paper, we focus on two well-known ranking methods [16]: Centroid Index (CI) (Center of Gravity) and Integral of Means (IM ). The goal of this contribution is the development of a family of FMCDA-Sort models based on Fuzzy TOPSIS (FTOPSIS) models as an example and their application. As a result, the following outcomes, which emphasize the novelty of this work, have been achieved: – a family of original models, FTOPSIS-Sort, for fuzzy multicriteria sorting of alternatives based on a fuzzy extension of the TOPSIS method is proposed; – the developed FTOPSIS-Sort models are based on the use of different approaches to assess functions of FNs and different fuzzy ranking methods; – FNs of the general form can be used as input values; – the developed models are applied within the case study on multicriteria sorting of anti-COVID measures. This paper is structured as follows. Section 2 revises the family of FTOPSISSort models. In Sect. 3 the case study on sorting of non-pharmaceutical antiCOVID measures is shown and analyzed. Finally Sect. 4 concludes this paper.

2

FTOPSIS-Sort Models

The development of ordinary multi-criteria sorting methods originates from the ELECTRE-TRI method [13], and family of ELECTRE-TRI methods is most widely represented in the literature. The other commonly used MCDA sorting methods are UTADIS, Flow-Sort. Ordinary MCDA sorting methods can be extended with FNs/linguistic variables to fuzzy models. The FMCDA sorting studies mainly concentrated on fuzzy Flow-Sort [3], fuzzy ELECTRE TRI [11], and fuzzy AHPSort [8] models. About 50% of these studies applied ordinary fuzzy sets, which is followed by interval type-2 fuzzy sets and intuitionistic fuzzy sets by 20% each. Some of the more common applications are supplier selection and risk evaluation. There are few studies in the literature that compare different FMCDA-Sort models implemented for the same scenario [9,12]. To the best knowledge of the authors, there are no fuzzy multi-criteria sorting models that apply standard fuzzy arithmetic or transformation methods for determining functions of FNs except our works [17,18,20].

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2.1

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FTOPSIS Models

Any FTOPSIS-Sort model is an adjustment of FTOPSIS model to sorting alternatives. FTOPSIS models are fuzzy extensions of ordinary MCDA method TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) [6], and such extensions has been presented in many publications, e.g., [4,18]. Comprehensive survey with statistical data on FTOPSIS usage has been presented in [7,18]. The generalized criterion (coefficient of closeness) for TOPSIS/FTOPSIS within a multi-criteria problem with n alternatives and m criteria is as follows: Di = D(ai ) =

Di− Di− +Di+

=

(

 − 2 1/2 2 ( m 1 wk (xik −xk ) )  − 2 1/2 + 2 2 2 1/2 +( m 1 wk (xik −xk ) ) 1 wk (xk −xik ) )

m

,

(1)

here xik is a normalized criterion value of alternative ai for criterion k, i = − 1, ..., n, k = 1, ..., m, x+ k and xk are, respectively, normalized coordinates of ideal and anti-ideal points/alternatives in Rm , wk is a weight coefficient, Di+ and Di− are, correspondingly, weighted distances from the alternative ai = (xi1 , ..., xim ) + − − = (x− to ideal, I + = (x+ 1 , ..., xm ), and anti-ideal, I 1 , ..., xm ), alternatives. For FTOPSIS model(s), criteria values and weight coefficients are presented by FNs (or linguistic terms, which mainly are interpreted as FNs). In this contribution, normalization of source criteria values, cij , of alternative ai for criterion j, cij → xij , j, i = 1, ..., n, j = 1, ..., m, are based on a linear transformation described in details in [17,18]. Within this approach, ideal, I + , and anti-ideal, I − , alternatives are presented as global points: I + = (1, ..., 1), I − = (0, ..., 0). Assigning weight coefficients in TOPSIS/FTOPSIS can be based on one of the existing approaches, including the use of subjective and objective weighting [10]. The following FTOPSIS models [18,20] are used in this paper as a basis for developing corresponding sorting models: – Models FTTrCI and FTTrIM: here, FT means FTOPSIS; Tr means approximate computations with propagating TrFNs through all calculated formulas of the model; CI and IM are methods for ranking of FNs Di , i = 1, ..., n, Eq. (1). These models lead to overestimation of the generalized criterion value (1) [18]. It can be added, FTOPSIS model with the use of approximate method with propagating triangular/trapezoidal FNs along with CI ranking is the most popular in applications; – Models FTSCI, FTSIM: assessing functions in expression (1) is based on SFA along with CI and IM ranking correspondingly. It should be stressed, implementation of SFA leads to overestimation of the output value in comparison with the proper value of Di [18]; – Models FTRCI, FTRIM: determining Di (1) is based on RTM (Reduced Transformation Method) [5,18] with subsequent use of CI/IM ranking; these models result in proper values Di , i = 1, ..., n, (1) [18]. 2.2

The Family of Fuzzy Multicriteria Sorting Models FTOPSIS-Sort

Within MCDA/FMCDA sorting models, ordered categories, Q1 , ..., QK , are used to sort alternatives under consideration, where category Qh is preferred to Qh+1 .

Family of FTOPSIS-Sort Models

67

To avoid excessive consideration of cases with cost criteria, without loss of generality in the presentation of this work, we consider hereafter all criteria are benefit ones. To form the ordered categories within a multicriteria sorting problem, so called (multicriteria) limiting or central profiles are assigned [21]. In this contribution, only limiting profiles are considered. Fuzzy criteria values, cij , of alternative ai for criterion j, and fuzzy weight coefficients, wj , j = 1, ..., m, i = 1, ..., n, are considered within an FMCDA l l problem along with fuzzy limiting profiles, Ph = (Ph1 , ...., Phm ), h = 1, ..., K + 1, l where Phj is a FN (a limiting profile h for criterion j), and vector Ph+1 is dominated in Pareto by Ph : Ph+1 ≺P (M ) Ph , here M is a used fuzzy ranking l , h = 1, ..., K + 1, form a set of distinguishable FNs [19]. method, and FNs Phj The decision rule for assigning an alternative ai to corresponding category Q(ai ) within FTOPSIS-Sort model with ranking method M is as follows: Q(ai ) = Qh if D(Ph+1 ) ≺M D(ai ) M D(Ph ), h = 1, ..., K − 1; Q(ai ) = QK if D(PK+1 ) M D(ai ) M D(PK ),

(2)

here D(a) is the value of generalized criterion (1) for alternative a . According to [17], for the set of (strictly) distinguishable vectors of FNs, Ph , h = 1, ..., K + 1, D(Ph+1 ) ≺M D(Ph ), h = 1, ..., K, for ranking method M = CI, IM . In addition, a careful analysis of the Eq. (2) shows that for correct implementation of this decision rule, the marginal limiting profiles, P1 and PK+1 , h = 1, ..., K + 1, should be considered as singletons. It should be stressed, the suggested approach to normalizing criteria values with “global properties” for marginal limiting profiles allows sorting a given set of alternatives by FTOPSIS-Sort in one iteration. Taking into account different FTOPSIS models, indicated in Subsect. 2.1, the following FMCDA sorting models are introduced in this contribution: FTTrCISort, FTTrIM-Sort, FTSCI-Sort, FTSIM-Sort, FTRCI-Sort, and FTRIM-Sort.

3

Sorting Anti-COVID Measures

Fuzzy logic has been integrated with MCDA studies on COVID-19 with the use of several FMCDA models based on ordinary and novel fuzzy sets [1,14,15]. In this section, FTOPSIS-Sort models, presented in Subsect. 2.2, are used for analysis of anti-COVID Non-Pharmaceutical Interventions/measures (NPI). 3.1

Description of the Case Study

The analysis of medical, economic, and social anti-COVID measures attracts the interests of a wide range of specialists from all over the world. In this study, the NPI alternatives defined in [14] are sorted by the proposed models. These NPI alternatives are: A1 : Quarantine/lockdown of patients and those suspected of infection, A2 : Internal border restrictions reducing the ability to move freely (transportation) within a country, A3 : Social distancing, A4 : Health monitoring, A5 : Public awareness campaigns, A6 : Restriction of nonessential businesses, A7 : Restrictions of mass gatherings, A8 : External border restrictions reducing

68

A. Radaev et al. Table 1. Linguistic terms and their TrFNs correspondences Linguistic Term

TrFN for benefit/cost criterion

Low (L)

(0, 0, 0.25)/(0.75, 1, 1)

Between Low and Middle (LM)

(0, 0.25, 0.5)/(0.5, 0.75, 1)

Middle (M)

(0.25, 0.5, 0.75)/0.25, 0.5, 0.75

Between Middle and High (MH) (0.5, 0.75, 1)/(0, 0.25, 0.5) High (H)

(0.75, 1, 1)/(0, 0, 0.25) Table 2. Limiting profiles

Criteria

Limiting profiles l l P1,j P2,j

C1 : Common satisfaction of the society (Benefit)

1

l P3,j

l P4,j

(0.5, 0.6, 0.7) (0.4, 0.5, 0.6) 0

C2 : Maximum required time to implement (Cost) 0

(0, 0.2, 0.4)

(0.2, 0.4, 0.6) 1

C3 : Financial burden to the economy (Cost)

0

(0, 0.2, 0.4)

(0.2, 0.4, 0.6) 1

C4 : Effectiveness on virus spread (Benefit)

1

(0.2, 0.4, 0.6) (0, 0.2, 0.4)

0

the ability to exit or enter a country, A9 : Closure of schools, A10 : Government policies that affect the country’s health resources (materials and health worker), A11 : Formation of new task units/bureaus and government policies changing administrative capacity to respond to the crisis, A12 : Common health testing (independent of suspected infection), A13 : Curfew, A14 : Restriction of nonessential government services, and A15 : Declaration of emergency. These alternatives are analyzed based on four criteria: C1 : Common satisfaction of the society (benefit), C2 : Maximum required time to implement (cost), C3 : Financial burden to the economy (cost), C4 : Effectiveness on virus spread (benefit). Table 1 shows the linguistic terms, which are used in this paper for setting (dimensionless) criteria values. The four limiting profiles for this fuzzy multicriteria sorting problem, see Table 2, define three ordered categories, Gh , h = 1, 2, 3, with the following interpretation: G1 : the category of effective interventions; G2 : slightly effective; G3 : poorly effective. The performance table (criteria values for all alternatives) are presented in Table 3 with the use of linguistic terms, described in Table 1. Fuzzy weight coefficients have been evaluated as averaging expert judgments in linguistic scale, see Table 4. The decision rule (2) is used for assigning each alternative Ai , i = 1, ..., 15, to categories Qh , h = 1, 2, 3.

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69

Table 3. Performance table Alternatives

C1 : Common satisfaction of the society (Benefit)

C2 : Maximum required time to implement (Cost)

C3 : Financial burden to the economy (Cost)

C4 : Effectiveness on virus spread (Benefit)

A1

LM

LM

MH

H

A2

L

LM

H

H

A3

MH

L

LM

H

A4

MH

M

MH

MH

A5

H

MH

M

M

A6

LM

MH

M

M

A7

L

L

L

H

A8

L

H

H

H

A9

L

LM

H

MH

A10

L

H

H

MH

A11

H

MH

MH

M

A12

H

MH

MH

MH

A13

L

LM

H

H

A14

L

M

LM

LM

A15

L

LM

MH

H

Based on input values, Tables 2, 3, and 4, alternatives Ai , i = 1, . . . , 15, are assigned to categories G1 , G2 , G3 , using FTOPSIS-Sort models, introduced in Subsect. 2.2. The results of sorting alternatives are shown in Table 5; the value of the ranking method, I(V (Ai )), I = CI, IM, i = 1, ..., 15, corresponding to the model, is indicated in brackets. For all computations, the numbers of α-cuts Nα = 20 and Nα = 40 were used; the output results are the same for both cases. Table 4. Weighting criteria depending on three expert views C1 : Common satisfaction of the society

C2 : Maximum required time to implement

C3 : Financial burden to the economy

Expert 1

LM; (0, 0.25, 0.5)

M; (0.25, 0.5, 0.75) H; (0.75, 1, 1)

Expert 2

H; (0.75, 1, 1)

MH; (0.5, 0.75, 1)

C4 : Effectiveness on virus spread H; (0.75, 1, 1)

M; (0.25, 0.5, 0.75) MH; (0.5, 0.75, 1)

Expert 3

MH; (0.5, 0.75, 1)

H; (0.75, 1, 1)

MH; (0.5, 0.75, 1)

H; (0.75, 1, 1)

Aggregated Fuzzy Criteria Weight

(0.42, 0.67, 0.83)

(0.5, 0.75, 0.92)

(0.5, 0.75, 0.92)

(0.67, 0.92, 1)

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Table 5. The results of assigning alternatives to categories by FTOPSIS-Sort models Method

Categories G3

G2

G1

FTTrCI-Sort

A7 (0.524), A14 (0.609)

A3 (0.709), A2 (0.739), A13 (0.739), A15 (0.752), A9 (0.772), A1 (0.823), A8 (0.847), A10 (0.877)

A6 (0.977), A5 (1.072), A11 (1.143), A4 (1.235), A12 (1.389)

FTTrIM-Sort

A7 (0.499), A14 (0.529)

A3 (0.664), A2 (0.699), A13 (0.699), A15 (0.701), A9 (0.712), A1 (0.764), A8 (0.805), A10 (0.818)

A6 (0.86), A5 (0.962), A11 (1.027), A4 (1.097), A12 (1.237)

FTSCI-Sort

A7 (0.493), A14 (0.528)

A3 (0.657), A2 (0.691), A13 (0.691), A15 (0.695), A9 (0.707), A1 (0.755), A8 (0.799), A10 (0.814)

A6 (0.852), A5 (0.949), A11 (1.018), A4 (1.091), A12 (1.216)

FTSIM-Sort

A14 (0.435), A7 (0.466)

A3 (0.608), A15 (0.64), A9 (0.642), A13 (0.648), A2 (0.648), A1 (0.691), A6 (0.718), A10 (0.75), A8 (0.754)

A5 (0.824), A11 (0.888), A4 (0.932), A12 (1.042)

FTRCI-Sort

A14 (0.309), A7 (0.427)

A6 (0.513), A3 (0.521), A9 (0.531), A15 (0.544), A2 (0.563), A13 (0.563), A1 (0.568)

A5 (0.614), A10 (0.634), A8 (0.662), A11 (0.665), A4 (0.672), A12 (0.768)

FTRIM-Sort

A14 (0.303), A7 (0.425)

A6 (0.512), A3 (0.523), A9 (0.532), A15 (0.545), A2 (0.567), A13 (0.567), A1 (0.573)

A5 (0.619), A10 (0.636), A8 (0.667), A11 (0.671), A4 (0.675), A12 (0.772)

According to Table 5, models with different ranking methods but the same approach to assess functions of FNs lead to the same sorting of alternatives, except for the models FTSCI-Sort and FTSIM-Sort: alternative A6 belongs to the category G1 for models FTSCI-Sort and does not belong to this category for model FTSIM-Sort. It can be stressed, for FTSCI-Sort model the difference CI(V (P2 )) − CI(V (A6 )) = 0.013 may be interpreted as noticeable distinction. This case may indicate a greater impact of overestimation, when using SFA, on the results of ranking by CI method. Remark 1. In [20], the authors suggest an approach for analysis of distinctions in ranking alternatives with the use of the square of linguistic distinctions based on linguistic variable “level of distinction”. For this, three zones/terms of distinctions in ranking FNs (with normalized support in [0, 1]) for differences of defuzzified values for defuzzification based ranking methods have been suggested with the following interpretation: Z1 = [0, 0.01] - no/negligible distinctions, Z2 = (0.01, 0.1] - noticeable distinctions, and Z3 = (0.1, 1] - significant distinctions. The implementation of this concept within FMCDA-Sort models is not considered in this short paper. At the same time, according to Table 5, models with different computational algorithms lead to different sorting alternatives: e.g., alternatives A8 and A10 belong to the category G1 for proper models, FTR[CI, IM]-Sort, and do not belong to this category for all other models under consideration.

Family of FTOPSIS-Sort Models

71

The authors demonstrated [20] that distinctions, including the level of distinctions, in ranking alternatives by different FMCDA models, which are fuzzy extensions of an ordinary MCDA method, can be significant. According to Table 5, different FTOPSIS-Sort models can result in different sorting alternatives. In these circumstances, the following question is natural: which of the specified sorting models can be recommended for applications? Taking into account the significant overestimation of the output results by approximate models FTTr[CI, IM]-Sort and FTS[CI, IM]-Sort as well as Remark 1, the authors believe that the use of models with proper assessing functions of FNs, FTRCISort and FTRIM-Sort, is justified.

4

Conclusions

Fuzzy MCDA sorting models developed to the moment are based on approximate computations. In this paper, an original approach to developing a family of FTOPSIS-Sort models, which are fuzzy extensions of an ordinal TOPSISSort method, has been suggested. FTOPSIS-Sort models differ by approaches to assessing functions of fuzzy numbers (approximate and proper ones) and methods for ranking of fuzzy numbers. This paper raises the following question, which is important from a methodological and applied point of view: which of the fuzzy multicriteria sorting models can be recommended for applications? The authors argue the use of “proper” models. The analysis of the following problems and questions forms further directions of research and development within this problematic: – creating and exploring families of FMCDA-Sort models based on other ordinary MCDA methods (e.g., PROMETHEE, MAVT, VIKOR, etc.); – exploring the frequency and the level/significance of distinctions in sorting alternatives by different FMCDA-Sort models, which are fuzzy extensions of the same ordinary MCDA method.

References 1. Alkan, N., Kahraman, C.: Evaluation of government strategies against COVID-19 pandemic using q-rung orthopair fuzzy TOPSIS method. Appl. Soft Comput. 110, 107653 (2021). https://doi.org/10.1016/j.asoc.2021.107653 2. Alvarez, P.A., Ishizaka, A., Mart´ınez, L.: Multiple-criteria decision-making sorting methods: a survey. Exp. Syst. Appl. 183, 115368 (2021) 3. Campos, A.C.S.M., Mareschal, B., de Almeida, A.T.: Fuzzy FlowSort: an integration of the FlowSort method and fuzzy set theory for decision making on the basis of inaccurate quantitative data. Inf. Sci. 293, 115–124 (2015) 4. Chen, C.T.: Extensions of the TOPSIS for group decision-making under fuzzy environment. Fuzzy Sets Syst. 114(1), 1–9 (2000) 5. Hanss, M.: Applied Fuzzy Arithmetic. Springer, Heidelberg (2005). https://doi. org/10.1007/b138914

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6. Hwang, C.L., Yoon, K.: Multiple Attribute Decision Making: Methods and Applications. Lecture Notes in Economics and Mathematical Systems, vol. 186. Springer, Berlin (1981). https://doi.org/10.1007/978-3-642-48318-9 7. Kahraman, C., Onar, S.C., Oztaysi, B.: Fuzzy multicriteria decision-making: a literature review. Int. J. Comput. Intell. Syst. 8(4), 637–666 (2015) 8. Krejˇc´ı, J., Ishizaka, A.: FAHPSort: a fuzzy extension of the AHPSort method. Int. J. Inf. Technol. Decis. Making 17(04), 1119–1145 (2018). https://doi.org/10.1142/ s0219622018400011 9. Liu, J., Xu, Z., Qin, J.: A sorting method: BWMSort II in interval type-2 fuzzy environment. In: 2019 IEEE International Conference on Fuzzy Systems (FUZZIEEE), pp. 1–6. IEEE (2019) 10. Olson, D.: Comparison of weights in TOPSIS models. Math. Comput. Modell. 40(7-8), 721–727 (2004) 11. Pereira, J., de Oliveira, E.C.B., Gomes, L.F.A.M., Ara´ ujo, R.M.: Sorting retail locations in a large urban city by using ELECTRE TRI-c and trapezoidal fuzzy numbers. Soft. Comput. 23(12), 4193–4206 (2019) 12. Remadi, F.D., Frikha, H.M.: The FlowSort for multi criteria decision making in intuitionistic fuzzy environment. In: 2019 6th International Conference on Control, Decision and Information Technologies (CoDIT), pp. 238–244. IEEE (2019) 13. Roy, B.: Multicriteria Methodology for Decision Aiding. Springer, New York (1996). https://doi.org/10.1007/978-1-4757-2500-1 14. Samanlioglu, F., Kaya, B.E.: Evaluation of the COVID-19 pandemic intervention strategies with hesitant f-AHP. J. Healthc. Eng. 2020, 1–11 (2020) 15. Sayan, M., Yildirim, F.S., Sanlidag, T., Uzun, B., Ozsahin, D.U., Ozsahin, I.: Capacity evaluation of diagnostic tests for COVID-19 using multicriteria decisionmaking techniques. Comput. Math. Meth. Med. 2020, 1–8 (2020). https://doi.org/ 10.1155/2020/1560250 16. Wang, X., Ruan, D., Kerre, E.: Mathematics of Fuzziness Basic Issues (2009). https://doi.org/10.1007/978-3-540-78311-4 17. Yatsalo, B., Korobov, A., Mart´ınez, L.: From MCDA to Fuzzy MCDA: violation of basic axiom and how to fix it. Neural Comput. Appl. 33(5), 1711–1732 (2021). https://doi.org/10.1007/s00521-020-05053-9 18. Yatsalo, B., Korobov, A., Oztaysi, B., Kahraman, C., Mart´ınez, L.: A general approach to Fuzzy TOPSIS based on the concept of fuzzy multicriteria acceptability analysis. J. Intell. Fuzzy Syst. 38, 979–995 (2020) 19. Yatsalo, B., Mart´ınez, L.: Fuzzy rank acceptability analysis: a confidence measure of ranking fuzzy numbers. IEEE Trans. Fuzzy Syst. 26, 3579–3593 (2018) 20. Yatsalo, B., Radaev, A., Mart´ınez, L.: From MCDA to fuzzy MCDA: presumption of model adequacy or is every fuzzification of an mCDA method justified? Inf. Sci. 587, 371–392 (2022). https://doi.org/10.1016/j.ins.2021.12.051 21. Zopounidis, C., Doumpos, M.: Multicriteria classification and sorting methods: a literature overview. Eur. J. Oper. Res. 138, 229–246 (2002)

A Hybrid Fuzzy Rule-Based Polyhedral Separation Approach: Medical Diagnosis Application Halil ˙Ibrahim Ayaz

and Bilal Ervural(B)

Industrial Engineering Department, Necmettin Erbakan University, Konya, Turkey {hiayaz,bervural}@erbakan.edu.tr

Abstract. Discrimination of two linearly inseparable sets using hyperplane(s) is considered one of the most successful classification methods. There is an expanding body of literature that realize the significance of classification of data accurately. Particularly, medical applications of classification provide meaningful early diagnosis results. However, medical datasets in real-world applications possess some noise and uncertainty. Therefore, dealing with uncertainty is a critical factor for accurate diagnosis. To overcome mentioned drawbacks, this study presents a hybrid fuzzy rule-based robust linear programming (RLP) and h-polyhedral separation (h-PolSep) approaches for breast cancer diagnosis through several consequent stages. In the proposed two-stage model, firstly the data is relabeled according to the fuzzy rule-based system, then the new outputs and original input values are classified using RLP and h-PolSep methods. Input fuzzification, generating membership functions, extracting fuzzy rules, and output defuzzification are examined in detail. A frequently used real-world medical dataset from the UCI Repository: the Wisconsin breast cancer is employed to evaluate the effectiveness of the classification using a number of metrics. Finally, the results demonstrate that the proposed approach effectively handles medical data classification problems. Keywords: Fuzzy logic · Classification · Medical data · Polyhedral separability

1 Introduction In statistical problems, the use of optimization tools provides some advantages. Discriminant analysis is one of the areas where optimization tools are used. Classification is widely used in methods and algorithms of discriminant analysis. The classification process aims to assign each element of a given set to a specific subset. In this study, fuzzy classification problems are discussed. There is a growing body of literature and application areas for classification problems. One of the well-known examples is microscopy image analysis [1]. Text classification enables the classification of new documents into pre-defined classes [2]. There is class information on music considering their features. The classification approach is used to classify music automatically [3]. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 73–81, 2022. https://doi.org/10.1007/978-3-031-09173-5_10

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Classification approaches are instrumental in assisting experts or overcoming information overload problems. Basic models have simple methods and are easily applicable. One of the most well-known basic models is the k nearest neighbor model is used for fall detection [4]. Another helpful and straightforward classification method is a decision tree. This method is used to increase the efficiency of the human–robot interaction process [5]. These methods are easily applicable and updated for new problems. Traditional methods are preferable, considering their advantages. However, these methods can be insufficient for some problems. In this case, mathematical-based classifiers are used for more accurate models and high accuracy rates. One of the earliest mathematical classification algorithms is Robust Linear Programming (RLP), proposed by Bennett and Mangasarian [6]. In this method, if the intersection of convex hulls of two sets is empty, these sets can be separated using a hyperplane. If this condition is not provided, the RLP method gives the best hyperplane that minimizes classification error. Followingly, h-polyhedral separability (h-PolSep) is proposed for linearly inseparable sets [7]. Suppose the intersection of the convex hull of set A and B is empty. In that case, h-PolSep method can be separate these sets with h hyperplanes. In the same manner, as RLP, h-polyhedral separability gives h-hyperplanes that minimize classification error if a condition is not provided. Convex hull may be too large in some cases, so a max–min classification approach is proposed to separate two classes from emptying their intersection [8]. Accuracy is a principal phenomenon in classification problems. Although the methods mentioned above run high accuracy rates, there are some grey points in the used datasets. Linguistic fuzzy rules help to cope with mentioned limitations. There has been a growing popularity of hybrid fuzzy classification methods in the last decade. In [9], a neural network and fuzzy method are hybridized to increase classification accuracy. A novel hybrid kernel density estimation and fuzzy rule are used to classify medical data [10]. Similarly, [11] presents a fuzzy hybrid method with harmony search optimization for medical diagnosis applications. Mathematical-based classification, like extreme learning and support vector machines (SVM), and fuzzy methods are hybridized in [12] to obtain higher classification accuracy. This study integrates a fuzzy process into RLP and h-polyhedral models. In this way, higher accuracy rates for points in grey fields are aimed. The rest of paper is organized as follows. Preliminaries for classification models and the dataset are given in Sect. 2. Error functions and constraints are given for both models. The proposed model is given in Sect. 3. The fuzzification process and rules are explained in detail. Experimental evaluation is presented in Sect. 4. Evaluation metrics and results of these metrics are explained. This section gives accuracy, precision, recall, specificity, and F-measure rates for training and testing sets. Finally, conclusions and future directions are presented in the Sect. 5.

2 Preliminaries 2.1 Robust Linear Programming Robust linear programming is proposed by Bennett and Mangasarian [6] to classify sets that the intersection of convex hulls is empty, conv(A) ∩ conv(B) = Ø. The aim is to create

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a separation criterion between 2 cluster elements. To separate two finite sets of points, A and B, the approach of constructing a convex polyhedron in n-dimensional space using h hyperplanes is considered. This problem is handled with a mathematical programming approach. If the convex hulls of these two sets do not intersect, a hyperplane can be found that linearly separates A and B. If the convex hulls of sets A and B intersect, a hyperplane that minimizes misclassification γ ∈ R, w ∈ Rn (γ , w) can be found (see Fig. 1a). The sum of the distances of the misclassified points from the separator hyperplane can be minimized. Other formulations (γ , w) maximize the separation quality provided by the hyperplane. If the separation is not complete, (γ , w) measures the largest error associated with the hyperplane (see Fig. 1b).

Fig. 1. (a) Linearly separable data (b) Linearly inseparable data

The error function and constraints are shown in linear models in RLP. The objective function and constraints of RLP are given in Eqs. 1–3. min1/m(−Aw + eγ + e)1 + 1/k(Bw − eγ + e)1

(1)

−Aw + eγ + e ≤ 0

(2)

Bw − eγ + e ≤ 0

(3)

w,γ

where A and B represents set A and B. w is the coefficient of a hyperplane that maximizes the number of correctly classified points. m and k are the number of elements in sets A and B, respectively. 2.2 Polyhedral and h-Polyhedral Separation Astorino and Gaudiso [7] showed that if the intersection of the convex hull, the set A and the set B is the empty set, conv(A) ∩ B = Ø, these two sets can be separated by h-polyhedral generating a convex polyhedron (see Fig. 2).

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Fig. 2. H-polyhedral separation example

H-polyhedral separability classifies the problems that linearly inseparable datasets with successive linear programming approach. In the method, h hyperplanes are used to construct a classification model. Thus, the error function of methods shows neither a linear nor nonlinear model. Error functions and constraints are given Eqs. (4–6). minz = 1/m

m   i=1

k       max aiT w(j) − γj + 1 + 1/k min −bTi w(j) + γj + 1

1≤j≤h

  max aiT w(j) − γj + 1 ≤ 0

1≤j≤h

  min −bTl w(j) + γj + 1 ≤ 0

1≤j≤h

i=1

1≤j≤h

(4) ∀i = 1, . . . , m

(5)

∀l = 1, . . . , k

(6)

where j is the number of hyperplanes used in the model, it ranges from 1 to h. Other variables indicate the same manner in RLP model. In this model, nonlinearity comes from Eq. 6 as a maximum of minimums are desired in Eq. 6. 2.3 Dataset Details We have used the Wisconsin Breast Cancer Dataset (WBCD) to analyze the functionality of the presented classification model. The data set concerns diagnosing two classes of breast cancer, benign and malignant, incorporating 699 patient data record observations. The malignant observations comprise about 35% of the whole set, whereas the remaining represent benign observations. Nine numerical attributes describe them: (i) clump thickness, (ii) cell size uniformity, (iii) marginal adhesion, (iv) single epithelial cell size, (v) cell shape, (vi) bare nuclei, (vii) bland chromatin, (viii) normal nucleoli, and (ix) mitoses.

3 Proposed Model In this study, we have developed a hybrid classification model that combines polyhedral separability techniques with fuzzy set techniques and applies it to medical diagnosis. Figure 3 demonstrates the framework of the proposed fuzzy expert system that consists of three phases.

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Fig. 3. Flow chart of the hybrid fuzzy rule-based methodology

In the fuzzification step, the numeric input variables are first transformed into linguistic values before being evaluated, conforming to the fuzzy rules. A regular fuzzy set function is assigned values between 0 and 1, indicating the degree of membership of an element in a specific set. In this study, we have selected the triangular and trapezoidal fuzzy membership functions because they are easy to understand and commonly used. Table 1 gives the input fuzzy linguistics for each feature, and Fig. 4 demonstrates the membership functions for detecting breast cancer by verifying attributes. Table 1. Fuzzy linguistics and ranges for each feature. Features

Fuzz linguistic variables

Range

F1_Clump_Thickness

[Low, Medium1, Medium2, High]

(1–10)

F2_Cell_Size_Uniformity

[Low, Medium, High]

(1–10)

F3_Cell_Shape_Uniformity

[Low, Medium, High]

(1–10)

F4_Marginal_Adhesion

[Low, Medium, High]

(1–10)

F5_Single_Epith_Cell_Size

[Low, Medium, High]

(1–10)

F6_Bare_Nuclei

[Low, Medium, High]

(1–10)

F7_Bland_Chromatin

[Low, Medium, High]

(1–10)

F8_Normal_Nucleoli

[Low, High]

(1–10)

F9_Mitoses

[Low, High]

(1–10)

The simplest way to express human knowledge using artificial intelligence is to transform it into natural language expressions through IF–THEN rules. The knowledge base stores a set of fuzzy rules the fuzzy inference engine uses to get a single exact output value. Some of the rules developed based on nine fuzzy input variables are given in Table 2. The fuzzy linguistic inputs for the nine features and the generated fuzzy rules are analyzed in the defuzzification step and an appropriate single crisp label is assigned to each data. Then, the relabeled data as the output of the fuzzy inference process is transferred to the classification stage.

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Fig. 4. The generated input membership functions for each feature

The final stage aims to classify the WBCD dataset using a RLP method and a 2polyhedral separation method (2-PolSep) to detect the benign or malignant samples. At this point, the dataset is separated into two groups, training, and testing. Then, using data relabeled according to the rule-based system, the new outcomes and original input values are classified using RLP and h-PolSep methods. Table 2. A few of the rules derived for the breast cancer data. Clump Cell size Cell thickness shape

Marginal Sin. ep. adhesion cell size

Bare nuclei

Bland Normal Mitoses Class chromatin nucleoli

Low

Low

Medium Low

Medium Low

Low

Low

Low

Benign

Med_2

Low

Low

Medium

High

Low

Medium

Low

Low

Benign

High

Medium Low

Low

High

Low

Low

Low

Low

Benign

Med_1

Medium High

High

Low

Medium Low

High

Low

Malign

Med_2

Medium Medium High

High

High

High

Low

High

Malign

High

High

High

Medium High

High

Low

Malign

High

High

4 Experimental Analysis 4.1 Performance Metrics The performance of proposed classification models is compared by employing accuracy, precision, recall, specificity, and f-measure. These metrics utilize the number of true

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positives (TP), true negatives (TN), false positives (FP), and false negatives (FN) in the calculations. The calculations of mentioned metrics are given in Eqs. (7–11): Acc = (TN + TP)/(TP + FP + FN + TN )

(7)

Pr = TP/(TP + FP)

(8)

Rec = TP/(TP + FN )

(9)

Sp = TN /(TN + FP)

(10)

F − meas = 2 ∗ (Pr ∗ Rec)/(Pr + Rec)

(11)

4.2 Results and Discussion In experimental analysis, a tenfold cross-validation method is employed. The dataset is randomly partitioned into ten equal-sized partitions. Then, one partition is used to test, whereas the rest is reserved for training the model. The procedure is replicated in ten iterations so that each partition is used for testing precisely one time. The performance metrics of subsets for each iteration are acquired. Then the mean results of the tenfold cross-validation are achieved. In Table 3 and Table 4, the values of evaluation metrics by the classification models are introduced in Sect. 2. As regarded from the results listed, the hybrid classification models perform well for breast cancer diagnosis. As can be seen from the results, the F-RLP model has a slightly more reasonable performance compared to the F-2PolSep model. For the 9:1 learn-to-test ratio, the accuracy of the F-RLP model is found as 98.0% and 97.3% in the training and testing sets, respectively. Besides that, for the F-2PolSep model, the accuracy is 97.6% in the training part and 97.1% in the testing part. Table 3. Classification accuracy on the dataset. Classification model

Accuracy (%) Training set

Testing set

RLP

98.0

97.3

2-PolSep

97.6

97.1

In addition to the classification accuracy results obtained by the models, the values obtained for the other metrics are also encouraging. The precision, recall, specificity, and F-measure metrics values are listed in Table 4. The results indicate that the proposed classification models can be used as an acceptable approach for aiding researchers in the process of diagnosing breast cancer.

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H. ˙I. Ayaz and B. Ervural Table 4. Performance validation of methods on training and testing data.

Classification model

Training set

Testing set

Pr. (%)

Rec. (%)

Sp. (%)

F-meas. (%)

Pr. (%)

Rec. (%)

Sp. (%)

F-meas. (%)

RLP

95.9

98.4

97.7

97.2

95.4

97.1

97.4

96.1

2-PolSep

95.0

98.2

97.2

96.6

94.7

97.5

96.9

95.9

5 Conclusion and Future Work Classification methods have broad literature and application areas. Practical and easily applicable methods can be applied to the most classification problem. However, conventional methods can be insufficient for solving problems in some cases. Mathematical and derivative-based classification methods can be overcome this problem. This study applies two well-known derivative-based classification methods, RLP and h-PolSep in a fuzzy environment. In this way, evaluation metrics are increased with the proposed approach. Five metric evaluation results are given, and results are presented in detail. The experiment results of the two methods we have obtained display the good performance of the approach in terms of classification correctness. In future directions, the effectiveness of the proposed hybrid approach can be studied on other medical datasets using different membership structures by interested researchers. Also, parameters of RLP and hPolSep can be estimated using meta-heuristics like genetic algorithm and particle swarm optimization. Developing novel integrated versions of the rule-based approach using supervised machine learning methods, such as SVM, naïve bayes, and neural networks can also be an interesting research direction.

References 1. Liu, Z., et al.: A survey on applications of deep learning in microscopy image analysis. Comput. Biol. Med. 134, 104523 (2021) 2. Miro´nczuk, M.M., Protasiewicz, J.: A recent overview of the state-of-the-art elements of text classification. Expert Syst. Appl. 106, 36–54 (2018) 3. Burred, J.J., Lerch, A.: A hierarchical approach to automatic musical genre classification. In: Proceedings of the 6th International Conference on Digital Audio Effects, pp. 6–9 (2003) 4. De, A., Saha, A., Kumar, P., Pal, G.: Fall detection method based on spatio-temporal feature fusion using combined two-channel classification. Multimed. Tools Appl. (2022) 5. Abu Al-Haija, Q., Al-Saraireh, J.: Asymmetric identification model for human-robot contacts via supervised learning. Symmetry (Basel) 14, 591 (2022) 6. Bennett, K.P., Mangasarian, O.L.: Optimization methods and software robust linear programming discrimination of two linearly inseparable sets. Opt. Met. Softw. 1, 23–34 (1992) 7. Astorino, A., Gaudioso, M.: Polyhedral separability through successive LP. J. Optim. Theory Appl. 112, 265–293 (2002) 8. Bagirov, A.M.: Max-min separability. Optim. Methods Softw. 20, 271–290 (2005)

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9. Priyadarshini, L., Shrinivasan, L.: Design of an ANFIS based decision support system for diabetes diagnosis. In: Proceedings of the 2020 IEEE International Conference Computer Signal Processing, pp. 1486–1489 (2020) 10. Song, X., Qin, B., Xiao, F.: FR–KDE: A hybrid fuzzy rule-based information fusion method with its application in biomedical classification. Int. J. F. Syst. 23, 392–404 (2021) 11. Mousavi, S.M., Abdullah, S., Niaki, S.T.A., Banihashemi, S.: An intelligent hybrid classification algorithm integrating fuzzy rule-based extraction and harmony search optimization: Medical diagnosis applications. Knowledge-Based Syst. 220, 106943 (2021) 12. Mojrian, S., Pinter, G., Joloudari, J.H., Felde, I., Szabo-Gali, A., Nadai, L., Mosavi, A.: Hybrid machine learning model of extreme learning machine radial basis function for breast cancer detection and diagnosis; A multilayer fuzzy expert system. In: Proceedings of 2020 RIVF International Conference on Computing and Communication Technologies (2020)

Fuzzy Pedestrian’s Risk Perception and Notification in Fuzzy Neighborhoods Azedine Boulmakoul1(B)

, Souhail El Kaissi1

, and Ahmed Lbath2

1 Computer Science Department, FSTM, Hassan II University of Casablanca, Casablanca,

Morocco [email protected] 2 LIG/MRIM, CNRS, University Grenoble Alpes, Grenoble, France [email protected]

Abstract. Analyzing pedestrians’ behavior in smart cities relies on the understanding of the human cognitive abilities, including the ability to focus on the traffic environment, and the understanding of the perceived spatiotemporal object’s semantics. It relies also on understanding the flow activity on a high-level scale of what’s circulating around the pedestrian and over all the corners of the cities. There is a lot of risk on pedestrian while they are interacting with the world and sadly that can lead to accidents. We find that one of the causes of pedestrian accidents is inattention, pedestrian gets easily distracted by their digital devices, or also by events nearby. To minimize the pedestrian accidents and help increasing their assurance of safety, we propose in this paper, a model oriented over road crossing to percept risk on pedestrian, based on spatial analysis and notify the pedestrian as fast as possible using a scalable distributed architecture and a push-based notifications approach. We used a theory of risk perception in a spatial neighborhood, by constructions based on fuzzy neighborhoods and fuzzy pretopology. Keywords: Distributed systems · Fuzzy topology · Fuzzy neighborhood · Fuzzy perception · Pedestrian’s safety

1 Introduction We are living in a fast-growing world; we are now (2022) 7.9 billion people in Earth, and we expect the number to increase to 10 billion by 2050. More people in planet Earth means more cars and more cars means more accidents leading to pedestrians’ death. Hence the necessity to act towards lowering death rates of the pedestrians and increasing their sense of awareness. That could be done by taking into consideration the This work was partially funded by Ministry of Equipment, Transport, Logistics and Water − Kingdom of Morocco, The National Road Safety Agency (NARSA) and National Center for Scientific and Technical Research (CNRST). Road Safety Research Program# An intelligent reactive abductive system and intuitionist fuzzy logical reasoning for dangerousness of driver-pedestrians interactions analysis: Development of new pedestrians’ exposure to risk of road accident measures. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 82–88, 2022. https://doi.org/10.1007/978-3-031-09173-5_11

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fast-growing internet of thing and the connected devices that retrieve everyday millions of useful data about the pedestrians’ places, environment, and others. We proposed in this paper a solution to enhance awareness at pedestrians by first building a fuzzy neighborhood [2, 5–7] encompassing the pedestrians as well as the environment around them, secondly, we collect all useful data within the neighborhood like roads, cars, buildings…, and finally we make sure to track the behavior of the pedestrians so that we could retrieved their point of interest [1] and deduce the risk point [2] which we call in this paper the risk data. After collecting the risk data, the solution is designed to spread the information over pedestrians’ devices well enough to increase the chances that they percept the data. When pedestrians get the risk data, they will be notified by using different kinds of signals (visual, sound and feel). About the organization of the paper, we will begin by giving some information reminder about how we calculate the risk, and we will explain how the notification system work end to end in a global way in the Second Section entitled notification in fuzzy neighborhood. In the Sect. 3, we will give details information about the internal design of the system, and we will give some metrics about the performance of the application. And finally, we conclude by giving an overview about the paper in the conclusion and we list future perspectives.

2 Notification in Fuzzy Neighborhood In this section, we explain how the pedestrian get notified about an eventual risk, and we will talk about the different forms of signal triggered to make pedestrians more aware. The notification system is composed of two parts, the push notifications, and the shared Bluetooth notifications. The push notifications are originated from the risk already calculated by our risk engine; they are calculated in real time by analyzing the behavior of the pedestrian in a fuzzy neighborhood [2, 4, 8–11]. As we already defined in the paper [2], we consider a pedestrian has a risk if there is an element in the fuzzy neighborhood that its attractivity coefficient is greater than the total of attractivity of the other elements in the fuzzy neighborhood (see Eq. 1). We proposed relevant indicators for the evaluation of pedestrian risk according to the fuzzy perception of its environment using fuzzy neighborhood [5–7] and fuzzy pretopology [2, 3, 13] perception model.  θ εθ (xi (t)) ∈ ]0, 1] (1) ∃k : ε,k (xk (t)) > iNxε,α(t),i=k i

θ is the attractivity of the With xk (t) is an element in the fuzzy neighborhood, ε,k current element. In the fuzzy neighborhood [5–7, 12], pedestrians have installed in their smart phones our application. The application requires GPS access and can trigger sound, flash, and vibration event in the phone, to signal the pedestrian that there is a risk in their actual coordinates and should be aware of the road and the cars beside them. The application receives notifications data from the risk engine server and send a receive notifications data from pedestrians’ smart phones in the same neighborhood (see

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Fig. 1). Pedestrians’ phones in the fuzzy neighborhood communicates (send and receive data) over Bluetooth, while they receive notifications data over http from the risk engine server. Having many sources of getting information, it ensures that pedestrians will receive the data in the fastest way possible, so that it could be notified and be aware of the risk and the danger.

Fig. 1. Architecture of the notification system to pedestrians while walking on the zebra crossing

The risk engine server is the system that calculates the attractivity and the risk of every pedestrian at real time rate in a fuzzy neighborhood. We can see the risk engine components details and its architecture in the previous work [2]. A single notification data contains two information (see Fig. 2): • Danger_Area_Center: Center coordinates of the dangerous area (the area that evolves pedestrians at risk). • TTL: The TTL (the time to live) of the risk. Note that the time is arbitrary and related to the type of the point of interest. After the application receives the notifications data, it processes it one by one. For every notification data, the algorithm is as following: • It checks whether the coordinates of the location of the pedestrian fall in the same danger area centered by Danger_Area_Center and within a radius R. If yes, the algorithm continues. Otherwise, it deletes the notification data and go to the next notification data. • It checks if the TTL is still valid. If yes, the application activates the signals of awareness. Otherwise, it deletes the notification data and go to the next notification data. The signal of awareness is the most important part, it should be the more explicit to inform the pedestrian that there is danger.

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Fig. 2. Pedestrian getting notification in risk area only

The signals come with 3 main forms. These forms are considerate the 3 most effective to steal a human attention: • Sound signals: The application plays a siren sound, in a periodic time until the TTL hits. • Visual signal: The application: The application activates and deactivate the phone flashlight, in a periodic time until the TTL hits. • Touch signal: The application keeps vibrating, in a periodic time until the TTL hits. Theses 3 types of signals increase the chances for the pedestrian to be aware, and are designed to touch more people, including people with disabilities. While signaling the pedestrians, it is the pedestrian’s responsibility to react the signals in the proper and faster way.

3 System and Application In this section, we will explain how the notification system works and what are the mandatory components that makes it work (see Fig. 3). First, as we can see in the flowing figure, the risk engine sends risk data to the notification server, after calculating it, and before storing it in the graph database. The risk notification server after it receives the risk data, it stores it in RabbitMQ queue, following the TTL order. If a risk data hits its TTL time, this data will be automatically deleted (see Fig. 3). The risk notification sends risk data in the queue as push notifications to the client android application at the pedestrian level.

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Fig. 3. Risk notification server sends push notification to subscribed android phones.

Of course, pedestrians should install the android application. It requires while installing, Bluetooth, GPS, flash, push notifications, vibration, and sound notifications permissions. After receiving the risk data, as a push notification, the android application updates its local risk data queue, and trigger the awareness signals if there is risk at the same danger area as the pedestrian. The android application is designed to receive send and updates also risk data by Bluetooth. Indeed, as the following figure shows (see Fig. 4), at the same fuzzy neighborhood, pedestrians’ android applications share and circulate the risk data, from pedestrian to another, to ensure that the risk data is received in case if a pedestrian is not connected to the internet.

Fig. 4. Sending risk data over Bluetooth.

The following figure shows how risk data circulate from global RabbitMQ queue to client queues (see Fig. 5).

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Fig. 5. Global queue design system.

3.1 Receive Time Duration Our system ensures to send risk data to the pedestrian in no more than 18 ms. Over internet, it is related to the latency and the throughput of the internet network, but by minimizing the size of the data being sent to the pedestrian (160 bits = localization data size + TTL size), we ensure that data will be sent at a low latency, by testing in many iterations the application in a 3G network, we confirm that the data is received in no more than 10 ms. Over Bluetooth, the application uses a BLE Bluetooth protocol, after realizing many tests, we confirm that the time the android application receives the data from another phone is calculated as following: 1 ms (time to send from the phone) + 6 ms (time to receive the data) + 1 ms (time to process the data) = 8 ms + 10 (time to receive the data from the internet) = 18 ms. 3.2 Pedestrian Reaction Time The reaction time for a normal human is between 150 ms and 300 ms. Our application ensures the reaction time for a normal human being will be in no more than 318 ms.

4 Conclusion In conclusion, we proposed in this paper, a solution to enhance the awareness of pedestrians based on calculating the risk matching their behavior in a fuzzy neighborhood. This type of solution is a requirement in a fast-changing environment to ensure pedestrians safety. We are aware that we could add more medium features in our solution, like taking into consideration iOS phones and smart watches. We could also add big features by taking into consideration self-driving cars and design a solution to manipulate cars’

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brakes to lower the speed of the car or stop it completely if there is a possibility of a risk on pedestrians. Also, one of the limitations of the proposed solution is to that should wait to calculate risk, which add some latency layer that decrease the duration time which the risk notification will be received by pedestrians. What we could do in the future is use machine learning algorithms to predict in advance the risk and lower the latency. All these ideas will be processed and detailed in further works.

References 1. Elkaissi, S., Boulmakoul, A.: Virtual spider for real-time finding things close to pedestrians. In: Ben Ahmed, M., Teodorescu, H.-N., Mazri, T., Subashini, P., Boudhir, A.A. (eds.) Networking, Intelligent Systems and Security. SIST, vol. 237, pp. 749–761. Springer, Singapore (2022). https://doi.org/10.1007/978-981-16-3637-0_53 2. Boulmakoul, A., ElKaissi, S., Lbath, A.: Fuzzy pretopological space for pedestrians’ risk perception modeling. In: Kahraman, C., Cebi, S., Cevik Onar, S., Oztaysi, B., Tolga, A.C., Sari, I.U. (eds.) INFUS 2021. LNNS, vol. 308, pp. 687–695. Springer, Cham (2022). https:// doi.org/10.1007/978-3-030-85577-2_81 3. Aluja, J.G., Gil-Lafuente, A.M.: Towards an advanced modelling of complex economic phenomena: Pretopological and topological uncertainty research tools. Studies in Fuzziness and Soft Computing, vol. 2762012. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3642-24812-2 4. Atilgan, C., Nasibov, E.: On reducing space complexity of fuzzy neighborhood-based clustering algorithms. In: Proceedings of the 2017 International Conference on Computer Science and Engineering (UBMK), Antalya, 2017, pp. 577–579 (2017). https://doi.org/10.1109/ UBMK.2017.8093467 5. Nasibov, E., Gozde, U.: A new unsupervised approach for fuzzy clustering. Fuzzy Sets Syst. 158(19), 2118–2133 (2007). ISSN 0165-0114, https://doi.org/10.1016/j.fss.2007.02.019 6. Nasibov, E.: Robustness of density-based clustering methods with various neighborhood relations. Fuzzy Sets Syst. 160(24) 3601–3615 (2009). ISSN 0165-0114, https://doi.org/10. 1016/j.fss.2009.06.012 7. Nasibov, E., Can, A., Murat, E., Resmiye, N.: Fuzzy joint points-based clustering algorithms for large data sets. Fuzzy Sets Syst. 270, 111–126 (2015). ISSN 0165-0114, https://doi.org/ 10.1016/j.fss.2014.08.004 8. Esther, G., Konstantino, P., Evimaria, T.: Urban Navigation Beyond Shortest Route. Inf. Syst. 57(C), 160–171 (2016) 9. Kim, J., Cha, M., Sandholm, O.: SocRoutes: Safe routes based on tweet sentiments. In: Proceedings of the 23rd International Conference on World Wide Web, pp. 179–182. ACM (2014) 10. Tabibi, Z., Pfeffer, K.: Choosing a safe place to cross the road: The relationship between attention and identification of safe and dangerous road-crossing sites. Child Care Health Dev. 29(4), 237–244 (2003). https://doi.org/10.1046/j.1365-2214.2003.00336.x. PMID: 12823328 11. Tabibi, Z., Pfeffer, K.: Finding a safe place to cross the road: The effect of distractors and the role of attention in children’s identification of safe and dangerous road-crossing sites. Inf. Child Dev. Int. J. Res. Pract. 16, 193–206 (2007) 12. Zadeh, L.: Fuzzy sets. Inform. Control 8 (1965) 13. Zhang, D.: Fuzzy pretopological spaces, an extensional topological extension of FTS. Chin. Ann. Math. 20(03), 309–316 (1999). https://doi.org/10.1142/S0252959999000345

The Approximate Method for Solving Second-Order Fuzzy Boundary Value Problems Nurain Zulaikha Husin1(B) , Muhammad Zaini Ahmad1,2 and Mohd Kamalrulzaman Md Akhir1,2

,

1 Institute of Engineering Mathematics, Faculty of Applied and Human Sciences,

Universiti Malaysia Perlis, 02600 Arau, Perlis, Malaysia [email protected] 2 Centre of Excellence for Social Innovation and Sustainability (CoESIS), Universiti Malaysia Perlis, 02600 Arau, Perlis, Malaysia

Abstract. Nowadays, the topic of fuzzy differential equations (FDEs) has received a lot of attention among researchers. The FDE formed a mathematical modelling of the real-world problems, such as in medicine, hydraulic systems, population models and modelling of periodic phenomena. The FDE can be divided into two parts, which are fuzzy initial value problem (FIVP) and fuzzy boundary value problem (FBVP). Due to many real-world problems modelled using FBVP, there has been a lot of interest in investigating the solution of FBVP. The purpose of this study is to provide a method of solution for second-order FBVP. Based on the generalized fuzzy derivative, four systems of FBVP are formulated. For each system, the second-order FBVP is split into two parts, namely fuzzy nonhomogeneous and fuzzy homogeneous equations. By appropriate substitution, these two equations are then reduced to first-order FDE. By proposing the RungeKutta Cash-Karp (RKCK) method in a fuzzy setting, the approximate solution is obtained. To make sure the result is acceptable, the approximate solution is then compared with Runge-Kutta of Order Four (RK4) method. From numerical solutions, the result showed that the approximate solution of the proposed method is better compared to the result obtained using RK4 method. Keywords: Fuzzy differential equations · Generalized fuzzy derivative · Runge-Kutta Cash-Karp

1 Introduction In the last few years, the research on fuzzy differential equations (FDEs) has rapidly expanded into a new field of mathematics in fuzzy setting. Zadeh was the first scholar who proposed the idea of fuzzy set [1]. Later, FDEs are investigated for solving fuzzy initial or fuzzy boundary conditions, which are used to model several problems in science and engineering [2]. Besides, the solution of FDEs which involves fuzzy initial or fuzzy boundary value problem (FBVP) can be solved for most all the practical problems. However, not all fuzzy initial or FBVP could be solved precisely due to the difficulty in © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 90–97, 2022. https://doi.org/10.1007/978-3-031-09173-5_12

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finding analytical solution [3]. As a result, an appropriate technique may be required to solve the problem related to FDEs. There are two strategies to approach the FBVP [4]. The first strategy is to assume that the boundary values are fuzzy and the solution is a fuzzy function, in which the derivative of the differential equation can be regarded as the derivative of the fuzzy function. The second strategy is to create a fuzzy solution from a crisp solution. Numerically, the FDEs can be solved by different methods. Rajkumar and Rubanraj [5] studied the seventh order Runge-Kutta (RK) method to increase the order of accuracy and enhancing the number of Taylor’s series term. The RK Nystrom of order three is used to solve numerical algorithm using Seikkala’s derivative and comparing it with Euler’s method [6]. In 2016, the developed RK4 method which is based on generalized Hukuhara differentiability is presented by several researchers to solve FDEs [7]. There are other numerical approaches can be used to solve FDEs besides the RK method. Jamshidi and Avazpour [8] studied the Adomian decomposition method for solving the fuzzy boundary value differential equations, whereas Can, Bayrak and Hicdurmaz [9] proposed the chasing method to solve the FBVP. [8, 9] solved the problems using generalized differentiability concept. On the contrary, Armand and Gouyandeh [10], and Arqub, Al-Smadi, Momani and Hayat [11] proposed variational iteration method and reproducing kernel Hilbert space, respectively. Both of the papers solved the problems by using generalized Hukuhara differentiability and strongly generalized differentiability. Based on the previous studies, none of the researchers has studied the Runge-Kutta Cash-Karp (RKCK) method. Therefore, the contribution in this paper is to propose the RKCK method for solving the second-order FBVP and the approximate solution is compared with exact solution and RK4 method. The process involve throughout this paper are divided into several sections. In Sect. 2, some fundamental ideas on fuzzy numbers and generalized differentiability are reviewed. In Sects. 3 and 4, the shooting method for FBVP and RKCK method for the system are defined. The numerical example is discussed in Sect. 5 while the Sect. 6 will end with conclusion.

2 Preliminaries Let R be the set of all real numbers and RF be the set of fuzzy number on R. Definition 1 (see [8]). A fuzzy number is mapping u : R → [0, 1] with the following properties: 1. u is upper semi-continuous, 2. u is fuzzy convex, i.e. u(λx + (1 − λ)y) ≥ min{u(x), u(y)} for all x, y ∈ R, λ ∈ [0, 1], 3. u is normal, i.e. ∃x0 ∈ R for which u (x) = 1, 4. supp u = { x ∈ R | u (x) > 0} is the support of the u and its closure cl (supp u) is compact.

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Definition 2 (see [7]). A fuzzy number u is determined by any pair u = and satisfied the following conditions:

  u(α) , u(α)

1. u(α) is a bounded left continuous increasing function ∀ α ∈ [0, 1], 2. u(α) is a bounded left continuous decreasing function ∀ α ∈ [0, 1], 3. u(α) ≤ u(α), 0 ≤ α ≤ 1. Definition 3 (see [12]). Let F : [a, b] → RF and fixed t0 ∈ [a, b]. F is differentiable at t0 if 1. For all h > 0 sufficiently near 0, there are F(t0 + h)  F(t0 ); F(t0 )  F(t0 − h) and the limit (D-metric) lim

h→0+

F(t0 + h)  F(t0 ) F(t0 )  F(t0 − h) = lim = F  (t0 ) + h h h→0

2. For all h > 0 sufficiently near 0, there are F(t0 + h)  F(t0 ); F(t0 )  F(t0 − h) and the limit F(t0 + h)  F(t0 ) F(t0 )  F(t0 − h) lim = lim = F  (t0 ) −h −h h→0+ h→0+ Definition 4 (see [13]). Let F : [a, b] → RF and n, m = 1, 2. F is said (n, m)− differentiable at t0 ∈ [a, b], if Dn1 F exist on a neighborhood of t0 as a fuzzy function 2 F(t ) and it is (m)− differentiable at t0 . The second derivative of F is denoted by Dn,m 0 for n, m = 1, 2. 1 1 Theorem 1 (see [13]). Let  D1 F : [a, b] → RF or D2 F : [a, b] → RF , where α [F(t)] = fα (t), gα (t) :

1. If D11 F is (1)-differentiable, the fα and gα are differentiable functions and  α     2 F(t) D1,1 = fα (t), gα (t) .

2. If D11 F is (2)-differentiable, the fα and gα are differentiable functions and α      2 F(t) D1,2 = gα (t), fα (t) . 3. If D21 F is (1)-differentiable, the fα and gα are differentiable functions and  α     2 F(t) D2,1 = gα (t), fα (t) . 4. If D21 F is (2)-differentiable, the fα and gα are differentiable functions and  α     2 F(t) D2,2 = fα (t), gα (t) .

3 The Shooting Method for FBVP The concepts of FBVP under generalized fuzzy derivative are introduced in this section. Given a second-order FBVP     Y (t) = f t, Y (t), Y  (t) = P(t)Y  (t) + Q(t)Y (t) + R(t) (1) Y (a) = γ , Y (b) = β,

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where γ , β ∈ RF and f : [a, b] × RF × RF → RF is a continuous function. Then, by focusing only the first system associated with Theorem 1 (Case 1), Eq. (1) is written in system as shown in Eq. (2). ⎧  y (t, α) = P(t)y (t, α) + Q(t)y(t, α) + R(t), ⎪ ⎪ ⎪ ⎪ ⎨ y (t, α) = P(t)y (t, α) + Q(t)y(t, α) + R(t), (2) ⎪ y(a, α) = γ (α), y(a, α) = γ (α), ⎪ ⎪ ⎪ ⎩ y(a, α) = β(α). y(b, α) = β(α), Equation (2) is then split into fuzzy non-homogeneous and fuzzy homogeneous equations as shown in Eqs. (3) and (4), respectively. ⎧  u (t, α) = P(t)u (t, α) + Q(t)u(t, α) + R(t), ⎪ ⎪ ⎪ ⎪ ⎨ u (t, α) = P(t)u (t, α) + Q(t)u(t, α) + R(t), (3) u(a, α) = γ (α), u(a, α) = γ (α), ⎪ ⎪ ⎪ ⎪ ⎩  u (a, α) = 0(α). u (b, α) = 0(α), ⎧  v (t, α) = P(t)v  (t, α) + Q(t)v(t, α), ⎪ ⎪ ⎪ ⎪ ⎨ v  (t, α) = P(t)v  (t, α) + Q(t)v(t, α), (4) ⎪ v(a, α) = 0(α), v(a, α) = 0(α), ⎪ ⎪ ⎪ ⎩  v  (a, α) = 1(α). v (b, α) = 1(α), Next, Eqs. (3) and (4) are converted into the system of first order FDEs by setting u = w1 , u = w1 , u = w2 , u = w2 , v = w3 , v = w3 , v  = w4 and v  = w4 . We then construct the procedures of solution as discussed in the following section.

4 Runge-Kutta Cash-Karp Method in Fuzzy Setting This section is discussed the RKCK method in fuzzy setting and show how this method can be used for solving the first order FDEs. Consider the following general equation of RKCK method: ⎧ 6

⎪ ⎪ ⎪ hsi (tn , w(tn , α)), ⎪ w(tn+1 , α) = wn (tn , α) + ⎪ ⎨ i=1 (5) 6 ⎪

⎪ ⎪ ⎪ hsi (tn , w(tn , α)), ⎪ ⎩ w(tn+1 , α) = wn (tn , α) + i=1

where     s1 (t, w(t, α)) = f (t, u1 , u2 , u3 , u4 )  uk ∈ wk (t, α), wk (t, α) , k = 1, 2, 3, 4,     s1 (t, w(t, α)) = f (t, u1 , u2 , u3 , u4 )  uk ∈ wk (t, α), wk (t, α) , k = 1, 2, 3, 4,

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  1 1 s2 (t, w(t, α)) = f t + h, w(t, α) + hs1 (t, w(t, α)) , 5 5   1 1 s2 (t, w(t, α)) = f t + h, w(t, α) + hs1 (t, w(t, α)) , 5 5   s3 (t, w(t, α)) = f t +

3 3 9 h, w(t, α) + hs (t, w(t, α)) + hs (t, w(t, α)) , 10 40 1 40 2

  9 3 3 h, w(t, α) + hs1 (t, w(t, α)) + hs2 (t, w(t, α)) , s3 (t, w(t, α)) = f t + 10 40 40 ⎞ 9 3 3 hs (t, w(t, α)) − hs (t, w(t, α))+ t + h, w(t, α) + ⎟ ⎜ 5 10 1 10 2 s4 (t, w(t, α)) = f ⎝ ⎠, 6 hs3 (t, w(t, α)) 5 ⎛

⎞ 9 3 3 h, w(t, α) + hs1 (t, w(t, α)) − hs2 (t, w(t, α)) + ⎟ ⎜ 5 10 10 s4 (t, w(t, α)) = f ⎝ ⎠, 6 hs3 (t, w(t, α)) 5 ⎛

t +

⎛

⎞ 11 5 t + h, w(t, α) − w(t, α)) + w(t, α)) − hs hs (t, (t, ⎜ ⎟ 54 1 2 2 ⎟, s5 (t, w(t, α)) = f ⎜ ⎝ 70 ⎠ 35 hs3 (t, w(t, α)) + hs4 (t, w(t, α)) 27 27 ⎛

⎞ 11 5 t + h, w(t, α) − hs hs w(t, α)) + w(t, α)) − (t, (t, 1 2 ⎜ ⎟ 54 2 ⎟, s5 (t, w(t, α)) = f ⎜ ⎝ 70 ⎠ 35 hs3 (t, w(t, α)) + hs4 (t, w(t, α)) 27 27 ⎞ 7 1631 175 t + h, w(t, α) + hs hs w(t, α)) + w(t, α)) + (t, (t, 1 2 ⎟ ⎜ 8 55296 512 ⎟, s6 (t, w(t, α)) = f ⎜ ⎠ ⎝ 575 44275 253 hs3 (t, w(t, α)) + hs4 (t, w(t, α)) + hs5 (t, w(t, α)) 13824 110592 4096 ⎛

⎞ 7 1631 175 ⎟ ⎜ t + 8 h, w(t, α) + 55296 hs1 (t, w(t, α)) + 512 hs2 (t, w(t, α)) + ⎟. s6 (t, w(t, α)) = f ⎜ ⎠ ⎝ 575 44275 253 hs3 (t, w(t, α)) + hs4 (t, w(t, α)) + hs5 (t, w(t, α)) 13824 110592 4096 ⎛

Given ⎧ 37 ⎪ ⎪ f (t, w(t, α)) = s (t, w(t, ⎪ ⎪ ⎪ 378 1 ⎪ ⎪ ⎪ 125 ⎪ ⎪ s (t, w(t, α)) ⎨ 592 4 37 ⎪ ⎪ ⎪ f (t, w(t, α)) = s1 (t, w(t, ⎪ ⎪ 378 ⎪ ⎪ ⎪ ⎪ 125 ⎪ ⎩ s4 (t, w(t, α)) 592

α)) +

250 s (t, w(t, α)) + 621 3

512 s (t, w(t, α)) , 1771 6 250 s3 (t, w(t, α)) + α)) + 621 512 s6 (t, w(t, α)) , + 1771 +

(6)

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Then, by using Eq. (5), the solutions for first order FDEs can be obtained. The following formula can be used to find the approximate solutions of Eq. (2). ⎧ y(b, α)  w1 (b, α) ⎪ ⎪ w3 (tn , α); w3 (b, α) = 0, ⎨ y(tn , α) = w1 (tn , α) + w3 (b, α) (7) ⎪ ⎪ ⎩ y(tn , α) = w1 (tn , α) + y(b, α)  w1 (b, α) w3 (tn , α); w3 (b, α) = 0. w3 (b, α)

5 Numerical Examples This section illustrates an implementation of the above method for solving FBVP. Consider the following FBVP,   Y (t) = Y  (t) + Y (t) + t, 

Y (0) = 0,



Y (1) = 1,

(8)

where [0]α = [α − 1, 1 − α] and [1]α = [α, 2 − α]. The exact solution of Eq. (8) is given by 

   0.461α + 1.078 1.6180t 4.0430α − 10.086 −0.6180t e e + , ⎜ 4.5040 4.5040 Y (t, α) = ⎜     ⎝ −4.0430α − 2 −0.6180t −0.461α + 2 1.6180t + 1 − t + e e 4.5040 4.5040 ⎛

1 − t +

⎞ ⎟ ⎟. ⎠

(9)

Using the procedures as proposed in Sects. 3 and 4, the numerical solution of Eq. (8) is obtained and compared with exact solution and RK4 method as shown in Table 1. Table 1. The exact solution, RKCK method and RK4 method at t = 0.5. α

Exact solution

RKCK method

RK4 method

y(t, α)

y(t, α)

y(t, α)

y(t, α)

y(t, α)

y(t, α)

0.0

– 0.6065996

1.1711725

– 0.6065735

1.1711708

– 0.6065724

1.1711728

0.2

– 0.4288224

0.9933953

– 0.4287991

0.9933963

– 0.4287979

0.9933983

0.4

– 0.2510452

0.8156181

– 0.2510246

0.8156219

– 0.2510234

0.8156237

0.6

– 0.0732680

0.6378409

– 0.0732502

0.6378475

– 0.0732487

0.6378492

0.8

0.1045093

0.4600637

0.1045242

0.4600731

0.1045257

0.4600747

1.0

0.2822865

0.2822865

0.2822986

0.2822986

0.2823002

0.2823002

Based on the results listed in Table 1, the solution of RKCK method is more accurate compared to RK4 method. The comparisons for all t ∈ [0, 1] can be seen in Fig. 1. This prove that the RKCK method in fuzzy setting is able to produce high accuracy as the solution very close to exact solution.

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Fig. 1. The exact solution (red line), RKCK method (green line) and RK4 method (‘x’ mark)

6 Conclusion This paper proposed RKCK method and implemented it into a numerical example based on generalized fuzzy derivatives. Practically, the RKCK method is to be superior compared to RK4 method as the RKCK method requires six evaluations per step while RK4 method requires four per step. As the number of function evaluations of each step rises, the approximate solution becomes closer to the exact answer. As a conclusion, the RKCK method produced better solutions compared to the RK4 method. This proposed method can be extended in the future for higher order FDEs. Acknowledgement. This research was funded by the Ministry of Higher Education of Malaysia under Fundamental Research Grant Scheme (FRGS): 9003–00821.

References 1. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965) 2. O’Regan, D., Lakshmikantham, V., Nieto, J.J.: Initial and boundary value problems for fuzzy differential equations. Nonlinear Anal. Theor. Meth. Appl. 54, 405–415 (2003) 3. Jameel, A.F., Anakira, N.R., Alomari, A.K., Alsharo, D.M., Saaban, A.: New semi-analytical method for solving two point nth order fuzzy boundary value problem. Int. J. Math. Model. Numer. Optimisation 9, 12 (2019) 4. Gasilov, N., Amrahov, S.E., Fatullayev, A.G.: Linear differential equations with fuzzy boundary values. In: Proceedings of the 2011 5th International Conference on Application of Information and Communication Technologies, AICT 2011, pp. 1–5 (2011) 5. Rajkumar, P., Rubanraj, S.: Seventh order Runge-Kutta method. J. Comput. Math. Sci. 10, 1518–1528 (2019) 6. Kanagarajan, K., Sambath, M.: Runge-Kutta nystrom method of order three for solving fuzzy differential equations. Comput. Meth. Appl. Math. 10, 195–203 (2010) 7. Ramli, A., Ahmad, R.R., Din, U.K.S., Salleh, A.R.: Fuzzy version of a developed fourth order Runge Kutta method for solving differential equations with fuzzy initial values. In: Proceedings of the AIP Conference, pp. 1–6 (2016)

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8. Jamshidi, L., Avazpour, L.: Solution of the fuzzy boundary value differential equations under generalized differentiability by shooting method. J. Fuzzy Set Valued Anal. 136, 1–19 (2012) 9. Can, E., Bayrak, M.A.: A novel numerical method for fuzzy boundary value problems. J. Phys. Conf. Ser. 707, 012053 (2016) 10. Armand, A., Gouyandeh, Z.: Solving two-point fuzzy boundary value problem using variational iteration method. Commun. Adv. Comput. Sci. Appl. 2013, 1–10 (2013) 11. Arqub, O.A., Al-Smadi, M., Momani, S., Hayat, T.: Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems. Soft. Comput. 21(23), 7191–7206 (2016). https://doi.org/10.1007/s00500-016-2262-3 12. Bede, B., Gal, S.G.: Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations. Fuzzy Sets Syst. 151, 581–599 (2005) 13. Khastan, A., Nieto, J.J.: A boundary value problem for second order fuzzy differential equations. Nonlinear Anal. Theor. Meth. Appl. 72, 3583–3593 (2010)

Deployment of Software Agents and Application of Fuzzy Controller on the UWB Localization Based Mobile Robots Burak Karaduman1(B) , Baris Tekin Tezel2 , and Moharram Challenger1 1

Department of Computer Science, University of Antwerp and Flanders Make, Antwerp, Belgium {burak.karaduman,moharram.challenger}@uantwerpben.be 2 Department of Computer Science, Dokuz Eylul University, Konak, Turkey [email protected]

Abstract. Mobile robots allow us to achieve tasks independently from human intervention. Mobile robots follow their long-term goals according to a given way-point while observing the environment and reacting to the uncertain events around them. Therefore, a localization technology such as ultra-wide-band should be used to permit their movement along a path. Moreover, they can receive their goals from a remote terminal at any instant of time. Since these robots consist of the cyber, the physical and the network parts they can be inspected under the cyber-physical systems paradigm as well. The physical side describes the concrete form of the robot while the cyber part represents its software-based features. They can establish a network in order to achieve communication between that remote terminal. As these systems are quite complex because of their heterogeneity (multi-component), complexity (programming effort) and environmental changes (noisy or imprecise information), software agents can be a suitable paradigm to implement these systems from a higher abstraction level including communication capabilities while fuzzy-logic control (FLC) can be a way to deal with environmental effects. Specifically, the FLC for speed control can enhance and smoothen the capabilities of mobile robots while they are moving towards their locations compared to conventional controllers. In this study, LEGO Mindstorms EV3, Brick PI and JADE agents were used including fuzzy logic to create a mobile robot case study. Keywords: Software agents · Jade framework · Fuzzy logic controller Fuzzy inference system · Ultra-wide band · Cyber-physical system

1

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Introduction

In today’s world, mobile robots are used for various goals such as transportation, delivery and exploration. They can benefit from well-known techniques such c The Author(s), under exclusive license to Springer Nature Switzerland AG 2022  C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 98–105, 2022. https://doi.org/10.1007/978-3-031-09173-5_13

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as magnetic wires, physically-drawn lines, wireless localisation etc. to navigate. Each of them has its trade-offs, but mobile robots can be quite efficient while being used in specific tasks. Therefore a technology such as the ultra-wideband can work precisely thanks to the high refresh rate. In this way, the mobile robots can move toward their waypoints by updating their rotation angle and position. However, one of the fundamental problems is that a mobile robot encounters uncertainties while navigating from one place to another one. Even though the mobile robot can freely navigate an indoor area, uncertainties can still emerge. Moreover, as the mobile robots sense their local environment via sensors, the data can also be inaccurate. Sometimes the sensors may not have linear characteristics. Therefore, any inefficient or unwanted behaviour can be performed by mobile robots. A mobile robot should also be able to consume its path autonomously which requires a control mechanism that allows the mobile robot to deal with uncertainty. In order to deal with environmental uncertainty, a platform-independent approach such as fuzzy logic should be applied considering the real-time requirements due to speed and rotation synchronisation as well as low-computation power because of embedded hardware’s resource constraint. The mobile robot’s behaviour can be defined as a feature that can be programmed to achieve a goal based on a type. For this reason, the need for highlevel software abstraction arises. The software agents of the JADE framework emerged from agent-oriented programming (AOP) and can be used for the implementation of the cyber part of these mobile robots. In addition, the software agents provide the required autonomy based on the JADE’s behaviour types, they can enhance the target mobile system with their distributed and social features as well. The rest of the paper is organised as follows: Sect. 2 gives the related works of this study, Sect. 3 gives the background information of the paper, the system implementation is mentioned in Sect. 4, the fuzzy controller and software agents are introduced in Sect. 5. Section 6 the discusses the paper while the paper is concluded in Sect. 7 along with the future work.

2

Related Works

In today’s world, robot systems are advancing to meet the delivery, transportation and exploration requirements. Autonomous mobile robots have a significant role in achieving these demanding tasks, such as picking up the products and delivering them to the planned locations while reducing the time cost. In this way, they provide safety and easiness for humans by taking off the burden and risks of hazardous goals. In the literature development of mobile robots has been addressed from various perspectives. Bolturk and Kahraman. [3] review and show the relationship between robots and fuzzy sets. They focus on the benefits of fuzzy logic as it is a flexible way to model human behaviour. Moreover, study [2] mentions fuzzy sets and their extensions. They underline that the fuzzy set extensions aim at providing more capability to deal with uncertainty.

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Cuevas et al. [5] propose to use Type-2 fuzzy logic for controlling the mobile robot’s behaviour to deal with uncertainty. They consider that mobile robots should be able to tolerate a high level of imprecision in their operating environment. They planned to navigate their mobile robots in an unknown environment in their work. Valdez et al. [11] presents a comparative study of conventional and type-2 fuzzy logic controllers for velocity regulation. They compare PI, PID and fuzzy logic controllers using the EV3 LEGO Mindstorms kit and simulate their controllers in MATLAB. The motivation in this study is to present a proof-of-concept for fuzzification of our previous studies [10,12] by deploying fuzzy-logic based software agents onto resource constraint systems to deal with uncertainty. Moreover, we also benefit from the ultra-wide-band technology as it allows for navigating the mobile robots without being dependent on any physical line or pointer. Considering the aforementioned technologies and approaches, Fragapane et al. [6] provides a research agenda and mentions the ultra-wide-band technology can support simultaneous localisation and mapping features for indoor application. Furthermore, it was also underlined that decentralisation is required for large-scale product delivery and transportation work such as warehouses. Hence, in this study, we provide a study that creates a substance for using the software agents and the UWB based on fuzzy logic. In this way, the future requirements of creating autonomous mobile robots can be tackled in this scope.

3

Background

This section mentions the background information which describes the components in the scope of this study. The section explains the multi-agent systems, cyber-physical systems, LEGO, ultra-wide-band technology and fuzzy logic. Multi-Agent Systems: Multi-agent systems (MAS) is a paradigm that provides higher-level programming abstraction based on software entities called agents. They have been researched and developed for providing autonomy for dynamic systems, decentralization for distributed topology and communication for systems’ collaboration. They are deployed to large systems to ease the complexity while enhancing that system with behavioural features [9]. Cyber-Physical Systems: Cyber-physical systems (CPS) enhance the conventional mechatronic systems by adding capabilities such as data collection, software intensiveness, and established networks to create communication. Basically, CPS consists of the cyber, the physical and the networking sides where the cyber and the physical side influence each other according to the events which are generated by the local environment. The network is used for establishing communication between other networked systems or the same system instances. LEGO Mindstorms EV3: LEGO can be defined as a composable physical abstraction to create concrete systems in fast prototyping. It eases to physically construct the systems to mimic any actual system by scaling down but trying to protect the functionalities. In our study, LEGO was used for creating mobile

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robots. The LEGO motors/sensors were used and merged with some LEGO parts to shape the robot’s body. Ultra-Wide-Band Technology: Ultra-Wide Band technology is a radio technology that operates short-range using very low energy. Moreover, It has high bandwidth, making it a preferable technology for indoor localisation and robot. It works in a dense environment while keeping the localisation accuracy high and synchronised with the moving objects. We used the Pozyx tags and anchors to receive angle and position values via the MQTT protocol from the cloud service. Fuzzy Logic: The fuzzy theory was introduced by Zadeh [13] to handle problems that emerged because of imprecise and uncertain information. A fuzzy set, considered an extension of a classical notation set, is a class of objects defined via a membership function. The membership function assigns a grade of membership to each object, representing the degree of belonging to a relevant class, ranging between zero and one. The definition of a fuzzy set is given below. Definition 1. A fuzzy set is a pair A = (U, m) where U = (−∞, ∞) is described with the aid of its membership function µA : U → [0, 1] using to map each elements of the fuzzy set to [0, 1]. In 1973, Zadeh [1] published his second most influential paper, outlining a new approach to the analysis of complex systems, in which he proposes to capture human knowledge with fuzzy rules. A fuzzy rule usually takes the form R : if x is A, then y is B where A and B are linguistic values defined by fuzzy sets on discourse universes X and Y, respectively. In recent years, fuzzy set theory has become a significant paradigm for complex systems theory and decision processes. Subsequently, fuzzy-based approaches, such as FLC, are quite applicable for dynamic systems, such as cyber-physical systems, mechanical systems and robots, to deal with uncertainty while achieving smooth behaviour.

4

System Implementation

The LEGO Mindstorms EV3 was preferred to construct the mobile robot. The robot consists of two LEGO’s large regulated motors with two wheels, a free-wheel, three ultrasonic sensors, one RaspberryPI 3 board, 8 AA batteries, one battery holder, one and one BrickPI board [10,12]. Figure 1 represents an instance of the mobile robots which had been constructed. The mobile robots in an indoor area should have a set of basic features, such as they might be able to receive a waypoint that consists of specific points. The mobile robots should consume these points by navigating each point. Once all points are consumed, the mobile robot should wait for a new waypoint. While they are travelling, they should be able to arrange their speed. If they detect any obstacle, they should be able to stop and try to avoid the collision. In our perspective, the cyber part of the mobile robots runs the software agents, hardware API and the MQTT application. The physical parts of the robots include the system’s hardware and physical entities such as wheels and LEGO parts. The batteries were put on the wheels to increase the friction.

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4.1

System Hardware

The hardware consists of a RaspberryPI 3 board, a BrickPI 3 hardware interface, three ultrasonic sensors and batteries. The BrickPI 3 allows us to deploy the JADE and the Java application on the RaspberryPI 3, while BrickPI 3 actuates the LEGO motors and gathers data from the LEGO sensors. A relevant reader can find more information about the JADE and BrickPI API interplay in the study [10].

Fig. 1. A mobile robot.

4.2

System Software

In the JADE framework, there is various type of behaviour. They can be used in combination as well. For brevity, we focus on the most significant excerpt of the software. Moreover, there are two software agents, namely the remote agent and the robot agent, that establishes a multi-agent system. The remote agent sends X and Y coordinates to the robot agent. The robot agent consumes these points by travelling and navigating itself. During the movement, the robot agent checks the environment using ultrasonic sensors. As listing 1.1 shows, the sensor data which belong to ultrasonic sensors are gathered in each cycle using a Cyclic-Behaviour. In each cycle of an agent, this behaviour is called. For example, if the agent is communicating with a server using another behaviour, a cyclic behaviour is run by the agent simultaneously. In this way, the two tasks do not block each other. As three ultrasonic sensors are positioned at the front, left, and right, we create local coverage for the mobile robot. Moreover, another Cyclic-Behaviour receives position and yaw angle values from the Pozyx cloud. In the next section, fuzzy controllers and software agents are mentioned. Listing 1.1. Ultrasonic sensor data gathering 1 2 3 4

CyclicBehaviour ultrasonic check = new CyclicBehaviour(){@Override public void action() { try { ultra front = Device.lookAhead front(); ultra left = Device.lookAhead left(); ultra right = Device.lookAhead right();} catch (Exception e){ e. printStackTrace();}}};

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Fuzzy Controller and Software Agents

To create a fuzzy controller, jFuzzyLogic [4] was preferred and integrated into the JADE framework. The .fcl file and the Java application were uploaded to the RaspberryPI 3. The ultrasonic sensor data and the distance of the waypoint were fed into the fuzzy inference system. In the defuzzification phase, crisp values of rotation and speed values are received. We selected Center of Gravity as the defuzzification method. Figure 2 illustrates the fuzzy functions. We assumed an environment where we expect less uncertainty at the start and endpoint of a waypoint. Moreover, we also assume that more distance has more risk. Therefore, the speed of the mobile robot should be arranged according to the distance of the way-point and the distance between an obstacle in front. Because in case there is an obstacle at a side of the mobile robot, it can turn left or right, and then it can align its navigation. The mobile robot sets its speed according to the distance between an obstacle in front. Moreover, stopping the mobile robot would be hard if it goes fast. Therefore, we used Gauss shape fuzzy function to have the mobile robot decelerate quickly but not instantly. The rules between 1 and 9 were defined for setting the speed. The demonstration video can be reached on https://youtu.be/gEg1mB NBhs.

Fig. 2. Fuzzy functions

Furthermore, the ultrasonic sensors on the left and the right of the mobile robot were fuzzified to rotate the mobile robot in case there were obstacles to be avoided. The fuzzy inference system generates a rotation angle between 0– 30 and 330-360◦ C according to the distance between an obstacle on the left or the right. Rule 10 and 11 define rotation output regarding the states of the ultrasonic sensors. As the ultrasonic sensor does not work linear, we created the fuzzy function based on integer values. In our case, the ultrasonic sensor generates integer values between 0 and 150. Therefore, any value between 0 and 25 can be considered close, while 25–150 can be said near (safe). The near variable can also be thought of as a tolerance interval. If an obstacle on the left appears close while the right side is in a safe state. The mobile robot then turns to the right to avoid the obstacle and vice versa. The demonstration video can be found on https://youtu.be/VjzC5MG31wc.

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1 2 3 4 5 6 7 8 9 10 11

IF IF IF IF IF IF IF IF IF IF IF

distance IS begin AND obstacle front IS close THEN speed IS stop; distance IS begin AND obstacle front IS near THEN speed IS low; distance IS begin AND obstacle front IS far THEN speed IS high; distance IS middle AND obstacle front IS close THEN speed IS stop; distance IS middle AND obstacle front IS near THEN speed IS low; distance IS middle AND obstacle front IS far THEN speed IS high; distance IS end AND obstacle front IS close THEN speed IS stop; distance IS end AND obstacle front IS near THEN speed IS low; distance IS end AND obstacle front IS far THEN speed IS low; obstacleRight IS close AND obstacleLeft IS near THEN rotation IS rotLeft; obstacleRight IS near AND obstacleLeft IS close THEN rotation IS rotRight;

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Discussion

In this study, fuzzy logic-based multi-agent and mobile systems were proposed. The main objective is to enhance the implementation of these complex systems using a high-level programming abstraction based on AOP. The navigation of the mobile robots was achieved using UWB technology. However, uncertainty is a fact that should be tackled even in an indoor area. As fuzzy logic is a way to deal with uncertainty and a platform-independent paradigm that can be integrated into any target system, we created a fuzzy-logic controller and wrapped it to the software agent’s behaviour. In this way, we developed a multi-agent and complex robot using behavioural level programming on the cyber side, whereas the physical side was constructed using a LEGO kit. Furthermore, the mobile robot’s behaviour was enhanced using the fuzzy logic controller to sustain its navigation to deal with uncertainty.

7

Conclusion and Future Work

This study benefited from the JADE framework, which uses simple-reflex agents for behavioural level programming. Since the JADE framework is based on JAVA, it allows us to integrate JAVA-based API and libraries. In this way, we developed a mobile system and applied fuzzy logic approach. As fuzzy logic is a mathematical platform-independent paradigm, we constructed a fuzzy logic controller integrated into agent software that runs fuzzy rules and controls the behaviour of the mobile robot. In the future, we plan to use a BDI-based agent development framework for plan selection based on fuzzy logic. In this way, we will use a more abstract level of agent programming while tackling the uncertainty using fuzzy logic, which mimics human control logic [8]. It is also planned to benefit from model-driven engineering approaches [7].

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References 1. Zadeh, L.A.: Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans. Syst. Man Cybernetics 1, 28–44 (1973) 2. Bolturk, E., Kahraman, C.: Fuzzy sets and extensions: A literature review. In: Toward Humanoid Robots: The Role of Fuzzy Sets, pp. 27–95 (2021) 3. Bolturk, E., Kahraman, C.: Humanoid robots and fuzzy sets. In: Kahraman, C., Bolturk, E. (eds.) Toward Humanoid Robots: The Role of Fuzzy Sets. SSDC, vol. 344, pp. 3–25. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-6716311 4. Cingolani, P., Alcal´ a-Fdez, J.: jfuzzylogic: a java library to design fuzzy logic controllers according to the standard for fuzzy control programming. Int. J. Comput. Int. Syst. 6(sup1), 61–75 (2013) 5. Cuevas, F., Castillo, O., Cortes, P.: Control strategies based on interval Type2 fuzzy logic for autonomous mobile and humanoid robots. In: Kahraman, C., Bolturk, E. (eds.) Toward Humanoid Robots: The Role of Fuzzy Sets. SSDC, vol. 344, pp. 221–236. Springer, Cham (2021). https://doi.org/10.1007/978-3-03067163-1 8 6. Fragapane, G., de Koster, R., Sgarbossa, F., Strandhagen, J.O.: Planning and control of autonomous mobile robots for intralogistics: literature review and research agenda. Eur. J. Oper. Res. 294(2), 405–426 (2021) 7. Karaduman, B., Challenger, M.: Model-driven development for ESP-based IoT systems. In: 2021 IEEE/ACM 3rd International Workshop on Software Engineering Research and Practices for the IoT (SERP4IoT), pp. 9–12. IEEE (2021) 8. Karaduman, B., Tezel, B.T., Challenger, M.: Towards applying fuzzy systems in intelligent agent-based cps: a case study. In: 2021 6th International Conference on Computer Science and Engineering (UBMK), pp. 735–740. IEEE (2021) 9. Leitao, P., Karnouskos, S., Ribeiro, L., Lee, J., Strasser, T., Colombo, A.W.: Smart agents in industrial cyber-physical systems. Proc. IEEE 104(5), 1086–1101 (2016) 10. Schoofs, E., Kisaakye, J., Karaduman, B., Challenger, M.: Software agent-based multi-robot development: A case study. In: 2021 10th Mediterranean Conference on Embedded Computing (MECO), pp. 1–8. IEEE (2021) 11. Valdez, F., Castillo, O., Caraveo, C., Peraza, C.: [Comparative study of conventional and interval Type-2 fuzzy logic controllers for , in Lego Mindstorms Ev3 Humanoids]. In: Kahraman, C., Bolturk, E. (eds.) Toward Humanoid Robots: The Role of Fuzzy Sets. SSDC, vol. 344, pp. 201–219. Springer, Cham (2021). https:// doi.org/10.1007/978-3-030-67163-1 7 12. Yalcin, M.M., Karaduman, B., Kardas, G., Challenger, M.: An agent-based cyberphysical production system using lego technology. In: 2021 16th Conference on Computer Science and Intelligence Systems (FedCSIS), pp. 521–531. IEEE (2021) 13. Zadeh, L.A.: Fuzzy sets. In: Fuzzy sets, fuzzy logic, and fuzzy systems: selected papers by Lotfi A Zadeh, pp. 394–432. World Scientific (1996)

Real-Time Distributed System for Pedestrian Assistance Using Fuzzy Logic: Application and Results Azedine Boulmakoul1(B)

, Kaoutar Bella1

, and Ahmed Lbath2

1 Computer Science Department, FSTM, Hassan II Casablanca, Casablanca, Morocco

[email protected]

2 LIG/MRIM, CNRS, Grenoble-Alpes University, Grenoble, France

[email protected]

Abstract. Year after year, traffic accident fatalities continue to grow, with the probability of such accidents increasing to the point where they are nearly unavoidable. And studies have established that traffic accidents are strongly associated with pedestrian psychology, indicating that they are no longer the outcome of randomness nor cannot be prevented. A set of indicator variables is used to model pedestrians’ exposure to risks. The method appears to have potential since it enables the application of intuitive approaches based on fuzzy set theory to pedestrian behavior. In this paper, we provide preliminary findings of a real-time distributed solution for pedestrian navigation assistance, as well as fuzzy indications of pedestrian exposure to a traffic accident. The opportunity for the adoption of an existing system architecture, which was built as part of our previous work. Keywords: Fuzzy logic · Risk and exposure · Risk fussy indicators · Safe urban walkability · Fuzzy indicators

1 Introduction Despite ongoing attempts to improve traffic safety in major cities, pedestrian run-overs continue to be a serious problem [1]. In this study, a system is offered with the purpose of minimizing the incidence of pedestrian crossing run over by using a cohesion detection system. A fuzzy system evaluates the speed of oncoming automobiles as well as the distance between them and pedestrians to estimate the level of risk. If the driver’s speed has been altered, the system may prescribe a speed for him or her to restore to normality. The system responds to the behaviors of the driver or pedestrian. When he or she progressively slows down when he or she spots a pedestrian, the level of the alert decreases at the same pace. Additionally, this project aims to establish a more efficient method for helping pedestrians to navigate safely. We propose fuzzy indicators of pedestrians’ probability be implicated in traffic accidents, which we include in the safest fuzzy routefinding service. Additionally, the paper involves the creation of a real-time architecture for obtaining real-time pedestrian and vehicle locations using a GPS tracker. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 106–111, 2022. https://doi.org/10.1007/978-3-031-09173-5_14

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Numerous studies have been undertaken to enhance pedestrian safety [2]. Works given in [3] developed a composite measure of pedestrian exposure that considers pedestrian characteristics, road and traffic variables, and pedestrian compliance with traffic regulations. While the authors of [4] launched an Android mobile application called WalkSafe to assist individuals who chat on their phones while walking, therefore increasing pedestrian smartphone users’ safety [5]. It detects automobiles approaching the user using the back camera of the mobile phone, alerting the user to a potentially dangerous scenario. This program is designed particularly for pedestrians who walk and talk. Since it requires the usage of the camera, it may deplete the battery. The system is mainly concerned with detecting vehicles in close vicinity to the phone’s owner, which needs a trained dataset. In the United States of America, 47% occur between 6 and 12 p.m., which is why the system must be effectively trained on automobile identification at night, which will require at least a medium-quality camera and eventually increase the phone’s battery consumption. The paper is organized as follows. Section 2 is devoted to defining the risk indicators we rely on and how we define the possibility for cohesion to happen. In Sect. 3, we describe the architecture of our system and different results and findings. We end with a conclusion summarizing the main results and their potential limits to evolve in our future work.

2 Pedestrian Exposure Model Research has been conducted before on how people see and predict when an approaching entity will arrive in their range of view. According to the study, the information necessary to define a first-order temporal connection (without regard for speed changes) [6, 7] may be obtained in the ratio of the relative rate of expansion and contraction of the moving object’s visual perimeter. In the absence of a contour expansion section, viewers were more aware of the information including the pace at which the optical distance is being shortened, and the pace at which the moving target’s visible perimeter expands and contracts compared to its initial size. Therefore, pedestrians often underestimate motor speeds, especially when they surpass 50 km per hour. They revealed a greater proclivity to grossly underestimate speed limits below 50 km per hour when comparing the speeds of two autos. Consequently, speed is consistently underrated. On a measured speed section, if the speed is more than 50, force 1 underestimates the speed, if not, force 2 underestimates the speed (++). We compute the “perceived” exposure in comparison to the real exposure using the underestimated speed indicate risk of exposure. Then we determine the exposure along a path. Indicators for each segment of a transport system are used to quantify pedestrian risk exposure (see Fig. 1). It is referred to as the link’s fuzzy temperature and it is formulated as a Gaussian fuzzy number. The temperature of a link I is defined as: θ i = (vi)2 × Tpi, where (vi) indicates the fuzzy perceived speed and  Tpi is the link crossing time (i). The temperature of a network N is equal to θ (N) = iN θ i. Zadeh’s [8] fuzzy logic has been widely employed by researchers to solve problems of traffic congestion at intersections, and the evolution of fuzzy logic in traffic

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Fig. 1. Human perception of distant car speed.

management was thoroughly explored in [9]. The benefits of using this kind of traffic signal management in Saudi Arabia were discussed in [10] and had a positive effect on intersection accidents. The triplet (A− , A0 , A+ ) is known as triangular Fuzzy Number TFN (see Fig. 2). Where A− rerepresentshe smallest likely value, A0 the probable value, and A+ the largest value of any fuzzy event.

Fig. 2. Triangular Fuzzy Number (TFN)

     x − A0 x − A0 , max 0, 1 + 0 ∀x ∈ R uA (x) = min max 0, 1 − + A − A0 A − A− (A− , A+ ) are the left and right-hand expansions of A. It is referred to as the TFN’s kernel value, and its membership value is 1.

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3 Application and Results To maximize the efficiency of our system’s resources and boost its responsiveness, we employed docker as a container and Kubernetes as an orchestrator (see Fig. 3). We record pedestrian and driver positions via the use of Traccar [11–13], an open-source GPS server. Traccar automatically generates a pipeline of event handlers for each connection. The GPS messages are structured and stored in the database. The Traccar server continually records the locations of pedestrians and drivers through the Traccar client application installed on their smartphones. We record real-time user coordinates with a latency of less than 0.63 s. We may use these coordinates to create pedestrian tracks using the Traccar client The data acquired from the GPS server is still in an unprocessed state and needs be further processed and modified before they can be employed for display. Kafka serves as a message broker. Once the data is uploaded to the cluster, our consumers are generated automatically. The consumer collects and analyses the data.

Fig. 3. System design

The fuzzy indications of the risk of pedestrians being exposed to traffic accidents are combined into a service that provides the safest fuzzy route finding [14, 15]. We

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measure pedestrian-vehicle cohesiveness by considering how pedestrians perceive the moving vehicle and its walking pace. In terms of vehicle assistance [16], we determine the cohesiveness that is possible depending on the vehicle’s speed and the link temperature. This is accomplished via the use of the Valhalla routing engine. We selected it because it is adaptable to variable query customization; every route request may be constructed using a unique combination of indicators and penalties to reflect the road network’s fuzzy temperature. When dealing with a big amount of data, preserving and extracting it becomes a significant issue. Additionally, our data is highly interconnected. As a result, we choose to employ a Graph Database. NEO4J’s Graph Database holds data in a node-oriented object format and ties it to the edges (association). Our ReactJs apps also visualize our real time data as well as processed data. Each time the system calculates an alert for cohesion, we store the information: time, exact location of the pedestrian, exact location of the driver, as well as speed. This information helps us categorize the areas from safe to dangerous. These criteria can leverage the temperature of a safe path.

4 Conclusion Road accidents are one of the most dangerous types of accidents facing the transportation sector. Pedestrian safety is a problem that must be addressed to transition to a smart and secure city environment. Our primary focus was pedestrians since they are the most vulnerable casualties of road accidents. As an improvement from our previous work, we were able to reduce the latency for pedestrians collecting locations from 3 to 0.6 s. This enhancement enables our system to do calculations and alerts more rapidly. Thus, we’ve seen that certain locations are not 100 percent accurate in some zones because of parasites or connection loss. As a future goal, we may estimate the pedestrian’s future position based on its speed and available path in order to improve the accuracy of the pedestrian’s location. As a result, we will improve his safety. Acknowledgments. This work was partially funded by the Ministry of Equipment, Transport, Logistics and Water-Kingdom of Morocco, The National Road Safety Agency (NARSA) and National Center for Scientific and Technical Research (CNRST). Road Safety Research Program# An intelligent reactive abductive system and intuitionistic fuzzy logical reasoning for dangerousness of driver-pedestrians interactions analysis: Development of new pedestrians’ exposure to risk of road accident measures.

References 1. Albusac, D., Vallejo, J.J., Castro-Schez, C.: An expert fuzzy system for improving safety on pedestrian crossings by means of visual feedback. Control Eng. Pract. 75, 38–54 (2018) 2. AlKheder, S., AlRukaibi, F.: Enhancing pedestrian safety, walkability and traffic flow with fuzzy logic. Sci. Total Environ. 701, 134454 (2020). ISSN 0048–9697 https://doi.org/10.1016/ j.scitotenv.2019.134454 3. Kreps, J., Narkhede, N., Rao, J.: (2011). http://cis.csuohio.edu/~sschung/cis611/KafkaDist ributedMessagingSystemforLogProcessing.pdf

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4. Escoffier, C., Finnigan, K.: Reactive Systems in Java Resilient, Event-Driven Architecture with Quarkus. O’Reilly Media Inc, USA (2022) 5. Boulmakoul, A., Mandar, M.: Virtual pedestrian risk modeling. Int. J. Civ. Eng. Technol. 5(10), 32–42 (2014) 6. Boulmakoul, A., Bella, K., Lbath, A.: Real-time distributed system for pedestrians’ fuzzy safe navigation in urban environment. In: Kahraman, C., Cebi, S., Cevik Onar, S., Oztaysi, B., Tolga, A.C., Sari, I.U. (eds.) INFUS 2021. LNNS, vol. 308, pp. 655–662. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-85577-2_77 7. Bootsma, R.J., Oudejans, R.R.: Visual information about time-to-collision between two objects. J. Exp. Psychol. Hum. Percept. Perform. 19(5), 1041–1052 (1993). https://doi.org/ 10.1037//0096-1523.19.5.1041 8. Zadeh, L.: On fuzzy algorithms. In: Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems: Selected Papers by Lotfi Zadeh. Advances in Fuzzy Systems – Applications and Theory, vol. 6. World Scientific Publication (1996). ISBN:978–981–02–2422–6 9. Koukol, M., Zajíˇcková, L, Marek, L., Tuˇcek, P.: Fuzzy logic in traffic engineering: A review on signal control. Mathematical Problems in Engineering 2015, Article ID 979160, 14 (2015). https://doi.org/10.1155/2015/979160 10. Rahman, S.M., Ratrout, N.T.: Review of the fuzzy logic-based approach in traffic signal control: Prospects in Saudi Arabia. J. Trans. Syst. Eng. Inform. Technol. 9(5), 58–70 (2009) 11. Bella, K., Boulmakoul, A.: Real-time messaging system in KafkaNeo4j pipeline architecture. In: Proceedings of The Ninth International Conference (INTIS 2020), Tanger Morocco (2020). ISBN: 978–9920–35–679–4 12. Bella, K., Boulmakoul, A.: Real-time distributed pipeline architecture for pedestrians’ trajectories. In: Ben Ahmed, M., Teodorescu, H.-N., Mazri, T., Subashini, P., Boudhir, A.A. (eds.) Networking, Intelligent Systems and Security. SIST, vol. 237, pp. 243–255. Springer, Singapore (2022). https://doi.org/10.1007/978-981-16-3637-0_17 13. Boulmakoul, A., Mandar, M.: Fuzzy pheromone potential fields for virtual pedestrian simulation. Adv. Fuzzy Syst. 2016, 4027687:1-4027687:11 (2016) 14. Boulmakoul, A., Mandar, M.: Fuzzy ant colony paradigm for virtual pedestrian simulation. The Open Operational Research Journal, 19–29 (2011). Corpus ID: 17088050 https://doi.org/ 10.2174/1874243201105010019 15. Jablonowski, M.: Managing high-stakes risk: Toward a new economics for survival. ISBN-10: 0230238270, Palgrave Macmillan (2009) 16. FHWA.: Synthesis of Methods for Estimating Pedestrian and Bicyclist Exposure to Risk at Areawide Levels and on Specific Transportation Facilities. In January 2017, Publication No. FHWA-SA-17–041, US DOT (2017)

Fuzzy Clustering Based Association Rule Mining: A Case Study on Ecommerce Ba¸sar Öztay¸si1(B) , Pelin Yurdadön2 , and Sezi Çevik Onar1 1 Industrial Engineering Department, ˙Istanbul Technical University, 34367 ˙Istanbul, Turkey

[email protected]

2 Modanisa Head Office, Altunizade, Ku¸sbakı¸sı Cd. No:27/1, 34662 Istanbul, Turkey

[email protected]

Abstract. Association rule mining (ARM) refers to a procedure that focuses on finding frequent patterns in various data sources. The most commonly used area is the retail sales data and rules which show an association between sales of two products are investigated. To this end, sales data is preprocessed, and algorithms are used to find the association rules by using the specific threshold values of Support and Confidence parameters. In this study, we investigated the effects of using fuzzy clustering with association rule mining. A case study from the E-commerce area is selected and sales data for a specific period is analyzed. First ARM is applied to the whole data, then the data is segmented by using Fuzzy Clustering, and ARM is applied to all segments. Later the resulting rules are compared and the effects of segmentation on ARM results are analyzed. Keywords: E-Commerce · Fuzzy clustering · Association rule mining

1 Introduction The new normal after the pandemic has caused significant changes in our daily lives. Depending on these changes, E-Commerce transactions have increased and gained importance. Unlike classical commerce, e-commerce is a more convenient field of study for collecting data on customer movements. Effective use of customer data offers various opportunities for companies. Discovery of association rules and creation of customer segments are among such examples. Customer segmentation is the study of identifying customer groups with similar characteristics or similar behaviors. Association analysis rules, on the other hand, aim to identify co-occurring events and relate them as a precursor to a sequel. Fuzzy sets provide a systematic approach to formalize precision and vagueness in engineering problems. In the literature, there are various applications of fuzzy sets on different problems such as supplier selection [1], customer analytics [2], risk management [3], engineering economics [4] and public transportation [5]. In this study, it is aimed to compare the results of the association analysis study performed using all customer data in a real e-commerce site and the association analysis rules applied separately to the segments determined by the fuzzy cluster method. Theoretically, association analysis © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 112–118, 2022. https://doi.org/10.1007/978-3-031-09173-5_15

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studies performed only on the data of similar customers are expected to yield better results than using all data. The study findings support this theory. In the following sections of the paper, association rule mining and fuzzy clustering methods are explained in the Methodology section. Then, in the Real-World Application section, the implementation steps are specified. Finally, the results of the study are evaluated in the conclusion and recommendations section.

2 Methodology 2.1 Association Rule Mining Association rule mining focus on analyzing past data and detecting associations in this data. It is intended to identify strong rules discovered in databases using some support and confidence measures. In any given transaction with a variety of items, association rules are meant to discover the rules that determine how or why certain items are connected. Association rules are show as X → Y, where X is the antecedent and Y is the consequent. Support and confidence are the core measure used for finding association rules. Support is an indication of how frequently the itemset appears in the dataset. Confidence, on the other hand, is the percentage of all transactions satisfying X that also satisfy Y. Support =

frq(X , Y ) N

Confidence =

frq(X , Y ) frq(X )

(1) (2)

Association rules are usually required to satisfy a user-specified minimum support and a user-specified minimum confidence at the same time. Association rule generation is usually split up into two separate steps. First, minimum support is applied to find all frequent item sets in a database. Finding all frequent item sets in a database is difficult since it involves searching all possible item sets (item combinations). Second, these frequent item sets and the minimum confidence constraint are used to form rules. 2.2 Fuzzy Clustering Clustering method is used to define subgroups of customers who have common properties. Each customer is defined by a data point in a multi-dimensional space where each dimension represents different properties. There are various techniques in the literature which convert input data into clusters. In the literature fuzzy clustering is used by using two points of view; either considering uncertain data or considering crisp data with uncertain clusters [6]. Fuzzy c-means algorithm is based on similarity or dissimilarity measures which are extracted from distance measurement such as Euclidean distance [7]. The main definition is the partition matrix, which represents the extracted clusters. A fuzzy partition matrix is defined from [6] with the conditions given in the following: µik ∈ [0, 1], 1 ≤ i ≤ c,

(3)

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c i=1

0
0 and the norm-inducing matrix A, the algorithm tracks the following steps: (l)

Step 1: compute prototypes for cluster (means): Vi

=

N

(l−1) m ) xk k=1 (uik (l−1) m (u k=1 i,k )

N

,1 ≤ i ≤ c

2 = (x − v )T A(x − v ), 1 ≤ i ≤ c, 1 ≤ k ≤ n Step 2: calculate the distances:DikA i i k k (l) 1 Step 3: update the partition matrix: uik = c 2/(m−1) j=1 (DikA /DjkA )

this step will be repeated for l = 1, 2, . . . until U (l) − U (l−1)  < . 2.2 Ant Colony Optimization (ACO) Algorithm 2.2.1 Path Election The likelihood given to a node s in the candidate list C, taking into account that node r in the ant’s current position, may be found using the equation: p(r, s) = 

τ (r, s).ηβ (r, s) β u∈C τ (r, u).η (r, u)

(3)

where τ is the pheromone, η is the inverse of the distance δ(r, s), and β is a parameter that defines the pheromone’s relative importance to distance. τ (r, s).ηβ (r, s) multiplication result denotes node’s convenience. After determining the probability associated with node s, the probabilistic selection method will be used to choose node s from several candidates based on Eq. (3). The following equation may be used to determine the next node for route formation in an ant colony system:  argmaxs∈C τ (r, s).ηβ (r, s), ifrand (0, 1) < q0 (4) s = f (x) = S, otherwise q0 is a deterministic parameter in an ant colony system, while S is a random variable that follows the probability distribution described in Eq. (3). 2.2.2 Local Pheromone Update Each ant upgrades the pheromone on every edge it uses along its path by using the following equation: τ (r, s) = (1 − ρ).τ (r, s) + ρ.τ0

(5)

where ρ is local pheromone decay parameter and τ0 = (n.LNN )−1 is the amount of pheromone in the first repetition that can be calculated by constructing a path in a greedy method based on nearest-neighbor heuristic and calculating its length that is represented as LNN .

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2.2.3 Global pheromone update On conclusion of the best global path, pheromone is updated globally, only on edges included in the best global path as per equation: τ (r, s) = (1 − α).τ (r, s) + α. τ (r, s) where

 τ (r, s) =

(Lgb )−1 , if (r, s) ∈ Global − Best − Tour 0, otherwise

(6)

(7)

α is a pheromone decay parameter, Lgb is the global optimum path length. The previous equation ensures that only edges on the global optimal path get more pheromone. 2.3 Mathematical Model We have formulated the problem as the standard uncapacitated TSP problem with only one modification to the objective function (Fig. 1).

Fig. 1. The flow chart of the proposed strategy (P-FCM-ACO)

Our study utilized two objective functions to solve the problem and verify our proposed novel objective function’s superiority. This first objective’s goal as presented in Eq. (8) is to reduce route length within each cluster. The function’s equation is as follows: Min

n m   i=1 j=1

xij dij

(8)

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The proposed novel objective function in Eq. (9) maximizes survivor survival probability while minimizing deaths and robot travel distance. The function equation is as follows: Min

Nsj Nc   c=1 i=1

    0.2 SRicj O; b) Surface - X1 , X3 ->O

Mamdani’s algorithm is used as a fuzzy inference mechanism of the developed system, which has received the greatest practical application in fuzzy modeling problems and consists in the use of a minimax composition of fuzzy sets. The processing of fuzzy inference rules in this case consists of four stages, which are described in more detail in [7]. The scheme of the described fuzzy inference system implemented in the MATLAB environment is shown in Fig. 3.

Fig. 3. Scheme of the fuzzy inference system in the MATLAB environment

A feature of this fuzzy inference model is the simultaneous operation of all rulesproductions, with varying degrees of their influence on the output of the model.

3 An Example of Evaluating the Quality of Marketing Activities The developed fuzzy inference model was applied to evaluate the quality of marketing activities among 10 commercial enterprises. The results showed that the marketing policies of 3 of these businesses were ineffective, 2 were low, 1 were moderate, 2 were good, and 2 were high.

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The study of the results showed that the commercial enterprises of Coca-Cola Azerbaijan, BazarStore, Bravo Supermarket Azerbaijan, AzerSun Holding MMC, established their marketing activities quite well and with high efficiency, which indicates that they have their own ERP systems, pricing policy, their trading network and online collect information about the market, about customers, consumers, can manage the assortment and can quickly assess the degree of impact of new marketing solutions on monetary and commodity turnover.

4 Conclusıon This approach is based on the fact that rather quickly without complex mathematical calculations and taking into account a large number of factors, based on the experience and intuition of managers and employees of the marketing department, to assess the quality of marketing activities. The conducted studies and the results obtained confirm the correctness and expediency of applying the theory of fuzzy sets to solve the problems of assessing the quality of enterprise marketing, using the above complex of factors reflecting qualitative characteristics marketing activities of the enterprise. This approach can be used by the marketing department of enterprises, marketing centers, marketing researchers. Further research on this work should be carried out to create a global model that covers all criteria for assessing the quality of an enterprise’s marketing activities. It is also necessary to create a software module with open capabilities for integration with other application packages.

References 1. McDonald, M.: Strategic Marketing Planning [Strategicheskoye Planirovaniye Marketinga], pp. 320. Piter (2000) 2. Assel, H.: Marketing: Principles and Strategy: Textbook for Universities Marketing: [Printsipy i strategiya: Uchebnik dlya vuzov], p. 804. INFRA-M, M. (1999) 3. Randall Richard, C.: The Quality Yearbook. Published by McGraw-Hill, Inc. 4. Tugan-Baranovsky, M., Balabanova, L.V.: Marketing management. Scientific publication [Mapketing menedment. Hayqnoe izdanie], p. 594. DonGUET, Donetsk (2001) 5. Galina, Y.: Marketing efficiency: methodology, evaluation and results. Practical Marketing [Effektivnost’ marketinga: metodika, otsenki i rezul’taty. Prakticheskiy marketing g]. No 8 (78) (2003) 6. Zadeh, L.A.: Fuzzy logic, neural networks, and soft computing. Commun. ACM 37(3), 77–84 (1994) 7. Zadeh, L.A., Aliev, R.A.: Fuzzy Logic Theory and Applications: Part I and Part II, p. 610. WSPC (5 Dec 2018) 8. Fuzzy Logic Toolbox. https://www.mathworks.com/products/fuzzy-logic.html 9. Oglu, A.R.B., Kizi, I.I.T.: A method for forecasting the demand for pharmaceutical products in a distributed pharmacy network based on an integrated approach using fuzzy logic and neural networks. In: Kahraman, C., Onar, S.C., Oztaysi, B., Sari, I.U., Cebi, S., Tolga, A.C. (eds.) INFUS 2020. AISC, vol. 1197, pp. 998–1007. Springer, Cham (2021). https://doi.org/10.1007/ 978-3-030-51156-2_116

Sparse Weighted Multi-view Possibilistic C-Means Clustering with L1 Regularization Josephine Bernadette Benjamin1(B) , Shazia Parveen2 , and Miin-Shen Yang2 1 Department of Mathematics, University of Santo Tomas, Manila, Philippines

[email protected] 2 Department of Applied Mathematics Chung, Yuan Christian University, Taoyuan, Taiwan

Abstract. Sparse clustering algorithms create clusters with a sparsity of features and are effectively applied to extremely high-dimensional single-view datasets containing irrelevant features, noise data, outliers, and missing data. Multi-view datasets contain features extracted from various measuring devices using the same sample. Each distinct group of features constitutes a specific view of the data. Although these data are extracted from diverse settings and domains, they must be highly correlated since they are from the same sample. Most of the sparse clustering methods can only handle single view datasets. Thus, they may encounter difficulty obtaining the desired result when clustering multi-view datasets, leading to poor performance. Therefore, there is a need to develop a suitable multi-view clustering method to address the above problem. In this paper, we propose an algorithm called Sparse Weighted Multi-view Possibilistic C-means with L1 Regularization (S-WMV-PCM-L1) designed to perform multi-view clustering as well as view and feature selection with Possibilistic C-Means (PCM) as its base function and using L1 (LASSO) Regularization as a penalty term. This algorithm uses a weighting scheme within its clustering framework to determine the comparative significance of each view of data points and features. Experimental results using real-world datasets show the feasibility and effectiveness of our proposed algorithm. Also, S-WMV-PCM-L1 performs better when compared to other existing multi-view clustering algorithms. Keywords: Sparse clustering · Multi-view clustering · Possibilistic C-means · L1 (LASSO) regularization

1 Introduction Clustering analysis explores the basic structure of a dataset. Clustering methods divide the data points into clusters such that similar data points are grouped in one cluster while different data points are grouped into different clusters. It is used and applied in machine learning, pattern recognition, data mining, social media computing, health, and biological sciences, image processing, and the like. The traditional clustering algorithms such as k-means [1], fuzzy c-means (FCM) [2], and possibilistic c-means (PCM) [3] have been constantly studied through the years to improve their clustering capabilities. Although © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 142–150, 2022. https://doi.org/10.1007/978-3-031-09173-5_19

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they are popularly used, drawbacks are still inherent, which need to be resolved. One of these is their applicability only to single-view datasets. Due to new innovative technologies, a massive amount of data with a complex structure on its size, high-dimensional features, and multiplicity can now be collected. Multi-view datasets consist of several views with heterogeneous features. Multi-view clustering methods were proposed [4–8] to harmonize the features in each view. The information extracted among views can improve clustering performance compared to single-view clustering algorithms. Each view may contain many features where some may be irrelevant, affecting the clustering performance. The result may lead to high computational complexity and low clustering accuracy [7]. Features that can contribute to good clustering results need to be appropriately selected. The existing traditional clustering algorithms [1–3] may not be able to handle high-dimensional datasets. Feature selection is considered in most clustering algorithms to handle datasets with highdimension. They use weights to identify and select relevant features by assigning larger weights and smaller weights to discriminate the irrelevant features [6–8]. Aside from weight assignments, regularization terms are used to penalize the irrelevant features [9, 10]. The algorithms proposed by Witten and Tibshirani [9] and Qiu et al. [10] use regularization terms as a constraint in their objective function. Inokuchi and Miyamoto [11] and Xenaki et al. [12] proposed sparse clustering methods with regularization terms in their objective function. They focus more on the degree of membership of data rather than features. However, none of the multi-view clustering methods considered sparsity in features, and none of the sparse clustering methods are applied to multi-view datasets. Hence, we propose a clustering algorithm for multi-view datasets of high dimensions in each view via a sparse clustering approach called Sparse Weighted Multiview Possibilistic C-Means with L1 regularization (S-WMV-PCM-L1). Its goal is to select and discriminate features via a weighting scheme and perform cluster analysis of multi-view datasets. Relevant features will be assigned with nonzero weights while zero weights are assigned to irrelevant features. Furthermore, with PCM as its base function, S-WMV-PCM-L1 recognizes and eliminates outliers/noisy data points. The inclusion of the L1 regularization and PCM in the objective function shows that S-WMV-PCM-L1 can obtain a clustering performance with high accuracy in a multi-view setting. The rest of the paper is organized as follows: Sect. 2 gives a brief description of some related clustering algorithms; Sect. 3 discusses the framework of S-WMV-PCML1; Sect. 4 presents the analysis and results in applying S-WMV-PCM-L1to selected real datasets as well as its comparison to existing multi-view clustering algorithms such as W-MV-PCM-L2 [8], and MinimaxFCM [13]; Conclusion and future works follows in Sect. 4.

2 Related Works Witten and Tibshirani [9] proposed a sparse clustering algorithm called Sparse k-means using L1 (LASSO) regularization penalty as a constraint in the objective function. That is, assigning zero weights to the irrelevant features. Qiu et al. [10] extended Sparse K-means to Sparse FCM following the framework proposed by Witten and Tibshirani.

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Benjamin and Yang [8] proposed a weighted multi-view possibilistic c-means with L2 regularization (W-MV-PCM-L2) that determines the comparative significance of views and features in each dataset view through a weighting schema within its clustering framework. Using L2 regularization as a penalty term in its objective function, W-MVPCM-L2 discriminates views and features by assigning smaller weights to irrelevant features. The MinimaxFCM proposed Wang and Chen [13] uses an FCM-based minimax optimization that generates consensus clustering among views using a weighting scheme. Although W-MV-PCM-L2 detects irrelevant features by assigning smaller weights, its clustering performance is still affected since it did not eliminate the presence of irrelevant features. On the other hand, MinimaxFCM discriminates only among views but not the features. The proposed S-WMV-PCM-L1 will perform a sparse clustering analysis of multi-view datasets and discriminates views and features using a weighting scheme that assigns zero weights to irrelevant features. The presence of irrelevant features will not affect its final clustering process since they are assigned zero weights.

3 The Sparse Weighted Multiview Possibilistic C-Means with L1 Regularization (S-WMV-PCM-L1) Clustering Framework Traditional clustering algorithms such as K-means [1], FCM [2], and PCM [3] apply only to single-view datasets treating all features with equal importance. Even though the use of PCM addresses the drawbacks of FCM, resulting in an improved clustering performance, still, it cannot handle datasets of high dimensions. We propose a sparse weighted multiview clustering algorithm with L1 regularization with PCM as its base function (SWMV-PCM-L1). This algorithm designs a weighting scheme that discriminates each view and identifies and selects relevant features in each view. Relevant features are assigned nonzero weights while it shrinks to zero the weights of irrelevant features Let X be a multi-view data set with H views and D features, where X ={xi }ni=1 and  H  xi = xih h=1 for xih ∈ Rdh , and H dh = D. Here, dh is the number of features   h=1 that belong to the hth view. W = wjh represents the feature weight vector of each 1×D

view, and V = [vh ]1×H represents the view weight vector. The S-WMV-PCM-L1 aims to minimize JS−WMV −PCM −L1 (U , Z, W , V ) = +λ

c  n 

(1 − uki ) + α m

k=1 i=1

subject to,

(h) d

j=1

H  h=1

H  h=1

vh 22

(vh )2

(h) C  N d 

k=1 i=1 j=1

  2 m wh xh − z h uki j ij kj (1)

+ δ wjh

1 H 

wjh = 1, wj ∈ [0, 1], 1 < j < d (h) and

1 ≤ h ≤ H with

n  i=1

h=1 2

vh = 1, vh = [0, 1],

uki ≥ 1, 1 ≤ k ≤ c, uki > 0 and wjh ≤ 1. Also, we define 2

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2 d  2  



h wjh , and wjh = dj=1 wjh wjh ≥ 0, ∀j where wjh is a weight cor wj = 2

1

j=1

responding j, dh as  the number of dimensions with λ = β/m2 C where n to a feature 2 β = i=1 xi − x /N and x = ni=1 xi /n, and δ is a tuning parameter which controls the number of features to be selected. Theorem 1: The necessary conditions for minimizing JS−WMV −PCM −L1 (U , Z, W , V ) for any distance measure are ⎞ 1 ⎤−1 m−1 H d (h)     2 1 ⎥ ⎢ 2 h h h ⎝ ⎠ uki = ⎣1 + wj xij − zkj (vh ) ⎦ λ ⎡

⎛

h zkj =

⎡⎛

N 

N  m h m uki xij / uki

i=1

(3)

i=1

⎞ ⎞⎤−1 ⎛ (h) N d H C   2  2   m h h h m h h h ⎝ vh = ⎣⎝ uki wj xij − zkj + α ⎠/ uki wj xij − zkj + α ⎠⎦ k=1 i=1 j=1 h=1 k=1 i=1 j=1 ⎧ dh   N  C  H   ⎪ m xh −z h 2 −δ ⎪ − uki (vh )2 ⎪  2 ij kj ⎪ dh C  H N  ⎪   h=1 k=1 i=1 j=1 ⎪ m xh − z h ⎪ uki > −δ (vh )2 ⎪ 2 when ij kj ⎪ dh    ⎪ N  C   ⎪ h=1 k=1 i=1 j=1 H m xh −z h 2 −δ ⎪ ⎪ uki − (vh )2 ⎪ ij kj ⎪ k=1 i=1 j=1 ⎪ h=1 (h)

N d C  

⎪ ⎪ ⎨

2

wjh = 0 ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩

when −

(2)

j=1

h=1

H 

(vh )2

H 

h=1

dh   N  C   m xh −z h 2 +δ uki ij kj

(vh )2

 2 dh C  N   m xh − z h uki ≤ |δ| ij kj

(4)

(5)

k=1 i=1 j=1

 2 dh C  H N    m xh − z h uki 0), K = 1, and m > 1. Initializations: Matrix for values, U (0) and cluster centers, Z (0) , the feature   membership dh h , 1 ≤ j ≤ dh with j=1 wj = 1 by wjh = 1/dh and the weight vector, W (0) = wjh 1xdh

view weight vector, V (0) = [vh ]1×H , 1 ≤ h ≤ H by vh = 1/H .   , and V (q+1) = [vh ]1×H , 1 ≤ h ≤ H . Output: U (q+1) , Z (q+1) , W (q+1) = wjh Set q = 1. Step 1: Calculate α = C/dh and β =

1xdh

2 N   xih − xih /N where C is the number of

i=1

clusters, dh is the number of features that belong to the hth view and β is the covariance of the data points in the hth view

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Step 2: Calculate ηk values by equation ηk = K

n  i=1

Z (0) , U (0) .

m x − z 2 / uki i k

n 

i=1

m using uki

Step 3. Update U (q) with W (0) and V (0) by Eq. (2) Step 4. Update Z (q) , with U (q) , by Eq. (3) Step 5. Update V (q) with U (q) , Z (q) , W (0) by Eq. (4) Step 6. Update W (q) , with U (q) , Z (q) , and V (q) by Eq. (5) Step 7. Obtain δ through the binary search method (or gap statistic) between max(W ∗ (q), 0) and a weighted bound in the interval (a > 0, 1/dh ).



p

(t) h(t) (t−1) p (t−1)

Step 8. IF j=1 wj − wj

/ j=1 wj

< ε where wj is the t th step update of wjh then STOP; ELSE, set t = t + 1 and return to Step 2. In using the S-WMV-PCM-L1 algorithm, nonzero weights are assigned to relevant features of each view in the dataset while the weights for irrelevant features are shrunk to 0. Each nonzero feature weight defines the feature’s contribution to form the cluster. Similarly, varied view weights are distributed among the different views of the multiview dataset. Each view weight defines the view’s contribution to forming the cluster. The balancing parameters α and δ control the distribution of the view weights and feature weights in each view. The parameter α is estimated using α = C/dh and is constant during the entire clustering process. If α → 0, the dimension of each view, dh , is larger compared to the number of clusters, C. This would imply that the weight of all views are almost equal. Hence, we need α to be large enough to discriminate among the views by reducing the view weights. The parameter δ induces sparsity of the feature weights in each view which can be determined thru binary search method or gap statistic [14] modified based on PCM. During the process of the S-WMV-PCM-L1 algorithm, with the updated values of the degree of possibilistic membership, cluster centers, and view weights, the feature weights are first calculated using the equation h∗

wj = −

H  h=1

(vh )2

N C   k=1 i=1

m uki



2 dh  H N C  2  2   h m h h xijh − zkj xij − zkj / −uki (vh )2 j=1 h=1 k=1 i=1 2

(6)  ∗  We choose w∗ = max wjh , 0 among the calculated wj∗ s. Then, either the binary search method or the gap statistic is used to determine an optimal value for δ. This value will then be used to update the final feature weights in each view. The process stops once it reaches convergence with an error threshold ε ≤ 1 × 10−5 .

4 Experimental Comparisons and Results This section performs experiments on real datasets to show that our proposed S-WMVPCM-L1 is effective and efficient. We compare the performance of S-WMV-PCM-L1

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147

with other clustering algorithms such as PCM, W-MV-PCM-L2, and MinimaxFCM. The final clustering label resulting from the clustering process is compared with the ground-truth label of the dataset. We use the accuracy rate (AR), the normalized mutual information (NMI) [15], the Rand Index (RI) [16], and the Jaccard Index (JI) [17] to evaluate the performance of the clustering algorithms, such as. Indexes with higher values imply a higher degree of similarity. The higher the value of these indexes, the more similar they are. The values of the external validity indexes indicate the existence of compact clusters resulting from the algorithm. We perform 100 simulations of each clustering algorithm for consistency checking. We also set 100 as the maximum number of iterations and the convergence error tolerance of ε = 1 × 10−5 . Three multi-view real datasets are considered to show the performance of our proposed algorithm S-WMV-PCM-L1: Prokaryotic phyla dataset [18]. Caltech101-7 [19], and UCI Digitdataset[20].Ourstudyonlyusedthetextualdataandthegenerepertoireinprokaryotic phyla since they have more features than the proteome composition. Table 1 summarizes the properties of these real datasets. Table 1. The real datasets and its’ properties Real data set

View information

Caltech101-7

GABOR WM CENTRIST

Prokaryotic Phyla UCI-Digits

Dimension 48

No. of clusters

1474

7

551

4

2000

10

40 254

HOG

1984

GIST

512

LBP

928

Gene Repertoire

393

Text

438

Fourier coefficients

76

Profile correlations

216

Karhunen-Love coefficients

Size

64

Example 1. In this example, we investigate the performance of S-WMV-PCM-L1 in selecting the relevant features from the irrelevant ones. S-WMV-PCM-L1 uses a weighting scheme in its algorithm that will shrink to zero those features with minimal contribution to its clustering performance while assigning nonzero weights to relevant features. This process is performed for every feature in each view. The results showing the number of features with nonzero weights and the number of features with zero weights are summarized in Table 2. Table 2 shows that S-WMV-PCM-L1 could shrink to zero the feature weights but not necessarily all the feature weights on some views. It is also evident that the algorithm can handle large dimensions. The average accuracy of S-WMV-PCM-L1 is relatively high (above 95%), indicating that the algorithm’s performance is good.

148

J. B. Benjamin et al. Table 2. The behavior of S-WMV-PCM-L1 on feature weights in each view

Real data set

View

Caltech101-7

GABOR WM

No. of features

48

No. of features with nonzero weights 48

No. of features with zero weights 0

40

40

0

254

254

0

HOG

1984

751

1233

GIST

512

511

1

LBP

928

731

197

Prokaryotic Phyla

Gene Repertoire

393

224

169

Text

438

344

94

UCI-Digits

Fourier coefficients

76

61

15

Profile correlations

216

95

121

64

64

20

CENTRIST

Karhunen-Love coefficients

Accuracy rate

0.953

0.961 0.951

Example 2. In this example, we compare the clustering performance of S-WMVPCM-L1 with PCM and other multi-view clustering algorithms: W-MV-PCM-L2, MinimaxFCM. Each algorithm is applied to the real multi-view datasets in Table 1. The same initializations on the membership degree of the data points, cluster centers, feature weights, and view weights are used. For PCM, S-WMV-PCM-L1, and W-MV- PCM-L2. PCM, and W-MV- PCM-L2, we set m = 2 and K = 1. For MinimaxFCM, α = 0.5, the midpoint of [0, 1). We first concatenate all the views for PCM to obtain a single view dataset. The algorithms are applied to the real datasets, and their results are shown in Table 3. We observed that S-WMV-PCM-L1 performs well with high accuracy results as compared to other clustering algorithms. Table 3. Comparison among the clustering algorithms using the given datasets Dataset

Algorithm

AR

RI

NMI

JI

Caltech101-7

PCM

0.564

0.579

0.410

0.465

MinimaxFCM

0.597

0.550

0.214

0.346

S-WMV-PCM-L1

0.953

0.691

0.317

0.481 (continued)

Sparse Weighted Multi-view Possibilistic C-Means Clustering

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Table 3. (continued) Dataset Prokaryotic

UCI-Digits

Algorithm

AR

RI

NMI

JI

W-MV-PCM-L2

0.940

0.700

0.327

0.480

PCM

0.561

0.407

0.013

0.392

MinimaxFCM

0.550

0.404

0.001

0.383

S-WMV-PCM-L1

0.961

0.609

0.257

0.356

W-MV-PCM-L2

0.951

0.582

0.221

0.347

PCM

0.207

0.380

0.377

0.130

MinimaxFCM

0.434

0.864

0.459

0.241

S-WMV-PCM-L1

0.951

0.565

0.296

0.153

W-MV-PCM-L2

0.925

0.577

0.292

0.154

5 Conclusion This study proposes a multi-view clustering algorithm called Sparse Weighted Multiview Possibilistic C-means with L1 Regularization (S-WMV-PCM-L1). The algorithm SWMV-PCM-L1 can perform multi-view clustering and feature selection simultaneously. A weighting scheme is used within its clustering framework to determine the comparative significance of each view of data points and features in each view. Weights are assigned to discriminate among views. S-WMV-PCM-L1 was able to identify and select relevant features in each view by assigning them with nonzero weights while the irrelevant features were assigned zero weights. In this way, the irrelevant features are disregarded in the final clustering process yielding a better clustering performance with high accuracy. As observed, S-WMV-PCM-L1 is effective for non-sparse multi-view datasets. Our future work will entail extending our algorithm to be able to consider sparse multi-view datasets. Also, we intend to extend S-WMV-PCM-L1 to perform feature reduction.

References 1. MacQueen, J.B.: Some methods for classification and analysis of multivariate observations. In: Proceedings of the Fifth Symposium on Math, Statistics, and Probability 1967, pp. 281–297. University of California Press, Berkeley, CA (1967) 2. Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Springer US, Boston, MA (1981). https://doi.org/10.1007/978-1-4757-0450-1 3. Krishnapuram, R., Keller, J.M.: A possibilistic approach to clustering. IEEE Trans. Fuzzy Syst. 1, 98–110 (1993) 4. Bickel, S., Scheffer, T.: Multi-view clustering. In: Proceedings of the 4th IEEE International Conference on Data Mining 2004, vol. 4, pp. 19–26. ICDM (2004) 5. Cai, X., Nie, F., Huang, H.: Multi-view k-means clustering on big data. In: Proceedings of the 23rd International Joint Conference on Artificial Intelligence 2013, pp. 2598–2604 (2013) 6. Jiang, B., Qiu, F., Wang, L.: Multiview clustering via simultaneous weighting on views and features. Appl. Soft Comput. 47, 304–315 (2016)

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7. Xu, Y.M., Wang, C.D., Lai, J.H.: Weighted multi-view clustering with feature selection. Pattern Recogn. 53, 25–35 (2016) 8. Benjamin, J.B.M., Yang, M.S.: Weighted multi-view possibilistic C-means clustering with L2 regularization. IEEE Trans. Fuzzy Syst. (2021). https://doi.org/10.1109/TFUZZ.2021.305 8572 9. Witten, D.M., Tibshirani, R.: A framework for feature selection in clustering. J. Am. Stat. Assoc. 105(490), 713–726 (2010) 10. Qiu, X., Qiu, Y., Feng, G., Li, P.: A sparse fuzzy c-means algorithm base on sparse clustering framework. Neurocomputing 157, 290–295 (2015) 11. Inokuchi, R., Miyamoto, S.: Sparse possibilistic clustering with L1 regularization. In: Proceedings of 2007 IEEE International Conference on Granular Computing, pp. 442–445, (2007) 12. Xenaki, S.D., Koutroumbas, K.D., Rontogiannis, A.A.: Sparsity-aware possibilistic clustering algorithms. IEEE Trans. Fuzzy Syst. 24(6), 1611–1626 (2016) 13. Wang, Y., Chen, L.: Multi-view fuzzy clustering with minimax optimization for effective clustering of data from multiple sources. Expert Syst. Appl. 72, 457–466 (2017) 14. Tibshirani, R.: Regression shrinkage and selection via the Lasso. J. Roy. Stat. Soc. B 58, 267–288 (1996) 15. Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley, New York (1991) 16. Rand, W.M.: Objective criteria for the evaluation of clustering methods. J. Amer. Statist. Assoc. 66, 846–850 (1971) 17. Jaccard, P.: Distribution de la flore alpine dans le basin des Dranses et dans quelques regions voisines. Bull. De la Soc. Vaudoise des Sci. Naturelles 18, 1008–1018 (2016) 18. Brbi´c, M., Kopriva, I.: Multi-view low-rank sparse subspace clustering. Pattern Recogn. 73, 247–258 (2018) 19. Fei-Fei, L., Fergus, R., Perona, P.: Learning generative visual models from a few training examples: an incremental Bayesian approach tested on 101 object categories. Comput. Vis. Image Underst. 106, 59–70 (2007) 20. Xu, P., Deng, Z., Choi, K.S., Cao, L., Wang, S.: Multi-view information-theoretic co-clustering for co-occurrence data. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 33, no. 01, pp. 379–386 (2019) 21. Gao, H., Nie, F., Li, X., Huang, H., Multiview subspace clustering. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 4238–4246 (2015)

Picture Fuzzy Simple Additive Weighting Method for Food Presentations Scoring of Gastronomy Students Fatma Ya¸slı1(B)

and Sema Ekincek2

1 Transportation Vocational School, Eskisehir Technical University, Eskisehir, Turkey

[email protected]

2 Tourism Faculty, Department of Gastronomy and Culinary Arts, Anadolu University,

Eskisehir, Turkey [email protected]

Abstract. Eating is one of the basic activities that people carry out throughout their lives to survive and to get pleasure. Today, this basic activity is handled within the framework of gastronomy, which is also defined as the “art of living”, which includes many industrial sub-fields and various research disciplines. Service providers of the food and beverage industry compete fiercely for the privilege of being favored by the customers. For gastronomy education institutes, introducing unique products for restaurant menus and creating innovative recipes is vital. This is due to the fact that one of the qualities required of prospective chefs is ingenuity. In this study, scoring the food presentations created by the students within the scope of the Korean Cuisine course taught in a gastronomy education institution is considered as a multi-criteria decision-making problem. Food presentations by the students in the final examination are evaluated by considering the criteria such as its visuality, creativity of the name, taste perception created by the expert, and the fusion balance of the product (coming together of different cultures in the product). The Picture fuzzy Simple Additive Weighting (SAW) method was used for this multi-criteria evaluation, which was considered for the scoring of food presentations of the students. There is no doubt that the developed methodology can be applied to many different evaluations related to the cuisine. Keywords: Picture fuzzy sets · Simple additive weighting · Scoring of food presentation

1 Introduction Multicriteria decision-making (MCDM) techniques offer very functional solutions when it comes to alternatives evaluated within the scope of different criteria. If the values of the alternatives under the criteria are determined by empirical or historical data, solution approaches can often proceed smoothly. But the complexity of the considered problem may lead to less reliable results when all criteria of the evaluation are handled by experts [1]. In this study, the problem of scoring the food presentations of gastronomy students within the scope of a final exam has been considered an MCDM problem. Within © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 151–159, 2022. https://doi.org/10.1007/978-3-031-09173-5_20

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the scope of the Korean Cuisine course given in a gastronomy education institution, students demonstrate high performance and present their food presentations. Relevant faculty members also directly score these presentations for grading the students. While evaluating the food presentations, experts take into account 4 different elements such as visuality, creativity of the name, taste perception. However, the high reliability of the assessment of the students’ presentation is essential, a quantitative scoring problem has not been addressed before in the literature. The problem is based on scoring the products presented by the students in a course, out of 100, through purely cognitive assessments of the evaluators. There are many MCDM methods proposed in the literature to evaluate alternatives under different criteria. Within the scope of the study, the Simple Additive Weighting (SAW) method and fuzzy theory were used for real number evaluation of the food presentations of the students. The fuzzy SAW method is defined as a systematic MCDM method that enables a group of decision-makers to evaluate alternatives under different criteria with linguistic expressions [2]. And it has been used in many MCDM studies for various fields about the evaluation of renewable power sources [3], project manager selection [2], cultural websites’ evaluation [4], strategy selection [5], etc. Thanks to its systematic and simple logic, it also has become a frequently used method in fuzzy extension-based studies [6–10]. To the best of our knowledge, this paper is the first study to score the food presentations quantitatively using the fuzzy logic and fuzzy SAW method. Evaluations for the food presentations made by experts according to their subjective knowledge and also taste perceptions contain very high imprecision and uncertainty. Fuzzy theory, which enables experts to use linguistic expressions instead of assigning a real number directly, provides a great advantage in making qualitative evaluations quantitatively. The Fuzzy theory proposed by Zadeh [11] in 1965 has been introduced many extensions over the years. In addition to the membership function to represent uncertainty, with extensions such as Intuitionistic fuzzy sets [12], Hesitant fuzzy sets [13], Pythagorean fuzzy sets [14], and Picture fuzzy sets [15] non-membership function and hesitant values are also taken into account. Provided that the sum of positive (membership), negative (non-membership), and neutral (hesitant) memberships should be less or equal to 1 [16] the uncertainty in expert judgments is dealt with more comprehensively by taking into account the aggregation, disagreement, and neutral situations of decision-makers. In this paper, for the first time in the literature, a fuzzy evaluation methodology is presented for grading the food presentations of the students within the scope of the gastronomy. Picture fuzzy SAW method was used for comprehensive evaluation of food presentations under different criteria. The organization of the paper is as follows: In Sect. 2, the basics of picture fuzzy sets are given. Then the proposed methodology and its application for evaluation of gastronomy plates in Sect. 3. And finally Sect. 4 is presented the conclusion of the study including future research suggestions.

2 Picture Fuzzy Sets Picture fuzzy sets are direct extensions of fuzzy sets and intuitonistic fuzzy sets. When intuitionistic fuzzy sets give a degree of membership and a degree of non-membership

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153

in a given set, Picture fuzzy sets give also a degree of neutral membership additionally [17]. Definition 1: A Picture fuzzy set F˜ p on a universe X is an object of the form     F˜ p = x, μA˜ p (x), vA˜ p (x), πA˜ p (x) |x ∈ X

(1)

where μA˜ p (x), vA˜ p (x) and πA˜ p (x) are the degree of membership, non-membership, and neutral of x to F˜ p , respectively. μF˜ p (x) : X → [0, 1], vF˜ p (x) : X → [0, 1], πF˜ p (x) : X → [0, 1]

(2)

μF˜ p (x), vF˜ p (x) and πF˜ p (x) satisfy the following condition: 0 ≤ μF˜ p (x) + vF˜ p (x) + πF˜ p (x) ≤ 1 ∀x ∈ X

(3)

and 1 − μF˜ p (x) + vF˜ p (x) + πF˜ p (x) is called as a refusal degree [15]. Definition 2: Basic operators of Single-valued picture fuzzy sets;   ˜p = μ˜ + μ˜ − μ˜ μ˜ ,π˜ π˜ ,v˜ v˜ F˜ p ⊕ G Fp Fp Gp Fp Gp Fp Gp Gp   ˜p = μ˜ μ˜ ,π˜ + π˜ − π˜ π˜ ,v˜ + v˜ − v˜ v˜ F˜ p ⊗ G Fp Gp Fp Fp Gp Fp Fp Gp Gp Gp  λ   , πFλ˜ , vFλ˜ for λ > 0 1 − 1 − μF˜ p λ.F˜ p = p p   λ   λ   , 1 − πF˜ p for λ > 0 F˜ pλ = μλF˜ , 1 − 1 − vF˜ p p

(4) (5) (6) (7)

Definition 3: Single-valued Picture Fuzzy Weighted

Averaging operator (PFWA) with respect to, w = (w1 , w2 , . . . . . . ., wn ); w1 ∈ (0, 1); ni=1 w1 = 1 is defined as;  PFWAw F˜ 1 , F˜ 2 , . . . . . . ., F˜ n ) = w1 F˜ 1 + w2 F˜ 2 + . . . . . . . + wn F˜ n  wi  (8) n  wi n wi n = 1 − i=1 1 − μF˜ p , i=1 v ˜ , i=1 π ˜ Fp

Fp

Definition 4: Score functions and Accuracy functions of gradation picture fuzzy numbers are defined by;    1 πF˜ 1 + 2μF˜ p − vF˜ p − s (9) Score F˜ p = 2 2   Accuracy F˜ p = μF˜ p + vF˜ p + πF˜ p (10) Note that: ˜ p if and only if F˜ p < G     ˜ p or i. Score F˜ p < Score G         ˜ p and Accuracy F˜ p < Accuracy G ˜p . ii. Score F˜ p = Score G

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3 The Proposed Methodology Using Picture Fuzzy SAW A methodology has been developed for the scoring of the food presentations by the students in a gastronomy education institution using Picture fuzzy SAW. Let S = {s1 , s2 , . . . . . . ., si } be a discrete set of the food presentations by the students, C = {C1 , C2 , . . . . . . ., Cm } be a finite set of criteria and w

j = {w1 , w2 , . . . . . . ., wn } be the weights of the criteria, provided that 0 ≤ wj ≤ 1 and nj=1 wj = 1. 3.1 Determination of the Picture Fuzzy Linguistic Scales In this study, the scales given in Table 1 were used to evaluate the importance of the criteria and the alternatives. Table 1. Picture fuzzy linguistic scales [18]. Picture fuzzy value (μ, π, v)

Linguistic terms for alternative evaluation

Linguistic terms for criteria evaluation

Very High Success (VHS)

Very High Importance (VHI) (0.9, 0, 0.05)

High Success (HS)

High Importance (HI)

(0.75, 0.05, 0.1)

Slightly More Success (SMS)

Slightly More Importance (SMI)

(0.6, 0, 0.3)

Equally Success (ES)

Equally Importance (EI)

(0.5, 0.1, 0.4)

Slightly Low Success (SLS)

Slightly Low Importance (SLI)

(0.3, 0, 0.6)

3.2 Specifying the Importance of the Experts Various methods can be used to determine expert weights. There are 6 experts for evaluation in this study. Two of the experts are the instructors of the course in which the students are scored, while the others are the instructors of different culinary courses. The weight of the lecturers was accepted as twice the weight of the other lecturers. Accordingly, the weights of these experts are determined as 0.125, 0.25, 0.125, 0.125, 0.125 and 0.25 respectively. 3.3 Specifying the Criteria and Determination of the Importance In this study, 4 criteria given in Table 2 were determined for evaluation. The experts evaluated the criteria using the linguistic terms in Table 1. The judgments presented for the weights of the criteria are combined with Eq. (8) using the importance weights of the experts, then the results are defuzzified by Eq. (9), and finally normalized, provided

that nj=1 wj = 1.

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155

Table 2. Picture fuzzy linguistic evaluations. Criteria

E1

E2

E3

E4

E5

E6

C1 - Visuality

HI

HI

HI

HI

SMI

HI

C2 - Creativity of the name

HI

SMI

SMI

EI

EI

SMI

C2 - Taste

VHI

VHI

VHI

VHI

VHI

VHI

C4 - Fusion balance

EI

SMI

HI

SMI

SLI

SMI

3.4 Evaluation of the Alternatives Under the Criteria Each expert fills in the decision matrix based on the linguistic terms given in Table 1. ⎛

Mi×n

⎜ ⎜ ⎜ =⎜ ⎜ ⎜ ⎝

(μ11 , π11 , v11 ) (μ12 , π12 , v12 ) . . . (μ1n , π1n , v1n ) (μ21 , π11 , v11 ) (μ22 , π22 , v22 ) . . . (μ2n , π2n , v2n ) .. .. .. . . ... . .. .. .. . . ... . (μi1 , πi1 , vi1 ) (μi2 , πi2 , vi2 ) . . . (μin , πin , vin )

⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠

(11)

3.5 Aggregation of the Experts’ Judgments Using PFWA Operator The evaluations of the experts on the alternatives are aggregated using Eq. (8), taking into account the importance weights of the experts. Thus, the judgments of all experts are transferred to a single decision matrix. 3.6 Calculation of the Picture Fuzzy SAW Values of the Alternatives Picture fuzzy SAW values of the alternatives are calculated using the aggregated values of the alternatives under different criteria and the importance weights of the criteria by utilizing Eq. (12). PFSAWi =

n 

x˜ ij ∗ w˜ j ∀i

(12)

j=1

3.7 Determination of the Scores of the Alternatives Employing of the PFSAW values of the alternatives utilizing Eq. (9), the score function values of the alternatives are determined and the final relative grading of the alternatives is performed.

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4 Application In this study, a multi-criteria evaluation methodology was developed by using the Picture fuzzy SAW method for grading the food presentations by the students within the scope of the final exam of the Korean Cuisine course of a gastronomy institution that provides education at the undergraduate level. Students’ food presentations are the considered alternatives in this MCDM problem, and the evaluation criteria were determined by the lecturers of the course as “visuality, the creativity of the name taste perception and the fusion balance”. The number of considered food presentations is 20 and there are 6 experts, 2 of which are this course’s lecturers and 4 lecturers who instruct other culinary practice courses in the faculty. In Fig. 1, two examples for considered food presentation are illustrated. The importance weight of the lecturers of the Korean Cuisine course was accepted as twice the weight of the other experts. Accordingly, the importance weights of these experts are determined as 0.125, 0.25, 0.125, 0.125, 0.125 and 0.25 respectively.

Fig. 1. The name of the dessert seen in the left is “Chingu”. Chingu means friend in Korean. Patjook, a Korean dessert, is filled with tas kadayif to create a fusion meal. In the middle, the name of the dish is “Bulgogi with Begendi”. The bulgogi, made of Korean marinated meat, is served on a bed of “fidget”, which has an important place in Turkish cuisine. And the name of the plate in the right side is “Pazıbap”. In this dish, the ingredients of Kimbap, which is frequently consumed in Korean cuisine, are wrapped in chard leaves instead of leaf seaweed.

Through the linguistic expressions given in Table 1, the lecturers evaluated the weights of the criteria and the food presentations of the students. All assessments related to criteria are given in Table 3. Table 3. Determination of the importance weights of the criteria. Criteria

Aggregated values for criteria (μ, π, v)

Score function values

Normalized weights

C1 - Visuality

(0.734, 0.043, 0.127)

1.159

0.266

C2 - Creativity of the name

(0.584, 0.019, 0.339)

0.909

0.209

C3 - Taste

(0.9, 0,0 0.05)

1.375

0.316

C4 - Fusion balance

(0.584, 0.019, 0.339)

0.909

0.209

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157

Then the assessments for all food presentations are gathered from the lecturers with respect to the criteria, based on the linguistic terms given Table 1. The aggregated decision matrix is determined for all alternatives utilizing the Eq. (8). In Table 4, the evaluations and the aggregated fuzzy values related to alternative s1 are given. Table 4. Assessments for the Alternative s1 . Criteria

E1

E2

E3

E4

E5

E6

Aggregated values (μ, π, v)

C1

VS

SMS

SMS

VS

SMS

SMS

(0.644, 0.012, 0.254)

C2

VS

SMS

VHS

ES

VHS

VS

(0.756, 0.031, 0.185)

C3

VS

VHS

VS

VS

VHS

VS

(0.822, 0,031 0.081)

C4

VS

VS

VS

VHS

VHS

VS

(0.801, 0.037, 0.087)

After obtaining the Picture Fuzzy SAW values for each alternative utilizing Eq. (11), the following Table 5 for the result of the analysis is obtained through the score function given in Eq. (9). Table 5. Results of the analysis. Student

PFWA result

Scoring

Student

PFWA result

S1

1.298

88.8

S11

1.200

Scoring 82.1

S2

1.388

95.0

S12

1.364

93.4

S3

1.324

90.6

S13

1.150

78.7

S4

1.218

83.4

S14

1.382

94.6

S5

1.234

84.5

S15

1.391

95.2

S6

1.410

96.5

S16

1.203

82.3

S7

1.153

78.9

S17

1.189

81.4

S8

1.222

83.7

S18

1.352

92.5

S9

1.227

84.0

S19

1.461

100.0

S10

1.338

91.6

S20

1.209

82.7

5 Conclusion This study provides a comprehensive methodology that can be used in many unique MCDM problems that require quantitative evaluation of food presentations under different criteria. The evaluation criteria used in the study are used by the juries in many cooking competitions and course exams in the field of gastronomy. Within the scope of the study, the plates presented by the gastronomy students for the exam of the Korean

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Cuisine course were evaluated under the evaluations that are frequently used in the evaluation of food presentations. The study findings were the final grades of the students. With the fuzzy approach, the evaluation of the students was done fairly. However, there is no analysis in the literature and practical application for the quantification of these evaluations. Picture fuzzy sets, are more effective than other fuzzy sets in uncertain or neutral situations of evaluations. They better represent the uncertainty in expert judgments through a larger preference domain about the membership, non-membership, and hesitancy. SAW method, offers an MCDM environment that is simple and practical to implement, easily understood by experts, and has a structure similar to real life problems. In future studies, the proposed evaluation methodology can be used in many real-life evaluations such as exams of applied courses in the field of gastronomy, and will also make great contributions to the evaluation of cooking competitions held around the world. The developed methodology can also be expanded with different fuzzy extensions to capture the uncertainty in expert judgments more effectively.

References 1. Duong, T.T.T., Thao, N.X.: A novel dissimilarity measure on picture fuzzy sets and its application in multi-criteria decision making. Soft. Comput. 25(1), 15–25 (2020). https://doi.org/ 10.1007/s00500-020-05405-6 2. Afshari, A.R., Yusuff, R., Derayatifar, A.R.: Project manager selection by using fuzzy simple additive weighting method. In: 2012 International Conference on Innovation Management and Technology Research. IEEE (2012) 3. Wu, Y., Xu, C., Zhang, T.: Evaluation of renewable power sources using a fuzzy MCDM based on cumulative prospect theory: a case in China. Energy 1471227–1239 (2018) 4. Kabassi, K., KarydisA, C.: Botonis: Ahp, fuzzy saw, and fuzzy wpm for the evaluation of cultural websites. Multimodal Technol. Interact. 4(1), 5 (2020) 5. Sagar, M.K., JayaswalK, P.: Kushwah: exploring fuzzy SAW method for maintenance strategy selection problem of material handling equipment. Int. J. Curr. Eng. Technol. 3(2), 600–605 (2013) 6. Ajay, D., ManivelJ, M.: Aldring: neutrosophic fuzzy SAW method and it’s application. Int. J. Anal. Exp. Modal Anal. 11(8), 881–887 (2019) 7. Kutlu Gündo˘gdu, F.M.: Yörüko˘glu: decision making with spherical fuzzy sets. In: Decision Making with Spherical Fuzzy Sets, pp. 241–258. Springer (2021) 8. Gundo˘gdu, F.K., Bolturk, E.: Simple additive weighting and weighted product methods using picture fuzzy sets. In: Kahraman, C., Onar, S.C., Oztaysi, B., Sari, I.U., Cebi, A.S., Tolga, C. (eds.) Intelligent and Fuzzy Techniques: Smart and Innovative Solutions: Proceedings of the INFUS 2020 Conference, Istanbul, Turkey, July 21-23, 2020, pp. 110–117. Springer International Publishing, Cham (2021). https://doi.org/10.1007/978-3-030-51156-2_14 9. Kaur, P., Kumar, S.: An ˙Intuitionistic Fuzzy Simple Additive Weighting (IFSAW) Method for Selection of Vendor. Xiang Li 31 (2012) 10. Roszkowska, E., Kacprzak, D.: The fuzzy SAW and fuzzy TOPSIS procedures based on ordered fuzzy numbers. Inf. Sci. 369564–584 (2016) 11. Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965). https://doi.org/10.1016/S00199958(65)90241-X 12. Atanassov, K.: Intuitionistic fuzzy sets. Int. J. Bioautomation 201 (2016) 13. Torra, V.: Hesitant fuzzy sets. Int. J. Intell. Syst. 25(6), 529–539 (2010)

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14. Yager, R.R.: Pythagorean fuzzy subsets. In: 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS). IEEE (2013) 15. Cuong, B.C.V.: Kreinovich: picture fuzzy sets. J. Comput. Sci. Cybern. 30(4), 409–420 (2014) 16. Akram, M., Shabir, M.: Complex T-spherical fuzzy N-soft sets. In: International Conference on Intelligent and Fuzzy Systems. Springer (2021) 17. Cuong, B.C., Kreinovich, V.: Picture fuzzy sets-a new concept for computational intelligence problems. In: 2013 third world congress on information and communication technologies (WICT 2013). IEEE (2013) 18. Meksavang, P., Shi, H., Lin, S.-M., Liu, H.-C.: An extended picture fuzzy VIKOR approach for sustainable supplier management and its application in the beef industry. Symmetry 11(4), 468 (2019). https://doi.org/10.3390/sym11040468

A Proposed Methodology for Risk Classification Using Fuzzy Group Decision Making and Fuzzy C-Means Fatih Yi˘git(B)

and ˙Ilknur Dönmez

Istanbul Arel University, 34537 ˙Istanbul, Turkey {fatihyigit,ilknurdonmez}@arel.edu.tr

Abstract. Clean production and resource efficiency are two major concerns of contemporary manufacturing processes. The main reason is that the resources and environment are significant concerns for the future. The study proposes the assessment of risks in a butchery unit in a major retail company. The regular assessment using impact and probability requires concrete input from the relevant expert. The possible impact and probability are challenging to measure because of their vagueness in nature. The proposed study uses the aggregation of fuzzy opinions under group decisions to assess the impact and probability of each risk in the butchery unit for the first phase. The outputs of the first phase are the impact and probability values for each risk based on group decisions under fuzzy logic. The second phase involves converting global risk values to classified risk groups. In our study, Fuzzy-C-Means will be used to classify risks based on their importance to 3 groups. By applying classification, the responsible for the relevant actions can take preventive actions for the risks that deserve the most attention. The proposed methodology is applied to a real data set of risk analysis. Results of the research demonstrate that the use of fuzzy logic in the assessment of risk analysis shows a promising approach and is accepted as an improvement over the existing practice to define the risk and classify it. Keywords: Risk analysis · Group decision making · Fuzzy c-means clustering · Risk classification · Fuzzy logic

1 Introduction In an organization, there are different kinds of risk factors. Assessment of risks is one of the critical issues. The risk may be in every choice. In an organization, there are different kinds of risk factors. Assessment of risks is one of the critical issues. The risk may occur in every area like supplier, product, recommendation system, management techniques, investment, human resources, and project team. Fuzzy group decision-making is a new way of using fuzzy collaborative intelligence to make decisions. The principle of fuzzy collaborative intelligence is to look at an issue from several angles to ensure that no critical components of the problem are overlooked. Some decision-makers from varied backgrounds seek optimum choice cooperatively in a fuzzy group decision-making system [1]. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 160–167, 2022. https://doi.org/10.1007/978-3-031-09173-5_21

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In our study, the fuzzy group decision making method is applied to a real business case. Due to the nature of the problem, the decision making is complex. The proposed study covers a two-phase, fuzzy decision making and clustering approach. The goal is to classify risks based on experts’ opinions. The organization of the paper is as follows: In Sect. 2, a literature review is given for fuzzy decision making, risk analysis, and c-means clustering. In Sect. 3, the two-phase approach used for the study is explained in detail. In Sect. 4, a numerical study of a real business case. The last section covers the conclusion of the study representing the outcomes, areas for further research and drawbacks of the study.

2 Literature Review Incorporating environmental variables into traditional supplier selection methods is critical for organizations looking to encourage green supply chain management. In a study, fuzzy group decision-making methods are applied to green supplier selection [2]. In other studies, in 2018, fuzzy group decision making is applied to influence aware recommendations [3], prototype design selection [4], and sustainable-supplier selection [5]. In a multi-criteria fuzzy group decision-making study, classes of fuzzy soft β-coveringsbased fuzzy rough sets are used [6]. A modified fuzzy group decision-making approach is utilized to risk assessment of cost-overrun in power plant projects [7]. Experts using the modified method evaluate risks using the most widely used probability-impact (P-I) approach [8]. To determine the critical units in different project phases by assessing the risk detection level using work breakdown structure (WBS). The method also assesses experts’ ability to make judgments based on their professional competence [9]. It evaluates individual risks and those proven to improve decisionmaking reliability [10]. In a study in 2021, strategic mapping of green nuclear energy investments was done using a group decision-making approach with spherical fuzzy sets [11]. In another study in 2021, two-phase multi-criteria fuzzy group decision-making techniques are applied for supplier evaluation [12]. In the same year, the Pythagorean fuzzy group decision model selects the clean energy investment projects [13]. Fuzzy c-means clustering (FCM) is another important application field of fuzzy methods. FCM algorithm is one of the most widely used Fuzzy clustering algorithms developed by J. C. Dunn in 1973 [14] and improved by J. C. Bezdek in 1981 [15]. The centroid of a cluster in fuzzy c-means is the mean of all points weighted by their degree of cluster membership. Because of its success to improve the accuracy of clustering under noise [16], It is widely used in bioinformatics [17, 18], image analysis [19, 20], and other fields like clustering the risk characteristics [21], fire danger segmentation [22]. After determining the risk factor values using fuzzy group decision-making application, our study categorized these risk factor values using fuzzy c-means clustering.

3 Method The goal of the study is to cluster risks associated with a butcher shop. The study is proposed as a part of the existing task associated with the quality department. The motivation of the study is to propose a combined fuzzy approach to the problem. The

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approach involves multiple phases, and each phase is given in the following subsections. The first phase involves fuzzy opinions under group decision making, and details of the method are given in Sect. 3.1. 3.1 Group Decision Making In complex environments involving multiple disciplines and opinions, it is essential to combine different opinions efficiently and fairly. The study involved fuzzy opinions under group decision-making in the first phase to apply this approach. Hsu and Chen [23] propose the approach. The authors underlined the importance of aggregating the estimated ratings to a common opinion in the mentioned study. The study proposed a similarity aggregation method (SAM) to combine individual subjective estimates. Subjective estimates are vital in the current decision-making study as both importance and probability are subjective values in nature. There is an inherent fuzzy nature in human decisions [24]. The existence of fuzziness is also a principle that lies behind fuzzy logic. An aggregation procedure is applied to apply fuzzy sets in group decision-making. The proposed model is developed using the aggregation method. The details of the approach are given as follows [25]. Step 1. Suppose different opinions are shown as where n is the number of experts. The where i, j < n and i = j. The proportion agreement degree is represented with of the consistent area to the total area represents the agreement degree. The minimum area represents the intersection of two fuzzy sets, and the maximum area represents the union of different fuzzy sets. Equation (1) represents the agreement degree. (1) is also called as similarity measure function [26]. The number of crosscomparisons increases with the increased number of experts. Step 2. The agreement degrees between two experts will be used for the agreement matrix (AM) [23].    1 S12 . . . S1j . . . S1n    .. .. ..   .. ..  . . . . .    AM =  Si2 Si2 . . . Sij . . . Sin   . . .. .. ..   .. .. . . .   S S ... S ... 1  n1

n2

nj

where , if i = j and Sij = 1, if i = j. Based on AM, average agreement degree of expert is calculated according to Eq. (2). A(Ei ) =

1 n Sij where i = j j=1 n−1

(2)

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The number of agreement degrees of experts will be equal to the number of experts. The relative degree of experts is calculated according to Eq. (3), ensuring that the total relative degree of experts will be equal to 1. The relative degree of expert (RADi ) will be Eq. (3). A(Ei ) i = (1, 2, . . . n) RADi = n i=1 A(Ei )

(3)

In some cases, the importance of different experts can be categorized differently. In our case, the weights are equal. The experience and position of the experts are similar. The method proposed by Hsu and Chen [23] also represents a lack of weight in fuzzy group decision making. Step 3. The study uses trapezoidal fuzzy numbers as the outputs of group decision making. The output of the first phase will be global rankings of each risk. The output of the global rating will be calculated according to the multiplication of Impact (IMx ) and Probability (PRx ). x represents the set of risks, and s is the number of real risks. Equation (4) represents the calculation of Global Rating (GRx ). GRx = IMx ∗ PRx where x = 1, 2, . . . s

(4)

3.2 Fuzzy C-Means The global rating and the degree of each risk in terms of impact and probability are the results of the first phase. Clustering the risks are vital to accurately focusing on the most critical risks. There are different methods used for clustering. K-Means, Fuzzy C-Means, and Self-Organizing Map are just a few examples. The output of Fuzzy C-Means is the membership values of clusters for each member. The membership functions are vital as membership in a single cluster is not mandatory. As a result, transfer between different clusters is possible. The second phase involves clustering by using fuzzy c-means. The detail of the method is given below. Fuzzy C-Means clustering is a type of soft clustering. Rather than placing each data point into a specific cluster, a probability of that point being in that cluster is assigned. The Fuzzy c-means clustering technique takes a step-by-step approach: Step 1 Randomly select c cluster centers as vj . Step 2 Repeat. I. Assign the data point to clusters with a probability, so calculate the fuzzy membership function µij for each data in a cluster vj II. Compute the new centroids for vj for each cluster Step 3 Until stopping criteria are achieved. The membership of ith data to the jth cluster center is denoted by µij , and the jth cluster center is denoted by vj ; the Formulation of the membership function is seen in Eq. (5). Here, c is for the number of cluster centers, and m is for the fuzziness index

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between 1 and infinity. The Euclidean distance between ith data and the jth cluster center is denoted by dij seen in Eq. (6). µij =

c k=1

1   dij dik

2 m−1

d ij = |xi − vj |; d ik = |xi − vk |

(5)

(6)

In each iteration, for finding the new centroids of each cluster, sum of all the weighted values over the sum of data is utilized as seen in Eq. (7). Iteration will stop when the membership values of the data for the clusters do not change or small enough through kth and k + 1th iteration. The stop criteria is seen in Eq. (8). n m j=1 (µij ) xi vj = n (7) m j=1 (µij )     (8) ε > maxij µijk+1 − µkij  Unlike the k-Means algorithm and many other classical algorithms, where data points can only belong to one cluster, the fuzzy c-means algorithm allows data points to belong to multiple clusters with a likelihood. For overlapped data sets, fuzzy c-means clustering produces better results. Due to these advantages, fuzzy c-means are chosen for clustering.

4 Numerical Study According to their importance, risk analysis and classification are vital for using resources efficiently. The efforts and resources such as capital, time, attention, and human resources should be directed to the most critical risks, which have the highest impact and probability. Risk classification is a significant problem in some retail companies. The company sells multiple products, but food products possess the highest risks according to their experience. The study revealed 201 different risks involved with the butchery section. They all have different impacts and probabilities. To use different opinions, three experts are chosen from the quality department to share their opinions regarding the impact and probability of each risk. Due to their experience of more than 10 years, the weight of each expert is considered equal. Their consent to the study is asked via an email representing the scope of the study and possible application areas and benefits. Their consent is required for the application. After receiving the consent, an Excel file is shared representing the trapezoidal fuzzy opinions using the Likert Scale with nine values. Using nine instead of five values increases the possibility of having 81 options compared to 25 values. The linguistic variables used for inputs are given in Table 1.

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The rest of the calculations are performed using Matlab. Excel file is used as the database of the expert opinions. Based on the mentioned outputs, clustering is performed. Clustering is performed using impact and probability as separate values for each risk. Fuzzy C-Means is performed using the existing function in Matlab and run 1000 times to validate the consistency among each run. The average values and standard deviation of the clustering application are given in Table 2. Table 1. Linguistic variables. Linguistic variables

Trapezoidal fuzzy number

Extremely low (EL)

(0, 1, 2, 3)

Very low (VL)

(1, 2, 3, 4)

Low (L)

(2, 3, 4, 5)

Medium low (ML)

(3, 4, 5, 6)

Medium (M)

(4, 5, 6, 7)

Medium high (MH)

(5, 6, 7, 8)

High (H)

(6, 7, 8, 9)

Very high (VH)

(7, 8, 9, 10)

Extremely high (EH)

(8, 9, 10, 10)

Table 2. Average values and standard deviations of objective function after 1000 runs Average objective

Standard deviation

183.15

0.69

The graphical representation of clusters before and after clustering is shown in Fig. 1. The summary is given in Table 3. Each cluster represents a risk classification group.

Fig. 1. Impacts and probabilities of risks and phase 3 clustering results of risks

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Number of risks

Impact center

Probability center

A B

32

6.00

3.55

133

7.60

2.71

C

39

3.16

1.79

5 Conclusion Risks are essential from both business and societal perspectives. Assessment of risks in a process is the first and most crucial step in preventing risky incidents. The study proposes a methodology that assesses risks and classifies them according to their impact and probability. The first step of the study involves the aggregation of fuzzy opinions under group decision-making based on perceived impact and probability. The second phase involves clustering the risks using FCM; the inputs are the outputs of the first phase. The outputs of the whole application are membership values of each risk per cluster. The clusters are performed based on the maximum membership value. The numerical study is performed in the butchery shop of a well-known company. Three experts’ opinions on risk items are collected, and clustering is performed with the real dataset of risks. The results indicate that the clusters will allow the decisionmakers to focus on the critical aspects. To the best of our literature analysis, there is no study of opinions aggregation and clustering, which are fuzzy in risk analysis. An increased number of experts may contribute to the outcomes of further research. The main areas that need further analysis are crisp values instead of fuzzy numbers. They may be beneficial to reduce the complexity of the proposed model.

References 1. Chen, T.-C.: Fuzzy group decision-making methods. In: Advances in Fuzzy Group Decision Making. SAST, pp. 11–27. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-862 08-4_2 2. Banaeian, N., Mobli, H., Fahimnia, B., Nielsen, I.E., Omid, M.: Green supplier selection using fuzzy group decision making methods: a case study from the agri-food industry. Comput. Oper. Res. 89, 337–347 (2018) 3. Capuano, N., Chiclana, F., Herrera-Viedma, E., Fujita, H., Loia, V.: Fuzzy group decision making for influence-aware recommendations. Comput. Hum. Behav. 101, 371–379 (2019) 4. Maghsoodi, A.I., Mosavat, M., Hafezalkotob, A., Hafezalkotob, A.: Hybrid hierarchical fuzzy group decision-making based on information axioms and BWM: prototype design selection. Comput. Ind. Eng. 127, 788–804 (2018) 5. Foroozesh, N., Tavakkoli-Moghaddam, R., Meysam Mousavi, S.: Sustainable-supplier selection for manufacturing services: a failure mode and effects analysis model based on intervalvalued fuzzy group decision-making. The Int. J. Adv. Manuf. Technol. 95(9–12), 3609–3629 (2017) 6. Zhang, L., Zhan, J., Alcantud, J.C.R.: Novel classes of fuzzy soft β-coverings-based fuzzy rough sets with applications to multi-criteria fuzzy group decision making. Soft. Comput. 23(14), 5327–5351 (2019)

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7. Islam, M.S., Nepal, M.P., Skitmore, M.: Modified fuzzy group decision-making approach to cost overrun risk assessment of power plant projects. J. Constr. Eng. Manag. 145(2), 04018126 (2019) 8. Taroun, A.: Towards a better modelling and assessment of construction risk: insights from a literature review. Int. J. Project Manag. 32(1), 101–115 (2014) 9. Jung, J.H., Kim, D.Y., Lee, H.K.: The computer-based contingency estimation through analysis cost overrun risk of public construction project. KSCE J. Civ. Eng. 20(4), 1119–1130 (2016) 10. Kabir, G., Sadiq, R., Tesfamariam, S.: A fuzzy Bayesian belief network for safety assessment of oil and gas pipelines. Struct. Infrastruct. Eng. 12(8), 874–889 (2016) 11. Yuan, G., Xie, F., Dinçer, H., Yüksel, S.: The theory of inventive problem solving (TRIZ)based strategic mapping of green nuclear energy investments with spherical fuzzy group decision-making approach. Int. J. Energy Res. 45(8), 12284–12300 (2021) 12. Bera, A.K., Jana, D.K., Banerjee, D., Nandy, T.: A two-phase multi-criteria fuzzy group decision making approach for supplier evaluation and order allocation considering multiobjective, multi-product and multi-period. Ann. Data Sci. 8(3), 577–601 (2021) 13. Meng, Y., Haoyue, W., Zhao, W., Chen, W., Dinçer, H., Yüksel, S.: A hybrid heterogeneous Pythagorean fuzzy group decision modelling for crowdfunding development process pathways of fintech-based clean energy investment projects. Finan. Innovation 7(1), 1–34 (2021) 14. Dunn, J.C.: A fuzzy relative of the ISODATA process and its use in detecting compact wellseparated clusters. J. Cybern. 3(3), 32–57 (1973) 15. Wenlong, W., Keller, J.M., Dale, J.., Bezdek, J.C.: StreamSoNG: a soft streaming classification approach. IEEE Trans. Emerg. Top. Comput. Intell. 6(3), 700–709 (2022) 16. Proença, H.: Fast and globally convex multiphase active contours for brain MRI segmentation. Comput. Vis. Image Underst. 125, 237–250 (2014) 17. Pravin Kumar, S.K., Sumithra, M.G., Saranya, N.: Artificial bee colony-based fuzzy c means (ABC-FCM) segmentation algorithm and dimensionality reduction for leaf disease detection in bioinformatics. J. Supercomput. 75(12), 8293–8311 (2019) 18. Al-Janabee, O., Al-Sarray, B.: Fuzzy C means based evaluation algorithms for cancer gene expression data clustering. Iraqi J. For Comput. Sci. Math. 3(2), 27–41 (2022) 19. Xu, R.: Fuzzy C-means Clustering Image Segmentation Algorithm Based on Hidden Markov Model. Mob. Netw. Appl. (2022). https://doi.org/10.1007/s11036-022-01917-7 20. Zhang, M., Zhu, L., Sun, Y., Niu, D., Liu, J.: Computed tomography of ground glass nodule image based on fuzzy C-means clustering algorithm to predict invasion of pulmonary adenocarcinoma. J. Radiat. Res. Appl. Sci. 15(1), 152–158 (2022) 21. Xiao, T., Zhang, T., Zhang, N.: Research on energy supply chain risk prediction based on the fuzzy C-means clustering algorithm. Int. J. Global Energy Issues 44(1), 65–75 (2022) 22. Júnior, J.S.S., Paulo, J.R., Mendes, J., Alves, D., Ribeiro, L.M., Viegas, C.: Automatic forest fire danger rating calibration: exploring clustering techniques for regionally customizable fire danger classification. Expert Syst. Appl. 193, 116380 (2022) 23. Hsu, H.M., Chen, C.T.: Aggregation of fuzzy opinions under group decision making. Fuzzy Sets Syst. 79(3), 279–285 (1996) 24. Zadeh, L.A.: Fuzzy algorithms. Inform. Control 8, 338–353 (1965) 25. Chen, B.T., Chen, Y.S., Hsua, W.H.: Performance evaluation of a parameterized fuzzy processor (PFP). Fuzzy Sets Syst. 81(3), 293–309 (1996) 26. Bezdek, J.C., Ehrlich, R., Full, W.: FCM: the fuzzy c-means clustering algorithm. Comput. Geosci. 10(2–3), 191–203 (1984)

Prediction of the Annual Yield of Citrus Growth in the Guzelyurt District Using Fuzzy Inference Systems Filiz Al-Shanableh(B) Near East University, via Mersin 10, 99138 Nicosia, North Cyprus, Turkey [email protected]

Abstract. In this study, the annual revenue estimation that can be obtained from citrus fruits grown in the Guzelyurt region is modeled based on weather conditions using the Multiple Input and Single Output Fuzzy Interference System (MISOFIS). The average temperature, average rainfall, and average relative humidity in the Guzelyurt district were chosen as input parameters and citrus fruits yield was selected as the output parameter. The data obtained that belonged 1980–2019 period were used to construct a MISOFIS model. Within 40 input/output data sets, the last five years were utilized for testing. The citrus yield estimated by the proposed MISOFIS model and its compliance with the actual values can be understood from the fact that R2 is equal to 0.913. The results showed that modeling with MISOFIS is an easy and effective method for predicting citrus fruit yield if the input parameters and rules generated were chosen appropriately. Keywords: Fuzzy inference systems · Yield prediction · Citrus fruits

1 Introduction Citrus fruits are playing the most important role in total agricultural production and export items in the Northern Cyprus economy. Approximately 37% of the Northern Cyprus lands are used in the agriculture sector and approximately 40% of this belongs to citrus cultivation. Fruits and vegetables such as citrus fruits, barley, wheat, olives, olive oil, and potatoes are grown in the country. Citrus cultivation including oranges, mandarin, clementine, grapefruit, and lemons is 40% of the total agricultural products which has a major role in Northern Cyprus’s economy. Almost 98% of all citrus is cultivated in North Cyprus from Guzelyurt and Lefke district - West Mesaria region [1]. According to the 2019 statistics of the TRNC Ministry of Agriculture and Natural Resources, 64,784 tons of the 112,376.5 tons of citrus produced in Northern Cyprus belong to the Late-Valencia, Jaffa-Shiamouti, and Washington types of oranges, and out of this 98% coming from West Mesaria region. Factors affecting the productivity of citrus trees are irrigation, weather conditions, and soil types and conditions. The arid and semi-arid climate of Cyprus is providing optimum weather conditions for citrus growth. However, the average of 200–700 mm © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 168–176, 2022. https://doi.org/10.1007/978-3-031-09173-5_22

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of rainfall for a year in the region will create water deficiency, because at least 700 mm rainfall requirement of water plays important role in the productivity of citrus trees [2]. Accurate, early estimation of any agricultural crop yield is important due to the need for planning at the micro-level and especially in the demand for agricultural products. These forecasts alert decision-makers of possible declines in crop yields and early detection allow import and export decisions to be made on time. Crop yield estimation in many countries is based on traditional data collection techniques and yield estimation techniques based on harvesting reports. These methods usually not accurate, timeconsuming, and susceptible to large errors. Besides, they can lead to poor crop yield assessment, crop area estimates, and predicted results emerge too late to take appropriate action. Although the results were not so much supportive, many researchers have commonly used for prediction multiple linear regression, factor analysis, and principal component analysis with multiple regressions to predict the yield of different crops [3–5]. Fuzzy Inference System (FIS) is a potential soft computing modeling tool that is enable to the identification of the complex and nonlinear relationship between inputoutput data using the degrees of truth approach. FIS has been used to solve a wide variety of nonlinear problems, especially where conventional modeling methods fail [6, 7]. FIS is not the only soft computing method that could be utilized for yield prediction modeling, more recent soft computing techniques such as machine learning or deep learning algorithms are also used for modeling prediction problems. Many related publications could be found in the area of soft computing; Khoshnevisan et al., [8] used adaptive neuro-fuzzy inference systems (ANFIS) and artificial neural networks (ANN) to predict potato yield based on energy inputs. In their work ANFIS model gave better results than the ANN model due to the implementation of fuzzy rules. Pankaj [9] also performed an ANFIS-based model to predict wheat yield. Han et al., [10] used random forest models for modeling the early detection of sugarcane yield. The use of fuzzy time series for crop yield forecasting is also popular. While Sakin [11] developed fuzzy time series for rice yield prediction, Narendra et al., [12] predicted wheat yield with the same methodology. None of these soft computing methods used the Mamdani-FIS structure as a tool for predicting any crop yield. In the present study, the paper is organized as follows for predicting the annual yield of citrus fruit grown in the Guzelyurt district of Northern Cyprus. First, data sets for the total yield of Valencia, Jaffa-Shiamouti, and Washington types of oranges growth annually in West Mesaria and the weather condition of this region were collected and used as input/output data sets to construct the fuzzy logic model. Then, all data sets were fuzzified and rules were created in the FIS section using expert knowledge. When the estimated values are far from the real values, the membership functions of the FIS model have been manually adjusted to obtain fewer estimation errors. And the last section discussed the predictive capability of FIS generated.

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2 Methodology 2.1 Data Gathering For the prediction of citrus yield, historical data sets for the 1980–2019 harvesting period were collected. Data included the total amount of orange harvested and weather conditions during this period in the West Mesaria region mainly from Guzelyurt district. The average temperature, average rainfall, and average relative humidity in this region were chosen as input parameters. Three varieties of orange are grown in the region, which is added value to the Northern Cyprus economy, these are Valencia, Jaffa-Shiamouti, and Washington. The total orange yield was taken as the response value. The value range for input/output data sets within 40 years of time interval are listed in Table 1. If weather condition chosen falls within these ranges then, the FIS model proposed here could be employed to predict the annual citrus fruit yield. Table 1. Range of input/output data sets for FIS modelling.

Inputs

Output

Data description

Range

Average temperature (C)

17.0–25.0

Average rainfall (mm)

140.0–600.0

Average relative humidity (%)

55.0–80.0

Citrus yield (kg/donum)

6,000–17,000

2.2 Fuzzy Logic Modelling Fuzzy Logic establishes a relationship between input and output parameters whether they have linear or nonlinear interactions. These relationships are more functional than those evaluated by mathematical or statistical models. Fuzzy logic as a computational method provides fast and cost-effective solutions based on “degrees of truth” that is dissimilar to the usual “true or false” (1 or 0) Boolean logic. Figure 1 illustrates computational procedures of fuzzy logic modeling which has three main units; fuzzification unit, fuzzy inference system (FIS), and defuzzification unit. Conversion of crisp data set into linguistic terms using fuzzy membership functions (MFs) take place in the fuzzification section. In the FIS section which is the most important part of fuzzy logic, if-then rules are created between input and output fuzzified data. And in the last section, predicted output data convert from fuzzified to crisp data [13].

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Fig. 1. Flow chart for fuzzy logic system computational procedure.

Multi-Input Single Output Fuzzy Inference System (MISOFIS) – Mamdani [14] was constructed, trained, and tested for annual citrus fruit production from 1980 to 2019. A total of 40 data sets of regional weather conditions including average values of temperature, rainfall and relative humidity together with annual citrus yield were used to construct MISOFIS structure. MATLAB R2015a (8.5.0.197613., Mathworks Inc., Natick, USA) Fuzzy Logic Designer were used to create the FIS model. The specifications of MFs and their linguistic terms with base width boundaries were determined and summarized in Table 2. The trapezoidal MFs (trapmf) were used for all input and output variables and constructed MFs for each input/output variable are shown in Fig. 2. Intervals of base width of trapmfs were arranged so that pursuing to predict the output data with small prediction error. Table 2. Summary of fuzzification process. Input/Output

Linguistic term

Base width*

Ave. temperature (°C)

Very low

[15 17 17.9 18.3]

Low

[17.4 18 18.5 19]

Mid

[18.1 18.6 18.9 19.3]

Midhigh

[18.7 19.1 19.5 20]

Ave. rainfall (mm)

Ave. relative humidity (%)

High

[19.4 19.6 21 21.5]

Very high

[20.6 22 25 27]

Very low

[90 140 180 210]

Low

[150 200 295 350]

Moderate

[280 300 410 500]

High

[420 440 600 700]

Very low

[45 55 59 59.5]

Low

[56 60 65 65.5]

Mid

[64.5 66 69 69.5] (continued)

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F. Al-Shanableh Table 2. (continued)

Input/Output

Citrus yield (kg/donum)

Linguistic term

Base width*

High

[68 70 73 75]

Very high

[71 74 78 82]

Very low

[5000 6500 7900 8500]

Low

[7500 8100 9700 10500]

Mid

[9500 1000 11700 12500]

High

[11000 12000 13800 14500]

Very high

[13500 14000 16900 18000]

* Fuzzy trapezoidal MFs (trapmf) for all parameters.

Fig. 2. The fuzzy MFs for three inputs; (a) average temperature, (b) average rainfall, (c) average relative humidity, and an output; (d) annual citrus yield.

The next step was to generate if-then rules between the fuzzified input/output data sets. Out of 40 input/output data sets, 35 of them were used for creating rules of the FIS, and the remaining 5 data sets were used to test the prediction capabilities of the FIS developed. Because some of the generated rules had the same inputs but different outputs, the ranges of fuzzy sets have been edited several times to achieve small prediction errors. A total of 32 rules were hired in the MATLAB Fuzzy Logic Designer rule editor, Fig. 3 shows a part of generated rules. The last step was defuzzification in which fuzzified output data was converted into crisp data by applying the center of area method to the rules generated. Predicted citrus yields were obtained by providing input data sets to MATLAB Fuzzy Logic Designer rule reviewer section and this is illustrated in Fig. 4 for data set no. 40. Data set no. 40 is one of the test data sets, belongs to the year 2019, taking average temperature as 19.7 °C, average rainfall as 465.4 mm and average relative humidity as 62.6% annual citrus yield predicted as 11,000 kg/donum for which the actual

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value was 10,736 kg/donum. For each data sets, input values were entered individually and the predicted results were obtained.

Fig. 3. Examples of rules generated for the prediction of citrus fruits yield.

The coefficient of determination (R2 ) and root mean square error (RMSE) had been calculated to define the accuracy and predictive capability of FIS generated as follows: n (yact,i − yp,i )2 R2 = 1 − n i=1 (1) 2 i=1 (yp,i − yact,ave )  n RMSE = 1n (yact,i − ypt,i )2 (2) i=1

Fig. 4. Evaluation of output-citrus yield from generated rules.

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F. Al-Shanableh

3 Results and Discussions MISOFIS model is constructed to predict the annual yield of citrus fruit in Guzelyurt district of Northern Cyprus. The model was trained using 35 historical data sets belonging to the 1980–2014 interval and tested using 5 data sets covering the last five years 2015– 2019. 32 rules were created in the FIS section and using these rules citrus yields were predicted for training and testing data sets. Table 3 shows input/output variables of testing data sets with their fuzzified values in parenthesis, citrus yield predicted, and applied rule(s). Since rules were created only for training data sets, the results for the test phase were impressive with a closer prediction of actual values. Table 3. Predicted citrus yield and rules fired for testing data sets. Year

Temp (°C)

Rainfall (mm)

R. humidity (%)

Actual citrus yield (kg/donum)

Predicted citrus yield (kg/donum)

Rules fired

2015

19.3 (midhigh)

357.2 (moderate)

61.4 (low)

9,368 (low)

10,100 (mid)

R2-R13-R25

2016

19.9 (high)

282.9 (low)

58.5 (very low)

7,819 (very low)

8,060 (very low)

R5-R26

2017

19.4 (midhigh)

146.6 (low)

60.7 (very low)

9,192 (low)

8,950 (low)

R31

2018

20.1 (high)

405.8 (moderate)

57.2 (very low)

8,441 (low)

8,950 (low)

R26-R28-R29

2019

19.7 (high)

465.4 (high)

62.6 (low)

10,736 (mid)

11,000 (mid)

R25-R29-R30

The prediction capability of the FIS model developed is illustrated in Fig. 5. The prediction error was obtained for data set no. 8 with 2273 kg/donum was the highest. Prediction error of data set no. 14 and no.23 were obtained as 1216 and 2130, respectively, those were also relatively high. The reason for the high prediction error was due to different input variables but similar corresponding output values. R2 and RMSE of the proposed FIS model for citrus yield prediction were found as 0.915 and 29.11 for the training phase and 0.899 and 46.94 for the testing phase, respectively. These results showed that FIS rules were appropriately generated and implemented.

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Fig. 5. Comparison of citrus yield values of the proposed FIS with actual counterparts.

4 Conclusions A FIS model for predicting the annual yield of citrus fruit grown in the Guzelyurt district of Northern Cyprus was created and implemented. Although, there are many factors affecting the growth yield and production yield of citrus fruits such as irrigation, soil types, and its conditions, easily obtainable statistical weather conditions of the region were used to construct the fuzzy logic model. Each data set has its own characteristic and relations between input and output parameters are highly nonlinear, so they cannot be formulated in a mathematical or statistical approach. Within 40 historical and meteorological input/output data sets, 35 of them were used to construct the FIS model, and 32 rules were generated. The last five years were utilized for testing using those rules. The citrus yield estimated by the proposed MISOFIS model and its compliance with the actual values can be understood from the fact that R2 is equal to 0.913. The results showed that modeling with MISOFIS is an easy and effective method for predicting citrus fruit yield if the input parameters and rules generated were chosen appropriately. For future work, it would be possible to construct yield prediction models for citrus fruits individually as Yafa, Valencia, and Washington. Modeling for a yield of other fruits or crops grown in northern Cyprus can be implemented by supervised or non-supervised soft computing methods.

References 1. TRNC Agriculture and Natural Resources Ministry Homepage (2022). http://tarim.gov.ct.tr/ tr-tr/istatistik.aspx 2. Aydin¸sakir, K., Uluca, E., Dinç, N., Küçükco¸skun, S: ¸ Effects of different irrigation levels on fruit yield and quality of Valencia late orange under Northern Cyprus conditions. J. Agric. Sci. 27(3), 276–284 (2021) 3. Kravchenko, A.N., Bullock, D.G.: Correlation of corn and soybean grain yield with topography and soil properties. Agron. J. 92(1), 75–83 (2000) 4. Park, S.J., Hwang, C.S., Vlek, P.L.G.: Comparison of adaptive techniques to predict crop yield response under varying soil and land management conditions. Agric. Syst. 85, 59–81 (2005)

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5. Drummond, S.T., Sudduth, K.A., Joshi, A., Birrell, S.J., Kitchen, N.R.: Statistical and neural methods for site-specific yield prediction. Trans. ASAE 46(1), 5–14 (2003) 6. Al-Shanableh, F., Evcil, A., Savas, M.A.: Fuzzy logic model for prediction of cold filter plugging point of biodiesel from various feedstock. Procedia Comput. Sci. 120, 245–252 (2017) 7. Al-Shanableh, F., Bilin, M., Evcil, A., Savas, M.A.: A study of jojoba oil extraction based on a fuzzy logic model. In: 4th International Symposium on Multidisciplinary Studies and Innovative Technologies, ISMSIT 2020 - IEEE Conferences Proceedings (2020) 8. Khoshnevisan, B., Rafiee, S., Omid, M., Mousazadeh, H.: Prediction of potato yield based on energy inputs using multi-layer adaptive neuro-fuzzy inference system. Measurement 47, 521–530 (2014) 9. Pankaj, K.: Crop yield forecasting by adaptive neuro fuzzy inference system. Math. Theory Model. 11(1), 1–7 (2011) 10. Han, S.Y., Bishop, T.F.A., Filippi, P.: Data-driven, early-season forecasts of block sugarcane yield for precision agriculture. Field Crop. Res. 276, 108360 (2022) 11. Sakin, K., Kumar, N.: A novel method for rice production forecasting using fuzzy time series. Int. J. Comput. Sci. Issues 9, 455–459 (2012) 12. Narendra, K., Ahuja, S., Kumar, V., Kumar, A.: Fuzzy time series forecasting of wheat production. Int. J. Comput. Sci. Eng. 2, 635–640 (2010) 13. Al-Shanableh, F., Evcil, A.: Prediction of energy consumption of residential buildings in northern Cyprus using fuzzy interference system. Energy Buildings 256, 111555 (2022) 14. Mamdani, E.H.: Advances in the linguistic synthesis of fuzzy controllers. Int. J. Man Mach. Stud. 8(6), 669–678 (1976)

Parallel Machine Scheduling with Fuzzy Processing Times and Sequence Dependent Setup Times: An Application in a Textile Company Gülce Çini1(B)

, Ayhan Özgür Toy2

, and Önder Bulut2

1 Yasar University Graduate School, Izmir, Turkey

[email protected] 2 Industrial Engineering Department, Yasar University, Izmir, Turkey

Abstract. The textile company we consider receives orders from customers for different types of products and with different quantities. The company has several production lines as a “machine” and an order for a product type as a “job” to comply with the scheduling terminology. We assume that not all machines are suitable for processing all jobs, i.e., jobs can only be processed on their eligible machines. When there is more than one eligible machine, those machines are identical in terms of their setups and processing times. We assume that all jobs and machines are ready to be processed at time zero. We also assume that the times required to set up the machine for the next job depend on the job completed and the job in order, hence setup times are sequence-dependent. The processing time of a job is not deterministic due to various factors such as operator learning curve and fatigue, and machine maintenance requirements. Likewise, setup times also vary depending on human and technical factors. We choose to model these uncertainties by assuming fuzzy processing times and fuzzy setup times. Our objective is to assign and schedule jobs to minimize the makespan, the completion time of the last job. Our solution approach relies on the comparison of solutions through a randomized search algorithm, a Monte Carlo simulation, with an improvement routine. We conduct a numerical study and present the solution quality of the proposed methodology. Keywords: Parallel machine scheduling · Fuzzy processing times · Fuzzy setup times · Scheduling · Application in textile industry

1 Introduction and Problem Definition In this study, the production scheduling problem of a textile company is considered. The company has its own nine sewing factories and produces knitting and woven group products for the world’s leading high-segment brands in a seasonal manner. Typically, a year consists of four main seasons. For each season, brands (customers of the company) place high-volume orders to be produced. Thereafter, the company orders the required amount of fabric and accessories from its suppliers. When the fabric and accessories are © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 177–183, 2022. https://doi.org/10.1007/978-3-031-09173-5_23

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replenished, orders become ready for sewing. An order consists of different styles with different colors. Each color of a style is referred as a ‘job’. Table 1 depicts a sample order of the company where each row corresponds to a job. Table 1. Product group and order type Style Name

Color

Total Qty

Confirmed Buy date

Confirmed

Product A

Smooth Stone

7,350

11. Nov.20

3. May.21

Product A Product A

Black

18,000

11. Nov.20

3. May.21

White

18,050

11. Nov.20

2. Apr.21

Product A

Pollen

7,250

11.Nov.20

2. Apr.21

Product B

Frigid Blue

2,000

11. Nov.20

3. Mar.21

Product B

White

10,000

11. Nov.20

3. Mar.21

There are several sewing lines in each factory where each line is referred as a ‘machine’. A job can be processed at any one of the lines that are eligible to process that job. When a job is completed, the line needs to be reconfigured for the next one. Reconfiguration depends on both the finished and the next job. The company aims to schedule the jobs so that the last job will be completed as early as possible. Using the standard scheduling terminology, the problem of the company can be defined as a parallel machine scheduling problem with sequence-dependent set-up times and machine eligibility constraints to the minimization makespan. Most research on scheduling problems assumes deterministic processing and setup times [1]. However, the processing times are not deterministic due to various factors such as operator learning curve, operator fatigue, environmental conditions, material problems, machine maintenance and repair times [2]. Likewise, setup times also vary depending on human and technical factors. A preliminary study indicates that these times can be interpreted as fuzzy numbers. Therefore, we approached the problem assuming fuzzy processing times and fuzzy setup times. We assume that the machines are always available, jobs are ready, and preemption and job splitting are not allowed. In Table 2, we provide a review of the relevant parallel machine scheduling literature. Table 2. Literature review on the parallel machine scheduling. Makespan minimization

Sequence dependent set-up times

Machine eligibility

[3, 4, 11–18]

[12–15, 18]

[3, 4, 16, 17]

For the above-described problem, we develop the fuzzy mixed-integer linear programming formulation. Our solution approach relies on the comparison of solutions through a randomized search algorithm, a Monte Carlo simulation, with improvement routines. With an extensive numerical study, we assess the performance of the proposed algorithm for different problem instances.

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The remainder of the study is organized as follows: in the second section, we present the problem formulation and solution methodology, and in the third section the numerical study. We conclude our work in section four.

2 Problem Formulation and Solution Methodology 2.1 Fuzzy Processing and Sequence Dependent Set-Up Times Various definitions of fuzzy numbers are found in the literature [5–10]. In this study, we represent processing times and sequence-dependent setup times as triangular fuzzy numbers (TFN). A triangular fuzzy number A˜ can be defined by a triplet (a1 ,a2 ,a3 ) ∈ R3 such that a1 < ⎧ a2 < a3 . The membership function of A is defined as follows [10]: x−a1 ⎪ ⎨ a2 −a1 , a1 ≤ x ≤ a2 −x µA˜ (x) = aa3−a , a2 < x ≤ a3 . ⎪ ⎩ 3 2 0, otherwise P˜ i is the fuzzy processing time of job i denoted by the triplet (P1i (optimistic value), P2i (most plausible value), P3i (pessimistic value)). The fuzzy sequence-dependent setup time between job i and i is S˜ ii which is denoted by (S1ii (optimistic value), S2ii (most plausible value), S3ii (pessimistic value)). For two fuzzy numbers A˜ = (a1 ,a2 ,a3 ) and B˜ = (b1 ,b2 ,b3 ) addition operation is defined as A˜ + B˜ = (a1 + b1 ,a2 + b2 ,a3 +b3 ) [10, 19]. Fuzzy addition operation is required for our study since the completion time of any job i (˜ci ) is calculated as the summation of fuzzy processing and setup tis of all jobs that are processed before job i on the same machine. Our objective function makespan is denoted by C˜ max , which is the maximum of all c˜ i values. For the defuzzification, we employ the centroid method and hence defuzzified times are represented by a1 +a2 +a3 . 3 2.2 Fuzzy MILP Formulation In this section, we provide the fuzzy mixed integer linear programming formulation of the considered P/Mi /Cmax scheduling problem with identical parallel machines, fuzzy sequence-dependent set-up times, fuzzy processing times and machine eligibility restrictions where Mi is the index set of machines that are capable of processing job i. It is assumed that all jobs are ready, and all machines are available at time zero. In short, the problem is a fuzzy P/Mi /Cmax scheduling problem. The notation used in the fuzzy MILP model is given below: Sets and Indices. J = {1,2, . . . .,n}: set of all jobs. i, i , i : job indices, i, i , i ∈ J (job index 0 is for dummy job). M = {1,2, . . . .,m}: set of all machines. j: machine index, j ∈ M . Mi : set of machines that can process job i, Mi ⊂ M . Jj : set of jobs that can be processed by machine j, Jj ⊂ J .

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Fuzzy parameters. P˜ i : fuzzy processing time of job i. S˜ ii : fuzzy setup time when job i is the immediate successor of job i on the same machine Decision variables.  1, if job i immediately precedes of job i on machine j xii j = 0, otherwise.   1, if job i is the first job on machine j x0i j = 0, otherwise C˜ max = fuzzy makespan, the maximum completion time of all jobs. The fuzzy MILP formulation is as follows: min C˜ max . s.t.   xii j = 1 ∀i ∈ J

(1)

i∈J ,i=i j∈Mi ∩Mi





i ∈Jj

xii j ≤

i ∈Jj ,i =i

C˜ max ≥



x0i j = 1 ∀j ∈ M 

xi ij ∀i ∈ J , ∀j ∈ Mi

(2)

(3)

i ∈Jj ∪{0},i =i



(S˜ ii + P˜ i )xii j ∀j ∈ M

(4)

i ∈Jj i∈Jj ∪{0},i=i

xii j ∈ {0,1} ∀j ∈ M ,i ∈ Jj ∪ {0}, i ∈ Jj , i = i

(5)

The objective is to minimize the makespan. Constraint (1) ensures that all jobs are processed. Constraint (2) is to determine the first job of each machine. Constraint (3) indicates that for any job that is processed on any machine, there might not be a successor (if the job is the last one, then there is no successor) but there should always be a predecessor (if the job is the first one, then dummy job 0 is the predecessor). Constraint set (4) specifies that makespan is greater than equal to the completion time of all jobs assigned to any machine which is the sum of fuzzy setup and processing times of all assigned jobs. Finally, constraint (5) is to say that decision variables are binary. 2.3 Randomized Search Algorithm Since the considered P/Mi /Cmax scheduling problem is in the NP-hard class, heuristic approaches that provide near-optimal solutions in a reasonable amount of time are needed. In this study, we propose a randomized search algorithm enriched with an improvement routine. At each replication, the algorithm first randomly assigns jobs to

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the eligible machines and for each machine randomly sequences the assigned jobs. Afterwards, it identifies the machine with the longest completion time. The last job of that machine is assigned to the machine with the shortest completion time. The position to which the job to be assigned on the new machine is chosen randomly. This transfer routine is repeated until no improvement in the makespan is obtained and the best solution of this sub-routine is recorded as the solution of the current replication. This procedure is repeated until the replication counter is reached to a predetermined number, and among all replications, the solution which has the minimum makespan is reported as the best solution.

3 Numerical Study We conduct a numerical study to present the solution quality of the proposed algorithm. We generate 200 problem instances with different combinations of number of jobs (n) and number of machines (m): number of jobs can be 20, 30, 40, 50, and 60; number of machines can be 2, 4, 6, and 8; for each pair of number of jobs and number of machines 10 problems are randomly generated with different randomly generated fuzzy processing and setup times so that defuzzified representations are from Uniform(10, 80) and Uniform(20, 40), respectively. For the numerical study it is assumed that all machines are eligible to process all the jobs. For each problem instance, we run the randomized search algorithm with three different total number of replications: 103 , 104 and 105 . We also obtain the OPL CPLEX 20.1.0 solutions under 1-h time limitation. Table 3. The percentage gap between the randomized algorithm and mathematical model solutions. m/n

105 replications 20

30

40

104 replications 50

60

20

30

40

103 replications 50

60

20

30

40

50

60

2

3.51 6.32 7.09 8.49 9.04 4.18 6.99 7.62 9.27 9.65 5.22 7.79 8.23 10.1

4

3.43 4.73 5.96 6.37 6.91 4.33 5.38 6.62 6.94 7.34 5.58 6.47 7.4

8.07

6

2.31 3.03 3.82 4.86 5.49 3.47 3.98 4.36 5.62 5.89 3.96 4.7

6.38

6.96

8

2.00 2.39 2.17 3.63 3.44 2.76 3.32 2.68 4.26 4.06 4.1

4.88

5.02

Avg

2.81 4.12 4.76 5.84 6.22 3.69 4.92 5.32 6.52 6.74 4.72 5.98 6.19

7.36

7.55

G. Avg 4.75

5.44

5.45

4.97 3.7

10.04 8.19

6.36

An exhaustive search for the optimal solution requires a prohibitive long time as the number of machines and jobs increase. This confirms that the optimal solution is in the NP-hard class, and we set a time limit of 3600 s for OPL Cplex. Alternatively, we proposed the aforementioned randomized search algorithm and implemented it in C++. We compare the solutions obtained by the algorithm and the solution of the mathematical model and report the % gap between them in Table 3. Intuitively, as the number of replications increase the randomized algorithm starts performing better and in return % gap decreases in all test instances. In all test instances we observe that randomized

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algorithm never beats the mathematical model solution with the time limit, although the gap between is around 10% in the worst case. The performance of the heuristic aggravates as the number of jobs increases and the number of machines decreases. This is commensurate with the complexity of the problem, and indicates that as the number of feasible solutions increases the randomized heuristics can only search a smaller fraction of those solutions, yielding a higher deviation from the best solution by the math model. This suggests employment of smarter search algorithm instead of purely randomized algorithm. In terms of running time of the algorithm we observe that it increases both in number of jobs and in number of machines. However, the increase look like linear in number of jobs and convex in number of machines. As an illustration, consider 40 jobs case when the replication count is 105 , the run time of the algorithm are 29.47, 109.35, 141.95, and 165.23 s for m = 2, 4, 6, and 8, respectively. Consider next, the 8 machines case when the replication count is 105 , the run time of the algorithm are 49.64, 90.82, 165.23, and 253.25 s for n = 20, 30, 40, and 60, respectively. The run times are well below the 3,600 s limit of the OPL solution.

4 Conclusion In this study, we consider identical parallel machine scheduling problem with sequence dependent setup times and machine eligibility constraint for a textile company. A preliminary study indicates that processing times and setup times are far away from to be assumed deterministic. Moreover, the analysis of the system shows that both processing times and setup times can be modeled with fuzzy numbers due to problems such as various operators’ errors, problems in raw materials, and machine repairs. Hence, we develop a model a fuzzy model for the problem at hand. In order to, solve the problem in a reasonable time, we propose an algorithm assigning jobs to the machines and sequencing them for each machine in a purely randomized fashion. This is a first attempt to solve the problem through algorithms due to its NP-hard nature. We conducted a numerical study to analyze the performance of the proposed algorithm. As the benchmark solution, we used the mathematical model solution with a time limit. Considering the time required to obtain a reasonable solution our randomized algorithm is consistent and fair. However, our analysis also indicates that the algorithm should be improved by employment of new subroutines. Moreover, smart algorithms such as Genetic Algorithms, Simulated Annealing, or machine learning techniques are the solution methods we will try later. Using these methods can be useful to get better solutions.

References 1. Pinedo, M.L.: Scheduling: Theory, Algorithms, and Systems, 3rd edn. Prentice Hall, New York, NY (2008) 2. Biskup, D.: Single-machine scheduling with learning considerations. Eur. J. Oper. Res. 115, 173–178 (1999) 3. Mokotoff, E.: An exact algorithm for the identical parallel machine scheduling problem. Eur. J. Oper. Res. 152, 758–769 (2004)

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4. Su, L.-H.: Scheduling on identical parallel machines to minimize total completion time with a deadline and machine eligibility constraints. The Int. J. Adv. Manuf. Technol 40(5), 572–581 (2009) 5. Yeh, W.-C., Lai, P.-J., Lee, W.-C., Chuang, M.-C.: Parallel-machine scheduling to minimize makespan with fuzzy processing times and learning effects. Inform. Sci. 269, 142–158 (2014) 6. Peng, J., Liu, B.: Parallel machine scheduling models with fuzzy processing times. Inform. Sci. 166(1–4), 49–66 (2004) 7. Li, K., Chen, J., Hong, F., Jia, Z., Weizhong, F.: Uniform parallel machine scheduling with fuzzy processing times under resource consumption constraint. App. Soft Comput. 82, 105585 (2019) 8. Xue, F., Wansheng, T., Ruiqing, Z.: The expected value of a function of a fuzzy variable with a continuous membership function. Comput. Mathem. Appl. 55(6), 1215–1224 (2008) 9. Wang, C., Wang, D., Ip, W.H., Yuen, D.W.: The single machine ready time scheduling problem with fuzzy processing times. Fuzzy Sets Syst. 127(2), 117–129 (2002) 10. Ahmadizar, F., Hosseini, L.: Single-machine scheduling with a position-based learning effect and fuzzy processing times. The Int. J. Adv. Manuf. Technol. 56(5–8), 693–698 (2011) 11. Mokotoff, E.: An exact algorithm for the identical parallel machine scheduling problem. Eur. J. Oper. Res. 152(3), 758–769 (2004) 12. Tahar, D.N., Yalaoui, F., Chu, C., Amodeo, L.: A linear programming approach for identical parallel machine scheduling with job splitting and sequence-dependent setup times. Int. J. Prod. Econ. 99(1–2), 63–73 (2006) 13. Vallada, E., Ruiz, R.: A genetic algorithm for the unrelated parallel machine scheduling problem with sequence dependent setup times. Eur. J. Oper. Res. 211(3), 612–622 (2011) 14. Fanjul-Peyro, L., Ruiz, R., Perea, F.: Reformulations and an exact algorithm for unrelated parallel machine scheduling problems with setup times. Comput. Oper. Res. 101, 173–182 (2019) 15. Unlu, Y., Mason, S.J.: Evaluation of mixed integer programming formulations for nonpreemptive parallel machine scheduling problems. Comput. Ind. Eng. 58(4), 785–800 (2010) 16. Low, C., Wu, G.H.: Unrelated parallel-machine scheduling with controllable processing times and eligibility constraints to minimize the makespan. J. Ind. Prod. Eng. 33(4), 286–293 (2016) 17. Edis, E.B., Ozkarahan, I.: A combined integer/constraint programming approach to a resourceconstrained parallel machine scheduling problem with machine eligibility restrictions. Eng. Optim. 43(2), 135–157 (2011) 18. Rocha, P.L., Ravetti, M.G., Mateus, G.R., Pardalos, P.M.: Exact algorithms for a scheduling problem with unrelated parallel machines and sequence and machine-dependent setup times. Comput. Oper. Res. 35(4), 1250–1264 (2008)

Integrated Warehouse Layout Planning with Fuzzy C-Means Clustering Tarık Küçükdeniz

and Özlen Erkal Sönmez(B)

Istanbul University-Cerrahpa¸sa, Avcılar, 34320 Istanbul, Türkiye {tkdeniz,ozlenerkal}@iuc.edu.tr

Abstract. Warehouses are regarded as critical junction points of supply chains by determining their cost and service level to designate the potential degree of the business success. Warehouse layout planning is related to a wide-ranging problem area regarding complex warehouse operations. Including the determination of items’ positioning in warehouses, order picking planning performance may affect the overall warehouse achievements. This study contributes to develop Fuzzy CMeans (FCM) based integrated order picking strategy for items’ warehouse layout planning. The aim and originality of the paper is to apply fuzzy clustering as a first phase to categorize the stock keeping units (SKUs) to design the warehouse layout by integrating the order frequency of SKUs and their weights. For this purpose, a specifically defined factor (Q factor) is calculated for each SKU. It represents both the order frequency of SKUs and the spread of the orders throughout the year. Q factor and the weights of SKUs are togetherly used for the analysis in order to generate distinct clusters of SKUs. Experimental results show that FCM clustering methodology outperforms K-Means clustering and also the case that solely considers the weight factors of SKUs. Keywords: Warehouse layout planning · Order picking · Fuzzy C-Means clustering

1 Introduction Warehouses connect supply chain elements. They may have significant roles especially for determining the cost and service level of the supply chain, as well as designating the potential degree of the business success. Warehouses are the storage systems designed for keeping functional items, including WIPs (Work-in-processes) or finished goods, until they are in use. Movements of the items are frequently observed in any warehouse. The complexity of transportation activities performed in and out of the warehouses gets more complicated for larger scaled elements and connections. Hence, effective warehouse management is regarded as a challenging and nonignorable task. As the diversity of items and demands is increased, warehouse planning activities and attempts may complexify and come into more prominence [1]. Warehouse layout problems (WLPs) represent an aggregated form of various problems in facilities design and planning area. Even the generic operations may vary to a great extent. Besides arranging the timely orders to © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 184–191, 2022. https://doi.org/10.1007/978-3-031-09173-5_24

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satisfy the demands within the supply chain dynamics, operations in warehouses may include physical configurations, purchasing, receiving, controlling, packing, unpacking, loading, routing, transporting, storing, scheduling and carrying out maintenance for the items in the storage system. Effective integrated practices may have a vital role to reduce the potential costs to be faced, and improve the standardized service level of that business. Normally, successful companies necessitate to hold minimum level of inventories while ensuring shorter response times even for higher volumes of production [2]. These expectations indicate the continuing requirement for the effectively planned warehouses. Conventionally, warehouse planning operations may include to manage the items and assign proper locations for them. In warehouses, the main goal is generally to produce a layout plan that minimizes storage expenses. As an approach to reduce the order picking time that is spent by the workers and material handling systems, items that are frequently shipped from the warehouse must be put in a close proximity to the entry/exit points. In the literature, various approaches have been developed to solve the mathematical model of the problems, regarded to the placement of stock keeping units (SKUs) in a warehouse layout. This study contributes to develop Fuzzy C-Means (FCM) based integrated order picking strategy for items’ warehouse layout planning. The aim and originality of the paper is to apply fuzzy clustering as a first phase to categorize the stock keeping units (SKUs) to design the warehouse layout by integrating the order frequency of SKUs and their weights. The study is organized as follows. Firstly, a brief summary of literature review is presented in Sect. 1.1. In Sect. 2, the methodology is introduced. Theory of FCM clustering is presented. Afterwards, in Sect. 3, applicational details on the experimental data are shown. In discussion part (in Sect. 4), the comparison of alternative methods and results are interpreted. Finally, study is concluded with Sect. 5 by emphasizing the general outcomes. Further direction of research is remarked thereby. 1.1 Literature Review In the earlier attempts, items’ storage locations are determined by using COI (Cube Per Order Index) based assignments in the literature. Reference [3] introduces that index. A ratio, which considers the required space for the storage of that item divided by the related order frequency, is calculated for the items with this methodology. Lower COI necessitates the related item to be located closer to the entry/exit points of the warehouse. Comprehensive policies are determined by various COI based applications, such as in References [4] and [5]. Some studies in this group are merged the methodology with heuristics, such as in Reference [6]. WLPs, which can be defined in single or multi-level structure, are substantially discussed in the literature. Multi-level warehouse problems are the group of problems assuming that warehouses have a multi-level structure, generally with both vertically located (like a ground and upper – lower levels), and horizontally located storage areas. Items are expected to be located to the predetermined locations such as cells and/or levels. Transportation between these interconnected levels of the facility is managed by using (mostly electronical) carriers or connectors. Problems in this field are frequently solved by using various heuristics. Within the context of complex problems, Reference [7] proposes greedy tabu search and dynamic neighborhood approaches to solve the

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problem with adjacency constraints. Reference [8] combines genetic algorithm (GA) and path relinking methodology. Reference [9] proposes a novel methodology based on chance-constrained programming model and tabu search algorithm on fuzzy simulation. Demands and distances data is defined with fuzzy numbers in that study. Reference [10] formulates a multiple-level warehouse shelf configuration model for different product groups to minimize material handling costs. Authors develop particle swarm optimization (PSO) algorithm to determine the optimal warehouse layout. Developing Lagrangian heuristic approach, Reference [11] presents an optimization policy by aggregating the layout with a capacitated lot-sizing problem. Authors prefer to use mixed integer linear programming model to minimize the total cost of operations. Reference [12] introduces a novel (worm optimization) algorithm whose performance is compared with three methodologies as GA, ant colony optimization (ACO) and an exact methodology only for the small-scaled problems. In a further study (Ref. [13]), authors adapt ACO algorithm whose results are compared with the results of GA applied to both small and large-scaled problems. Reference [14] is on uncertainty theory method, whose demands and distances data is indeterminately defined. Authors compared two uncertain methodologies as 1. Chance-constrained programming and 2. Chance-maximum programming with a deterministic model. Joint (Integrated) problems for warehouse management are also current in the literature. Reference [15] is on mixed-integer programming model for the joint order batching of orders considering the routing problem. Its objective function is an integrated form of both unit cost-distance relations of orders and the fixed transportation costs of vehicles. Authors compare the solutions of three metaheuristics as GA, PSO and honey artificial bee algorithms via several test indexes. Reference [16] proposes bi-objective mixed integer linear programming model for an integrated production planning and warehouse layout model under uncertainty. Fuzzy parameters and chance constraints are used. Objective functions are set for 1. cost associated parameters/variables, 2. fluctuations of the labor defined for each planning period. Joint order batching procedures also include picker routing problem presented by mixed-integer programming model. According to the evaluation of the brief literature review, heuristic methodologies are seen as in the popular side of the effective approaches preferred in relatively novel studies in the field. Some specifically defined integrated objective functions may be used for the warehouse layout optimization problems both for single and multi-level structured warehouses. Some generalized policies and procedures, including the overall planning activities of the warehouse, may be offered in this way. The models developed for warehouse layout optimization determine the locations of items in a storage system, under certain constraints. Order frequency may be a commonly used indicator at this point. In conventional warehouse management, items may be placed considering the sales frequency factor purely. In this case, most frequently sold items are simply located to the closest place to entry/exit points of the warehouses. However, apart from the order frequency factor of SKUs, other factors such as weight, volume, shape of SKUs or other kind of items’ properties such as the risk or cleanliness level of SKUs etc. may be taken into consideration.

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2 Methodology This study stands for fuzzy clustering based warehouse layout optimization, addressing SLAP (Storage Location Allocation Problem) models for order picking processes. An integrated warehouse planning approach is proposed based on order frequency of SKUs and their weights. Considering the potential idle time for the charging activities of electrical material handling equipment, this study attaches importance to improve the efficiency of electrical material handling equipment. Efficiency of material handling equipment is defined as the ratio of the available or active time to the total time. Thus, extending the material handling systems’ usage times in order to improve the ratio of their active time versus total time is aimed. Equation 1 shows the calculation of efficiency ratio of electrical material handling equipment. ta is the available (active) time and tc is charging time of electrical material handling equipment. E = ta /(ta + tc )

(1)

Weight of the load may have a direct effect on the carrying speed of material handling equipment [17, 18]. Thus, heavier parts can chance the energy consumption levels of the equipment during the movements. It can make the equipment move slower which means a visible decrease in the efficiency. Load capacity can also strongly affect the carried batch size at one time, and utilization level of material handling equipment. Moreover, lighter loads can work with lower carbon footprints on some electrical material handling devices [19]. On the basis of the method, heavier SKUs are assumed to be picked up later than the lighter ones by the material handling equipment in our study. Equipment picks up the lighter SKUs earlier than the heavy ones to minimize the energy consumption of the electrical material handling systems being used. By this approach, equipment is protected from taking longer distances with heavier loads with one time of charging activity. This may be fundamental for both the efficiency and environmental sensitivity of material handling equipment. Load × Time or Load × Distance value is aimed to be minimized for the orders in the picking activity. However, all SKU orders cannot show homogeneous spread during the year. Some SKUs perform more frequent movements in the warehouse during the whole year, while others are observed only at certain times due to seasonality or other factors. For this purpose, a hybrid indicator called Q factor is calculated for each SKU initially. The value of Q factor basically measures both the warehouse entry/exit frequency of SKUs and how much of the relevant SKU demand covers a year’s demand according to the existing records. Hereby, Q factor is defined as a specific frequency indicator, also including the expansion level of the order picking activities in a year. Formula 2 shows the calculation of Q Factor for each SKU. In Eq. 2, d represents the order dates and di represents the order date of SKU i. fi is the total number of orders containing SKU i. In order to specify distinct SKU families, SKUs are clustered according to their Q factor values and the weights of SKUs. By the way, clusters are determined to specify the layout of SKUs in the warehouse so as to minimize the total load of the electrical material handling devices during their movements in the warehouse. max(di ) − min(di ) × fi (2) qi = max(d ) − min(d )

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2.1 Fuzzy C-Means (FCM) Clustering The FCM can be seen as the fuzzified version of the K-Means algorithm and is based on the minimization of an objective function called C-Means functional: J(X ; U ; V ) =

c i=1

N k=1

(uik )m xk − v2A

(3)

where Ai is a set of objects (data points) in the ith cluster, vi is the mean for those points over cluster i, V = [v1 , v2 , . . . , vc ], vi ∈ m is the vector of cluster centers which have 2 = x − v 2 = (x − v )T A(x − v ) is a squared inner product to be determined, DikA i A i i k k k distance norm, and the N × c matrix U = [uik ] represents the fuzzy partitions, where uik denotes the membership degree that the ith data point belongs to the kth cluster. Its conditions are given by: uik ∈ [0, 1], ∀i , k,

c k=1

uik = 1, ∀i , 0
1, the termination tolerance  > 0 and the norm-inducing matrix A, the algorithm tracks the following steps [20]: N  (l−1) m xk k=1 uik (l) Step 1 : compute prototypes for cluster (means) : Vi =   m , 1 ≤ i ≤ c (l−1) N k=1 ui,k (5) 2 Step 2 : calculate the distances : DikA = (xk − vi )T A(xk − vi ), 1 ≤ i ≤ c, 1 ≤ k ≤ n (6)

1 (l) Step 3 : update the partition matrix : uik =   2/(m−1) c j=1 DikA /DjkA

(7)

this step will be repeated for l = 1, 2, . . . until U (l) − U (l−1)  < 

(8)

3 Numerical Study WLP is an NP-hard problem. In order to assign each SKU to a location in the warehouse, the heuristic solution of the problem is frequently preferred due to the large number of decision variables. Clustering SKUs according to various criteria and assigning them to a location according to this clustering result is also a preferred method in the literature. In this study, the weight-based SLAP methodology is applied to an experimental dataset. The dataset consists of a total of 131,706 records for 64,682 different orders related to 5,242 SKUs over a year. Firstly, using this data, the Q factor values of each SKU are calculated. These values are togetherly used with the weights of SKUs. By using FCM method, SKUs are divided into four different clusters. Generated clusters are shown in Fig. 1. The indentified SKU numbers for each cluster definedin Fig. 1 are 278, 1854, 1920, and 114, respectively.

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Conventional warehouse management approaches generally offer to locate the items starting from the closest place to the entry/exit points of warehouses according to their order frequency. In proposed study, the cluster to which each SKU belongs to is defined by clustering analysis. It is ensured that the SKUs in the same cluster are located together in the warehouse in an orderly perspective according to their Q-factors. 0.9

700 0.8

600 0.7

Q

500

400

0.6

300 0.5

200 0.4

100

100

200

300

400

500

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Weight

Fig. 1. Clustering map of SKUs grouped by FCM according to their weights and Q factor.

Afterwards, Total Weight × Distance value of the movements is calculated by simulating the order data. For instance, if there is more than one stock item in an order, sum of Load × Distance value is calculated. Summing operation starts from the product that is placed closest to the entry/exit points, and then continues with the second product closest to that inventory item. In this way values for all SKUs are sequentially calculated for both directions (forward from and back to entry and exit points). This process is performed separately for 64,682 different orders, and then, the resulting total movement is reported. As an alternative method, K-Means clustering is also applied to the same dataset in order to compare with the clustering performance of FCM. Moreover, the case that considering solely the weight factor of SKUs is simulated. Comparison of results is presented in Table 1. Table 1. Comparison of the results of alternative methods according to Total Q Factor. Method

Total Q Factor

FCM

10,876,982.7

K-Means clustering

11,359,211.8

Placement considering solely the weight of SKUs

11,666,548.3

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4 Discussion The purpose of the proposed approach was to minimize the total travelled distance and the total transported weight for each order in warehouse operations. This is achieved by clustering SKUs according to their weights and a defined Q factor based on the SKU’s order frequency and order date homogeneity. According to Load × Distance values separately calculated for the numerical study with 64,682 different orders, FCM algorithm outperforms alternative methodologies. H is the result of the proposed (FCM) model. M shows the result of alternative methods.  is the percentage of the difference between the objective functions of compared two models. Equation 9 shows the ratio used for the relative evaluation of results. H−M (9) = H Thus, resulting percentage improvements in costs are calculated as FCM −K_means = −0.044, and FCM −only_weight = −0.072. FCM method is shown to improve the cost minimization by the proposed approach.

5 Conclusion Warehouse operations are associated with supply chain management. Effective warehouse management techniques are vital, and mostly necessitate an integrated point of view. Both researchers and practitioners need accessible and applicable road maps in order to adapt to current operations. Layout planning is one of the most decisive factors on cost calculations in warehousing. Order picking strategies may affect the performance. In this study, items’ positioning is determined with an order picking strategy which also considers energy consumption of electrical material handling equipment. The aim is to provide energy savings for longer operational times when the equipment is once fully charged. Therefore, heavy loads are considered to be transported in the shortest distance. This necessitates collecting lighter loads earlier and to leave the heavy loads to the former phases of the movement during the sequential activities of order picking. Thus, a longer operational time with single charge may be provided. As the active time that electrical material handling equipment spend with one time of charge level, it results in an increase in electrical equipment’s efficiency. The proposed approach is shown to improve the total travel distance and total transported weight for the operations in the warehouse. Energy efficiency of the material handling systems can be improved in this way. Moreover, heavy loads in shorter distances may cause lower carbon footprints on some electric material handling devices. Future research for warehouse planning is likely to focus on smarter infrastructures and implementations to provide real-time traceability of items and locations. Additional criteria may be added to the proposed integrated strategy for more comprehensive scenarios reflecting the actual cases confidentially.

References 1. Faber, N., de Koster, M.B.M., Smidts, A.: Organizing warehouse management. Int. J. Oper. Prod. Manage. 33(9), 1230–1256 (2013)

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2. Van den Berg, J.P., Zijm, W.H.M.: Models for warehouse management: classification and examples. Int. J. Prod. Econ. 59, 51–528 (1999) 3. Heskett, J.L.: Cube-per-order index – a key to warehouse stock location. Transp. Distrib. Manage. 3(1), 27–31 (1963) 4. Heskett, J.L.: Putting the cube-per-order index to work in warehouse layout. Transp. Distrib. Manage. 4, 23–30 (1964) 5. Caron, F., Marchet, G., Perego, A.: Routing policies and COI-based storage policies in pickerto-part systems. Int. J. Prod. Res. 36(3), 713–732 (1998) 6. Muppani, V.R., Adil, G.K.: Efficient formation of storage classes for warehouse storage location assignment: a simulated annealing approach. Omega 36(4), 609–618 (2008) 7. Zhang, G.Q., Lai, K.K.: Tabu search approaches for the multi-level warehouse layout problem with adjacency constraints. Eng. Optim. 42(8), 775–790 (2010) 8. Zhang, G.Q., Lai, K.K.: Combining path relinking and genetic algorithms for the multiplelevel warehouse layout problem. Eur. J. Oper. Res. 169, 413–425 (2006) 9. Yang, L., Feng, Y.: Fuzzy multi-level warehouse layout problem: new model and algorithm. J. Syst. Sci. Syst. Eng. 15, 493–503 (2006) 10. Onut, S., Tuzkaya, U.R., Dogac, B.: A particle swarm optimization algorithm for the multiplelevel warehouse layout design problem. Comput. Ind. Eng. 54, 783–799 (2008) 11. Zhang, G., Nishi, T., Turner, S.D.O., Oga, K., Li, X.: An integrated strategy for a production planning and warehouse layout problem: modeling and solution approaches. Omega 68, 85–94 (2016) 12. Arnaout, J.-P.: Worm optimization for the multiple level warehouse layout problem. Ann. Oper. Res. 269(1–2), 29–51 (2017) 13. Arnaout, J.-P., ElKhoury, C., Karayaz, G.: Solving the multiple level warehouse layout problem using ant colony optimization. Oper. Res. Int. J. 20(1), 473–490 (2017) 14. He, R., Li, H., Zhang, B., Chen, M.: The multi-level warehouse layout problem with uncertain information: uncertainty theory method. Int. J. Gen Syst. 49(5), 497–520 (2020) 15. Attari, M.Y.N., Torkayesh, A.E., Malmir, B., Jami, E.N.: Robust possibilistic programming for joint order batching and picker routing problem in warehouse management. Int. J. Prod. Res. 59(14), 4434–4452 (2021) 16. Sabbaghnia, A., Heydari, J., Razmi, J.: Integrated production planning and warehouse layout problem under uncertainty: a robust possibilistic approach. J. Ind. Syst. Eng. 13(4), 81–97 (2021) 17. Gürel, S., Gultekin, H., Akhlaghi, V.E.: Energy conscious scheduling of a material handling robot in a manufacturing cell. Rob. Comput. Integr. Manuf. 58, 97–108 (2019) 18. Boenzi, F., Digiesi, S., Facchini, F., Mossa, G., Mummolo, G.: Greening activities in warehouses: a model for identifying sustainable strategies in material handling. In: Annals of DAAAM & Proceedings, vol. 26, no. 1, p. 16. DAAAM (2015) 19. Facchini, F., Mummolo, G., Mossa, G., Digiesi, S., Boenzi, F., Verriello, R.: Minimizing the carbon footprint of material handling equipment: comparison of electric and LPG forklifts. J. Ind. Eng. Manage. 9(5), 1035–1046 (2016) 20. Balasko, B., Abonyi, J., Feil, B.: Fuzzy clustering and data analysis toolbox. http://www.fmt. vein.hu/softcomp/fclusttoolbox (2005). Accessed 15 March 2022

Planning and Scheduling Scheme Based on Fuzzy Finite State Machine Model Margarita Knyazeva , Alexander Bozhenyuk(B)

, and Stanislav Belyakov

Southern Federal University, Nekrasovskiy Str., 44, 347928 Taganrog, Russia [email protected]

Abstract. Planning and scheduling is an important optimization problem in many transportation and robotic applications. To solve planning problems, the main approaches are based on optimization methods, sampling-based methods, and usually such kinds of problems are NP-hard and high dimensional. In this paper, the method for planning and scheduling is introduced; the implementation of fuzzy finite state machine model is suggested. Graph-based presentation of the scheduling problem and operation planning is given. The algorithm for planning based on decision tree and the state enumeration is developed. Using this idea, the scheduling problem can be formulated as a state-decision problem with operations to be planned. The idea of temporal-ordered partial schedule associated with the planning state of the system is discussed. And the concept of fuzzy finite state machine model for the planning system under is suggested. Keywords: Planning and scheduling · Fuzzy graph · Temporal modelling · Fuzzy finite state machine · Operation planning

1 Introduction Scheduling problems are the problems of constructing special plans for operation performance, temporal arrangement of the operations with respect to the given constraints. Resources are required to perform the operations and are available with limited capacities, allowing to capture manpower, machines etc. So the problem of automated temporal planning is to have the formalized environment, an initial state of the system, a set of goal states and to search a sequence of temporal inputs so the machine could transit from its initial state to the goal states while satisfying the problem constraints. The planning and scheduling problems are computationally hard and the resource-constrained scheduling problem (RCSP) and its extensions is complex NP-hard problem [1–3]. Uncertainty of input variables during the operational stage of planning means that all acceptable values are not indifferent, so that some of them will be preferred in scheduling process while others are tolerated. Moreover partial solutions at each state can be represented as combinations (so-called “modes” or “alternatives”) of starting times of operations, resource requirement as a function of duration of the following operation, and finally and resource usage [4]. Multi-mode resource-constrained project © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 192–199, 2022. https://doi.org/10.1007/978-3-031-09173-5_25

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scheduling problem (MRCPSP) presupposes discrete “time-cost” preferences or tradeoff problem (DTCTP), resource allocation and resource leveling problem (RLP) and when considered simultaneously it affects the computation complexity of the problem [5]. Practical solution methods usually came around with decomposition methods able to relax the completeness requirement to resolution completeness. This means that the algorithm will be able to find a feasible solution in a reasonable time. Considering the aspects of environment sampling-based algorithms check feasibility of the solution and construct a graph (roadmap); they provide probabilistic completeness guarantees. This kind of algorithms are used for pre-analysis or as a backup method compared with faster and non-complete, optimization based planner [6, 7]. The most famous sampling-based planning algorithms are Probabilistic Road Maps (PRMs) [8] and Rapidly-exploring Random Trees (RRTs) [9]. A decision tree method used to find the best performing priority rule for single-mode planning problem is introduced in [10]. And finally uncertainty of the project performance model is introduced in [11] for multi-mode case of scheduling and planning problem under uncertain activity cost, where the objective function maximizes the probability of the summarized project cost. However, in this work we introduce a unifying representation for the planning algorithm based on fuzzy nondeterministic state-machine model to construct schedule for the operations performance that satisfies possible dynamic of the constraints. The paper is organized as follows. Section 2 introduces planning and scheduling problem formalizations as well as mathematical programming statement of multi-mode scheduling problem. Section 3 is devoted to the problem of planning with fuzzy nondeterministic finite automata and the following algorithm for precedence tree approach. In conclusion we summarize the results.

2 Planning and Scheduling Problem Formulation for Multi-mode Resource-Constrained Project Scheduling Problem (MRCPSP) A project consists of J operations, where j = 1,…,J. They are predefined by two types of restrictions: precedence relations between operations and resource limitations. For each operation, its duration, resource requirement and availability and precedence relations are given, as well as time windows and critical pass of the project graph are calculated. The processing time of operation (duration) is denoted by pj , assuming that the whole planning interval is discrete. Once starts an operation needs to be finished, so the preemption relations are not allowed. Let’s consider the precedence relations scheme: given the sets of immediate predecessors Pj (an operation j cannot be started before each of its predecessors i ∈ Pj is completed), and Sj as the set of immediate successors of operation j. And let’s consider two auxiliary dummy operations j = 0 and j = J+1 as a logical source start and end-sink of the project. The processing time of them is p0 = pJ +1 = 0 and J + = {0, . . . , J + 1} is the set of all operations. Each operation j requires rjk units of k resource in each discrete period of time it is in process, for k ∈ K p . The idea is to construct a plan of operation performance for the earliest possible end of the project, with respect to objective function to be minimized (the total makespan) and precedence and resource constraints are satisfied. Temporal aspect of scheduling problem presupposes

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both time moments and periods (intervals), so that a period t starts at the time moment t-1 and ends at time moment t. So the operation j starts at the time sj and finishes at the time fj = sj + pj ; and operation is in process during the interval t = {sj + 1, . . . , fj }. Temporal planning also presuppose deriving time windows that provide information about start and finish times of operations, allowing to compute the whole project duration. The critical path method (CPM) is a graph-based method that allows computing time windows for project performance and determining flexibilities while operational stage of planning. A critical path method allows to compute the longest sequence of operations that are be finished in time to satisfy the complete project  deadline with respect to upper bound T on the project’s makespan as follows: T := Jj=1 pj . Let’s consider the following notations for forward propagation: ESj - is the earliest possible start time for each operation j ∈ J + ; EFj - is the earliest possible finish time for each operation j ∈ J + ;

Algorithm 1. Forward propagation ES0 = 0; EF0 = 0; FOR g:= 1 TO J + 1 DO BEGIN ESj := max{EFi |i ∈ Pj }; EFj := ESj + Pj } ; END. After that we perform backward propagation, that allows calculating the following variables: LSj - is the latest possible start time for each operation j ∈ J + ; LFj - is the latest possible finish time for each operation j ∈ J + ;

Algorithm 2. Backward propagation LFJ +1 = T ; LSJ +1 = T ; FOR g:= J DOWNTO 0 DO BEGIN LFj := min{LSi |i ∈ Sj }; LSj := LFj − pj ; END.

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The algorithms above shows that operation should start in fuzzy time window {ESj , . . . , LSj } and finish not later than interval {EFj , . . . , LFj }, in other case the precedence relations would be violated. Let’s consider the following example and operation-on-node representation of the planning graph (see Fig.1). 3/2

2/4

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Fig. 1. An example of project’s graph precedence relations and constructed schedule.

Considering the example on Fig.1 we compute T =16 and calculate the earliest and latest start and finish times of operations given in Table 1. Table 1. Time windows for the operation performance. j

0

1

2

3

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6

7

ESj

0

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0

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EFj

0

3

4

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LSj

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10

6

13

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1

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LFj

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16

2.1 Mathematical Programming Formulation of Multi-mode Scheduling Problem The multi-mode case of scheduling and planning problem assumes that there are several modes an operation can be executed and the mode itself is determined by the operation duration and its resource requirements trade-off.

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Mathematical formulation for multi-mode resource-constrained project scheduling problem MRCPSP m,1T|cpm,mu|Cmax problem can be stated as follows. Given the decision variable xjmt for each operation j: xjmt =

⎧ ⎨

1, if activity jfinished at moment t and performed in m − execution mode; ⎩ 0, otherwise. LFJ Minimize t · xJ +1,1,t t=EFJ

(1)

(2)

subject to Mj LFj m=1

Mh LFh m=1

t=EFh

J

t · xhmt ≤

Mj

j=1

m=1

J j=1

t=EFj

xjmt = 1, j ∈ J +

Mj LFj

rjmk

Mj m=1

m=1

t=EFj

t+pjm −1 b=t

rjmk

  t − pjm · xjmt , j ∈ J + , h ∈ Pj p

xjmb ≤ Rk , k ∈ K p , t ∈ T

LFj t=EFj

xjmb ≤ Rvk , k ∈ K v

xjmt ∈ {0, 1}, j ∈ J + , m ∈ Mj , t ∈ T

(3) (4) (5) (6) (7)

Thus the objective function minimizes the total duration of the project with respect to constraints (2) that each operation will be executed with one selected mode (3), precedence relations are satisfied by (4), constraints (5) and (6) show the limitations of renewable and non-renewable resources, respectively. And expression (7) illustrates binary decision variable for each operation to be performed. The MRCPSP can be also extended by the precedence concept of minimal and maximal time lags between the operations, and their different configurations [12, 13]. Different extensions of scheduling problem and solution methods were grouped by S. Hartmann, including resource parameters varying in time, alternative objectives and relations to packing and cutting optimization problems [14]. 2.2 Exact and Heuristic Solution Procedures to Solving Multi-mode Resource-Constrained Project Scheduling Problem (MRCPSP) with Time Windows To compute optimal operation allocations and schedules for MRCPSP different algorithms and solutions were developed including exact and heuristic procedures. Due to NP-hardness of the stated problem above it is difficult to apply exact algorithms to achieve optimal solutions within the reasonable computation times. Such kind of exact procedures can be used to obtain benchmark solutions for test instances for small projects and further they can be used to evaluate heuristics. Among them are branch-and-bound methods [15] to enumerate the set of solutions and fix decision variables.

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Enumeration scheme for branch-and-bound procedure presupposes using decision trees, where each node is assigned a so-called start time restriction, a time window Wj := { ESj , LSj } and for each operation the earliest and latest time-feasible start times ESj and LSj are estimated according to forward and backward propagation algorithms. In our approach we suggest using theory of automata and fuzzy finite state machine model to construct decision graph by forward propagations enumeration nodes in topological ordering and computing the values of nodes given theirs inputs and transition function. There are two main approaches to construct decision graphs: static declaration and dynamic declaration. Static declaration presupposes defining certain architecture, structured and variable-sized data with some primitive flows and conditions, like scheduling graphs. Dynamic declaration presupposes that graph is defined implicitly as the forward computation is executed, which allows to compute combinatorial algorithms (e.g., dynamic programming) and reveal independencies between variables.

3 Planning with Fuzzy Finite State Machine Model A finite-state machine (FSM) or finite-state automata is a mathematical and computation model that is presented by an abstract machine and the finite number of states at any given time t. The functioning of state machines was implemented in many problems that execute a predetermined sequence of operations depending on a topological sequence of these operations. Let’s consider deterministic and nondeterministic fuzzy finite automata for scheduling process and decision tree approach. For the deterministic automata we can predict every state which will have only one transition for each possible input. In non-deterministic automata, a certain input may be associated with more than one, or no transition for a given state. Let’s consider the following notation. A finite automata is a 5-tuple M = (S, , σ, s0 , F), where S - is a finite set of possible states or partially constructed schedules; Σ - is a finite set called alphabet or temporal inputs; σ : S ×  → S - is the transition function from state to possible state with respect to precedence relations of operations; s0 ∈ S - is the start state; F ⊆ S - is the set of accept states or final states of the planning system. The definition of transition function above was presented for the deterministic finite automata, but in practice of planning several ways may exist for the next state at any discrete moment t for the planning and scheduling problem. So every branching level g in the decision tree will correspond to a point in the computation at which the machine has multiple choices to select. In a nondeterministic finite automata the transition function would be stated as follows: σ : S ×  → Pos(S), so that σ returns a set of states. The main characteristic of Fuzzy Finite State Automata (FFSA) is that transitions are caused by fuzzy variables, or the states themselves can be uncertain. So for the planning system at any discrete time moment, the system can be in undefined state, so it can be more than one state at the same given time, and each state will have its own membership

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value. Each state of the system S is associated with fuzzy state operation: μS ∈ [0, 1], which represents the grade on how much the system is in that state, i.e., 1 – for the active eligible states, 0- for all other non-eligible states. For time-independent FFSA, state transitions may take place as soon as inputs vary. Let’s consider the precedence tree approach based on estimation of each state g of the solution procedure and determine the set SJg of the currently scheduled operations and the set EJg of the eligible operations, those operations whose predecessors are already scheduled. Then select an eligible operation jg and mode mjg of this operation. Then compute the earliest feasible start time sjg that is not less than the start time assigned on the previous level of the decision tree. Then branch to the next level. Algorithm 3. Decision tree

Step 1: Initialization Set g := 0; j0 := 0; mj0 := 1; sj0 := 0; SJ0 := φ; Step 2: Compute eligible operations Increase state g := g + 1; SJg := SJg−1 ∪ {jg−1 }; EJg := {j ∈ {1, . . . , J + 1}\(SJg |Pj ⊆ SJg }; if J + 1 ∈ EJ g then store current solution and go to step 5; Step 3. Select next operation if no untested eligible operation is left in EJ g then go to step 5, else select untested jg ∈ EJ g ; Step 4. Select next mode and compute start time if no untested mode alternative is left in Mig then go to step 7, else select untested mjg ∈ Mig ; if a non-renewable resource conflict occurs then go to step 4. compute the earliest precedence and resource feasible start time sjg with sjg ≥ sjg−1 ; go to step 2; Step 5: Backtracking g:= g-1; if g = 0 then STOP, else go to step 4. If the dummy sink operation is eligible, the procedure have found the schedule, backtracking to the previous level occurs and the selection of next untested mode happens. If there is no mode, the procedure selects the next eligible operation. Each level of decision tree corresponds to a permutation of the set of operations j1 , . . . , jJ .

4 Conclusion The paper discusses the approach to solving multi-mode resource-constrained project scheduling problem (MRCPSP) with time windows. Two algorithms were introduced for calculating start and finish time windows for processing the operations. The mathematical programming formulation and decision procedures were discussed. The theory of automata and fuzzy nondeterministic finite state machine model was suggested to construct decision tree by forward propagation. For each state the algorithm evaluates all eligible operations and stores the current solution in the subsets until all the operations

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are scheduled. As for the future research, the approach to unfolding fuzzy graph can be developed as a model for illustrating branching structure for all possible computations for MRCPSP. Acknowledgments. The reported study was funded by RFBR according to the research project N 20-01-00197.

References 1. Brucker, P., Knust, S.: Complex Scheduling, pp. 29–115. Springer-Verlag, Heidelberg (2012) 2. Blazewicz, J.: Scheduling subject to resource constraints: classification and complexity. Disc. Appl. Math. 5(1), 11–24 (1983) 3. Billaut, J-C., Moukrim, A., Sanlaville, E.: Flexibility and Robustness in Scheduling. Control Systems, Robotics and Manufacturing Series. Willey-ISTE (2013) 4. Dubois, D., Fargier, H., Fortemps, F.: Fuzzy scheduling: modelling flexible constraints vs. coping with incomplete knowledge. Eur. J. Oper. Res. 147, 231–252 (2003) 5. Cheng, J., Fowler, J., Kempf, K., Mason, S.: Multi-mode resource-constrained project scheduling problems with non-preemptive activity splitting. Comput. Oper. Res. 53, 275–287 (2015) 6. Luna, R., Sucan, I.A., Moll, M., Kavraki, L.E.: Anytime solution optimization for samplingbased motion planning. In: Proceedings of 2013 IEEE International Conference on Robotics and Automation, pp. 5068–5074 (2013) 7. Hartmann, V.N., Oguz, O.S. Toussaint, M.: Planning planning: the path planner as a finite state machine. In: ICAPS Planning and Robotics Workshop (2020) 8. Kavraki, L.E., Svestka, P., Latombe, J.-C., Overmars, M.H.: Probabilistic roadmaps for path planning in high-dimensional configuration spaces. IEEE Trans. Robot. Autom. 12(4), 566– 580 (1996) 9. Orhagen, O.P., Thoresen, M., Mathiassen, K.: The rapidly exploring random tree funnel algorithm. In: Proceedings of 8th International Conference on Mechatronics and Robotics Engineering, ICMRE 2022, pp.136–143 (2022) 10. Guo, W., Vanhoucke, M., Coelho, J., Luo, J.: Automatic detection of the best performing priority rule for the resource-constrained project scheduling problem. Expert Syst. App. 167, 1–19, 114116 (2021). 11. Xie, F., Li, H., Xu, Z.: Multi-mode resource-constrained project scheduling with uncertain activity cost. Expert Syst. Appl. 168, 114475 (2021) 12. Knyazeva, M., Bozhenyuk, A., Kaymak, U.: Managing temporal uncertainty in multi-mode Z-number fuzzy graph structures. In: Proceedings of 11th Conference of the European Society for Fuzzy Logic and Technology, EUSFLAT 2019, pp. 580–587 (2020) 13. Knyazeva, M., Bozhenyuk, A., Kaymak, U.: Fuzzy temporal graphs and sequence modelling in scheduling problem. In: Lesot, M.-J., et al. (eds.) Information Processing and Management of Uncertainty in Knowledge-Based Systems. CCIS, vol. 1239, pp. 539–550. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-50153-2_40 14. Hartmann, S.: Project Scheduling under Limited Resources, Models, Methods, and Applications. Lecture Notes in Economics and Mathematical Systems Book Series. LNE, vol. 478 (1999). https://doi.org/10.1007/978-3-642-58627-9 15. Watermeyer, K., Zimmermann, Jürgen.: A branch-and-bound procedure for the resourceconstrained project scheduling problem with partially renewable resources and general temporal constraints. OR Spectrum 42(2), 427–460 (2020). https://doi.org/10.1007/s00291-02000583-z

Electric Vehicle Selection by Using Fuzzy SMART Basar Oztaysi(B) , Cengiz Kahraman, and Sezi Cevik Onar Industrial Engineering Department, ˙Istanbul Technical University, 34367 Istanbul, Turkey {oztaysib,kahramanc,cevikse}@itu.edu.tr

Abstract. Global warming is disturbing both the environment and quality of life. A cause of global warming is greenhouse gas (GHG) emissions which are caused by using fossil fuels for transportation and power generation. As a novel source of energy, the world is moving towards renewable and clean energy. In the transportation sector, usage of electric vehicles supports decreasing GHG emissions. As a result, we face a new decision problem about the selection of electric vehicles. The electric vehicle selection problem is a multicriteria decision-making problem that includes various criteria and alternatives. The criteria considered within the scope of the problem may involve objective criteria such as max speed and subjective criteria such as the design of the car. In this study, we propose Fuzzy SMART (Simple Multi Attribute Rating Technique) as an extension of the crisp SMART method. With the proposed method both crisp and imprecise criteria can be integrated within a decision problem. In this study, we construct a sample decision model for the electric vehicle selection problem and solve it by using the proposed Fuzzy SMART method. Keywords: Smart · Fuzzy sets · Electric vehicle selection

1 Introduction Nowadays we face some global environmental threats, such as ozone depletion and increasing global warming. The usage of non-renewable fossil fuels and their reduction with time increase the level of threats. Countries are trying to handle the issue by formulating new energy policies and investing in sustainable technology. One of the examples of the new clean technology is the electric vehicles (EV) which uses electricity as a source of energy. The initial EVs were on the market in the mid-nineteenth century, but the cost was high and speed and battery range was limited so the adaptation was low [1]. Today, as a result of emerging technologies EVs are capable of all that was absent before and as a result, they become good alternatives. Some of the countries adopt energy policies that give incentives to individuals for low emission vehicles and also provide sources for the construction of charging outlets [2]. As a result of the decrease in the battery prices, the adaptation of EVs has become very feasible [3]. The EVs can be classified into three groups: in the first group hybrid electric vehicle which runs on both engine and battery takes place; in the second group, a plug-in hybrid EV takes place which has a battery © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 200–207, 2022. https://doi.org/10.1007/978-3-031-09173-5_26

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that can be charged from the engine itself as well as from an external source; and in the third group, all-battery-EV takes place which has lyon batteries that can be charged from an external source [4]. In countries with high economic power, EVs that run entirely on batteries is popular, this is a result of the favorable conditions such as incentives about charging stations and incentives given to the consumers and auto manufacturers. Some numbers from the literature show that as of 2018 USA had one million plug-in cars [5], Europe registered more than one million light-duty plug-ins [6]. The fuzzy set theory, which was developed by Zadeh [6] has been successfully used in multi-criteria decision-making problems. As mentioned previously there are various types of EVs and various companies are producing EVs with different capabilities. The selection of proper EVs is a multi-criteria decision-making (MCDM) problem since there are multiple alternatives and various criteria. SMART (Simple Multi-Attribute Rating Technique) is a multicriteria decision-making method introduced by Winterfeldt and Edwards [7, 8] which can be used for decision problems with a limited number of alternatives and a limited number of attributes. In this paper, we propose a novel fuzzy SMART technique for the EV selection problem which enables better representation of imprecise data. The rest of this paper is organized as follows. Section 2 presents a literature review on the electronic vehicle selection problem. Section 3 presents the proposed methodology In Sect. 4, the decision model is explained by summarizing the technology alternatives and the evaluation criteria. In Sect. 5, the application with numerical calculations is given. Finally, the concluding remarks are given in Conclusion.

2 Literature Review In the literature, the vehicle selection problem has been modeled by including criteria representing environmental considerations. In a study, Biswas and Das [9] compare commercially available battery EVs by a decision model including five criteria and seven commercially available battery EV vehicles by using Fuzzy AHP-MABAC (Analytic Hierarchy Process-Multi-Attributive Border Approximation Area Comparison) technique. In another study, Biswasa and Saha use fuzzy AHP, TOPSIS, and MABAC techniques are used together to select the best commercially available scooter in the Indian market keeping in view five attributes [10]. In another study, the selection of a hybrid vehicle has been carried out using MABAC among nine commercially available vehicles based upon five distinct criteria [11]. Cihat Onat et al. [12] use fuzzy TOPSIS and VIKOR to select the most sustainable electronic vehicle among the available plug-in hybrid EVs. Rouyendegh et al. [13] use the fuzzy TOPSIS method for the most sustainable green supplier. Samaie et al.[14] compare different sustainable electric vehicles by using fuzzy TOPSIS. Memari et al. [15] focus on the selection of a sustainable supplier and reliable spare parts of vehicles by using fuzzy TOPSIS. Oztaysi et al. [16] propose using a fuzzy Analytic Network Process for the selection of green energy alternatives. Oztaysi and Kahraman [17] use hesitant fuzzy TOPSIS and interval Type-2 fuzzy AHP method for the evaluation of renewable energy alternatives. Kahraman et al. [18] propose using intuitionistic and hessitanr fuzzy sets in engineering economics. Yanık et al. [19] propose an integrated genetic algorithm and location-allocation approach for designing

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sustainable energy regions in Turkey. Kahraman et al. [20] intuitionistic fuzzy sets to evaluate outsource manufacturers.

3 Proposed Methodology The SMART (Simple Multi Attribute Rating Technique) was introduced by Winterfeldt and Edwards in 1986 [7, 8]. The technique can be used for decision problems with a limited number of alternatives and a limited number of attributes. SMART is an easyto-use technique that is regarded as a compensatory method. It can handle independent and dependent attributes and qualitative attributes can also be included in the problem after converting them to quantitative attributes [21]. Based on the steps of Winterfeldt and Edwards [22]’s SMART techniques, we propose a novel fuzzy SMART as follows: Step 1: Max and Min Values for the Criteria are Determined The decision maker defines, the minimum (Pmin ) and maximum value (Pmax ) are defined for all attributes. The decision making interval is divided into sub-intervals with equal lengths Pmin , Pmin + e0 , Pmin + e1

(1)

Equation 1 is used to calculate e ev − ev−1 = εev−1

(2)

The geometric progression is created, and Eq. 3 is obtained. ev = (1 + ε)ev−1 = (1 + ε)2 ev−1 = (1 + ε)v e0

(3)

Finally, Eq. 4 can be deduced [4]. Pmax = ev + Pmin

(4)

Step 2: Effective Weight of the Alternatives is Obtained The judgment of the decision maker about the alternative Ai against the attribute Cj is shown as gij and it is called the effective weight of alternatives. For the qualitative attributes Table 1 is used. For quantitative attributes Eq. 5–7 are used. Pv −Pmin P −Pmin ×64

v = log 2 max

(5)

gij = gmin + v

(6)

gij = gmax − v

(7)

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Table 1. . Poor

Fairly weak

Medium

Fairly good

Good

Very good

Excellent

Original scale

4

5

6

7

8

9

10

Fuzzy scale

(4, 4, 6)

(4, 5, 7)

(4, 6, 8)

(5, 7, 9)

(6, 8, 10)

(7, 9, 10)

(8, 10, 10)

where gmin is the minimum crisp value in Table 1 and gmax is the maximum crisp value in Table 1. For cases where Pv is imprecise we fuzzified version as P˜ v = (PvL , PvM , PvR ) and v˜ = L (v , vM , vR ) can be calculated as in Eq. 8 Pvi −Pmin Pmax −Pmin ×64

v = log 2 i

(8)

Step 3: Normalized Weights of the Criteria The decision maker is asked to rank the attributes according to his priority using Table 1. h˜ j = (hjL , hjM , hjR ) shows the rank allocated to the attribute j by the decision maker. The denormalized fuzzy weight obtained from Eq. 9.      √ hjL √ hjM √ hjR ; j = 1, . . . , n (9) w˜ j = 2 , 2 , 2 The normalized fuzzy weight of each criterion is calculated as given in Eq. 10. ⎛ √ h √ hjM √ hjR ⎞ jL 2 2 2 ⎟ ⎜ nw ˜ j=⎝ (10) , ,      √ hjL n √ hjM n √ hjR ⎠; n 2 2 2 j=1 j=1 j=1 Step 4: The Final Weights of Alternatives The final fuzzy weights of the alternatives are calculated by using Eq. 11

n n wj × g˜ ij f˜i = j=1

(11)

Step 5: The Final Ranking of the Alternatives The fuzzy weights are defuzzified and the alternatives are ranked.

4 Sample Application A company aims to get electronic cars for its managers. The company defines five criteria for the selection problem.

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• Price: The initial cost of the car. The company wants it to be between 20,000 $ and 40,000 $. • Maximum Capacity: This shows the maximum number of kms before it needs to be charged. The minimum value is selected as 150 km and the maximum value is selected as 300 km. • Acceleration 0–100: The number of seconds the car needs to reach 100 km/h. The company defines the interval as 8–20 s • Second-hand price: The expected price of the car in the second-hand market. The company defines 10000 $–30000$ as maximum and minimum prices. • Maintenance Cost: Expected cost of annual maintenance cost of the car. The company defines 2000 $ as the minimum and 12000 $ as the maximum cost. Based on the Pmin and Pmax values the rating of the attributes is calculated as given in Table 2. Table 2. . Rank

Performance

Price

Max capacity

Acceleration

2. Hand price

Annual maintenance cost

10

Excellent

20312.5

300

8.2

30000

2156.3

20625

225

8.4

20000

2312.5

8

Good

21250

187.5

8.8

15000

2625

22500

168.8

9.5

12500

3250

6

Medium

25000

159.4

11

11250

4500

30000

154.7

14

10625

7000

40000

152.3

20

10000

12000

4

Poor

The company defines three alternative cars (A1, A2, A3). The performance values of the alternatives are as follows (Tables 3 and 4). Table 3. . Price

Max capacity

Acceleration

2. Hand price

Annual maintenance cost

A1

22.000

160

15

Around 15000

Around 2750

A2

31.000

250

11

Around 24000

Around 3250

A3

40000

300

9

Around 28000

Around 4500

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Table 4. . Price

Max capacity Acceleration 2. Hand price Annual maintenance cost

Ranking Medium Fairly good

Fairly weak

Medium

Medium

The effective weights of the alternatives are calculated by using Eq. 5–8 for example 2. Hand price criteria for alternative A2 is given as “Around 24000”. We convert this number to a triangular fuzzy number as (22000, 24000, 26000) since the term around bears an uncertainty. By using Eq. 8 the associated effective weight is found as (5.26, 5.48, 5.67). 22000−10000 ×64

v L = log230000−10000

24000−10000 ×64

= 5.26, v M = log230000−10000

26000−10000 ×64

= 5.48, v M = log230000−10000

= 5.67

Similarly, other effective weights are also calculated (Table 5). Table 5. Table effective weights Price

Max capacity

Acceleration

2. Hand price

Annual maintenance cost

A1

7.32

6.09

5.61

(7.26, 8, 8.49)

(10.71, 8.05, 7.17)

A2

4.86

7.42

6.89

(9.26, 9.49, 9.68)

(8.05, 7.17, 6.63)

A3

4

10

8.70

(9.68, 9.85, 10)

(6.42, 6.07, 5.79)

In step 3, the normalized weights are calculated. For example, the importance of the criteria Price is defined as medium which can be represented by (4, 6, 8). When we apply Eq. 9 the denormalized weight is calculated as (4, 8, 16) and the normalized weight is calculated as (0.04, 0.16, 0.62). The final weights of the alternatives are calculated by using Eq. 11. The fuzzy weights are obtained as given in Table 6. Table 6. Fuzzy weights of the alternative Price

Max capacity

Acceleration

2. Hand price

Annual maintenance cost

(0.59, 2.61, 10.58)

(0.44, 1.32, 4.47)

A1

(0.3, 1.2, 4.56) (0.35, 1.41, 5.37)

(0.23, 0.65, 2.48)

A2

(0.2, 0.79, 3.03)

(0.43, 1.71, 6.54)

(0.28, 0.8, 3.04) (0.76, 3.1, 12.07)

(0.33, 1.17, 4.13)

A3

(0.16, 0.65, 2.49)

(0.58, 2.31, 8.82)

(0.36, 1.01, 3.84)

(0.26, 0.99, 3.61)

(0.79, 3.22, 12.47)

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After defuzzifying the values the weights of the alternatives are calculated as 4.90, 5.14, and 5.56 respectively (Table 7) and the associated rankings are A3 > A2 > A1. Table 7. Total Fuzzy weights and crisp weights Total fuzzy weights

Defuzzified weights

A1

(1.91, 7.19, 27.46)

4.90

A2

(2, 7.57, 28.81)

5.14

A3

(2.15, 8.18, 31.23)

5.56

5 Conclusion In today’s world, sustainability has become very important and as a result, electronic vehicles have become popular. Comparison of electric vehicles is a multicriteria decisionmaking problem with uncertainty and imprecise data. In this paper, we propose Fuzzy SMART as an extension of the SMART technique so that imprecise data can be handled during the problem-solving stage. In future studies, the SMART technique can be extended by novel fuzzy extensions such as Intuitionistic fuzzy sets, hesitant fuzzy Sets, Spherical fuzzy sets, q-rung Fuzzy sets, and the results can be compared with the result of this paper. Another group of studies can focus on solving the same problem with other MCDM methods such as AHP, TOPSIS, EDAS, VIKOR, and comparing the results.

References 1. Matulka, R.: Energy gov (2014). https://www.energy.gov/articles/history-electric-car. Accessed 13 Dec 2019 2. Waller, H.: Bloomberg technology (2019). https://www.bloomberg.com/news/articles/201909-14/u-k-energy-review-could-offer-incentives-for-electric-car-sales. Accessed 5 Nov 2019 3. Nykvist, B., Nilsson, M.: Rapidly falling costs of battery packs for electric vehicles. Nat. Clim. Change 5, 329–332 (2015) 4. Khan, F., Ali, Y., Khan, A.U.: Sustainable hybrid electric vehicle selection in the context of a developing country. Air Qual. Atmos. Health 13(4), 489–499 (2020). https://doi.org/10.1007/ s11869-020-00812-y 5. Kane, M.: INSIDEEVs (2018). https://www.insideevs.com/news/340135/plug-in-electriccars-sales-in-us-surpass-1-million/. Accessed 13 Nov 2019 6. Vaughan, A.: The Guardian (2018). https://www.theguardian.com/environment/2018/aug/26/ electric-cars-exceed-1m-in-europe-as-sales-soar-by-more-than-40-percent. Accessed 13 Nov 2019 7. Edwards, W., Barron, F.H.: SMARTS and SMARTER: Improved simple methods for multiattribute utility measurement. Organ. Behav. Hum. Decis. Process. 60(3), 306–325 (1994) 8. Lootsma, F.A.: A model for the relative importance of the criteria in the multiplicative AHP and SMART. Eur. J. Oper. Res. 94(3), 467–476 (1996)

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9. Biswas, T.K., Das, M.C.: Selection of commercially available electric vehicle using fuzzy AHP-MABAC. J. Inst. Eng. (India) Ser. C 100(3), 531–537 (2019) 10. Biswasa, T.K., Saha, P.: Selection of commercially available scooters by new MCDM method. Int. J. Data Netw. Sci. 3(2), 137–144 (2019) 11. Biswas, T.K., Das, M.C.: Selection of hybrid vehicle for green environment using multiattributive border approximation area comparison method. Manage. Sci. Lett. 8(2), 121–130 (2018) 12. CihatOnat, N., Gumus, S., Kucukvar, M., Tatarid, O.: Application of the TOPSIS and intuitionistic fuzzy set approaches for ranking the life cycle sustainability performance of alternative vehicle technologies. Sustain. Prod. Consum. 6, 12–25 (2016) 13. Rouyendegh, B.D., Yildizbasi, A., Üstünyer, P.: Intuitionistic fuzzy TOPSIS method for green supplier selection problem. Methodol. Appl. 24, 2215–2228 (2019) 14. Samaie, F., Meyar-Naimi, H., Javadi, S., Farahani, H.F.: Comparison of sustainability models in development of electric vehicles in Tehran using fuzzy TOPSIS method. Sustain. Cities Soc. 53, 101912 (2020) 15. Memari, A., et al.: Sustainable supplier selection: a multi-criteria intuitionistic fuzzy TOPSIS method. J. Manuf. Syst. 50, 9–24 (2019) 16. Öztay¸si, B., U˘gurlu, S., Kahraman, C.: Assessment of green energy alternatives using fuzzy ANP. In: Cavallaro, F. (ed.) Assessment and Simulation Tools for Sustainable Energy Systems, pp. 55–77. Springer, London (2013). https://doi.org/10.1007/978-1-4471-5143-2_3 17. Öztay¸si, B., Kahraman, C.: Evaluation of renewable energy alternatives using hesitant fuzzy TOPSIS and interval type-2 fuzzy AHP. In: Management Association, Inc. (ed.) Renewable and Alternative Energy: Concepts, Methodologies, Tools, and Applications, pp. 1378–1412. IGI Global (2017). https://doi.org/10.4018/978-1-5225-1671-2.ch048 18. Kahraman, C., Çevik, O.S., Öztay¸si, B.: Engineering economic analyses using intuitionistic and hesitant fuzzy sets. J. Intell. Fuzzy Syst. 29(3), 1151–1168 (2015) 19. Yanık, S., Sürer, S., Oztaysi, B.: Designing sustainable energy regions using genetic algorithms and location-allocation approach. Energy 97, 161–172 (2016) 20. Kahraman, C., Oztaysi, B., Cevik, O.S.: An integrated intuitionistic fuzzy AHP and TOPSIS approach to evaluation of outsource manufacturers. J. Intell. Syst. 29(1), 283–297 (2020) 21. Alinezhad, A., Khalili, J.: New Methods and Applications in Multiple Attribute Decision Making (MADM). Springer, Cham (2019). https://doi.org/10.1007/978-3-030-15009-9 22. von Winterfeldt, D., Edwards, W.: Decision Analysis and Behavioral Research. Cambrdge University Press, Cambridge, UK (1986)

Fuzzy Periodic Patterns from Super-Market Datasets Fokrul A. Mazarbhuiya1(B) , Limainla Kichu1 , and M. Y. AlZahrani2 1 School of Fundamental and Applied Sciences, Assam Don Bosco University,

Kamarkuchi, India [email protected] 2 Department of IT, College of Computer Science and IT, AlBaha University, Alaqiq, Kingdom of Saudi Arabia

Abstract. Finding periodicity of the patterns from super-market data has been found to be an important data mining problem which many researchers encounter often. Such patterns reflect the buying nature of the customers in the super-market. There may be yearly, half-yearly, quarterly, monthly, daily, hourly or any other type of periodicity. In such patterns, it has been observed that the pattern is not exactly periodic that is the length of the time interval of frequency of a frequent itemset is not always equal. Furthermore, the time gap between successive time intervals of frequency of the frequent itemset is also not equal. However, there is a sufficient overlapping in the time intervals. In this situation, if the time intervals of frequency can be retained as a compact form it becomes fuzzy time interval describing the period of frequency of the frequent itemset. We designate the corresponding pattern as fuzzy periodic pattern. We propose here a method of discovering such patterns from the super-market dataset. The effectiveness of the method can be verified with the help of experiment conducted with a synthetic data collected from FIMI website. Keywords: Periodic frequent patterns · Superimposition of intervals · Superimposed intervals · Non-empty intersection of intervals · Super-market datasets · Temporal datasets · Fuzzy interval · Fuzzy periodic patterns

1 Introduction Over the last couple of years, the methods of temporal data mining have been found to be useful in many applications. One such application is in super-market [1]. In this problem [1], the underlying dataset is the collection of transactions in the super-market where each transaction consists of the set of items purchased and the time of transaction (or purchase). In [1], the time attribute of the dataset has been treated similar to any other attributes. However, taking time attribute differently, more interesting and time dependent patterns can be extracted. In [2], the authors did the pioneering work in this direction by considering the item’s life-time in a dataset as the time interval between first and last transaction holding it. It is to be mentioned here that the item’s lifetime and dataset’s lifetime are not necessarily the same. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 208–218, 2022. https://doi.org/10.1007/978-3-031-09173-5_27

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In [3], the method of finding local patterns from super-market datasets has been proposed. The local patterns are those which are frequent in certain interval of time, but may be infrequent in their lifetime. The proposed method [3] breaks the lifetime of the itemset into a sequence of subintervals where the itemset may be frequent. That is why the itemset extracted by [3] is termed as locally frequent itemset. The time interval sequence linked with each locally frequent itemset could exhibit some remarkable patterns. If the time-stamps which is the time of transactions is taken as time hierarchy some interesting patterns like periodicity may be extracted. In finding such periodicity in the locally frequent itemset [3, 4] it may be observed that the repetition may not be exact, however, there may be a substantial overlapping of intervals of frequency. Using this property, yearly, half yearly, quarterly, daily etc. fuzzy periodic patterns can be generated [4]. In [5], a scheme called set superimposition is applied to retain overlapping time intervals associated to each locally frequent itemsets in a compact form which becomes fuzzy time interval and the corresponding locally frequent itemset is termed as fuzzy periodic [6–8]. For finding yearly periodicity the year of the time hierarchy is not considered. Similarly, for finding monthly periodicity year and month are dropped from time hierarchy and so on. The objective of the paper is three-fold. First of all, we define the superimposition of intervals which is a slight variation of [5]. Next, we describe the method of construction of fuzzy interval from the set of superimposed intervals. Finally, we propose an algorithm to unearth fuzzy periodic patterns. The article is prepared as follows. In Sect. 2, the recent developments in the line of our work are discussed. In Sect. 3, the terminology of the article is discussed. The proposed scheme is explained with a flowchart in Sect. 4. The experimental studies are discussed in Sect. 5. In Sect. 6, we illustrate some possible application areas of our problem. Finally, in Sect. 7, a brief conclusion and lines for future works are given.

2 Related Works In [1] Agrawal et al. proposed the method of discovering association rules from supermarket datasets. In [9] the temporal data mining is discussed in detail. If time feature is considered separately, some exciting time-dependent patterns can be found. Integrating association rule detection problem with temporal features is to discover the association rule holding within a valid time periods and potential periodic natures of such patterns. In [2], the authors have proposed a method for the discovering temporal patterns by taking the lifetime of each item (or itemset) in the dataset. Then the itemsets are evaluated only during their lifetime. Accordingly, each rule has associated time-frame where it holds. The method [2] is extended in [3] by incorporating the gap between two time-stamps associated with two successive transactions including an itemset. In [10], the authors have proposed an algorithm for finding cyclic patterns where cycles are specified by users. In [11], the authors have proposed a method to discover temporal patterns with reference to fuzzy match. Their approach extracts patterns holding in “enough” intervals specified by the given calendar pattern. Similarly, in [12], the authors have put forwarded a nice algorithm for finding both cyclic and user defined calendar patterns. In [13–15], the authors have presented an approach to discover fuzzy temporal patterns.

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In [16], the authors have made a review on fuzzy frameworks arising from fuzzy transactions. In [17], the authors have proposed an F-transform based method for the detection of course-grained fuzzy association rules from datasets. In [18], the authors have explored the impact of two datasets characteristics on the performances of three most popular frequent itemset mining algorithm. An algorithm for finding clusters of periodically frequent itemsets is discussed in [19]. In [20], the authors have proposed a TW-Apriori algorithm which is an improvement of traditional Apriori algorithm for the status set sequential pattern mining with time-window. An algorithm for finding automatically the periodic or seasonal diseases is discussed in [21]. In [22], the authors have made a study on bike-sharing company’s failure in Taiwan using a combined approaches of text mining and fuzzy association rule mining. In [23, 24], the authors have proposed method of extracting the periodic fuzzy patterns from temporal databases with quantitative features. In [25], the authors have presented a method of mining very large temporal databases to find maximal frequent patterns. In our work, we are going to find the fuzzy periodic patterns from locally frequent itemsets [3, 4] based on their associated sequence of time intervals. For generating fuzzy intervals, we have used a method which is a slight variation of the one given in [5].

3 Terminology Used Let us explained definitions, notations and terms used in this method. 3.1 Fuzzy Set Let us consider X to be the universe of discourse. A fuzzy set A in X is characterized by μA (x) ∈ [0, 1], x ∈ X where μA (x), the membership function representing the membership grade of x in A. 3.2 Convex Normal Fuzzy Set A fuzzy set A is called as normal if ∃ at least one x ∈ X, for which µA (x) = 1. For a fuzzy set A, an α-cut Aα [26] is represented by Aα = {x ∈ X; µA (x) ≥ α}. If all the α-cuts of A are convex sets then A is said to be convex. 3.3 Fuzzy Number A convex normal fuzzy set A on R (real line) with the property that ∃ an x0 ∈ R such that µA (x0 ) = 1, and µA (x), piecewise continuous is called fuzzy number. 3.4 Fuzzy Interval Fuzzy intervals are types of fuzzy numbers such that ∃ [a, b] ⊂ R such that µA (x0 ) = 1for all x0 ∈ [a, b], and µA (x) is piecewise continuous.

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3.5 Support and Core of a Fuzzy Set The support of a fuzzy set A in X is the crisp set containing every element of X with membership grades greater than zero in A and is notified by S(A) = {x ∈ X; µA (x) > 0}, whereas the core of A in X is the crisp set containing every element of X with membership grades 1 in A. 3.6 Set Superimposition In [5] an operation named superimposition (S) was proposed. We re-write the operation as follows. A1 (S)A2 = (A1 − A2 )(1/2) (+) (A1 ∩ A2 )(1) (+) (A2 − A1 )(1/2)

(1)

where (A1 − A2 )(1/2)) and (A2 − A1 )(1/2) are fuzzy sets having fixed membership (1/2), and (+) denotes union of disjoint sets. To elaborate it, let A1 = [x 1 , y1 ] and A2 = [x 2 , y2 ] are two real intervals such that A1 ∩ A2 = φ, we would get a superimposed portion. It can be seen from (1)   (1/2)      (2) x1 , y1 (S) x2 , y2 ]= [x(1) , x(2) (1/2) (+) x(2) , y(1) (1) (+) y(1) , y(2) where x(1) = min(x1 , x2 ), x(2) = max(x1 , x2 ), y(1) = min(y1 , y2 ), and y(2) = max(y1 , y2 ).   if we superimpose three intervals [x 1 , y1 ], [x 2 , y2 ], and [x 3 , y3 ], with 3 Similarly, i=1 xi , yi  = φ the resulting superimposed interval will look like  (1/3)     x1 , y1 (S) x2 , y2 ] (S) [x3 , y3 ] = [x(1) , x(2) (1/3) (+) x(2) , x(3)      (1/3) (+) x(3) , y(1) (1) (+) y(1) , y(2) (2/3) (+) y(2) , y(3)

(3)

where the sequence {x (i) ; i−1, 2, 3} is found from {x i ; i = 1, 2, 3} by arranging ascending order of magnitude and {y(i) ; i−1, 2, 3} is found from {yi ; i = 1, 2, 3} in the similar fashion. In this way we can apply set superimposition on any number say n, of intervals if they have non-empty intersections. For large value of n, using Glivenko-Cantelli Lemma of order statistics [5], the Eq. (3), will give us a fuzzy interval.

4 Proposed Algorithm In the proposed method the time-stamps associated with each transaction in the supermarket is stored as hierarchy of the kind year_month_day_hour_minute_second. To extract yearly patterns the year of the hierarchy is dropped and for monthly pattern year_month are dropped and so on. The locally frequent itemsets are mined by using the technique given in [3, 4]. A sequence of time-intervals of frequency is connected to each

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locally frequent itemset where it is frequent which is used to construct set of superimposed intervals [5]. As every set of superimposed interval produces fuzzy interval, each locally frequent itemset will be associated with one or more fuzzy time interval depending on the number of set of superimposed intervals it has. We call such locally frequent itemsets as fuzzy periodic frequent itemsets as the associated period of frequency is a fuzzy time interval. The method is described as follows. The method takes input from output of the method given in [3, 4]. For finding fuzzy periodicity of the locally frequent itemset, the algorithm explores each locally frequent itemsets [3, 4] one by one. The method consists of two steps. In the first step, a set of superimposed intervals is maintained with each locally frequent itemset which is initially empty. Then the associated time intervals of frequency are visited sequentially. The first time interval is visited and kept in the superimposed time interval set maintained for the locally frequent itemset. When next time interval is visited it is checked whether it has non-empty intersection or overlapping with the first one or not. If it has then the it is superimposed on first with the re-construction of the membership values [The membership value calculation is given in Eq. (3)] else a new set superimposed time interval will start with the second time interval as starting time interval. In any stage if the visited time interval is found to be overlapping with the core of any of the superimposed time intervals set maintained for the locally frequent itemset, then it has to be superimposed on the concern superposed time intervals set with the re-construction of the membership values [The definition of core of a fuzzy set is given in Sect. 3] else a fresh superimposed time interval set will start with the current time interval as the starting time interval. It will continue till the end sequence of time intervals linked with the given locally frequent itemset. The above process will be carried out for all locally frequent itemsets. After the completion of step-1, each locally frequent itemset will be accompanying with one or more set of superimposed time intervals describing their period of frequencies. In step-2, every superimposed time interval set is used to produce a fuzzy time interval [5]. Consequently, every locally frequent itemset will be accompanying with one or more fuzzy time interval describing their period of frequencies. We call such frequent itemsets as fuzzy periodic. The flowchart of the method is given below in Fig. 1. The algorithm uses two functions namely Compsuperimp(lt, lst) and Superimp(lt, lst). The Compsuperimp(lt, lst) initially finds the intersection between lt and core of lst, the set of superimposed interval. If it has non-empty intersection then lt is superimposed on lst by calling Superimp(lt, lst) which effectively carries out the process by updating the membership values described in Eqs. (3) which will produce a fuzzy time interval. The same process is performed for all the locally frequent itemsets supplied by the method [3, 4]. Thus, the algorithm supplies all the fuzzy periodic frequent itemsets.

Fuzzy Periodic Patterns from Super-Market Datasets Start

Input the set of frequent itemsets extracted by method [3, 4]

Choose an itemset s with its sequence of time intervals (L)

Read first interval lt(0) from L and put it to lst (set of superimposed intervals) initially empty

Read rest of the intervals lt(i)

i=i+1 go to next itemset

If (lst lt[i])!=null

no

yes Compsuperimp(lst, lt[i]) with the suitable readjustment of the membership functions

no

If no frequent itemset remains

yes Display the fuzzy periodic hourly itemsets along with peiods where yestime intervals each itemset is associated fuzzy

End

Fig. 1. Flowchart of the proposed algorithm

i=i+1

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5 Experimental Setting and Results For the experiment conducted in this paper, a synthetic dataset named T10I4D100K is used which accessible from FIMI website [27]. A brief dataset description is given in Table 1. The experiment has been conducted on an Intel Core 7i machine, with 8 GB RAM with MS-Windows 2010 64-bit OS. As the dataset is non-empty, we have incorporated time attribute (calendar dates) on it. For this we write a program, the program takes as input dataset, start date (01-01-2020), and two whole numbers. The program randomly selects a number between two input whole numbers and set this number of transactions against a particular date which means these number of transactions were happened in that date. The inputs were selected in such a manner that the lifetime of the dataset has to be almost one year. In this way a temporal dataset is generated which then be used to find locally frequent itemsets by the method given [3, 4]. Then the outputs of [3, 4] Table 1. T10I4D100K dataset characteristics Dataset

#Items

#Transactions

Min|T|

max|T|

Avg|T|

T10I4D100K

942

100 000

4

77

39

Table 2. The fuzzy periodic frequent itemsets for different set of transactions for itemset Data size in terms of no. of transactions

0

10000

15000

25000

50000

60000

75000

100000

No of fuzzy periodic patterns

0

1

2

3

4

4

4

4

Dataset sizes vs fuzzy periodic patterns 4.5 No of fuzzy periodic patterns

4 3.5 3 2.5 2 1.5 1 0.5 0 0

20000

40000

60000 Dataset sizes

80000

100000

Fig. 2. Graph of Dataset sizes vs fuzzy periodic frequent itemsets

120000

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are used to find the fuzzy periodic frequent itemsets. The experiments were conducted taking the different sizes of the datasets and the results were noted. A partial view of the result is shown in Table 2, Fig. 2, and Fig. 3. Dataset sizes vs fuzzy periodic patterns

100000

Dataset sizes

75000 60000 50000 25000 15000 10000 0 0

0.5

1

1.5

2 2.5 3 No of fuzzy periodic patterns

3.5

4

4.5

Fig. 3. Bar diagram of Dataset sizes vs fuzzy periodic frequent itemsets

It is observed from the results that, for the dataset with 10,000 transactions, the number of fuzzy periodic pattern extracted is 1, for 15,000 transactions its number is 2, for 25,000, 3, and for 50,000 to 100,000 the algorithm gives us 4 fuzzy periodic patterns.

6 Proposed Applications Although the problem of mining fuzzy periodic patterns is originated from super market to study and understand the customer buying patterns as a problem of extracting patterns that holds repeatedly or periodically, one of the applications of such patterns is the cold drink whose transaction goes up during summer in every calendar year. Our algorithm is able to extract both fully periodic as well as partially periodic patterns i.e. patterns holding enough number of subintervals. Similarly, other type of patterns such as half yearly patterns, quarterly patterns, bi-monthly patterns, monthly patterns, weekly patterns etc. can be extracted, Since, many types data can be represented as transaction databases and most of the transaction databases are associated with temporal features explicitly or implicitly, our method can be applied in a wide-range of domains such as bioinformatics [28], network data analysis [29], activity monitoring [30], malware detection [31], anomaly detection [32] etc. The algorithm can be modified according to the specific requirement of the given problem.

7 Conclusions and Lines for Future Works In this article, we have proposed an algorithm to detect fuzzy periodic patterns from super-market datasets. The algorithm takes input from the result of [3, 4], which gives

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locally frequent itemsets along with a set of sequence of time intervals where every locally frequent itemset will be accompanied with one sequence. If the time stamp is taken as the calendar date, some interesting patterns such as yearly, monthly, daily etc. can be observed. The paper explores such properties and proposed a simple method to extract such patterns. Our proposed algorithm visits the sequence of time intervals one by one and uses a method which is slightly different from the method discussed in [5] and keeps the time interval in a compact manner called superimposed intervals. Thus, each locally frequent itemset will be accompanying with time intervals superimposed in one or more places which generates one or more fuzzy time intervals. In this manner, we will have each frequent itemset along with a fuzzy time interval. We call such locally frequent itemset as fuzzy periodic frequent itemset. The method’s efficiency is established by the experiment conducted with T10I4D100K dataset collected from FIMI website [27]. As the dataset is non-temporal, we have included the calendar dates on it. The calendar dates were inserted in such a way that the lifetime of the dataset appears to be almost one year which is then used to find locally frequent itemsets by the method given in [3, 4]. Each locally frequent itemset has an associated sequence of time intervals which describes its periodicity. Our method takes each locally frequent itemset one at a time, visit its time interval sequentially and superimpose the intervals at their proper places to get fuzzy time intervals. This way each locally frequent itemset will have one or more fuzzy time intervals describing its periodicity. We term them as fuzzy periodic patterns. The experiments are conducted by taking different sizes of the dataset (in terms of number of transactions), the results were recorded and presented in Table 2, Fig. 2 and Fig. 3. It is observed from the results that for 10000 transaction dataset, the algorithm discovers 1 fuzzy periodic patterns, for 15000 and 25000 transaction datasets it gives 2 and 3 fuzzy period patterns respectively and for 50000 to 100000 transaction datasets the number of fuzzy periodic patterns discovered is 4. In future the works can be done in the following directions. 1. In future we will try to explore non-binary or qualitative dataset for finding similar patterns. 2. In future we will try to extract other types of patterns such as sequential patterns, classification rules etc. 3. In future we will try to apply the method in different other domains like network data analysis, malware and anomaly detection, activity monitoring and bioinformatics.

References 1. Agrawal, R., Imielinski, T., Swami, A.N.: Mining association rules between sets of items in large databases. In: Proceedings of 1993 ACM SIGMOD International Conference on Management of Data, vol. 22(2) of SIGMOD Records, pp. 207–216. ACM Press (1993) 2. Ale, J.M., Rossi, G.H.: An approach to discovering temporal association rules. In: Proceedings of 2000 ACM Symposium on Applied Computing (2000) 3. Mahanta, A.K., Mazarbhuiya, F.A., Baruah, H.K.: Finding locally and periodically frequent sets and periodic association rules. In: Pal, S.K., Bandyopadhyay, S., Biswas, S. (eds.) PReMI 2005. LNCS, vol. 3776, pp. 576–582. Springer, Heidelberg (2005). https://doi.org/10.1007/ 11590316_91

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4. Mahanta, A.K., Mazarbhuiya, F.A., Baruah, H.K.: Finding calendar-based periodic patterns. Pattern Recogn. Lett. 29(9), 1274–1284 (2008) 5. Baruah, H.K.: The Randomness-Fuzziness consistency principle. Int. J. Energy Inf. Commun. 1(1), 37–48 (2010) 6. Mazarbhuiya, F.A.: Discovering yearly fuzzy patterns. Int. J. Comput. Sci. Inf. Secur. 12(9), 7–12 (2014) 7. Shenify, M., Mazarbhuiya, F.A.: Discovering monthly fuzzy patterns. Int. J. Intell. Sci. 5, 37–43 (2015) 8. Mazarbhuiya, F.A.: Extracting daily fuzzy patterns. Kasmera 44(1), 2006–2016 (2018) 9. Antunes, C.M., Oliviera, A.L.: Temporal data mining an overview. In: Workshop on Temporal Data Mining-7th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (2001) 10. Ozden, B., Ramaswamy, S., Silberschatz, A.: Cyclic association rules. In: Proceedings of the 14th International Conference on Data Engineering, pp. 412–421 (1998) 11. Li, Y., Ning, P., Wang, X.S., Jajodia, S.: Discovering calendar-based temporal association rules. Data Knowl. Eng. 44, 193–218 (2003) 12. Zimbrado, G., Moreira de Souza, J., Teixeira de Almeida, V., Arauja de Silva, W.: An algorithm to discover calendar-based temporal association rules with item’s Lifespan restriction. In: Proceedings of the 8th ACM SIGKDD (2002) 13. Subramanyam, R.B.V., Goswami, A., Prasad, B.: Mining fuzzy temporal patterns from process instances with weighted temporal graphs. Int. J. Data Anal. Tech. Strat. 1(1), 60–77 (2008) 14. Jain, S., Jain, S., Jain, A.: An assessment of fuzzy temporal rule mining. Int. J. Appl. Innov. Eng. Manage. 2(1), 42–45 (2013) 15. Lee, W.J., Jiang, J.Y., Lee, S.-J.: Mining fuzzy periodic association rules. Data Knowl. Eng. 65(3), 442–462 (2008) 16. Marin, M., Ruiz, M.D., Sanchez, D.: Fuzzy frameworks for mining data association fuzzy association rules and beyond. Wires Data Min. Knowl. Disc. 6, 50–69 (2016) 17. Martino, F.D., Sessa, S.: Detection of fuzzy association rules by fuzzy transforms. In: Advances in Fuzzy Systems, vol. 2012, pp. 1–12. Hindawi Publication (2012) 18. Heaton, T.J.: Comparing dataset characteristics that favor the Apriori Eclat or FP-growth frequent itemsets mining algorithm. Cornell University Archive (2017) 19. Mazarbhuiya, F.A.: A novel approach for clustering periodic patterns. Int. J. Intell. Sci. 7(1), 1–8 (2017) 20. Zhou, S., et al.: Status set sequential pattern mining considering time windows and periodic analysis of patterns. Entropy (Basel) 23(6), 738 (2021) 21. Mazarbhuiya, F.A.: Automatic detection of seasonal diseases from medical data. Des. Eng. 2021(8), 3247–3259 (2021) 22. Wu, S.: A fuzzy association rules mining analysis of the influencing factors on the failure of oBike in Taiwan. Mathematics 8(11), 1908 (2020) 23. Pamalla Veena, R., Kiran, U., Ravikumar, P., Aggrawal, S.: Discovering fuzzy periodic patterns in quantitative temporal databases. In: Uday Kiran, R., Fournier-Viger, P., Luna, J.M., Lin, J.-W., Mondal, A. (eds.) Periodic Pattern Mining, pp. 57–67. Springer, Singapore (2021). https://doi.org/10.1007/978-981-16-3964-7_4 24. Kiran, R.U., et al: Discovering fuzzy periodic frequent patterns in quantitative temporal databases. In: Proceedings of the 29th IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2020, New York, pp. 1–8 (2020) 25. Kiran, R.U., Watanobe, Y., Choudhury, B., Zettsu, K., Toyoda, M., Kitsuregawa, M.: Discovering maximal frequent patterns in very large databases. In: Proceedings of the 7th IEEE International Conference on Data Science and Advanced Analytics, DSAA 2020, New York, pp. 11–20 (2020)

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26. Klir, J., Yuan, B.: Fuzzy Sets and Logic Theory and Application. Prentice Hill Pvt. Ltd. (2002) 27. http://fimi.cs.helsinki.fi/data/ 28. Naulaerts, S., et al.: A primer to frequent itemset mining for bioinformatics. Brief. Bioinf. 16(2), 216–231 (2015) 29. Goyal, P., Challa, G.S., Srivastava, S., Goyal, N.: Anytime frequent itemset mining of transactional data streams. Big Data Res. 21, 100146 (2020) 30. Amirul Islam, M., Acharjee, U.K.: Mining periodic patterns and accuracy calculation for activity monitoring using RF tag arrays. In: Uddin, M.S., Bansal, J.C. (eds.) Proceedings of International Joint Conference on Computational Intelligence. AIS, pp. 85–95. Springer, Singapore (2020). https://doi.org/10.1007/978-981-13-7564-4_8 31. Martin Korec, B.: Malware Detection based on periodic behavior. Master thesis, Faculty of Informatics, Msaryk University, Brno, Spring 2018 (2018) 32. Soheily-Khah, S., Wu, Y.: Ensemble learning using frequent itemset mining for anomaly detection. In: Meghanathan, N., et al. (eds.) CCSEA, CLOUD, SIPRO, AIFU, SEA, DKMP, NCOM - 2019. © CS & IT-CSCP 2019, pp. 373–389 (2019)

A Supervised Approach to Community Detection Problem: How to Improve Louvain Algorithm by Considering Fuzzy Measures Mar´ıa Barroso1(B) , Daniel G´ omez1,2 , and Inmaculada Guti´errez1 1

2

Faculty of Statistics, Complutense University, Avenida Puerta de Hierro, s/n, 28040 Madrid, Spain {mbarro10,inmaguti}@ucm.es, [email protected] Instituto de Evaluaci´ on Sanitaria. Complutense University, Madrid, Spain Abstract. Community detection problems are one of the most important problems in Social Network Analysis. Based on the Louvain algorithm, in this paper we propose a supervised technique to address the classic community detection problem in both directed and undirected networks. Our proposal is developed on the basis of extended fuzzy graphs, specifically paying attention to the notion of flow. We present a parametric and aggregation supervised approach that uses the flow capacity in terms of fuzzy information, in order to obtain realistic and global solutions, going one step further than local previous results. We evaluate the performance of that supervised technique by considering several benchmark and real-world networks. Taking into account the directed modularity, this new approach is developed under the machine learning paradigm, carrying through with two consecutive phases. The results obtained allow us to assert the goodness of our new supervised technique, beyond others existing algorithms. Keywords: Complex networks · Community detection · Louvain algorithm · Modularity · Fuzzy measures · Flow Capacity Louvain

1

Introduction

Social networks are an important representation tool, whose analysis from graph theory perspective has become really popular in different areas in last decades. One of the hottest topics in this field is community detection [8,9]. The purpose is to analyze the group structure of social networks formed by nodes that establish several types of interdependency. This problem is addressed in several disciplines, for example, in epidemiology, in which it is useful to understand the patterns of human contact that influenced the spread of a disease, such as COVID-19 [25]. Researchers are very interested in the search of the ‘best community structure technique’, trying to quantify the quality of the partitions obtained, in general, This research has been partially supported by PGC2018096509-B-I00. c The Author(s), under exclusive license to Springer Nature Switzerland AG 2022  C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 219–227, 2022. https://doi.org/10.1007/978-3-031-09173-5_28

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by considering the structural information of the graph [8,18]. Among all the existing methods, it is worth mentioning the Louvain Algorithm [7]. It is a multiphase greedy algorithm based on modularity optimization heuristic [19]. Due to its speed and high-quality results, the Louvain algorithm has turned into one of the most popular and used methods in community detection. However, as is often the case with greedy methods [24], the Louvain algorithm occasionally gets stuck on local solutions. The issue with these techniques is that they do not take into account the global information of the problem. As previous step to solve it, we agree on the importance of modeling as much information as possible. In general, the use of fuzzy measures [23] considerably improves modeling when dealing with networks. In the framework of community detection, we suggest to use fuzzy measures based on flow, which provide a more general view of network connectivity and its underlying structure. On this basis of having a rich and realistic representation, there are several works in the literature which tackle the community detection problem in networks with additional information represented by fuzzy measures [13–15], by working with extended fuzzy graphs. This idea may be also considered to exploit the information of directed networks [12], for example, in terms of flow [3]. Those works have in common a process to aggregate all the modeled information, usually by considering an importance parameter to balance each information source. Nevertheless, the analysis of this aggregation process is an open problem, which is meant to be addressed in this paper. Following the philosophy of those previous works, we propose a supervised technique with the purpose of improving the clustering methods in community detection problems, and measurement of the quality of the obtained partitions. It is based on an extended fuzzy graph, in which we differentiate two different and independent knowledge sources: the structural part of the graph, and some additional information on the individuals; both are combined with an importance parameter. The key is to determinate the parameter with which a higher modularity value is reached, in both undirected and directed networks [2,19]. With extended fuzzy graphs, we can integrate the new fuzzy measure which models the flow [3] in the objective function of community detection algorithms, considering a parameter to balance its importance. The idea is to obtain the needed parameters in the aggregated model. The rest of the paper is organized as follows. In Sect. 2 we introduce some preliminaries. In Sect. 3 we illustrate the proposed supervised technique. The evaluation benchmarking process is described in Sect. 4. We finish in Sect. 5 with some conclusions about the work done.

2

Preliminaries

This section introduces some concepts of graph theory, community detection and fuzzy measures, necessary to understand the work developed here.

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Definition 1. Undirected Networks. [22] An undirected network is a pair GU = (V, E), where V = {1, . . . , n} is the set of vertices or nodes and E = {{i, j} : i, j ∈ V } is an unordered set of unordered pairs of nodes named edges. Every GU can be represented by its adjacency matrix A, a symmetric matrix which represents the direct connections between nodes. Definition 2. Directed Networks. [18] A directed network is a pair G = (V, E), where V = {1, . . . , n} is the set of vertices or nodes and E = {(i, j) : i, j ∈ V } is an unordered set of ordered pairs of nodes named directed edges. Every G can be represented by its adjacency matrix A, a non-symmetric matrix which represents the immediate directed connections between nodes. The community detection problem is one of the most relevant issues concerning networks analysis. Obtaining a partition, the network allows a proper understanding of the similarities and synergies of its individuals. There are many measures to asses the quality of a partition. One of the most used is the well-know modularity, based on density [19]. Several algorithms consider the modularity as objective function, as the Louvain Algorithm [7]. It is one of the most used and popular methods in community detection, because of its speediness and high quality results, being especially appropriate when dealing with large networks. It is a heuristic and greedy method based on modularity algorithm, divided into two phases that are iteratively repeated. The process evaluates the gain of the modularity (undirected modularity [19] or directed modularity [2], depending on the nature of the considered network), when a node is moved to its neighbours’ community. This process stops when a local maximum of modularity is reached. Then we recall fuzzy measures. These are really useful functions to manage imprecise and vague information [5,6,10,11]. The consideration of fuzzy measures is a key factor to model additional information beyond the graph. Definition 3. Fuzzy Measure. [23] A fuzzy measure on the set V = {1, . . . n} is a function μ : 2V → [0, 1] satisfying (1) boundary conditions (μ(∅) = 0; μ(V ) = 1), and (2) monotonicity (∀A, B ⊆ V with A ⊆ B, μ(A) ≤ μ(B)). Then, we introduce the extended fuzzy graph. It was defined to deal with additional information in graphs by means of fuzzy measures. Definition 4. Extended Fuzzy Graph [13, 15]. Let G = (V, E) denote a crisp graph, and let μ : 2V −→ [0, 1] denote a fuzzy measure defined over the set  = (V, E, μ) obtained from considering together the of nodes, V . The triplet G graph with the fuzzy measure, is called extended fuzzy graph. The extended fuzzy graph was adapted to deal with directed networks, specifically to represent the flow by the corresponding fuzzy measure [3]. Definition 5. Flow Extended Fuzzy Graph [3]. Let G = (V, E) denote a directed graph, being (i, j) ∈ E a directed edge. Being fij the flow between nodes 

i, j ∈ V , let μF (S) =

 i,j∈S i,j∈V

fij fij

denote a 2−additive fuzzy measure which models

 = (V, E, μF ) is called flow extended fuzzy graph. the flow of G. The triplet G

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 = (V, E, μF ), it was defined the Flow Capacity Louvain On the basis of G algorithm [3], a multi-phase heuristic method based on the directed Louvain [17]. This method, summarized by its pseudo-code in Algorithm 1, not only considers the structural information of the graph to find a partition, but also the flow, which provides a more general vision of the relations between the individuals. To do so, in [3] it was introduced the directed interaction index  D f =  ij flm , as a matrix with which manage the information of [11], Iij i,j∈V l,m∈V

μF . Then, being A the adjacency matrix of G, the matrix M was obtained by  = (V, E, μF ). the combination of A and I D to summarize the information of G Hence, the directed modularity variation used in Algorithm 1 which occurs when moving the node i to the community of one of its neighbours j, is calculated as:   kiin kjout 1  d (1) Mij − ΔQi (j)(P ) = δ(ci , cj ) m i,j m where P is a partition of the nodes, m = |E|, kiin is the input degree of i ∈ V , kjout is the output degree of j ∈ V , δ(ci , cj ) = 1 if ci and cj belongs to the same community in P and δ(ci , cj ) = 0 otherwise. Algorithm 1.

Flow Capacity Louvain Input: G = (V, E), α ∈ [0, 1] Output: P

1: Build μF from G;  = (V, E, μF ); A ← G = (V, E); I ← μF ; M = αA + (1 − α)I D ; 2: G 3: Phase 1. 4: Let each node of the graph be an isolated community ← P ; 5: o ← permutation(V ); 6: for k ∈ o do 7: search in A all the neighbours of k, j; 8: ∀j, calculate ΔQd k (j)(P ) in matrix M ; ∗ d 9: j ∗ = { j | ΔQd k (j ) = maxj {Qk (j)} }; ∗ d 10: if ΔQk (j ) > 0 then 11: Move node k to j ∗ ’s community and Update P ; 12: else 13: k remains in its community; 14: end if 15: end for 16: Phase 1 Ends 17: Phase 2. 18: A∗ and M ∗ are the aggregated matrix obtained from A and M respectively,

whose nodes are

the communities found in Phase 1; 19: Apply Phase 1 considering A∗ and M ∗ ; 20: Phase 2 Ends

3

A Supervised Approach

 = (V, E, μF ) and considering the Flow Capacity Louvain preOn the basis of G viously explained with α ∈ [0, 1] as importance parameter used to summarize  in M = αA + (1 − α)I D , in this work we suggest a superthe information of G vised technique with which we try ‘to learn’ the better α(or a good one). In previous works, the authors approach the problem of community detection in

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directed networks by considering some additional information in terms of fuzzy measures based on flow [3]. Nevertheless, the way in which the whole information is aggregated is still an open problem which we try to solve. Now we propose a comprehensive study to determine with which values of α provide high values of modularity in the Flow Capacity Louvain method. This algorithm was proposed to deal with directed networks, however, undirected graphs may also be analyzed just understanding a non directed edge {i, j} as two directed edges (i, j) and (j, i). The first step is to obtain the two components of the corresponding extended fuzzy graph to define the objective function: the adjacency matrix of the crisp graph, A, and the interaction matrix build from the fuzzy measure μF which models the flow, I D , taking into account that μF is 2-additive [3]. On the basis of machine learning supervised techniques, and considering two phases of training and test respectively, in this work, we implement a process by considering different α values within [0, 1] to perform the Flow Capacity Louvain algorithm. Several networks are considered as training data set in the supervised technique, labeling each α with the modularity obtained in the community detection process. In the training phase, the average modularity is calculated for each value of α and the α with the maximum modularity is returned. In the second phase, the networks taken for the test are evaluated in order to probe the reliability of α with maximum modularity. As mentioned, we perform this new supervised technique using Flow Capacity Louvain algorithm; however, another community detection algorithm could have been established instead. We illustrate the proposed parametric supervised technique with the corresponding pseudo-code in Algorithm 2. Supervised Technique Input: 100 Networks: N 1 . . . N 80 Training Data and N 1 . . . N 20 Test Data. α1 . . . α100 ∈ [0, 1]. Output: α∗ ∈ [0, 1] provides the highest Average(Qd ).

Algorithm 2 .

1: Randomly classification of the networks in training and validation: 2: 80% Training data and 20% Evaluation data; 3: Step 1. i = (V i , E i , μFi ) is calculated in N i , ∀i = {1 . . . 80} ∈ T raining; 4: G i = (V i , E i , μFi ) ; 5: Ai and I Di are obtained from G 6: ∀i = {1 . . . 80}, ∀ = {1 . . . 100} F lowCapacityLouvain(N i , α ), obtaining 80 i i=1 Qd and find α∗ = α where max(Q. ) ; 7: Calculate Q. d = d 80 8: Step 2. Fj j j j j  9: G = (V , E , μ ) is calculated in N , ∀j = {1 . . . 20} ∈ T est; j = (V j , E j , μFj ) 10: Aj and I Dj are obtained from G 11: ∀j = {1 . . . 20}, F lowCapacityLouvain(N j , α∗ ), obtaining Qj∗ d ; 12: Do Hypothesis Testing: 13: if H0 : Average(QLouvain ) − Average(QF CLα∗ ) = 0 is rejected then 14: α∗ = α is accepted; 15: end if

Qi d ;

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Evaluation and Benchmarking

In this section we provide some computational results in order to test the effectiveness of the proposed supervised technique. We work with a sample network data set obtained from several repositories [4,16,21], including directed and undirected networks (seen as directed). Summarising in Table 1 those networks used in the training process and in Table 2 the networks used to test the effectiveness of the supervised technique. Table 1. Training networks data set: N 1 . . . N 80 Air traffic contro l [16]

A01 [4]

bio-Yeast [21]

Euroroad [21]

American football [16]

Arc130 [21]

CAG-mat72 [21]

Galesburg [4]

bio-Celegans [21]

Ash219 [21]

Chebyshev1 [21]

GlossTG [4]

Centrality Literature [4]

Attiro [4]

Chesapeake [21]

Highschool [16]

Congress votes [16]

Bibd-9-5 [21] Email-univ [21]

Hi-tech [4]

Contiguous USA [16]

Bison [16]

Enron email [21]

Iceland [16]

Delaunay-n10 [21]

Cage6 [21]

Everglades [4]

Kangaroo [16]

ENZYMES-g295 [21]

Can-187 [21] FilmTrust [16]

ModMath [4]

Facebook pages: food [21] Cattle [16]

Flying Teams [4]

Moreno-Hens [16]

Florida ecosystem dry [16] CS-phd [4]

Gene Fusion [16]

Physicians [16]

ia-Crime-Moreno [21]

DD244 [21]

Infect Hyper [21]

Ragusa16 [4]

Japanese macaques [16]

Dolphin [21] Jazz musician [21]

SanJuanSur [4]

Les Miserables [16]

GD02-b [21] Mexican-power [4]

SmallWord [4]

Literature 1976 [4]

Gene [21]

Power 662 bus [21]

The cities [21]

Little Rock Lake [16]

Karate [26]

Power bcspwr09 [21] Tina-AskCal [4]

Mouse Visual Cortex [21] Movies [4]

Sandi-auths [4]

Tina-DisCog [4]

Power 1138 bus [21]

s50-d01 [4]

SocialWorkJ [4]

Trefethen-150 [21]

Residence hall [16]

Sawmill [4]

Tina-DisCal [4]

US air 97 [4]

Rhesus macaques [16]

Sheep [16]

Train bombing [16]

Wiki-talk [16]

Seventh graders [16]

Strike [4]

Twitter Copen [21]

World trade [4]

Fig. 1. Summarise the average modularity  Q. d , performing α ∈ [0, 1],  = 1 . . . 100

Following the performance of the Algorithm 2, using the library ortools of Python, with the module pywrapgraph [20], we built the interaction matrix I D for each network. The Flow Capacity Louvain algorithm is performed on each network of the training set by considering 100 different values for the parameter of importance α ∈ [0, 1]. Depending on the value of α, different communities are proposed for the network. By the end of the process, those sets were assessed based on the quality measure directed modularity Qd [2]. The best α = 0.77 was selected on the basis of the high average modularity in all data set. See Fig. 1. To assess the goodness of the α above, Flow Capacity Louvain was executed in a test data set. Table 2 compares the results obtained in modularity. Then we work with hypothesis testing to establish whether significant results reject the null hypothesis (i.e., the average modularity calculated under both algorithms is equal). In this sense, significance levels were set at the 1.25% level using the Wilcoxon signed rank test in the MATLAB software [1]. We consider several networks with V ∈ {10, . . . , 2000} and E ∈ {40, . . . , 10000} which are divided into two different sets: training and test sets. The training data is exhaustively analysed, and then, the testing data is considered to assess the work, which is submitted to the hypothesis contrast. We do not find significant evidence to accept the equality in means of modularity: α = 0.77 is accepted to improve the obtained modularity.

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Table 2. Test networks data set: N 1 . . . N 20 Name

Q

Qα=0.77 Name

Q

Qα=0.77

bio-diseasome [21]

0.8072

0.8119

econ-wm3 [21]

0.2491

0.267

Dining-table partners [4]

0.4704

0.4830

eco-stmarks [21] 0.2149

0.219

Internet industry partnerships [21]

0.3484

0.3732

HIV [16]

0.6805

0.6805

Mixed-species brain-1 [21]

0.2979

0.2979

IG5-7 [21]

0.2864

0.3383

Netscience [21]

0.8322 0.8285

Korea1 [4]

0.4777

0.4777

Mangwet [21]

0.1901 0.1888

Reptilia-tortoise-network-fi-2010 [21] 0.9342 0.9311 Southern women [21]

0.3285

0.3308

PDZBase [16]

0.7877

Student government [4]

0.2058

0.2058

Retweet [21]

0.6652 0.6646

Taro exchange [16]

0.4474

0.4474

Scotland [4]

0.6813

0.6909

Webkb-wisc[21]

0.658

0.6657

Soc-tribes[21]

0.1529

0.169

5

0.7877

Conclusions

Community detection problems in network analyses have gained importance in recent years. Modularity [19] is a quality measure for partition analysis, the higher it is, the better the chosen communities. However, few works have been developed to evaluate algorithms. In this sense, a comparison approach has been used to handle this view, especially considering its computational complexity. What stands out in our research is the in-depth analysis of the existing techniques in detecting communities in the directed and non-directed field. Hence, we try to evidence the parameter proposed by the supervised algorithm in 2, where the average modularity of the data set reserved for testing is higher from the modularity obtained by the Louvain algorithm method. It is important to note that heuristic techniques allow the resolution of the optimization function in the Louvain algorithm, regardless will not find necessary the global maximum. So that, any information added to this problem means searching further with better results. In particular, the additional information in Social Networks allows to represent in a realistic way the real problem. In this framework, a ’good’ parameter α should increase the modularity proposed by [19]. As further work, we will develop this supervised approach to other algorithms further than Louvain, using other aggregation approach which incorporates new group definitions. We agree on the importance of this supervised process, because of a lack of methods in algorithmic evaluation.

References 1. The math works, inc. (2020). https://uk.mathworks.com/help/stats/signrank.html 2. Arenas, A., Duch, J., Fern´ andez, A., G´ omez, S.: Size reduction of complex networks preserving modularity. New J. Phys. 9(6), 176 (2007)

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3. Barroso, M., Guti´errez, I., G´ omez, D., Castro, J., Esp´ınola, R.: Group definition based on flow in community detection. In: Lesot, M.-J., Vieira, S., Reformat, M.Z., Carvalho, J.P., Wilbik, A., Bouchon-Meunier, B., Yager, R.R. (eds.) IPMU 2020. CCIS, vol. 1239, pp. 524–538. Springer, Cham (2020). https://doi.org/10.1007/ 978-3-030-50153-2 39 4. Batagelj, V., Mrvar, A.: Pajek datasets (2006). http://vlado.fmf.uni-lj.si/pub/ networks/data/ 5. Beliakov, G., G´ omez, D., James, S., Montero, J., Rodr´ıguez, J.: Approaches to learning strictly-stable weights for data with missing values. Fuzzy Sets Syst. 325, 97–113 (2017) 6. Beliakov, G., Wu, J.: Learning k-maxitive fuzzy measures from data by mixed integer programming. Fuzzy Sets Syst. 412, 41–52 (2021) 7. Blondel, V., Guillaume, J., Lambiotte, R., Lefevre, E.: Fast unfolding of communities in large networks. J. Stat. Mech. Theory Exp. 2008, P10008 (2008) 8. Fortunato, S.: Community detection in graphs. Phys. Rep. 486, 75–174 (2010) 9. Girvan, M., Newman, M.: Community structure in social and biological networks. Proc. Natl. Acad. Sci. 99(12), 7821–7826 (2002) 10. Grabisch, M.: The representation of importance and interaction of features by fuzzy measures. Patter Recogn. Lett. 17(6), 567–575 (1996) 11. Grabisch, M.: k-order additive discrete fuzzy measures and their representation. Fuzzy Sets Syst. 92(2), 167–189 (1997) 12. Guti´errez, I., Barroso, M., G´ omez, D., Castro, C., Esp´ınola, R.: Pattern-based clustering problem based on fuzzy measures. Dev. Artifi. Intell. Technol. Comput. Robot. 12, 412–420 (2020) 13. Guti´errez, I., G´ omez, D., Castro, J., Esp´ınola, R.: Fuzzy measures: A solution to deal with community detection problems for networks with additional information. J. Intell. Fuzzy Syst.39(5), 6217–6230 (2020) 14. Guti´errez, I., G´ omez, D., Castro, J., Esp´ınola, R.: Multiple bipolar fuzzy measures: an application to community detection problems for networks with additional information. IJCIS 13(1), 1636–1649 (2020) 15. Guti´errez, I., G´ omez, D., Castro, J., Esp´ınola, R.: A new community detection algorithm based on fuzzy measures. In: Kahraman, C., Cebi, S., Cevik Onar, S., Oztaysi, B., Tolga, A.C., Sari, I.U. (eds.) INFUS 2019. AISC, vol. 1029, pp. 133– 140. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-23756-1 18 16. Kunegis, J.: KONECT – the koblenz network collection. In: Proceeding of International Conference on World Wide Web Companion, pp. 1343–1350 (2013) 17. Li, L., He, X., Yan, G.: Improved Louvain method for directed networks. In: International Conference on Intelligent Information Processing, pp. 192–203 (2018) 18. Malliaros, F., Vazirgiannis, M.: Clustering and community detection in directed networks: A survey. Phys. Rep. 533(4), 95–142 (2013) 19. Newman, M., Girvan, M.: Finding and evaluating community structure in networks. Phys. Rev. 69, 026113 (2004) 20. Perron, L., Furnon, V.: Or-tools. https://developers.google.com/optimization/ 21. Rossi, R.A., Ahmed, N.K.: The network data repository with interactive graph analytics and visualization. In: AAAI (2015). http://networkrepository.com 22. Schaeffer, S.E.: Graph clustering. Comput. Sci. Rev. 1(1), 27–64 (2007) 23. Sugeno, M.: Fuzzy measures and fuzzy integrals-a survey. In: Readings in fuzzy sets for intelligent systems, pp. 251–257. Elsevier (1993) 24. Traag, V., Waltman, L., van Eck, N.: From Louvain to Leiden: guaranteeing wellconnected communities. Sci. Rep. 9, 5233 (2019)

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Hierarchical Fuzzy Inference System for Diabetes Mellitus Prediction Daud Mohamad(B) and Aisya Irdina Hissamudin Universiti Teknologi MARA, 40450 Shah Alam, Selangor, Malaysia [email protected]

Abstract. Diabetes Mellitus is one of the major non-communicable diseases that occurs when the pancreas does not produce enough insulin or the body does not respond effectively to the insulin, which causes blood sugar levels to increase. Uncontrollable diabetes may lead to many serious complications, including damage to the eye, kidney, nerves, heart and peripheral vascular system. Early diagnosis is vital to enable patients to be treated early, thus avoiding and reducing the risk of complication. Fuzzy Inference System (FIS) is widely used to predict disease at an early stage where it imitates human thinking by incorporating the IF-THEN rules to solve a problem systematically. However, this method can cause computational complexity when involving many attributes. In this study, Hierarchical Fuzzy Inference System (HFIS) is proposed to overcome this limitation in diabetes prediction. There are eight attributes under consideration and decomposed into three subsystems based on their similar characteristics which represent the first level of the HFIS. The outputs of the subsystems are then used as input variables for the main system at the second level to generate the output indicating the diabetes severity. The proposed HFIS significantly reduced the number of generated rules without compromising the accuracy of the prediction and can be developed into a more comprehensive system for predicting diabetes. Keywords: Diabetes mellitus · Hierarchical Fuzzy Inference System · Disease prediction

1 Introduction Diabetes mellitus or diabetes is one of the major non-communicable diseases that cause death. According to World Health Organization, diabetes mellitus was among the ten leading causes of death in 2019 [15]. There are three main types of diabetes which are type-1 diabetes, type-2 diabetes and gestational diabetes. Type-1 diabetes is characterized by insulin deficiency which results from the loss of pancreatic β cells that leads to hyperglycemia. Those with type-1 diabetes are insulin-dependent, which requires them to take insulin daily. Whereas, in type-2 diabetes, hyperglycemia occurs due to insufficient insulin production and the body’s inability to respond effectively to insulin. Meanwhile, gestational diabetes occurs when pregnant women develop high blood sugar levels without a history of diabetes [3]. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 228–236, 2022. https://doi.org/10.1007/978-3-031-09173-5_29

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Early diagnosis is required to enable patients to be treated aptly, thus reducing the risk of complication. The increase in cases of diabetes has led to the need for a reliable system that can diagnose diabetes with great accuracy. Several techniques have been implemented to classify diabetes patients, such as support vector machine, generalized discriminant analysis, naïve Bayes and k-nearest neighbor algorithm and decision tree. The fuzzy logic (FL) approach is also among the popular solutions for classification methods based on the concept of fuzzy set theory [1]. It is an extension of a crisp set that allows the membership function to take any values between 0 to 1 [16]. Due to its similarity in conceptual structure, fuzzy sets have been used to generalize the definition of fuzzy logic [14] and become an important discipline in soft computing [9, 13]. Unlike classical logic, FL offers powerful reasoning techniques for dealing with uncertainty and imprecision, which a precise mathematical model cannot describe [10, 14]. For this reason, FL has been widely used to handle the uncertainties and imprecision of medical diagnosis, where the linguistic rules are engaged to assist in decision making. Many researchers have implemented the FL approach in the prediction of diabetes diseases, such as fuzzy expert systems, adaptive-neuro fuzzy inference systems, and fuzzy ant colony optimization. The vast applications of FL in the diagnosis of diabetes undeniably add strong evidence on the significant roles of FL in predicting disease [1]. This paper aims to develop a Hierarchical Fuzzy Inference System (HFIS) for diabetes prediction with good accuracy but lesser complexity. A new hierarchical structure of the system is proposed for this purpose using the Pima Indian Diabetes Dataset. This paper is organized in the following manner. The introduction and the background of the work are discussed in Sect. 1. In Sect. 2, the Fuzzy Inference System (FIS) and the Hierarchical Fuzzy Inference System (HFIS) are given meanwhile Sect. 3 discusses the development of the model for Diabetes Mellitus prediction. Results and discussion are presented in Sect. 4 and finally, Sect. 5 concludes the paper.

2 Literature Review Fuzzy Inference System (FIS) is one of the earliest and most successful fuzzy logic and fuzzy set applications [5]. FIS imitates how humans make decisions by incorporating the IF-THEN rules to solve a problem systematically [6]. FIS has been successfully applied in various fields such as education, engineering, medicine, business and technology [1, 7, 9, 10, 12]. The advantage of solving problems using FIS is that it can deal with realworld problems, usually involving vague and subjective factors [7, 9]. However, FIS has a limitation where the number of rules in the system increases exponentially with the number of variables involved [8], resulting in high complexity for human processing. Suppose FIS with n input variables and m fuzzy sets defined for each variable generates mn rules. As n increases, the rule base will quickly overload the memory and make the FIS difficult to implement [4]. This limitation restricts the use of FIS in solving complex problems and real-life applications with large dimensions.

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The Hierarchical Fuzzy Inference System (HFIS) is a viable and effective option to deal with the rule explosion problem faced by the conventional FIS [8]. The HFIS consists of several low-dimensional fuzzy systems that are connected in a hierarchical structure [2, 13]. The idea of HFIS is to place the input variables into a collection of low-dimensional FIS instead of a single high-dimensional FIS [4]. In HFIS, the number of rules is determined by the equation k=

L 

mni

(1)

i=1

where L is the number of hierarchical levels, ni is the number of input variables in the ith level and m is the number of fuzzy sets. According to [11], the number of rules involved in the hierarchical system is reduced to a linear function of the input variables instead of an exponential function of the conventional FIS. The advantage of using HFIS over conventional FIS is that the number of rules can be reduced without compromising the accuracy and efficiency of the system [2, 12]. As a result, HFIS requires less computational time than FIS as it has fewer rules to process [4].

3 The Proposed Model 3.1 Data Collection The proposed model of the diabetes prediction system using HFIS starts with the data collection obtained from UCI Machine Learning Repository, namely Pima Indian Diabetes Dataset (PIDD). The list of attributes used in this study is shown in Table 1. Table 1. List of attributes from PIDD. Attribute

Description

Units

Pregnant

Pregnancy frequency

–

Glucose

Oral glucose tolerance test

mg/dl

Blood pressure

Diastolic blood pressure

mm Hg

Skin thickness

Triceps skinfold thickness

Mm

Insulin

2-h serum insulin

mu U/ml

BMI

Body mass index

kg/m2

Diabetes pedigree function Provides information about diabetes history in relatives – and genetic relationship of those relatives with patients Age

Age of the patient

Years

DM

Diabetes mellitus where ‘0’ is tested for negative and ‘1’ is tested for positive

–

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3.2 Architecture of the Hierarchical Fuzzy Inference System In developing the FIS, one main concern is how to reduce the number of fuzzy rules involved in the system. In this case study with eight input variables and three linguistic terms for each variable, there is a need to generate a total number of 38 = 6561 rules. Developing a FIS with thousands of rules is impractical [4], thus deploying HFIS with three subsystems, each with two or three linguistic terms and one main system, then the total number of rules can be significantly reduced to (32 + 33 + 33 + 53 = 188) rules. In this way, the computational times can be significantly reduced, resulting in a more efficient system. Therefore, the eight input variables are grouped accordingly with the help of experts’ knowledge to reflect the relationship of variables better as shown in Fig. 1.

Diabetes Mellitus predicon

Physical Examinaon

Blood Pressure

BMI

Risk Factor

DPF

Skin Thickness

Lab Evaluaon

Age

Glucose

Insulin

Pregnancy

Fig. 1. Structure of Hierarchical Fuzzy Inference System for predicting Diabetes Mellitus.

The first subsystem consists of three input variables: blood pressure, Body Mass Index (BMI) and skinfold thickness, while the output is labeled as physical examination. The input variables for the second subsystems are diabetes pedigree function (PDF), frequency of pregnancy and age, while the output label is the diabetes risk factors. Lastly, the third subsystem consists of two input variables: glucose and serum insulin, and the output for this subsystem is labeled as laboratory evaluation. The outputs of the subsystems are then integrated and used as input variables for the main system to generate a single output for diabetes prediction. The prediction will give not only whether the person is with diabetes or not but will also indicate the level of severity of the disease in the range [0, 1]. A high level of severity is shown by a value close to 1 while a value below 0.5 will indicate the diabetes level is not serious. 3.3 Selection of Membership Functions In this study, trapezoidal fuzzy numbers for linguistic variables are derived based on the approach of [5] that utilizes the minimum, mean, standard deviation and maximum of the data. Table 2 summarizes the membership functions and linguistic terms for each input variable.

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D. Mohamad and A. I. Hissamudin Table 2. Membership functions of input variables.

Linguistic variable

Linguistic term

[a, b, c, d]

Pregnant (A1)

LowPREG

[0, 0, 0.09, 3.3]

ModeratePREG

[0.09, 3.3, 3.3, 6.51]

HighPREG

[3.3, 6.51, 17, 17]

LowGLU

[56, 56, 90.2, 122.3]

NormalGLU

[90.2, 122.3, 122.3, 153.7]

HighGLU

[122.3, 153.7, 198, 198]

HypotensionBP

[24, 24, 58.2, 70.67]

NormalBP

[58.2, 70.67, 70.67, 83.14]

HypertensionBP

[70.67, 83.14, 110, 110]

GoodST

[7,7, 18.62, 29.12]

FairST

[18.62, 29.12, 29.12, 39.62]

PoorST

[29.12, 39.62, 63, 63]

LowINS

[14, 14, 37, 155.7]

NormalINS

[37, 155.7, 155.7, 274.4]

HighINS

[155.7, 274.4, 846, 846]

NormalBMI

[18.2, 18.2, 26.05, 33.07]

OverweightBMI

[26.05, 33.07, 33.07, 40.09]

ObeseBMI

[33.07, 40.09, 67.1, 67,1]

LowDPF

[0.085, 0.085, 0.18, 0.52]

MediumDPF

[0.18, 0.52, 0.52, 0.86]

HighDPF

[0.52, 0.86, 2.42, 2.42]

YoungAGE

[21, 21, 21, 30.84]

MiddleAGE

[21, 30.84, 30.84. 41.03]

OldAGE

[30.84, 41.03, 81, 81]

Glucose (A2)

Blood pressure (A3)

Skinfold thickness (A4)

Insulin (A5)

BMI (A6)

Diabetes pedigree function (A7)

Age (A8)

On the other hand, the membership functions for the output variables, such as Laboratory Evaluation, Physical Examination, Risk Factor and Diabetes Mellitus are automatically generated using MATLAB Fuzzy Editor by setting up the range values of [0, 100] for subsystems outputs and [0, 1] for the main system output. Table 3 summarizes the membership function for each output variable.

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233

Table 3. Membership functions of output variables. Linguistic variable

Linguistic term

[a, b, c, d]

Laboratory evaluation

Very LowLE

[0, 0, 2.5, 22.5]

LowLE

[2.5, 22.5, 27.5, 47.5]

ModerateLE

[27.5, 47.5, 52.5, 72.5]

HighLE

[52.5, 72.5, 77.5, 97.5]

Physical examination

Risk factor

Diabetes mellitus

Very HighLE

[77.5, 97.5, 100, 100]

Very LowPE

[0, 0, 2.5, 22.5]

LowPE

[2.5, 22.5, 27.5, 47.5]

ModeratePE

[27.5, 47.5, 52.5, 72.5]

HighPE

[52.5, 72.5, 77.5, 97.5]

Very HighPE

[77.5, 97.5, 100, 100]

Very LowRF

[0, 0, 2.5, 22.5]

LowRF

[2.5, 22.5, 27.5, 47.5]

ModerateRF

[27.5, 47.5, 52.5, 72.5]

HighRF

[52.5, 72.5, 77.5, 97.5]

Very HighRF

[77.5, 97.5, 100, 100]

Very LowDM

[0, 0, 0.01667, 0.15]

LowDM

[0.01667, 0.15, 0.1834, 0.3166]

Moderately LowDM

[0.8134, 0.3166, 0.35, 0.4833]

ModerateDM

[0.35, 0.4833, 0.5167, 0.65]

Moderately HighDM

[0.5167, 0.65, 0.6834, 0.8166]

HighDM

[0.6834, 0.8166, 0.85. 0.9833]

Very HighDM

[0.85, 0.9833, 1, 1]

3.4 Development of the IF-THEN Rule Statement Once the membership functions are determined, the fuzzy IF-THEN rules are developed to illustrate the relationship between input and output variables. The IF-THEN rules in FIS imitate how humans, in this case, medical doctors, diagnose patients with diabetes. In this study, Fuzzy Associative Memory (FAM) is constructed to simplify the process of defining rules. Some examples of the fuzzy IF-THEN rules used in this study can be stated as: IF AND THEN . ii. IF AND AND THEN . i.

234

D. Mohamad and A. I. Hissamudin

iii. IF AND AND THEN .

4 Result and Discussion In this study, 195 data from PIDD are randomly selected to test the proposed system. Table 4 shows the sample comparison between actual outcomes and the predicted outcomes yielded by the proposed HFIS. From this table, the ninth column represents the actual outcome of the dataset, while the tenth column represents the predicted outcomes of HFIS. For the actual outcome from the data, the value of ‘0’ indicates that the person has no diabetes, while ‘1’ indicates the person has diabetes, Meanwhile, for the predicted outcomes using the proposed HFIS, the value above 0.5 is classified as the person has diabetes, while the value below 0.5 is classified as the person has low diabetes. Table 4. Sample comparison between actual outcomes and predicted outcomes.

A1

A2

A3

A4

A5

1

89

66

23

3

88

58

11

8

155

62

26

7

160

54

0

162

76

1

117

1

100

0

120

Actual

Predicted

A6

A7

A8

DM

HFIS

94

28.1

0.167

21

0

0.19

54

24.8

0.267

22

0

0.13

495

34

0.543

46

1

0.718

32

175

30.5

0.588

39

1

0.621

56

100

53.2

0.759

25

1

0.67

88

24

145

34.5

0.403

40

1

0.541

72

12

70

25.3

0.658

28

0

0.282

74

18

63

30.5

0.285

26

0

0.271

4.1 Performance Evaluation The performance of the proposed HFIS is evaluated by computing the percentages of classification accuracy [5]. The accuracy is the proportion of the total number of predictions that were correctly classified, determined by the equation Accuracy =

TN + TP × 100% TN + TP + FN + FP

(2)

where TP and FN are the number of diabetic patients classified as diabetic and healthy respectively while TN and FP are the number of healthy people classified as healthy and diabetic respectively. The classification of the data is as in Table 5 and using Eq. (2), it is found that the accuracy of the prediction system based on HFIS is 90.77%.

Hierarchical Fuzzy Inference System

235

Table 5. Summarization of correct and incorrect prediction yielded by HFIS. Predicted Actual

Total

Positive

Negative

True (1)

89

88

177

False (0)

10

8

18

5 Conclusion This study developed a diabetes prediction system using the HFIS. The proposed system consists of several steps that include designing the hierarchical structure for diabetes mellitus, selecting the suitable membership functions for input and output variables and developing fuzzy IF-THEN rules statement. Since the diagnosis of diabetes depends on many factors, using the conventional FIS can lead to considerable complexity. This is because a large number of rules might be required to produce reliable results in a highdimensional system. Reducing the number of input variables involved in the FIS would affect the system’s accuracy. Thus, HFIS is used to overcome this issue. Compared to a single-level FIS, the proposed HFIS allows a significant reduction in the number of rules while preserving its accuracy. A new hierarchical structure for diabetes prediction system was proposed and developed. The implementation was done on the 195 samples of PIDD, and the results proved that HFIS is reliable in predicting the severity of diabetes with high accuracy. Since its advantageous is vast, the HFIS is useful as a prediction tool for many medical diagnoses and can also be implemented in other fields with large data and attributes.

References 1. Ahmadi, H., Gholamzadeh, M., Shahmoradi, L., Nilashi, M., Rashvand, P.: Diseases diagnosis using fuzzy logic methods: a systematic and meta-analysis review. Comput. Meth. Program. Biomed. 161, 145–172 (2018) 2. Kamthan, S., Singh, H.: Hierarchical fuzzy logic for multi-input multi-output systems. IEEE Access 8, 206966–206981 (2020) 3. Katsarou, A., et al.: Type 1 diabetes mellitus. Nat. Rev. Disease Primers 3(1), 1–17 (2017) 4. Lee, M.L., Chung, H.Y., Yu, F.M.: Modeling of hierarchical fuzzy systems. Fuzzy Sets Syst. 138(2), 343–361 (2003) 5. Lee, C.S., Wang, M.H.: A fuzzy expert system for diabetes decision support application. IEEE Trans. Syst. Man Cybern. Part B Cybern. 41(1), 139–153 (2010) 6. Magdalena, L.: Fuzzy rule-based systems. In: Kacprzyk, J., Pedrycz, W. (eds.) Springer Handbook of Computational Intelligence, pp. 203–218. Springer, Heidelberg (2015). https:// doi.org/10.1007/978-3-662-43505-2_13 7. Mancini, E., et al.: Prevention of dialysis hypotension episodes using fuzzy logic control system. Nephrol. Dial. Transplant. 22(5), 1420–1427 (2007) 8. Mohamad, D., Jamal, L.D.M.: A hierarchical fuzzy logic control system for Malaysian motor tariff with risk factors. In: Berry, M.W., Hj. Mohamed, A., Yap, B.W. (eds.) SCDS 2016. CCIS, vol. 652, pp. 224–236. Springer, Singapore (2016). https://doi.org/10.1007/978-98110-2777-2_20

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9. Mohamad, D., Mukhtar, F.L.: Weighted Mamdani-type fuzzy inference system based on relative ideal preference system. J. Soft Comput. Decis. Support Syst. 5(5), 1–7 (2018) 10. Najib, L., Ahmad, A.: Students’ satisfaction in online distance learning using fuzzy logic and inference system. In: 2021 6th IEEE International Conference on Recent Advances and Innovations in Engineering (ICRAIE), vol. 6, pp. 1–5 (2021) 11. Raju, G., Zhou, J., Kisner, R.A.: Hierarchical fuzzy control. Int. J. Control 54(5), 1201–1216 (1991) 12. Razak, T.R., Halim, I.H.A., Jamaludin, M.N.F., Ismail, M.H., Fauzi, S.S.M.: An exploratory study of hierarchical fuzzy systems approach in recommendation system. arXiv preprint arXiv:2005.14026 (2020) 13. Sulaiman, N.H., Mohamad, D.: A fuzzy logic model for students’ scholarship selection. Jurnal Teknologi Maklumat dan Sains Kuantitatif 8(1), 35–41 (2006) 14. Wang, L.X.: A course in fuzzy systems (1999) 15. World Health Organization Global Health Estimates (2020). https://www.who.int/news-room/ fact-sheets/detail/the-top-10-causes-of-death 16. Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)

Danger Level Ranking of Possible Dam Failures in Turkey by Grey Relational Analysis Halid Akdemir1,2

and Cihan Bayindir1,3(B)

1 ˙Istanbul Technical University, Sarıyer, 34469 ˙Istanbul, Turkey

{akdemirh20,cbayindir}@itu.edu.tr

2 Antalya Bilim University, Dö¸semealtı, 07190 Antalya, Turkey 3 Bo˘gaziçi University, Bebek, 34342 ˙Istanbul, Turkey

Abstract. Although dam failures are not very common in the course of engineering history, they can be catastrophic disasters causing many life losses, so they need to be investigated. Dam failures are difficult problems to analyze due to the complexity of the associated parameters which can be very hard to determine. With this motivation, in this study, grey relational analysis (GRA) was used to rank the danger levels of Turkey’s aging 15 dams in case of a possible collapse. The failure mode of each dam was assumed to be a sudden collapse, thus breach development is not considered. This type of failure mode is more commonly observed during major earthquakes. The dams chosen for this study have been selected from the engineering point of view as they have the highest hazard potential in case of failure across the country. Accordingly, the important involved attributes of the model were determined as follows: surrounding population, distance from that population, elevation relative to that population, and reservoir size. The weights of these involved attributes were preferred as 0.40, 0.30, 0.10, and 0.20, respectively. In conjunction with the literature on the subject, the distinguished coefficient was selected as 0.5. The risk assessment based on the GRA results is performed for Turkey’s 15 dams involved in the study. The output of this study will contribute to the disaster and risk management policies of Turkey’s dams and will have similar applications worldwide. Keywords: Grey relational analysis · Dam failures · Danger level ranking · Turkey’s dams

1 Introduction Although dam failures are not a very common event that engineers encountered, when it occurs, it can be catastrophic for human population living in close proximity [1]. In addition, dam failures cause a financial burden to the region [2] and a disruption in infrastructure service [3]. Dams can collapse due to aging, faulty design or extreme natural events [4]. These natural events can be major earthquakes, extreme weather conditions etc. [5]. Dam failures can develop over time [6] but also they can happen suddenly which that means sudden collapse [7]. Sudden collapse is one of the failure modes for dam failures [8, 9]. There isn’t any breach development in such failure mode. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 237–243, 2022. https://doi.org/10.1007/978-3-031-09173-5_30

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In these failure events, after the collapse of the dam body, the first wave reaches the population living nearby, and then the water level rises over time [10]. Dam operations and risk management of dams are important issues to work on as they affect large populations. Dam failure scenarios for risk management have been the subject of researchers and rule-makers [11, 12]. In the literature, dam failures have generally simulated by numerical analysis methods [13]. This is a time-consuming and labor-intensive method in fact sometimes it is impossible due to lack of data. Recently, researchers have been using grey methods [14] for the analysis of grey systems (GS) for identification of the problems that is fuzzy to describe. GS theory including many different concepts in it has been developed for the solution of GS. One of them is grey relational analysis (GRA), which evaluates alternatives by comparing them with each other using their attributes. GRA is an efficient tool to analysis complicated problems, which has been used in many different branches such as medical [15, 16], data analysis [17], structural engineering [18], industry [19], aviation [20], etc. so far. The intend of this study is to contribute to the analysis of such a complex and multivariable included problem as dam failure problems with the GRA method. In this context, it is aimed to evaluate the danger levels in case of sudden collapse of Turkey’s aging 15 dams with GRA. This paper is organized by headings as ıntroduction, methodology, applying GRA on risk assessment of dams, results, conclusion. Information on the subject of this paper is introduced and its literature is shared in the Sect. 1. Methodology used in this paper is presented in Sect. 2. In Sect. 3, the GRA application is carried out for the case of dam failures in question and its results are discussed. The implications are given in Sect. 4.

2 Methodology Systems that lack information are called GS which means poor, incomplete, uncertain etc. GS theory is a method that enables the analysis of problems with incomplete information. It bridges the gaps between social sciences and natural sciences. Grey system theory contains many concepts in it, such as grey relational analysis (GRA), grey generation (GG), grey modeling (GM), grey control (GC), grey prediction (GP) and grey decision making (GDM). GRA is one of the most efficient concepts to measure and interpret alternatives each other quantitatively. See [21] for more descriptive and enhanced definition. The main procedure of GRA is to make the performance of all alternatives comparable. The degree of similarity and variability among all alternatives to interrelate each other bases to the unique merit of this approach. Procedure of GRA is as follows; xi∗ (k) = xi∗ (k) =

xi0 (k) − minxi0 (k) maxx0i (k) − minx0i (k) maxx0i (k) − xi0 (k) maxx0i (k) − minx0i (k)

(1) (2)

Equation 1 is defined for a beneficial attribute, meaning that the attribute and the expected outcome are positively correlated. Equation 2 is defined for a non-beneficial

Danger Level Ranking of Possible Dam Failures

239

attribute, meaning that the attribute and the expected outcome are negatively correlated. These equations serve to determine the strength of the relevant attribute of corresponding alternative among the others, in other words, the value, which is xi∗ (k) in this case, of an attribute of corresponding alternative is scaled between 0 and 1 according to the other values. ξi (k) =

min + ζ max oi (k) + ζ max

(3)

Equation 3 is given above where ξi (k) states the grey relational coefficient. oi (k) = ||x∗0 (k) − xi∗ (k)|| denotes the deviation sequence, min = minmin||xi∗ (k) − xi∗ (k)|| and max = maxmax||xi∗ (k) − xi∗ (k)|| are the expressions of the maximum and minimum values of the absolute differences for each sequence, respectively. ζ states distinguished coefficient, which takes a value between 0 and 1. γi =

1 n Cξi (k) k=1 n

(4)

γi is tuned as the grey relational grade, which assigns a value to the relevant alternative. C specifies the weighed coefficient of the corresponding attribute. So that each alternative has a value that can be compared with each other after these sequential processes. The reader is referred to [22] for more comprehensive explanation.

3 Applying GRA and Results The dams chosen for this study have been selected intuitively from the engineering point of view as they have the highest hazard potential in case of failure across the country. The 15 dams studied in this paper are as follows; Seyhan Dam and Hydroelectric Power Plant (HPP), Borçka Dam and HPP, Ürkmez Dam, E˘grekkaya Dam, Tahtalı Dam, Mamasın Dam, Dim Dam and HPP, Kurtbo˘gazı Dam, Atasu Dam, Alibey Dam, Akköprü Dam and HPP, Suat U˘gurlu Dam and HPP, Derbent Dam and HPP, Manavgat Dam and HPP, Kirazlıköprü Dam. The attributes likely to affect the problem were determined by the engineering approach. The effective attributes of the model were selected as follows: surrounding population (sp), distance from that population (d), elevation relative to that population (e) and reservoir size (rs) as tabulated in Table 1. The numerical values of the attributes were assigned by engineering evaluation. The population in the vicinity of the downstream was taken into account while determining the sp. This attribute is the one that is most dependent on engineering judgement among the attributes. The distance along the downstream from the center of this population to the dam body gives the d values. The e values were obtained with the difference in elevation between these two points. These d and e attributes are partially dependent on engineering judgment but mostly far from interpretation. The values of the rs attribute were acquired directly from the municipalities where the dams located.

240

H. Akdemir and C. Bayindir Table 1. The values of the dams’ attributes

Dams

rs (hm3 )

sp (person)

d (km)

e (m)

5000

8.2

65

Manavgat Dam and HPP

100000

15.0

18

89

Seyhan Dam and HPP

300000

5.5

32

1200

Akköprü Dam and HPP

100000

22.0

100

384

Ürkmez Dam

5000

1.8

30

7

Tahtalı Dam

7500

4.0

44

307

20000

3.2

35

113

Dim Dam and HPP

E˘grekkaya Dam Kurtbo˘gazı Dam

251

10000

8.5

55

102

Mamasın Dam

200000

11.0

130

166

Alibey Dam

150000

9.5

15

67

Borçka Dam and HPP

25000

2.5

33

419

Derbent Dam and HPP

15000

12.5

35

213

Kirazlıköprü Dam Suat U˘gurlu Dam and HPP Atasu Dam

20000

20.0

23

100

100000

16.0

45

182

10000

17.3

150

36

The dams’ attributes mean the following respectively. The attributed sp is the most important attribute in the dam failure risk assessment problems because the hazard risk of the event is related to the impact on the human population living in close proximity. Therefore, it is included into the analysis as a beneficial attribute due to the its positive correlated. The attributed d represents the distance to the population likely to be affected by the dam failure, and as this distance gets shorter, the size of the hazard risk increases, so that is referred to non-beneficial attribute. The attributed e is the elevation difference between the populated area and the dam, this is the force driving the flow of water, so that means it is a beneficial attribute. The attributed d and e represent the arrival time of the first wave after dam failure. The attributed rs denotes the water held by the dam and it symbolizes the amount of water rise in the relevant residential area, so it is also beneficial attribute. The weights of the involved attributes were selected as 0.40, 0.30, 0.10 and 0.20, respectively. In conjunction with the literature on the subject, the distinguished coefficient was selected as 0.5. The python source code of the danger level ranking of possible dam failures application, which is generic algorithm, is convenient for use of any dam data-set in a suitable format. The values of the dams’ attributes were formed from the Google Earth engine and the data shared by the municipalities where the dams located. The danger level ranking according to the grey values which are the outcome of GRA are displayed in Table 2.

Danger Level Ranking of Possible Dam Failures

241

Table 2. Danger level ranking of the dams No

City

Dams

Grey values

1

Adana

Seyhan Dam and HPP

0.2140

2

Aksaray

Mamasın Dam

0.1364

3

Artvin ˙Izmir

Borçka Dam and HPP

0.1358

Ürkmez Dam

0.1340

Ankara ˙Izmir

E˘grekkaya Dam

0.1273

6

Tahtalı Dam

0.1249

7

˙Istanbul

Alibey Dam

0.1177

8

Antalya

Dim Dam and HPP

0.1096

9

Ankara

Kurtbo˘gazı Dam

0.1068

10

Trabzon

Atasu Dam

0.1052

11

Mu˘gla

Akköprü Dam and HPP

0.1029

12

Samsun

Suat U˘gurlu Dam and HPP

0.1019

13

Antalya

Manavgat Dam and HPP

0.1009

14

Samsun

Derbent Dam and HPP

0.0986

15

Bartın

Kirazlıköprü Dam

0.0875

4 5

Table 2 gives the ranking of the Turkey’s 15 aging dams that would have the most hazardous consequences in case of their sudden collapse without any breach development. Accordingly, Seyhan Dam and HPP in the city of Adana has potential to cause the most catastrophic consequences in case of its failure comparing with the other dams’ failure.

4 Conclusion In this paper, Turkey’s 15 aging dams have been ranked from the aspect of their potential danger level in case of their sudden collapse by GRA. It has been demonstrated that GRA can be efficient tool for disaster and risk assessment of dams. The danger level ranking of possible dam failures in case of their sudden collapse application was formed in order to perform future risk assessment of dams. Our ranking results will contribute to disaster and risk management policies of Turkey’s 15 aging dams. In addition, this study can be a reference for researchers or rule makers that risk management of dams’ failures can be assessed effectively with GRA. The use of GRA may become widespread in other sub-branches of water science. Turkey’s 15 aging dams mentioned in this paper and their danger level in case of their failure can be evaluated by numerical analysis and these outputs can be compared with GRA outputs for future studies. Acknowledgment. Authors thank for the support of the ˙Istanbul Technical University. This work was supported by the Research Fund of the ˙Istanbul Technical University. Project Code: MYL2022-43677. Project Number: 43677.

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References 1. Proske, D.: Comparison of dam failure frequencies and failure probabilities. Beton- und Stahlbetonbau 113, 2–6 (2018). https://doi.org/10.1002/best.201800047 2. Ellingwood, B., Corotis, R.B., Boland, J., Jones, N.P.: Assessing cost of dam failure. J. Water Resour. Plan. Manage. 119(1), 64–82 (1993) 3. Cionek, V.M., Alves, G.H.Z., Tófoli, R.M., Rodrigues-Filho, J.L., Dias, R.M.: Brazil in the mud again: lessons not learned from Mariana dam collapse. Biodivers. Conserv. 28(7), 1935– 1938 (2019). https://doi.org/10.1007/s10531-019-01762-3 4. Imbrogno, D.F.: Analysis of Dam Failures and Development of a Dam Safety Evaluation Program (2014) 5. Lyu, Z., Chai, J., Xu, Y., Qin, Y., Cao, J.: A comprehensive review on reasons for tailings dam failures based on case history. Adv. Civ. Eng. 2019, 1–18 (2019). https://doi.org/10.1155/ 2019/4159306 6. Zhu, Y.H., Visser, P.J., Vrijling, J.K.: Review on embankment dam breach modeling. In: New Developments in Dam Engineering: Proceedings of the 4th International Conference on Dam Engineering, August 2016, pp. 1189–1196 (2004). https://doi.org/10.1201/9780203020678. ch147 7. Neupane, R., Chen, H., Cao, C.: Review of moraine dam failure mechanism. Geomatics Nat. Hazards Risk 10(1), 1948–1966 (2019). https://doi.org/10.1080/19475705.2019.1652210 8. Raman, A., Liu, F.: An investigation of the Brumadinho Dam Break with HEC RAS simulation (2019) 9. Rotta, L.H.S., et al.: The 2019 Brumadinho tailings dam collapse: possible cause and impacts of the worst human and environmental disaster in Brazil. Int. J. Appl. Earth Observ. Geoinf. 90, 102119 (2020). https://doi.org/10.1016/j.jag.2020.102119 10. Di Cristo, C., Evangelista, S., Greco, M., Iervolino, M., Leopardi, A., Vacca, A.: Dam-break waves over an erodible embankment: experiments and simulations. J. Hydraul. Res. 56(2), 196–210 (2018). https://doi.org/10.1080/00221686.2017.1313322 11. Marche, C., Robert, B.: Dam failure risk: Its definition and impact on safety assessment of dam structures. J. Decis. Syst. 11(3–4), 513–534 (2002). https://doi.org/10.3166/jds.11.513-534 12. Viseu, T., Betamio de Almeida, A.: Dam-break risk management and hazard mitigation. In: WIT Transactions on State of the Art in Science and Engineering, vol. 36, pp. 211–238 (2009) 13. Altinakar, M.S. Matheu, E.E., Mcgrath, M.Z.: New generation modeling and decision support tools for studying impacts of dam failures. In: 2009 Association of State Dam Safety Officials Annual Conference, Dam Safety 2009, January, vol. 3, pp. 1256–1288 (2009) 14. Pan, W., Jian, L., Liu, T.: Grey system theory trends from 1991 to 2018: a bibliometric analysis and visualization. Scientometrics 121(3), 1407–1434 (2019). https://doi.org/10.1007/s11192019-03256-z 15. Dang, H.-S., Nguyen, T.-M.-T., Wang, C.-N., Day, J.-D., Dang, T.M.H.: Grey system theory in the study of medical tourism industry and its economic impact. Int. J. Environ. Res. Pub. Health 17(3), 961 (2020). https://doi.org/10.3390/ijerph17030961 16. Huang, J.C.: Application of grey system theory in telecare. Comput. Biol. Med. 41(5), 302– 306 (2011). https://doi.org/10.1016/j.compbiomed.2011.03.007 17. Kayacan, E., Ulutas, B., Kaynak, O.: Grey system theory-based models in time series prediction. Exp. Syst. Appl. 37(2), 1784–1789 (2010). https://doi.org/10.1016/j.eswa.2009. 07.064 18. Chen, X.-Z., Hong-ping, Z., Chuan-yao, C.: Structural damage identification using test static data based on grey system theory. J. Zhejiang Univ. Sci. A 6(8), 790–796 (2005). https://doi. org/10.1631/jzus.2005.A0790

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An Adaptive Fuzzy Assisted Fault Identification Observer for Bearing Using AE Signals Farzin Piltan and Jong-Myon Kim(B) School of Electrical Engineering, University of Ulsan, Ulsan 680-749, South Korea [email protected]

Abstract. Active acoustic emission (AE) signal estimation is crucial for realizing high-precision bearing fault diagnosis. However, the identification of the bearing fault in the low-speed motor is still a challenging issue. In this article, observerbased low-speed bearing fault identification is investigated, and an observer with adaptive fuzzy switching gain is proposed for improving the accuracy and stability of anomaly identification. First, a normal signal modeling (NSM) is established, based on the Gaussian autoregressive approach integrated with the Laguerre method. Second, a fault observer (FOB) is proposed in the bearing, based on the tracking differentiator technique in different conditions. Third, a fuzzy with an adaptive law is designed to increase the fault estimate accuracy of the FOB. The proposed method instantly increases the signal differentiation when the bearing is working in abnormal conditions. The proposed scheme is robust against suddenly changing the motor speed. Moreover, the fuzzy with adaptive law decay the difference between two crack sizes in the same condition of signal. The fuzzy with adaptive law is designed to guarantees the convergence (robustness) of the proposed FOB. Furthermore, the support vector machine (SVM) is used for residual signal classification. This approach is not only suitable for the bearing fault diagnosis using AE signals but also extendable to the bearing anomaly identification using vibration signals. The proposed algorithm was evaluated experimentally; the results demonstrated that it increases the accuracy of fault identification in the bearing using AE signals. Keywords: Acoustic emission · Bearing fault diagnosis · Low-speed motor · Adaptive approach · Fuzzy technique · Normal signal modeling · Gaussian autoregressive integrated with Laguerre · Fault observer approach · Support vector machine

1 Introduction Fault diagnosis in industrial systems is exceptionally significant to increase safety and reduce maintenance costs. Motors are used in several industries, and one of the main pieces of motors is bearing. Bearings are utilized to reduce friction between different parts. According to statistics, about 70% of the defects in industrial motors are mechanical defects, the principal component of which is mechanical defects of the bearings [1, 2]. The new robust algorithm for bearing anomaly diagnosis is introduced in this work. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 244–251, 2022. https://doi.org/10.1007/978-3-031-09173-5_31

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Sensors play a substantial role in investigating the defects of industrial procedures such as bearings. They are used to extract data at different times, places, and working conditions. Various sensors have been introduced to extract the bearings’ signals, including vibrations, stator current, shaft voltage, and acoustic emission sensors [3]. In this work acoustic emission (AE) sensor is used to collect the data in normal and abnormal conditions from the bearing. Although there are various researches for anomaly detection in bearings, they can be classified into three main groups; model-based approaches, data-driven techniques, and hybrid-based algorithms [3]. Although the model-based approaches are highly robust and require small data for anomaly detection, the strong dependence on system dynamics is one of the most critical challenges of this approach. One of the most popular model-based methods is system estimation based on observation techniques [4]. These approaches fall into two groups: linear and nonlinear. Although linear techniques such as proportional-integral, proportionalmulti-integral, and proportional-integral-derivative observers have the challenge of stability and accuracy, their considerable consequential strength is the easy implementation in industries. TayebiHaghighi and Koo [5] have proposed proportional-multi-integral observer for anomaly diagnosis in bearing using vibration signals. Nonlinear techniques such as the sliding approach, feedback linearization, backstepping, Lyapunov, fuzzy, and neural observers are other ways to fault estimation in systems using model-based approaches. The application of sliding observer and feedback linearization observation techniques have been analyzed in [6, 7]. Moreover, the Lyapunov-based observer was introduced in [8] for bearing anomaly detection and identification. Furthermore, the use of data-driven approaches has increased in recent years. Apart from strengths such as high accuracy and adaptability, these techniques suffer from reliability and enormous historical data [3, 9]. Hybrid methods have been introduced to increase the positive points in anomaly detection and identification algorithms [3]. In this research, a new hybrid method for detecting anomalies in low-speed bearings by AE signals is investigated. To design the proposed observer, first, the AE signals in the normal conditions must be modeled. Thus, the Gaussian autoregressive approach integrated with the Laguerre (GAUL) method is used for AE signal modeling. In the second step, a robust and adaptable observer is designed. To design the proposed observer, the linear Proportional-Integral Observation technique is combined with the robust sliding approach and introduces a reliable fault observer (FOB). In the next step, an external observer (EXO) is introduced to increased adaptability and fault modeling. The EXO is designed by an adaptive fuzzy assisted and will strengthen the FOB. After designing the proposed observer, the residual signal is generated. Then, residual signals are resampled and extracted the energy feature from resampled residual signals. Next, the resampled energy of residual signals is classified by a support vector machine (SVM). This work has the following contributions: • AE signal modeling using the combination of autoregressive gaussian approach and Laguerre filter. • Design proposed fault observer for AE signals. • Improve the fault estimation accuracy in FOB using adaptive fuzzy assisted technique.

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This article has the following parts. The experimental dataset of the bearing is explained in the Sect. 2. The third part clarifies the combination of the proposed data-driven AE signal modeling, hybrid-based proposed adaptive external observer and machine learning-based classification algorithm for bearing anomaly identification. The results and discussions are presented in the Sect. 4. In the Sect. 5, conclusions and future works are expressed.

2 Experimental AE Bearing Dataset In this research, the AE signals extracted by PAC WSα sensor in normal and abnormal conditions when the sampling rate frequency is 250 kHz from FAG NJ206-E-TVP2 bearing have been used to evaluate the power of anomaly detection by the proposed algorithm. Figure 1 illustrates the benchmark to collect the AE bearing data in normal and abnormal conditions when the crack sizes are 3-mm and 6-mm.

Fig. 1. Benchmark of AE bearing data, a) generate the bearing data and collect the data using AE sensors, and b) data acquisition.

Table 1 illustrates the information of AE bearing dataset in this work. Table 1. The information of AE bearing dataset. States

Motors’ speed test [RPM]

Crack sizes [mm]

Normal Condition (NC)

300, 400, 450, 500

–

Inner faulty Condition (IC)

300, 400, 450, 500

3; 6

Outer faulty Condition (OC)

300, 400, 450, 500

3; 6

Ball faulty Condition (BC)

300, 400, 450, 500

3; 6

Inner-Outer faulty Condition (IOC)

300, 400, 450, 500

3; 6

Inner-Ball faulty Condition (IBC)

300, 400, 450, 500

3; 6

Outer-Ball faulty Condition (OBC)

300, 400, 450, 500

3; 6

Inner-Outer-Ball faulty Condition (IOBC)

300, 400, 450, 500

3; 6

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3 Adaptive Fuzzy Assisted Fault Observer Algorithm Figure 2 shows the proposed hybrid technique, which is a combination of the autoregressive Gaussian-Laguerre approach, adaptive fuzzy assisted fault observer, and support vector machine to detect anomalies in bearings.

Fig. 2. Bearing fault diagnosis using proposed adaptive fuzzy assisted fault observer.

3.1 Autoregressive Gaussian-Laguerre AE Signal Modeling Based on Fig. 2, the first step to design the proposed assisted fault observer for bearing anomaly identification is AE signal modeling. The state-space equation of the Gaussian autoregressive (GAU) technique is represented in the following equation.  SGAU (k + 1) = [∅GAU SGAU (k) + ∅i I (k)] + eGAU (k) + ∂GAU (k) (1) MGAU (k) = (∅M −GAU )T SGAU (k) here, SGAU (k), ∅GAU , I (k), eGAU (k), ∂GAU (k), MGAU (k), and (∅i , ∅M −GAU ) are the state modeling of AE signal in NC using GAU technique, the AE bearing signal covariance matrix using GAU technique, the measurement AE signal in NC, the error of state modeling using GAU technique, the uncertainty of the AE signal in NC using GAU technique, the state output for AE signal using GAU technique, and the coefficients of the state-space function based on GAU technique, respectively. To improve the robustness and reliability of AE signal modeling in NC, the Laguerre filter is applied to GAU approach. The state-space function of GAU-Laguerre (GAUL) is represented as follows. 

  SGAUL (k + 1) = ∅GAUL SGAUL (k) + ∅i I (k) + ∅o MGAUL (k) + eGAUL (k) + ∂GAUL (k) MGAUL (k) = (∅M −GAUL )T SGAUL (k)

(2) here, SGAUL (k), ∅GAUL , eGAUL (k), ∂GAUL (k), MGAUL (k), and (∅o ) are the state modeling of AE signal in NC using GAUL technique, the AE bearing signal covariance matrix

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using GAUL technique, the error of state modeling using GAUL technique, the uncertainty of the AE signal in NC using GAUL technique, the state output for AE signal using GAUL technique, and the coefficients of the state-space function based on GAUL technique, respectively. In order to improve the performance of anomaly estimation in the next step, we will design an adaptive fuzzy assisted fault observer. 3.2 Adaptive Fuzzy Assisted Fault Observer Approach According to Fig. 2, after modeling the AE signal, the proposed fault observer (FOB) using the combination of the application of the sliding technique in the linear PI observer is used to increase the accuracy of estimating obscure signals. In this work, unknown signals are introduced by uncertain conditions and various types of anomalies. In the proposed FOB procedure unknown conditions can be estimated by the following definition. ϕFOB (k + 1) = ∅1 ϕFOB (k) + ∅2 [ϕFOB (k) − ∂GAUL (k)] + ∅3 sgnϕFOB (k) − ∂GAUL (k)

(3)

here, ϕFOB (k) and (∅1 , ∅2 , ∅3 ) are the unknown AE signal estimation using FOB technique and the coefficients of the unknown estimation using FOB approach, respectively. Moreover, the state-space of the FOB technique is utilized by the following equation.  SFOB (k + 1) = [∅GAUL SFOB (k) + ∅i I (k) + ∅o MGAUL (k)] + eGAUL (k) + ϕFOB (k) MFOB (k) = (∅4 )T SFOB (k) + ∅2 [ϕFOB (k) − ∂GAUL (k)] (4) here, SFOB (k), MFOB (k), and (∅4 ) are the state of unknown signal estimation using FOB algorithm, the state output of unknown signal estimation using FOB technique, and the coefficients of the signal estimation using FOB approach, respectively. In the next step, an external observer (EXO) is introduced to increased adaptability and fault modeling accuracy. The EXO is designed by an adaptive fuzzy approach and will strengthen the FOB. The application of EXO in FOB (EX-FOB) to estimate the anomalies in bearing signals is introduced using the following explanation.   ϕEX −FOB (k + 1) = ∅1 ϕEX −FOB (k) + ∅2 ϕEX −FOB (k) − ∂GAUL (k) + ∅3−new sgnϕEX −FOB (k) −∂GAUL (k) + ∅5 CF

(5)

here, ϕEX −FOB (k), CF , and (∅5 ) are the unknown AE signal estimation using EX-FOB technique, the assisted fuzzy approach for fault estimation, and the coefficient of the unknown estimation using EX-FOB approach, respectively. Moreover, the ∅3−new (adaptive tunned coefficient) can be calculated using adaptive approach based on the following technique. ∅3−new = ∅3 × CF

(6)

Furthermore, the state-space of the EX-FOB technique is exploited by the following calculation.

An Adaptive Fuzzy Assisted Fault Identification Observer



249

  SEX −FOB (k + 1) = ∅GAUL SEX −FOB (k) + ∅i I (k) + ∅o MGAUL (k) + eGAUL (k) + ϕEX −FOB (k)   T MEX −FOB (k) = (∅4 ) SEX −FOB (k) + ∅2 ϕEX −FOB (k) − ∂GAUL (k)

(7) here, SEX −FOB (k), and MEX −FOB (k) are the state of unknown signal estimation using EX-FOB algorithm and the state output of unknown signal estimation using EX-FOB technique, respectively. After anomaly estimation using the adaptive fuzzy assisted fault observer, the residual signals will be generated in the next part. 3.3 Residual Signal Generation and Signal Classification Based on Fig. 2, the residual signal that is the difference between estimated signals and original AE signals can be generated using the following equation. EX −FOB = MEX −FOB (k) − I (k)

(8)

where EX −FOB is a residual signal using EX-FOB algorithm. To improve the performance of classification, the residual signal is resampled and the energy feature is extracted from it. Moreover, the SVM is used for classification of bearing signals.

4 Experimental Results The error of signal modeling using the proposed autoregressive Gaussian-Laguerre (GAUL) approach is demonstrated in Fig. 3.

Fig. 3. Error of signal modeling using the proposed autoregressive Gaussian-Laguerre approach

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Based on Fig. 3, the error of AE signal modeling using the proposed GAUL is closed to zero. So, this technique is an effective method for modeling AE signals. The resampled energy of residual signals based on the proposed adaptive fuzzy assisted fault observer illustrates in Fig. 4. It can be seen that the proposed adaptive fuzzy assisted fault observer greatly increases the degree of resolution between normal and various abnormal conditions.

Fig. 4. Resampled energy of residual signals using adaptive fuzzy assisted fault observer.

To compare the accuracy of the proposed adaptive fuzzy assisted fault observer, this method is compared with classical fault observer and its results are shown in Table 2. Table 2. Accuracy of bearing signal classification using EX-FOB and FOB. Conditions

EX-FOB & SVM (%)

FOB & SVM (%)

NC IC OC BC IOC IBC OBC IOBC

100 98 95 97 97 97 98 97

100 88 89 90 87 88 90 89

Average

97.4

90.1

The proposed EX-FOB algorithm was able to improve the classification sensitivity by about 7.3% compared to FOB technique.

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5 Conclusions In this study, the anomaly diagnosis of bearing when operating at low speeds was investigated. The adaptive fuzzy assisted fault observer has been used the diagnosis the abnormality. Three steps were required to design the proposed algorithm. First, the AE signals were modeled by the autoregressive Gaussian-Laguerre approach and their state-space function was extracted. In the second step, the anomaly signals were estimated using the proposed fault observer. Next, an adaptive fuzzy assisted technique was applied to the fault observer to increase the accuracy and the power of estimation. Finally, SVM was used to classify the resampled energy of residual signals. Moreover, the classification accuracy using the proposed algorithm is 97.4%. Despite the favorable results in the proposed algorithm, when we have a multi-crack in the bearing, deep-learning with observers seems to be a better option for future work. Acknowledgements. This work was supported by the Korea Technology and Information Promotion Agency (TIPA) grant funded by the Korea government(SMEs) (No. S3126818).

References 1. Gao, Z., Cecati, C., Ding, S.X.: A survey of fault diagnosis and fault-tolerant techniques—part I: fault diagnosis with model-based and signal-based approaches. IEEE Trans. Ind. Electron 4(62), 3757–3767 (2015) 2. Cecati, C.: A survey of fault diagnosis and fault-tolerant techniques—part II: fault diagnosis with knowledge-based and hybrid/active approaches. IEEE Trans. Ind. Electron 2(62), 3768– 3774 (2015) 3. Piltan, F., et al.: Strict-feedback backstepping digital twin and machine learning solution in ae signals for bearing crack identification. Sensors 22(2), 539 (2022) 4. Piltan, F., Duong, B.P., Kim, J.-M.: Deep learning-based adaptive neural-fuzzy structure scheme for bearing fault pattern recognition and crack size identification. Sensors 21(6), 2102 (2021) 5. TayebiHaghighi, S., Koo, I.: SVM-based bearing anomaly identification with self-tuning network-fuzzy robust proportional multi-integral and smart autoregressive model. Appl. Sci. 11(6), 2784 (2021) 6. Wang, Q., Zheng-Guang, W.: Robust output feedback control for input-saturated systems based on a sliding mode observer. Circ. Syst. Sig. Process. 40(5), 2267–2281 (2021) 7. Meng, X., Yu, H., Zhang, J., Xu, T., Wu, H., Yan, K.: Disturbance observer-based feedback linearization control for a quadruple-tank liquid level system. ISA Trans. 122, 146–162 (2022) 8. Piltan, F., Kim, J.-M.: Fault diagnosis of bearings using an intelligence-based autoregressive learning Lyapunov algorithm. Int. J. Comput. Intell. Syst. 14(1), 537–549 (2021) 9. Gonzalez-Jimenez, D., Del-Olmo, J., Poza, J., Garramiola, F., Madina, P.: Data-driven fault diagnosis for electric drives: a review. Sensors 21(12), 4024 (2021)

Using Fuzzy Set Based Model for Pharmaceutical Supply Chain Risks Assessment Irem Yalcinkaya

and Selcuk Cebi(B)

Department of Industrial Engineering, Yildiz Technical University, Besiktas, 34349 Istanbul, Turkey [email protected], [email protected]

Abstract. Risk assessment in the pharmaceutical supply chain is very important as it directly affects patient health. The importance of access to medicine, especially in today’s pandemic conditions, has been demonstrated this once again. Manufacturer pharmaceutical companies that use outsourcing service providers for their logistics processes are faced with many risks. In this study, the risks of outsourcing in logistics were determined in the context of the pharmaceutical industry. Since the problem contains many criteria due to its structure, multicriteria decision-making methods were used in the proposed model. In the study, Pythagorean fuzzy sets (PFS) were used to include expert opinions in the process since PFS perform well in dealing with uncertainty and they represent decision makers’ evaluations in a wider range of definitions in the evaluation process. In the study, the importance levels of the risk criteria were determined by the interval-valued Pythagorean fuzzy AHP method, while the risk performance of the logistics service provider 3PL companies was determined by the Pythagorean fuzzy WASPAS method. In this study, procurement services in the pharmaceutical sector were evaluated under three main criteria as delivery, quality and operational, and quality was determined as the most important criterion. Among the quality criteria, the quality management system and good manufacturing practices were obtained as the two most important criteria, respectively. This study contributes to the literature by showing the importance degree of the criteria in outsourcing service of pharmaceutical supply chain and how these risks can be assessed with a fuzzy-based model. Keywords: Pharmaceutical supply chain risk assessment · Pythagorean fuzzy AHP · Pythagorean fuzzy WASPAS

1 Introduction Pharmaceuticals have critical importance for human health as they have therapeutic or preventive properties. The pharmaceutical supply chain, which is one of the basic building blocks of a country’s health system, faces risks at every stage of the chain.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 252–260, 2022. https://doi.org/10.1007/978-3-031-09173-5_32

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Since any deficiencies in the assessment and management of these risks may adversely affect the patient’s health, minimizing and managing the risks in the chain gains great importance. It has been revealed how important and vital the pharmaceutical supply chain is in terms of patients’ access to drugs, especially in an environment where breaks in the supply chain are experienced under pandemic conditions. Mokrini and Aouam [1] investigated the risks of public-private cooperation in the Moroccan pharmaceutical supply chain and presented a case study. F-AHP, F-TOPSIS, and F-PROMETHEE methods were used together in the study methodology. Silva et al. [2] investigated how industry players from different fields, including industry, distributors, retailers, and buyers, identify, assess, and prioritize risks in the Brazilian pharmaceutical supply chain. In the study, risk priority ranking was carried out according to different sector players with the OM-AHP method. Kumar and Jha [3] proposed a model for quality risk management in the pharmaceutical supply chain. In the study, the quality risk is measured with a parameter called the risk priority number. Researchers stated that a systematic quality risk management approach during drug distribution would be beneficial in minimizing customer complaints, drug disposals, or recalls. Mokrini et al. [4] presented a study evaluating the risks of outsourcing logistics for the pharmaceutical industry. While the researchers determined the importance of risk assessment criteria with F-AHP, they determined the risk priority order with the F-PROMETHEE method. Vishwakarma et al. [5] presented a study based on fuzzy AHP approach to identify risks specific to the Indian pharmaceutical industry and prioritize and analyze identified risks. Manufacturers in the pharmaceutical industry may prefer to receive services from logistics service providers called third-party logistics “3PL” to increase their competitiveness in the market by focusing on their core competencies. While outsourcing in logistics offers the advantage of benefiting from the expertise of the service provider company, it also includes many risks. In this context, businesses should be careful about the selection of the 3PL company they will receive service from. Fuzzy sets support decision makers in dealing with uncertainties. In problems with multiple criteria and alternatives, MCDM methods help the decision stage. In this study, a fuzzy cluster-based model is proposed to evaluate the supply chain performance of 3PL companies in the pharmaceutical supply chain. In the proposed model, supply chain risks are grouped under four main and twenty-eight sub-criteria. The main risk criteria are delivery reliability, quality, operational, communication and technology were defined, and the importance levels of the criteria were determined using the Pythagorean Fuzzy AHP method. Depending on the weighting obtained, the risk performance of 3PL firms was obtained by the Pythagorean Fuzzy WASPAS method. The rest of the paper is organized as follows: In Sect. 2, Pythagorean Fuzzy AHP and Pythagorean Fuzzy WASPAS methods and steps to be used in the application are explained. The application is explained in Sect. 3. Finally, in Sect. 4, the results and contributions of the study are included.

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2 Methodology 2.1 Pythagorean Fuzzy Sets Pythagorean fuzzy numbers, proposed by Yager in 2013, are an extension of the intuitive fuzzy numbers that offer a wider definition range. According to this extension, the sum of membership and non-membership degrees can exceed 1, but the sum of their squares can be 1 at most. It is defined by following definition [6]. P˜ ∼ = {x, μP˜ (x), vP˜ (x); x ∈ X }

(1)

while μP˜ (x) : X → [0, 1] expresses the degree of x being a member of the fuzzy set P, vP˜ (x) : X → [0, 1] denotes the degree of not being a member of the fuzzy set P. For every x ∈ X , 0 ≤ μP˜ (x)2 + vP˜ (x)2 ≤ 1

(2)

2.2 Interval Valued Pythagorean Fuzzy AHP (IVPF-AHP) Method IVPF-AHP is a combination of Pythagorean fuzzy numbers and AHP method. Decision makers determine the importance weights of the criteria by performing a pairwise comparison of the criteria with a linguistic scale. The steps of the IVPF-AHP method are as follows [7]: Step 1. Using the linguistic evaluation given in Table 1, a pairwise comparison matrix R = (r jt )m×m containing the evaluations of the decision makers is created.

Table 1. An IVPFN pairwise comparison scale for criteria [7] Linguistic terms

μL

μU

vL

vU

Certainly low importance (CLI)

0

0

0.9

1

Very low importance (VLI)

0.1

0.2

0.8

0.9

Low importance (LI)

0.2

0.35

0.65

0.8

Below average importance (BAI)

0.35

0.45

0.55

0.65

Equal importance (EI)

0.5

0.5

0.5

0.5

Average importance (AI)

0.45

0.55

0.45

0.55

Above average importance (AAI)

0.55

0.65

0.35

0.45

High importance (HI)

0.65

0.8

0.2

0.35

Very high importance (VHI)

0.8

0.9

0.1

0.2

Certainly high importance (CHI)

0.9

1

0

0

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Step 2. The difference matrix D = (dij )m×m according to high and low values of membership and non-membership degrees is performed as in Eqs. (3) and (4).

2 dijL = μ2ijL − vijU

(3)

2 dijU = μ2ijU − vijL

(4)

Step 3. The interval multiplicative matrix S = (sij )m×m is calculated by Eq. (5) and (6). sijL = sijU =



1000dijL



1000dijU

(5) (6)

Step 4. Using Eq. (7), the indeterminacy value H = (hij )m×m of rjt is calculated.     2 2 hij = 1 − μ2ijU − μ2ijL − vijU − vijL

(7)

Step 5. The unnormalized weight matrix T = (τij )m×m is calculated according to Eq. (8).  τij =

 sijL + sijU hij 2

(8)

Step 6. The criteria weights wi are calculated according to Eq. (9). m

j=1 wij wi = m m i=1

j=1 wij

(9)

2.3 Interval Valued Pythagorean Fuzzy WASPAS (IVPF-WASPAS) Method IVPF-WASPAS is a combination of Pythagorean fuzzy numbers and WASPAS method. Decision makers determine the scores of the alternatives by evaluating the alternatives with a linguistic scale according to certain criteria. The steps of the IVPF-WASPAS method are as follows [8]: Step 1. Decision makers evaluate alternatives with linguistic terms given in Table 2 according to certain criteria and these evaluations are converted into IVPFNs. These IVPFNs are combined according to the Pythagorean fuzzy weighted power geometric (PFWPG) operator Eq. (10) [9].

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PFWPG(p 1 ,p 2 , . . . , p n ) =



1−



n i=1

1 − μ2i

wi 1/2 

n , 1−



i=1

1 − vi2

wi 1/2 

(10) Table 2. An IVPFN scale to rate alternatives with respect to criteria [8] Linguistic terms

μL

μU

vL

vU

Very very good (VVG)

0.75

0.9

0.03

0.18

Very good (VG)

0.66

0.81

0.12

0.27

Good (G)

0.57

0.72

0.21

0.36

Medium good (MG)

0.48

0.63

0.3

0.45

Fair (F)

0.39

0.54

0.39

0.54

Medium bad (MB)

0.3

0.45

0.48

0.63

Bad (B)

0.21

0.36

0.57

0.72

Very bad (VB)

0.12

0.27

0.66

0.81

Very very bad (VVB)

0.03

0.18

0.75

0.9

Step 2. The combined decision matrix is normalized according to whether the criteria are benefit or cost based. If the criterion is benefit-based, it is normalized according to Eq. (11), if it is cost-based, it is normalized according to Eq. (13).

∼ x ij

=

x˜ ij maxx˜ ij

(11)

i

maxi x˜ ij is calculated by using Eq. (12).



  maxi x˜ ij = maxi μLij , maxi μUij , mini vLij , mini vUij ∼ x ij

=

(12)

minx˜ ij i

x˜ ij

mini x˜ ij is calculated by using Eq. (14). 



 mini x˜ ij = mini μLij , mini μUij , maxi vLij , maxi vUij

(13)

(14)

For division operator, the extension principle of IVIFS is applied [10]. For P˜ 1 = ([a1 , b1 ], [c1 , d1 ]) and P˜ 2 = ([a2 , b2 ], [c2 , d2 ]) as to IVFNs, the division operator is defined as Eq. (15). P˜ 1 = ([min(a1 , a2 ), min(b1 , b2 )], [max(c1 , c2 ), min(d1 , d2 )]) P˜ 2

(15)

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Step 3. The determined criteria weights are multiplied with the normalized matrix and ˜ 1 is calculated according to Eq. (16). EquaPythagorean fuzzy weighted sum values, Q i tions (17) and (18) are used for IVPFNs operations when calculating the fuzzy weighted sum values. n ˜ i1 = Q r˜ij w˜ j (16) j=1

    λ λ λ λ 2 2 1 − (1 − μL ) , 1 − (1 − μU ) , vL , vU λ˜p = p˜ 1 ⊕ p˜ 2 =

(17)

     2 2 2 2 2 U )2 − (μU )2 (μU )2 , v L v L , v U v U (μL1 ) + (μL2 ) − (μL1 ) (μL2 ) , (μU ) + (μ 1 2 1 2 1 2 1 2

(18) ˜ 2 , is performed as provided in Step 4. Pythagorean fuzzy weighted product values, Q i Eq. (19). Equations (20) and (21) are used for IVPFNs operations when calculating fuzzy weighted product values. ˜ i1 = Q

n

w˜ r˜ j j=1 ij

    λ λ λ λ 2 2 p˜ = μL , μU , 1 − (1 − vL ) , 1 − (1 − vU ) λ

(19) (20)

     U , L )2 + (v L )2 − (v L )2 (v L )2 , (v U )2 + (v U )2 − (v U )2 (v U )2 (v p˜ 1 ⊗ p˜ 2 = μL1 μL2 , μU μ 1 2 1 2 1 2 1 2 1 2

(21) Step 5. The relative importance values of the alternatives are calculated according to Eq. (22). Equations (17) and (18) are used here. ˜ i = 0, 5Q ˜ i1 + 0, 5Q ˜ i2 Q

(22)

˜ i values are defuzzified according to Eq. (23). Accordingly, the ranking of Step 6. The Q alternatives is obtained, the alternative with the highest value is determined as the best alternative.

p=

μL + μU +



1 − vL2 +

   2 +μ μ − 2 1 − vU 1 − vL2 1 − vU L U 4

(23)

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3 Application Manufacturers in the pharmaceutical industry can receive services from logistics service providers called third-party logistics “3PL”. This situation causes manufacturers to face some risks. In this study, the risks faced by pharmaceutical companies benefiting from outsourcing logistics service providers are respectively; delivery reliability (C1), complete product delivery (C1.1), undamaged product delivery (C1.2), on-time delivery (C1.3), appropriate vehicle use (C1.4), delivery flexibility (C1.5), cost-effective delivery (C1.6), delivery traceability (C1.7); quality (C2), quality management system (C2.1), good manufacturing practices (GMP) (C2.2), good storage practices (GSP) (C2.3), good distribution practices (GDP) (C2.4), exceeding storage temperature conditions (C2.5), contaminated drug (C2.6), waste management (C2.7); operational (C3), operations standardization (C3.1), insufficient storage space (C3.2), lack of coordination (C3.3), unmet demand (C3.4), loss of control over the service provider (C3.5), damage while handling (C3.6), pest activity (C3.7); technology and communication (C4), lack of information (C4.1), information flow (C4.2), communication consistency (C4.3), inventory management system accuracy (C4.4), information technology system interruption (C4. 5), technology level (C4.6), adaptation to technology change (C4.7). The criteria weights were determined by the experts using the Pythagorean fuzzy AHP method using the linguistic expressions in Table 1. The criteria weights are given in Table 3. Decision makers evaluated the performance of the alternatives according to the criteria by using the linguistic expressions in Table 2 with the Pythagorean fuzzy WASPAS method. In the study, the evaluations of the decision makers were brought together according to Eq. 10 using the PFWPG operator. The WASPAS results and ranking of the alternatives are given in Table 4. According to the defuzzified values, A1 is the best alternative, followed by A3 and A2, respectively. Table 3. Criteria weights in the form of crisp values Criteria

Weight

Criteria

Weight

Criteria

Weight

Criteria

Weight

C1 C1.1

0.14

C2

0.03

C2.1

0.52

C3

0.12

C3.1

0.24

C4

0.1

0.08

C4.1

0.02

C1.2

0.03

C2.2

0.14

C3.2

0.03

C4.2

0.02

C1.3 C1.4

0.04

C2.3

0.01

C2.4

0.06

C3.3

0.04

C4.3

0.01

0.06

C3.4

0.04

C4.4

0.02

C1.5

0.01

C2.5

0.07

C3.5

0.02

C4.5

0.01

C1.6 C1.7

0.01

C2.6

0.04

C3.6

0.02

C4.6

0.00

0.01

C2.7

0.03

C3.7

0.01

C4.7

0.01

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Table 4. Results of IVPF WASPAS Alternatives

WASPAS results

Defuzzified value

Rank

μL

μU

vL

vU

A1

0.60

0.76

0.20

0.35

0.69

1

A2

0.55

0.71

0.23

0.38

0.65

3

A3

0.58

0.73

0.20

0.35

0.67

2

4 Conclusions As pharmaceutical supply chain risk management directly interacts with human health, an effective risk assessment strategy in this chain is critical. Pharmaceutical manufacturers can receive services from logistics service providers, from which they will benefit from their expertise in this field, for their logistics processes. For this reason, manufacturers should be careful when choosing 3PL companies. While MCDM methods help the decision stage in problems involving multiple risk criteria and alternatives, fuzzy sets support decision makers in dealing with uncertainties. In this context, in the proposed approach, while the importance levels of risk criteria were determined with the IVPF-AHP method, the risk performance score of the alternatives was determined with the IVPF-WASPAS method. In the study, the most important risk was obtained as quality. Losing the effectiveness of a drug may mean that the drug loses its therapeutic properties and even harms the patient. In this case, it has been shown that minimizing the quality risk in the chain is very important. The study determined the risks that the use of outsourcing in logistics may pose to the pharmaceutical manufacturers and contributed to the literature by performing an application on the importance of risk criteria and alternative evaluation with a Pythagorean fuzzy set-based model approach. In this study, we consider the importance degrees of 3PL companies in terms of producers. For future research, the internal audit risks of 3PL companies should be analyzed to improve the procurement process. Furthermore, interdependencies among the criteria may be analyzed.

References 1. Mokrini, A.E., Aouam, T.: A fuzzy multi-criteria decision analysis approach for risk evaluation in healthcare logistics outsourcing: case of Morocco. Heal. Serv. Manag. Res. 33(3), 143–155 (2020). https://doi.org/10.1177/0951484820901668 2. Silva, J., Araujo, C., Marques, L.: Siloed perceptions in pharmaceutical supply chain risk management: a Brazilian perspective. Lat. Am. Bus. Rev. 21(3), 223–254 (2020). https://doi. org/10.1080/10978526.2020.1731315 3. Kumar, N., Jha, A.: Quality risk management during pharmaceutical ‘good distribution practices’ – a plausible solution. Bull. Fac. Pharm. Cairo Univ. 56(1), 18–25 (2018). https://doi. org/10.1016/j.bfopcu.2017.12.002

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4. El Mokrini, A., Kafa, N., Dafaoui, E., El Mhamedi, A., Berrado, A.: Evaluating outsourcing risks in the pharmaceutical supply chain: case of a multi-criteria combined fuzzy AHPPROMETHEE approach. IFAC-PapersOnLine 49(28), 114–119 (2016). https://doi.org/10. 1016/J.IFACOL.2016.11.020 5. Vishwakarma, V., Prakash, C., Barua, M.K.: A fuzzy-based multi criteria decision making approach for supply chain risk assessment in Indian pharmaceutical industry. Int. J. Logist. Syst. Manag. 25(2), 245–265 (2016). https://doi.org/10.1504/IJLSM.2016.078915 6. Ilbahar, E., Kara¸san, A., Cebi, S., Kahraman, C.: A novel approach to risk assessment for occupational health and safety using Pythagorean fuzzy AHP & fuzzy inference system. Saf. Sci. 103, 124–136 (2018). https://doi.org/10.1016/j.ssci.2017.10.025 7. Karasan, A., Ilbahar, E., Kahraman, C.: A novel pythagorean fuzzy AHP and its application to landfill site selection problem. Soft. Comput. 23(21), 10953–10968 (2018). https://doi.org/ 10.1007/s00500-018-3649-0 8. Ilbahar, E., Cebi, S., Kahraman, C.: Assessment of renewable energy alternatives with pythagorean fuzzy WASPAS method: a case study of Turkey. In: Kahraman, C., Cebi, S., Cevik Onar, S., Oztaysi, B., Tolga, A.C., Sari, I.U. (eds.) INFUS 2019. AISC, vol. 1029, pp. 888–895. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-23756-1_106 9. Peng, X., Yang, Y.: Some results for pythagorean fuzzy sets: some results for pythagorean fuzzy sets. Int. J. Intell, Syst. 30(11), 1133–1160 (2015). https://doi.org/10.1002/int.21738 10. Li, D.F.: Extension principles for interval-valued intuitionistic fuzzy sets and algebraic operations. Fuzzy Optim. Decis. Mak. 10(1), 45–58 (2011). https://doi.org/10.1007/s10700-0109095-9

A New Fuzzy Based Risk Assessment Approach for the Analysis of Occupational Risks in Manufacturing Sector Selcuk Cebi1(B)

and Merve Karamustafa2

1 Department of Industrial Engineering, Yildiz Technical University, Istanbul, Turkey

[email protected]

2 Occupational Health and Safety Coordinatorship, Yildiz Technical University, Istanbul, Turkey

[email protected]

Abstract. The analysis of occupational risks involves a set of uncertainties caused by various factors. One of them is that potential risks are considered according to the most probable situation although there may be able to occur rare outcomes rather than probable situations. Besides, the degree of effectiveness of the measure applied against any risk is another uncertainty factor encountered in risk assessment. In addition, the risk assessment takes place depending on the subjective judgments and degrees of expertise of occupational safety specialists, and subjective judgments involve uncertainty. For this reason, there are various studies using risk analysis models based on fuzzy set theory to address these uncertainties in risk assessments. However, there is not any risk assessment tool that considers the uncertainties caused by the factors mentioned above, simultaneously. Therefore, within the scope of this study, to consider uncertainty a fuzzy set-based approach has been proposed to the literature, which addresses all of the factors mentioned above, simultaneously. Keywords: Risk analysis · Neutrosophic sets · Fuzzy inference system

1 Introduction Risk assessment consists of “the determination of the hazards that may exist in the workplace or that may come from outside, the factors that cause these hazards to turn into risks, analyzing and classifying the risks arising from hazards, and deciding control measures”. Current risks are analyzed via to risk assessment methods to eliminate or reduce the detected risks to an acceptable level that will not cause loss or injury with the measures taken. In terms of occupational health and safety (OHS), risk assessment methods considering the probability and severity of the detected hazards are widely used. These methods generally involve the measurement and classification of risks according to both probability and consequences and their relative importance. The risk assessment matrix which is one of these methods is a tool for subjective risk assessment. The advantage © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 261–270, 2022. https://doi.org/10.1007/978-3-031-09173-5_33

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of conventional risk matrix is that it presents a standard tool to provide the relationship between the risk severity and the risk probability. However, the disadvantage of the conventional risk matrix is that it includes uncertainties caused by OHS specialists’ linguistic evaluations [1]. Therefore, risk assessment method based on fuzzy inference system has been proposed to literature to consider falsity and indeterminacy in the specialist judgments. The proposed method is used neutrosophic membership functions of the parameters of truth (T), indeterminacy (I) and falsity (F) in defining a case. Since the occurrence probability and the severity of risk may differ depending on the specialist assessment, it is important to express this variability by using three dimensions in order to determine the risk magnitude more accurately. In the scope of the proposed study, we will consider truth (T), indeterminacy (I) and falsity (F) in defining the parameters probability and severity while obtaining risk magnitude. Thus, in the risk assessment phase, it will be ensured that the value before and after the control measures are taken are analyzed together. Furthermore, the If-Then rules structure will be used to obtain the risk magnitude whereas fuzzy product operation. The rest of this paper is organized as follows: In Sect. 2, matrix risk assessment method, fuzzy inference system, and fuzzy logic. Steps to be used in the application are explained in Sect. 3. Finally, in Sect. 4, the results and contributions of the study are included.

2 Methodology 2.1 Matrix Risk Assessment Method The L-matrix method is the simplest and systematic approach that is broadly used in OHS risk assessment. The risk assessment matrix, has been developed to the system security program requirement, also known as the US military standard MIL_STD_882D. Probability and severity are two parameters of method that incorporate measuring and categorization of risks on an informed judgment basis. Risk value is found by multiplying probability and severity. A risk matrix is a table that has categories of “probability,” for its row and categories of “severity,” for its column [2]. Matrix type risk analysis, which is used to determine which risk needs more or more detailed analysis and which risks should be intervened first, is calculated by the scalar product of probability and severity components. In cases requiring urgency and precautionary measures, it should be preferred first [3]. Risk magnitude (RM) = Probability(P) × Severity(S)

(1)

A risk, qualitatively, identify as a low, medium, or high risk. likelihood and impact are used to identify risk priority. A risk with a product falling within a range of values identifies the risk priority as follows; Acceptable risks 1–3; Minor risks 4–6; Major risks 8–12; Catasrophic risks 15–25.

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2.2 Neutrosophic Set Theory The fuzzy set theory was introduced by L. Zadeh in 1965, to consider uncertainties in complex problems. Over time, new types of fuzzy sets have been introduced to the literature for the solution of uncertainties in complex problems [4]. Smarandache [5] introduced the neutrosophic set (NS) theory, where incomplete information is represented by truth (T), falsity (F), and indeterminacy (I) degrees. Differ the fuzzy set theory, the total membership degree does not need to be equal to 1 in NS theory. 0− ≤ TA (x) + IA (x) + FA (x) ≤ 3+

(2)

The four operations in neutrosophic sets are as follows; A + B = TA (x) + TB (x) − TA (x) · TB (x), IA (x) · IB (x), FA (x) · FB (x),

(3)

A − B = (T A (x) − TB (x))/(1 − TB (x)), IA (x)/IB (x), FA (x)/FB (x),

(4)

A = TA (x)/TB (x), (I A (x) − IB (x))/(1 − IB (x)), (FA (x) − FB (x))/(1 − FB (x)) (5) B A.B = TA (x) · TB (x), IA (x) + IB (x) − IA (x) · IB (x), FA (x) + FB (x) − FA (x) · FB (x) (6)

2.3 Mamdani Fuzzy Inference System In fuzzy inference systems (FISs) proposed by Mamdani [6], a real system is characterized by IF-THEN rules including the logical expressions such as AND, OR, and NOR. The general structure of the system is represented by Eq. 7 [6]. If x1 Ai1 AND x2 Ai2 AND x3 Ai3 AND . . . xn Ain THEN y Bi i = 1, 2, 3 . . . k

(7)

where xr (r = 1, 2, 3, . . . n) and y are input and output variable, respectively. These rules are generally combined by MAX - MIN operator and output are obtained [6]. The graphical representation of Mamdani’s FIS is represented if Fig. 1 [11].

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Fig. 1. Mamdani fuzzy inference system

3 Application The proposed method consists of three main phases including (i) Definition of parameter values for each control point, (ii) Obtaining Membership Degrees of Fuzzy Numbers, and (iii) Calculation of risk magnitudes with Fuzzy Inferences System. 3.1 Definition of Parameters The degree of severity and probability of the risks are defined by using a linguistic scale given in Table 1 [11]. In the proposed approach, different dimensions of the OHS specialists’ assessment for the determined risks and uncertainties regarding this assessment are considered by using the membership degrees of T, I, and F parameters. In the proposed model, two questions for the possibility and severity parameter of each risk parameter are asked to OHS specialists. In this evaluation, T presents the possibility of the risk occurrence before the required control measures are applied for the potential risk while F presents the possibility of the risk occurrence after the determined control measures are applied for the potential risk. Similarly, T presents the possible severity of the risk occurrence before the determined control measures are applied for the potential risk while F presents the possible severity of the risk occurrence after the determined control measures are applied for the potential risk. Calculation of uncertainty is carried out by using Table 2 based on the answers for the questions given in Table 3. Hence, I which represents the indeterminacy is obtained based on the differences between T and F for each control point [11] (Table 4).

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Table 1. Linguistic variable for the proposed method Fuzzy numbers

Linguistic variable

Possibility meaning

Severity meaning

(0, 0, 2.5)

VL

Very low/rare

There is no loss of working days or affecting production downtime

(0, 2.5, 5)

L

Low/faraway possibility

There is minor injury causing short time stops or slows down of the operations

(2.5, 5, 7.5)

M

Moderate/occasional

There is serious injury or damage affecting the operations

(5, 7.5, 10)

H

High/quite possible

There is permanent injury or death case

(7.5, 10, 10)

VH

Very high/almost certain

Lethal accident and/or environmental disaster

Table 2. Determination of indeterminacy value Falsity questions Truth questions

VL

L

M

H

VH

VL

VL

–

–

–

–

L

VL

VH

–

–

–

M

VL

H

VH

–

–

H

VL

M

H

VH

–

VH

VL

L

M

H

VH

Table 3. Truth and falsity question types for the control point Variable Probability Truth (Current Situation)

Question What is the risk possibility if there is not an appropriate control measure?

Falsity (Status after taking precautions) What is the risk possibility if there is an appropriate control measure? Severity

Truth (Current Situation)

What is the possible severity if there is not an appropriate control measure?

Falsity (Status after taking precautions) What is the possible severity if there is an appropriate control measure?

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S. Cebi and M. Karamustafa Table 4. Control lists application of electric arc welding machine

Risk

Risk

Control point

Cp

R1

Vision loss due to splashes of burr/purple and infrared rays

Glasses and masks should be selected according to the intensity of the current

Ctrl1

Yellow, green, or orange-colored ultraviolet (UV) absorbent materials should be used on cabin curtains to prevent glare and reduce reflections

Ctrl2

The process should be done outdoors or ventilation systems should be used

Ctrl3

A suitable gas mask must give the employee and training on use

Ctrl4

R2

R3

Acute and chronic respiratory system diseases or cancer

Serious injury/death from electric shock

While attaching / removing the cables of Ctrl5 the device, before starting the maintenance repair, calibration, adjustment, or measurement, LOTO should be applied and the system is in the off position Worn, damaged cables, clamps / torches Ctrl6 should be checked and changed before starting work During breaks, the electrode holder should be placed on a non-conductive plate

Ctrl7

A residual current device should be used Ctrl8 on the system The whole system (control box, welding Ctrl9 machine, and other parts) must be properly grounded R4

R5

Skin irritation, burning due to high temperature

The operator must wear suitable gloves

Ctrl10

It should not be in direct contact with Ctrl11 metal surfaces that are heated during the working

Injury/death from fire during an Easily flammable objects should be Ctrl12 operation removed from the workplace or a screen should be erected with sheet metal Feeding cables should be protected from Ctrl13 mechanical and chemical effects

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In Table 5, OHS specialist’ evaluations for the determined potential risks in electric arc welding machine are given. In the table, linguistic evaluations for both risk probability and risk severity are given. Table 5. Linguistic variables of electric arc welding machine Risk Control point Probability

Severity

T

I

F

T

I

F

R1

Ctrl1

H

M

L

VH H

H

R1

Ctrl2

H

VL

VL

VH H

H

R2

Ctrl3

H

M

L

VH H

H

R2

Ctrl4

H

VL

VL

H

M

L

R3

Ctrl5

H

M

L

H

M

L

R3

Ctrl6

H

M

L

H

M

L

R3

Ctrl7

H

M

L

H

M

L

R3

Ctrl8

H

M

L

VH H

H

R3

Ctrl9

VH L

L

VH H

H

R4

Ctrl10

H

VL

H

M

L

R4

Ctrl11

VH L

L

VH M

M

R5

Ctrl12

H

M

L

H

M

L

R5

Ctrl13

H

H

M

VH H

H

VL

3.2 Obtaining Membership Degrees Table 6 presents the membership degrees of the linguistic variables obtained by using the scale. Table 6. Table of membership degrees Linguistic Fuzzy variable triangular numbers

VL L

VL

(0, 0, 2.5)

1

L

(0, 2.5, 5)

0.5 1

M

(2.5, 5, 7.5)

H

(5, 7.5, 10)

VH

(7.5, 10, 10)

M

H

VH

0.5 0.5

0.5 1

0.5

0.5 1

0.5

0.5 1

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3.3 Calculation of Risk Magnitudes with Fuzzy Inferences System Mamdani fuzzy inference system is used to calculate the risk magnitude of each risk. The rule base of the inference system is represented by Eq. 8: Rk : IF RS(T , I , F) AND RP(T , I , F) THEN RM(T , I , F)

(8)

where k, is the number of rules while µRS , µRP , and µRM are the membership degrees of possibility, severity, and risk magnitude, respectively. Considering the union operation of two single valued neutrosophic numbers the fuzzy risk magnitude (RM) calculated using the following equations:    k k k k k (9) TRM (x) = max min TRS (x), TRP (x), TRD (x), TRF (x) ,    k k k k k IRM (x) = max min IRS (x), IRP (x), IRD (x), IRF (x) ,

(10)

   k k k k k FRM (x) = min max FRS (x), FRP (x), FRD (x), FRF (x) ,

(11)

Finally, the considered risk magnitude is represented by four levels of risk consequence such as catastrophic (Cs), major (Mj), minor (Mn), and negligible (Ng). The rule base of the study is given in the Table 7. Table 7. Rule base for matrix Severity (S)

Possibility (P) VL

L

M

H

VH

Ng

Ng

Ng

Mn

Mn

L

Ng

Mn

Mn

Mj

Mj

M

Ng

Mn

Mj

Mj

Cs

H

Mn

Mj

Mj

Cs

Cs

VH

Mn

Mj

Cs

Cs

Cs

VL

The score function formula given by Eq. 12 is used to convert the risk magnitudes obtained from rule base into a single value. S(RM k ) =

k (x) + I k (x) + F k (x) 4 ∗ TRM RM RM 6

(12)

Then the center of gravity method given in Eq. 13 is used to converted fuzzy numbers to crisp values [7]. The obtained risk magnitudes are given in Table 8.  Zi µRM (y) RM i = i=1 (13) i=1 µRM (y)

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Table 8. Risk magnitudes Risk

Control point

Score function

Risk magnitude

Ng

Mn

Mj

Cs

R1

Cp 1

0.083

0.167

0.583

0.833

7.900

R1

Cp 2

0.083

0.250

0.500

0.667

7.500

R2

Cp 3

0.083

0.167

0.583

0.833

7.900

R2

Cp 4

0.250

0.167

0.417

0.667

7.000

R3

Cp 5

0.083

0.083

0.583

0.750

8.000

R3

Cp 6

0.083

0.083

0.583

0.750

8.000

R3

Cp 7

0.083

0.083

0.583

0.750

8.000

R3

Cp 8

0.083

0.167

0.583

0.833

7.900

R3

Cp 9

0.167

0.167

0.250

0.833

7.706

R4

Cp 10

0.250

0.167

0.417

0.667

7.000

R4

Cp 11

0.167

0.250

0.167

0.667

7.200

R5

Cp 12

0.083

0.083

0.583

0.750

8.000

R5

Cp 13

0.000

0.083

0.500

0.917

8.667

According to Table 8, “R5-Injury/death from fire during an operation” risk was found as the highest risk. In electric arc welding, the center of arc temperature is around 5500 °C. These temperatures cause the metal to heat up and a high flame may occur during cutting with a torch. In accordance with this description, R5 was identified as the highest risk in application.

4 Conclusions In this study, a new risk analysis method has been proposed to the literature in order to contribute to the development of occupational health and safety processes and to reduce occupational accidents and occupational diseases. In the study, the L-type risk analysis method, which is widely used in risk assessment, is extended to neutrosophic sets for the first time in order to address the uncertainty arising from different perspectives, the randomness of events, and the indeterminacy of decision makers. In the study, Mamdani fuzzy inference system was used to obtain the risk size. The method has been applied to welding processes to illustrate the application of the proposed approach. By determining the sources of danger in the application, checklists were created to eliminate the risks. While evaluating each of these control points, the probability and severity parameters are expressed in three dimensions with T, I and F. In this way, both the current situation at the control point and the situation that will occur after taking precautions are evaluated simultaneously, and the deficiency caused by the uncertainty and indecision in the risk environment has been tried to be prevented. In addition, we propose an alternative calculation method for the score function of neutrosophic sets to assess risk magnitudes.

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For future studies, a decision support system can be developed based on the proposed approach.

References 1. Haggag, O.Y.A., Barakat, W.: Application of fuzzy logic for risk assessment using risk matrix. Int. J. Emerg. Technol. Adv. Eng. 3(2013), 49–54 (2013) 2. Gul, M., Guneri, A.F.: A fuzzy multi criteria risk assessment based on decision matrix technique: a case study for aluminum industry. J. Loss Prev. Process Ind. 40, 89–100 (2016) 3. Ceylan, H., Bashelvaci, V.S.: Risk analysis with risk assessment matrix method: an application. Int. J. Eng. Res. Dev. 3(2), 25–33 (2011) 4. Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986) 5. Smarandache, F.: Definition of neutrosophic logic, a generalization of the intuitionistic fuzzy logic. In: Proceeding of the 3rd Conference of the European Society for Fuzzy Logic and Technology (2000) 6. Mamdani, E.H., Assilian, S.: An experiment in linguistic synthesis with a fuzzy logic controller. Int. J. Man-Mach. Stud. 7(1), 1–13 (1975) 7. Ross, T.J.: Fuzzy Logic Engineering Applications. Wiley, USA (2004) 8. Acuner, O., Cebi, S.: An effective risk-preventive model proposal for occupational accidents at shipyards. Brodogradnja/Shipbuilding/Open Access 67(1) (2016) 9. Ilbahar, E., Karasan, A., Cebi, S., Kahraman, C.: A novel approach to risk assessment for occupational health and safety using Pythagorean fuzzy AHP & fuzzy inference system. Saf. Sci. 103, 124–136 (2018) 10. Karasan, A., Ilbahar, E., Cebi, S., Kahraman, C.: A new risk assessment approach: safety and critical effect analysis (SCEA) and its extension with Pythagorean fuzzy sets. Saf. Sci. 108, 173–187 (2018) 11. Karamustafa, M., Cebi, S.: Extension of safety and critical effect analysis to neutrosophic sets for the evaluation of occupational risks. Appl. Soft Comput. 110, 107719 (2021)

Fuzzy Predictor of Daily Average Water Consumption Per Capita for Turkey Halid Akdemir1,2

and Cihan Bayindir1,3(B)

1 ˙Istanbul Technical University, Sarıyer, 34469 ˙Istanbul, Turkey

{akdemirh20,cbayindir}@itu.edu.tr

2 Antalya Bilim University, Dö¸semealtı, 07190 Antalya, Turkey 3 Bo˘gaziçi University, Bebek, 34342 ˙Istanbul, Turkey

Abstract. The amount of daily water demanded by individuals is used as a basic parameter in the design of infrastructure systems. The purpose of this study is to examine the daily average water consumption per capita (WCPC) values used as infrastructure basic design parameters and suggested by Turkish Standards across Turkey. Accordingly, one of the aims of this study is to reveal how accurately these standards predict WCPC values, the other one is to create a model predicting better with low error rate and trend-reflecting values. WCPC belonging to 2018 for 30 Turkish cities was introduced. According to this research study, the population weighted average WCPC was found out to be 131.9 L across the country and it ranges from 67.7 to 208 L. The population weighted average loss percent of discharge across the country is 36% while it ranges from 23% to 71%. 10 parameters for each city that had the potential to influence water consumption are following; average temperature, maximum temperature, average precipitation, humidity, water price, population, population density, sunshine duration, tourism intensity, and industry level. Since the problem is complex, the fuzzy logic method, which is a rule-based algorithm from the soft computing methods, was preferred and found suitable on the stage of creating the predictor model. The fuzzy model was formed with an expert perspective approach. The accuracy of the values proposed by the fuzzy model and the standards were measured and compared with R2 and RMSE parameters. The coefficient of determination of Altınbilek’s values, 2013 Provincial Bank, which are Turkish Standards, and the fuzzy model were found out as −4.77, −0.55, and 0.41, respectively. The poor estimation ability of the standards has revealed the need for the model that is able to make better estimation and measurement results proved the necessity of future examination of the predictions. Keywords: Daily average water consumption per capita · Fuzzy logic · Water consumption of Turkey

1 Introduction The amount of daily water demanded by individuals is used as the fundamental design parameter such as the design of the infrastructure systems which has a significant impact © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 271–278, 2022. https://doi.org/10.1007/978-3-031-09173-5_34

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on growth, the region’s planning projections, the water policy and the welfare level of the region. Specifically, it is the topic as the daily average water consumption per capita value (WCPC). The water consumption is shaped according to the needs and preferences of a person [1]. The daily water demand of a person can vary greatly from region to region throughout the world. According to many researches in the literature, this value varies approximately from 50 L to 550 L. In Australia, which is an Oceania country, WCPC varies between 370–550 L by years for the Sydney [2]. In Germany, which is a European country, this value was found as an average of 128 L [3]. In Uganda standards, which is an African country, WCPC can vary from 50 L for some regions to 200 L for some other regions and economic level is determined as the effective parameter [4]. Recently, artificial intelligence methods have been very preferred in hydrological analysis due to the fuzziness that comes from the nature of hydrology [5]. Fuzzy logic method is one of them and it is a very useful method; it has been shown in many studies to be useful in water science [6, 7]. The literature also draws attention to the lack of models that estimate the WCPC across countries. It was aimed to fill this gap with this study as an example. There are 2 Turkish Standards named Altınbilek’s values and 2013 Provincial Bank to get WCPC required for the design of infrastructure projects [8, 9]. One of the purposes of this study is to find out to how successful Turkish Standards can predict WCPC, the other one is to form a model to be able to forecast WCPC better across the country. The preferred methodology in this study is explained in Sect. 2. In Sect. 3, the variables were examined and data set was created. The comparative results of the estimation capabilities of the fuzzy model and the standards are presented in Sect. 4. The implications of this study can be found in Sect. 5.

2 Methodology The dataset was formed using database of Turkish Statistical Institute, Turkish municipalities annual reports, Meteorological Directorate General, Ministry of Industry and Ministry of Tourism. The estimation capabilities of the values suggested by the standards and the fuzzy model created in this study, were measured with RMSE and R2 parameters. 2.1 Turkish Standards 2013 Provincial Bank and Altınbilek’s values have been used to obtain WCPC for the aim of infrastructure project designs. Designers may prefer using both Altınbilek’s values or 2013 Provincial Standard to select WCPC. This depends on their engineering judgement. The WCPC values suggested by Altınbilek and 2013 Provincial Bank are tabulated in Table 1 [8, 9].

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Table 1. Altınbilek’s and 2013 Provincial Bank Standard’s WCPC. Altınbilek’s WCPC

2013 Provincial Bank Standard’s WCPC

Population

Population

WCPC (L/capita/day)

WCPC (L/capita/day)

3000

60

Up to 50000

80–100

5000

70

50000–100000

100–120

10000

80

More than 100000

120–140

30000

100

50000

120

100000

170

500000

230

1000000

280

2000000

330

3000000

370

According to Table 1, the standards propose rule-based values depending on the population density parameter. In fact, there is complexity in the ruler proposed by the standards. Since the population parameter is namely specific, it is not mentioned how much these values are valid for an area. Therefore, it remains to the discretion of the designer in some amount. WCPC suggested by the standards vary greatly as Table 1 shows. 2.2 Fuzzy Logic Algorithm suitable for the model were determined by considering the availability and conformity of the data. Fuzzy logic which is one of soft computing techniques was preferred in this paper due to its success on estimation. As there are not enough number of samples to train, a rule-based algorithm was preferred. In this study, the fuzzy model was formed with an expert approach. Contrary to Aristotelian logic, fuzzy logic ranges cases between 0 and 1 instead of assigning them as 0 or 1 [10]. Fuzzy logic defines problems by establishing a relationship with the set of rules between inputs and outputs. See [11] for more comprehensive explanation.

3 Fuzzy Predictor on Water Consumption Pattern The independent variables obtained for the aim of forming the fuzzy model as a result of literature review that may affect the water consumption pattern were selected as follows; average temperature, maximum temperature, average rainfall, humidity, sunshine duration, water price, population density, tourism intensity, industry level.

274

H. Akdemir and C. Bayindir 210.00

lt/capita/day

180.00

Average

150.00 120.00 90.00 60.00

0.00

Adana Ankara Antalya Aydın Balıkkesir Bursa Denizli Diyarbakır Erzurum Eskişehir Gaziantep Hatay İstanbul İzmir Kahramanmaraş Kayseri Kocaeli Konya Malatya Manisa Mardin Mersin Muğla Ordu Sakarya Samsun Şanlıurfa Tekirdağ Trabzon Van

30.00

Turkish cities

Fig. 1. End-use of WCPC of Turkish cities.

WCPC of Turkish cities and the discharge losses of the cities were introduced in Fig. 1 and Fig. 2 respectively. The values of each parameter belong to 2018, the most recent date of data release. Figure 1 illustrates an overall view on the distribution of WCPC across country. Water consumption of Turkish cities range from about 67.7 L to 208 L. The average water consumption of a citizen across the country was calculated as 131.9 L, taking into account the water consumption and the population weight of the cities. 100.0%

L (%)

80.0%

Average

60.0% 40.0%

0.0%

Adana Ankara Antalya Aydın Balıkkesir Bursa Denizli Diyarbakır Erzurum Eskişehir Gaziantep Hatay İstanbul İzmir Kahramanmaraş Kayseri Kocaeli Konya Malatya Manisa Mardin Mersin Muğla Ordu Sakarya Samsun Şanlıurfa Tekirdağ Trabzon Van

20.0%

Turkish cities

Fig. 2. Discharge loss percent of Turkish cities.

The discharge loss percent of each city which is introduced in Fig. 2 are shared in the annual reports published by the administration of each city in every year. The population weighted loss percent of average discharge across country was calculated as 36%. This means that on average across the country, 36% of discharges transmitted through water transmission lines leaks or is lost in the supply system. The city of Trabzon has the lowest performance of infrastructure or administrative systems with a value of approximately

Fuzzy Predictor of Daily Average Water Consumption Per Capita

275

30000.00 25000.00 20000.00 15000.00 10000.00 5000.00

ep İst Ka a hr nb am ul an m ar aş Ko ca el i M al at ya M ar di n M uğ la Sa ka ry a Şa nl ıu rfa Tr ab zo n

m

nt

Ga z

ia

ru

zli

zu

ni Er

De

sir

Ba

lık

ke

lya ta

An

an

a

0.00

Ad

total turnover of city($)/capita

71%. It seems that developed cities have relatively low losses for example Bursa and ˙Istanbul have the lowest discharge losses with a loss percent of 23%.

Turkish cities

Fig. 3. Industrial level for each city.

2.80 2.40 2.00 1.60 1.20 0.80 0.40 0.00

Adana Ankara Antalya Aydın Balıkkesir Bursa Denizli Diyarbakır Erzurum Eskişehir Gaziantep Hatay İstanbul İzmir Kahramanmaraş Kayseri Kocaeli Konya Malatya Manisa Mardin Mersin Muğla Ordu Sakarya Samsun Şanlıurfa Tekirdağ Trabzon Van

number of tourist/capita

Figure 3 reveals the industrial activity of each city across the country. Kocaeli has an industrial density ahead of other cities with a big difference. The industrial activity difference between cities is relatively noticeable. There are a few industrial establishments in a large number of cities.

Turkish cities

Fig. 4. Tourism intensity for each city.

Turkey is a country of tourism with charm so periodically exposed to intense tourism activity. Antalya and Mu˘gla stand out as the cities with the highest tourism density as seen in Fig. 4. Tourism intensity seems to be present at a certain rate in every city.

H. Akdemir and C. Bayindir

900.00 750.00 600.00 450.00 300.00 150.00 0.00

Adana Ankara Antalya Aydın Balıkkesir Bursa Denizli Diyarbakır Erzurum Eskişehir Gaziantep Hatay İstanbul İzmir Kahramanmaraş Kayseri Kocaeli Konya Malatya Manisa Mardin Mersin Muğla Ordu Sakarya Samsun Şanlıurfa Tekirdağ Trabzon Van

population/area(km2)

276

Turkish cities

Fig. 5. Population density for each city.

Figure 5 shows that ˙Istanbul and Kocaeli as the cities with highest population density. Erzurum appears to have the least population density. The correlation study done in this study between the effective variables and the water consumption pattern is following; R2 values of average rainfall, tourism level, humidity, water price, industry level, population, population density, average temperature, sunshine duration and maximum temperature are 0.1522, 0.1245, 0.0889, 0.0876, 0.0789, 0.0189, 0.0174, 0.0161, −0.0030 and −0.0015 respectively. The fuzzy model was created by utilizing the results of this correlation study. Fuzzy logic was found suitable for the convenience of the analysis since there are not many samples and the data set are more suitable for the rule-based algorithm. Matlab software was used to create the fuzzy model. The structure of the fuzzy model which was implemented in this paper for WCPC predictions can be seen in Fig. 6.

Average Rainfall (3) Fuzzy Consumption Predictor Water Price (3) (mamdani)

Tourism Activty (3)

81 rules

Water Consumption (5)

Industry Level (3)

System Fuzzy_Consumption_Predictor: 4 inputs, 1 outputs, 81 rules

Fig. 6. Structure of the fuzzy model.

Mamdani fuzzy model has been adapted. Centroid was preferred as defuzzification method. 3 membership functions were preferred for each 4 input which are average

Fuzzy Predictor of Daily Average Water Consumption Per Capita

277

rainfall, water price, tourism intensity and industry level resulting in 81 rules. Since the fuzzy logic method was a rule-based modeling system, the most accurate model was formed with an expert opinion approach. The range in water consumption values of cities is relatively high, so the output of this structure has 5 membership functions in order to obtain more sensitive results.

4 Comparative Results Table 2 shows that the ability of the standards to make predictions is weak. On the other hand, the fuzzy model performed better with low error rate and trend-reflecting forecasting ability as depicted in Fig. 7. Table 2. R2 and RMSE of the standards and the model.

lt/capita/day

Models

R2

RMSE (L)

Altınbilek values

−4.77

74.07

2013 provincial bank

−0.55

38.48

The fuzzy predictor

0.41

24.5

210.00

End-Use Values

180.00 150.00

The Fuzzy Predicons

120.00 90.00 60.00 30.00 Adana Ankara Antalya Aydın Balıkkesir Bursa Denizli Diyarbakır Erzurum Eskişehir Gaziantep Hatay İstanbul İzmir Kahramanmaraş Kayseri Kocaeli Konya Malatya Manisa Mardin Mersin Muğla Ordu Sakarya Samsun Şanlıurfa Tekirdağ Trabzon Van

0.00

Turkish cities

Fig. 7. End-use values and values predicted by the fuzzy model (L/capita/day).

The margin of error appears to be relatively greater in the cities of Balıkesir, Malatya, Kahramanmara¸s and Mu˘gla. The consumption values of the other cities seem very close to the predicted values. While the end-use values seem to vary between 208 L/capita and 67.7 L/capita, the predicted values vary between 165 L/capita and 85.5 L/capita. The estimation error of the fuzzy model is lower than the other standards. Thus, the model was developed that offers better forecasting than those suggested by the standards currently in use for the whole country.

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5 Conclusion The adequacy of current standards used for projects and planning has been examined aspect of predictive capabilities and based on this, the more developed model has been introduced in this study for the prediction of WCPC of Turkish cities. Accordingly, the fuzzy predictor successfully gave better results than the standards currently in use gave. More accurate estimates obtained in this paper will contribute to infrastructure projects and regional planning, by making it more economical or more demand-oriented thus being obtained better welfare level in regions. Our study can be extended beyond obtaining end-uses for each city by revealing how consumptions has changed and at what levels compared to previous years and by including it in the training set.

References 1. Hussien, W.A., Memon, F.A., Savic, D.A.: Assessing and modelling the influence of household characteristics on per capita water consumption. Water Resour. Manage. 30(9), 2931–2955 (2016) 2. Barrett, G.: Water conservation: the role of price and regulation in residential water consumption. Econ. Pap. A J. Appl. Econ. Policy 23(3), 271–285 (2004). https://doi.org/10.1111/j. 1759-3441.2004.tb00371.x 3. Schleich, J., Hillenbrand, T.: Determinants of Residential Water Demand in Germany (2007) 4. The Republic of Uganda Ministry of Water and Environment: Water Supply Design Manual, 2nd edn. The Republic of Uganda, Ministry of Water and Environment. Gov. Uganda, vol. 3, pp. 3–26 (2013) 5. Oyebode, O., Ighravwe, D.E.: Urban water demand forecasting: a comparative evaluation of conventional and soft computing techniques. Resources 8(3), 156 (2019). https://doi.org/10. 3390/resources8030156 6. Akdemir, H., Alaybeyo˘glu, A., Mehr, A.D.: A new perspective to design phase of water supply systems from aspect of water demand using fuzzy automation. In: Kahraman, C., Cevik Onar, S., Oztaysi, B., Sari, I.U., Cebi, S., Tolga, A.C. (eds.) INFUS 2020. AISC, vol. 1197, pp. 1242–1249. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-51156-2_145 7. Uyumaz, A., Altunkaynak, A., Özger, M.: Fuzzy logic model for equilibrium scour downstream of a dam’s vertical gate. J. Hydraul. Eng. 132(10), 1069–1075 (2006). https://doi.org/ 10.1061/(asce)0733-9429(2006)132:10(1069) 8. Yanmaz, A.M.: Applied Water Resources Engineering. Metu Press, Ankara (2018) 9. Turkish Standard: Technical Specification for Preparation of Drinking Water Facilities, Survey, Feasibility and Projects (2013) 10. Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man. Cybern. 15(1), 116–132 (1985) 11. Ross, T.J.: Fuzzy Logic With Engineering Applications (2005)

Distributed No-Wait Flow Shop with Fuzzy Environment Ramazan Ba¸sar1

, Kadir Büyüközkan2

, and Orhan Engin3(B)

1 Industrial Engineering Department, Aksaray University, Aksaray, Turkey 2 Industrial Engineering Department, Karadeniz Technical University, Trabzon, Turkey 3 Industrial Engineering Department, Konya Technical University, Konya, Turkey

[email protected]

Abstract. In the no-wait flow shop scheduling problem, n-job should be proceeded on m-machine with the same order and do not permit the jobs to wait during the scheduling periods. Also, at the distributed no-wait flow shop scheduling problem, there are multi-factory for processing n-job with m-machine for no-wait constraint. In this study, distributed no-wit flow shop scheduling with the fuzzy due date is considered. The due date of the jobs is defined with fuzzy numbers. A parallel kangaroo algorithm is proposed to solve the distributed no-wait flow shop scheduling problem with the fuzzy due date. The proposed algorithm is tested from the literature by the benchmark problems. The results show that the proposed parallel kangaroo algorithm is efficient for distributed no-wit flow shop scheduling problems with fuzzy due date problems. Keywords: Distributed no-wait flow shop · Scheduling · Parallel kangaroo algorithm · Fuzzy due date

1 Introduction The most common scheduling problem is the flow shop scheduling problem. In the flow shop scheduling problem (FSSP), n-jobs are processed on the m-machine with the same order. The FSSP is well-known as a NP-hard [1]. In the FSSP, if do not permitted the jobs for waiting during the scheduling process, the problem is defined no-wait flow shop scheduling problem (NW-FSSP). Also, the NW-FSSP is known as a NP-hard [2]. It can be seen in the chemical, pharmaceutical, and metallurgical industry commonly. The NW-FSSP is intensively studied in the literature last years. Some of them are given below. Allahverdi [3] provided an extensive literature review about NW-FSSP between 1993 to 2016. Engin and Güçlü [4] proposed a hybrid ant colony optimization algorithm for NW-FSSP with setup times. Keskin and Engin [5] developed a hybrid genetic local and global search algorithm for solving the NW-FSSP to minimize the total flow time and makespan performance criterion. Distributed NW-FSSP is a new research problem from the literature. There are a few studies about distributed NW-FSSP. These are explained as follows. Shao et al. [6] proposed an iterated greedy algorithm (IAG) for distributed NW-FSSP. The minimization © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 279–286, 2022. https://doi.org/10.1007/978-3-031-09173-5_35

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of makespan is used as a performance criterion. Miyata et al. [7] investigated the distributed NW-FSSP with sequence-dependent setup times and maintenance operations. They studied to minimize makespan as a performance criterion. They described the problem with a mixed-integer programming model. They proposed an IAG to solve the problem. Allali et al. [8] studied a multi-objective optimization distributed no-wait permutation flow shop with sequence-dependent setup time. They solved the problem with the two performance criteria. These criteria are to minimize makespan and maximum tardiness. For solving the problem, they used a mixed-integer linear programming model and three metaheuristics algorithms. The metaheuristics methods are genetic algorithm, artificial bee colony algorithm, and migratory bird optimization algorithm. Manufacturers should deliver customer orders just in time. But, due to human and manufacturing factors, the orders cannot be delivered just in time. Thus, in this research, the distributed NW-FSSP is considered with a fuzzy due date. There are only a few studies about NW-FSSP with fuzzy due dates from the literature. These are given below. Zhou and Gu [9] interested with the NW-FSSP with the fuzzy due date. Ba¸sar and Engin [10] proposed a scatter search algorithm to solve the NW-FSSP with the fuzzy due dates to maximize the satisfaction index objective. In this study, a distributed NW-FSSP with a fuzzy due date is considered. A parallel kangaroo algorithm is proposed for solving the distributed NW-FSSP with fuzzy due dates. This is the first attempt to consider distributed NW-FSSP with fuzzy due dates. Also, the first time, the considered problem is solved with the parallel kangaroo algorithm (PKA) from the literature. The paper is organized as follows. The parallel kangaroo algorithm is defined in Sect. 2. The considered problem and solution results are explained in Sect. 3. The conclusions and future research are given in Sect. 4.

2 Parallel Kangaroo Algorithm Scheduling is a known NP problem. For solving these problems, exact methods, heuristic, and metaheuristic algorithms are developed from the literature. Some metaheuristic methods are developed by inspired from the animals’ behavior like an ant colony, bee colony, and kangaroo algorithm. The kangaroo algorithm (KA) is inspired by the jumping movements of kangaroos in nature. KA is known as “Pollard’s Kangaroo”, “Pollard’s Rho algorithm” in the literature [11]. KA was first proposed by Pollard in 1978 [12]. In a parallel kangaroo algorithm (PKA), there are two operators (kangaroo) that jump independently of each other in the same period of time. For local search, tame kangaroo searches in solution space by jumping in small steps. Also, wild kangaroo searches in solution space by jumping in big steps. Two kangaroos start their movements simultaneously at different points. They keep jumping until they reach the target value or reach the maximum number of iterations. The objective function is recalculated after each jump. If the calculated new objective function is better than the previous one, the iteration continues with the new solution. In the literature, KA has been used for solving the scheduling problems. Some of them are given below. Yılmaz et al. [13] proposed a parallel kangaroo algorithm for the bi-objective flow shop scheduling problem. Also, Yılmaz et al. [14] generated a hybrid

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PKA and simulated annealing algorithm for solving multi-objective flow shop scheduling problems. Da˘g and Keskintürk [15] developed a genetic and kangaroo algorithm for solving the permutation FSSP.

3 Considered Problem and Solution In this study, the distributed NW-FSSP with setup times for fuzzy due date (FDD) is considered. The due date is defined by trapezoidal fuzzy numbers. The parameters are defined as follows. F:

Number of factories

n:

Number of jobs

m:

Number of machines

i,k:

Indices of machine

:   S j , i :   P j , i : j : dd

Job Permutation

CTj :

The job j’s completion time

Setup time of the job j on machine i The job j ’s processing time on machine i The job j’s fuzzy due date

  2 , d˜ d 3 , dd 4 . The customer satisfaction index 1 , dd The FDD is defined by a dd (CSI) for jobs has been calculated with Eq. 1 [16, 17]. ⎫ ⎧ 1 ⎪ ⎪ 0 CTj ≤ dd ⎪ ⎪ ⎪ ⎪ 1 ⎪ ⎪  ⎪ ⎪ 1 2 Ctj −dd  ⎪ ⎪  ⎪ ⎪ < CT < dd dd j 2 1 ⎪ ⎪ dd   −dd ⎬ ⎨ 2 3   (1) μ˜ dd = 1 dd ≤ CT ≤ dd j j ⎪ ⎪ ⎪ ⎪ 4 −Ctj ⎪ ⎪ 3 4 dd ⎪  ⎪  < CTj < dd ⎪ ⎪ dd ⎪ ⎪ 3 4 −dd ⎪ ⎪ dd ⎪ ⎪ ⎭ ⎩ 4  ≤ CTj 0 dd For solving the distributed NW-FSSP with a fuzzy due dates a PKA is proposed. The pseudo-code of the proposed PKA is given below.

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Set initial parameters: Factory, job, and operation numbers; Processing times, due dates, and job constraints; Set the parallel kangaroo algorithm parameters: Wild kangaroo step size; Tame kangaroo step size; Wild kangaroo iteration number; Tame kangaroo iteration number; Maximum iteration number; Create an initial population by random: Calculated customer satisfaction index for jobs; Select a job sequence from population; Select a job from sequence by random and assign a tame kangaroo; Select a job from sequence by random and assign a wild kangaroo; Do; Local search; Global search; Calculate CSI; Check stopping criterion; End

The developed PKA is tested with the improved scatter search (ISS) and hybrid ant colony optimization (HACO) from the literature with Engin and Günaydın [2] benchmark instances. The results of the proposed PKA are compared with the HACO [4] and ISS [10]. The performance of the proposed PKA is defined as a relative percentage deviation (RPD) and given in Eq. 2. RPD =

PKA(Cmax ) − Best(Cmax ) ∗ 100 Best(Cmax )

(2)

In Eq. 2, the Best (C max ) is calculated by CPLEX [4]. The results of the proposed PKA, ISS, and HACO are given in Table 1. It can be seen in Table 1, that the proposed PKA found the Best (C max ) values for 45 of the 48 benchmark instances such as ISS. But HACO found the Best (C max ) values for only 21 of the 48 benchmark instances. The proposed PKA provides a better solution for NW-FSSPs. Also, the proposed PKA is compared with the ISS [10] for the customer satisfaction index on the 10 × 15-a benchmark instance. The CSI is defined in Eq. 3.   (3) CSIj = max μ˜ dd j

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The results of the CSIj are shown in Table 2. Table 1. The proposed PKA results comparison with ISS and HACO Instances

RPD

Instances

PKA

ISS

HACO

8 × 2-a

0.0000

0.0000

0.0000

8 × 2-b

0.0000

0.0000

8 × 2-c

0.0000

0.0000

8 × 3-a

0.0000

8 × 3-b 8 × 3-c

RPD PKA

ISS

HACO

10 × 2-a

0.0000

0.0000

0.0000

0.0000

10 × 2-b

0.0000

0.0000

1.4836

0.6451

10 × 2-c

0.0000

0.0000

0.3442

0.0000

0.0000

10 × 3-a

0.0000

0.0000

0.8547

0.0000

0.0000

4.1379

10 × 3-b

0.0000

0.0000

0.0000

0.0000

0.0000

0.3584

10 × 3-c

0.0000

0.0000

0.7496

8 × 5-a

0.0000

0.0000

0.0000

10 × 5-a

0.0000

0.0000

0.0000

8 × 5-b

0.0000

0.0000

0.5050

10 × 5-b

0.0000

0.0000

8.4415

8 × 5-c

0.0000

0.0000

0.0000

10 × 5-c

0.0000

0.0000

2.4054

8 × 8-a

0.0000

0.0000

0.0000

10 × 8-a

0.0000

0.0000

0.5917

8 × 8-b

0.0000

0.0000

0.0000

10 × 8-b

0.0000

0.0000

7.5306

8 × 8-c

0.0000

0.0000

0.0000

10 × 8-c

0.0000

0.0000

8.3643

8 × 10-a

0.0000

0.0000

0.6622

10 × 10-a

0.0000

0.0000

1.1363

8 × 10-b

0.0000

0.0000

0.0000

10 × 10-b

0.0000

0.0000

7.1895

8 × 10-c

0.0000

0.0000

0.0000

10 × 10-c

0.0000

0.0000

2.8472

8 × 15-a

0.0000

0.0000

0.0000

10 × 15-a

0.4651

0.4651

0.0000

8 × 15-b

0.0000

0.0000

0.2587

10 × 15-b

0.0000

0.0000

0.8244

8 × 15-c

0.0000

0.0000

0.0000

10 × 15-c

0.0000

0.0000

1.5913

8 × 20-a

0.0000

0.0000

0.0000

10 × 20-a

0.0000

0.0000

1.1673

8 × 20-b

0.0000

0.0000

0.5636

10 × 20-b

0.0959

0.0959

1.8216

8 × 20-c

0.0000

0.0000

0.0000

10 × 20-c

0.0000

0.0000

1.8271

8 × 25-a

0.0000

0.0000

0.0000

10 × 25-a

0.0000

0.0000

1.0909

8 × 25-b

0.0000

0.0000

1.1428

10 × 25-b

0.0000

0.0000

1.6736

8 × 25-c

0.0000

0.0000

0.0000

10 × 25-c

0.1707

0.1707

0.0000

In Table 2, by the proposed PKA, the maximum CSIj is found 1 for job J1 , J2 , J4 , J6 . Also, for jobs, J9 the CSI is higher than 0.90. For only job J3 , the CSIj is smaller than 0.5. But, the ISS [10] found the CSIj 1 for job J1 . Also, for jobs, J3 , J4 , J8 , the CSI is higher than 0.90. For only job J9 , the CSI is smaller than 0.5.

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Table 2. Comparison of the PKA results with ISS for CSIj at 10 × 15-a benchmark instance Jobs

ISSCSIj

PKACSIj

Jobs

ISSCSIj

PKACSIj

1

1.0

1.0

6

0.562

1.0

2

0.893

1.0

7

0.582

0.843

3

0.957

0.453

8

0.984

0,682

4

0.943

1.0

9

0.348

0.920

5

0.763

0.741

10

0.869

0.694

Average CSj

0.790

0.833

By the proposed PKA, the sequence of jobs is found, J3 , J2 , J4 , J6 , J1 , J9 , J7 , J5 , J10 , J8 . By the ISS [10], the job sequence was found, J6 , J1 , J9 , J7 , J5 , J10 , J2 , J4 , J3 , J8 . For the 10 × 15-a benchmark instance, the makespan is found 216 by the proposed PKA and ISS. The proposed PKA is coded in Visual Basic. The instances are solved by using an Intel Core i5 2.5 GHz computer. The performance of the proposed PKA is dependent on the initial parameters. Therefore, parameter optimization is done. The best parameter sets are found and are shown in Table 3. Table 3. Parameter sets for proposed PKA. Parameters

Values

Wild kangaroo step size

3

Tame kangaroo step size

2

Wild kangaroo iteration number

30

Tame kangaroo iteration number

20

Maximum iteration number

100

For 2 and 3 factories, the 10 × 15-a instance [2] is solved. The found maximum CSIj by the proposed PKA is given in Table 4. Table 4. According to the factories the CSIj values for 10 × 15-a benchmark instance Factories

Jobs J1

J2

J3

J4

J5

J6

J7

J8

J9

J 10

2

1.0

0.362

0,453

1.0

1.0

1.0

1.0

1.0

1.0

1.0

3

1.0

0,673

0,712

0,598

1.0

1.0

1.0

1.0

1.0

1.0

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It can be seen in Table 4, for two factories; by the proposed PKA the maximum CSIj is found 1 for jobs J1 , J4 , J5 , J6 , J7 , J8 , J9 , J10 . For only jobs J2 and J3 , the CSIj is smaller than 0.5. For three factories; by the proposed PKA the maximum CSIj is found 1 for jobs J1 , J5 , J6 , J7 , J8 , J9 , J10 . Also, for jobs, J2 , J3 , J4 the CSI is higher than 0.50.

4 Conclusions and Future Research In this research, distributed NW-FSSP is first considered with the fuzzy due dates. The fuzzy due dates are defined by trapezoidal fuzzy numbers. Also, the first time, to solve the problem a PKA is considered. To increase the performance of the proposed PKA, parameter optimization is done. The proposed PKA is first tested with ISS and HACO from the literature. Then, a distributed NW-FSSP with the fuzzy due date is solved by the proposed PKA. The distributed NW-FSSP is solved for 1, 2, and 3 factories for the customer satisfaction index objective. The results show that the proposed PKA is an effective approaches for distributed NW-FSSP with fuzzy due date problems. In the future, a real-life distributed NW-FSSP in a fuzzy environment can be solved by the proposed parallel kangaroo algorithm.

References 1. Engin, O., Döyen, A.: A new approach to solve flowshop scheduling problems by artificial immune systems. Do˘gu¸s Üniversitesi Dergisi 8(1), 12–27 (2007) 2. Engin, O., Günaydın, C.: An adaptive learning approach for no-wait flowshop scheduling problems to minimize makespan. Int. J. Comput. Intell. Syst. 4(4), 521–529 (2011) 3. Allahverdi, A.: A survey of scheduling problems with no-wait in process. Eur. J. Oper. Res. 255, 665–686 (2016) 4. Engin, O., Güçlü, A.: A new hybrid ant colony optimization algorithm for solving the no-wait flow shop scheduling problems. Appl. Soft Comput. 72, 166–176 (2018) 5. Keskin, K., Engin, O.: A hybrid genetic local and global search algorithm for solving no-wait flow shop problem with bi criteria. SN Appl. Sci. 3, 628 (2021) 6. Shao, W., Pi, D., Shao, Z.: Optimization of makespan for the distributed no-wait flow shop scheduling problem with iterated greedy algorithms. Knowl.-Based Syst. 137, 163–181 (2017) 7. Miyata, H.H., Nagano, M.S.: Optimizing distributed no-wait flow shop scheduling problem with setup times and maintenance operations via iterated greedy algorithm. J. Manuf. Syst. 61, 592–612 (2021) 8. Allali, K., Aqil, S., Belabid, J.: Distributed no-wait flow shop problem with sequence dependent setup time: optimization of makespan and maximum tardiness. Simul. Model. Pract. Theory 116, 102455 (2022) 9. Zhou, Y., Gu, X.: Research on no-wait flow shop scheduling problem with fuzzy due date based on evolution games. In: IEEE International Conference on Computer Science and Information Technology, pp. 495–499 (2009) 10. Ba¸sar, R., Engin, O.: A No-wait flow shop scheduling problem with setup time in fuzzy environment. In: Kahraman, C., Cebi, S., Cevik Onar, S., Oztaysi, B., Tolga, A.C., Sari, I.U. (eds.) INFUS 2021. LNNS, vol. 307, pp. 607–614. Springer, Cham (2022). https://doi.org/ 10.1007/978-3-030-85626-7_71

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11. Baysal, M.E., Durmaz, T., Sarucan, A., Engin, O.: To solve the open shop schedulıng problems wıth the parallel Kangaroo algorithm. J. Fac. Eng. Archit. Gazi Univ. 27(4), 855–864 (2012) 12. Kökçam, A.H., Engin, O.: Solving the fuzzy project scheduling problems with metaheuristic methods. J. Eng. Nat. Sci. Sigma 28, 86–101 (2010) 13. Yılmaz, M.K., Engin, O., Fı˘glalı, A., Yavuz, M.: Parallel kangaroo algorithm for biobjective flow shop scheduling with a new weight combining approach. In: 1st International Symposium on Computing in Science & Engineering, ISCSE-2010, Gediz University (˙Izmir), 3–5 June 2010, Ku¸sadası, Aydın Turkey, pp. 823–827 (2010) 14. Yılmaz, M.K., Fı˘glalı, A., Terzi, U., Yavuz, M., Engin, O.: A hybrid parallel kangaroo & simulated annealing algorithm for multi-objective flow shop scheduling. J. Manage. Eng. Integr. 3(2), 97–105 (2010) 15. Da˘g, S., Keskintürk, T.: Hybrid metaheuristic for the permutation flowshop scheduling problems. J. Multidisc. Eng. Sci. Technol. (JMEST) 2(2), 148–152 (2015) 16. Emin Baysal, M., Sarucan, A., Büyüközkan, K., Engin, O.: Distributed fuzzy permutation flow shop scheduling problem: a bee colony algorithm. In: Kahraman, C., Cevik Onar, S., Oztaysi, B., Sari, I.U., Cebi, S., Tolga, A.C. (eds.) INFUS 2020. AISC, vol. 1197, pp. 1440–1446. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-51156-2_167 17. Baysal, M.E., Sarucan, A., Büyüközkan, K., Engin, O.: Artificial bee colony algorithm for solving multi-objective distributed fuzzy permutation flow shop problem. J. Intell. Fuzzy Syst. 42(1), 439–449 (2022)

Fuzzy Based Weighted, Arithmetic Optimization Algorithm (AOA) for Cash Management Optimization on Automatic Teller Machines (ATM) Ali Tunç1(B) and Sakir Ta¸sdemir2 1 Kuveyt Türk Participation Bank Konya R&D Center, Konya, Turkey

[email protected] 2 Computer Engineering of Technology Faculty, Selcuk University, Konya, Turkey

Abstract. ATM cash management is a set of transactions to optimize the amount of money that should be kept on ATM devices. ATM Cash Management Optimization studies are the studies carried out to keep the most appropriate amount of cash on the ATM by the types and models of ATMs in the banking system, following each time zone. In this study, ATM cash management will be handled as an optimization problem, and the decision variable values that will minimize the treasury and operation costs will be calculated. The main purpose of the study is to estimate the most appropriate amount of money that should be in ATM devices daily and to recommend the amount of cash that should be in the ATM to the system owners. In this study, the most ideal result was tried to be found by using metaheuristic multi objective optimization algorithms used in the literature. First of all, the decision variables and features of ATM data were determined by a detailed study. The optimization algorithm was decided to produce results with a new approach for the determined data areas. The arithmetic Optimization Algorithm (AOA) algorithm, one of the newly proposed metaheuristic algorithms, was chosen as the optimization algorithm. The fuzzy logic algorithm was used to find the weighting coefficients of the values used as input parameters for the AOA algorithm. By using the fuzzy logic algorithm, the effect values of the features on the result were weighted, and together with the obtained weighting information, it was proposed as research that the most appropriate cash amount value should be used in the AOA algorithm. In this way, it is aimed to present a successful solution by exhibiting a hybrid approach. The results obtained were compared with the values in the system and the success rates were tried to be revealed. Keywords: Fuzzy logic · AOA · Arithmetic Optimization Algorithm · Cash Management · Optimization · ATM

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 287–294, 2022. https://doi.org/10.1007/978-3-031-09173-5_36

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1 Introduction ATM is the abbreviation of Automatic Teller Machines in English, although it is translated as Turkish same name, they are the tools we call banking operational transaction devices. While it was used only for depositing and withdrawing money to your account in the early days, today it has turned into a technology where you can perform almost all the transactions you can do at the branch. With the increase in ATM usage, the need for the management and optimization of the cash amount on the ATM has increased. Banks are heading towards the use of artificial intelligence (AI) to meet customer demands and better manage ATM processes. ATM devices are technological machines that recognize your account with a unique identification number and provide 24/7 service. The main purpose of the use of ATMs is to provide 24/7 cash withdrawal and deposit services to customers to provide uninterrupted banking services. These cash operations, which constitute the basic banking service, also constitute the majority of the transaction load at the bank’s box office. For these reasons, a well-planned and managed ATM location and cash management model can be considered as a suitable banking instrument for cost savings and revenue generation. The use of Automatic Cash Machines (ATMs) has become increasingly popular worldwide due to the widespread adoption of electronic financial transactions and better access to financial services in many countries. As the ATM network intensifies as users access them at a higher rate, existing financial institutions have to use optimal policies of cash management and cash replenishment to manage large numbers of ATMs [1]. This will provide benefits to the bank both in terms of customer satisfaction and financial management, as the most appropriate amount of monetary value will be provided on the ATM with a correctly designed strategy. ATM Cash Optimization Model is a model study that is planned to always keep the optimum amount of denominations and money according to the denomination type for each ATM in the banks. The main purpose of our study is to try to optimize the amount of money that should be date-based in the ATM device by Using Fuzzy AHP and a new heuristic algorithm. In this way, an original approach was tried to be exhibited by using two different algorithms hybrid. With the study, the amount of cash that should be on the ATM is the process of estimating by analyzing the historical data with an intuitive algorithm. In this context, the parameters affecting the cash flow are weighted with the help of the Fuzzy AHP method, and the areas that affect the result are revealed. These weighted values are optimized with the help of a new heuristic algorithm, the Arithmetic Optimization Algorithm (AOA), to estimate the most appropriate cash value. Success rates were calculated by comparing the success of the study and the results of the study with the data in the existing system. Within the scope of the paper, information about ATM Cash Management was given, and brief information about the algorithms used in our study, Fuzzy Logic, Fuzzy-AHP, and AOA, was presented. The details of the study were explained and the results obtained were shared and presented for discussion. After this study, information is given about the studies planned to be done in the future by using different artificial intelligence algorithms for ATM cash optimization.

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2 ATM Cash Management “ATM Cash Management and Optimization Model Study” is a model study planned to keep the most appropriate amount of cash on an ATM basis, by the types and models of ATMs in the banking system. ATM Cash Management System is a set of tools that helps organizations manage cash. It is an automated system that optimizes the amount of cash required by knowing customer behavior. It can also be used to detect customer behavior, temporal trends, patterns and predict the approaches required for this data. The process is the process of monitoring the amount and usage of cash available at ATMs and strategically redistributing it for maximum efficiency. Since ATM devices can be thought of as bank branches, the amount of cash that should be on the devices is very important for banks. ATM cash optimization is a process where ATMs are managed to ensure they are always stocked with the right amount of cash. The process includes managing the cash at the ATM and managing the money supply. ATM cash management is important for financial items and management, especially for banks that have a large number of ATM devices. As data fields in the ATM Cash Optimization Model study; Data such as ATM Data, ATM Transactions, ATM Interruptions duration, and reasons are used. There are different models and varieties of ATM devices used by banks. Since the system and structure of each are different, their operating performances and fault diversity are also different. Banks are looking for ways to optimize their ATM networks with the help of artificial intelligence (AI), which will monitor and analyze the daily tasks of monitoring ATMs, optimally distributing cash, and ensuring that all ATMs operate at optimum performance levels.

3 Literature View There are many studies in this area. Ekinci et al. [1] investigated the rules of loading the least amount of money into ATMs with their study. They proposed a model by trying to optimize daily/weekly cash movements by grouping them into clusters of locations near ATMs. Bilir and Dö¸seken [2] With their study on data from a medium-sized bank in Turkey, they tried to ensure that the correct amount of cash is kept in the right location at branches and ATMs and to minimize the excess cash in ATMs without reducing the level of customer satisfaction. In their study using machine learning methods, they proposed a transfer schedule considering many parameters according to the characteristics of the ATM. Batı and Gözüpek [3] conducted a study on the joint optimization of cash management and routing in ATMs with an integer linear program. Simutis et al. [4] have proposed a model that predicts the amount of demand to be loaded by estimating the amount of cash to be withdrawn on ATMs daily with the ANN algorithm. Goyal et al. [5] tried to put forward a mathematical model based on reliability and precision over ATM. Ágoston et al. [6] conducted a cash supply optimization study for ATM cash transport vehicles using the Pareto improvement method and focused on cost reduction. Rajwani et al. [7] presented a model by making daily estimations of the absence of cash or excess cash in ATMs with the regression analysis method and time series LSTM model on the 2.5-year historical transaction records of distributed ATMs in the Karachi region of Pakistan. Gökçay et al. [8] tried to estimate the amount of money withdrawal at ATMs using different machine learning methods.

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4 Method Two basic methods were used in this study. These methods are fuzzy logic [9], FuzzyAHP [10], and Arithmetic Optimization Algorithm (AOA) [11] methods defined as the heuristic algorithm. 4.1 Fuzzy Logic Fuzzy logic is a logic structure created in 1961 by an article by Lutfü Aliasker Zade. In classification studies according to the classical approach, an entity is either a member of a set or is not. When this concept is expressed mathematically, it takes the value “1” when the entity is an element of the creative, and the value “0” when the element is not an element of the set. Fuzzy logic is a more extended representation of the classical set representation. In a fuzzy entity set, each entity has a membership rating. Assets can have any value in the membership degree range (0, 1). Unlike traditional tools, the degree of membership of elements in twisted sets can vary infinitely in between [0, 1]. There are many studies in the field of fuzzy logic in the literature. L. Szilagyi and et al. [12] present a new algorithm for fuzzy segmentation of MR brain images for the medical image processing area. Jaspreet Kaur and Preeti Gupta [13] studied Fuzzy logicbased Adaptive Noise filters for real-time image processing applications. Tunc et al. [14] studied age and gender estimation using fuzzy logic. 4.2 Fuzzy AHP The fuzzy-AHP method is one of the most used methods for criterion weighting in studies with fuzzy logic [10]. It is a decision-making method proposed by Thomas Saaty in 1977. It is a mathematical model that takes into account priorities, produces results by considering quantitative and qualitative values, is easy to apply, and is effective in improving decision-making processes [15]. When the studies on fuzzy-AHP were examined Yildiz et al. [16], they used the fuzzy-AHP algorithm to solve the ATM location problem. Syahputra et al. [17] studied ATM location selection and cash management. AlShammari et al. [18] tried to model the bank choices of customers in Bahrain by using the fuzzy-AHP algorithm in their study. 4.3 Arithmetic Optimization Algorithm (AOA) The Arithmetic Optimization Algorithm (AOA) is a population-based heuristic algorithm developed by Abualigah et al. [11] consisting of two main stages based on exploration and exploitation. It operates using four arithmetic operations in mathematics. It tries to produce results with two basic approaches, exploration and exploitation in the search space. It performs local search operations, called exploitation, by using addition and subtraction operators. It provides the global search approach, called discovery, by using the multiplication and division operators. When the studies using this algorithm were examined, Emine Ba¸s [19] proposed a hybrid solution by combining the AOA algorithm with the Tree Seed algorithm for the solution of limited optimization problems. Cihan

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[20] used the AOA algorithm to optimize the convergence rate defined on a multi-agent network. Yıldırım et al. [21] studied the path planning of robots in a grid plane and compared the results obtained in AOA and other algorithms.

5 Study and Results and Discussion Within the scope of the study, a system that estimates the amount of cash that should be on the date-based ATM device and optimizes by obtaining the calendar information and the amount of money withdrawn on the data of an ATM device has been designed. The criticality levels of that date were created by taking into account the date of the transaction. The amount of cash required is estimated according to information such as national day, religious day, a day before a holiday, weekend and mid-week. To weigh these criteria given here, various articles were examined based on the weight determination methods in the literature. Since the Fuzzy AHP method was specified as one of the most preferred methods in criterion weighting, the Fuzzy AHP method was used in the weighting of the criteria in our study. The five main evaluation criteria constituting the calendar feature determined within the scope of the study were made by using linguistic variables in pairwise comparisons. The weights between the logical evaluations were determined by the fuzzy AHP method by five different experts. To combine the evaluations of different evaluators, the formulas in Buckley’s [22] study were combined using the geometric mean method. In the process stepping phase, the definitions and methods used in Ozkan’s [23] study were used. The evaluation and weighting results of the variables are given in Table 1. When the results are examined, the highest weight value is the “pre-holiday days” variable, while the lowest weight value is the “mid-week” variable. The weight values obtained here were used in the calculation of the results in the AOA algorithm according to the weights. Table 1. Weights of evaluation criteria. Criteria

Weights

National days

20.2%

Religious days

21.6%

Pre-holiday days

22.2%

Weekend

19.2%

Mid-week

16.8%

In our study, it was tried to determine the most appropriate cash amount value by analyzing the data of an ATM device by using the AOA algorithm. Considering the data of an ATM device between the years 2015–2021, it was tried to reach the optimum value of the cash amount that should belong to that device. First of all, the calendar data of the ATM was created according to the date values that reveal the importance of depositing and withdrawing money. The daily total values were calculated based on

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the date information for all transactions specific to the ATM device. According to the dating information, the data were grouped in five categories by taking the information on a national day, religious day, a day before the holiday, weekend, and week on a daily basis. Since the amount information of daily transactions for the years used in the study are values for different years, they show value at different intervals due to inflation and transaction volumes. It seems that the transaction amounts in 2015 (3,500–68,000 range) and the transaction amounts in 2021 (6,000–140,000 range) have different minmax range values. In order to represent these amounts at the same level, the values for each year were normalized according to the min-max amount data of that year and reduced to the values in the [0–1] range. This normalized value is included in the data set as a new field. In this way, the amount of data normalized according to the annual value range has been made ready as a parameter for the AOA to be used in the study. The AOA algorithm takes the data as the working logic and ensures that the most appropriate data value is found here. The data belonging to the five categories we created were ordered according to the normalized amount information, and the minimum value of 30 amount information and the maximum value of 30 amount information were included in the calculations as the parameters of the AOA algorithm. Thanks to AOA, based on these minimum and maximum values, it was tried to find the optimum result for that group. The results were found by applying 100 iterations for each group data set by the AOA, and the most appropriate optimum value for that group was tried to be determined by taking the average of the iteration results obtained. The data belonging to the five categories we created were ordered according to the normalized amount information, and the minimum value of 30 amount information and the maximum value of 30 amount information were included in the calculations as the parameters of the AOA algorithm. Thanks to AOA, based on these minimum and maximum values, it was tried to find the optimum result for that group. The results were found by applying 100 iterations for each group data set by the AOA, and the most appropriate optimum value for that group was tried to be determined by taking the average of the iteration results obtained. Since this value is a normalized value, the actual values are calculated by considering the min-max values of the last year’s amount information. The normalization values and result values found according to the grouped data are shown in Table 2. Table 2. Optimum values calculated according to calendar criteria with AOA algorithm. Criteria

Normalization value

Amount value

National days

0.8083

114,212

Religious days

0.8655

121,907

Pre-holiday days

0.8239

116,311

Weekend

0.8742

123,077

Mid-week

0.7512

106,531

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By analyzing the data on the Data Set (2015–2021 ATM cash loading data), it was tried to calculate the cash amount that should be on the ATM the next day according to the results obtained with AOA and weighted values with AHP. The result is shown in Table 3. In the continuation of our study, the results obtained will be evaluated with the F1-Score method, and the success and success rates of the study will be shared. Table 3. Optimum values found with AOA algorithm and AHP Criteria

AHP weight

AOA amount value

National days

20.2%

114,212

Amount 23,070

Religious days

21.6%

121,907

26,331

Pre-holiday days

22.2%

116,311

25,821

Weekend

19.2%

123,077

23,630

Mid-week

16.8%

106,531

17,897 Sum = 116,749

6 Conclusion and Future Works The rapid development and spread of technology have made it more important for banks to provide quality service and continuity through different distribution channels. Especially with the widespread use of card systems and the increase in the number of ATM users, new solutions and strategies have emerged for banks in terms of cash management and business continuity. High financial gains can be achieved by making analyzes on cash optimization with algorithms that have a high success rate, produce fast results, and show high performance. With this study we have done, a feasible model has been put forward by using the Fuzzy-AHP and AOA algorithms with a hybrid approach. With this model, the amount of cash that should be on ATM devices is estimated and the success rates of the optimization study in ATM cash management are shown. Future studies will aim to try new hybrid algorithms by using different algorithms such as genetic algorithm (GA), LSTM together with AOA, and to solve the problem with the algorithm that provides the most optimal solution by comparing the success rates obtained. The success rates obtained with the F1-Score method will be shown.

References 1. Ekinci, Y., Lu, J.-C., Duman, E.: Optimization of ATM cash replenishment with group-demand forecasts. Expert Syst. Appl. 42(7), 3480–3490 (2015) 2. Bilir, C., Dö¸seyen, A.: Optimization of ATM and branch cash operations using an integrated cash requirement forecasting and cash optimization model. Bus. Manage. Stud. Int. J. 6(1), 237–255 (2018)

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3. Batı, S, ¸ Gözüpek, D.: Joint optimization of cash management and routing for new-generation automated teller machine networks. IEEE Trans. Syst. Man Cybern. Syst. 49(12), 2724–2738 (2017) 4. Simutis, R., Dilijonas, D., Bastina, L., Friman, J., Drobinov, P.: Optimization of cash management for ATM network. Inf. Technol. Control 36, 1 (2007) 5. Goyal, N., Sharma, P., Ram, M.: Automated teller machine performance evaluation through cash transactions. Math. Eng. Sci. Aerospace (MESA) 6, 2 (2015) 6. Ágoston, K.C., Benedek, G., Gilányi, Z.: Pareto improvement and joint cash management optimisation for banks and cash-in-transit firms. Eur. J. Oper. Res. 254(3), 1074–1082 (2016) 7. Rajwani, A., Syed, T., Khan, B., Behlim, S.: Regression analysis for ATM cash flow prediction. In: 2017 International Conference on Frontiers of Information Technology (FIT), pp. 212–217 (2017) 8. Gökçay, D.E., Co¸skun, F., Yanıko˘glu, B., Turan, A., Ertem, S.: ATM cash stock prediction using different machine learning approaches (2020) 9. Zadeh, L.A.: Fuzzy sets. Inf. Control. 8(3), 338–353 (1965) 10. Wind, Y., Saaty, T.L.: Marketing applications of the analytic hierarchy process. Manage. Sci. 26(7), 641–658 (1980) 11. Abualigah, L., Diabat, A., Mirjalili, S., Abd Elaziz, M., Gandomi, A.H.: The arithmetic optimization algorithm. Comput. Methods Appl. Mech. Eng. 376, 113609 (2021) 12. Szilagyi, L., Benyo, Z., Szilagyi, S.M., Adam, H.S.: MR brain image segmentation using an enhanced fuzzy C-means algorithm. In: Proceedings of the 25th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE Cat. No. 03CH37439). IEEE Xplore, 5 April 2004 13. Jaspreet, K., Preeti, G.: Fuzzy logic based adaptive noise filter for real time image, processing applications. IJCSI Int. J. Comput. Sci. Issues 9(4), 1–6 (2012) 14. Tunc, A., Tasdemir, S., Koklu, M., Cinar, A.C.: Age group and gender classification using convolutional neural networks with a fuzzy logic-based filter method for noise reduction. J. Intell. Fuzzy Syst. 42, 491–501 (2021) 15. Da˘gdeviren, M., Akay, D., Kurt, M.: ˙I¸s De˘gerlendirme Sürecinde Analitik Hiyerar¸si Prosesi Ve Uygulamasi. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi 19(2), 131–138 (2004) 16. Yildiz, A., Ayyildiz, E., Taskin Gumus, A., Ozkan, C.: A modified balanced scorecard based hybrid pythagorean fuzzy AHP-topsis methodology for ATM site selection problem. Int. J. Inf. Technol. Decis. Mak. 19(02), 365–384 (2020) 17. Syahputra, A., Puspita, K., Maulida, R., Elnovreny, J., Fahrozi, W.: Analytic hierarchy process (AHP) modelling for ATM machine placement. In: 2020 8th International Conference on Cyber and IT Service Management (CITSM), pp. 1–4. IEEE, October 2020 18. Al-Shammari, M., Mili, M.: A fuzzy analytic hierarchy process model for customers’ bank selection decision in the Kingdom of Bahrain. Oper. Res. Int. J. 21(3), 1429–1446 (2019). https://doi.org/10.1007/s12351-019-00496-y 19. Ba¸s, E.: Hybrid the arithmetic optimization algorithm for constrained optimization problems. Konya Mühendislik Bilimleri Dergisi (2021) 20. Cihan, O.: Çok Etmenli Sistemlerde Bir Da˘gıtık Denklem Çözüm Algoritmasının Yakınsama Hızı En ˙Iyilemesi. Avrupa Bilim ve Teknoloji Dergisi 26, 262–269 (2021) 21. Yildirim, M.Y., Akay, R.: Izgara Bazlı Yol Planlama için Matematik Tabanlı Metasezgisellerin Kar¸sıla¸stırılması. Avrupa Bilim ve Teknoloji Dergisi 32, 521–530 (2021) 22. Buckley, J.J.: Fuzzy hierarchical analysis. Fuzzy Sets Syst. 17(3), 233–247 (1985) 23. Uluta¸s, A., Özkan, A.M., Ta˘graf, H.: Bulanik analitik hiyerar¸si süreci ve bulanik gri ili¸skisel analizi yöntemleri kullanilarak personel seçimi yapilmasi. Electron. J. Soc. Sci. 17(65), 223– 232 (2018)

Site Selection of Grid-Connected Photovoltaic Power Plants with Fuzzy Hybrid Method Veysel Çoban1(B)

and Sezi Çevik Onar2

1 Bilecik Seyh Edebali University, Gulumbe, Bilecik, Turkey

[email protected] 2 Istanbul Technical University, Besiktas, Istanbul, Turkey

Abstract. Fossil-based traditional energy sources have significant disadvantages based on environmental, economic and social problems. These disadvantages enable societies to turn to renewable energy sources (solar, wind, hydro, tidal, biomass, geothermal) against fossil energy sources. Technological developments and increasing economic benefits allow solar energy systems to become widespread and stand out. Making the right site selection decision is of great importance in the installation of grid-connected photovoltaic power plants, which require high initial costs. In the study, comparison and evaluation of alternative sites are made by fuzzy AHP and TOPSIS methods according to the main and sub-criteria defined by the literature review. The order of importance according to the criteria weights ensures the determination of the priority criteria that should be considered in the selection of the site. Sensitivity analyzes provide information on the effects of criteria in site selection evaluation. Keywords: Site selection · Photovoltaic · Multi-criteria decision making · Fuzzy AHP · Fuzzy TOPSIS

1 Introduction Increasing energy demand is met by using renewable energy methods besides traditional energy sources. Renewable energy production methods emerge as an important alternative to traditional energy production methods with efficiency and cost advantages [1]. Renewable energies are accepted as clean and safe energy production methods against traditional energy sources, which harm the environment and societies with global warming and climate changes [2]. Environmentally and economically sensitive nations develop policies for the adoption and dissemination of renewable energy systems. An increase in efficiency with technological development and cost reduction with economies of scale provide a rapid increase in the demand for solar energy production methods. Photovoltaic (PV) energy systems are the most important solar energy technology with their features of direct electricity generation and providing the produced energy to use. High initial investment and installation costs require the correct positioning of PV solar energy systems [3]. Positioning the PV solar energy system in the most suitable place shortens the return on investment and prolongs the period of positive © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 295–302, 2022. https://doi.org/10.1007/978-3-031-09173-5_37

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environmental and social impact. In this study, the factors involved in the selection of the most suitable location for PV solar energy systems are examined and the effect values of the factors are observed with a sample application. Fuzzy decision making methods are used to reduce the effect of uncertainty in measurement and subjective values and to reach more valid results [4]. The AHP decisionmaking method, which provides an easy and fast pairwise comparison of factors, and the TOPSIS decision-making method, which allows site selections to be selected for the most appropriate location, are used in the decision-making process [5, 6]. The most influential factors in solar field selection are identified and the suitability and usability of the fuzzy decision-making tools are proven at the end of this study. The originality of the study consists of the use of STEEP criteria in Fuzzy AHP and TOPSIS hybrid methods and the selection of PV site with this method. The following sections of the work are organized as follows. Section 2 gives information about the studies on solar field selection in the literature. Section 3 discusses the factors referenced in the PV solar site selection study. In Sect. 4, fuzzy AHP and TOPSIS tools used in the decision making process are mentioned. In Sect. 5, solar energy site selection study is carried out with a sample application according to the factors discussed. Section 6 evaluates the results from the case study and makes recommendations for future work.

2 Literature Review The placement of grid-connected mega-solar PV energy systems on a suitable site is an important multi-criteria decision making problem. There are studies in the literature that contribute to the decision-making processes by addressing the environmental, economic, social, technical and political factors in the development of PV systems [6]. Studies highlight the main obstacles to the development of PV systems as cost, dependence on traditional energies, political uncertainties, and uncertainties in societal and environmental risks [3, 7]. Different multi-criteria decision making tools were used in site selection studies. TOPSIS (Technique for Order Preference by Similarity to Ideal Solution), ELECTRE (ELimination Et Choice Translating REality), ANN (Artificial Neural Network), SAW (Simple Additive Weighting), VIKOR (VIseKriterijumska Optimizacija I Kompromisno Resenje) and WLC (Weighted Linear Combination) decision making tools, especially AHP (Analytical Hierarchical Process), were used in the decision making process independently and hybridly [5, 8]. The uncertainties in the factors and the subjective evaluations of the decision makers have led to the use of decision making tools integrated with fuzzy logic. The common factors used in PV site selection are revealed by examining the main and sub-criteria obtained from different studies in the literature [9, 10]. AHP and TOPSIS methods based on fuzzy logic are applied to more accurately incorporate uncertainties in measurements and evaluations into the decision-making process. Thus, the effects of the factors in the decision-making process and the validity of the methods are revealed.

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3 Factors in PV Site Selection In this study, STEEP (Social, Technical, Economical, Environmental, Political) titles are considered as the main criteria. The sub-criteria under these main criteria are explained to the decision makers and the decision makers are expected to evaluate in this perspective. The main criteria and sub-criteria are defined as follows [4, 6, 9, 11]: • Social: Social factors reflect the views and behavior of local residents about the project. The shape of the environmental and economic perception created by the project determines the social acceptance of the project. • Technical: The suitability of the structural, environmental and climatic conditions that maximize the electricity value that can be obtained from PV systems is taken into account. The number of sunny days, radiation value, temperature, climatic conditions and the presence of competent personnel are important evaluation sub-criteria. • Economical: Initial investment and installation costs, which are the most important disadvantages of PV energy systems, are expected to be minimized. Infrastructure requirements, proximity to networks and proximity to transport networks trigger potential costs. • Environmental: The most important expectation from renewable energy methods, especially solar energy, is the creation of environmentally friendly structures. Evaluation can be made in the sub-criteria of visual impact, wildlife and migration routes, noise and environmentally harmful gas emissions encountered during the installation and operation phase. • Political: PV site selection and operation is expected to comply with local, national and international rules and regulations. Incentive programs and legal restrictions are the most important political instruments in the decision-making process. Decision makers evaluate alternative PV sites according to STEEP main criteria based on their knowledge and experience. First of all, with the fuzzy AHP study, the decision makers are expected to make a prioritization study between the criteria and the priority values of the criteria are calculated. The criterion weight values obtained at this stage are used in the grading and ranking of the alternatives in the fuzzy TOPSIS method.

4 Methods 4.1 Fuzzy Set Theory Fuzzy set theory [12] is based on the definition of objects (x) called fuzzy sets (˜a) with a certain degree of membership (˜a(x)) in the [0, 1] interval. Values containing uncertainty and hesitancy are expressed with fuzzy numbers so that the evaluations are reflected more easily and easily. Triangular fuzzy numbers defined as a˜ = (al , am , ar ) are the most common fuzzy numbers used to express evaluations [13]. The linguistic evaluations of the decision makers are expressed with triangular fuzzy numbers by applying a scale between 1–9. Linguistic terms for criteria are defined as Very Low (VL), Low (L), Medium (M), High (H), Very High (VH) and linguistic terms for alternatives are represented as Very Poor (VP), Poor (P), Fair (F), Good (G), Very Good (VG).

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4.2 Fuzzy AHP Decision makers are expected to make pairwise evaluations in pairwise comparison matrices with logical consistency. The Consistency Ratio (CR) defined by Saaty [14] is used to measure the inconsistencies in the evaluations of the decision makers. Pairwise ˜ reflect preference values between criteria [15]. In case comparison matrices (PCMs,P) of p˜ ij = p˜1ji , (i, j = 1, 2, . . . , n), P˜ is reciprocal of PCM. The Consistency Index (CIn ) of the PCM is defined as: CIn =

λmak − n n−1

(1)

where λmak represents the largest eigenvalue of PCM and n is the dimension of PCM. If the PCM is strictly mutually reversible, the consistency index is calculated as CIn = 0 to represent absolute consistency. CR =

λmak − n CIn = RIn RI (n − 1)

(2)

where λmak is the largest eigenvalue of the PCM , RIn is the random consistency index, and n is the size of the PCM . RIn defines the expected CIn values of n-dimensional reversible PCMs randomly derived on the Saaty scale [15, 16]. CR reflects the relationship between the calculated consistency ratio, CIn , and the expected consistency ratio, RIn . The threshold value for CR is defined as 0.1, and if CR ≥ 0.1 the assessment is considered inconsistent and reassessment is recommended. The classical matrix transforma n tion of fuzzy PCM is performed as PP˜ = pij i,j=1 and the consistency ratio is calculated   using the Saaty CR formula. The crisp transformation of TFN, p˜ ij = pijl , pijm , pijr can be calculated by the weighted average method [6, 13]: pij =

pijl + 4pijm + pijr 6

(3)

The FAHP method provides the opportunity to make pairwise comparisons and evaluations among criteria. In addition, the priority vector obtained during the consistency index calculation process also reflects the importance levels of the criteria. 4.3 Fuzzy TOPSIS Alternative PV sites are evaluated based on location criteria using fuzzy TOPSIS. TOPSIS method, which aims to determine the most suitable solution according to the distance between positive and negative ideal solutions, was developed by Hwang and Yoon [17] and expanded by Chen [18] with fuzzy logic theory. The main application steps are as follows [5, 6]:   Step 1: Alternatives, A = A1 , A2 , ..., Aj are evaluated according to criteria, C = {C1 , C2 , ..., Cm }. The weights of criteria are defined as wi (i = 1, 2, ..., m). Each decision maker’s, Dk (k = 1, 2, ..., K) evaluation of each alternative Aj (j = 1, 2, ..., n) according to the criteria Ci (i = 1, 2, ..., m) is shown as R˜ k = x˜ ijk .

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  for alternatives Step 2: Aggregated fuzzy ratings,R˜ = al , am, ar are calculated  l m r whose fuzzy ratings are defined with TFNs, x˜ ijk = aijk ; aijk , aijk .

K    am l m a = min ak , a = k=1 k , ar = max akr (k = 1, 2, . . . , K) (4) k k K   The aggregated fuzzy ratings, x˜ ij = aijl ; aijm , aijr of the alternatives according to the fuzzy rating, x˜ ijk and the weights of the decision makers, w˜ ijk are expressed as follows:

K m   k=1 aijk l l m r aij = min aijk , aij = , aijr = max aijk (i = 1, 2, . . . , m; j = 1, 2, . . . , n) k k K (5) l

Step 3: The fuzzy decision matrix is calculated for the alternatives, X˜ = x˜ ij and ˜ = w˜ j . criteria, W Step 4: Fuzzy decision matrices normalized to reduce decision data to common 

l are  aij aijm aijr scale as R˜ = r˜ij mn . r˜ij = ar+ , ar+ , ar+ , ajr+ = max aijr (for benefit criteria) and i j j j

l− l− l−  aj aj aj r˜ij = ar , am , l , ajl− = min aijl (for cost criteria). aij ij ij i   = v˜ ij Step 5: The weighted normalized decision matrix, V = r˜ij (·)w˜ j is obtained mn ˜ values with the normalized fuzzy decision matrix, by multiplying the criterion weight, W ˜ R. Step 6: The fuzzy ideal solution (FPIS, I + ) and the fuzzy negative ideal solution (FNIS, I − ) are defined for alternatives as follow:         I + = v˜ 1+ , v˜ 2+ , . . . , v˜ n+ , v˜ j+ = max vij3 and I − = v˜ 1− , v˜ 2− , . . . , v˜ n− , v˜ j− = min vij1 i

i

(6) Step 7: The distances (di+ , di− ) of the weighted normalized alternatives, v˜ ij to FPIS and FNIS are calculated.   2 2      n  n + −  J =1 v˜ ij − v˜ j  J =1 v˜ ij − v˜ j di+ = and di− = , i = 1, 2, . . . , m (7) 3 3 Step 8: The closeness coefficient, CCi is calculated for each alternative, and the alternatives are ranked from largest to smallest, reflecting the order of preference as CCi =

di− . The highest CCI value representing the closest to FPIS and furthest from di+ +di−

FNIS indicates the most suitable alternative PV site.

5 Numerical Application Suppose a renewable energy company plans to install a grid-connected mega-solar PV solar power system. Three expert decision makers, Ek are consulted to evaluate three

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alternative sites, Aj . STEEP (Social (C1), Technical (C2), Economical (C3), Environmental (C4), and Political (C5)) criteria are used in the evaluation of grid-connected PV energy sites. Since the criteria are considered with a positive impact perspective, all criteria are included in the benefit category, that is, an increase in the evaluation scale value indicates the desire to prefer the alternative. The criteria and alternative evaluations made by the experts using the linguistic evaluation scales. The priority weights of the criteria are calculated as 0.130, 0.144, 0.157, 0.082 and 0.488, respectively. Pairwise comparison matrices created for the criteria are obtained with the consensus of the experts. In PCM, the criteria are compared by experts and the superiority of the criteria is defined linguistically. According to linguistic evaluations with proven consistency, the “political” criterion is observed as the most important and dominant decision criterion. The “environmental” criterion stands out as the least important criterion, although there are no significant differences between the other criteria. The linguistic assessments of the experts are converted into TFNs and total fuzzy weights for the alternatives are calculated using Step 2. TFNs are normalized at the [0, 1] level using the Steps 3 and 4 equations and a normalized fuzzy decision matrix for alternative sites is obtained. The criterion weights obtained from the fuzzy AHP method are associated with the fuzzy normalized decision matrix to obtain the fuzzy weighted normalized decision matrix (as mentioned in the fifth step of Fuzzy TOPSIS). Fuzzy positive ideal solutions (FPIS, + + + = (0.13, 0.13, 0.13), IC2 = (0.14, 0.14, 0.14), IC3 = (0.16, 0.16, 0.16), I + ) as IC1 + + IC4 = (0.08, 0.08, 0.08), IC5 = (0.49, 0.49, 0.49) and fuzzy negative ideal solu− − − = (0.01, 0.01, 0.01), IC2 = (0.02, 0.02, 0.02), IC3 = tions (FNIS, I − ) as IC1 − − (0.02, 0.02, 0.02), IC4 = (0.01, 0.01, 0.01), IC5 = (0.05, 0.05, 0.05) for the alternatives are calculated using Steps 5 and 6. The distance values of each alternative according to the positive and negative ideal results are calculated according to Step 7 and the closeness coefficient of each alternative is calculated according to Step 8 as dA−1 = 0.58, dA−2 = 0.61, dA−3 = 0.61 and dA+1 = 0.57, dA+2 = 0.45, dA+3 = 0.54. Alternatives are ranked according to their closeness coefficients (CC1 = 0.51, CC2 = 0.58, CC3 = 0.53) and the A2 alternative with the highest CCi value is selected as the most suitable alternative for the grid connected PV field. Sensitivity Analysis Sensitivity analyzes are performed in different scenarios to determine the impact level of the criteria determined in the grid-connected PV site selection decision-making process. In the scenarios, the weight values of the STEEP criteria in the evaluation process of the alternatives are changed and the changes in the closeness coefficients and ranking values of the alternatives are observed. In addition to the weight values (w0 ) obtained from the application study, four different weighting scenarios are created for the criteria. In the first scenario, it is assumed that all criteria are of equal weight (w1 ). In the second scenario, the social criterion weight is dominated and the other criterion weights are kept constant (w2 ). In the third scenario, the weight of the environmental criteria is dominated and the weights of the other criteria are evenly distributed (w3 ). In the fourth scenario, in the absence of a political criterion, the other criteria are assumed to be of equal weight (w4 ).

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In the first scenario, if the criteria are equally weighted, the most suitable alternative site changes to A3, although there is no significant difference between the alternatives. In the second scenario, the social criterion makes significant changes in the alternative site ranking and A1 remarks as an alternative site. The environmental criterion highlighted in the third scenario causes the A2 alternative to be not preferred, which has poor environmental sensitivity (with VP linguistic evaluations). In the fourth scenario, which defines the absence of the political criterion, although there is no dominant alternative, the most suitable alternative changes.

6 Conclusion This study deals with the selection of the most suitable site for the installation of grid-tied PV energy systems. STEEP (Social, Technical, Economical, Environmental, Political) criteria are considered as evaluation criteria and the sub-criteria are separately explained to the decision maker during the decision-making process. Linguistic expressions and triangular fuzzy numbers corresponding to linguistic expressions are used to evaluate criteria and alternatives. The criteria are evaluated in pairwise comparison and the priority vector is determined for the criterion within the fuzzy AHP method. The priority vector indicates that the political criterion is the dominant criterion (0.488) and that the other criteria have approximate weights. Alternative PV sites are linguistically evaluated by three decision makers, taking into account the STEEP criteria, and linguistic assessments are converted into TFNs. The distances of the alternative sites to the ideal solutions and the closeness coefficients are calculated with the fuzzy TOPSIS method. Different criteria weights are determined over four different scenarios and their effects on alternative site selection are observed within sensitivity analysis. The study aims to contribute to the most suitable site selection process for the installation of high initial cost PV power plants. Developing the scope of the main and sub-criteria and selecting the most suitable PV site using different fuzzy decision making methods are planned for future studies.

References 1. Kahraman, C., Otay, I.: Solar PV power plant location selection using a Z-fuzzy number based AHP. Int. J. Anal. Hierarchy Process 10(3), 409–430 (2018) 2. Green, M.A.: How did solar cells get so cheap? Joule 3(3), 631–633 (2019) 3. Vasconcelos Sampaio, P.G., et al.: Prospecting technologies for photovoltaic solar energy: overview of its technical-commercial viability. Int. J. Energy Res. 44(2), 651–668 (2020) 4. Al Garni, H.Z., Awasthi, A.: Solar PV power plants site selection: a review. In: Advances in Renewable Energies and Power Technologies, pp. 57–75 (2018) 5. Sadat, S.A., Fini, M.V., Hashemi-Dezaki, H., Nazififard, M.: Barrier analysis of solar PV energy development in the context of Iran using fuzzy AHP-TOPSIS method. Sustain. Energy Technol. Assessments 47, 101549 (2021) 6. Sindhu, S.V., Nehra, V., Luthra, S.: Investigation of feasibility study of solar farms deployment using hybrid AHP-TOPSIS analysis: case study of India. Renew. Sustain. Energy Rev. 73, 496–511 (2017) 7. Yang, F., Zhao, X.: Policies and economic efficiency of China’s distributed photovoltaic and energy storage industry. Energy 154, 221–230 (2018)

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8. Awasthi, A., Govindan, K., Gold, S.: Multi-tier sustainable global supplier selection using a fuzzy AHP-VIKOR based approach. Int. J. Prod. Econ. 195, 106–117 (2018) 9. Doljak, D., Stanojevi´c, G.: Evaluation of natural conditions for site selection of groundmounted photovoltaic power plants in Serbia. Energy 127, 291–300 (2017) 10. Doorga, J.R., Rughooputh, S.D., Boojhawon, R.: Multi-criteria GIS-based modelling technique for identifying potential solar farm sites: a case study in Mauritius. Renew. Energy 133, 1201–1219 (2019) 11. Choudhary, D., Shankar, R.: An STEEP-fuzzy AHP-TOPSIS framework for evaluation and selection of thermal power plant location: a case study from India. Energy 42(1), 510–521 (2012) 12. Zadeh, L.A.: Information and control. Fuzzy Sets 8(3), 338–353 (1965) 13. Yeh, C.-T.: Existence of interval, triangular, and trapezoidal approximations of fuzzy numbers under a general condition. Fuzzy Sets Syst. 310, 1–13 (2017) 14. Saaty, T.L.: Decision making with the analytic hierarchy process. Int. J. Serv. Sci. 1(1), 83–98 (2008) 15. Aguarón, J., Escobar, M.T., Moreno-Jiménez, J.M., Turón, A.: The triads geometric consistency index in AHP-pairwise comparison matrices. Mathematics 8(6), 926 (2020) 16. Kahraman, C., Onar, S.C., Oztaysi, B.: Fuzzy multicriteria decision-making: a literature review. Int. J. Comput. Intell. Syst. 8(4), 637–666 (2015) 17. Hwang, F., Chen, S.-J., Hwang, C.-L.: Fuzzy Multiple Attribute Decision Making: Methods and Applications. Springer, Cham (1992). https://doi.org/10.1007/978-3-642-46768-4 18. Chen, C.-T.: Extensions of the TOPSIS for group decision-making under fuzzy environment. Fuzzy Sets Syst. 114(1), 1–9 (2000)

Classification of Provinces in Turkey in Terms of Health Indicators with Fuzzy Clustering Analysis Aslı Dolu(B)

and Ümit Kuvvetli

Izmir Bakircay University, Izmir, Turkey [email protected]

Abstract. Health services are critical indicators in determining countries’ sustainable development and socio-economic development levels. Especially in the process of the Covid-19 pandemic, it has been understood how important countries’ health systems are for their economic status. While the countries compare their health indicators, they also try to implement health policies to reduce the development differences. Therefore, determining and classifying the existing social and economic structures of provinces is very important in examining the development status and possible development trends of provinces and informing regional health policies in parallel. This study it is aimed to classify 81 provinces in Turkey with their health indicators using fuzzy clustering analysis. As a result of the study, homogeneous provincial groups with the same characteristics in terms of health indicators will be determined. In light of the results, policy suggestions will be made to eliminate the development differences between clusters in the proposed regional health policies. Keywords: Fuzzy clustering · Health · Health indicators · Statistics · Classifications · Provinces · Equality

1 Introduction The Covid-19 virus, which first appeared in Wuhan, China, in December 2019 and caused a worldwide pandemic, showed the whole world why health and health systems are the most important. Due to the Covid-19 pandemic, all countries in the world have been directly or indirectly affected by the pandemic and have faced many significant losses, especially human life. In addition, the Covid-19 pandemic has shown that countries with a strong health system have suffered minor economic damage, especially human loss. Although countries need to have a strong health system, this health system should be accessible equally and fairly to all citizens living in all provinces of the country. Although the Covid-19 pandemic has once again shown the importance of health and health systems to the whole world, it is a fact that health systems are one of the essential criteria that guide the development level of countries even before the pandemic. Increasing the health status of society is very important for people to be happier and increase their level of well-being. In healthy communities, life expectancy is longer, and © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 303–310, 2022. https://doi.org/10.1007/978-3-031-09173-5_38

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the longer people live, the more productive they contribute to the economy [15]. Ensuring socio-economic development, increasing social welfare, and citizens’ quality of life will only be possible if society is healthy in all aspects. This situation is directly related to people living in different regions and cities with equal access to health services. Moreover, the right of people to access health services and adequate health care has been considered a significant issue by many national and international organizations [14]. Besides, the World Health Organization believes improving health equity, both international and national, is one of the new century [5, 14]. Countries are responsible for creating a quality health service by using the resources allocated to the health sector in the most economical way and distributing it equally and fairly among people living in every country. Still, it is not always possible to say that this can be achieved. The level of health services differs from country to country and even from province to province within the same country. One of the possible sources of this difference is the level of social and economic development. In Turkey, which is considered one of the developing countries, there are many studies in which provinces are ranked in socio-economic terms. The typical result of these studies is that provinces have different socio-economic levels, and there are significant differences between provinces. It will be beneficial to carry out similar studies in terms of health services to manage health services, determine health policies, make comparisons between provinces and follow the effects of changes, identify provinces and areas open to improvement, and eliminate differences between provinces. In this study, the health systems of 81 provinces in Turkey were measured using 14 health indicators, and the provinces were clustered with fuzzy-clustering methods. According to the study results, cities with similar health system levels were determined. It is thought that the results obtained can help the decision-makers in terms of providing the necessary information in the policies to be created to reduce the differences between the cities. The paper’s outline is as follows: we begin with the literature review on this topic. Section 3, we introduce our data sets and our model. We present our results in Sect. 4, and then we conclude.

2 Literature Review In the literature, there are many studies mostly on evaluating and comparing the health status of countries. The literature on the subject examined in Turkey regarding health indicators can be summarized as follows. [11] compared and grouped OECD countries in terms of the performance of their health systems. Countries were classified according to their performance levels in the study in which multiple clustering analysis was used. [3] made a clustering analysis for 81 provinces in Turkey using ten health indicators of 2010. The study’s primary purpose is to determine the provinces in the worst situation in terms of health indicators. As a result; it has been determined that Hakkari, Sırnak, ¸ Sanlıurfa, ¸ Kilis, A˘grı, Kars, Mu¸s and Van are the provinces with the worst health level. [6] performed clustering and multidimensional scaling analysis with 2010 data using seven health indicators for 27 European Union Countries and Turkey. As a result of the

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multidimensional scaling analysis, it was determined that the countries were gathered in three different groups in the two-dimensional spaceplane. As a result of the clustering analysis, they were supposed to be in four clusters. [9] analyzed 31 OECD countries and analyzed the relationship between health care expenditures and gross national product with the help of data for the period 1970–2009. As a result, they determined that the income elasticity of health expenditures differs in the short and long run and that changes in per capita income are effective on health expenditures. [1] examined the level of out-of-pocket health expenditures that would lead to negative results using the Household Budget Surveys conducted from 2003 to 2008 in Turkey. As a result, it has been determined that the health expenditures that are not made because they cannot be met financially cause significant negativities in the health level of the households. [12] made a cluster analysis for 81 provinces in Turkey using 16 health indicators of 2013. He evaluated the results of the level of development and health indicators. In general, it has been concluded that the difference in growth between Turkey’s eastern and western provinces is also reflected in the health variables. [7] used the analytical hierarchy process (AHS) and TOPSIS methods to rank 21 countries in the Eastern Mediterranean region in terms of health indicators. According to the weights determined by the AHP, the infant mortality rate was selected as the most critical factor in evaluating the health performances of countries. In the performance ranking made with the TOPSIS method, Bahrain took first place, and Somalia took last place. This study differs from the studies on the same subject in the literature regarding the methods used. Cluster analysis is a method that is frequently used in the country grouping, as it is in many other issues. However, the distinctions between units or countries may not be evident in real life. Fuzzy logic can give more reliable results as it allows being more cautious and flexible in separating units from each other. For this reason, the fuzzy clustering method was preferred in this study. In addition, the groups that emerged as a result of the cluster analysis only give information about the similarities of the units to each other but do not give an idea about the superiority of the clusters as a whole in terms of related variables. However, fuzzy clustering like this one allows us to make much more helpful information and detailed comments.

3 Data and Methodology 3.1 Data Fourteen variables, which are considered health indicators of provinces in Turkey, were used in the study. The most up-to-date data of the variables were used in the study, while the data of 12 variables belong to the year 2019, while one variable belongs to the years 2017 and 2020. The data were obtained from the Ministry of Health and TURKSTAT; the variables used in the study are summarized in Table 1 [10, 13]. 3.2 Methodology The study applied the fuzzy clustering method to classify Turkey’s provinces in terms of health indicators. Classical clustering methods take a final decision for each unit

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A. Dolu and Ü. Kuvvetli Table 1. Descriptions, sources, and years of the variables

Variable

Description

Source

Year

x1

Number of beds per 10.000 people

Ministry of Health

2019

x2

Number of intensive care beds per 10,000 people

Ministry of Health

2019

x3

Population per family medicine department

Ministry of Health

2019

x4

Number of applications to the physician per person

Ministry of Health

2019

x5

Number of applications to the dentist per person

Ministry of Health

2019

x6

Bed occupancy rate

Ministry of Health

2019

x7

Crude mortality rate (hospital)

Ministry of Health

2019

x8

Number of health personnel per 10,000 people

Ministry of Health

2019

x9

Population per 112 stations

Ministry of Health

2019

x10

Population per 112 ambulances

Ministry of Health

2019

x11

Infant mortality rate

TURKSTAT

2019

x12

Expected life expectancy at birth (years)

TURKSTAT

2017

x13

Under-5 mortality rate (per thousand)

TURKSTAT

2019

x14

Crude birth rate by provinces

TURKSTAT

2020

and assign it to a cluster. As a result, it can be observed that some units are located in different units in clustering algorithms that give approximately the same results. In such cases, there is a blur in the units’ cluster membership, and instability arises in the cluster membership of the units. The fuzzy clustering method is a crucial method developed to describe such situations [2]. Any unit can theoretically belong to more or more little whole clusters. The membership degree denoted by µ indicates the cluster to which the unit belongs (0 < µ < 1). Based on the minimization of a quadratic function, the method was first developed by [4] and improved by [8]. While performing Fuzzy Clustering Analysis, the data handled are standardized in the range of 0–1. Then the mathematical model under the constraint is solved. n  c k  2   xip − vpj . µij Objective function: zmin = Constraints: and 0
Sj + sj i

⎧ if Z > Z0 + z ⎨ 0, µO (Z) = 1 − (Z − Z0 )/z, if Z0 ≤ Z ≤ Z0 + z ⎩ 1, if Z < Z0 µO can be found by taking min of µj such that µFLP = min{µ1 , µ2 , ..., µn , µO } since minimum is used while considering intersection of multiple membership functions in FST. According to the FST, the objective function of the fuzzy facility location model should be maximizing µFLP by determining optimal values of decision variables xij and yi . (see [26] for the final model).

3 Literature Review In this section, initially, the literature about FFLP is reviewed and the articles are categorized based on the fuzzy parameters included (see Table 1). We observe that fuzzy demand and fuzzy cost are widely seen parameters in FFLP. Besides articles with fuzzy cost and/or demand, most of the articles are composed of

The Facility Location Problem with Fuzzy Parameters

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Table 1. FFLP vs. Fuzzy parameter Reference #

Fuzzy distance

Fuzzy demand

Fuzzy cost

Fuzzy weight

Multiple Fuzzy components

√

[25, 28, 30, 39, 46]

√

[4, 6, 8–10, 16, 21, 24]

√

[5, 22, 40, 44]

√

[43] [7, 11, 12, 15, 26, 27, 27, 33, 37, 37, 38, 41, 47]

√

√

[2, 3, 5, 13, 14, 17–20, 23, 29, 31, 32, 34–36, 41, 42, 45]

√

Table 2. FFLP vs. Solution methods Reference #

Method

[13, 19, 22, 23, 43, 46]

Fuzzy TOPSIS

[5]

Picture fuzzy CODAS

[1, 7–9, 11, 15, 27]

Hybrid and particle swarm-based algorithms

[2, 36]

Quality function deployment (QFD)

[3, 4, 17, 19, 42]

Fuzzy Analytical Hierarchy Process (AHP)

[14]

Utilization of a convex polygon with maximin, minimax and minisum location

[12, 21]

A parametric optimization method

[20, 38–40]

Fuzzy C-means clustering method

[29]

Fuzzy Random Weighted Weber Problems in Facility Location

[16, 26, 28, 30–32, 41, 45]

Multi-objective and Goal Programming

[10, 34, 35, 47]

Other heuristic methods (Fuzzy ARAS, Lagrangian, fuzzy synthetic evaluation etc.)

multiple fuzzy components. Next, the studies in the literature are classified depending on the solution methods (See Table 2). From Table 2, it is observed that fuzzy TOPSIS, Hybrid and particle swarm-based algorithms, AHP, multi-objective and goal programming are widely used to solve FFLP.

4 Conclusions and Future Work In this study, the literature is reviewed to provide information about Fuzzy Facility Location Problems (FFLP). A basic FLP model is provided and then membership functions are defined as a first step to include fuzzy cost and demand to the conventional FLP. Next, reviewed articles are categorized and tabulated based on the fuzzy parameters and methods. In summary, fuzzy demand, and fuzzy cost are widely encountered

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fuzzy parameters in the FFLP literature while most of the articles include more than one fuzzy parameter. Furthermore, fuzzy TOPSIS, hybrid method and particle swarm-based algorithms, AHP, multi-objective and goal programming are the most frequently used methods. This study provides an overview of fuzzy parameters and methods available in FFLP literature. This survey can be extended in various dimensions to cover the fuzzy modelling approaches in FLP as a future work.

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20. Esnaf, S, ¸ Küçükdeniz, T.: A fuzzy clustering-based hybrid method for a multi-facility location problem. J. Intell. Manuf. 20(2), 259–265 (2009) 21. Sarıkaya, H.A., Çalı¸skan, E., Türkbey, O.: Fuzzy multi-objective programming model for facility location in an integrated supply chain network. Pamukkale Univ. J. Eng. Sci. 20(5), 150–161 (2014) 22. Ulukan, H.Z., Kop, Z.: A Two Step Solution Procedure to a Fuzzy Medical Waste Disposal Facility Location Problem (2009) 23. Temur, G.T., Kaya, T., Kahraman, C.: Facility location selection in reverse logistics using a type-2 fuzzy decision aid method. In: Kahraman, C., Öztay¸si, B. (eds.) Supply Chain Management Under Fuzziness. SFSC, vol. 313, pp. 591–606. Springer, Heidelberg (2014). https:// doi.org/10.1007/978-3-642-53939-8_25 24. Sharma, A., Sharma, A., Jalal, A.S.: Distance-based facility location problem for fuzzy demand with simultaneous opening of two facilities. Int. J. Comput. Sci. Math. 9(6), 590 (2018) 25. Bredtmann, J., Nowotny, K., Otten, S.: Linguistic distance, networks and migrants’ regional location choice. Labour Econ. 65, 101863 (2020) 26. Chung, K., Tcha, D.: A fuzzy set-theoretic method for public facility location. Eur. J. Oper. Res. 58(1), 90–98 (1992) 27. Shuming, W., Watada, J., Pedrycz, W.: Recourse-based facility-location problems in hybrid uncertain environment. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 40(4), 1176–1187 (2010) 28. Ardil, C.: Facility location selection using preference programming. World academy of science, engineering and technology, open science index 157. Int. J. Industr. Syst. Eng. 14(1), 1–12 (2020) 29. Uno, T., Kato, K., Katagiri, H.: Fuzzy random weighted Weber problems in facility location. Procedia Comput. Sci. 60, 936–943 (2015) 30. Can, M.: Fuzzy multiple objective models for facility location problems. Southeast Eur. J. Soft Comput. 1(1), 93–98 (2012) 31. Cedolin, M., Göker, N., Dogu, E., Albayrak, E.Y.: Facility location selection employing fuzzy DEA and fuzzy goal programming techniques. In: Advances in Intelligent Systems and Computing, vol. 641, pp. 466–476 (2017) 32. Sirbiladze, G., Ghvaberidze, B., Matsaberidze, B., Midodashvili, B.: New fuzzy approach to facility location problem for extreme environment. J. Intell. Fuzzy Syst. 37(6), 1–11 (2019) 33. Wang, S., Watada, J.: VaR-based fuzzy random facility location model with variable capacity. In: Fuzzy Stochastic Optimisation, pp. 181–197. Springer, Cham (2012). https://doi.org/10. 1007/978-1-4419-9560-5_7 34. Karagöz, S., Deveci, M., Simic, V., Aydin, N.: Interval type-2 Fuzzy ARAS method for recycling facility location problems. Appl. Soft Comput. 102, 107107 (2021) 35. Zhang, Y., Kwon, O.K.: Location decision of city logistics facility based on fuzzy synthetic evaluation. Appl. Mech. Mater. 33, 351–355 (2010) 36. Jamalnia, A., Mahdiraji, H.A., Sadeghi, M.R., Hajiagha, S.H.R., Feili, A.: An integrated fuzzy QFD and fuzzy goal programming approach for global facility location-allocation problem. Int. J. Inf. Technol. Decis. Mak. 13(02), 263–290 (2014) 37. Wang, S., Watada, J., Yaakob, S.B.: A variable-capacity-based fuzzy random facility location problem with VaR objective. Integr. Uncertain. Manag. Appl. 68, 209–220 (2010) 38. Küçükdeniz, T., Baray, A., Ecerkale, K., Esnaf, S: ¸ Integrated use of fuzzy c-means and convex programming for capacitated multi-facility location problem. Expert Syst. Appl. 39(4), 4306–4314 (2012) 39. Kocakaya, M.N., Türkakın, O.H.: Solution of facility location problem in Turkey by using fuzzy C-means method. AIP Conf. Proc. 1558, 433–436 (2013)

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Fuzzy Network Data Envelopment Analysis in the Evaluation of Project Success Across the Project Life Cycle Dorota Kuchta(B)

and Agata Klaus-Rosi´nska

Wroclaw University of Science and Technology, Wybrze˙ze Wyspa´nskiego 27, 50-370 Wrocław, Poland [email protected]

Abstract. Project success has been the subject of extensive research, but there exists a rather limited repertoire of results regarding project success assessment across the project life cycle, taking into account consecutive project stages. Here, we propose an approach to evaluate overall project success on the basis of the inputs and outputs of different project stages. The inputs and outputs may be fuzzy. Our proposal is a modification of the network Data Envelopment Analysis approach, which was originally developed to measure the relative efficiency of production units with an internal structure (production stages). This approach has its fuzzy versions, which allow the consideration of the hard-to-measure project inputs and outputs. An adequate model is described, and its application is illustrated with a computational example. Keywords: Network DEA · Project success · Project life cycle

1 Introduction Project success is today seen as a complex issue. In numerous cases, it is not possible to unambiguously say whether a project is successful or not. The evaluation of project success is a multicriteria problem, and the selection, values, and weights of individual criteria depend not only on various stakeholders but also on the moment in time when they are evaluated. The problem of time is also related to the fact that projects usually go through consecutive stages. For example, a computer system is first produced, then implemented, and then actually used. The project may seem successful after the production stage, maybe also (but not necessarily) after the implementation stage, but if all its functionalities are not actually used in the day-to-day organisation practice, the overall success of the project will be far from evident. Thus, the problem arises of how to determine an overall project success with respect to time and consecutive project stages. Data Envelopment Analysis has been used for years to evaluate the performance of units that transform several inputs into several outputs. Projects can also be seen as such units, and their inputs and outcomes cannot always be expressed as crisp numbers (due to uncertainty, subjectivity, and immeasurability). That is why Data Envelopment © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 319–327, 2022. https://doi.org/10.1007/978-3-031-09173-5_40

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Analysis (DEA), also in its numerous fuzzy versions, has been applied to project success evaluation. However, in all the existing DEA applications, projects are treated as onestage endeavours. Network Data Envelopment Analysis, which also has fuzzy versions, was developed for the analysis of units where the transformation of inputs into outputs is performed in more than one stage. This can be treated as a natural analogy to multi-stage projects. In this paper, we propose the application of fuzzy network Data Envelopment Analysis to the success evaluation of multistage projects. To achieve this goal, we propose a modification of the existing DEA models. According to the general philosophy of DEA, project success will be evaluated based on the ratio of weighted outputs over weighted inputs in consecutive stages, with weights being determined for each project individually. A proposal of how to aggregate the success of various project stages into one overall measure will also be addressed. Furthermore, the project success appraisal will be relative: we will be interested not so much in numerical values measuring each project’s success, but in ranking of projects (e.g. those implemented by an organisation in a certain period of time) from most to least successful. To arrive at useful conclusions for the future, it is important to compare projects implemented in the same context. Our proposal can be applied both to the evaluation of completed projects, to improve project management in the organisation in the future, and to the evaluation of potential success degree of a set of projects proposed to be implemented, to select projects for actual implementation within a set budget. In Sect. 2 we present the state-of-the-art of the evaluation of projects success assessment across the project life cycle. In Sect. 3 the existing network DEA models are described. In Sect. 4 we propose a modification of the network DEA approach adjusted to the needs of project management. In Sect. 5 we present a computational example that illustrates our approach. The paper ends with some conclusions.

2 Project Success and Project Life Cycle In the literature, project success is often treated as a feature of a static endeavour with a set of inputs (e.g., project budget, project team competencies) and a set outputs (e.g. requirements fulfilment, project stakeholder satisfaction). However, in the 1970s researchers began to realise that project success assessment can change over time. J. Pinto and S. Mantel noted that the project success criteria would be different during the duration of the project [1]. This concept was further developed by A. Shenhar, D. Dvir, O. Levy, and A. Maltz [2], who established four main success criteria linked to the passage of time (also after project closure): • achievement of project objectives within the planned time, cost and at the required quality and meeting other requirements (project performance); • benefits to the project stakeholders (stakeholder influence); • benefits for the organisation implementing the project, such as profits, market share, or business development (business success); • The dimension related to the post-project future, which answers the question: How has the project prepared the organisation for future challenges? (preparing the future).

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The first success criterion (project performance) should only be considered in a very short term, during the project, or immediately after its closure. The second success criterion (impact on stakeholders) should be considered still in a rather short term, e.g. when the project products are delivered to the customer and the customer starts using them. Stakeholder satisfaction should be measured within a few months after the completion of the project. The third criterion (business success) can only be taken into account when a considerable amount of time has already passed, allowing the achievement of long-term benefits to be measured (usually 1–2 years after project closure). The fourth criterion (preparation for the future) can be assessed over a very long period of time, usually after 2–5 years. The time reference in project success appraisal is in fact a direct consequence of the various stages that occur on the project life cycle. However, in the literature, hardly any research has been devoted to a systematic appraisal of each project stage success and to their aggregation. Only one paper has been identified in this research area [3]. And still, this is an important issue: the success of a project should be assessed across the phases of the project life cycle (e.g. conceptual, planning, execution, termination [4]) and in the post-project phase, taking into account the views of different stakeholders. Only then due objectivity will be given to each stage and its role for the overall success. This stage-related project success assessment should be applied both in the projects’ selection stage (performed on the basis of project proposals, where fuzzy modelling inputs and outputs of consecutive stages would be especially appropriate) and in post factum analysis, when useful “lessons learnt” should be generated. We propose here to use network Data Development Analysis.

3 Network Data Envelopment Analysis - State-of-the-Art Network Data Envelopment Analysis is a generalisation of “standard” Data Envelopment Analysis (DEA), a non-parametric method of assessing the relative efficiency of the socalled decision making units (DMU) [5]. The DMUs may be production or service units, but also projects [6] – any entity that uses input to produce output. The efficiency of a DMU is measured as the ratio of the weighted totals of outputs and the weighted totals of inputs. The idea is that the weights are not a priori imposed: they can be chosen by each DMU individually. If, in spite of this possibility, the efficiency of the DMU being evaluated is lower than that of another DMU, it is impossible to undermine the inferiority of the DMU in question. Standard DEA treats the DMUs as black boxes, it only considers the inputs that enter the units and the outputs that leave it. Network DEA takes into account the internal structure of the DMU, the fact that the production process may be composed of several (parallel or serial) phases and each phase may have its own inputs and outputs. Some of the intermediate inputs naturally become outputs for the next phases. For the objective of this paper, which is the application of network DEA to the assessment of project success, we can limit ourselves to the DMUs with serial phases or stages. A general formulation of this network DEA problem can be found in [7]. For sake of simplicity, we will present it in the two-stage version, using Fig. 1.

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x2

x1

y2

Stage 1

z2

Stage 2

y1

z1

Fig. 1. Structure and variables of the two-stage network DEA

The models considered in the literature are one-criterion or bi-criteria problems: either the overall efficiency of the whole system is maximised and later decomposed to partial deficiencies of individual stages, or the two-stage efficiencies are maximised and then composed to an overall efficiency [8]. The two efficiencies of the individual stages are defined as for each DMU p = 1, . . . , P as follows [7]: J1 1 p1 J2 2 p2 j=1 uj yj + j=1 uj yj p1 (1) Stage 1 efficiency : S = I1 p1 1 i=1 wi xi L1 1 p1 2 p2 v z + vl2 zl p2 (2) Stage 2 efficiency : S = Il=1 l lp2 l=1 J2 2 2 2 p2 i=1 wi xi + j=1 uj yj  I2  I1 p1 p2 and xi are external inputs into the system (to Stage 1 and where (Fig. 1) xi i=1 i=1  J1  J2 p1 p2 Stage 2 respectively), yj and yj are two groups of outputs of Stage 1: the j=1 i=1   L1 p1 first one is not used in Stage 2, the second one is used as inputs to Stage 2, zj l=1  L2 p2 and zl are two groups of outputs of Stage 2: the first one is important for the l=1 whole project, the second one is locally important to for the second stage. Additionally,  1 I1  2 I2  1 J1  2 J2  1 L1  2 L2 vl l=1 are weights of the respective wi i=1 , wi i=1 , uj , uj , vj j=1

i=1

l=1

inputs and outputs. According to the general philosophy of DEA, the inputs and outputs are known because they can be measured (although sometimes have to take a fuzzy form [9]), but the weights can be selected by each decision unit. Thus, P mathematical programming problems are solved, one of each DMU. In the po -th problem the respective objective function(s) based on S p0 1 and S po 2 and the selected bi-criteria model is constructed and maximised, normalised expressions (1) and (2) for the other DMU serve as constraints, the decision variables being the weights. In the po -th problem weights

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            p 1 I1 p 2 I2 p 1 J1 p 2 J2 p 1 L1 p 2 L2 wi 0 vl 0 , wi 0 , uj 0 , uj 0 , vj 0 correspond to the i=1

i=1

j=1

i=1

l=1

l=1

optimal solution and show the po -th DMU in the best possible light (maximising its partial and overall efficiencies according to the accepted concept). S p1 and S p2 or a selected aggregation used in the respective bi-criteria model are used as the basis for the evaluation of individual DMUs p = 1, . . . , P, but all the DMU’s for p = p0 use the             p 1 I1 p 2 I2 p 1 J1 p 2 J2 p 1 L1 p 2 L2 vl 0 , wi 0 , uj 0 , uj 0 , vj 0 . Thus, each weights wi 0 i=1

i=1

j=1

i=1

l=1

l=1

DMU is evaluated relative to the other DMUs, using ‘its own’ weights. It has to be emphasized that in all the network DEA models identified in the literature, two assumptions are taken:  J2  J2 p2 p2 are the same whether yj are used as inputs or outputs; • weights uj i=1 i=1 • when the aggregation of objectives (1) and (2) in the bi-criterial problem is achieved through additive weighting (which is by the way not recommended, multiplicative aggregation is preferred [10]), the weights are not arbitrarily selected but are based on the proportion of the total input used in the respective stage [7]. On top of that, additional constrains on the weights and efficiencies can be imposed [11].

4 Fuzzy Network DEA Models for Project Evaluation When an organization is facing the problem of selecting projects for implementation within a predestined budget or when it is performing a post factum evaluation of already completed projects, they have to decide about project success criteria and a method of aggregating the criteria into a total scoring. Among the different models used to evaluate project success we find crisp [12] and fuzzy [13, 14] DEA models. DEA models are suitable here, as they allow each ‘project owner’ to present their project in the best light. Choosing weights is always a delicate issue [15] – thus this process should thus be as transparent as possible. These models naturally suit the problem of project success evaluation, as each project uses certain inputs, whose usage should be minimized, and produces certain outputs, whose usage should be maximized. As mentioned above, most projects have their life cycle and will be composed of various stages. Thus, network DEA models would be needed here. However, in the literature, no case of application of network DEA to project selection and evaluation has been identified. Figure 1 can be seen as representing two stages of a project. Therefore, the application of network DEA to the project success appraisal model will be almost straightforward. ‘Almost’ - because two important modifications should be introduced. First of all, weights  J2  J2 p2 p2 cannot be assumed to be the same whether yj are used as inputs or uj i=1 i=1 outputs.

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The first stage output of the project of the project of the project may be, for example, ‘team competencies increase’. It serves as input to the second stage. However, in the role of the output, the ‘team competencies increase’ may have a different weight than in the role of the input. Team competencies can be considered as something durable and important for the future of the organisation (a very important output), but this team alone may play a limited role in the second project stage (a secondary input). Therefore,  J2  J2 and u2j : for inputs and outputs we propose to introduce two weights sets: u2j i=1 i=1 respectively. The other modification with respect to the network DEA known from the literature (detached from the project context) will be the preference of additive weighting of (1) and (2) over the multiplicative one and a freedom in the choice of stage weights. The weights based on the inputs consumed, assumed in the additive network DEA models in the literature, have no justification in the case of projects. We propose to leave the choice of weights assigned to individual stages to decision makers and even to each project ‘owner’. In the latter case, the stage weights would be subject to the same selection procedure as the other weights in the model, being part of the decision variables in each of the P mathematical programming models solved. Obviously, they can be subject to certain constraints. For example, we use num fuzzy stage weights

(here, for simplicity, triangular fuzzy    bers), T˜ 1 = t11 , t21 , t31 , with support t11 , t31 and core t21 , for Stage 1, and ˜t2 = t12 , t22 , t32 , respectively, for Stage 2, whose membership functions express the satisfaction of the organisation management with the crisp weights (T1 , T2 ). The project owner will be able to choose the weights freely, but within the imposed λ-levels of fuzzy numbers T˜ 1 and T˜ 2 , with the additional constraint T1 + T2 = 1. This simple approach will make it possible to find a compromise between the understanding of the role of each stage by organisation management and the freedom of each project owner to see these roles their way. In addition to the fuzziness in the stage weights that express preferences, several fuzzy network DEA models [9, 16] have been considered in the literature, where inputs and outputs are expressed as fuzzy numbers. This approach is especially natural for projects evaluated not post factum but before their initiation, for the purpose of choosing projects for implementation. But also in a post factum project success evaluation, such outputs as satisfaction of project stakeholders or future perspectives, or such inputs as project team effort may need fuzzy modelling. In these cases the fuzzy network DEA models, modified taking into consideration the above remarks and possibly other project management peculiarities, can find a natural application.

5 Computational Example Let us consider a set of eight projects consisting of two stages. All inputs and outputs are measured here qualitatively, using fuzzy values, on a scale from very small to very high. Their defuzzified values are given in Table 1.

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Table 1. Input and output values for the projects from the example, p = 1,…,8 (1 stands for very low, 5 – for very high) p1

p1

p1

p2

p2

p2

p1

p1

p

x1

x2

y1

y1

y2

x1

z1

z2

1

1

2

5

5

2

5

1

1

2

5

4

1

1

3

1

4

5

3

1

2

2

2

4

2

5

4

4

5

3

3

3

1

3

2

1

5

5

5

1

3

2

1

5

3

6

3

3

3

3

1

1

5

1

7

3

4

3

3

5

1

5

4

8

3

4

1

4

5

4

1

5

The model proposed in Sect. 4 was applied, with T˜ 1 = (0, 1, 0, 4, 0, 7), T˜ 2 = (0, 2, 0, 5, 0, 8) and λ = 0. Table 2 presents the results, with r representing the position of the project in the ranking from the most to the least successful projects. Table 2. Input and output values for example projects p = 1,…,8 (1 stands for very low, 5 – for very high), r is the ranking position of the project. p1

p1

p1

p2

p2

p2

p2

p2

p1

p1

p (r)

w1

w2

u1

u1 / u1

u2 / u2

w1

v1

v2

1 (3)

0

1

0,5

0,5 /0,4

0/0,6

0

0

0,4

2 (2)

0

1

0

0/0.1

0,5/0

1

0

1

3 (4)

0,5

0,5

0

0/0,6

0,7/04

0

0,4

0

4 (7)

0

1

0,3

0,1/0,6

0/0,4

0

0,4

0

5(5)

0

1

0

0,2/0

0,4/0

1

0,3

0

6 (5)

0

1

0,4

0/0,1

0/0

1

0,3

0

7 (1)

0

1

0,2

0/0

0,4/1

0,2

0,8

0

8 (6)

0

1

0

0,2/0,4

0,4/0,6

0

0

0,4

For p = 2 and 7, the stage weights were selected to be T1 = 0, 2, T2 = 0, 8, in all the other cases the selection was different: T1 = 0, 7, T2 = 0, 3. The 2nd and 7th projects are shown to be the most successful. They have managed to occupy this high-ranking position thanks to the possibility to reverse the order of importance of the two stages: contrary to the other projects, they put emphasis on the second stage and downplayed the role of the first stage. Naturally, this can and should be the subject of discussion on the actual importance of the stages. However, the projects ranked low (p = 4, 8, 5, 6) are clearly those far from being successful. In spite of the freedom to choose the weights of individual inputs and outputs and of the stages, their efficiency (success rate) is clearly

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lower than that of the other projects. For example, the 4th project has very high inputs and low outputs, the 8th project has medium inputs, and some of its outputs are low. The method allows us to avoid the discussion about weights of inputs, outputs, and stages. Of course, we can and should put some constraints on them (which is recommended in project management [15]), but some freedom may be left to the model. The projects rated as least successful will certainly deserve this name (relatively to the other projects being evaluated) and should be subject to a close analysis.

6 Conclusions We considered the problem of project success evaluation in the case of projects consisting of more than one stage, which is, in fact, a feature that most real world projects possess. For example, first a product is manufactured, there is the conceptualization phase, the manufacturing phase, and then the commercialization phase. Each stage of the project is implemented using other resources, in a different context, under the responsibility of someone else. Each stage should thus be evaluated separately, taking into account the mutual dependencies (e.g., outputs of one stage may be inputs for another stage), without losing sight of the overall project appraisal. We propose to apply here the network DEA model and its fuzzy versions, modified accordingly. The computational example shows the potential usefulness of the approach. The method allows us to rank a given set of projects from most to least successful ones (before they have been approved – in this situation we accept the potentially most successful ones for implementation; or after they have been closed – to draw conclusions for the future) in the most objective way possible: leaving the selection of the weights of inputs, outputs, and stages to the optimization model (within preset preferences). Further research is needed to implement to approach for real world cases, using the criteria selected by practitioners and modelling the respective requirements and parameters using fuzzy modelling. Additionally, the mathematical programming models that have to be solve are fractional, thus a reflection on solution algorithms is needed. Funding. The work of Dorota Kuchta was funded by the National Science Centre (Poland), grant number 484071, 2020/37/B/HS4/03125, Grant title: Non-parametric approaches for the performance measurement of units with complex internal structure. The work of Agata Klaus-Rosi´nska was funded by the National Science Centre (Poland), grant number 394311, 2017/27/B/HS4/01881 Grant title: Selected methods supporting project management, taking into consideration various stakeholder groups and using type-2 fuzzy numbers.

References 1. Pinto, J.K., Mantel, S.J.: The causes of project failure. Eng. Manag. IEEE Trans. 37, 269–276 (1990) 2. Shenhar, A.J., Dvir, D., Levy, O., Maltz, A.C.: Project success: a multidimensional strategic concept. Long Range Plann. 34, 699–725 (2001) 3. Do Ba, K., Kyne, D.: Success criteria and factors for international development projects: a life-cycle-based framework. Proj. Manag. J. 39, 72–84 (2008)

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4. Pinto, J.K., Prescott, J.E.: Variations in critical success factors over the stages in the project life cycle. J. Manage. 14, 5 (1988) 5. Farrell, M.J.: The measurement of productive efficiency. J. R. Stat. Soc. Ser. A 120, 253–281 (1957) 6. Kuchta, D., Despotis, D., Fr˛aczkowski, K., Stanek, S.: Applications of data envelopment analysis for the evaluation of IT project success. Oper. Res. Decis. 29, 17–36 (2019) 7. Cook, W.D., Zhu, J., Bi, G., Yang, F.: Network DEA: additive efficiency decomposition. Eur. J. Oper. Res. 207, 1122–1129 (2010) 8. Despotis, D.K., Koronakos, G., Sotiros, D.: Composition versus decomposition in two-stage network DEA: a reverse approach. J. Prod. Anal. 45(1), 71–87 (2014). https://doi.org/10. 1007/s11123-014-0415-x 9. Despotis, D., Kuchta, D.: Fuzzy weak link approach to the two stage DEA. RAIRO-Oper. Res. 55, S385–S399 (2021) 10. Despotis, D.K., Sotiros, D., Koronakos, G.: A network DEA approach for series multi-stage processes. Omega 61, 35–48 (2016) 11. Lu, C., Cheng, H.: Alternative secondary goals in multiplicative two-stage data envelopment analysis. Math. Probl. Eng. 2021, 9931796 (2021) 12. Eilat, H., Golany, B., Shtub, A.: Constructing and evaluating balanced portfolios of R&D projects with interactions: a DEA based methodology. Eur. J. Oper. Res. 172, 1018–1039 (2006) 13. Azadeh, A., Kokabi, R.: Z-number DEA: a new possibilistic DEA in the context of Z-numbers. Adv. Eng. Inform. 30, 604–617 (2016) 14. Wen, M., Li, H.: Fuzzy data envelopment analysis (DEA): model and ranking method. J. Comput. Appl. Math. 223, 872–878 (2009) 15. Kerzner, H.R.: Project Management Metrics, KPIs, and Dashboards. Wiley, New York (2013) 16. Lozano, S., Moreno, P.: Network fuzzy data envelopment analysis. Stud. Fuzziness Soft Comput. 309, 207–230 (2014)

Solving Matrix Games Involving the Level (glower , g upper ) Interval Valued Pentagonal Fuzzy Payoffs: Signed Distance Ranking Approach V. Kamal Nasir1

and A. Jamal Barakath2(B)

1 The New College, Chennai, India 2 KCG College of Technology, Chennai, India

[email protected]

Abstract. The main objective of this article is to deal with matrix games, involving fuzzy payoffs extended to the level (glower , g upper ) - Interval valued Pentagonal Fuzzy Payoffs. For the parameters, we use the level (glower , g upper ) - Interval valued Pentagonal Fuzzy numbers rather than the normal Fuzzy numbers. Signed distance ranking method have been proposed to rank Interval valued Triangular and Interval valued Trapezoidal Fuzzy numbers. In this article, very first time, we introduced the Signed distance ranking formula to rank the Interval valued Pentagonal Fuzzy numbers. Using the signed distance ranking method to transform the (glower , g upper ) - Interval valued Pentagonal Fuzzy Payoffs into Crisp Payoffs matrix, then it is solved by the method of dominance to get the Optimum Strategies. This proposed method is also demonstrated with the help of practical examples and then validate the results. Keywords: g-Pentagonal Fuzzy numbers · (glower , g upper ) - Interval valued Pentagonal Fuzzy numbers · Signed distance ranking

1 Introduction If we achieve our desired outcome, required set of acts is called operations. Morse and Kimball said that operations research is a scientific method which provides the quantitative basis for decisions for the executive departments with the operations. Game theory, it is a branch of mathematics, which deals with the general features of competitive situations. In such circumstances, decision making is critical, because these will affect the outcome of any. Mathematically, to optimize the outcome within the given constraints, Game theory is the better way to find out the best strategy. It has set of outcomes and rules. It’s first general formulation by John von Neumann and Oskar Morgenstern (1944). A two-person zero sum game is one in which one player’s success is equivalent to the failure of the other. [7] In 1965, Zadeh introduced the theory whose objects are called Fuzzy sets, with boundaries that are not precise. The degree of membership for a fuzzy number is a crisp number, however for Interval valued fuzzy numbers, the degree of membership is an interval. [2] In 2014, B. Farhadinia proposed the sensitivity analysis in interval valued trapezoidal fuzzy numbers in Linear programming problems. [6] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 328–338, 2022. https://doi.org/10.1007/978-3-031-09173-5_41

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In 2015, Mohammed Ghasem Akbari and Gholamreza Hesamian proposed the signed distance measures oriented to rank interval valued fuzzy numbers. [3] In 2018, Jishu Jana and Sankar Kumar Roy proposed the solution of matrix games with generalised Trapezoidal Fuzzy payoffs. [1] In 2019, Avishek Chakraborty, Sankar Prasad Mondal, Shariful Alam, Ali Ahmadian Norazak Senu, Debashis De and Soheil Salahshour proposed the pentagonal fuzzy number: its different representations, Properties, Ranking, Defuzzification and Application in Game problems. [5] In 2019, H.A. Khalifa and Mahmoud proposed a new approach for solving Two-person zero sum games with interval valued triangular fuzzy payoffs. [4] In 2022, We proposed the solution of matrix games involving the level (Klower , Kupper ) interval valued trapezoidal fuzzy payoffs using the signed distance ranking method. In fuzzy decision making, the concept of ranking fuzzy numbers is very important in research areas. Based on our research and observations, numerous research scholars have used various ranking systems to rate the fuzzy numbers in their research articles. No one has used the Signed distance ranking method to rank the Interval valued Pentagonal fuzzy numbers. First time we introduced the Signed distance ranking formula to rank the Interval valued Pentagonal Fuzzy numbers. Using the signed distance ranking approach, the (g_lower, g upper) - Interval valued Pentagonal Fuzzy Payoffs matrix is transformed into a Crisp Payoffs matrix, which is then solved using the dominance method to provide the Optimum Strategies. This article is divided into five sections for the remainder. Preliminary definitions appear in section two. The Geometric representation of IVPentFN, as well as demonstrations of the proposed ranking technique, are presented in section three. The Flow chart and application of the suggested ranking approach for addressing Game problems are included in section four. The results are in section five. Section six concludes with a conclusion and a discussion of future possibilities.

2 Preliminaries Definition 2.1: g - Pentagonal Fuzzy Number (g -PentFN) [1]. A Fuzzy number A˜ = (a1 , a2 , b, a3 , a4 ; g) is called a g- Pentagonal fuzzy number if its membership function is defined as follows:

Definition 2.2: Interval valued Pentagonal Fuzzy Number (IV PentFN) [1].  An IVPentFN is denoted by A˜ I = A˜ lower , A˜ upper .    = (a1lr , a2lr , b, a3lr , a4lr ; glr , q), a1ur , a2ur , b, a3ur , a4ur ; g ur , p .

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The lower and upper membership function is defined as,

a1lr ≤ a2lr ≤ b ≤ a3lr ≤ a4lr ; a1ur ≤ a2ur ≤ b ≤ a3ur ≤ a4ur 0 < glr ≤ g ur ≤ 1; μA˜ lower (x) ≤ μA˜ upper (x) The family of all (glr , g ur )-level Pentagonal fuzzy number is denoted as FIVPentFN (g) and is defined as FIVPentFN (glr , g ur )

Remark 1: If glr = g ur = 1, then A˜ I will be a normal IVPentFN. Remark 2: If A˜ lower = A˜ upper then A˜ I will be a general Pentagonal   fuzzy number. ur . Then the α − g , g Definition 2.3: α − cutsetof A˜ I [2] Let A˜ I ε FIVPentFN lr  upper cut set of A˜ I is given as A˜ I (α) = A˜ lower (α), A˜ (α) = ⎧  ⎨ A˜ upper (α), A˜ left (α)]∪[A˜ right (α), A˜ upper (α) , 0 ≤ α ≤ glr ; lower left right  lower  upper upper ⎩ ˜ A˜ ≤ A , g (α), (α) lr α ≤ g ur left

right

  ur upper   upper upper ˜ A˜ 1left (α) = a1ur + a2ur − a1ur αp ; A˜ 2left (α) = a2ur + b − a2ur gg ur −α −p ; A1right (α) =      ur upper ˜ a4ur − a4ur − a3ur αp ; A˜ 2right (α) = a3ur − a3ur − b gg ur −α −p ; A1leftlower (α) = a1lr +(a2lr −

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 ; A˜ 1rightlower (α) = a4lr − (a4lr − a3lr ) αq ; a1lr ) αq ; A˜ 2leftlower (α) = a2lr + (b − a2lr ) gglrlr −α  −q A˜ 2rightlower (α) = a3lr − (a2lr − b) gglrlr −α −q .

3 Geometric Representation of IVPentFN

Fig. 1. (glower , g upper )- Interval valued Pentagonal Fuzzy number

Theorem 3.1: Let A˜ I ∈ FIVPentFN (glr , g ur ) then the signed distance of    A˜ I = (a1lr , a2lr , b, a3lr , a4lr ; glr , q), a1ur , a2ur , b, a3ur , a4ur ; g ur , p from O (Origin) is given by, (F1) If 0 < glr < g ur ≤ 1, then

(F2) If 0 < glr = g ur ≤ 1 and p = q, then

Proof: Case (i): Signed distance of the interval [P, Q] and [R, S] from O as,   1  upper upper d A˜ 1left (α), A˜ 1leftlower (α) , O = A˜ 1left (α) + A˜ 1leftlower (α) 2

(1)

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 α 1 ur  ur α a1 + a2 − a1ur + a1lr + (a2lr − a1lr ) 2 p q     1 ˜ upper upper d A˜ 1rightlower (α), A˜ 1right (α) , O = A1rightlower (α) + A˜ 1right (α) 2

 α  1 α a4lr − (a4lr − a3lr ) + a4ur − a4ur − a3ur 2 q p =

(2) (3) (4)

Here [P, Q] ∩ [R, S] = ∅. Then the signed distance of [P, Q] ∪ [R, S] from O can be attained as     upper upper d A˜ 1left (α), A˜ 1leftlower (α) ∪ A˜ 1rightlower (α), A˜ 1right (α) , O

 α  α 1 a1lr + a1ur + a4lr + a4ur + a2ur − a1ur − a4ur + a3ur + (a2lr − a1lr − a4lr + a3lr ) = 4 p q

Signed distance of the interval [P1 ,Q1 ] and [R1 ,S1 ] from O as,     upper upper d A˜ 2left (α), A˜ 2leftlower (α) , O = A˜ 2left (α) + A˜ 2leftlower (α)

(5)

(6)



    g ur − α glr − α 1 ur  ur a + b − a2 + a2lr + (b − a2lr ) (7) = 2 2 g ur − p glr − q   1    upper upper d A˜ 2rightlower (α), A˜ 2right (α) , O = d A˜ 2rightlower (α), O + d A˜ 2right (α), O 2  1˜ upper = A2rightlower (α) + A˜ 2right (α) 2       g ur − α glr − α 1 a3lr − (a2lr − b) + a3ur − a3ur − b = 2 glr − q g ur − p (8) Here [P1 ,Q1 ] ∩ [R1 ,S1 ] = ∅. The signed distance of [P1 ,Q1 ] ∪ [R1 ,S1 ] from O can be attained as     upper upper d A˜ 2left (α), A˜ 2leftlower (α) ∪ A˜ 2rightlower (α), A˜ 2right (α) , O     (9) 1   ˜ upper upper d A2left (α), A˜ 2leftlower (α) , O + d A˜ 2rightlower (α), A˜ 2right (α) , O =

2       g ur − α g −α 1 a2lr + a2ur + a3lr + a3ur + (2b − a2lr − a3lr ) lr + 2b − a2ur − a3ur = (10) ur 4

glr − q

g

−p

  We observe that the function d in (5) and (7) is continuous of α on 0, glr . This will allow us to evaluate the average of d using the definite integral (Fig. 1). For 0 < α ≤ glr ,

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(11)

(12) For glr < α ≤ g ur , (13)  1  ˜ upper upper A2left (α) + A˜ 2right (α) (14) 2

     g ur − α  ur  g ur − α 1 ur  ur a2 + b − a2ur + a (15) = − a − b 3 3 2 g ur − p g ur − p

   g ur − α  1 ur = a2 + a3ur + 2b − a2ur − a3ur (16) 2 g ur − p   1    d A˜ 2leftlower (α), A˜ 2rightlower (α) , O = d A˜ 2leftlower (α), O + d A˜ 2rightlower (α), O 2 (17)   1 (18) = A˜ 2leftlower (α) + A˜ 2rightlower (α) 2  

  glr − α glr − α 1 a2lr + (b − a2lr ) + a3lr − (a2lr − b) (19) = 2 glr − q glr − q 

 glr − α 1 = a2lr + a3lr + (2b − a2lr − a3lr ) (20) 2 glr − q   upper upper upper upper d A˜ 1left (α), A˜ 2left (α), A˜ 1right (α), A˜ 2right (α) , O (21)  1  upper upper upper upper = A˜ 1left (α) + A˜ 2left (α) + A˜ 1right (α) + A˜ 2right (α) 2  

  α  g ur − α α     g ur − α 1 ur  ur = (22) a1 + a2 − a1ur + a2ur + b − a2ur + a4ur − a4ur − a3ur + a3ur − a3ur − b ur ur 2 p g −p p g −p =

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=



  α   g ur − α 1 ur a + a2ur + a3ur + a4ur + a2ur − a1ur − a4ur + a3ur + 2b − a2ur − a3ur 2 1 p g ur − p

(23)

  We observe that the function d in (16), (20) and (23) are continuous of α on glr , g ur . This will allow us to evaluate the average of d using the definite integral. For glr < α ≤ g ur ,  g ur  1 ˜ upper (α), A˜ upper (α) , O d α ∫ d A 2left 2right g ur − glr glr

  g ur  g ur − α  1 ur ur ur ur ∫ a + a3 + 2b − a2 − a3 = dα 2(g ur − glr ) glr 2 g ur − p

     g ur − glr 1  ur ur ur ur = 2 a2 + a3 + 2b − a2 − a3 4 g ur − p

(24)

 g ur  1 ∫ d A˜ 2leftlower (α), A˜ 2rightlower (α) , O d α ur g − glr glr 

 g ur glr − α 1 ∫ a2lr + a3lr + (2b − a2lr − a3lr ) dα = 2(g ur − glr ) glr glr − q  ur

 1 g − glr = 2(a2lr + a3lr ) − (2b − a2lr − a3lr ) 4 glr − q

(26)

(25)

(27)

 g  1 upper upper upper upper ∫ A˜ 1left (α), A˜ 2left (α), A˜ 1right (α), A˜ 2right (α) , O d α − glr glr ur

g ur

  g ur α   g ur − α  1 ∫ aur + a2ur + a3ur + a4ur + a2ur − a1ur − a4ur + a3ur dα + 2b − a2ur − a3ur 2(g ur − glr ) glr 1 p g ur − p  ur  ur

     g + glr  g − glr  1  ur = 2 a1 + a2ur + a3ur + a4ur + a2ur − a1ur − a4ur + a3ur + 2b − a2ur − a3ur 4 g ur − p g ur − p

=

(28) (29)

For glr < α ≤ g ur ,  g  1 upper upper upper upper ∫ A˜ 1left (α), A˜ 2left (α), A˜ 1right (α), A˜ 2right (α) , O d α − glr glr ur

g ur

 g ur  1 1 ˜ upper (α), A˜ upper (α) , O d α − ∫ d A 2left 2right g ur − glr glr g ur − glr  g ur  ∫ d A˜ 2leftlower (α), A˜ 2rightlower (α) , O d α −

g

lr

        g ur + glr  g ur − glr 1  ur = 2 a1 + a4ur − a2lr − a3lr + a2ur − a1ur − a4ur + a3ur + 2b − a2lr − a3lr ur 4 p g −q

(30)

Consequently, the signed distance of A˜ I from O, 0 < glr < g ur ≤ 1, can be attained as

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 g  1 upper upper upper upper ∫ A˜ 1left (α), A˜ 2left (α), A˜ 1right (α), A˜ 2right (α) , O d α − glr glr  g ur  1 upper upper ∫ d A˜ 2left (α), A˜ 2right (α) , O d α − ur g − glr glr  g ur  1 ∫ d A˜ 2leftlower (α), A˜ 2rightlower (α) , O d α − ur g − glr glr ur

g ur

(31) Case (ii) If 0 < glr = g ur ≤ 1 and p = q, then by the support of (12) and (27) we can get the signed distance of A˜ I from O as follows:

(32)

4 Application of Proposed Method to Game Problems We are looking at a two-person zero-sum game where all of the payoff matrix components are IVPentFN. Assume that the maximisation player is player I, who has three strategies, and that the minimisation player is player II, who also has three strategies. Both players must choose a strategy from the set of pure strategies (Fig. 2). ⎛ ⎞ a˜ 11 a˜ 12 a˜ 13 A˜ I = ⎝ a˜ 21 a˜ 22 a˜ 23 ⎠ a˜ 31 a˜ 32 a˜ 33 . a˜ 11 = [(3, 4, 5, 6, 7; 0.7, 0.3), (1, 2, 5, 8, 9; 0.9, 0.4)] a˜ 12 = [(4.5, 4.75, 5, 5.5, 6; 0.7, 0.3), (3.5, 4, 5, 6.75, 7; 0.9, 0.4)] a˜ 13 = [(4, 4.5, 5, 5.75, 6.25; 0.7, 0.3), (3, 3.75, 5, 6.5, 7.5; 0.9, 0.4)] a˜ 21 = [(2, 3, 5, 6.5, 7.5; 0.7, 0.3), (0.5, 1, 5, 8.5, 9.5; 0.9, 0.4)]

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a˜ 22 = [(0.6, 0.8, 5, 5.2, 5.4; 0.7, 0.3), (0.2, 0.4, 5, 5.6, 5.8; 0.9, 0.4)] a˜ 23 = [(2.5, 3, 5, 5.5, 6; 0.7, 0.3), (1.5, 2, 5, 6.5, 7; 0.9, 0.4)] a˜ 31 = [(3.5, 4, 5, 5.5, 6.5; 0.7, 0.3), (2.5, 3, 5, 7, 7.5; 0.9, 0.4)]

Fig. 2. Flowchart for solving Game Problems

a˜ 32 = [(4, 4.5, 5, 5.5, 6; 0.7, 0.3), (3, 3.5, 5, 6.5, 7; 0.9, 0.4)] a˜ 33 = [(3.5, 4.5, 5, 6, 6.5; 0.7, 0.3), (2, 3, 5, 7, 7.5; 0.9, 0.4)] The fuzzy payoff values are changed into crisp values after applying the suggested ranking mechanism (F1) defined in Theorem 3.1, and the problem is reduced to a crisp game problem as follows: PlayerII ⎞ 10 10.56 9.98 A = PlayerI ⎝ 9.58 8.48 9.43 ⎠ 10.15 10 10.08 ⎛

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There is no saddle point in matrix A. The value of the Game is 10.07 units after using the dominance principle [4]. The fuzzy payoff values are changed into crisp values after applying the suggested ranking approach (F2) defined in Theorem 3.1, and the problem is simplified to the crisp game problem as follows: PlayerII ⎞ 5 4.91 5.01 A1 = PlayerI ⎝ 4.95 4.75 4.91 ⎠ 4.84 5 5.18 ⎛

There is no saddle point in matrix A. The value of the Game is 4.9424 units after using the dominance principle [4]. We discovered that every element in the matrix A1 is about half of the corresponding element in the matrix A after applying two formulas described in Theorem 3.1. ⎛ ⎞ ⎛ m11 m12 m13 ⎞ m11 m12 m13 2 2 2 Proposition 4.1 (i) If A = ⎝ m21 m22 m23 ⎠ then A1 ∼ = ⎝ m21 m22 m23 ⎠ m31 m32 m33 (ii) Value of the Game for A ∼ = Value of the2Game for A1

2 2 2 m31 m32 m33 2 2 2

5 Conclusion This article solves the matrix games with fuzzy payoffs extended to the level (g lower , g upper ) - Interval valued Pentagonal Fuzzy Payoffs. We use level (g upper ) - Interval lower , g valued Pentagonal Fuzzy numbers for the parameters instead of regular Fuzzy numbers. In this article, very first time, we introduced the Signed distance ranking formula to rank the Interval valued Pentagonal Fuzzy numbers. These IVPentFN are converted to crisp numbers using the Signed Distance Ranking method, and then solved using the dominance approach to provide the Optimal Strategies. This suggested strategy is also demonstrated with examples before the results are validated. In future, the proposed formulae can be applied to solve transportation and linear programming problems and also compare the results with other ranking methods.

References 1. Chakraborty, A., et al.: The pentagonal fuzzy number: its different representations, properties, ranking, defuzzification and application in game problems. Symmetry 248, 1–31 (2019) 2. Farhadinia, B.: Sensitivity analysis in interval-valued trapezoidal fuzzy number linear programming problems. Appl. Math. Model. 38, 50–62 (2014) 3. Jana, J., Roy, S.K.: Solution of matrix games with generalised Trapezoidal Fuzzy payoffs. Fuzzy Inf. Eng. 10(2), 213–224 (2018) 4. Kamal Nasir, V., Jamal Barakath, A.: Solving matrix games involving the level (Klower, Kupper) interval valued trapezoidal fuzzy payoffs: signed distance ranking approach. AIP Conf. Proc. 2385, 13004 (2022) 5. Khalifa, H.A., Masoud, M.: Solving two-person zero-sum games with interval-valued fuzzy payoffs. Int. J. Appl. Optim. Stud. 2(04), 1–8 (2019)

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6. Akbari, M.G., Hesamian, G.: Signed distance measures oriented to rank interval valued fuzzy numbers. IEEE Trans. Fuzzy Syst. 14(8), 3506–3513 (2015) 7. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

A Literature Review on Supplier Selection Problem and Fuzzy Logic Mert Paldrak(B)

, Gamze Erdem , Melis Tan Taco˘glu , Simge Güçlükol , and Efthimia Staiou

Industrial Engineering Department, Ya¸sar University, Bornova, ˙Izmir, Turkey {mert.paldrak,gamze.erdem,melis.tacoglu,simge.guclukol, effi.staiou}@yasar.edu.tr

Abstract. Given the recent increasing competition in global market, supplier selection and evaluation has attracted a great deal of attention especially at academic levels. Supplier selection problem is a complex problem since there exist a great number of unpredictable and uncontrollable factors which have a huge impact on decision-making process. Due to this complexity, there are several criteria that must be taken into consideration such as cost, quality, on-time delivery, proximity of suppliers, long-term relationship etc. Although some of these criteria (quantitative) can be expressed using pure numeric scales, some (qualitative) are linguistic due to the human assessments which contain some degree of subjectivity. Since involvement of human assessment causes vagueness for deterministic models, the authors apply fuzzy logic which enables the decision makers to be able to convert their linguistic expressions into fuzzy numbers with the help of fuzzy membership functions. Considering that fuzzy logic plays a vital role in solving multi-criteria supplier selection problem, this paper aims to present a review of supplier selection problem and its relation with fuzzy logic. In this paper, several studies that highlight supplier selection problem and the importance of fuzzy logic involvement in the problem have been reviewed. An analysis of multi-criteria decision-making methods for supplier selection problem is conducted. Keywords: Global market · Supplier selection problem · Multi-criteria decision making · Fuzzy logic

1 Introduction In now-a-day competitive market, an efficient management of supply chain is of an outsized importance in order for all companies to achieve their goals. Every company is supposed to have a better communication with other companies to be able to be helped for outsourcing when needed. The majority part of these companies is covered by suppliers which provide raw materials to production-oriented companies. Considering this fact, suppliers have always become an integral component of a company’s management policy. As companies are more dependent on their suppliers, a poor-decision making related to supplier selection is becoming more severe. Consequently, selection of the © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 339–351, 2022. https://doi.org/10.1007/978-3-031-09173-5_42

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appropriate supplier(s) is a big requirement for a company to sustain effective supply chain. Generally, the supplier selection problem is the issue of purchasing department which aims at procuring right product at the right cost with the right quantity at the right time from the right source. Whenever a supplier selection decision needs to be made, a set of evaluation criteria that can be utilized to compare candidate sources must be determined. The most basic criteria related to supplier selection are costs (including order placement, transportation), pricing strategy of suppliers, delivery time of raw materials, product or service quality, proximity of suppliers. In most of the cases, these criteria are conflicting and their importance may change from one purchase to another. This situation is more complex when some of the evaluation criteria are quantitative and some are qualitative. Due to the involvement of multi-criteria in decision making process, supplier selection problem is generally considered as a multi-criteria decision-making problem in the literature. In this study, the main objective is to construct a literature review framework about the supplier selection problem with fuzzy methods as solution procedures. In the existing literature about this topic, to the best of our knowledge, there is not a framework that includes solely fuzzy decision techniques to solve multi-criteria supplier selection problems. In Sect. 2, multi-criteria supplier selection problem is discussed, then in Sect. 3, supplier selection criteria are categorized and summarized. Next, in Sect. 4, the main idea behind the fuzzy logic is given. Then, in Sect. 5, solution methodologies for supplier selection problem and fuzzy logic are mentioned. Finally, in Sect. 6, concluding remarks and future directions are given.

2 Multi-criteria Supplier Selection Problem A supplier selection problem is inherently a multi-criteria problem in which mostly conflicting evaluation criteria are taken into account. Therefore, determination of criteria involved in the problem depends on the objective of the theoretical and empirical studies. The study of [1] determined 23 different criteria in order to evaluate the performance of suppliers processing responses from 170 managers and purchasing agents. Since the criteria involved in the supplier selection problem are important to final decision, the respondents are requested to specify the importance of each criterion on Likert scale and the average values over all the respondents are calculated in order to sort the criteria according to their degree of importance. Most of the studies related to supplier selection problem have benefited from the results of [1] and come up with various techniques to rank these attributes. A brief overview of the approaches for assessment of selection of suppliers are summarized in [2]. • Categorical Method: This method contains the attributes to be considered in the evaluation process. The performance of candidate suppliers is evaluated using categorical terms, namely “good”, “fair” and “poor”. The supplier with highest “good” rating is selected as the best one among others. The application of this technique is practical and it does not require an ample amount of data. Nonetheless, it largely depends on

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•

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personal judgement of the evaluators and the importance of criteria is assumed to be equal [3, 4]. Linear Weighted Average Method: This method considers allocating importance weight to each criterion. Then, the suppliers’ performance is evaluated by the evaluators with respect to each criterion. To calculate weighted score of each supplier, the supplier performance ratings are multiplied by the weight of each criteria. The total weighted score of each supplier is found by summing all weighted scores over all the criteria. The supplier having the highest total weighted score is selected. Due to the subjectivity of decision-maker involved in the weight assignment, it is an issue to be dealt with. Cost-Ratio Method: According to [3], this method is comparably more precise to the other methods since it considers the total costs related to such criteria as quality, delivery and service. Nonetheless, to be able to identify the precise cost data, a comprehensive cost-accounting system is necessary. Vendor Profile Analysis: This technique is applied by [5] and it is a modified version of weighted average method that aims to reduce the affect of uncertainty on the ratings of suppliers. In order to determine the ratings, a Monte Carlo simulation technique is employed to replace the ratings based on subjective judgements. Dimensional Analysis: In dimensional analysis, the evaluation process includes comparison of one-by-one of two suppliers [4, 6]. The dimensional analysis ratio can be lower or greater than 1. Although dimensional analysis seems reasonable, the process is rather time consuming, specially when number of suppliers is large. Vendor rating with AHP: According to [2], the difficulty of the aforementioned methods is the allocation of the weights to the criteria. Since these weights are determined solely based on the judgements of decision-maker(s), the evaluation of criteria is rather subjective. To surmount the difficulty due to the high subjectivity, researchers propose Analytical Hierarchy Process (AHP) where a systematic way for determining the attributes weights are determined by making a series of pair wise comparisons for all criteria [7–10].

The multi-criteria supplier selection problem focuses on selection of the best supplier among all alternatives considering evaluation criteria. To do so, the aforementioned rating techniques are employed to rank the candidate suppliers with respect to predetermined criteria. Consequently, determination of the evaluation criteria for supplier selection problem is of a paramount importance to the problem. The following section outlines the list of criteria mostly considered in the literature.

3 Supplier Selection Criteria In order to be able to evaluate the performance of suppliers, the firm needs to determine criteria that help see if the candidate suppliers have potential to satisfy the firm’s requirement. Consideration of more than one criteria in supplier selection process makes the selection complex and uncertain [11]. Based on the measurability of the criteria, they can be divided into two categories, namely quantitative and qualitative. Such criteria as cost criteria are quantitative whereas such criteria as environmental criteria are qualitative.

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Ware et al. (2012) [12] demonstrate widely used criteria and their sub-criteria having impact on supplier selection process, considering the criteria measurability. On the other hand, Kahraman et al. (2013) [13] use a grouping technique as below: Supplier-Oriented Criteria: These criteria are those criteria which are directly related to the performance of suppliers independent of the product or service provided. Supplier-oriented criteria aim to measure such aspects of suppliers as financial strength, management approach and capability, technical ability, support resources and quality. Product Performance-Oriented Criteria: Product performance criteria are those criteria which help firms evaluate the functionality and usability of the products that they purchase from their suppliers. However, determination of such criteria depends on the type of the product purchased. Product performance-oriented criteria is generally related to conformance to specifications [13]. Service Performance-Oriented Criteria: Service performance-oriented criteria are employed in order to evaluate the benefits provided by supplier services. Since evaluation of service is related to firm’s expectations, a clear definition of expectation plays a vital role for suppliers to establish service standards. Any purchase carried out by a firm also involves some degree of service, such as order processing, delivery and support after sale. Cost-Oriented Criteria: In order for a firm to maximize profit, the cost minimization is of a paramount importance in any process including supplier selection. Cost criteria consider elements of cost associated with the purchase made by the firm. The most remarkable elements of the costs attributed to a product are such expenses as purchase price, transportation cost, taxes that are taken into considerations during supplier selection process. Although some of the costs are foreseeable, such operational expenses transaction processing and cost of rejects require more effort to estimate. Consequently, obtention of reliable estimates of such costs should be involved for a higher level of supplier selection. Sustainability-Oriented Criteria: In most of the supplier selection problems, product, service and cost-oriented criteria are taken into account, however, these sort of criteria do not help the firms seeking to innovative supply chain management issues, especially those that focus on social and environmental concerns, namely sustainability [14]. Sustainable supplier selection process needs consideration of different attributes beyond those used in operational decisions. On the other hand, sustainability-oriented criteria are important especially when the suppliers supply critical products that may do harm on environment. Sustainability dimensions can be economic, social and environmental [15]. Table 1 recapitulates mostly considered criteria in supplier selection problem. Majority of the supplier selection problems focus on identification aforementioned supplier criteria and then usage of various methods to evaluate candidate suppliers. In most cases, the importance weights of criteria are determined and suppliers’ performances are calculated with respect to these criteria. However, both of these two factors depend on decision maker evaluation and should be solicited from the individuals [2].

A Literature Review on Supplier Selection Problem and Fuzzy Logic Table 1. Criteria considered in multi-criteria supplier selection problem Criteria Category Supplier-Oriented

Product Performance-Oriented

Criteria Supplier Properties

End Product-Related Criteria

Handling of Product Components-Related Criteria Other Considerations

Service PerformanceOriented

Customer Support

Customer Satisfaction Follow-up Professionalism Cost-Oriented

Purchase-Oriented Costs

Others SustainabilityOriented

Economic Social

Environmental

Sub-Criteria Financial Status Managerial Stability Technical Availability Support Resource Availability Quality Systems and Process Globalization and Localization Background and Reputation Qualification Reliability Durability Maintainability Compatibility Shelf-Life Packaging Store Requirements Performance Testability Manufacturability Availability On-time Delivery Recyclability Ergonomic Environmental-friendly Accessibility Responsiveness Flexibility Delivery Reliability Dependability Value-added service Information Sharing Information Reliability Accuracy Knowledge Attitude Commination Costs Ordering Cost Logistic Costs Documentation Costs Tariff and Taxes Import Cost Economic Acceptability Operational Acceptability Reduction in Late Delivery Working Hours Human Rights Safety Health Education Carrier Opportunities Energy Efficiency Green Image Pollution Consideration Gas Emission Consideration Reverse Logistics Green Purchasing Green Designing

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The evaluation is often conducted by asking the decision makers to express their preferences in pure numeric scales. The subjectivity and imprecision associated with the perception of decision-maker are lost due to the fact that they are obliged to use numeric scales. However, this difficulty is surmountable with the help of a mechanism that is capable of capturing the subjectivity in the expression of individual preferences. Subjectivity involved in human assessments and beliefs are best expressed using linguistic terms without numeric scales boundaries. The methodology that enables decisionmakers to express their preferences using linguistic terms is called fuzzy logic. Fuzzy set theory is a powerful tool for solving real life problems involving some degree of vagueness and ambiguity. In supplier selection problem, such criteria as quality, reliability, sustainability etc. are qualitative and they must be evaluated using linguistic terms. Due to the involvement of subjective criteria in multi-criteria supplier selection problem, fuzzy logic is coupled with solution methodologies to solve this problem. Consequently, the objective of this study is to demonstrate the necessity of usage of fuzzy logic in complex multi-criteria supplier selection problem.

4 Fuzzy Logic In many engineering applications, models are constructed based on deterministic or probabilistic data. However, in real-life decisions, especially if there are not sufficient historical data, decisions should be made similar to human reasoning. In a vague environment, Fuzzy Logic or Fuzzy Set theory is a good manner to handle uncertainties. This theory is firstly introduced by Lotfi A. Zadeh in 1965. Differently from the crisp variables that mostly consist of binary values, fuzzy variables can take more than two values. Membership functions are used to define membership degree of a variable to a fuzzy set. Membership functions can take values between 0 and 1. These values mostly defined after inference and defuzzification steps. In inference step, linguistic values can be sequenced and rated and then converted into crisp values by gathering data obtained from decision-makers. These decision-makers are usually experts in a particular area (i.e., the area in which decisions should be made). These steps in Fuzzy Logic is very similar to human judgement in real-life and can be applicable whenever data vagueness is encountered. Therefore, Fuzzy Logic is necessary to cope with models that comprise vagueness or uncertainty.

5 Solution Methodologies for Supplier Selection Problem and Fuzzy Logic In this section, a literature review is presented related to solution techniques coupled with fuzzy logic in order to solve multi-criteria supplier selection problem. The reviewed papers are divided into groups on the basis of fuzzy methods used for the different studies in the papers. These methods are summarized in the following sections.

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Fuzzy TOPSIS: Fuzzy TOPSIS is a method where the ratings of various alternative suppliers under different subjective criteria and the importance of weights of all attributes are evaluated with the help of linguistic variables represented by fuzzy variables. Most of the time, these linguistic variables are expressed in triangular fuzzy numbers. Based on the concept of the TOPSIS, the proximity related to closeness coefficient is defined to determine the ranking order of all suppliers by calculating the distances to the both fuzzy ideal solution (FPIS) and fuzzy negative ideal solution (FNIS) simultaneously. To select the best alternative, the weights are aggregated to make the final decision with respect to primary goal. A mathematical model of fuzzy-TOPSIS used for robot selection proposed by [16]. Fuzzy AHP: Analytical Hierarchy Process is a method used in multi-criteria decisionmaking problem developed by Saaty (1970) where a framework is provided in order to deal with both qualitative and quantitative decision-making criteria. Generally, AHP involves a hierarchy three which consists of three levels, namely goal, the criteria and the alternatives. For the multi-criteria supplier selection problem, the ultimate goal is to select the best supplier considering all criteria simultaneously. Fuzzy AHP is utilized when the some or all criteria need subjective assessment of decision-makers. The reason why authors consider fuzzy AHP is that it uses a solution methodology to supplier selection problem involving many intangible factors, but still requiring a logical and rational control decisions [7]. Fuzzy ANP: Supplier selection evaluation is based on quantitative and qualitative criteria and the priority order of the decision makers according to the criteria differs. Therefore, Fuzzy Analytical Network Process (FANP) is a technique used to determine criteria weight and their significance level [17]. For example, Razmi et al. [18] applied fuzzy ANP for appropriate supplier selection among four alternative suppliers with respect to six criteria; quality, finish time, company’s rank, company’s antecedents, and company’s economic status. In last decades, economic, environmental and social (sustainability) factors are considered while selecting sustainable supplier from four alternatives by ANP and TOPSIS techniques in sustainable supply chain management [19]. Fuzzy SMART: Smart is a technique to evaluate a wide variety of quantitative and qualitative criteria together by using the simple additive weight (SAW) method to collect sum of for each alternative value. This method sorts alternatives with respect to its preferences [20]. This method is used for selecting best supplier from three alternatives with five qualitative and quantitative criteria in the Taiwanese IT sector and it is concluded that SMART method is an appropriate tool for supplier selection problems [21]. Fuzzy Multi-objective Programming: Fuzzy multi-objective programming is employed in order to solve multi-objective supplier selection problem where subjective criteria are evaluated using linguistic variables. In most of the time, the considered objective functions are conflicting which cannot be optimized simultaneously [22].

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Fuzzy Quality Function Deployment: Quality function deployment (QFD) is a planning methodology for translating customer needs into appropriate product features. In QFD operation, relationship matrices are used for describing the relations between different customer needs, between different design requirements and between customer need and design requirement [23]. However, in fuzzy quality function deployment these relations are expressed using linguistic terms. Other Fuzzy Hybrid Techniques: In the literature, other such fuzzy hybrid techniques as fuzzy adaptive resonance theory (ART), logarithmic fuzzy preference programming (LFPP) are also employed to solve multi-criteria supplier selection problem. One can refer to [11] in order to learn more about solution techniques related to supplier selection problem. Table 2 demonstrates the summary of articles used fuzzy hybrid techniques to solve multi-criteria supplier selection problem. Table 2. Summary of Articles using fuzzy hybrid technique for MCSSP Article

Year

Criteria

Method

Boran et al. [24]

2009

Product quality, relation imminence, delivery performance, price

Fuzzy TOPSIS

Amin & Razmi [25]

2009

Accessibility, reliability, Fuzzy QFD security, speed, effective marketing and promotion, experience, financial power, management resolution, strategically association, support source, monthly salary, set-up fee, supply diversity

Razmi et al. [18]

2009

Quality, end time, degree of the company, background of the company, economic condition of the company, price

Lee [26]

2009

Flexibility, quality, delivery, Fuzzy AHP common growth, supplier’s technology, relation structure, relation cost, product cost, supply restriction

Wang et al. [27]

2009

Cost, key quality characteristics, service

Fuzzy Hierarchical TOPSIS

Onut et al. [28]

2009

Cost, references, product quality, delivery time, institutionalism, application time

Fuzzy ANP, Fuzzy TOPSIS

Fuzzy ANP

(continued)

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Table 2. (continued) Article

Year

Criteria

Method

Tuzkaya et al. [29]

2009

Environmental process management, pollution control, environmental and legal management, environmental costs, environmental image, environmental product

Fuzzy ANP Fuzzy PROMETHEE

Wei et al. [30]

2010

Quality, service, reliability, cost

Fuzzy ANP

Sen et al. [31]

2010

Cost, quality, service, reliability

Fuzzy AHP

Liao & Kao [32]

2011

Relation imminence, product quality, delivery skill, guarantee level, experiment process

Fuzzy TOPSIS

Buyukozkan & Ciftci [33]

2011

Time, cost, quality, flexibility

Fuzzy ANP

Vinodh [34]

2011

Work enhancement, convenience dimension, quality, service, risks

Fuzzy ANP

Wang & Chin [35]

2011

Economic factors, social factors, political conditions

Fuzzy Preference Programming

Amid et al.[22]

2011

Quality, net cost, service

AHP-max-min Fuzzy Programming

Kilincci & Onal [36]

2011

Supplier-oriented criteria & product performance-oriented criteria

Fuzzy AHP

Lin [37]

2012

Price, quality, delivery, technique

Fuzzy ANP Fuzzy MOLP

Kannan et al. [38]

2013

Cost, quality, delivery, technology capability, environmental competency

Fuzzy AHP Fuzzy TOPSIS

Nazari & Shirkouhi [39]

2013

A number of defective units, and late delivered units

Fuzzy Multi Objective LP

Rouyendegh et al. [40]

2014

Supply capacity, production, capacity, response time, production technology, price, warranty, procedural compliance, purchase transaction, communication system, quality, completed shipping document, quantity, on time delivery, financial position, location, reputation

Fuzzy TOPSIS Multi-Choice GP

(continued)

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Article

Year

Criteria

Method

Rezaei et al. [41]

2014

Cost/price, product quality, delivery, financial stability, assortment, corporate social

Fuzzy AHP

Junior et al. [42]

2014

Quality, price, delivery, supplier profile, supplier relationship

Fuzzy TOPSIS Fuzzy AHP

Dargi [17]

2014

Quality, price, production capacity, technical capability, service & delivery, reputation

Fuzzy ANP

Deshmukh & Sunnapwar [43]

2015

Quality, Environment Fuzzy AHP Performance Assessment, Green Manufacturing, Customer Co-operation, Green Cost, Green Design, Green Logistic

Nag & Helal [44]

2016

Quality, delivery, price, agility, Fuzzy TOPSIS service, profile

Shiraz et al. [45]

2017

Delivery, the amount of past business, reciprocal arrangements, warranties, geographical location

Fuzzy TOPSIS

Kumar et al. [46]

2018

Cost, delivery capabilities, quality of product, performance, reputation

Fuzzy TOPSIS

Rouyendegh et al. [47]

2019

Quality, cost, service & delivery, sustainability, technology, green manufacturing system, green supplier image, cooperation, green application, environmental management

Fuzzy TOPSIS

Ulutas et al. [48]

2019

Cost, defective rate, late Fuzzy Integrated Model delivery rate, technological capability, technical assistance, pollution control, environmental management, green transportation, green warehousing

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6 Conclusion As a result of high global competition, many firms have to deal with the pressure of reducing their total costs related to production or service in order to be competitive in the market. One of the ways to minimize production cost and maximize productivity is to select the best possible supplier among all alternatives. Consequently, supplier selection has been an important topic especially in academic level. As one of the multi-criteria decision-making problems, supplier selection problems are often encountered in supply chain management. Due to involvement of multi-criteria, the decision-maker should determine the convenient ones with respect to their objectives. Majority of the supplier selection models in the literature identify criteria and then use different techniques to evaluate alternative suppliers with respect to these criteria. Although some of these criteria are quantitative, some of them are qualitative which cannot be assessed using numeric scale. These qualitative criteria involve subjectivity of human assessment and they must be expressed in linguistic terms. Fuzzy logic is a technique that allows decisionmakers to evaluate subjective criteria via linguistic terms. Based on this, a literature framework about multi-criteria supplier selection problem by emphasizing fuzzy logic solution methods is constructed and presented in this study. As a future direction, studies highlighting the difference between implementing fuzzy and crisp methods on multicriteria supplier selection problems can be performed.

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Fuzzy C-Means Clustering of Ships Passing Through Turkish Straits Cengiz Vefa Ekici1,2(B) , Ozcan Arslan1 , and Ulku Ozturk2 1

Department of Maritime Transportation Engineering, Istanbul Technical University, Tuzla, Istanbul, Turkey 2 Turkish Naval Forces, Ankara, Turkey [email protected] Abstract. Maritime authorities not only have ensured reactive but also proactive measures in the straits, canals and narrow waterways with geographical restrictions and high traffic density to mitigate possible accident risks. These measures include a variety of approaches to conducting a realistic risk analysis. Considering the previous accidents, increasing traffic density and unique difficulties in the Turkish Straits, taking proactive measures to ensure their safety has become an important issue. Furthermore, a wide variety of ships navigating this waterway have been having difficulties in making good judgments. Therefore, this study has focused on the clustering of the ships in the Turkish Straits which can be deemed as the first step of realistic risk analysis in narrow waterways. Fuzzy C-Means clustering method has been employed, based on Sailing Plan-1 reports data between 2005 and 2021 in order to reveal maritime traffic characteristics for further analysis. Results have shown that three clusters are suitable for ship risk profile as a first step but an additional hierarchical layer may be needed to overcome the contradictory situations.

Keywords: Fuzzy clustering Turkish Straits

1

· Maritime safety · Narrow waterways ·

Introduction

Given the fact that 90% of world trade is carried by maritime transportation, safety at sea is a crucial aspect [1]. It consists of three fundamental components, namely safety of life, property and environment, and is ensured by mitigating risks to acceptable levels and by preventing marine accidents. Accident risks in maritime transport are higher in ports, inland waters or narrow waterways rather than open seas [2]. Especially, the safety of navigation in narrow waterways is a major concern for maritime authorities [3]. Geographically, geopolitically and economically, some narrow waterways have strategic importance and have come to a position that will seriously affect maritime trade [4]. The Turkish Straits, which can affect maritime trade and world oil transportation, are among the most dangerous narrow waterways in the world due to their geographical structure and traffic density [5]. Consisting of the Istanbul c The Author(s), under exclusive license to Springer Nature Switzerland AG 2022  C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 352–359, 2022. https://doi.org/10.1007/978-3-031-09173-5_43

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Strait, the Canakkale Strait and the Sea of Marmara, the Turkish Straits also demonstrate their importance as the only waterway connecting the Black Sea and the Mediterranean [6]. The increasing ship sizes and traffic density in parallel with the world trade on this waterway endanger the safety of the Straits [7]. Based on this requirement, various measures have been taken in the Turkish Straits. In the light of this information, it is apparent that reducing the risk to an acceptable level appears to be the most appropriate solution considering the maritime accidents, which cannot be prevented, and it has been evaluated that measures can be increased by implementing risk assessments. Taking into consideration the academic studies on the Turkish Straits, it can be clearly seen that there has not been an effective scientific study that will enable the ships to pass through the Straits with safety by calculating the potential risks of those ships. In order to minimize the risk of possible accidents and environmental pollution, it is crucial to monitor the ships and to ensure that the necessary measures are taken proactively by Turkish Straits Vessel Traffic Services (TSVTS). From this point of view, this study has focused on the patterns and the clustering of the ships in the Turkish Straits which can be deemed as the first step of realistic risk analysis in narrow waterways. Fuzzy C-Means clustering (FCM) method has been employed, based on Sailing Plan (SP)-1 reports data between the years 2005 and 2021 in order to reveal maritime traffic characteristics for further analysis. According to FCM results, we have obtained 3 clusters for further analysis of the Turkish Straits. Correspondingly, trends in data have been extracted and presented. Within the scope of the aforementioned information, this study is organized as follows. In Sect. 2, the literature review is expressed. SP-1 reports data examination is introduced in Sect. 3. In Sect. 4, the application of the FCM method is explained and in Sect. 5, results are assessed. In the last section, the conclusion is presented. SP-1 reports data were obtained from the Directorate General of Coastal Safety.

2

Literature Review

The identification of ships with high risk has great importance for navigational safety, and many studies conducted on this topic. In Degr´e’s [8] paper, the principles and purpose of risk models are explained and the ship risk index is proposed as a proactive risk assessment approach for further studies. In addition to this, in the study by Sage [9], it was emphasized that high-risk ships can be monitored with more sensitivity by Vessel Traffic Services (VTS) and proactive measures can be taken effectively in order to mitigate risks. In Kao’s [10] study, a decision support system for VTSs is proposed by stating that VTSs are not technically capable of ensuring safety in highly congested waters, and shall be supported. In order to ensure navigation safety, a fuzzy-based maritime risk assessment (MARISA) model that reveals the ship risk index is developed by Balmat [11], and ship parameters and environmental factors are utilized. In another study of

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Balmat [12], MARISA was updated with two more ship parameters to enhance the model. In Dinis’s [13] study, a static ship risk profile model was developed with a probabilistic approach using the ship risk profile parameters of the Paris MoU. In the study, it is also stated that with the help of this model, the capacity of VTSs to manage the maritime traffic risk, will greatly increase. Whilst reviewing the studies on the Turkish Straits, it is observed that statistical analysis of accidents, analysis of maritime traffic and risk assessment of the straits have been carried out generally. The majority of the studies were focused on the Istanbul Strait, which is geographically more challenging and dangerous, followed by studies on the Canakkale Strait. However, the number of studies regarding the Sea of Marmara is negligible.

3

Data Examination

Maritime risk analysis should be conducted specifically in the region due to the complexity of the maritime environment. Maritime regions are unique and data obtained from these regions may not be reliable due to introduced regulations and practices. In this respect, when the practices and regulations in the Turkish Straits are examined, it is seen that the Turkish Straits have unique characteristics and data constraints. For this study, the SP-1 report’s data between the years 2005 and 2021 were obtained, and as ship characteristics, age during the passage, length, breadth, draft, gross tonnage, maximum maneuvering speed, flag and personnel on board were selected (see Table 1). Chosen ship characteristics are numerical variables except for the ship flag, which is a categorical variable. In order to transform the ship flag into a numerical variable, the Paris MoU excess factor for flag categorization 2021 is used. Data cleaning is conducted, ship types are categorized as Tanker, Cargo, Container and Passenger ships, and other types of ships are excluded. Table 1. SP-1 reports data. Count

Mean

Std

Min

25%

50%

75%

Max

Length

512218 151.07

55.42

34.84

106.80 140.00 183.17 399.99

Breadth

512218 22.93

9.06

5.20

15.80

21.00

29.99

68.00

Maneuvering speed 512218 11.85

2.39

3.50

10.00

11.60

13.00

40.40

512218 17837.97 20860.46 142

3700

8995

25065

232618

Gross tonnage

Age during passage 512218 16.90

11.41

0

7

15

26

60

Draft

2.79

3.01

5.00

6.70

8.90

19.93

31.27

5

13

18

22

1372

1.57

−1.80 −1.46

−1.34

−0.58

5.00

512218 7.16

Personnel on board 512218 19.12 Flag factor

512218 −0.63

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Whereas the data is inspected thoroughly, it has been observed that the ship length, breadth and gross tonnage are highly correlated (see Table 2). Considering correlation analysis, ship length was utilized, and breadth and gross tonnage were excluded. Besides, in order to obtain wholesome results, the Shapiro-Wilk test was conducted as a normality analysis, and it was observed that the selected variables were not well fitted to normal distribution. Therefore, normality transformation (Box-Cox, etc.) has been applied to the whole data set. Notwithstanding these shortcomings, FCM clustering has been applied in order to classify ship risk profiles. As can be seen in Table 2, the mean of Flag Factor is −0.63 which indicates that ships, passing through Straits, are above the standard safety level (White flag). Table 2. Correlation analysis Length

Breadth Speed

Tonnage Age

Length

1.0000

0.9417

0.4779

0.9154

−0.3907 0.7384

0.1873

−0.2656

Breadth

0.9417

1.0000

0.4253

0.9168

−0.4171 0.7473

0.1543

−0.2870

Maneuvering speed 0.4779

0.4253

1.0000

0.3916

−0.3513 0.3353

0.1339

−0.3057

Gross tonnage

0.9168

0.3916

1.0000

−0.3561 0.7003

0.1984

−0.2371

0.9154

Age during passage −0.3907 −0.4171 −0.3513 −0.3561 1.0000

Draft

Personnel Flag

−0.3048 −0.0354

0.4758

0.7384

0.7473

0.3353

0.7003

−0.3048 1.0000

0.0860

−0.2474

Personnel on board 0.1873

0.1543

0.1339

0.1984

−0.0354 0.0860

1.0000

−0.0510

Draft Flag factor

4

−0.2656 −0.2870 −0.3057 −0.2371 0.4758

−0.2474 −0.0510

1.0000

Methodology

Revealing the clusters of ships passing through straits in order to enlighten further risk assessment studies is the primary aim of this study. Therefore, for revealing patterns and subdividing datasets into clusters based on similarities and dissimilarities, clustering methods were evaluated, and it was seen that in hard clustering methods, data is divided into different clusters, whereas in soft clustering methods, data points can potentially belong to multiple clusters. Given the complexity of the maritime environment, it was assessed that soft clustering methods are more suitable in a complex environment. Therefore, FCM clustering was selected as a proper method in this study. The FCM clustering algorithm was first developed for a special case by Dunn [14] and was generalized [15] and improved by Bezdek [16]. FCM objective function is presented below. argmin

n  c  i=1 j=1

 2 m xi − cj  wij

(1)

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where: wij =

1  2  xi −cj   m−1 c   k=1 xi −ck 

(2)

where wij represents the membership degree of ith data to j th cluster center, and m is fuzziness index. xi , cj is the  d-dimensional data and the d-dimensional cluster, respectively, and xi − cj  is the euclidean distance of ith data to j th cluster center. Briefly, this algorithm attempts to minimize the objective function by assigning fuzzy membership to each data point corresponding to each cluster center based on the euclidean distance between the clusters and the data points. Following the data cleaning process, in order to reveal the patterns, the firstly fuzzy partition coefficient was calculated. Two clusters have the highest fuzzy partition coefficient as can be seen in Fig. 1. However, two clusters may lead to some management misunderstandings. It has been assessed that 3 clusters may provide more applicable results rather than 4 or 5 since the fuzzy partition coefficient of 3 clusters is relatively more close to that of 2. Therefore, FCM was utilized with 3 cluster centers, which was determined considering the high-risk ship, standard risk ship and low-risk ship categories as also used in the ship risk profile by Paris MoU.

Fig. 1. Partition coefficient

5

Results and Discussion

In Table 3, it is observed that ship length is a dominant feature which is a crucial attribute of ships in the view of safety issues, as expected. As a result of the scale economy, ships have been built in larger sizes more and more. Therefore, there is a negative correlation between length and age during the passage, new ships are larger and old ships are smaller as a comparison.

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Table 3. Explanatory data of clusters Cluster 1

Count

Length

247849 105.06 18.78 34.84

Mean

Std

Min

50%

89.90

105.94 119.10 142.42

75%

Max

Maneuvering speed 247849 10.63

1.82

9.50

10.50

12.00

30.00

Age during passage 247849 21.77

11.93 0.00

11.00

23.00

31.00

60.00

Draft

19.32

247849 5.26

3.50

25%

1.46

3.01

4.00

5.00

6.30

Personnel on board 247849 13.65

4.64

5.00

11.00

13.00

16.00

307.00

Flag factor

247849 −0.19

1.85

−1.80

−1.34

−1.13

0.63

5.00

Cluster 2

Count

Std

Min

25%

50%

75%

Max

Length

195899 173.08 18.34 127.44 157.12 177.5

Mean

Maneuvering speed 195899 12.72

2.10

Age during passage 195899 13.17

9.07

0.00

Draft

2.09

3.02

195899 8.23

Personnel on board 195899 21.92

4.00

16.24 5.00

11.40

185.22 216.00

12.50

14.00

40.40

6.00

11.00

20.00

58.00

6.60

8.10

9.90

19.93 1123.00

19.00

21.00

23.00

Flag factor

195899 −0.99

1.19

−1.80

−1.54

−1.40

−0.97

5.00

Cluster 3

Count

Mean

Std

Min

25%

50%

75%

Max

Length

68469

254.67 30.94 176.20 228.60 246.83 274.40 399.99

Maneuvering speed 68469

13.78

2.59

5.00

12.00

13.06

15.30

28.25

Age during passage 68469

9.98

7.09

0.00

4.00

9.00

14.00

55.00

Draft

3.2

8.64

10.90

12.90

18.00

21.00

23.00

25.00

1372.00

−1.63

−1.46

−1.34

5.00

68469

10.93

2.73

Personnel on board 68469

30.96

78.82 5.00

Flag factor

−1.24

0.81

68469

−1.80

Ship length and age during passage are depicted in Fig. 2 to demonstrate the boundaries of clusters. Data is color-scaled with membership degrees to determine the boundaries of clusters. Fuzzy boundaries of ship length are approximately 140 and 210 m. These values demonstrate consistency with the Turkish Straits “Large vessel” (ship larger than 200 m) and “Vessels having difficulties navigating within Traffic Separation Scheme” (ship larger than 150 m) definitions. Owing to the dominance of ship length, boundaries of clusters have been observed distinctly. However, boundaries for other parameters cannot be detected clearly due to the complexity of multidimensional clustering. Furthermore, age during passage doesn’t have any influence on ship length for determining fuzzy clusters since the low membership degree region doesn’t change as the age during passage changes according to Fig. 2. Age during passage is decreasing as the ship length is increasing according to fuzzy clustering results. As a general acceptance in the maritime domain, larger ships indicate high risk than small ships, especially in narrow waters. However, our results show that the flag factor indicates more reliable ships as the ship length increases which leads us to a contradictory outcome. Therefore, it has been assumed that each cluster should be analyzed independently in case of any ship risk profile analysis.

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Fig. 2. Ship length vs Age during passage

6

Conclusion

It is aimed to reveal the patterns and cluster number of ships passing through the Turkish Straits, which is one of the most dangerous narrow and congested waterways in the world with its economic and geopolitical importance. The main contribution of this study is to reveal the cluster number of ships for narrow waterways. It has been seen that the number of clusters determined in this study is consistent with not only the Paris MoU ship risk profile cluster number but also the classification scheme of Turkish Authorities. The proposed cluster size can lead us to understand the pattern in the straits. Furthermore, it is observed that there are no clear fuzzy boundaries in features except ship length, which lead ship risk assessment to become difficult. Taking into account other features such as Paris MoU inspection results (Deficiencies, detentions, etc.) can give more in-depth results. In this manner, new risk assessment approaches can be launched according to these data. Therefore, including port state control data and other additional characteristics with hierarchical or any other approaches can be considered for future studies. Acknowledgements. The article is produced from the Ph.D. thesis research of Cengiz Vefa Ekici entitled “Developing Ship Risk Profile Model for Turkish Straits” which has been executed in a Ph.D. Program in Maritime Transportation Engineering of Istanbul Technical University Graduate School.

References 1. AGCS: Safety and Shipping Review 2021. Allianz Global Corporate & Specialty (2021). https://www.agcs.allianz.com/content/dam/onemarketing/agcs/ agcs/reports/AGCS-Safety-Shipping-Review-2020.pdf ¨ ˙ Altıok, T.: Comprehensive scenario analysis for mitigation of 2. Ozba¸ s, B., Or, I., risks of the maritime traffic in the Strait of Istanbul. J. Risk Res. 16, 541–561 (2013). ISSN: 1366-9877 3. Li, S., Meng, Q., Qu, X.: An overview of maritime waterway quantitative risk assessment models. Risk Anal. Int. J. 32, 496–512 (2012). ISSN: 0272-4332

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4. Rodrigue, J.P.: Maritime transport. In: International Encyclopedia of Geography: People, the Earth, Environment and Technology: People, the Earth, Environment and Technology, pp. 1–7 (2016) 5. UEIA: World Oil Transit Chokepoints. US Energy Information Administration (2017). https://www.eia.gov/international/analysis/special-topics/World Oil Transit Chokepoints 6. K¨ ose, E., et al.: Simulation of marine traffic in Istanbul Strait. Simul. Model. Pract. Theory 11, 597–608 (2003). ISSN: 1569-190X ¨ Erol, S., Ba¸sar, E.: The analysis of life safety and economic loss in 7. U˘ gurlu, O., marine accidents occurring in the Turkish Straits. Marit. Policy Manag. 43, 356– 370 (2016). ISSN: 0308-8839 8. Degr´e, T., Glansdorp, C., van der Tak, C.: The importance of a risk based index for vessels to enhance maritime safety. IFAC Proc. Vol. 36, 185–189 (2003). ISSN: 1474-6670 9. Sage, B.: Identification of ‘High Risk Vessels’ in coastal waters. Marine Policy 29, 349–355 (2005). ISSN: 0308-597X 10. Kao, S.L., et al.: A fuzzy logic method for collision avoidance in vessel traffic service. J. Navig. 60, 17–31 (2007). ISSN: 1469-7785 11. Balmat, J.F., et al.: MAritime RISk Assessment (MARISA), a fuzzy approach to define an individual ship risk factor. Ocean Eng. 36, 1278–1286 (2009). ISSN: 0029-8018 12. Balmat, J.F., et al.: A decision-making system to maritime risk assessment. Ocean Eng. 38, 171–176 (2011). ISSN: 0029-8018 13. Dinis, D., Teixeira, A.P., Guedes Soares, C.: Probabilistic approach for characterising the static risk of ships using Bayesian networks. Reliab. Eng. Syst. Saf. 203, 107073 (2020). ISSN: 0951-8320 14. Dunn, J.C.: A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters (1973) 15. Bezdek, J.C.: Fuzzy-mathematics in pattern classification. Cornell University (1973) 16. Bezdek, J.C.: Models for pattern recognition. In: Pattern Recognition with Fuzzy Objective Function Algorithms. AAPR, pp. 1–13. Springer, Boston, MA (1981). https://doi.org/10.1007/978-1-4757-0450-1 1

Applying Fuzzy Decision Tree Method for Hypertension Classification in Adolescent Hizir Sofyan1

, Elfayani Elfayani1 , Azalya Rahmatika2(B) and Irvanizam Irvanizam3

, Marzuki Marzuki1

,

1 Department of Statistics, Universitas Syiah Kuala, Darussalam 23111, Indonesia {hizir,marzuki}@unsyiah.ac.id, [email protected] 2 Department of Mathematics, University of Syiah Kuala, Darussalam 23111, Indonesia [email protected] 3 Department of Informatics, Universitas Syiah Kuala, Darussalam 23111, Indonesia [email protected]

Abstract. As the number of hypertension patients in adolescents continues to grow in Banda Aceh, the local office of health services has a large amount of data on hypertensive medical records. However, these data are only to count the growth of patients and there is no model for using these data for developing an intelligence analysis tool. With applying the concept of fuzzy sets in artificial intelligence and deep learning, the fuzzy decision tree method was designed by combining the fuzzy set concept and decision tree approach. In this paper, we developed a model to determine the best number of rules based on the fuzzy decision tree model. In addition, we also determine the highest accuracy value to get the best model. We classified the data correspondent into two adolescent groups which are teenagers aged from 12–17 years old and 18–23 years old. The result shows that the model obtained 79 rules for respondent data aged 12–17 years old and 60 rules for respondent data aged 18–23 years old at the value of θr by 85% and the value of θn by 3% and 5%. The highest accuracy value obtained was 87.18% for respondent data aged 12–17 years old and 87.50% for respondent data aged 18–23 years old. The classification results show that 20% of respondents suffer from hypertension, 12% suffer from stage 1 hypertension, and 2% suffer from stage 2 hypertension. Keywords: Fuzzy decision tree · Hypertension · Fuzzy sets

1 Introduction Data mining is a process of extracting and determining patterns from large databases. There are 2 (two) types of prediction models, called classification and regression [1]. Decision tree is often used in classification method [2]. Fuzzy decision tree (FDT) is an extension of a decision tree that uses fuzzy set as a solution to the classification problem that is fuzzy and ambiguous. This method utilizes fuzzy entropy and a learning process. If the learning process of the FDT stops until all sample data has same class, the accuracy © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 360–368, 2022. https://doi.org/10.1007/978-3-031-09173-5_44

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will be decreased. To increase the accuracy value, the learning process can be stopped early using the fuzziness control threshold (θr ) and leaf decision threshold (θn ) [3]. One of the uses of the FDT method is in the process of determining the classification of hypertension. Hypertension is a condition when blood pressure in blood vessels increases chronically. Nationally, hypertension prevalence rate reached 34,1% in 2018. South Kalimantan Province has a higher prevalence rate compared to other provinces, which is 44,13%. While Papua has a lower prevalence rate among other provinces, which is 22,22%. Aceh is one of the provinces with a low prevalence of 26,45% or around 12.259 cases [4]. Many studies discuss the use of FDTs in the health sector. One of them is done by Umano et al. (2018) concerning the classification of hypertension risk using an iterative dichotomer 3 FDT. Classification of the risk of hypertension is based on age, blood pressure, abdominal circumference, height, weight, body mass index, smoking, sugar consumption, salt consumption, exercise, and caffeine consumption. Other research on FDTs was conducted by Romansyah et al. (2009). They discussed about the use of FDT with ID3 algorithm in diabetes data. The resulting accuracy value is 94,15% with fuzziness control threshold (θr ) = 75% and leaf decision threshold (θn ) = 8% or 10%. This study aims to determine the optimal number of rules to predict hypertension classification so that a high accuracy and adaptation model is used to predict hypertension based on age, systolic blood pressure, height, weight, and body mass index. The leftover of this paper is organized as follows. Section 2 provides literature review. Section 3 explains material and method used in this research. Section 4 address discussion and analysis. Finally, some conclusions and future studies are discussed in Sect. 5.

2 Literature Review Algorithm Iterative Dichotomicer 3: Iterative Dichotomicer 3 (ID3) is the most basic decision tree algorithm. ID3 was first defined by Quinlan (1986) which was used to induce a decision tree. This algorithm can be used on all categorical data, either numerical or ordinal [1]. The work steps of the ID3 algorithm are as follows: (1). Begins from the root node; (2). For all variables, compute all entropy values for all samples (training data) on the node; (3) Calculate information gain of each variable; (4). Choice the variable that has the largest information gain value; and (4). Formulate a node that contains these variables and is used as a branch and repeat the procedures of determining information gain will continue until all data is included in the class. The selected variable is no longer included in the information gain calculation. Fuzzy Entropy and Information Gain: Information gain is a value obtained statistically and used to specify attributes. Information gain is used in the ID3 algorithm as a measure of research attributes. The attribute with the highest acquisition of information is selected as the separating attribute [6]. An entropy is used to define the information gain value. The entropy value is formulated as follows (1): n Pi Log2 (Pi ) (1) Hs (S) = − i=1

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where Pi is the opportunity of the Ci class in the sample set S = {x1 , x2 , …, xn }. n is the number of categories S as (2). k j=1 xj ∈ Ci (2) Pi = S where k is the amount of data. xj is the data in the set S. Information gain is the result of reducing the entropy of the sample set after dividing the size of the sample set by the number of attributes [7] as defined as (3): G(S, A) = H (S) −

n v=1

|Sv | H (Sv ) |S|

(3)

with weights Wi = |S|S|v | is the ratio of the data with category v in the sample set. A is a category in the set S and Sv is the number of cases in the v-category. In the fuzzy data set, it exists an adjustment procedure to compute entropy values for categories and information gain due to the presence of fuzzy data expressions [5] as depicted as (4). n Pi Log2 (Pi ) (4) Hf (S) = Hs (S) = − i=1

To determine the fuzzy entropy and gain information of an attribute in the ID3 algorithm the following equation is used: C n C j μij j μij Hf (S, A) = − log2 (5) i=1 S S n |Sv | Hf (S) = Hf (S) − (6) Hf (Sv , A) v=1 |S| where μij is the membership value of the j-th pattern for the i-th class. Hf (S) shows the entropy of the set S from the training data. | Sv | is the size of the Sv ⊆S subset of μij training data with category v. | S | indicates the size of the set S. Threshold in the Decision Tree: If the learning process of the FDT is completed until all data each has a class label, it will be result low accuracy [8]. To increase the value of accuracy, the learning process can be stopped early by using 2 (two) parameters, namely [3]: (1). Fuzziness control threshold (FCT)/θr . If the proportion of the data set from Ck class is greater than or equal to the threshold value θr , the learning process is stopped. (2). Leaf decision threshold (LDT)/θn . If the number of data set members in a node is smaller than the θn threshold, the learning process is stopped.

3 Materials and Method This study uses secondary data sourced from a nutrition survey of adolescents in the city of Banda Aceh. The data of this study consisted of 556 observations consisting of 310 female adolescents and 246 male adolescents. The variables used in this study were age, systolic blood pressure, height, weight, body mass index, and hypertension classification as provide in Table 1.

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Table 1. The descriptions of variable used in this research Variables Age

The membership function

Body Mass Index (BMI) Respondent 12-17 years Respondent 18-23 years old

Weight & Height

Blood Pressure

Respondent 12-17 years Respondent 18-23 years

Data that has been transformed into fuzzy sets (fuzzification) is divided into testing data and training data. Data sharing uses the k-fold cross validation method. The number of k used is 10. Data is divided into 10 different parts with the same amount. Every time one part is used as testing data, then nine other parts are used as training data.

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Fig. 1. The results of training data expansion are based on height variables

The process of forming a FDT uses the ID3 algorithm and consists of several stages. The steps for forming a FDT with ID3 algorithm are as follows. (1). Calculate fuzzy entropy from existing training data. From the calculation results obtained by fuzzy entropy value of 0.9182958, we used it to calculate the information gain of each variable. (2). Calculate information gain for each variable. Information gain from variables of age, height, weight, body mass index, and blood pressure respectively are 0.000084, 0.0918, 0.0291, 0.0400, and 0.0106. (3). Expand the training data based on body mass index variables to obtain the results as shown in Fig. 1. (4). Calculate the proportion value of each class that exists in each node. (5). In this example fuzziness control threshold (θr ) is 80% and leaf decision threshold (θn ) is 20%*15 = 3. (6). Expend existing sub-nodes until there is no more data that can be expanded or there are no more variables that can be used to expand trees when the sub-node does not meet the requirements of a given threshold. (7). Make fuzzy rules based on the tree that is formed. (8). Perform a fuzzy inference system based on the fuzzy rules obtained. (9). Calculate the accuracy value. Figure 2 and Table 2 shows the results of the FDT.

4 Discussion and Analysis Descriptive Analysis: The data used in this study were 556 adolescents in Banda Aceh who were aged between 12 years and 21 years. Data sourced from a survey of adolescent nutrition in the city of Banda Aceh. The percentage of respondents by gender was dominated by women by 55,76% (310 people). A total of 392 respondents (70,50%) in this study were teenagers aged 12 years to 17 years. Based on body mass index, weight, and height, the highest percentage was teenagers who had a normal body mass index (73,38%), normal weight (74,28%), and normal height (69,96%). In addition, 90,83% (505 people) had normal blood pressure.

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Fig. 2. Fuzzy decision tree for training data examples

Table 2. Classification rules for training data examples No. Rules 1

IF Height is low AND Body Mass Index is normal AND weight is lightweight AND Blood Pressure is normal AND Age is adolescent THEN Normal

2

IF Height is low AND Body Mass Index is normal AND weight is normal THEN Normal

3

IF Height is low AND Body Mass Index is overweight THEN Prehypertension

4

IF Height is low AND Body Mass Index is obese THEN Prehypertension

5

IF Height is normal AND Body Mass Index is normal AND weight is lightweight AND Blood Pressure is normal AND Age is adolescent THEN Normal

6

IF Height is normal AND Body Mass Index is normal AND weight is normal THEN Normal

7

IF Height is normal AND Body Mass Index is overweight THEN Normal

8

IF Height is normal AND Body Mass Index is obese THEN Prehypertension

9

IF Height is high THEN Prehypertension

Fuzzy Inferences System Mamdani: Transformation data that has been divided using the 10-fold cross validation method are subject to the same treatment based on the ID3 algorithm to carry out the training process. The training process is carried out 60 times. For each training data, the process is carried out 6 times by changing θ r three times namely 75%, 80%, and 85%, and for each θ n two times namely 3% and 5%. The average number of rules generated in the training process can be seen in Table 3. Table 3 shows that every time the value of θr increases, the number of rules produced will increase. It also shows that the most significant increase occurred when the value of

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θr was increased from 80% to 85%. This condition occurs due to at the time of training data expansion that was first carried out there were many sub-nodes which the proportion of one of the classes had reached values above 80%. Table 3. Rules avarages θr

12–17-year-old (θn )

18–23-year-old (θn )

3%

5%

3%

5%

75%

65

65

48

48

80%

65

65

50

50

85%

70

70

57

57

Based on these criteria, the model chosen is the result of training with a value of θr of 85% and a value of θN of 3% and 5% of the training data pair and the first testing data for respondent data aged 12–17 years with a total rule of 79. The resulting accuracy value of 87,18%. Whereas for respondent data aged 18–23 years old, the model chosen was the result of training with a value of θr of 85% and a value of θN of 3% and 5% of the sixth pair of training data and testing data with 60 rules. The model produced an accuracy of 87,50%. ID3 Performance Evaluation: Evaluation of the performance of the ID3 algorithm can be determined by calculating the average accuracy of the entire testing process on 10 different testing data. Table 4 show the performance evaluation of the ID3 algorithm at different θ r and θ n values. Table 4. ID3 performance evaluation θr

12–17-year-old (θn )

18–23-year-old (θn )

3%

5%

3%

5%

75%

79,84

79,84

69,36

69,36

80%

79,84

79,84

69,36

69,36

85%

80,22

80,22

69,65

69,65

The results of the classification of hypertension in adolescents using the FDT method can be seen in Fig. 3. Almost all respondents do not suffer from hypertension. It showed that 63% no hypertension or normal, 20% prehypertension, 1% experienced hypotension. 14% stage 1 hypertension, and 2% stage 2 hypertension.

Applying Fuzzy Decision Tree Method

14% 2%

367

1% Hipotensi Normal

20%

Prehipertensi

63%

Hipertensi Stage 1 Hipertensi Stage 2

Fig. 3. Classification hypertension result

5 Conclusion and Future Studies After conducting this research, we might summarize that: (1). The optimal number of rules for respondent data aged 12–17-year-old is 79 rules at θr value of 85% and θn values of 3% and 5%, whereas for respondent aged 18–23-year-old are 60 rules at θr value of 85% and θn values of 3% and 5%; (2). The highest accuracy value for respondent data aged 12–17-year-old is 87.18%, obtained at θr value of 85% and θn value of 3% and 5%. For respondent data aged 18–23-year-old, the highest accuracy value is 87.50% and 5% at θr value of 85% and θn value of 3% and 5%; (3). There are 20% of respondents suffering from prehypertension, 14% suffer from stage 1 hypertension, 2% suffer from stage 2 hypertension, and 63% do not have hypertension. This research still has a lot of flaws that can be improved in future studies. For instances, we can improve the model using the concepts of decision-making methods such as [6–9].

References 1. Prasetyo, E.: Data Mining Mengolah Data menjadi Informasi Menggunakan Matlab. ANDI, Yogyakarta (2014) 2. Han, J., Micheline, K., Jian, P.: Data Mining Concepts and Techniques Preface and Introduction. Third Edit, Morgan Kaufman, USA (2012) 3. Umano, M., et al.: Fuzzy decision trees by fuzzy ID3 algorithm and its application to diagnosis systems. In: Proceedings of the Third IEEE Conference on Fuzzy Systems, Orlando, pp. 2113– 2118. IEEE (1994) 4. Romansyah, F., Sitanggang, I.S., Nurdiati, S.: Fuzzy decision tree dengan algoritme ID3 pada data diabetes. Internetworking Indones. J. 1(2), 45–52 (2009) 5. Irvanizam, I., Zi, N.N., Zuhra, R., Amrusi, A., Sofyan, H.: An extended MABAC method based on triangular fuzzy neutrosophic numbers for multiple-criteria group decision making problems. Axioms 9(3), 104 (2020) 6. Irvanizam, I., Syahrini, I., Afidh, R.P.F., Andika, M.R., Sofyan, H.: Applying fuzzy multipleattribute decision making based on set-pair analysis with triangular fuzzy number for decent homes distribution problem. In: 2018 6th International Conference on Cyber and IT Service Management (CITSM), Parapat, pp. 1–7. IEEE (2018) 7. Irvanizam, I., Marzuki, M., Patria, I., Abubakar, R.: An application for smartphone preference using TODIM decision making method. In: 2018 International Conference on Electrical Engineering and Informatics (ICELTICs), Banda Aceh, pp. 122–126. IEEE (2018)

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8. Irvanizam, I, et al.: An improved EDAS method based on bipolar neutrosophic set and its application in group decision-making. Appl. Comput. Intell. Soft Comput. 2021, 1–16 (2021) 9. Irvanizam, I., Azzahra, N., Nadhira, I., Zulfan, Z., Subianto, M., Syahrini, I.: Multiple criteria decision making based on VIKOR for productive economic endeavors distribution problem. In: 2021 Sixth International Conference on Informatics and Computing (ICIC), Jakarta, pp. 1–6 (2021)

Action Selection Based on Fuzzy AHP-Based TOPSIS Method in Fuzzy FMEA-Based Risk Assessment: A Case Study Murat Oturakçı1 and Aziz Kemal Konyalıo˘glu2(B) 1 Industrial Engineering Department, Adana Alparslan Türke¸s Science and Technology

University, Adana, Turkey [email protected] 2 Management Engineering Department, Istanbul Technical University, Istanbul, Turkey [email protected]

Abstract. Today, risk assessment has become one of the most important applications of companies in the field of occupational health and safety. Many risk assessment types in the literature are applied by companies, and the objectivity of the results is very important in terms of worker, employer and environmental health. The aim of this study is to propose an objective risk assessment method and to prioritize the actions that can be taken as a result of the assessment. Hence, in this study, the hazards and the risks associated with those hazards that may arise in the production facility of a medium-sized company were determined as a first step. Then, these hazards were evaluated by the Fuzzy-Failure Mode and Effect Analysis (FMEA) method. As a result of the evaluation, alternative action plans for each hazard were determined together with the company team to eliminate the hazards in the highest risk group or minimize their damages. Since it is practically impossible for companies to take all the actions at the same time due to time, cost and labor constraints, the next part of the study includes which of the alternative actions should be applied to the hazards in the highest risk group. A Fuzzy AHPbased TOPSIS method was applied to prioritize actions. Thus, the actions to be taken against the hazards in the highest risk group were attempted to be chosen most appropriately with an objective approach. Keywords: Risk assessment · Fuzzy FMEA · Fuzzy AHP · TOPSIS · Action selection

1 Introduction Social sustainability and safety have been always one of the most crucial topics to investigate. Also, in the literature, employee, company and environmental safety during working hours should be reconsidered to develop occupational health and safety conditions. In this case, many factors are included in order to assess the total risk. Considering that there are different factors for assessing risk, actions should be taken into consideration to minimize the total risk. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 369–377, 2022. https://doi.org/10.1007/978-3-031-09173-5_45

370

M. Oturakçı and A. K. Konyalıo˘glu

In that case, during the production in facilities, employees face many hazards that threaten occupational health and safety. Considering that these hazards occur not only in production facilities but also in companies, hospitals and other workplaces, managers should sometimes take action immediately in order to prevent risks and failures for not only their safety but also employees’ safety. Nevertheless, it is not always clear to find the main risks and failures threatening occupational health and safety and to determine which risks should be minimized (De Cieri and Lazarova 2021). Thus, assessing risks is very important to take an action in the light of an analytic view and the fuzzy failure mode and effect analysis (FMEA) method is a very useful tool to consider failures and risks (Balaraju et al. 2019). In this study, it is aimed to propose an objective risk assessment method and to prioritize the actions that can be taken as a result of the assessment. In the content of the study, the hazards and the risks associated with those hazards that may arise in the production facility of a medium-sized company were determined as a first step. Then, these hazards were evaluated by the Fuzzy-FMEA method. As a result of the evaluation, alternative action plans for each hazard were determined together with the team in the company to eliminate the hazards in the highest risk group or to minimize their damages. Since it is practically impossible for companies to take all the actions at the same time due to time, cost and labor constraints, the next part of the study includes which of the alternative actions should be applied to the hazards in the highest risk group. A Fuzzy AHP-based TOPSIS method was applied to prioritize actions. Thus, the actions to be taken against the hazards in the highest risk group were attempted to be chosen most appropriately with an objective approach. This study has originality in terms of implementation and action selection prioritization by using a fuzzy-based risk assessment method by integrating the fuzzy AHP-TOPSIS approach. This study consists of five main parts which include respectively an introduction section to introduce a general view for assessing risks and occupational health, a literature review to provide the studies integrating risk management and fuzzy FMEA method, a methodology section to provide information about fuzzy FMEA approach, an application and discussion part to prioritize the risks in a medium-sized company by integrating fuzzy FMEA, Fuzzy AHP and fuzzy TOPSIS and finally a conclusion part to discuss and conclude the main results of the study.

2 Literature Review In the literature, there exist several studies combining risk assessment, fuzziness and FMEA approaches to integrate these different disciplines. Firstly, Tay and Lim (2006) used the fuzzy FMEA approach for guided rules reduction systems with the aid of general RPN rules and this system designed by fuzzy FMEA provides ease of use while rules are increasing. Chin et al. (2008) used the fuzzy FMEA method in order to propose an evaluation approach for new product development, including robustness and conceptual design. Abdelgawad and Fayek (2010) integrated fuzzy FMEA and Fuzzy AHP for measuring and evaluating construction risk factors. Furthermore, Kumru and Kumru (2013) applied Fuzzy FMEA approach in order to respectively develop the purchasing process in a hospital and then provide effective solutions for this problem. Wessiani

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371

and Sarwoko (2015) tried to use fuzzy FMEA for analyzing the risks in the poultry production process by considering the failures and 39 corrective risks. Another study about FMEA presented by Chanamool and Naenna (2016) provided an improvement in the working processes of an emergency department and a decrease in failures. On the other hand, Ahmadi et al. (2017) proposed a model by fuzzy FMEA by focusing on the fact that there exist many risks in highway construction projects and these risks can be reduced by fuzzy FMEA risk analysis. As one of the latest studies, Baykaso˘glu and Gölcük (2020) aimed to propose a fuzzy FMEA model integrating with classical multi-attribute decision-making methods in order to reduce ERP implementation risks. Gul et al. (2020) studied manufacturing risks focusing on the approach of FMEA and Bayesian Networks in the plastic manufacturing field. In 2021, Karatop et al. (2021) integrated fuzzy FMEA, EDAS and AHP to evaluate renewable energy investment risks and concluded that hydropower energy has the lowest risk potential. Furthermore, Zhou et al. (2021) developed a fuzzy FMEA approach by using grey theory, especially focusing on grey interaction vector, and by extending Choquet integral to propose a new extended fuzzy FMEA. Then, they applied this novel method to a case study including product developing processes’ risks.

3 Methodology and Application In this study, the fuzzy FMEA (failure mode and effect analysis) method has been selected to use for an objective risk assessment method and for prioritizing the actions that can be taken into consideration as a result of the assessment. Hence, in this study, the hazards and the risks associated with those hazards that may arise in the production facility of a medium-sized company were determined as a first step by using fuzzy FMEA. After applying the fuzzy FMEA method, an integrated Fuzzy AHP-based TOPSIS approach is used for action selection. The fuzzy FMEA method can provide a cause-effect relationship in a large perspective (Chin et al. 2008). Furthermore, the FMEA method can be accepted as one of the risk analysis methods suggested by U.S Department of Defense (U.S. Department of Defense 1980). In the application section, the steps are given in order to better understand the application. Step 1. Identifying the Hazards The hazards that may be encountered in the busiest workshop of a medium-sized production company and the risks arising from these hazards have been determined by a team established in the company and are presented in Table 1 below. Table 1 shows the hazards and risks for occupational health and safety in a medium-sized company accordingly.

372

M. Oturakçı and A. K. Konyalıo˘glu Table 1. Hazards and risks for occupational health and safety

# of hazard

Hazard

Risk

H1

Not using personal protective equipment (PPE)

Injury, occupational diseases

H2

Breakdown of electrical wiring

Injury, death

H3

An insufficient lighting system in the workshop

Injury

H4

Inadequate warning signs in the workshop

Injury

H5

Irregular storage of semi-finished products in the production area

Injury

H6

The close positioning of the machines in the workshop and the absence of separate compartments for workspaces

Injury

H7

Insufficient ventilation system

Injury, occupational diseases

H8

Frequent usage of sharp tools

Injury

H9

Not having a specific route for forklifts used in Injury, death the production area

H10

Careless use of some chemicals used during work

Injury, occupational diseases

Step 2. Assessing Hazards with Fuzzy FMEA In Step 2, a fuzzy FMEA scale was formed based on the classical FMEA scale (which has 10 values in each parameter) and was coded using the Fuzzy Logic Designer Tool in MATLAB. Occurrence (O), Severity (S) and Detectability (D) parameters were provided as inputs, and the RPN was the output. The fuzzy design developed in this study is presented in Fig. 1. As illustrated in Fig. 1, the ‘Mamdani min max’ method was used in the study. Three inputs (O, S, D) and an output (RPN) include five levels where the triangular membership function was used. Membership plot functions of the inputs and output are presented in Figs. 2 and 3. The triangular membership function consists of the levels of very low, low, medium, high and very high where the values generated by the fuzzy FMEA scale are provided in Table 2.

Fig. 1. Fuzzy FMEA design (Da˘gsuyu et al. 2016)

Action Selection Based on Fuzzy AHP-Based TOPSIS Method

373

Fig. 2. Membership plot functions of occurrence & severity & detectability inputs (Da˘gsuyu et al. 2016)

Fig. 3. Membership plot functions of “RPN” output (Da˘gsuyu et al. 2016)

Table 2. Fuzzy scale of the inputs Class definition

Fuzzy number

Very low

(0, 1, 3)

Low

(1, 3, 5)

Medium

(3, 5, 7)

High

(5, 7, 9)

Very high

(7, 9, 10)

Considering the five levels of O, S and D inputs, 125 decision rules were formed for the design according to the evaluation team opinions who were responsible for identifying the risks in the first step. According to the developed decision rules, Fuzzy RPN classes were calculated and decided. In Table 3, Fuzzy FMEA results are presented.

374

M. Oturakçı and A. K. Konyalıo˘glu Table 3. Fuzzy FMEA results # of hazard

O

S

D

Fuzzy RPN class

H1

5

5

5

Medium

H2

5

8

5

High

H3

7

3

7

High

H4

7

6

5

High

H5

7

5

3

Medium

H6

5

7

7

High

H7

6

6

6

High

H8

4

4

5

Low

H9

4

3

4

Low

H10

3

7

4

Medium

When the Fuzzy RPN Classes are shown in Table 3 are evaluated; half of the 10 hazards resulted in a “High” level. Additionally, it is seen that 3 hazards are calculated at the “Medium” level and 2 hazards at the “Low” level. In risk assessment studies, starting from the highest class, it is expected that all hazards will be eliminated or their harmful effects will be minimized. However, considering the constraints of the company such as cost, labor, resources, materials, etc., it is not possible to eliminate all the hazards in order of importance. Since the action plans of the risks in the “High” risk group depend on the operational constraints, the actions within the relevant class should be prioritized. Hence, to determine the actions to be taken, the risks in the “High” class were considered and prioritization steps were carried out among the actions to be taken for these risks. Step 3. Defining actions for risks in the “High” Risk group The hazards in the same group and the possible actions that can be taken for the risks arising from these hazards have been determined by the expert team and are presented in Table 4. Table 4. Defined actions for the high-risk class hazards # of hazard

Hazards in high-risk class

Possible action

H2

Breakdown of electrical wiring

A1. Changing the Electrical Installation and creating the periodic control plan

H3

An insufficient lighting system in the workshop

A2. Inclusion of additional lighting system

H4

Inadequate warning signs in the workshop

A3. Hanging warning signs in appropriate places

H6

The close positioning of the machines in the workshop and the absence of separate compartments for workspaces

A4. Redesign of workshop space and grouping of workspaces

H7

Insufficient ventilation system

A5. Installing the new ventilation system and creating a periodic control plan

Action Selection Based on Fuzzy AHP-Based TOPSIS Method

375

Step 4. Action Selection An integrated Fuzzy AHP-based TOPSIS approach is used for action selection. First, according to the Fuzzy FMEA results, the weights of the five hazards in the high-class range were calculated with the Fuzzy AHP to be integrated into the TOPSIS application, and these values are shown in Table 5 below. Table 5. Fuzzy AHP weights of hazards Criteria

Fuzzy AHP weight

H2

0,2459

H3

0,1799

H4

0,1999

H6

0,2165

H7

0,1579

At the last stage of the study, action selection was carried out using the Fuzzy AHPbased TOPSIS method. Taking an action can not only minimize a hazard or its damages but also reduce the damage in other hazards. Rows in the decision matrix are actions (choices); columns are considered as hazards (indicators) and decision matrix values are assigned accordingly. After the calculations involving the TOPSIS steps are performed, the final weights of the actions are presented in Table 6. Table 6. Action weights of F-AHP based TOPSIS method Possible action

F-AHP based TOPSIS weight

Changing the Electrical Installation and creating the periodic control plan

0,4878

Inclusion of additional lighting system

0,3001

Hanging warning signs in appropriate places

0,3666

Redesign of workshop space and grouping of workspaces

0,3719

Installing the new ventilation system and creating a periodic control plan

0,3074

According to Table 6, “Changing the Electrical Installation and creating the periodic control plan” should be the first action to be taken. Afterward, actions A4, A3, A5 and A2 should be implemented by the company, respectively. Ultimately, action prioritization among hazards within the same risk class has been completed. Thus, it is expected that the company will continue with a more efficient production with a minimum hazard effect.

376

M. Oturakçı and A. K. Konyalıo˘glu

4 Conclusion The importance of occupational health and safety increases day by day and the working conditions force managers and workers to minimize the risks. It is not always clear how to assess the risks in facilities and companies and how to minimize the risks to protect workers’ safety. Furthermore, the risks and hazards change based on the working place, each and every working place generally does not have the actions to take according to the predetermined risks and hazards. In this study, the fuzzy AHP-TOPSIS based FMEA method is proposed to determine and prioritize the hazards and risks and to focus on action plans which should be taken into consideration. It is known that fuzzy FMEA is a widely used technique to determine the hazards and risks but in a medium-sized company, as a case study, the hazards, risks and action plan have been determined in this study to provide a perspective. On the other hand, the Breakdown of electrical wiring is seen as the most important hazard in the selected medium-sized company and Changing the Electrical Installation and creating the periodic control plan has been selected as the most important action to take. In future studies, different fuzzy sets, such as spherical or Pythagorean sets, can be used and several hazards, risks and action plans can be added to prioritize the risks. In addition, it is planned to conduct comparative studies with different fuzzy-based risk assessment methods in future studies.

References Abdelgawad, M., Fayek, A.R.: Risk management in the construction industry using combined fuzzy FMEA and fuzzy AHP. J. Constr. Eng. Manage. 136(9), 1028–1036 (2010) Ahmadi, M., Behzadian, K., Ardeshir, A., Kapelan, Z.: Comprehensive risk management using fuzzy FMEA and MCDA techniques in highway construction projects. J. Civ. Eng. Manag. 23(2), 300–310 (2017) Balaraju, J., Raj, M.G., Murthy, C.S.: Fuzzy-FMEA risk evaluation approach for LHD machine–a case study. J. Sustain. Min. 18(4), 257–268 (2019) Baykaso˘glu, A., Gölcük, ˙I: Comprehensive fuzzy FMEA model: a case study of ERP implementation risks. Oper. Res. Int. J. 20(2), 795–826 (2020). https://doi.org/10.1007/s12351-0170338-1 Chin, K.S., Chan, A., Yang, J.B.: Development of a fuzzy FMEA based product design system. Int. J. Adv. Manuf. Technol. 36(7), 633–649 (2008) Chanamool, N., Naenna, T.: Fuzzy FMEA application to improve decision-making process in an emergency department. Appl. Soft Comput. 43, 441–453 (2016) Da˘gsuyu, C., Göçmen, E., Narlı, M., Kokangül, A.: Classical and fuzzy FMEA risk analysis in a sterilization unit. Comput. Ind. Eng. 101, 286–294 (2016) De Cieri, H., Lazarova, M.: Your health and safety is of utmost importance to us: a review of research on the occupational health and safety of international employees. Hum. Resour. Manage. Rev. 31(4), 1–30 (December 2021), 100790 Gul, M., Yucesan, M., Celik, E.: A manufacturing failure mode and effect analysis based on fuzzy and probabilistic risk analysis. Appl. Soft Comput. 96, 106689 (2020) Karatop, B., Ta¸skan, B., Adar, E., Kubat, C.: Decision analysis related to the renewable energy investments in Turkey based on a Fuzzy AHP-EDAS-Fuzzy FMEA approach. Comput. Ind. Eng. 151, 106958 (2021) Kumru, M., Kumru, P.Y.: Fuzzy FMEA application to improve purchasing process in a public hospital. Appl. Soft Comput. 13(1), 721–733 (2013)

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Tay, K.M., Lim, C.P.: Fuzzy FMEA with a guided rules reduction system for prioritization of failures. Int. J. Qual. Reliab. Manag., 1047–1066 (2006) U.S. Department of Defense: “Military standard—Procedures for performing a failure mode effects and criticality analysis. 2.” MIL-STD-1929A, Washington, D.C (1980) Wessiani, N.A., Sarwoko, S.O.: Risk analysis of poultry feed production using fuzzy FMEA. Procedia Manuf. 4, 270–281 (2015) Zhou, J., Liu, Y., Xiahou, T., Huang, T.: A novel FMEA-based approach to risk analysis of product design using extended Choquet integral. IEEE Trans. Reliab., 1–17 (2021)

Forecasting Crop Yields Based on Fuzzy Analysis of the Dynamics of Remote Sensing Multispectral Data Elchin Aliyev

and Fuad Salmanov(B)

Institute of Control Systems of ANAS, Vahabzadeh str., 9, AZ1141 Baku, Azerbaijan [email protected]

Abstract. Modern technologies for satellite monitoring of the Earth’s surface provide agricultural producers with useful information about the health status of crops. The remote sensor’s ability to detect subtle differences in vegetation makes it a useful tool for quantifying variability within a given field, estimating crop growth, and managing land based on current conditions. Remote sensing data, collected on a regular basis, allows producers and agronomists to draw up a current vegetation map that reflects the condition and strength of crops, analyze the dynamics of changes in plant condition, and predict yields in a particular area under crops. To interpret these data, the most effective means are various vegetation indices calculated empirically, that is, by operations with different spectral ranges of satellite monitoring multispectral data. Based on the time series of one of these vegetation indices, the paper considers the annual dynamics of the development of a plant culture in a particular field. The possibility of predicting the yield of the given crop is considered based on fuzzy modeling of time series for the corresponding spectral ranges of vegetation reflection obtained from satellite monitoring images. The proposed fuzzy models of time series are investigated for adequacy and suitability in terms of analyzing the features of the intra-annual of average long-term dynamics of the vegetation index, typical for the given area under crop. Keywords: Crop · Multispectral reflection of plants · Vegetation index · Fuzzy set · Fuzzy time series

1 Introduction Most agricultural crops are characterized by changes in the phases of development, which is reflected in the dynamics of the spectral-reflective properties of plants. The study of seasonal and long-term changes in the spectral-brightness characteristics of crops is possible through the analysis and modeling of the dynamic series of vegetation indices, which makes it possible to quantify the features of the vegetation cover and the regularity of its temporal dynamics. At the same time, standard algorithms for solving problems of predicting the dynamics of the spectral-reflective properties of plants work, as a rule, with “crisp” or structured data from satellite sensing of the Earth, that is, with © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 378–386, 2022. https://doi.org/10.1007/978-3-031-09173-5_46

Forecasting Crop Yields Based on Fuzzy Analysis of the Dynamics

379

data presented in the form of averaged numbers. Therefore, averaging the results of measurements of spectral ranges for calculating vegetation indices is one of the most common empirical operations in data collection systems for accurate agriculture. In particular, the achievement of the required accuracy in the process of averaging the values of vegetation indices is achieved by multiple measurements, where the results of individual measurements are partially compensated for by positive and negative deviations from the exact value. At the same time, the accuracy of their mutual compensation improves with an increase in the number of measurements, since the average value of negative deviations in modulus verge towards the average value of positive deviations. Nevertheless, multispectral satellite monitoring data, for example, the values of spectral ranges should be considered as weakly structured, that is, those that are known to belong to a certain interval [1]. For example, the region of maximum reflection of plant cell structures is in the wavelength range from 750 nm to 900 nm, which is the near infrared region of the electromagnetic spectrum. More adequate reflections of weakly structured spectral ranges can be evaluative concepts of the type “high”, “low”, etc., which can be formally described by the corresponding fuzzy sets as the terms (values) of the linguistic variable “spectral reflectivity of plants” [2]. Based on this premise, it becomes obvious the importance and relevance of studying methods for predicting seasonal and long-term changes in agricultural crops in spectral-brightness characteristics using fuzzy time series (FTS) of satellite monitoring indicators relative to spectral ranges.

2 Problem Definition Existing approaches to the calculation of vegetation indices are usually based on two independent parts of the electromagnetic spectrum of vegetation reflectivity [3]: on the reflection in the red region of the spectrum in the range from 620 nm to 750 nm, which accounts for the maximum absorption of solar radiation by chlorophyll of higher vascular plants, and on the reflection in the near infrared region of the spectrum in the range from 750 nm to 900 nm, where the region of maximum reflection of the cellular structures of the leaf is concentrated. One of the wide-spread indicators for solving problems regarding the assessment of vegetation cover is the NDVI (Normalized Difference Vegetation Index), which is calculated by the formula NDVI =

NIR − RED , NIR + RED

(1)

where NIR and RED are the reflection coefficients in the near infrared and red regions of the electromagnetic spectrum, respectively. Both coefficients are calculated by mapping the red and infrared regions of the spectrum onto a unit segment using trivial equalities: RED =

λ2 − 750 λ1 − 620 , λ1 ∈ (620, 750), NIR = , λ2 ∈ (750, 900) 750 − 620 900 − 750

380

E. Aliyev and F. Salmanov

The NDVI value varies from 0 to 1: the higher its value, the higher the vegetation intensity, and vice versa, the lower the index value, the sparser the vegetation, and the tendency to zero generally indicates open ground. So, it is necessary to adapt a fuzzy method for forecasting seasonal and long-term changes in agricultural crops in the spectral-brightness characteristics using FTS of spectral ranges of remote sensing data and reflecting certain vegetation parameters in a particular pixel of a satellite image. As an example of testing fuzzy models, time series were selected that reflect the annual dynamics of the coefficients of the spectral ranges RED and NIR (see Table 1 and Fig. 1), obtained from images of a fixed pixel in the corresponding MODIS images (LPDAAC – Land Processes Distributed Active Archive Center) (see Fig. 2) of crop area in Jonesboro (USA, Arkansas) with geographic coordinates (−90.16, 35.81) [4]. Table 1 also shows the corresponding NDVI calculated using formula (1). Table 1. Time series of RED, NIR coefficients and vegetation index NDVI. NN

Date

NIR

RED

NDVI

NN

Date

NIR

RED

NDVI

1

18.02.2000

0.2036

0.0958

0.3599

16

25.06.2000

0.8565

0.1452

0.7101

2

26.02.2000

0.3175

0.1445

0.3745

17

02.07.2000

0.8651

0.1453

0.7124

3

05.03.2000

0.3639

0.1523

0.4099

18

11.07.2000

0.8702

0.1455

0.7135

4

15.03.2000

0.3623

0.1623

0.3812

19

20.07.2000

0.3357

0.1256

0.4554

5

21.03.2000

0.2219

0.1025

0.3680

20

27.07.2000

0.1125

0.0678

0.2479

6

29.03.2000

0.1717

0.0835

0.3457

21

02.08.2000

0.3666

0.1348

0.4623

7

06.04.2000

0.1676

0.0845

0.3296

22

12.08.2000

0.6051

0.1245

0.6587

8

15.04.2000

0.1407

0.0765

0.2957

23

20.08.2000

0.5828

0.1463

0.5987

9

22.04.2000

0.1106

0.0659

0.2535

24

28.08.2000

0.4628

0.1354

0.5473

10

29.04.2000

0.1214

0.0689

0.2759

25

03.09.2000

0.3492

0.1158

0.5019

11

08.05.2000

0.1502

0.0815

0.2966

26

13.09.2000

0.3523

0.1233

0.4815

12

15.05.2000

0.1529

0.0813

0.3058

27

20.09.2000

0.3450

0.1389

0.4259

13

24.05.2000

0.1664

0.0855

0.3211

28

29.09.2000

0.2457

0.1125

0.3719

14

09.06.2000

0.4084

0.1324

0.5104

29

07.10.2000

0.2173

0.1045

0.3505

15

15.06.2000

0.5890

0.1356

0.6257

30

15.10.2000

0.2058

0.1056

0.3217

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1.0 0.8 0.6 0.4 0.0

18-02-2000 26-02-2000 05-03-2000 15-03-2000 21-03-2000 29-03-2000 06-04-2000 15-04-2000 22-04-2000 29-04-2000 08-05-2000 15-05-2000 24-05-2000 09-06-2000 15-06-2000 25-06-2000 02-07-2000 11-07-2000 20-07-2000 27-07-2000 02-08-2000 12-08-2000 20-08-2000 28-08-2000 03-09-2000 13-09-2000 20-09-2000 29-09-2000 07-10-2000 15-10-2000

0.2

NDVI

NIR

RED

Fig. 1. Time series of the NDVI index against the background of the dynamics of the RED and NIR coefficients obtained for a fixed pixel of MODIS images (LPDAAC).

3 FTS: Main Stages of Predictive Modeling The existing approaches to fuzzy modeling of time series involve the sequential implementation of the following main stages (procedures): 1) establishing the coverage of the entire set of historical data in the form of a universal set (universe); 2) fuzzification of weakly structured historical data; 3) establishing internal relationships in the form of fuzzy relations and dividing them into groups; 4) finding fuzzy outputs (predicts) of the applied model and their defuzzification. One of the ways to establish the universe and calculate the optimal number of evaluative concepts for fuzzy evaluation of the historical data of the time series was proposed in [5], the essence of which is to sequentially perform the following steps. Step 1. Assorting the time series data {x t }t=1÷n into an ascending sequence {x p(i) }, where p is a permutation that sorts the data in ascending order: x p(t) ≤ x p(t+1) . Step 2. Calculation of the average value for all pairwise distances d i = |x p(i) − x p(i+1) | between any two consecutive values x p(i) and x p(i+1) and standard deviation by formulas: n−1 AD(d1 , d2 , ..., dn ) = |xp(i) − xp(i+1) |/(n − 1), (2) i=1  n−1 σAD = (di − AD)2 /(n − 1). (3) i=1

Step 3. Detection and elimination of anomalies – outliers that need to be reset. For this, both the mean distance AD and the standard deviation σ AD , established in the previous step, are used. In this case, the values of pairwise distances that do not satisfy the following condition are subject to outlier. AD−σAD ≤ di ≤ AD + σAD .

(4)

Step 4. Recalculation the mean distance AD for the set of remaining values d i . Step 5. Establishing the universe U in the form U = [Dmin – AD, Dmax + AD] = [D1 , D2 ], where Dmin and Dmax are the minimum and maximum data, respectively. Step 6. Finding the optimal number of evaluative concepts as criteria for evaluating the historical data of the time series. It is carried out based on the formula D2 − D1 − AD . (5) m= 2 · AD

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4 Models for Forecasting the NDVI FTS Considering the above step-by-step data fuzzification procedure FTS models of both the NDVI and the corresponding reflection coefficients NIR and RED are proposed below. In [5], to describe the qualitative evaluation criteria by appropriate fuzzy sets, the following trapezoidal membership functions (TMF) are used ⎧ 0, x < ak1 ⎪ ⎪ ⎪ x−ak1 ⎪ ⎪ , ⎨ ak2 −ak1 ak1 ≤ x ≤ ak2 , (6) μAk (x) = 1, ak2 ≤ x ≤ ak3 , ⎪ ak4 −x ⎪ ⎪ , a ≤ x ≤ a , k3 k4 ⎪ ak4 −ak3 ⎪ ⎩ 0, x > ak4 , whose parameters satisfy the conditions: ak2 − ak1 = ak3 − ak2 = ak4 − ak3 (k = 1 ÷ m). So, on the entire data set of the NDVI time series (see Table 1), using formulas (2) and (3) the mean value AD = 0.0161 and the standard deviation σ AD = 0.0140 are established, respectively. After resetting the pairwise distances d i that do not satisfy condition (4) or, more specifically, the condition 0.0161–0.0140 ≤ d i ≤ 0.0161 + 0.0140, based on the remaining set of pairwise distances the final value of the mean value was obtained as AD = 0.0132. In this case, the desired universe is constructed as a segment U = [0.2479–0.0132, 0.7135 + 0.0132] = [0.2347, 0.7267], where 0.2479 and 0.7135 are the minimum and maximum values of the NDVI index, respectively. At the same time, the number of fuzzy subsets of this universe, describing the qualitative criteria for evaluating NDVI indices, is calculated by equality (5) as follows. m=

0.7267 − 0.2347 − 0.0132 = 18.1424 ≈ 18. 2 · 0.0132

Based on the use of the TMF (6) with parameters aki summarized in Table 2, where i = 1 ÷ 4 and k = 1 ÷ 18, the corresponding fuzzy sets Ak are established (Fig. 2). Fuzzification of NDVI indices by the presented trapezoidal membership functions is carried out according to the principle: NDVI is described by the fuzzy set to which its value belongs with the highest degree. When the NDVI value belongs to the interval [ak2 , ak3 ], the appropriate fuzzy analog is easily determined. In other cases, clarifications are needed. According to (6) for NDVI = 0.5019 we have: μA11 (0.5019) = 0.2491 and μA10 (0.5019) = 0.7509 (see Fig. 2). Then the fuzzy set A10 is the analogue of NDVI, since the value of the corresponding membership function at the point 0.5019 is greater. The fuzzy analogues of all NDVIs are summarized in Table 3. As is known, FTS modeling is based on the analysis of internal relations, which are presented in the form of implication “If , then ”. Identified internal relations are grouped according to the principle: if the fuzzy set Ak or the bunch of sets Ai , Ai+1 relates to one or several sets, then a group of the 1st order is localized relative to Ak or the group of the 2nd order is localized relative to Ai , Ai+1 (see Table 4).

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Table 2. Fuzzy sets as qualitative criteria for evaluating NDVI indices. Fuzzy set Parameters of the TMF ak1

ak2

ak3

Fuzzy set Parameters of the TMF ak4

ak1

ak2

ak3

ak4

A1

0.2347 0.2479 0.2611 0.2743 A10

0.4722 0.4854 0.4986 0.5118

A2

0.4986 0.5118 0.5250 0.5382

A3

0.2611 0.2743 0.2875 0.3007 A11 0.2875 0.3007 0.3139 0.3271 A12

A4

0.3139 0.3271 0.3403 0.3535 A13

0.5514 0.5646 0.5778 0.5910

A5

0.5778 0.5910 0.6042 0.6174

A6

0.3403 0.3535 0.3667 0.3799 A14 0.3667 0.3799 0.3931 0.4062 A15

A7

0.3931 0.4062 0.4194 0.4326 A16

0.6306 0.6438 0.6570 0.6702

A8

0.4194 0.4326 0.4458 0.4590 A17 0.4458 0.4590 0.4722 0.4854 A18

0.6570 0.6702 0.6834 0.6965

A9

0.5250 0.5382 0.5514 0.5646

0.6042 0.6174 0.6306 0.6438

0.6834 0.6965 0.7097 0.7267

Fig. 2. Fuzzy sets as qualitative criteria for evaluating the NDVI indices.

Table 3. NDVI index FTS. NN

NDVI

Fuzzy set

NN

NDVI

Fuzzy set

NN

NDVI

Fuzzy set

1

0.3599

A5

11

0.2966

A3

21

0.4623

A9

2

0.3745

A6

12

0.3058

A7

22

0.6587

A16

3

0.4099

A7

13

0.3211

A4

23

0.5987

A14

4

0.3812

A6

14

0.5104

A11

24

0.5473

A12

5

0.3680

A5

15

0.6257

A15

25

0.5019

A10

6

0.3457

A4

16

0.7101

A18

26

0.4815

A10

7

0.3296

A4

17

0.7124

A18

27

0.4259

A7

8

0.2957

A3

18

0.7135

A18

28

0.3719

A5

9

0.2535

A1

19

0.4554

A9

29

0.3505

A5

10

0.2759

A2

20

0.2479

A1

30

0.3217

A4

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E. Aliyev and F. Salmanov Table 4. The groups of the 1st and 2nd order relationships.

If for the i-th day RED is described by the fuzzy set Aj , which forms only one relationship within the FTS, for example Aj ⇒ Ak , then the fuzzy predict for the next (i + 1)-th day will be the set Ak . If there is a group of relationships of the form Aj ⇒ Ak1 , Ak2 , …, Akp , then the union of fuzzy sets Ak1 ∪ Ak2 ∪ … ∪ Akp is considered as the fuzzy predict for the next day. Defuzzification of fuzzy predicts can be realized by formula [1] F(A) =

1 αmax

α max

M (Aα )d α

(7)

0

where Aα = {u|μA (u) ≥ α, u ∈ U} are α-level sets (α ∈ [0, 1]); M (Aα ) = nk=1 uk /n (uk ∈ Aα ) are the cardinalities of the corresponding α-level sets. For the fuzzy predict A4 = {0/0.3139, 1/0.3271, 1/0.3403, 0/0.3535} (see Table 2), we have: 0 < α < 1, α = 1, A4α = {0.3271, 0.3403}, M (A4α ) = (0.3271 + 0.3403)/2 = 0.3337.

According to (7) and α max = 1, the point estimate A4 or the defuzzified output of the 1st order model is the following number.  1 M (A4α )d α = M (A4α ) · α = 0.3337. F(A4 ) = 0

For relation Ai ⇒ Aj , At , Ap , where Ai is the fuzzy analog of the NDVI for the i-th day, the numerical predict for the next (i + 1)-th day is calculated as the arithmetic mean of the abscissas of the midpoints of the upper bases of trapezoids corresponding to the fuzzy sets Aj , At and Ap . In particular, the fuzzy predict for the date 29.09.2000 is the union A4 ∪ A5 ∪ A6 with the numerical estimate obtained as following 

0.3271 + 0.3403 0.3535 + 0.3667 0.3799 + 0.3931 + + /3 = 0.3601. F= 2 2 2 Thus, considering the internal relationships of the 1st and 2nd orders, for the NDVI FTS the corresponding predictive models were obtained (see Table 5 or Fig. 3).

Forecasting Crop Yields Based on Fuzzy Analysis of the Dynamics Table 5. Predictive models of NDVI FTS.

Fig. 3. Membership of the NDVI index located at the junction of two fuzzy sets.

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At the end of Table 5, the values of the MSE (Mean Squared Error), the MAPE (Mean Absolute Percentage Error) and the MPE (Mean Percentage Error) are presented, which reflect the quality of the constructed predictive models, their adequacy and accuracy. Errors according to these criteria are calculated by the formulas: MSE =

m |Ft − At | m Ft − At (Ft − At )2 ; MAPE = × 100%; MPE = × 100%, t=1 t=1 t=1 mAt m mAt

m

where m is the length of the TS; At is the NDVI at time t; F t is the predict of At .

5 Conclusion The article uses one of the methods of precision farming, associated with the use of the NDVI, which allows to predict crop volumes and most accurately assess the real state of plants. According to the multispectral data, it is possible to evaluate the development of crops and predict its future yield. It should be considered that the NDVI value changes throughout the entire growing season, that is, its indicators during the initial growth, the period of flowering and maturation, differ significantly as this is demonstrated by the dynamics of NDVI by the example of separate pixel. The proposed algorithm can be easily projected to process multispectral data obtained from all pixels of the images.

References 1. Rzayev, R.R.: Analytical support for decision-making in organizational systems. Palmerium Academic Publishing, Saarbruchen (2016). (in Russian) 2. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning. Inf. Sci. 8(3), 199–249 (1965) 3. MicaSense website. https://micasense.squarespace.com/atlasflight. Accessed 2 Feb 2022 4. Vegetation Indices 16-Day L3 Global 250 m MOD13Q1 (LPDAAC). https://goo.gl/maps/YAd domuoXsD4QQN36. Accessed 25 Jan 2022 5. Ortiz-Arroyo, D., Poulsen, J.R.: A weighted fuzzy time series forecasting model. Indian J. Sci. Technol. 11(27), 1–11 (2018)

Supplier Selection After Pandemic in SMEs Using Fuzzy Best Worst Method and Fuzzy WASPAS Irem Ucal Sari(B) , Arda Pesek, and Kami Bozukyan Industrial Engineering Department, Istanbul Technical University, Macka, Istanbul, Turkey [email protected]

Abstract. During the pandemic period, and the normalization process we are in, it has become much more important for all companies to ensure the continuity of the company. Especially small and medium-sized enterprises have to make more accurate decisions in managing their processes and choosing suppliers, which are very important for product cost, product quality, and sustainability of the company. In this study, the criteria that are important in supplier selection after the pandemic are determined for small and medium-sized enterprises and weighted by the fuzzy best-worst method, then the most suitable supplier among alternative suppliers is selected with the fuzzy WASPAS method. Keywords: Fuzzy best worst method · Fuzzy WASPAS · SMEs · Supplier selection

1 Introduction Since the beginning of humanity, humans have developed and manufactured tools and equipment that they use for their own benefits and, brought technology to its present level. Businesses that keep up with this technological development have always been one step ahead. In addition to the factories where the final manufacturing and large products are made, small and medium-sized enterprises that feed them and are their suppliers constitute an extremely crucial point of a country’s economy and supply chain. With the increase in global competition, small and medium-sized enterprises need to manage their own economies, analyze supplier preferences and make better decisions in order to survive. Due to the decrease in prices with the increase in competition between large enterprises, small and medium-sized enterprises should also reduce their own costs. Cost reduction can be achieved by reducing unnecessary expenses and changes in the production operation. At the same time, small and medium-sized enterprises also have suppliers for which they supply some parts or some services required for them, and the selection of these suppliers and better analysis of their costs are of great importance in terms of costs. Correct analysis of supplier selections can enable SMEs to gain profit and get ahead of the competition in the long or medium term. It can lead to approaching systems and agreements that seem very profitable from a different © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 387–395, 2022. https://doi.org/10.1007/978-3-031-09173-5_47

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perspective and perhaps finding a more profitable solution. To give an example to better emphasize the importance of supplier selection, raw materials and other components account for about 70% of a company’s cost in the manufacturing industry [7]. The selection of suppliers is fundamentally a multi-criteria decision-making concern, and there are several approaches in the management of the supply chain to cope with such situations. There are lots of multi-criteria decision-making techniques such as Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), Analytic Hierarchy Process (AHP), Best-Worst Method (BWM), Weighted Sum Model (WSM), Weighted Product Model (WPM) and the combination of these two; Weighted Aggregated Sum Product Assessment (WASPAS). According to [6] BWM needs fewer data for contrast relative to AHP, and the final result is compatible with AHP. BWM substantially decreases measurement complexity and the actual outcome would be more credible with more coherent contrasts. However, in an unpredictable environment, traditional BWM does not evaluate the weight, so scholars have enhanced BWM, and fuzzy BWM (F-BWM) has evolved. One of the application methods of F-BWM is based on triangular fuzzy numbers. In many fields, F-BWM has been used and some real issues have been solved, such as assessing the service efficiency of baggage handling systems, choosing cloud providers, airport performance appraisal, and rating, organization research, and development (R&D) identification, evaluation of urban waste sludge treatment technology [6]. On the other hand, the WASPAS method can give more accurate results compared to other analyzes, which has caused it to be accepted as an effective decision-making tool in recent years. Like the BWM, the WASPAS method allows modeling in fuzzy conditions and triangular numbers are also appropriate for the fuzzy WASPAS (F-WASPAS) method. During the pandemic period, disruptions in the supply chain, and full closure periods have led to a change in the relations with suppliers and the importance of supplier evaluation criteria. The objective of this paper is to determine important criteria in supplier selection for small and medium-sized enterprises in todays’ changed conditions, weighting and prioritizing these criteria, and with the help of this information, creating and applying an appropriate procedure for choosing the most beneficial supplier using the F-BMW and F-WASPAS Method. As a result of the interview with the managers of SMEs and the literature review, the criteria to be used are price, delivery time, quality, flexibility, service level, technology, and environment. Also, as a result of the meeting with the company owners, 5 different supplier alternatives from which raw materials are supplied and can be supplied were determined. At the end of the application part, the most appropriate selection among these supplier alternatives is chosen. This paper is organized as follows: After the introduction, general information about supplier selection, and the basics of the methodology are given. Then in the third section, the selection process for an SME is applied. Consequently, the conclusion is presented in section four.

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2 Supplier Selection and the Methodology With the globalization of the world, companies are in an economic environment where competition increases as well as commercial opportunities. With the increase in competition, companies need to manage their expenditures affordably. Of these several expenses, procurement costs have the largest share in company expenses. To give an example, even a small increase in our supply chain expenditures will affect the final price of the product we produce, so our possibility of offering a competitive price to our customers will decrease. In addition to the price, the quality standards to be provided by the supplier will ensure the satisfaction of the customers and the continuation of the company’s cooperation. The operational processes of the supplier directly affect the operation processes of the companies. The supplier’s failure to deliver the product on time due to problems arising from speed, capacity, or other reasons also delays the service that the company provides to its customers. This delay could result in the collapse of the cooperation in the future, which could cause enormous damage to the company. Due to the reasons exemplified above, supplier selection is crucial for all companies. Multiple criteria should be considered in the selection of suppliers. As a result of the literature research, the most used and the most important criteria for supplier selection are determined as price, delivery, quality, flexibility, service level, technology, and environment. Articles using these criteria are summarized in Table 1. Table 1. Supplier selection criteria in the literature. Criteria

References

Price

[2, 4, 5, 8–12, 14, 16–18]

Delivery time

[2, 5, 8–12, 14, 16–18]

Quality

[2, 4, 5, 8–12, 14, 16–18]

Flexibility

[2, 5, 8–12, 16]

Service level

[4, 5, 8–10, 12, 14, 17, 18]

Technology

[2, 4, 11, 16]

Environment

[2, 4, 5, 8, 9, 18]

In this paper, it is decided to use the 7 criteria mentioned above. First of all, price means the amount of money paid to the supplier per unit. To compete in the market, the supplier must offer the best price to the enterprises. Secondly, delivery represents the time and speed of the ordered product. This criterion is extremely vital for the company to be able to respond very quickly to the demands of the customers. Thirdly, quality can be defined as the criterion by which something is evaluated in comparison to other related things. In other words, supplied products can meet the customer’s anticipations. In addition, flexibility refers to the ability to respond quickly to the number and variety of requests from the company. Furthermore, the service level is high when the supplier

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takes the responsibility for the goods sold and ensures that the problem will be solved in case of any error. Moreover, technology is an indicator of the supplier’s ability to keep up with recent machinery. The supplier’s level of following the new technology enables the company to provide more quality, more and faster materials the company. Finally, the environment represents the capability of a provider to manage the use of energy and resources when delivering the ordered goods. The supplier’s over-spending on raw materials harms both itself and the environment. It also prevents us from obtaining more products. In this paper, F-BWM is selected as a weighting criterion due to its benefits, which include fewer comparative data requirements, more accurate comparisons, and more reliable performance. In F-BMW, the steps of [15] are applied and in F-WASPAS, the steps of [3] are followed. Linguistic variables are quantified using Table 2 in F-BWM. Table 2. Linguistic Scale for F-BWM [13] Linguistic variable

Triangular fuzzy number

Equal

(1, 1, 1)

Weakly important

(2/3, 1, 3/2)

Fairly important

(3/2, 2, 5/2)

Important

(5/2, 3, 7/2)

Very important

(7/2, 4, 9/2)

Absolutely important

(9/2, 5, 11/2)

After determining the weights of criteria, the F-WASPAS method is applied to find the ranks of alternatives. Linguistic variables are quantified using Table 3 in F-WASPAS. Table 3. Linguistic scale for F-WASPAS [1] Linguistic variable

Triangular fuzzy number

Very poor

(0, 1, 2)

Poor

(1, 2, 3)

Mostly poor

(2, 3.5, 5)

Fair

(4, 5, 6)

Mostly good

(5, 6.5, 8)

Good

(7, 8, 9)

Very good

(8, 9, 10)

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3 Application For the application, a workshop located in Istanbul which takes brass rods and turns them into final products such as safety valves, water regulators, etc. is chosen. As a result of the interviews with the founder and manager of the company, it has been decided to use the 7 criteria which are determined after the literature review in the selection of suppliers. C1, C2, C3, C4, C5, C6, and C7 are used to determine price, delivery quality, flexibility, service level, technology, and environment criteria, respectively. Based on the information received from the manager, it was determined that the most important criterion was quality (C3) and the worst criterion was technology (C6). Fuzzy preferences of the best criterion according to all criteria and the worst criterion according to all criteria are shown below in Table 4. Table 4. Fuzzy preferences of the criteria. Best to all

All to worst

C1: Weakly important

Very important

C2: Fairly important

C2: Important

C3: Equal

C3: Absolutely important

C4: Important

C4: Fairly important

C5: Fairly important

C5: Important

C6: Absolutely important C6: Equal C7: Very important

C7: Weakly important

The fuzzy Best-to-Others vector is obtained is shown below: A˜ B = {(2/3, 1, 3/2), (3/2, 2, 5/2), (1, 1, 1), (5/2, 3, 7/2), (3/2, 2, 5/2), (9/2, 5, 11/2), (7/2, 4, 9/2)} The fuzzy Others-to-Worst vector is obtained is shown below: A˜ B = {(7/2, 4, 9/2), (5/2, 3, 7/2), (9/2, 5, 11/2), (3/2, 2, 5/2), (5/2, 3, 7/2), (1, 1, 1), (2/3, 1, 3/2)} Then, the nonlinearly constrained optimization equation in terms of triangular numbers is obtained. By solving the equation, the optimal fuzzy weights of seven criteria are determined as follows: w˜ 1∗ = (0.2003, 0.2036, 0.2664); w˜ 2∗ = (0.1373, 0.1483, 0.1760); w˜ 3∗ = (0.2632, 0.2632, 0.2997); w˜ 4∗ = (0.0782, 0.0930, 0.1206); w˜ 5∗ = (0.1373, 0.1483, 0.1760); w˜ 6∗ = (0.0553, 0.0553, 0.0629); w˜ 7∗ = (0.0622, 0.0622, 0.0689); ξ˜ ∗ = (0.3180, 0.3180, 0.3180)

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Then, the crisp weights of the seven criteria are obtained as; w1∗ = 0.2135; w2∗ = 0.1511; w3∗ = 0.2693; w4∗ = 0.0951; w5∗ = 0.1511; w6∗ = 0.0566; w7∗ = 0.0633

Since aBW = a36 = (9/2, 5, 11/2), the consistency index is 9.35. The consistency ratio is 0.3180/9.35 = 0.034, which demonstrates a high consistency because the consistency ratio 0.034 is near to zero. After determining the weights of criteria, the F-WASPAS method is applied to find the ranks of alternatives. As a result of the conversations with the company manager, it was asked to give linguistic values to 5 companies from which they currently purchase raw materials, which are denoted by A1, A2, A3, A4, and A5 according to 7 predetermined criteria. Linguistic values of alternatives according to criteria are shown below in Table 5. Table 5. Linguistic evaluations of alternatives. Alternative

C1

C2

C3

C4

C5

C6

C7

A1

MP

VG

VG

P

VG

VG

VG

A2

VP

MG

VG

VP

VG

G

VG

A3

G

G

F

G

G

F

F

A4

VG

VP

MP

VG

F

MP

MP

A5

MG

F

G

MP

G

MG

F

Then the normalization process is performed for all alternatives & criteria and the normalized decision matrix is created. After that, the weighted normalized fuzzy decision matrix for the weighted sum model (WSM), and the weighted normalized fuzzy decision matrix for the weighted product model (WPM) are constructed. The results of the weighted sum model and weighted product model and integrated utility function using a 0.5 λ value are shown in Table 6. Table 6. Results of WSM, WPM and Integrated utility function. Alternative

WSM

WPM

Integrated utility function

A1

(0.605, 0.716, 0.827)

(0.488, 0.638, 0.769)

(0.547, 0.677, 0.798)

A2

(0.502, 0.610, 0.717)

(0.000, 0.432, 0.585)

(0.251, 0.521, 0.651)

A3

(0.583, 0.683, 0.783)

(0.563, 0.666, 0.769)

(0.573, 0.675, 0.776)

A4

(0.385, 0.505, 0.624)

(0.000, 0.409, 0.554)

(0.193, 0.457, 0.589)

A5

(0.534, 0.652, 0.771)

(0.503, 0.632, 0.756)

(0.519, 0.642, 0.763)

Normalized utility function memberships, alternative scores, and the ranks of the alternatives are represented in Table 7.

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Table 7. Normalized utility function membership functions, scores, and ranks of the alternatives. Alternative

Normalized utility function

Score

Rank

A1

(0.153, 0.228, 0.383)

0.2412

1

A2

(0.070, 0.175, 0.313)

0.1807

4

A3

(0.160, 0.227, 0.373)

0.2402

2

A4

(0.054, 0.154, 0.283)

0.1586

5

A5

(0.145, 0.216, 0.367)

0.2293

3

As a result of detailed examinations, supplier alternatives are ranked. When the scores of the alternatives are examined, it is seen that the A1 supplier is in the first place. The score of the A3 supplier in the 2nd place is also very close to A1. When purchasing raw materials, a high rate of raw materials should be purchased from these two suppliers. As a result of the interviews with the company manager, the rates of cooperation with suppliers are stated as follows: A1 (60%); A2 (5%); A3 (20%); A4 (10%); A5 (5%). The study suggests that the rate of cooperation with the Istanbul supplier can be increased. In addition, the A5 supplier is also a good competitor to these two suppliers. A4 supplier is considered to be preferred for products where quality is insignificant and cheapness is important. This explains the relatively high rate of cooperation with A4. A2, on the other hand, fell behind in this competition due to the extremely expensive price.

4 Conclusion Small and medium-sized companies ought to control their own markets, assess supplier demands and make better choices to succeed as international competitiveness grows. Appropriate examination of the choice of suppliers will help SMEs to make a profit and, in the long or medium term, to get ahead of the competition. It may lead to addressing processes and deals that, from a different angle, look very lucrative and can find a more profitable alternative. In addition, supplier selection, which has a strategic priority, has become an even more important decision for companies to survive, especially during the pandemic period and the normalization process we are in after. Supplier selection is a multi-criteria decision-making problem, and there are many techniques to deal with such circumstances in supply chain management. BWM diminishes calculation sophistication significantly and the real finding, by more reasonable comparisons, will be more reliable. However, conventional BWM does not measure the weight in an uncertain atmosphere. Especially in uncertain environments, F-BWM overcomes this problem. Furthermore, the WASPAS approach has the potential to provide

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more precise outcomes as compared to other analyses, which has led to its acceptance as a useful decision-making technique in recent times. The F-WASPAS approach, like the F-BWM, is suitable for use in uncertain environments. In this paper it is clarified that, to choose the most advantageous supplier by using the F-BWM and then F-WASPAS method, defining essential parameters in the choice of suppliers for small and medium-sized enterprises, weighing and optimizing these criteria, and using this data, designing and implementing an acceptable alternative. For future research, it is suggested to use fuzzy extensions, which can express uncertainty at different levels, of the BWM and WASPAS methods in the supplier selection process of SMEs.

References 1. Amoozad Mahdiraji, H., Arzaghi, S., Stauskis, G., Zavadskas, E.K.: A hybrid fuzzy BWMCOPRAS method for analyzing key factors of sustainable architecture. Sustainability 10(5), 1626 (2018) 2. Chauhan, A.S., Badhotiya, G.K., Soni, G., Kumari, P.: Investigating interdependencies of sustainable supplier selection criteria: an appraisal using ISM. J. Glob. Oper. Strateg. Sourc. 13(2), 195–210 (2020) 3. Daldir, I., Tosun, O.: Bulanık Waspas ile Ye¸sil Tedarikçi Seçimi. Uluda˘g University. J. Faculty Eng. 23(4), 193–208 (2018) 4. Dutta, P., Jaikumar, B., Arora, M.S.: Applications of data envelopment analysis in supplier selection between 2000 and 2020: a literature review. Ann. Oper. Res., 1–56 (2021). https:// doi.org/10.1007/s10479-021-03931-6 5. Fallahpour, A., Nayeri, S., Sheikhalishahi, M., Wong, K.Y., Tian, G., Fathollahi-Fard, A.M.: A hyper-hybrid fuzzy decision-making framework for the sustainable-resilient supplier selection problem: a case study of Malaysian Palm oil industry. Environ. Sci. Pollut. Res., 1–21 (2021). https://doi.org/10.1007/s11356-021-12491-y 6. Gan, J., Zhong, S., Liu, S., Yang, D.: Resilient supplier selection based on fuzzy BWM and GMo-RTOPSIS under supply chain environment. Discret. Dyn. Nat. Soc. (2019). https://doi. org/10.1155/2019/2456260. Article ID: 2456260 7. Ghodsypour, S.H., O’Brien, C.: A decision support system for supplier selection using an integrated analytic hierarchy process and linear programming. Int. J. Prod. Econ. 56, 199–212 (1998) 8. Hendiani, S., Liao, H., Ren, R., Lev, B.: A likelihood-based multi-criteria sustainable supplier selection approach with complex preference information. Inf. Sci. 536, 135–155 (2020) 9. Hendiani, S., Mahmoudi, A., Liao, H.: A multi-stage multi-criteria hierarchical decisionmaking approach for sustainable supplier selection. Appl. Soft Comput. 94, 106456 (2020) 10. Hsu, C.C., Kannan, V.R., Leong, G.K., Tan, K.C.: Supplier selection construct: instrument development and validation. Int. J. Logist. Manag. 17(2), 213–239 (2006) 11. Lee, A.H.: A fuzzy supplier selection model with the consideration of benefits, opportunities, costs and risks. Expert Syst. Appl. 36(2), 2879–2893 (2009) 12. Li, J., Yi, L., Shi, V., Chen, X.: Supplier encroachment strategy in the presence of retail strategic inventory: centralization or decentralization? Omega 98, 102213 (2020) 13. Liang, X., Chen, T., Ye, M., Lin, H., Li, Z.: A hybrid fuzzy BWM-VIKOR MCDM to evaluate the service level of bike-sharing companies: a case study from Chengdu, China. J. Clean. Prod. 298, 126759 (2021) 14. Mati´c, B., et al.: A new hybrid MCDM model: sustainable supplier selection in a construction company. Symmetry 11(3), 353 (2019)

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15. Moslem, S., Gul, M., Farooq, D., Celik, E., Ghorbanzadeh, O., Blaschke, T.: An integrated approach of best-worst method (BWM) and triangular fuzzy sets for evaluating driver behavior factors related to road safety. Mathematics 8(3), 414 (2020) 16. Sarkis, J., Talluri, S.: A model for strategic supplier selection. J. Supply Chain Manag. 38(4), 18–28 (2002) 17. Wu, M.: Topsis-AHP simulation model and its application to supply chain management. World J. Model. Simul. 3(3), 196–201 (2007) 18. Yu, J.R., Tsai, C.C.: A decision framework for supplier rating and purchase allocation: a case in the semiconductor industry. Comput. Ind. Eng. 55(3), 634–646 (2008)

Fuzzy TODIM for ELICIT Information ´ Alvaro Labella(B) , Diego Garc´ıa-Zamora , Rosa M. Rodr´ıguez , and Luis Mart´ınez Department of Computer Science, University of Ja´en, Ja´en, Spain {alabella,dgzamora,rmrodrig,martin}@ujaen.es

Abstract. The available information in some decision situations may be vague or imprecise, and the involvement of human experts, who usually manage qualitative information, results essential to address the underlying uncertainty in such contexts. However, human decision-makers are rationally bounded, particularly when the decision processes involve risk and uncertainty. To model human stakeholders’ behavior in such situations, the TODIM method (Portuguese acronym for Interactive MultiCriteria Decision-Making) based on the Prospect Theory was developed to address multi-criteria decision-making (MCDM) situations. Even though the classic TODIM method was adapted to manage fuzzy information and, consequently, to model uncertainty by using linguistic labels, that proposal neglected the management of more complex linguistic expressions able to represent the experts’ hesitancy among several linguistic labels, which is quite common due to the increasing complexity of decision problems. Therefore, this contribution introduces a multicriteria group decision-making (MCGDM) model based on fuzzy TODIM dealing with Extended Comparative Linguistic Expressions with Symbolic Translation (ELICIT) values, which were recently proposed to model such hesitancy and perform precise computations without losing the interpretability of linguistic information. Keywords: Linguistic TODIM multi-criteria decision-making

1

· ELICIT information · Linguistic

Introduction

Even though the use of decision models based on the analysis of data is quite demanded in today society, some real-world problems still require the use of human experts to provide their knowledge and make decisions, especially in This work is partially supported by the Spanish Ministry of Economy and Competitiveness through the Spanish National Project PGC2018-099402-B-I00, and the Postdoctoral fellow Ram´ on y Cajal (RYC-2017-21978), the FEDER-UJA project 1380637 and ERDF, by the Spanish Ministry of Science, Innovation and Universities through a Formaci´ on de Profesorado Universitario grant (FPU2019/01203) and by the Junta de Andaluc´ıa, Andalusian Plan for Research, Development, and Innovation (POSTDOC 21-00461). c The Author(s), under exclusive license to Springer Nature Switzerland AG 2022  C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 396–404, 2022. https://doi.org/10.1007/978-3-031-09173-5_48

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those situations in which the available data is vague or inaccurate [9]. In addition, including several experts’ points of view improves the decision process when facing complex situations which require a quick response. In this context, MCGDM models become essential to face such situations in which human experts’ knowledge is used to rate the considered alternatives under different criteria when the latter cannot be provided as objective values, but qualitative assessments. In this sense, preference modelling by means of linguistic information has become a milestone because of the flexibility that offers to the experts and its closeness to their natural way of thinking [7,12]. Among other proposals to model experts’ assessments by using the linguistic information [9], ELICIT information [7] has been recently proposed to provide precise computations with linguistic terms [11] and model experts’ hesitancy. In addition to uncertainty and hesitancy, decision solving processes also require considering humans’ behavior when their decisions may imply significant losses, either economical, material or even human. Such a behavior was analyzed in Prospect Theory [6], which received the Nobel Prize for Economics in 2002. This theory is based on four main aspects: (i) the evaluation of gains and losses from a reference point (ii) the existence of a greater sensibility to losses than to gains (iii) the aversion to losses (iv) and the tendency to overestimate the occurrence of an unlikely event and underestimate those very likely. In this contribution, it is proposed a MCGDM model based on ELICIT information and TODIM method [1,3], which manages humans’ behavior under risk circumstances and relies on Prospect Theory [6]. The main features of this ELICIT-TODIM model are: 1. It allows solving MCGDM problems by using qualitative information provided by human experts. 2. Uncertainty and experts’ hesitancy are modelled by using ELICIT information. 3. It considers the use of Prospect Theory to model human behavior towards gains and losses. The rest of this contribution is broken down into the following sections. Section 2 introduces the basic concepts related to the proposal. Section 3 presents the ELICIT-TODIM, whose performance is shown in the resolution of a MCGDM problem in Sect. 4. Finally, some conclusions and future researches are drawn in Sect. 5.

2

Background

To facilitate the understanding of the proposal, this section reviews the basic concepts regarding linguistic MCGDM and the 2-tuple and ELICIT linguistic representation models.

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Linguistic Multi-criteria Group Decision-making

Formally, a MCGDM problem is defined by a set of experts E = {e1 , e2 , . . . , em } who rate a predefined set of alternatives/options A = {a1 , a2 , . . . , an } on several criteria C = {c1 , c2 , . . . , cr } [5]. Under circumstances in which experts feel more confident by providing their assessments over the alternatives by means of linguistic expressions, we can talk about linguistic MCGDM. In MCGDM, the experts’ preferences are usually collected in preference structures, so-called decision matrices. A decision matrix is defined as, D = (dij )n×r whose value dij is the assessment of the alternative ai under the criteria cj . One of the most relevant steps in the resolution of a linguistic decision-making problem (see Fig. 1) consists of modelling the linguistic preferences provided by the experts. In this regard, there are several proposals introduced in the specialized literature, such as the 2-tuple linguistic representation model [8], which allows providing precise computations on linguistic expressions, the Comparative Linguistic Expressions (CLEs) [9], able to model the experts’ hesitancy, or the ELICIT information, which hybridizes both proposals by introducing a representation scheme to model doubt without losing either interpretability or precision [7]. After choosing the desired preference structure, the experts’ preferences are aggregated and then exploited in order to obtain a solution for the problem. Over the years, this scheme has been extended, which has given place to different MCGDM models [1]. Concretely, this proposal is based on the TODIM approach [3], which allows obtaining a ranking of the alternatives according to the experts’ behavior when dealing with potential gains and losses as a result of their decisions [6].

Fig. 1. Linguistic MCGDM resolution scheme.

2.2

2-Tuple Linguistic Model and ELICIT Information

The 2-tuple linguistic representation model [8] represents the linguistic information as a tuple (si , α) composed by a linguistic term si ∈ S, which belongs to a predefined linguistic term set S = {s0 , s1 , ..., sg }, and a numerical value α ∈ [−0.5.0.5[ so-called symbolic translation, which represents the displacement in a continuous linguistic expression domain of the si membership function.

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Together with this representation model, Mart´ınez et al. [8] also introduced a computational model which relies on the bijection Δ−1 : S → [0, g] defined by Δ−1 S (si , α) = i + α, ∀ (si , α) ∈ S, where S = S × [−0.5, 0.5[ is the set of all 2-tuple linguistic values. However, the 2-tuple linguistic modelling presents an important drawback, because it is not able to model the experts’ hesitancy between several linguistic terms. To overcome this shortcoming, Rodr´ıguez et al. [10] introduced the use of CLEs by using relations such as between, at most or at least that are more flexible and richer than single linguistic terms. Afterwards, Labella et al. [7] proposed the ELICIT information taking the advantages of the 2-tuple linguistic model and the CLEs, which it is not only able to model the experts’ hesitation, but also allows carrying out precise computations and obtaining interpretable results. Furthermore, any ELICIT value is uniquely identified with a trapezoidal fuzzy number (TrFNs) [7]: Remark 1. A TrFN is a function ⎧ 0 ⎪ ⎪ ⎪ x−a ⎪ ⎨ b−a 1 T (x) = ⎪ d−x ⎪ ⎪ d−c ⎪ ⎩ 0

T ≡ T (a, b, c, d) : [0, 1] → [0, 1] of the form if 0 ≤ x ≤ a if a < x < b if b ≤ x ≤ c ∀x ∈ [0, 1] if c < x < d if d ≤ x ≤ 1

for certain 0 ≤ a ≤ b ≤ c ≤ d. For the sake of clarity, the set of all TrFNs on the interval [0, 1] will be denoted by T = {T : [0, 1] → [0, 1] : T is a TrFN} . Formally, ELICIT information can be denoted by an expression [si , sj ]γ1 ,γ2 , where si , sj ∈ S, i ≤ j are two 2-tuple linguistic values and γ1 , γ2 are two parameters which allow to unequivocally retrieve the TrFN representation of the ELICIT value [7]: Proposition 1. Let S be the set of all possible ELICIT values. The mapping ζ −1 : S → T [s1 , s2 ]γ1 ,γ2 → T (a, b, c, d) defined by:



a = γ1 + max c=

Δ−1 S (sm ) , g

is a bijection.

Δ−1 S (s1 ) − g

1 g

 ,0 ,

Δ−1 S (s1 ) , g   −1 ΔS (sm ) + g1 d = γ2 + min ,1 , g b=

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ELICIT values can be ordered by translating the fuzzy envelopes of the ELICIT values, given by a TrFN, into a numerical value so-called magnitude [7], which is defined by: M ag([si , sj ]γ1 ,γ2 ) = M ag(T (a, b, c, d)) =

a + 5b + 5c + d ∈ [0, 1]. 12

To compare two ELICIT values it suffices to compute their respective magnitudes. According to Labella et al. [7] the larger the magnitude, the larger the ELICIT value. Finally, to measure the distance between two ELICIT values, they proposed the distance μ : S × S → [0, 1]: μ([s1i , s1j ]γ11 ,γ21 , [s2i , s2j ]γ1 ,2 γ22 ) = μ(T (a1 , b1 , c1 , d1 ), T (a2 , b2 , c2 , d2 )) = =

|a1 − a2 | + |b1 − b2 | + |c1 − c2 | + |d1 − d2 | , 4

for any ELICIT values [s1i , s1j ]γ11 ,γ21 , [s2i , s2j ]γ1 ,2 γ22 ∈ S.

3

ELICIT-TODIM

Here, it is considered a linguistic MCGDM problem in which a group of experts wants to select the best alternative according to different criteria, which have been rated by using ELICIT information. Let us assume m experts, n alternatives, and r criteria. Therefore, a decision matrix for each expert is given by Dk = (dkij )n×r , where dkij represents by means of ELICIT information the rating of the alternative ai under the criterion cj k2 provided by the expert ek . In other words, dkij is on the form dkij = [sk1 k1 ,γ k2 ij , sij ]γij ij k2 where sk1 ij and sij are 2-tuple linguistic terms. In addition, the importance of each criterion cj according to expert ek ’s opinion is given by Wjk , which is also an ELICIT value.

1. First, experts’ preferences are aggregated by using an aggregation operator F : T m → T [4]. dij := ζ(F (ζ −1 (d1ij ), ζ −1 (d2ij ), ..., ζ −1 (dm ij ))), Wj := ζ(F (ζ −1 (Wj1 ), ζ −1 (Wj2 ), ..., ζ −1 (Wjm ))). 2. The value of the weight Wc for each criterion cc is normalized according to its importance, which is computed by using the notion of magnitude of an ELICIT value: M ag(Wj ) wj = r l=1 M ag(Wl ) 3. Compute the dominance of the alternative ai over the alternative ah δ : r A × A → R given by δ(ai , ah ) = j=1 Φj (ai , ah ), ∀ ai , ah ∈ A, where Φj :

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A × A → R is defined by ⎧ ⎪ ⎪ wj μ(dij , dhj ) M ag(dij ) > M ag(dhj ) ⎨ M ag(dij ) = M ag(dhj ) Φj (ai , ah ) = 0

⎪ ⎪ ⎩ −1 μ(dij ,dhj ) M ag(dij ) < M ag(dhj ) θ wj 4. Compute the partial dominance of each alternative n ξi =

n

h=1 n

max i=1

δ(ai , ah ) − min

n h=1

n

i=1

n

δ(ai , ah ) − min i=1

h=1

δ(ai , ah )

n h=1

δ(ai , ah )

As it occurs in classical TODIM, the parameter θ > 0 is used to measure the importance of the losses, which is amplified if θ < 1 and reduced if θ > 1. According to Prospect Theory [6], humans are usually more concerned about losses than about gains (θ < 1). When choosing θ close to zero, the alternatives which produce small losses are the best ones. On the contrary, for high values of θ, TODIM provides solutions which prioritize benefits regardless of the losses.

4

Case Study

This section shows the performance of the proposal in the resolution of a linguistic MCGDM problem. A fast food franchise is considering building a new restaurant. This restaurant will require a large investment, thus an inappropriate location for the restaurant could lead to irreparable financial losses for the company. The company is evaluating 4 possible locations a1 : New York, a2 : Istanbul, a3 : Barcelona and a4 : Athens. Three experts are in charge to evaluate the possible locations according to four criteria, c1 : climate business, c2 : availability of raw materials, c3 : investment cost and c4 : labor characteristics. The experts provide their assessments through ELICIT information defined in the linguistic expression domain S1 ={Inadmissible (I), Very inadvisable (VI), Inadvisable (IN), Normal (N), Advisable (A), Very advisable (VA), Ideal (ID)}. The criteria importance are also provided linguistically by using another linguistic expression domain: S2 ={Nothing important (NI), Very unimportant (VU), Unimportant (U) Fair (F), Important (IM), Very important (VIM), Extremely important (EI)}. All these assessments are collected in the following decision matrices (see Table 1):

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´ Labella et al. A. Table 1. Experts’ preferences (bt stands for between).

Firstly, the experts’ preferences are transformed into TrFNs (see Table 2). Table 2. Experts’ preferences.

Then, the individual preferences and weights are aggregated by using the fuzzy arithmetic mean operator to obtain the collective opinion (see Table 3). Table 3. Collective opinion.

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Afterwards, the collective weights are normalized according to Eq. 2.: w1 = 0.27, w2 = 0.18, w3 = 0.38 and w4 = 0.17. Finally, the partial dominance degree is computed for each alternative (with θ = 0.5) to obtain the ranking for the alternatives: ξ1 =0, ξ2 =1, ξ3 =0.84 and ξ4 =0.04. Therefore, the final ranking is ξ2  ξ3  ξ4  ξ1 and, consequently, the best location for the new restaurant is x2 : Istanbul.

5

Conclusions

The resolution of MCGDM problems involves several aspects such as the management of uncertainty, the experts’ hesitancy between ratings, and their behavior when facing losses and gains, which may affect the final solution of the problem. This contribution has introduced an ELICIT-TODIM method for MCGDM problems, a novel approach able to model uncertainty and hesitancy in experts’ preferences by means of ELICIT information. This proposal also considers that human stake-holders act in a more conservative way under risk situations in which huge losses are involved. Afterwards, the application of the proposal is shown in an illustrative example. As future research, it would be of interest to analyze the use of nonlinear scales [2] in decision-makers’ opinions and deal with the interpretation of extreme values in Prospect Theory. In addition, other studies should be devoted to apply this proposal to solve decision problems which could involve numerous stakeholders. Furthermore, we will consider to include a consensus mechanism in the aggregation phase to obtain an agreed solution to the MCGDM problem.

References 1. Chen, C.: Extensions of the TOPSIS for group decision-making under fuzzy environment. Fuzzy Sets Syst. 114(1), 1–9 (2000) 2. Garc´ıa-Zamora, D., Labella, A., Rodr´ıguez, R.M., Mart´ınez, L.: Nonlinear preferences in group decision-making. extreme values amplifications and extreme values reductions. Int. J. Intell. Syst. 36(11), 6581–6612 (2021) 3. Gomes, L.F.A.M., et al.: An application of the TODIM method to the multicriteria rental evaluation of residential properties. Eur. J. Oper. Res. 193(1), 204–211 (2009) 4. He, W., Dutta, B., Rodr´ıguez, R.M., Alzahrani, A.A., Martinez, L.: Induced OWA operator for group decision making dealing with extended comparative linguistic expressions with symbolic translation. Mathematics 9(1), 20 (2020) 5. Ishizaka, A., Nemery, P.: Multi-criteria decision analysis: methods and software. John Wiley & Sons (2013) 6. Kahneman, D., Tversky, A.: Prospect theory: an analysis of decision under risk. In: Handbook of the fundamentals of financial decision making: Part I, pp. 99–127. World Scientific (2013)

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7. Labella, A., Rodr´ıguez, R.M., Mart´ınez, L.: Computing with comparative linguistic expressions and symbolic translation for decision making: ELICIT information. IEEE Trans. Fuzzy Syst. 28(10), 2510–2522 (2019) 8. Mart´ınez, L., Rodriguez, R.M., Herrera, F.: The 2-tuple Linguistic Model. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24714-4 9. Rodr´ıguez, R.M., Labella, A., Mart´ınez, L.: An overview on fuzzy modelling of complex linguistic preferences in decision making. Int. J. Comput. Intell. Syst. 9, 81–94 (2016) 10. Rodr´ıguez, R.M., Mart´ınez, L., Herrera, F.: A group decision making model dealing with comparative linguistic expressions based on hesitant fuzzy linguistic term sets. Inf. Sci. 241, 28–42 (2013) 11. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning-i. Inf. Sci. 8(3), 199–249 (1975) 12. Zadeh, L.A.: Fuzzy logic= computing with words. In: Computing with Words in Information/Intelligent Systems 1, pp. 3–23. Springer (1999). https://doi.org/10. 1007/978-3-7908-1873-4 1

A Novel MCDM Method Based on Possibility Mean and Its Application to Water Resource Management Problem Under Bipolar Fuzzy Environment Totan Garai1(B) , George Biswas2 , and Uttaran Santra3 1

2

Department of Mathematics, Syamsundar College, Shyamsundar, Purba Bardhaman 713424, West Bengal, India [email protected] Depetment of Geology, Presidency University, 86/1 College Street, Kolkata 700073, West Bengal, India [email protected] 3 Central Mine Planning and Design Institute Limited, Coal India Limited, Bilaspur 495 006, Chattisgarh, India

Abstract. Bipolar fuzzy sets are an extension of a fuzzy set. In this paper, we have introduced a possibility mean of a bipolar fuzzy number. We have invented a ranking method of bipolar fuzzy numbers using the possibility mean. A novel multi-criteria decision-making (MCDM) approach is proposed here. Finally, the proposed MCDM applied to a water resources management (WRM) problem in the Purulia district of West Bengal, India. The district is facing high water scarcity. People of this area are suffering from drinking water problems throughout the year. It goes more in the summer season. WRM is the potential technique to handle the drinking water problem in this area. We have applied the proposed MCDM to solve a drinking water problem in this district. The MCDM technique has the dynamic skill for developing this situation.

Keywords: Multi-criteria decision making fuzzy · Water resource management

1

· Possibility mean · Bipolar

Introduction

The concept of a fuzzy number has been established by Moore [10]. In 1987, Dubois and Prade [11] described fuzzy numbers as consonant random sets and defined an interval-valued expectation of them. They also proved that this prediction is cumulative when adding together fuzzy numbers. The mean value of a fuzzy number has remained a meaningless term so far, as fuzzy set (FS) theory fails to capture the standard concept of expectation. The authors, for example, used the term ‘mean value’ to describe the modal value of a fuzzy number’s membership function [12,15]. Atanassov [9] introduced the intuitionistic fuzzy c The Author(s), under exclusive license to Springer Nature Switzerland AG 2022  C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 405–412, 2022. https://doi.org/10.1007/978-3-031-09173-5_49

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set (IFS). When uncertain involved, IFS gives more flexible information to the fuzzy sets. It contains a prominent feature that assigns a membership and nonmembership degree to each element [8]. Atanassov & Gargov [3] have extended IFS in the spirit of the standard interval-valued fuzzy set (IVFS). An intuitionistic fuzzy number (IFN) appears to be a good generalization of fuzzy numbers for describing unknown quantities. For describing unknown quantities, an IFN looks to be an appropriate extension of fuzzy numbers. Zadeh proposed the possibility theory of FSs [7]. Due to a lack of data, decision-maker feels difficulties and uncertainty in many complex decision-making problems. As a result, incorporating the possible mean and variance into the fuzzy multi-attribute decision making (MADM) is critical for scientific studies and real-world applications. However, There is always bipolar judgemental thinking on the negative and positive sides of human decision-making [6]. As an extension of fuzzy set, Zhang [5] proposed the idea of bipolar fuzzy set. He described a bipolar fuzzy set as an extension of a fuzzy set. After that Akram [4] has devrameloped bipolar fuzzy set in graph theory. Water scarcity is currently the world’s most pressing issue. It is a constant threat to the residents of West Bengal’s Purulia District. This district has a history of being one of West Bengal’s drought-prone areas. The residents of this district go through a lot, especially during the summer. There are very few nalas, rivers, ponds, and lakes, which are the main water sources in the district. These dry up throughout the summer, which reveals a lot of water scarcity [13]. Groundwater is the alternative source of water. The area is a complex geological area with hard rock terrain. Secondary porosity plays a major role in groundwater occurrence and it also depends on the petrology of the area [14]. Water resource management can be organized using decision-making processes. In 2010, Yilmaz & Harmancioglu [1] established a multi-criteria decision-making (MCDM) approach for the Gediz River Basin in Turkey. Garai & Garg [2] have recently used possibilistic MADM In Purulia, West Bengal. In this paper, multicriteria decision making has been used to solve the water scarcity problem of Purulia District, West Bengal. Many workers use the MCDM method on water resources problems. But only a few researchers are focusing on solving the water crisis problem using the MCDM method on possibility mean. It gives the superior result in solving the drinking water problem. The paper’s main objectives are that an effective MCDM method on possibility mean is developed, and it has been applied to the water resource management problem to solve the water crisis. This method gives better results than other existing methods. The paper’s organization is done as follows: In Sect. 2, we present some basic preliminary concepts of bipolar fuzzy numbers. In Sect. 3, the possibility mean of Bipolar Triangular Fuzzy numbers is discussed. Section 4 proposes MCDM using possibility under GIFNs environments, followed by MCDM of Water resource management in Purulia District in Sect. 5. Finally, the conclusion and the object of the future work plan are given in Sect. 6.

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Basic Preliminaries

Definition 1. Let X be a universal set. A fuzzy set C˜ in X is defined as C˜ = {(x, μC˜ (x)) : x ∈ X}, where μC˜ (x) : X → [0, 1] is called the membership function ˜ of C. Definition 2. Let X be universal set. A bipolar fuzzy set C˜ b in X is defined as C˜ b = {(x, μpC˜ (x), μpC˜ (x)) : x ∈ X}, where μpC˜ (x) : X → [0, 1] and μpC˜ (x) : X → [−1, 0] is called the positive membership function and negative membership function of C˜ b respectively. Definition 3. Let C˜ b = {(x, μpC˜ (x), μpC˜ (x)) : x ∈ X} be bipolar fuzzy set and (α, β) ∈ [−1, 0] × [0, 1], the α-cut set of C˜ b is defined as Cαp = {x ∈ X : μpC˜ (x) ≥ α}, and β-cut set of C˜ b is defined as Cβ− = {x ∈ X : μ− ˜ (x) ≤ β}, and for every C p b ˜ λ ∈ [0, 1] the set λ-cut set of C defined as Cλ = Cλ ∩ Cλp . Definition 4. A bipolar fuzzy set C˜ in X, and a bipolar triangular fuzzy number (x) and c˜b is defined as c˜b = (cl , cp , cn , cr ) with positive membership function μ+ c˜b negative membership function μ− (x) as follows b c˜ ⎧ x − cL ⎪ ⎪ , if cL ≤ x < cP ⎪ P L ⎪ ⎪ ⎨c −c 1, if x = cP μpc˜b (x) = R x−c ⎪ ⎪ ⎪ , if cP < x ≤ cR ⎪ ⎪ c ⎩ P − cR 0 Otherwise and

⎧ L c −x ⎪ ⎪ , ⎪ N − cL ⎪ c ⎪ ⎨ 1, μnc˜b (x) = cR − x ⎪ ⎪ ⎪ , ⎪ ⎪ ⎩ cN − cR 0 P

N

if cL ≤ x < cN if x = cN if cN < x ≤ cR Otherwise

b

when c = c , c˜ is called triangular bipolar fuzzy number, and cP = cN , c˜b is called bipolar triangular fuzzy number. Definition 5. An (α, β)-cut set of C˜ b is a crisp sub set of R, which is defined as follows: Cαp = {x ∈ X : μpC˜ (x) ≥ α} & Cβn = {x ∈ X : μnC˜ (x) ≤ β} R So, it follows that α-cut set Cα+ is closed interval, denoted by Cαp = [cL α , cα ] and − n L R β-cut set Cβ is closed interval, denoted by Cβ = [cβ , cβ ], which are calculated as follows:

Cαp = [clα , crα ] = [cL + α(cP − cL ), cR − α(cR − cP )]

(1)

= [c − β(c − c ), c + β(c − c )]

(2)

Cβn

=

[clβ , crβ ]

L

N

L

R

R

N

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Definition 6. Let c˜b = (cl , cp , cn , cr ) and e˜b = (eL , eP , eN , eR ) be two BTrFnumbers, where cL , cP , cN , cR > 0 and eL , eP , eN , eR > 0, λ be any real number. Then, the arithmetic operations over BTrF-numbers are defined as follows: (i) (ii) (iii) (iv) (v)

c˜b + e˜b = (cL + eL , cP + eP , cN + eN , cR + eR ) c˜b − e˜b = (cL − eR , cP − eN , cN − eP , cR − eL ) c˜b e˜b = (cL eL , cP eP , cN eN , cR eR ) λ˜ cb = (λcL , λcP , λcN , λcR ) for λ > 0 k˜ cb = (λcR , λcN , λcP , λcL ) for λ < 0

3

Possibility Mean of Bipolar Triangular Fuzzy Numbers

Let c˜b = (cl , cp , cn , cr ) bipolar triangular fuzzy number and Cαp = [clα , crα ] be the α-cut set of c˜b . Assume that 0 ≤ α ≤ 1 and f : [0, 1] → R monotonic increasing function with f (0) = 0. Then f -weighted upper and lower positive possibility mean of c˜b defined as follows as:  1  1 p b M μ (˜ c )= f (P os[˜ cb ≤ α])clα dα = f (α)clα dα (3) 0

M pμ (˜ cb )



0

1

b

f (P os[˜ c ≥

= 0

α])crα dα



1

= 0

f (α)crα dα

(4)

where, P os[˜ cb ≤ α]) = sup {μpc˜b (x)} = α x≤μpb c ˜

and P os[˜ cb ≥ α]) = sup {μpc˜b (x)} = α x≥μpb c ˜

p

cb ) and M pμ (˜ cb ) be the f -weighted upper and lower posDefinition 7. Let M μ (˜ b itive possibility mean of c˜ . Then the f -weighted positive possibility mean of c˜b can be defined as p b M μ (˜ c ) + M pμ (˜ cb ) (5) cb ) = Mμp (˜ 2 Again, let c˜b = (cl , cp , cn , cr ) bipolar triangular fuzzy number and Cβp = [clβ , crβ ] be the β-cut set of c˜b . Assume that −1 ≤ β ≤ 0 and g : [−1, 0] → R monotonic increasing function with g(0) = 0. Then g-weighted upper and lower negative possibility mean of c˜b defined as follows:  0  0 n b M μ (˜ c )= g(P os[˜ cb ≥ α])clβ dβ = − g(β)clβ dβ (6) cb ) = M nμ (˜

−1 0



−1

g(P os[˜ cb ≤ α])crβ dβ = −

−1 0



−1

g(β)crβ dβ

(7)

where, P os[˜ cb ≥ β]) = infn {μnc˜b (x)} = −β x≥μ

c ˜b

and P os[˜ cb ≤ β]) = infn {μnc˜b (x)} = −β x≤μ

c ˜b

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n

Definition 8. Let M μ (˜ cb ) and M nμ (˜ cb ) be the g-weighted upper and lower posb itive possibility mean of c˜ . Then the g-weighted negative possibility mean of c˜b can be defined as n b M μ (˜ c ) + M nμ (˜ cb ) (8) cb ) = Mμn (˜ 2 Example 1. Let c˜b = (cl , cp , cn , cr ) bipolar triangular fuzzy number. If we chosen that f (α) = 2α for α ∈ [0, 1] and g(β) = 2β for β ∈ [−1, 0]. Then f -weighted positive possibility mean and g-weighted negative possibility mean can be calculated as follows. Solution 1. Since c˜b = (cl , cp , cn , cr ) bipolar triangular fuzzy number. Then, by the equation (5) f -weighted positive possibility mean is Mμp (˜ cb ) =

cL + 4cP + cR 6

and, by the equation (8) g-weighted negative possibility mean is Mμn (˜ cb ) = −

cL + 4cN + cR 6

 Let c˜b = (cl , cp , cn , cr ) and e˜b = (eL , eP , eN , eR ) be any two bipolar triangular fuzzy numbers, then by the f -weighted positive possibility mean and g-weighted negative possibility mean, we formulated the novel ranking method of bipolar triangular fuzzy numbers cb ) > Mμp (˜ eb ), then c˜b is bigger than e˜B , denoted by c˜b > e˜b . (1) If Mμp (˜ p b p b c ) < Mμ (˜ e ), then c˜b is smaller than e˜B , denoted by c˜b < e˜b . (2) If Mμ (˜ cb ) = Mμp (˜ eb ), then (3) If Mμp (˜ n b c ) > Mμn (˜ eb ), then c˜b is bigger than e˜B , denoted by c˜b > e˜b . (i) If Mμ (˜ n b n b c ) < Mμ (˜ e ), then c˜b is smaller than e˜B , denoted by c˜b < e˜b . (ii) If Mμ (˜ cb ) = Mμn (˜ eb ), then c˜B and e˜B represent the same information, (iii) If Mμn (˜ b b denoted by c˜ = e˜ .

4

Multi-criteria Decision Making Method Using Possibility Under GIFNs Environments

In this section, we developed a decision making method based on the possibility mean. Decision making problem has so many uncertain when we ranked the alternatives, therefore we have constructed the novel decision making method under bipolar fuzzy environment. Let A = {A1 , A2 , ..., Am } be the set of m alternatives and C = {C1 , C2 , ..., Cn } be the set of n criteria. Let w = (w1 , w2 , ..., wm )T be the normalized n weight vector of the decision maker Cj (j = 1, 2, 3, ..., n), where wj ≥ 0 and j=1 wj = 1.

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Now, we derived an algorithm of the multi criteria decision making method under bipolar fuzzy environments. Algorithm: Step 1: First, we have constructed the decision matrix of multicriteria decision making (MCDM) problem with bipolar triangular fuzzy informations. The alternative values Ai (i = 1, 2, ..., m) on the basis of criteria Cj (j = 1, 2, ..., n) can be expressed as bipolar triangular fuzzy number e˜bij = P N R (eL ij , eij , eij , eij ) where (i = 1, 2, 3, ..., m; j = 1, 2, 3, ..., n) and satisfies the conP N R dition eL ij ≤ eij ≤ cij ≤ eij . The decision-making matrix can be presented as:

A = [ e˜bij ]m×n

A1 A2 = . ..

C1 e˜b11 e˜b21 .. .

⎛ ⎜ ⎜ ⎜ ⎝

C2 e˜b12 e˜b22 .. .

e˜bm1

Am

e˜bm2

··· ··· ··· .. .

Cn e˜b1n e˜b2n .. .

⎞ ⎟ ⎟ ⎟ ⎠

(9)

e˜bmn

···

Step 2: Formulate the normalized decision-making matrix. To make normalized eL

eP

ij

ij

eN eR ij R ) ij eij

ij ij b decision-making matrix we use the formula r˜ij = ( eij R , eR , eR

where eR ij =

max{eR ij |i = 1, 2, ...m; j = 1, 2, ..., n} The normalized decision matrix R of A is represented as:

b R = [ r˜ij ]m×n

A1 A2 = . ..

⎛ ⎜ ⎜ ⎜ ⎝

C1 b r˜11 b r˜21 .. .

b r˜m1

Am

C2 b r˜12 b r˜22 .. .

b r˜m2

··· ··· ··· .. . ···

Cn b r˜1n b r˜2n .. .

⎞ ⎟ ⎟ ⎟ ⎠

(10)

b r˜mn

Step 3: We calculate weighted aggregate values of all decision maker for each b alternative using this formula u ˜bij = wj r˜ij where i = 1, 2, ..., m, j = 1, 2, ...n. The weighted decision making matrix U of R can be represented as:

U =[u ˜bij ]m×n

A1 A2 = . ..

⎛ ⎜ ⎜ ⎜ ⎝

Am

C1 u ˜b11 u ˜b21 .. .

u ˜bm1

C2 u ˜b12 u ˜b22 .. .

u ˜bm2

··· ··· ··· .. . ···

Cn u ˜b1n u ˜b2n .. .

⎞ ⎟ ⎟ ⎟ ⎠

(11)

u ˜bmn

Step 4: Calculate the comprehensive values s˜bi1 as; s˜bi1 =

n  j=1

u ˜bij

(12)

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The aggregated decision matrix is defined as:

S˜ = [ s˜bi1 ]m×1

A1 A2 == . .. Am

⎛ ⎜ ⎜ ⎜ ⎝

s˜b11 s˜b21 .. .

⎞ ⎟ ⎟ ⎟ ⎠

(13)

s˜bm1

Step 5: Determine the f -weighted positive possibility mean and g-weighted negative possibility mean of s˜b11 , s˜b21 , & s˜b31 using the Eqs. 5 & 8. Step 6: Finally, we rank the alternatives Ai (i = 1, 2, ..., m) according to the nonincreasing f -weighted positive possibility mean value and g-weighted negative possibility mean value for each i = 1, 2, ..., m.

5

Multi-criteria Decision Making of Water Resource Management in Purulia District

Purulia District is under the threat of water scarcity and passes serious water problems, particularly in the summer season. This district is covered by hard rock, and has very few rivers, nalas, and ponds. However, these rivers, nalas, and ponds are the main source of water. They go to dry during the summer. District faces several drought-prone years. Groundwater is an another source of water. The groundwater level is declining, particularly, during Summer, tubewells are being dried. So, the objective of this paper is to find the proper solution to supply safe and adequate drinking water for the people of the area by considering their health and improving their life hood condition. Water resource management has the potential technique to handle the drinking water problem in this area. We have developed a novel multi-criteria water resource management method for solving this water resources management problem under bipolar fuzzy environment. Assume that the alternatives Groundwater (A1 ), Surface Water (A2 ), Rainfall (A3 ). Now, we have ranking the alternatives according to the possible criteria Quality of water (C1 ), Affordability (C2 ), Availability (C3 ). Decision matrix of the proposed MCDM problem is given by C1 A1 (2.9, 4.5, 5.8, 8.2) A˜ = A2 ⎝ (4.2, 5.0, 7.0, 9.8) A3 (3.4, 4.8, 6.9, 10.5) ⎛

C2 (3.0, 5.4, 7.0, 9.8) (5.4, 6.5, 8.4, 10.8) (4.6, 6.8, 8.8, 10.5)

C3 ⎞ (2.8, 3.5, 6.0, 7.5) (4.5, 4.8, 5.8, 8.8) ⎠ (4.0, 5.8, 7.8, 9.8)

(14)

Hence, by the proposed MCDM technique (Algorithm) the ranking order of this problem A3 > A2 > A1 .

6

Conclusion

In the present day, human decision-making depends on the positive and negative sides of bipolar judgemental thinking. Therefore, bipolar fuzzy sets have great

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impotence in human decision-making. The concept of f -weighted positive possibility mean and g-weighted negative possibility mean are introduced. A novel ranking method of bipolar triangular fuzzy number is proposed with a possibility mean. Using the mean possibility mean concept, we have formulated an MCDM technique. We will employ different decision-making of bipolar fuzzy numbers and applied to water resource management problems in the future, which extends this paper.

References 1. Yilmaz, B., Harmancioglu, N.B.: Multi-criteria decision making for water resource management: a case study of the Gediz River Basin. Turkey. Water SA. 36, 1–12 (2010) 2. Garai, T., Garg, H.: Possibilistic multi-attribute decision making for water resource management problem under single valued bipolar neutrosophic environment. Int. J. Intell. Syst. 38, 1–28 (2021) 3. Atanassov, K.T., Gargov, G.: Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst. 31, 343–349 (1989) 4. Akram, M.: Bipolar fuzzy graphs with applications. Knowl. Based Syst. 39, 1–8 (2013) 5. Zhang, W.R.: Bipolar fuzzy sets. In: Proceeding of fuzzy-IEEE Physica A: Statistical Mechanics and its Applications, pp. 835-840 (1998) 6. Zhou, M., Li, S.: Applications of bipolar fuzzy theory to semi-rings. Int. J. Innovat. Comput. Inf. Control 10, 767–781 (2014) 7. Zhang, W.-G., Wang, Y.-L.: Portfolio selection: possibilistic mean-variance model and possibilistic efficient frontier. In: Megiddo, N., Xu, Y., Zhu, B. (eds.) AAIM 2005. LNCS, vol. 3521, pp. 203–213. Springer, Heidelberg (2005). https://doi.org/ 10.1007/11496199 23 8. Jafarian, E., Rezvani, M.A.: A valuation-based method for ranking the intuitionistic fuzzy numbers. J. Intell. Fuzzy Syst. 23, 1–12 (2012) 9. Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986) 10. Moore, R.: Interval Analysis. Prentice Hall, Englewood Cliffs (1966) 11. Dubois, D., Prade, H.: The mean value of a fuzzy number. Fuzzy Sets Syst. 24, 279–300 (1987) 12. Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York (1980) 13. Das, B., Pal, S.C., Malik, S., Chakrabortty, R.: Modeling groundwater potential zones of Puruliya district, West Bengal, India using remote sensing and GIS techniques. Geol. Ecol. Landscapes 3(3), 223–237 (2019) 14. Warsi, T., et al.: Integration of geophysics and petrography for identifying the aquifer and the rock type: a case study from Giddalur, Andhra Pradesh, India. J. Earth Syst. Sci. 129(1), 1–13 (2020). https://doi.org/10.1007/s12040-019-1321-4 15. Garai, T., Chakraborty, D., Roy, T.K.: Possibility mean, variance and covariance of generalized intuitionistic fuzzy numbers and its application to multi-item inventory model with inventory level dependent demand. J. Intell. Fuzzy Syst. 35, 1021–1036 (2018)

Fuzzy TOPSIS and Goal Programming Approaches to Multi Objective Facility Location Problem for Emergency Goods and Services Distribution and Bornova/Izmir Case Study Mert Paldrak(B)

, Simge Güçlükol , Mahmut Ali Gökçe , and Melis Tan Taco˘glu

Industrial Engineering Department, Ya¸sar University, Bornova, ˙Izmir, Turkey {mert.paldrak,simge.guclukol,ali.gokce, melis.tacoglu}@yasar.edu.tr

Abstract. Distributions of vital goods and services in emergency or post disaster situations are of paramount importance to be able to meet the requirements of those in need on time. Finding an appropriate location for facilities to distribute such goods and services efficiently and quickly is an important challenge. In such a situation, location decisions for these facilities must be made quickly considering multiple objectives. This problem is a multi-objective facility location problem (MOFLP). The main focus of this study is to present two solution methodologies for a MOFLP in a post disaster situation. We specifically consider objective of minimizing maximum weighted distance traveled and minimizing total cost of facilities to be opened in order to satisfy all demand. We also provide a version of the problem, when the number of facilities to be opened is limited and second objective becomes maximizing demand covered. Due to the conflicting nature of the objective functions, we propose to apply Fuzzy TOPSIS and Goal Programming and compare the solutions obtained using these two techniques with respect to solution quality and computational time. We present the developed models and provide results from a real-life application using existing emergency assembly areas and current census data for Bornova/˙Izmir. This paper contributes in two ways to existing literature. First is the comparison between multiple (two) solution methodologies for MOPLP. Studies in the literature provide only one solution technique such as Fuzzy TOPSIS, Goal Programming etc. Secondly, we implement these methodologies by using real life data for emergency situations. Keywords: Multi-objective facility location problem · Fuzzy TOPSIS · Goal programming · Emergency assembly areas · Post-disaster

1 Problem, Background and Literature Review 1.1 Problem and Background Post disaster times require fast and efficient decision making. The decisions are usually made under time pressure, with less than perfect data and the results can be very important © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 413–424, 2022. https://doi.org/10.1007/978-3-031-09173-5_50

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in limiting death and/or adverse effects of the disaster. The existence of imperfect data can sometimes be remedied by relying on expert opinions. These decisions also usually have to be made considering multiple objectives. There is also the time factor. Conditions and constraints post disaster can change quickly and making decisions under these changing conditions/constraints is part of the challenge. One such important decision is the selection of post disaster service facility locations. Distributions of vital goods and services in emergency or post disaster situations are of paramount importance, in order to be able to meet the requirements of those in need, on time. These facilities can be anything from field hospitals for immediate health services to kitchen services to distribute food and clean water to survivors. A common practice in urban areas is to determine of “post disaster emergency assembly areas” (referred to as assembly areas hereafter). These assembly areas are determined by administration for survivors to gather in a post disaster situation. Ideally, assembly areas should be large enough to accommodate a certain number of people, with enough infrastructure and easy access to health services and road network. Unfortunately, constraints and realities of urban life limits finding assembly areas, for which all requirements are satisfied. In choosing facility locations for distribution of vital goods and services post disaster, these assembly areas, with their relative advantages and disadvantages are natural candidates. Therefore, decision-makers need fast and reliable methods in selecting where to locate these facilities. In this study, we propose two methods, namely goal programming and fuzzy TOPSIS to solve multi-objective facility location problem for emergency goods and services distribution. We also provide a reallife implementation of proposed approaches for Bornova/IZMIR. This paper organized as literature review, methodology, real-life implementation of proposed approaches for Bornova/IZMIR and conclusion, respectively. 1.2 Literature Review Studies propound multi objective or single objective optimization solutions to distribute goods efficiently and effectively [1, 2]. For single objective optimization, methods for order preference by similarity to ideal solution (TOPSIS) and fuzzy analytic hierarchy process (AHP) are used for selecting appropriate facility for a textile company with a minimum cost [3]. Most of the single objective optimization studies aim to minimize cost; however, there are also critical objectives such as minimizing max weighted distance traveled or minimize transfer time for victim from incident location to shelter [1]. In this study, two objective functions are used; minimizing max weighted distance traveled and minimizing total cost of facilities to be opened in order to satisfy all demand. Several solution methods and objectives are used so as to solve multi-objective facility location problem (MOFLP) in the literature. Branch and bound (B&B) with iterative goal programming techniques are used to minimize victim transfer time with maximizing allocating number of victims to the closest facility [4, 5]. Epsilon constrained method and Goal Programming solution approaches are examined with three objective functions; firstly, to minimize opening, transportation and operating costs, secondly to minimize transfer time for victim from incident location to shelter and thirdly to minimize number of opening facilities [1]. Miç et al. considered three objectives maximizing victim

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covering and number of facilities be opened while minimizing the cost by Weighted Goal Programming and AHP [6]. Goal programming approach is widely used for second selected solution method to make comparison for different solution approaches regarding solution quality and computational power [1]. Due to the difficulty of determining priority of the objectives for nature of the problem, Chebyshev goal programming approach, minimization of the maximum goal deviation from each goal, is chosen. Since it considers the deviations of all the targets and distributes each equally, it produces a fair and balanced solution for each deviation [7]. Different types of factors have a great impact on the decision-making process for MOFLP such as infrastructure, geological properties, social and environmental factors [8]. Therefore, Fuzzy TOPSIS approach becomes attractive by academicians due to capability of solve problems in which many different subjective attributes involved and attributes values are linguistic [9]. To choose plant locations among alternatives, Fuzzy TOPSIS approach is used for the first time in the literature [10]. Each alternative location has a rate with respect to defined criteria and each criterion is evaluated based on linguistic terms which are descriptive of fuzzy numbers [10]. They examine three criteria; field property, geological characteristic, transportation and accessibility which are evaluated in linguistic terms demonstrated by triangular fuzzy numbers. This study contributes literature in two ways. First, the comparison of Chebyshev goal programming and Fuzzy TOPSIS solution methodology for MOFLP is done for the first time. Secondly, we implement these methodologies on a real-life problem at Bornova/IZMIR neighborhoods and present results.

2 Methodology In this section, we introduce methods used in this study. First, proposed goal programming method is explained. Then Fuzzy TOPSIS and its usage are studied. 2.1 Goal Programming Goal Programming is a technique used in order to solve multi objective optimization problems. The aim of this approach is to achieve each objective with acceptable satisfactory level by minimizing deviations from the predetermined goals. In the literature, goal programming is applied to many different areas, such as accounting, portfolio management, facility location problems and so on. There are variants of goal programming approach in the literature, namely weighted goal programming, lexicographic goal programming and Chebyshev goal programming. In this study, we proposed two different mathematical models where we applied Chebyshev goal programming methods to solve emergency assembly area facility location problem. By using Chebyshev goal programming, we desired to minimize the maximum deviation from each objective. In the first goal programming model, we minimize maximum weighted distance between each neighborhood and assembly area, while minimizing the fixed cost of opening new facility. In the second model, we maximize total demand covered by opening limited number of facilities. The first model is provided below: Minimize deviationmax

(1)

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e1 /Zf ≤ deviationmax

(2)

e2 /Zd ≤ deviationmax

(3)



(fj ∗xj ) − e1 + s1 = Zf

j∈J

DW − e2 + s2 = Zd  j∈J

(dij ∗ vij ) ≤ Dw

vij ≤ hi ∗ yij yij ≤ xj  i∈I

 i∈I

yij ≥ xj

vij ≤ cj ∗ xj

 j∈J

vij = hi

vij ≥ yij

(4) (5)

∀i ∈ I ∀i ∈ I , ∀j ∈ J

(6) (7)

∀i ∈ I , ∀j ∈ J

(8)

∀j ∈ J

(9)

∀j ∈ J

(10)

∀i ∈ I

(11)

∀i ∈ I , ∀j ∈ J

(12)

xj ∈ {0, 1}, yij ∈ {0, 1}, vij ≥ 0 ∀i ∈ I , ∀j ∈ J

(13)

e1 ≥ 0, e2 ≥ 0, s1 ≥ 0, s2 ≥ 0

(14)

Objective of this mathematical model (1) is minimizing maximum deviation from each predetermined goal. Therefore, deviationmax is the first decision variable for this mathematical model. Additionally, we intend to choose assembly areas to open facility, therefore xj is a binary decision variable representing whether facility is opened at emergency assembly area j or not. Moreover, yij is also a binary decision variable that is used to assign neighborhood i to emergency assembly area j and vij is the number of victims assigned from neighborhood i to emergency assembly area j. Constraints (2) and (3) ensure that each deviation should be less than maximum allowable deviation. Constraints (4) and (5) minimize the total fixed cost for opening new facility and maximum weighted distance respectively by minimizing deviations from target values Zf and Zd . These target values are found by solving model with each objective one by one and we aimed to achieve these goals. Constraint (6) ensures that total weighted distance to reach each facility does not exceed the allowable distance. Constraint (7) indicates that number of victims assigned to all assembly areas cannot exceed the total number

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of victims in each neighborhood. Constraint (8) represents that if assembly area is not selected to open new facility, none of the neighborhood assigned to this assembly area. Constraint (9) ensures that if facility is opened at assembly area j, at least one neighborhood should assign this facility. Constraints (10) and (11) are capacity restriction for each assembly area and assignment of all victims to any assembly area respectively. Constraint (12) represents that at least one person assigned to assembly area j if facility is opened. Constraint (13) and (14) are sign restrictions for each decision variables. This mathematical model opens the facility while covering all demand by minimizing fixed cost and maximum weighted distance of each neighborhood. We proposed second model as maximizing number of demands covered by facilities by minimizing maximum weighted distance with limited number of facilities. Mathematical model of the second model is given as following: Minimize deviationmax

(1)

s3 /Zv ≤ deviationmax

(15)

 i∈I ,j∈J

vij − e3 + s3 = Zv

 j∈J

xj = K

e3 ≥ 0, s3 ≥ 0,

(16) (17) (18)

Constraint (3) and Constraints (5)–(14) We remove Constraints (2) and (4), because objective function does not minimize fixed cost. Constraint (15) and (16) represent the restriction of deviation and new objective of model which is maximizing demand covered. The number of facilities to open is limited as K by Constraint (17) and Constraint (18) together give the domain of decision variables. Lastly, K represents the limited number of facilities. 2.2 Fuzzy TOPSIS The TOPSIS method was first proposed by Hwang and Yoon [11]. The main premise behind this method is that the best candidate is closest to the positive ideal solution, while the furthest away is closest to the negative ideal solution. A positive ideal solution optimizes the benefit criterion while minimizing the cost criteria, whereas a negative ideal solution accomplishes the opposite [12]. In the fuzzy TOPSIS, weights and candidate alternatives are assessed by linguistic variables defined by fuzzy numbers. By using linguistic variables, insufficiency of the classical TOPSIS is remedied [3]. In this study, the fuzzy TOPSIS technique proposed by Chen [13] and Chen et al. [14] is applied. The algorithm of the proposed method is recapitulated as follows:

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1. Firstly, the committee of decision-makers who live close to the pilot area is formed. The decision committee consists of 3 decision-makers and fuzzy ratings of each decision-maker Dk = {1, 2, 3} are represented as triangular fuzzy number with fuzzy membership function µ ∼ (x). Rk 2. The considered evaluation criteria are decided and the hierarchical structure of the facility location problem is determined. 3. Linguistic variables are selected in order to evaluate each criteria and alternatives which are demonstrated in Tables 1 and 2.

Table 1. Linguistic variables with respect to priority weights of criteria Linguistic variables

Triangular fuzzy numbers

Unimportant (UI)

(0, 0, 0.2)

Weakly Important (WI) (0.2, 0.35, 0.5) Fairly Important (FI)

(0.4, 0.5, 0.6)

Very Important (VI)

(0.5, 0.65, 0.8)

Absolutely Important (AI)

(0.7, 0.9, 1)

Table 2. Linguistic variables used for ratings for alternatives Linguistic variables

Triangular fuzzy numbers

Very Poor (VP)

(0, 1, 2)

Poor (P)

(1, 2, 3)

Fair (F)

(3, 5, 6)

Good (G)

(5, 7, 9)

Very Good (VG)

(9, 10, 10)

4. The decision-makers evaluate the importance of the criteria and determine the ratings of each alternative using the linguistic variables (Table3).

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Table 3. Importance weight of criteria of three decision-makers Criteria

Decision-makers D1

D1

D1

C1

FI

AI

FI

C2

VI

AI

VI

C3

WI

FI

VI

C4

FI

FI

VI

C5

VI

FI

FI

C6

AI

AI

VI

C7

WI

AI

FI

C8

FI

VI

VI

The weight of criteria combined as follows: Assuming that the fuzzy ratings of three decision-makers are described using fuzzy triangular members R˜ k = (ak , bk , ck ), k = 1, 2, 3, then the combined fuzzy rating is ∼

described as R= (a, b, c), k = 1, 2, 3. 1 3 1 3 ai , b= bi , a= k=1 k=1 K K

c=

1 3 ci k=1 K

(19) ∼

If the fuzzy rating and importance weight of kth decision-maker are x ijk = ∼

∼

(aijk , bijk , cijk ) and wijk = (w˜ ij1 , w˜ ij2 , w˜ ij3 ) then combined fuzzy ratings ( x ij ) of alterna∼

tives with regard to each criterion are computed as ( x ij ) = ( aij , bij , cij ). We can find this using: aij =

1 3 aijk , k=1 K

bij =

1 3 bijk , k=1 K

cij =

1 3 cijk k=1 K

(20)

∼

The combined fuzzy weights (wij ) of all criteria are calculated as follows:   (w˜ j ) = wj1 , wj2 , wj3 Here: wi1 =

1 3 wij1 , k=1 K

wi2 =

1 3 wij2 , k=1 K

wi3 =

1 3 wij3 k=1 K

5. The fuzzy decision matrix and fuzzy weights are constructed as follows: ⎤ ⎡ x˜ 11 x˜ 12 . . . x˜ 1n ⎢ x˜ 21 x˜ 22 · · · x˜ 2n ⎥  ⎥ ˜ = w ˜ =⎢ ˜ 1, w ˜ 2 , . . . ..w ˜n . D ⎥ and W ⎢ . . . . .. . . .. ⎦ ⎣ .. x˜ m1 x˜ m2 · · · x˜ mn

(21)

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6. The fuzzy decision matrix is normalized using a linear scale transformation, which combines the numerous criteria scales into a comparable scale. Consequently, the ∼

normalized fuzzy decision matrix R is obtained as follows:  R˜ = ˜rij mxn i = 1, 2, . . . m; j = 1, 2, . . . ..n where:

r˜ij =

aij bij cij , , cj∗ cj∗ cj∗

(22)

 where c∗j = max cij . i

7. The weighted normalized decision matrix is generated by multiplying the importance weights of criteria and the values in normalized fuzzy decision matrix. Then weighted ∼

normalized fuzzy decision matrix V is given in the following:  ˜ = v˜ ij i = 1, 2, . . . m; j = 1, 2, . . . ..n v˜ ij = ˜rij (.)w ˜j V mxn

(23)

Based on the weighted normalized fuzzy decision matrix, normalized fuzzy numbers can also be represented by the elements of v˜ ij , ∀i, j. 8.

9.

∗ negative ideal solution The fuzzy− positive ideal solution∗ (FPIS, A ) and fuzzy FNIS, A are determined as A = (1, 1, 1) and A− = (0, 0, 0), respectively. Consequently, vj∗ = 1andvj− = 0 for all j. The distance of each alternative from FPIS and FNIS are found using below equations:   n (24) dv v˜ ij , v˜ ∗j , i = 1, 2, . . . .m D∗i = j=1   n D− i = 1, 2, . . . .m (25) dv v˜ ij , v˜ − i = j , j=1

where dv (., .) measures the distance between two fuzzy numbers. 10. A closeness coefficient (CCi ) is used to be able to determine the ranks of all possible alternatives. The closeness coefficient measures how close an alternative is to both a fuzzy positive and a fuzzy negative ideal solution at the same time. The closeness coefficient of each alternative is calculated: CCi =

di−

di∗ + di−

(26)

3 Implementation: Bornova/IZMIR Case Study To be able to validate our proposed models, we present a real-life implementation. We consider the problem of choosing facility locations to open at Bornova/IZMIR to meet the demand requirements of victims. In our case, we have 27 candidate locations where a facility can be opened. The locations of the candidate facilities are the assembly areas determined by city municipality office. There are 45 neighborhoods in Bornova and the victims living in these neighborhoods are to be transferred to one of the opened assembly areas in case of emergency.

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3.1 Goal Programming For our proposed goal programming models in which the objectives are to minimize total fixed cost of opening facilities and to minimize maximum weighted distance. The necessary data to run these mathematical models are collected through Internet. For example, the data on emergency assembly areas for Bornova/IZMIR is obtained from municipality’s official website [15]. The data involve area size, capacity, latitude and longitude of each of 27 candidate assembly areas. Every assembly area is in the different neighborhoods of Bornova/IZMIR. The population data of 45 neighborhoods are collected using [16]. The actual distance matrix between neighborhoods and emergency areas are calculated with the help of Bing maps API using Python. It is assumed that fixed cost of opening a facility is directly proportional to the area size. Number of victims from each neighborhood is assumed to be proportional to population size. This proportion can change according to the severity of the disaster for different disaster scenarios. Two goal programming models harness these data to find optimal solutions. 3.2 Fuzzy TOPSIS For our fuzzy TOPSIS model, many criteria that might have an impact on the location decisions are considered, nonetheless only those criteria which tend to dominate the decision are utilized. In this study, we considered eight dominating criteria to be evaluated by decision-makers and shown in Fig. 1. After criteria had been determined, a committee of decision-makers was formed and they evaluated the importance of each criterion by using linguistic variables and evaluated the ratings of each candidate facility location with respect to each criterion using linguistic variables. As soon as obtention of necessary data for fuzzy TOPSIS was completed, the candidate alternatives were ranked according to evaluation criteria.

Fig. 1. The criteria considered in Fuzzy TOPSIS

3.3 Results According to the result of the first model, 8 assembly areas are chosen to open new facilities. On the other hand, the second model is implemented by changing number of facilities to open ranging from 4 to 9. The names of the chosen assembly areas to open

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new facilities for each model are given in Table 4. The demand coverage percentages for each case are listed in Table 5. When we compared the results obtained from these two models, all demand was covered with 8 facilities in the first model, whereas we needed 9 facilities in second model. The underlying reason why the number of facilities to open is more in second model than the first one is the fact that the second model lacks the objective minimizing fixed cost. In Table 4, it can be seen that there are common assembly areas to open for different number of facilities, which is due to the high population in those areas and large assembly area size. Moreover, in the second model, the results show that 95% of all demand is covered by opening 4 facilities. Additionally, when results of goal programming and Fuzzy TOPSIS are compared, even though there are common areas to open facilities, some of them are not selected in both of the goal programming models. This is due to subjectivity involved in Fuzzy TOPSIS approach. In goal programming models, we do not consider such subjective factors as proximity to health facilities, roads and highways, slope of area, geological structure while minimizing cost and distances. On the other hand, Fuzzy TOPSIS is myopic to consider cost and distance effects on the results. Table 4. Results for decided assembly areas to open facility Goal Programming 1

Goal Programming 2

Fuzzy TOPSIS

8 facilities

4 facilities

8 facilities

9 facilities

9 facilities

Atatürk

Atatürk

Atatürk

Atatürk

Kazımdirik

Çamiçi

Barbaros

Barbaros

Barbaros

Mevlana

Erzene

Erzene

Erzene

Erzene

Erzene

Kazımdirik

Kazımdirik

Kazımdirik

Kazımdirik

Çınar

Kızılay

Kızılay

Kızılay

Meriç

Karaçam

Be¸syol

Be¸syol

Barbaros

Ümit

Ümit

Gaziosmanpa¸sa

Ye¸silova

Evka-4

E˘gridere ˙Inönü Ümit

Yunus Emre

Serintepe

Table 5. Demand coverage percentages for each goal programming model GP 1

GP 2

Fuzzy TOPSIS

# of facilities

8

4

5

6

7

8

9

9

Demand Coverage (%)

100

94.8

97

99

99.5

99.8

100

100

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4 Conclusion and Future Research Directions In this study, we propose goal programming and fuzzy TOPSIS implementations to solve multi objective facility location problem in a post disaster situation. We model the problem where facilities to distribute vital goods and services from candidate locations (emergency assembly areas) must be located subject to multiple objectives. We solve two versions of the goal programming method and a Fuzzy TOPSIS model based on real life data for Bornova/IZMIR. Our results show which facilities to open with varying demand coverage with respect to multiple objectives. To the best knowledge of the authors, this study is the first to compare these methods for the problem on hand, and implementing them for a real-life problem. As future research, goal weights are calculated by the fuzzy TOPSIS method, then weighted goal programming approach is applied. Additionally, scope of this case study is extended to different region and cities.

References 1. Praneetpholkrang, P., Kanjanawattana, S.: A multi-objective optimization model for shelter location-allocation in response to humanitarian relief logistics. Asian J. Shipp. Logist. 37(2), 149–156 (2021) 2. Celik, E., Aydin, N., Gumus, A.T.: A stochastic location and allocation model for critical items to response large-scale emergencies: a case of Turkey. Int. J. Optim. Control Theor. Appl. (IJOCTA) 7(1), 1–15 (2017) 3. Ertu˘grul, ˙I, Karaka¸so˘glu, N.: Comparison of fuzzy AHP and fuzzy TOPSIS methods for facility location selection. Int. J. Adv. Manuf. Technol. 39(7), 783–795 (2008) 4. Karatas, M., Yakıcı, E.: A multi-objective location analytics model for temporary emergency service center location decisions in disasters. Decis. Anal. J. 1, 100004 (2021) 5. Karatas, M., Yakıcı, E.: An iterative solution approach to a multi-objective facility location problem. Appl. Soft Comput. 62, 272–287 (2018) 6. Miç, P., Koyuncu, M., Hallak, J.: Primary health care center (PHCC) location-allocation with multi-objective modelling: a case study in Idleb, Syria. Int. J. Environ. Res. Public Health 16(5), 811 (2019) 7. Romero, C.: A general structure of achievement function for a goal programming model. Eur. J. Oper. Res. 153(3), 675–686 (2004) 8. Wichapa, N., Khokhajaikiat, P.: Solving multi-objective facility location problem using the fuzzy analytical hierarchy process and goal programming: a case study on infectious waste disposal centers. Oper. Res. Perspect. 4, 39–48 (2017) 9. N˘ad˘aban, S., Dzitac, S., Dzitac, I.: Fuzzy TOPSIS: a general view. Procedia Comput. Sci. 91, 823–831 (2016) 10. Chu, T.-C.: Selecting plant location via a fuzzy TOPSIS approach. Int. J. Adv. Manuf. Technol. 20(11), 859–864 (2002) 11. Hwang, C.L., Yoon, K.: Multiple Attributes Decision Making Methods and Applications. Springer, Heidelberg (1981). https://doi.org/10.1007/978-3-642-48318-9 12. Wang, Y.-M., Elhag, T.M.S.: Fuzzy TOPSIS method based on alpha level sets with an application to bridge risk assessment. Expert Syst. Appl. 31(2), 309–319 (2006). https://doi.org/ 10.1016/j.eswa.2005.09.040 13. Chen, C.-T.: Extensions of the TOPSIS for group decision-making under fuzzy environment. Fuzzy Sets Syst. 114(1), 1–9 (2000). https://doi.org/10.1016/S0165-0114(97)00377-1

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14. Chen, C.-T., Lin, C.-T., Huang, S.-F.: A fuzzy approach for supplier evaluation and selection in supply chain management. Int. J. Prod. Econ. 102(2), 289–301 (2006). https://doi.org/10. 1016/j.ijpe.2005.03.009 15. Bornova Municipality Homepage. https://bornova.bel.tr/afet-ve-acil-durum-toplanma-ala nlari/. Accessed 7 Mar 2022 16. TUIK Homepage. https://www.tuik.gov.tr/. Accessed 10 Mar 2022

Determination of Competencies with Fuzzy Multi-criteria Decision Making Methods for Determining the Development Program for Analyst Position in a Participation Bank ˙Ibrahim Yel1(B)

, Ahmet Sarucan2

, and Mehmet Emin Baysal2

1 Research and Development (R&D) Center, Kuveyt Türk Participation Bank Inc.,

Konya, Turkey [email protected] 2 Konya Technical University, Konya, Turkey

Abstract. The management and training of human resources continues to increase in importance when considering the effects such as the increase in the demand for human resources in the field of information technologies during the pandemic process. Determining the competencies of the information technology personnel and developing the deficient ones according to the competencies can be considered as the main development policy. Based on this requirement, the problem of determining the competencies of system analysts at Kuveyt Türk Participation Bank is the main subject of this study. Within the scope of the study, a survey was conducted with the participation of 11 people with at least five years of experience in the analyst position on 24 core competencies. In line with the survey results, the importance weights of the competencies were determined with fuzzy AHP. Afterwards, 10 competencies with the highest weight among 24 core competencies were determined. Evaluations were made by five experts for system analysts working in an organization in the bank for the determined 10 competencies. Rankings of system analysts were made using Neutrosophic Z-Number sets (NZN) and Fuzzy EDAS methods. These rankings became an input to the competency development program that is planned to be prepared specifically for individuals. Keywords: Neutrosophic Z Number · Fuzzy EDAS · Competency evaluation

1 Introduction The role of analysts working in the field of Information Technologies is of great importance in determining the scope of the projects to be done, producing solutions suitable for the existing infrastructure, following and adapting technological developments. In this context, every large organization should determine the criteria suitable for its own culture for the analyst positions to be included in its own structure and prepare a development plan for its employees according to these criteria. With the aim of preparing such a plan, the main subject of the study is to determine the competencies that are suitable © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 425–432, 2022. https://doi.org/10.1007/978-3-031-09173-5_51

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for the corporate culture and that the current analyst position should possess from the 24 competency pools within Kuveyt Türk Participation Bank. When the literature is examined, many studies have been conducted on competencies. However, there are not many competency-based studies in the field of information technologies. Among the fuzzy decision making methods, the use of NZN method and fuzzy EDAS method in determining competence for information technology personnel is a rare example. Employees in the analyst position were compared over the 10 competencies obtained as a result of the study. In the following titles, explanations of literature research methods, case study details and results are given respectively. 1.1 Literature View There are many studies in the literature on the evaluation of competencies. Under this heading, the literature for the evaluation of competence in the field of information technologies and the studies that deal with the subjects close to this paper are included. Dinçer and Yüksel [1], compared their new service development capabilities for 16 banks operating in Turkey. In this comparison, they calculated the weights of the criteria with fuzzy AHP, and used the results of fuzzy ANP and fuzzy VIKOR methods for comparison. Kumar and Dixit [2], on the other hand, stated that enterprises that can integrate green competencies in the forward and backward supply chain should pay attention to this integration due to the increase in environmental awareness. The selection of the most suitable recycling partner company has been the main subject of their work. The weights of the criteria were determined with fuzzy AHP. Afterwards, they ranked the alternatives with VIKOR. In one of the examples dealing with the personnel selection problem using MCDM methods in the IT sector, the SWARA method and ARAS-G methods were used by including five competency criteria [3]. Afshari and Kowal [4] emphasized the critical impact of choosing the right project manager in the IT sector on project success. Similarly, Stanujkic, Popovic [5] suggested the use of MCDM methods to be used in the selection of employees to find more motivated and competent people in a more challenging work environment. The weights of the criteria were determined by the SWARA method. Alternatives are listed with the EDAS method. They used competencies such as technical skills, interpersonal skills, presentation skills, and education level in the IT field. In another study conducted by Erdem [6] on the software industry, three main criteria were defined as basic technical skills, individual skills and auxiliary skills. Ten subcompetence criteria such as time management, communication and reporting skills, analytical thinking, communication and reporting skills were defined, weight determination and ranking of candidate personnel were made with Fuzzy AHP. The fuzzy MCDM method was used, remembering that clearer decisions can be taken with the model closest to human thought, to the personnel selection problem defined by Mittal, Goel [7], specific to Leading Indian IT companies.

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Taghavifarda, Jalilib [8], who defined 98 key competencies for IT employees working in the health sector and grouped these diagnoses according to the levels of managers (expert - medium - operational), problem solving, conceptualization, business information, field knowledge, hacking an idea, they made definitions that include competencies such as creativity and many more. They created 32 competency lists for expert managers, 32 for mid-level managers, and 34 for operational managers. Among the competency-based studies in the field of information technologies, Yel, Sarucan [9] assigned criteria weights with fuzzy AHP, and project employee assignments with fuzzy EDAS and fuzzy WASPAS based on rankings. They also stated that fuzzy EDAS method produces more effective results with defect analysis. In addition, Yel [10], after determining the criterion weights with fuzzy AHP, sorted the projects and employees with fuzzy TOPSIS, and assigned the top-ranked projects to the top-ranked employees, allowing less errors to be produced and a more balanced workload. Antepara, Arzube [11] used neutrosophic sets in their studies to evaluate competence. In this study, they defined a new framework and ranked the students according to the criteria of analysis, database management and software development projects planning and management. In a different study conducted in the country of Ecuador, Palacio, Franco [12] used neutrosophic numbers to assess the ability of mayors to carry out government-issued plans. In a study by Do, Pham [13], trainers were evaluated by extending the TOPSIS method with interval-valued neutrosophic numbers. The evaluators of the trainers are themselves, their peers, managers and students. 1.2 Fuzzy AHP In the study by Heidary Dahooie, Beheshti Jazan Abadi [3] mentioned in the literature title, 15 articles were examined on the basis of weight determination methods in the literature. They stated that the AHP method was used as the most preferred method in criterion weighting. As mentioned in the introduction, the geometric mean method was used to combine the evaluations of different evaluators. Here, the formulas in the study of Buckley [14] are based. On the basis of the process steps, the definitions in the study of Uluta¸s, Özkan [15] were taken into account. 1.3 Fuzzy EDAS The fuzzy EDAS [16] method, which was first used by Keshavarz Ghorabaee et al., was added to this study because it gave good results in the study by Yel, Sarucan [9] in terms of comparison. The data in this study were calculated based on the calculation sequence defined by Stevic et al. [17].

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1.4 NZN Calculations on the neutrosophic Z number sets followed by Ye [18] are used in this study. The evaluations of the evaluators were combined over the geometric averages, as explained in the fuzzy AHP title. Evaluation results were obtained by using 11 neutrosophic rating scales [19].

2 Case Study The determination of the key competencies required of people working as system analysts at Kuveyt Türk Participation Bank was carried out specifically for this study. As mentioned before, the 10 most important of the 24 competencies were determined according to the results of the surveys completed by 11 system analysts who have been working in a similar position for five years. Afterwards, five experienced software developers who working with system analysts were evaluated the analysts. Evaluators and those who were evaluated were selected from among the employees in the same organizational unit. Another qualification sought for evaluators was to have at least five years of experience in the bank. The 24 competencies surveyed as the subject of this study are listed in Table 1. Table 1. Competencies subject to the survey. Competencies Systematic thinking

Problem solving

Decision making

Tools and techniques

SQL knowledge

Modeling techniques

Imagination

Innovative thinking

Requirement management

Presentation skill

Negotiation skill

Active listening skill

Data analysis

Continuous learning

Result oriented

Time management

Requirements management

Management and leadership

Job prioritization

Risk management

Meeting management

Interpersonal relationship

Prototyping

Stakeholder analysis

2.1 Weights of Competencies Twenty four competencies were evaluated on nine scales by 11 system analysts who are experts in their fields, with a pairwise comparison among themselves. Each evaluator made a great contribution to this study by completing their evaluation, which took approximately 2.5 h. As a result, 10 competencies in Table 2 below were determined and calculated to be used in the evaluation of system analysts in the next step of this study.

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Table 2. Competencies and their weights. Competencies

Weights

Competencies

Weights

Systematic thinking

11.36%

Negotiation skill

9.72%

Requirement management

11.01%

Result oriented

9.55%

Problem solving

10.79%

Active listening skill

9.36%

Decision making

10.16%

Interpersonal relationship

9.19%

Presentation skill

8.91%

Management and leadership

9.95%

2.2 Evaluation of System Analysts The geometrical averages of the linguistic variables given by each evaluator were taken over the corresponding scale. As a result, each analyst was evaluated over 10 competencies and the training requirements of the relevant organization were determined. As an example, Table 3 contains the evaluation results of five evaluators for fuzzy EDAS. Competencies in Table 2 form the columns of Table 3 according to their sequence number. Evaluators are represented by the abbreviation E and analysts by the abbreviation A in Table 3. Some evaluators represented “..” and reviews for NZN are not included due to page limitations. Table 3. Channel based relationship between agile teams. Evaluator

Analysts

1

2

3

4

5

6

7

8

9

10

E1

A1

VH

H

VH

H

H

MH

H

M

H

MH

E1

..

..

..

..

..

..

..

..

..

..

..

E1

A5

ML

MH

M

MH

L

M

MH

H

M

MH

E2

A1

MH

VH

H

MH

M

H

M

H

ML

M

E2

..

..

..

..

..

..

..

..

..

..

..

E2

A5

VL

MH

MH

MH

ML

MH

M

MH

MH

MH

E3

A1

H

MH

VH

MH

MH

H

ML

H

MH

H

E3

..

..

..

..

..

..

..

..

..

..

..

E3

A5

MH

H

M

L

L

M

ML

MH

H

MH

E4

A1

VH

H

VH

M

M

VH

H

MH

MH

H

E4

..

..

..

..

..

..

..

..

..

..

..

E4

A5

MH

MH

MH

VL

L

MH

ML

H

H

MH

E5

A1

VH

VH

MH

MH

H

MH

ML

ML

M

VH

E5

..

..

..

..

..

..

..

..

..

..

..

E5

A5

MH

H

MH

ML

ML

MH

ML

MH

H

MH

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In addition, it was ensured that analysts were ranked according to their competencies among themselves. Fuzzy EDAS and NZN results are represented in represented in Table 4 and Table 5 respectively. Table 4. Fuzzy EDAS analyst evaluation results. Competencies

Analyst 1

Analyst 2

Analyst 3

Analyst 4

Analyst 5

Systematic thinking

0.79

0.53

0.35

0.56

0.23

Requirement management

0.67

0.39

0.64

0.65

0.63

Problem solving

0.68

0.57

0.59

0.64

0.56

Decision making

0.77

0.62

0.25

0.89

0.23

Management and leadership

0.70

0.67

0.53

0.66

0.28

Negotiation skill

0.66

0.66

0.62

0.31

0.58

Result oriented

0.57

0.61

0.51

0.74

0.51

Active listening skill

0.57

0.47

0.58

0.69

0.65

Interpersonal relationship

0.55

0.54

0.64

0.62

0.63

Presentation skill

0.61

0.51

0.59

0.60

0.59

Average

0.66

0.56

0.53

0.64

0.49

Ranking

1

3

4

2

5

Table 5. NZN analyst evaluation results. Competencies

Analyst 1

Analyst 2

Analyst 3

Analyst 4

Analyst 5

Systematic thinking

1.00

0.97

0.89

1.00

0.94

Requirement management

1.00

0.92

0.99

1.00

0.99

Problem solving

1.00

0.96

0.97

0.99

0.93

Decision making

0.97

0.90

0.92

1.00

0.93

Management and leadership

1.00

0.97

1.00

0.99

0.95

Negotiation skill

1.00

0.99

0.98

0.93

0.94

Result oriented

0.98

0.93

0.98

1.00

0.94

Active listening skill

0.98

0.92

0.99

1.00

0.99

Interpersonal relationship

0.98

0.90

0.99

0.99

0.99

Presentation skill

1.00

0.88

0.99

0.99

0.98

NZN results

0.97

0.78

0.90

0.96

0.86

Ranking

1

5

3

2

4

Determination of Competencies

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3 Results A systematic data was obtained, which was determined numerically and that training plans could be carried out in the relevant organization over the level of competence of the analysts. Although the results of the fuzzy EDAS and NZN methods are close to each other (Table 6), there are some differences in the determination of the competencies that will be prioritized in the implementation of education policies. These differences are mainly due to the fact that the mathematical infrastructure of the two methods is different and the NZN method also uses information fields such as indeterminacy and falsity. Table 6. Ranking comparison and result values. Competencies

NZN results

NZN ranking

Fuzzy EDAS results

Fuzzy EDAS ranking

Analyst 1

0.97

1

0.66

1

Analyst 2

0.78

5

0.56

3

Analyst 3

0.90

3

0.53

4

Analyst 4

0.96

2

0.64

2

Analyst 5

0.86

4

0.49

5

As a result, when the ranking of the analyst is examined, they stated that the results of the NZN method are closer to the real-life evaluations when the rankings among the system analysts are shared with the experts participating in the surveys. In addition, the NZN method output gave accurate range of differences between the system analysts, allowing the evaluators to perceive the results more trustworthy.

4 Conclusion It is known that increasing the competencies of the personnel working in the field of information technologies has a direct impact on the success of the project and the infrastructural maintenance expenses that the project will need in the following periods. Increasing the competencies will increase the level of meeting the future requirements as well as the output quality of the products. This study gives us the solution to the first problem we encounter when we start the step of increasing the competencies, and defines which competencies are necessary for which positions through fuzzy multi-criteria decision making methods. Examples can be given to the studies to find a significant correlation between the opportunities for future development, the increase in the competencies acquired by the employees as a result of the training policies applied, and the success rates in the projects.

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References 1. Dinçer, H., Yüksel, S.: Comparative evaluation of BSC-based new service development competencies in Turkish banking sector with the integrated fuzzy hybrid MCDM using content analysis. Int. J. Fuzzy Syst. 20(8), 2497–2516 (2018). https://doi.org/10.1007/s40815-0180519-y 2. Kumar, A., Dixit, G.: A novel hybrid MCDM framework for WEEE recycling partner evaluation on the basis of green competencies. J. Clean. Prod. 241, 118017 (2019) 3. Heidary Dahooie, J., et al.: Competency-based IT personnel selection using a hybrid SWARA and ARAS-G methodology. Hum. Factors Ergon. Manuf. Serv. Ind. 28(1), 5–16 (2018) 4. Afshari, A.R., Kowal, J.: IT project manager selection review. In: 2018 IEEE 16th International Conference on Industrial Informatics (INDIN). IEEE (2018) 5. Stanujkic, D., Popovic, G., Brzakovic, M.: An approach to personnel selection in the IT industry based on the EDAS method. Transform. Bus. Econ. 17(2), 32–44 (2018) 6. Erdem, M.B.: A fuzzy analytical hierarchy process application in personnel selection in it companies: a case study in a spin-off company. Acta Phys. Pol., A 130(1), 331–334 (2016) 7. Mittal, K., Goel, A.K., Mohindru, P.: Fuzzy Multi-Criteria Decision Making (MCDM) in human resource selection procedure-a case study of Indian IT industry. BVIMR Manage. Edge 6(1), 89–97 (2013) 8. Taghavifarda, M.T., et al.: A comparison of competencies of senior, middle and operational IT managers in the healthcare sector. Int. J. Innov. Creat. Change 8(11), 60–82 (2019) 9. Yel, ˙I, Sarucan, A., Baysal, M.E.: An application of fuzzy AHP, EDAS and WASPAS for the selection of process method in software projects. In: Kahraman, C., Cebi, S., Cevik Onar, S., Oztaysi, B., Tolga, A.C., Sari, I.U. (eds.) INFUS 2021. LNNS, vol. 307, pp. 351–359. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-85626-7_42 10. Yel, ˙I: Project and analyst and software engineer ranking and job assignment problem solution in software development projects with fuzzy multi criteria decision making techniques. In: Kahraman, C., Cebi, S., Cevik Onar, S., Oztaysi, B., Tolga, A.C., Sari, I.U. (eds.) INFUS 2019. AISC, vol. 1029, pp. 787–795. Springer, Cham (2020). https://doi.org/10.1007/978-3030-23756-1_94 11. Antepara, E.J.H., et al.: Competencies evaluation based on single valued neutrosophic numbers and decision analysis schema. Neutrosophic Sets Syst. 17, 16–19 (2017) 12. Palacio, A.J.P., et al.: Neutrosophic multicriteria method to evaluate the competencies of mayoral candidates. Neutrosophic Sets Syst. 2020(37), 368–377 (2020) 13. Do, A.D., et al.: Evaluation of Lecturers’ Performance Using a Novel Hierarchical MultiCriteria Model Based on an Interval Complex Neutrosophic Set. Infinite Study (2020) 14. Buckley, J.J.: Fuzzy hierarchical analysis. Fuzzy Sets Syst. 17(3), 233–247 (1985) 15. Uluta¸s, A., Özkan, A.M., Ta˘graf, H.: Bulanık Analitik Hiyerar¸si Süreci ve Bulanık Gri Ili¸skisel Analizi Yöntemleri Kullanılarak Personel Seçimi Yapılması. Electron. J. Soc. Sci. 17(65), 223–232 (2018) 16. Ghorabaee, M.K., et al.: Multi-criteria inventory classification using a new method of Evaluation Based on Distance from Average Solution (EDAS). Informatica (Netherlands) 26(3), 435–451 (2015) ´ Ž., et al.: Evaluation of suppliers under uncertainty: a multiphase approach based on 17. SteviC, fuzzy AHP and fuzzy EDAS. Transport (16484142) 34(1), 52–66 (2019) 18. Ye, J.: Similarity measures based on the generalized distance of neutrosophic Z-number sets and their multi-attribute decision making method. Soft. Comput. 25(22), 13975–13985 (2021). https://doi.org/10.1007/s00500-021-06199-x 19. Bolturk, E., Kahraman, C.: A novel interval-valued neutrosophic AHP with cosine similarity measure. Soft. Comput. 22(15), 4941–4958 (2018). https://doi.org/10.1007/s00500-0183140-y

Z-Fuzzy Numbers

Using Fuzzy Z - Numbers When Processing Flexible Queries Ramiz Alekperov(B) Department of Computer Engineering, Odlar Yurdu University, Baku AZ1072, Azerbaijan [email protected]

Abstract. This work is devoted to the formalization of fuzzy conditions of fuzzy queries in the form of a Z-number without the direct intervention of experts. As you know, the number of alternatives involved in the decision-making process in multicriteria problems is usually not very large and is evaluated according to criteria with the help of experts. However, fuzzy queries are mainly used to evaluate and rank a large number of alternatives, for which it is almost impossible to carry out a preliminary assessment by criteria. On the other hand, how can you be sure of the reliability of the obtained results of fuzzy queries with fuzzy conditions, also expressed with certain reliability. A method is proposed for converting fuzzy conditions of fuzzy queries (criteria) to Z-number, with the help of which it is possible to use multi-criteria decision-making methods of Z-numbers to process fuzzy queries with a large number of records (alternatives). Keywords: Corporate information systems · Fuzzy queries · Fuzzy associations · Z-number · Decision-making methods · Decision-making matrix

1 Introduction The data processed in the databases of modern corporate information systems, to which the wholesale and retail trade enterprises can be attributed, are of a clear, numerical nature [1]. However, queries to these databases are often vague. That is connected with the semantic ambiguity of the language, in particular, with the inherent vagueness of the textual information with the help of which queries to databases are formulated. In this regard, the concept of fuzzy queries to databases appeared, which is a promising direction for storing and processing information in modern corporate information systems. A fuzzy query is a kind of flexible query, in which the user describes the requirements with fuzzy query conditions [1, 4–7, 9]. Mechanisms of fuzzy queries to relational databases based on the theory of fuzzy sets Zadeh [2], were first proposed in 1984 and subsequently developed in the works of D. Dubois and G. Prada [3, 4] and other researchers [10–15]. According to many authors [10–12], there are two main directions of research in the field of using fuzzy set theory in the context of a DBMS. The first assumes the © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 435–444, 2022. https://doi.org/10.1007/978-3-031-09173-5_52

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use of a regular database and, in fact, develops a fuzzy query interface using fuzzy sets, possibility theory, fuzzy logic, etc. The second line of research uses fuzzy or probabilistic elements to develop a fuzzy database model. In our research, we adhere to the concept: a fuzzy query system is an interface for users that allows you to obtain information from a database using a (quasi) sentence in a natural language [7]. Considering that there are some differences depending on the peculiarities of different implementations of the algorithm for processing fuzzy queries, however, the response to a fuzzy query sentence, as a rule, is a list of records ranked according to the degree of correspondence to the query [2]. Each of the fuzzy queries incorporates systems that can be considered as a multicriteria decision-making problem for the solution of which there are many methods [8, 16, 18, 19]. As you know, the alternatives involved in the decision-making process are usually not very large and are evaluated according to criteria with the help of experts. However, fuzzy queries are mainly used to evaluate and rank a large number of alternatives, for which it is almost impossible to conduct a preliminary assessment by experts on all criteria. On the other hand, how can experts practically assess the reliability of each fuzzy condition for each alternative? Recently, to solve the problem of evaluating the reliability of numbers, the concept of Z-number = number + its reliability has been used, which was first put forward by Zadeh. A number of decision-making methods have been developed based on the Z-number [2]. In this paper, a method is proposed for converting the conditions of fuzzy queries to Z-number, with the help of which decision-making methods can be used to process fuzzy queries with a large number of alternatives. The work is structured as follows. In Sect. 2, we present the necessary definitions and some material serving as a prerequisite. Section 3 formulates the problem statement. Section 4 presents a method and an algorithm for its solution. Section 5 shows an example of converting a fuzzy condition to the form Z-number. Final comments are included in Sect. 6. This article discusses the issues of formulating fuzzy Z-numbers for modeling linguistic uncertainty for processing fuzzy-flexible queries to a relational database using multi-criteria decision-making methods.

2 Basic Concepts and Definitions Definition 1. Fuzzy Z –number. A fuzzy Z-number is a tuple consisting of two fuzzy ˜ is a fuzzy number presented by an expert ˜ R ˜ ) [3, 8, 16–18], where X numbers Z = (X, X to assess the factor under investigation; RX˜ is a fuzzy number describing the degree of confidence in the expert’s assessment (Fig. 1). Definition 2. Triangular fuzzy numbers - most often used as predictive values of parameters and corresponds to a term-set for example T = {x is approximately equal to x*}. It is clear that x* ± x ≈ x*, and as x decreases to zero, the degree of confidence in the estimate grows to unity. This, from the point of view of the membership function, gives the latter a triangular appearance, and the degree of approximation is characterized by an expert. A more general form of a triangular fuzzy number can be described by the

Using Fuzzy Z - Numbers When Processing Flexible Queries

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Fig. 1. Graphical representation of a fuzzy z-number

following triplet (x1 , x2 , x3 ), where the membership can be determined as the following equation. ⎧ ⎪ 0 < x ≤ x1 ⎪0 ⎪ ⎨ x−x1 , x ≤ x ≤ x 1 2 1 μ(x) = xx23−x (1) −x ⎪ x −x , x ≤ x ≤ x 2 3 ⎪ 3 2 ⎪ ⎩ 0, x3 ≤ x Definition 3. Confidence interval and risks. Let us assume that N (x) is a fuzzy range of values x with a membership function Nα (x), and Nα (x) is a fuzzy set of level α. Then they say that α is the level of confidence, and Nα is the interval of the α -level of confidence, the confidence interval of the level of α, or the α-cut of the fuzzy value x. Here Nα is the interval of possible values of x, the degree of membership of which is equal to or greater than α. Confidence intervals of the α-level can be associated with the indicator of the riskcontent of a fuzzy value [3].

3 Problem Statement Currently, there is no single method for evaluating and ranking the results of fuzzy queries. A fuzzy query has a large number of alternatives that must be evaluated according to fuzzy criteria, which must be represented as fuzzy Z-numbers. Let’s say there is a fuzzy query with the following content: Make a list of drugs that are close to expiration date and are selling poorly. Here we find fuzzy classes [21]: QS1: Goods LV [expiration date, less], QS2: Goods LV [sales, bad]. At the same time, when you ask the manager what to take as a basis, he says that drugs with a shorter shelf life are of most interest to us, but for greater confidence, it is also necessary to consider the poor sales of the drug.

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As can be seen from the request, it is also necessary to evaluate the reliability of fuzzy conditions - fuzzy associations [21]. This request in the form of Z-numbers can be represented as follows: −Z1 = (the expiration date of the medicine is less than a month, the medicine with a shorter shelf life, I am sure that this medicine needs to be returned to the distributor). −Z2 = (the medicine sold less than 10 pieces in a month, the medicine is not selling well, I am very sure that this medicine needs to be returned to the distributor). What to say about the fact that the manager is sure that drugs with shorter shelf life must be returned first of all, but among them there may be drugs that are selling very well. Therefore, for greater confidence, it is necessary to choose medicines with poor sales. Usually, the number of drugs in the databases is over 40–50 thousand. Therefore, it is almost impossible to evaluate every medicine by expert means. In this connection, it is necessary to develop an approach with the help of which it was possible, without the intervention of experts, to formulate a fuzzy Z-number in a dynamic mode. The peculiarity of relational queries lies in the nature of the connection of relational tables, which depends on the formulation of the query itself. For our case, the table is taken as a basis, where information about the expiration dates of drugs is stored, which is linked through the LEFT OUTER JOIN with a relational table where the movements of goods are stored, etc. The next section proposes an approach that transforms fuzzy query conditions to Z-numbers, which allows multi-criteria decision-making techniques to be applied to evaluate and rank the results of fuzzy queries.

4 The Proposed Method of Converting Regular Fuzzy Number to Z-number Based on the statement “a fuzzy query is a kind of flexible query, in which the user describes the requirements with fuzzy query conditions” [1], a method is proposed to formalize fuzzy query conditions in the form of a Z-number. As can be seen from Definition 1, a fuzzy Z-number consists of X˜ – fuzzy number, which, when solving problems of multi-criteria decision-making, are presented by experts to assess the factor under study; R˜ x – is a fuzzy number describing the degree of confidence in the expert’s assessment. Select π(*) from tables where (2) Here, the tables list the tables used in the query π (*) are the projections of the columns of those tables, Zij is the transformation of fuzzy conditions into Z-numbers, N is the number of alternatives in the query, M is the number of conditions, and ⊕ is the logical operation between fuzzy conditions.

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∼

a. Formation of the first part of the Z-number X-fuzzy number. Managers usually use generalized interval values when determining the parameters of goods. For example, goods with a low price - goods with a price of 1 to 10 manat, goods with a small sales volume of 0 to 10 manat per day, goods with a short expiration date of 0 to 30 days, and so on. Thus, if we take into account the real prices of the goods participating in the survey, then each parameter can be described in the form of triangular fuzzy numbers - (x1 , x2 ,x3 ) (Fig. 2). Here x2 is understood as the expected value. In other words, managers simulate statements of the type: “Parameter X is equal to x2 and is in the interval [x1 , x3 ]”, writing as X˜ ∼ = [ x1 , x2 , x3 ]. In this case, the whole range is called the universe, and the number x*- supremum. For example, x = x* v μ(x*)/x* = ∝. In this case, the main task is to form a fuzzy number X˜ to solve the problem posed in the article. The following algorithm is proposed for this:: 1. Determining to which term-set x = x* belongs. For this case, the term-set with the maximum value among the values of the membership functions for all term-sets is found according to the following formula (Fig. 2):   n μti (x*) t (3) = max αx* i=1 x* where ti are term-sets, μti (x∗ ) are the values of the membership function for each term-set and x∗ .

Fig. 2. Determining to which term – set x = x* belongs

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As shown in Fig. 2 for the example, if the value of x = x* then αxt ∗ then it is safe to say that x = x∗ with a small number of sales term-plurality and QS: Goods belong to the fuzzy class [sales, less].

Fig. 3. Graphical representation of the fuzzy number X˜

2. Calculation of the initial and final boundary interval values of the fuzzy number X˜ . When x = x *, one of the main problems is to find the last boundary interval points of the fuzzy number X˜ , if it is certain that αxt ∗ belongs to the t-term-set of x (Fig. 3). First of all, we know that when x = x*, the value obtained by the membership t . And ifα t < 1, it is a violation of the principle of normalization of the function isαx∗ x∗ fuzzy number X˜ . But on the other hand, the main feature of fuzzy queries is that it is known in advance that x = x*, ie for the value of x* of the triangular fuzzy number X˜ , t = μ(x ∗ )/x ∗ = 1 and refers to the grass-term-set. To do this, it is suggested to use αx∗ the following formulas [20], which are most commonly used in practice: 



x1 = x1 + αxt ∗ (x∗ − x1 ); x3 = x3 − αxt ∗ (x3 − x4 )

(4)

The main issue here is the risk of accepting the triangular fuzzy X˜ in these intervals and at the expected value. That is, what percentage can be sure that the newly found formed X˜ fuzzy number x = x* is true: "The parameter x is equal to x* and is in the   interval [x1 , x3 ]- confidence and risk can be judged based on the value of the membership t is an confidence indicator, then 1 − α t function (Definition 2). In other words, if. αx∗ x∗ can be considered as a trisk indicator (uncertainty). To do this, the following rule is proposed in [20]: First, a universal formula for calculating x is proposed: 

xu =





2x∗ x3 − x1 x3 − (x∗ )2 



x3 − x1

(5)

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and the value of the membership function for xu is calculated: ∝ (xu ) =

xu − x∗ 



x3 − x1

(6)

The universality of formula 5 is that in the values found on its basis, the values of the belonging function of the fuzzy number x overlap at the boundaries of the numbers x < x * and x > x *. Then, based on the formula of an integral measure of the probability of the accepted fuzzy number: r(∝ (xu )) =

∝ (xu )2 ∗ 100 2

(7)

the risk rate (percentage) is calculated. b. R˜ x - of the second part of the Z-number - the formation of a fuzzy number. Determination of reliability describing the degree of confidence in the expert’s assessment. In our case, the expert is an algorithm for forming R˜ x - a fuzzy number, which is described below: 1. Confidence intervals of the α-level can be associated with the index of risk-content of a fuzzy quantity [3] In other words, α-levels of a fuzzy set can also be associated with the reliability of the statement that, for example, “Parameter X is equal to x∗ with reliability R˜ x and is in the interval [x1 , x3 ]”, where R˜ x is a fuzzy number. To define a fuzzy number - the reliability of R˜ x , you can use definition 2 in [8], where five linguistic concepts are given to describe the degree of safety of the R-universe of discourse - R = {Very Low, Low, Medium, High, Very High}, assuming that that only two adjacent linguistic variables have the same value. The mathematical formulas for calculating the value of the membership function for each linguistic variable and their graphical representations are given, which were modified by us to determine the intervals according to the α = 0.5 - section. This definition can also be used for our case - to determine the degree of confidence that the parameter X is equal to x∗ with the reliabilityR˜ x , according to the following algorithm. 2. According to the value obtained in step a, step 2, the value ∝ (xu ), using the formulas proposed by us below, the fuzzy number of the number R˜ x is determined: ⎧ ⎪ VL [0, 0, 0.125] where 0.000 ≤∝ (xu ) ≤ 0.125 ⎪ ⎪ ⎪ ⎪ ⎨ L [0.125, 0.25, 0.375] where 0.125 Z(ν+d +1) = · · · = Z(ν+d +a) > Z(ν+d +a+1) = · · · = Z(ν+d +a+b) > Z(ν+d +a+b+1) = · · · = Z(n) . 2n−2ν−d +1 Then we get: ω(i) = 2n−ν+1 n(n+1) , i = 1, ν, ω(i) = n(n+1) , i = ν + 1, ν + d , ω(i)

=

2n−2ν−2d −2a−b+1 , i n(n+1) 2n−2ν−2d −2a−2b−c+1 ,i = n(n+1)

2n−2ν−2d −a+1 ,i n(n+1)

=

=

ν + d + 1, ν + d + a, ω(i)

ν + d + a + 1, ν + d + a + b, ω(i)

= =

ν + d + a + b + 1, n. Suppose at the levelα < 1, we have two clusters with the same number of criteria. We assume that the first cluster contains criteriaZ1 , . . . , Zν , and the second cluster contains criteria Zν+1 , . . . , Z2ν . 5a. The remaining criteria are divided into single clusters. Let us calculate for the criteria of two numerous clusters the sums of similarity indicatorsθj =

 2ν i=1 μA Zi , Zj , j = 1, 2ν. We select the maximum sum θj , j = 1, 2ν from the found sums. Suppose that the maximum sum has a criterion from the cluster Z1 , . . . , Zν . We find the sums of similarity indicators of the elements of single clusters with the elements of the cluster Z1 , . . . , Zν and then rank all the criteria: Z1 = · · · = Zν > Zν+1 = · · · = Z2ν > Z(2ν+1) > . . . > Z(n) . 2n−3ν+1 Then ωi = 2n−ν+1 n(n+1) , i = 1, ν, ωi = n(n+1) , i = ν + 1, 2ν, ω(i) = 5.



2(n−i+1) n(n+1) , i

= 2ν + 1, n. 5b. The remaining criteria are divided into clusters with different elements, which are less than ν and greater than one or equal to one. In this case, the weight coefficients of two numerous clusters are found similarly to point 5a. The weight coefficients of the criteria of the remaining clusters are found similarly to the procedure of point 4. 5c. The remaining criteria are divided into clusters with different elements, which are less than ν and greater than one or equal to one, but among them there are several numerous ones containing the same number of expert criteria. Suppose that there are two such clusters with the number of elements equal to d, then we find the sums of similarity indicators of all the elements of these clusters with elements of the cluster Z1 , . . . , Zν determined from two clusters of such a number of criteria according to the point 5a. Based on these sums and the rules (1), (2), we rank all the criteria and determine the weight coefficients. 6. Suppose at the levelα = 1, we have n clusters whose elements are ranked according

  to the principle: the larger the sum θj = ni=1 μA Zi , Zj , j = 1, n, the greater the rank. To find the weight coefficients of expert criteria, we use (4). 

The weight coefficients of the expert criteria obtained as a result of the analysis are necessary to determine the group criterion. Some expert criteria that have significantly lower weights compared to other criteria can be removed from consideration. In that case the weight coefficients of the remaining criteria are recalculated.

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as a set of m Z-numbers Z =

expert criterion is defined  The group n ˜ Zl = B˜ l , R˜ l , l = 1, m , where B˜ l = i=1 ωi Bil , l = 1, m, and fuzzy number

R˜ l , l = 1, m equals to one of fuzzy number R˜ j = rj1 , rj2 , rjL , rjR , j = 1, k. To determine which value the reliability to, we determine the aggregating segments

corresponds n ˜ ˜ for Z-numbers Zl = Bl , Rl = i=1 ωi Zil , l = 1, m and for Z-numbers with fuzzy

numbers B˜ l , l = 1, m and R˜ j = rj1 , rj2 , rjL , rjR , j = 1, k.

Let us denote the aggregating segment of Zl = B˜ l , R˜ l , l = 1, m as

 1 2 zl , zl , l = 1, m and the aggregating segments of Zl1 = B˜ l , R˜ 1 , Zl2 =

  B˜ l , R˜ 2 , . . . , Zlk = B˜ l , R˜ k as zlj1 , zlj2 , l = 1, m, j = 1, k. Determine the dis

2

2  l zl1 − zlj1 + zl2 − zlj2 , j = 1, k. If dpl = minlj , j = 1, k, then tances: dj =

Zl = B˜ l , R˜ p , l = 1, m, p = 1, k. Similarly, the second components are determined

for all Z-numbers Zl = B˜ l , R˜ l , l = 1, m that are elements of the group expert criterion

  Z = Zl = B˜ l , R˜ l , l = 1, m .

4 Conclusion Comparative analysis of information coming from different experts plays an essential role in decision making problems, especially when such information is the only one available. The analysis of expert information becomes more complicated when taking into account its reliability, since the methods that allow it to be carried out are under development. In the paper, expert evaluation criteria are formalized using sets of linguistic Z-numbers. The paper develops a method for a comparative analysis of expert evaluation criteria based on pairwise distances between them, determined using their aggregating segments. On the basis of pairwise distances, a fuzzy binary similarity relation has been constructed, which makes it possible to divide expert criteria into clusters of similar ones and use these clusters to determine the significance of individual criteria in order to include them in a group expert criterion. The developed method opens up new possibilities for analyzing expert information, taking into account its reliability and reducing the risk of errors in making decisions based on it. It is expected that future research will focus on solving problem of evaluation of ecosystem services provided by green spaces in large cities under Z-information.

References 1. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning. Inf. Sci. 8, 199–249 (1975). https://doi.org/10.1016/0020-0255(75)90036-5

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2. Ryjov, A.P.: The concept of a full orthogonal semantic scope and the measuring of semantic uncertainty. In: Proceedings of the Fifth International Conference Information Processing and Management of Uncertainty in Knowledge-Based Systems, pp. 33–34 (1994) 3. Poleshchuk, O.M., Komarov, E.G., Darwish, A.: Comparative analysis of expert criteria on the basis of complete orthogonal semantic spaces. In: Proceedings of the 19th International Conference on Soft Computing and Measurements, SCM-2016, pp. 369–373 (2016) 4. Poleshchuk, O.M.: Creation of linguistic scales for expert evaluation of parameters of complex objects based on semantic scopes. In: Proceedings of the International Russian Automation Conference, (RusAutoCon – 2018), p. 8501686 (2018). https://doi.org/10.1109/RUSAUT OCON.2018.8501686 5. Zadeh, L.A.: A note on Z-numbers. Inf. Sci. 14(181), 2923–2932 (2011). https://doi.org/10. 1016/j.ins.2011.02.022 6. Wang, J.-Q., Cao, Y.-X., Zhang, H.-Y.: Multicriteria decision making method based on distance measure and Choquet integral for linguistic Z-numbers. Cogn. Comput. 9(6), 827–842 (2017) 7. Sari, I.U., Kahraman, C.: Intuitionistic fuzzy Z-numbers. Adv. Intell. Syst. Comput. 1197, 1316–1324 (2020) 8. Aliev, R.A., Alizadeh, A.V., Huseynov, O.H.: The arithmetic of discrete Z-numbers. Inf. Sci. 1(290), 134–155 (2015). https://doi.org/10.1016/j.ins.2014.08.024 9. Aliev, R.A., Huseynov, O.H., Zeinalova, L.M.: The arithmetic of continuous Z-numbers. Inf. Sci. 373, 441–460 (2016). https://doi.org/10.1016/j.ins.2016.08.078 10. Wang, F., Mao, J.: Approach to multicriteria group decision making with Z-numbers based on TOPSIS and power aggregation operators. Math. Probl. Eng. 2019, 1–18 (2019) 11. Aliyev, R.R., Talal Mraizid, D.A., Huseynov, O.H.: Expected utility based on decision making under Z- information and its application. Comput. Intell. Neurosci. 3, 364512 (2015). https:// doi.org/10.1155/2015/364512 12. Poleshchuk, O.M.: Novel approach to multicriteria decision making under Z-information. In: Proceedings of the International Russian Automation Conference, (RusAutoCon-2019), p. 8867607 (2019). https://doi.org/10.1109/RUSAUTOCON.2019.8867607 13. Kang, B., Wei, D., Li, Y., Deng, Y.: A method of converting Z-number to classical fuzzy number. J. Inf. Comput. Sci. 9(3), 703–709 (2012) 14. Jamal, M., Khalif, K., Mohamad, S.: The implementation of Z-numbers in fuzzy clustering algorithm for wellness of chronic kidney disease patients. In: Journal of Physics: Conference Series, vol. 1366, p. 012058 (2018) 15. Aliev, R.A., Pedrycz, W., Guirimov, B.G., Huseynov, O.H.: Clustering method for production of Z-numbers based if-then rules. Inf. Sci. 520, 155–176 (2020) 16. Poleshchuk, O.M.: Clustering Z-information based on semantic spaces. In: Kahraman, C., Cebi, S., Cevik Onar, S., Oztaysi, B., Tolga, A.C., Sari, I.U. (eds.) INFUS 2021. LNNS, vol. 308, pp. 888–894. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-85577-2_102 17. Poleshchuk, O.M.: Expert group information formalization based on Z-numbers. In: Journal of Physics: Conference Series, vol. 1703, p. 012010 (2020). https://doi.org/10.1088/17426596/1703/1/012010 18. Poleshchuk, O., Komarov, E.: The determination of rating points of objects with qualitative characteristics and their usage in decision making problems. Int. J. Comput. Math. Sci. 3(7), 360–364 (2009) 19. Averkin, A.N., Batyrshin., I.Z., Blishun, A.F., Tarasov, V.B.: Fuzzy Sets in Models of Control and Artificial Intelligence. Nauka, Moscow (1986) 20. Fishburn, P.: Utility Theory for Decision Making. Nauka, Moscow (1978)

Creation of a Group Expert Criterion for Evaluating the State of a Plant Species Under Z-Information Olga Poleshchuk(B) Bauman Moscow State Technical University, Moscow, Russia [email protected]

Abstract. In the paper, the author created a group expert criterion for evaluating the state of «Norway maple», growing in Moscow. The creation was carried out considering the reliability of information coming from experts. The state of urban plantations is represented as a set of Z-numbers, the number of which is equal to the number of levels on the scale used by experts. The first components of Znumbers are formalizations of scale levels and values of full orthogonal semantic spaces, which are constructed on the basis of individual expert information on the evaluations of plants of the Norway maple species. The second components of Z-numbers are fuzzy evaluations of information reliability of each of the experts, which are also the values of the full orthogonal semantic space. To construct a group expert criterion, an analysis of individual expert criteria was carried out. For this, similarity indicators were determined, using which all individual expert criteria were divided into similar clusters with a certain level of confidence. To determine the significance of each individual criterion for the contribution to the group expert criterion, their weight coefficients were determined with help of cluster analysis. The method developed in the paper for creating a group expert criterion based on the analysis of individual criteria, their clustering and determining the contribution of each of the criteria, taking into account the reliability, allows avoiding the risk of errors when making decisions based on the data obtained. Keywords: Z-information · Expert criterion · Plant species

1 Introduction When evaluating various parameters or characteristics, experts are often involved. The approaches and criteria of experts may differ, so the task of their analysis and the construction of a group expert criterion arises. The task of analyzing and constructing a group criterion becomes much more complicated when experts use fuzzy evaluations and statements, for example, “high efficiency”, “low potential”, “quite healthy tree” and so on. The task becomes even more complicated if we consider that expert evaluations are not absolutely reliable, but try to evaluate the reliability and take it into account when processing expert information. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 452–459, 2022. https://doi.org/10.1007/978-3-031-09173-5_54

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Fuzzy sets theory and, of course, a linguistic variable [1, 2] made it possible to formalize fuzzy expert evaluations. A Z-number determined in 2011 by Professor Lotfi Zadeh allows to consider the reliability of expert information when processing it [3]. Accounting for the reliability of expert information plays a significant role in all areas of human activity, but especially this role increases when we have the only expert information to make decisions. For example, when assessing the urban plantations, experts use visual inspection, during which, obviously, there is a possibility of error [4]. At the same time, physical measuring instruments are used selectively due to the large number of plants, saving time and material costs. In addition to taking into account reliability in such an evaluation, there are difficulties with choosing a scale and justifying this choice. As a rule, experts use ordinal scales, the elements of which are words or phrases of the professional language of experts, which means that methods for their formalization are needed [5]. To be able to consider the reliability of incoming information, operations on Znumbers [6, 7] and methods for their ranking [7, 8] were developed, distances between them were determined [9, 10], cluster analysis methods were developed [11–13], as well as decision-making methods under Z-information (information with Z-numbers). To improve the quality of real world models, linguistic Z-numbers [14] and intuitionistic Z-numbers [15] have been developed. In [16], a model of group expert opinion was developed. Obviously, developments are needed that allow aggregating expert opinions using not only discrete Z-numbers, but also continuous ones. Since linguistic variables are used to formalize expert opinions, models based on linguistic Z-numbers are objectively needed. Especially such methods are needed when evaluating the qualitative characteristics of urban ecosystems, which can only be evaluated by an expert. In this paper we will develop a group expert criterion for evaluating the urban plantations considering the reliability of expert information. The paper contains four sections. Section 2 includes the necessary basic concepts and definitions. Section 3 presents a group expert criterion model for evaluating the state of «Norway maple», growing in Moscow, under Z-information. Section 4 presents the conclusion.

2 Basic Concepts and Definitions {X , T (X ), U , V , S}- is a linguistic variable, where X is its name, T (X ) = {Xl , l = 1, m} is its term-set with terms Xl , l = 1, m, defined by the rule V . A rule S defines for each term the corresponding fuzzy set of U [1]. A full orthogonal semantic space is a linguistic variable with the following properties of continuous membership functions μl (x), l = 1, m: Ul = −

−

{x ∈ U : μl (x) = 1}∀l =1, m is a point ore an interval; μl (x), l =1, m does not increase and does not decrease correspondingly to the right and to the left of Ul ;  m l=1 μl (x) = 1, ∀x ∈ U [3]. ˜ R) ˜ R. ˜ is a pair of fuzzy numbers A, ˜ Fuzzy number A˜ has a A Z-number Z = (A, ˜ membership function μA (x) : X → [0, 1], fuzzy number R is fuzzy constraint on the

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measure of reliability of the first component with membership function μR (x) : [0, 1] → [0, 1] [3]. In [17], based on α- cuts a weighted segment [v1 , v2 ] for a fuzzy number A˜ = (a1 , a2 , aL , aR ) is determined: v1 = a1 −

aL aR , v2 = a2 + 6 6

(1)

In [18], using (1) an aggregating segment for a Z-number is determined in the form of a weighted segment of fuzzy number that is the product of the first and second ˜ R), ˜ A˜ = (a1 , a2 , aL , aR ), R˜ = (r1 , r2 , rL , rR ), component of a Z-number. If Z = (A, then the aggregation segment [δ1 , δ2 ] for this Z-number we determine such as:     1 1 1 δ1 = r1 a1 − aL − rL a1 − aL . 6 6 12     1 1 1 δ2 = r2 a2 + aR + rR a2 + aR . (2) 6 6 12 In [18], a distance between Z-numbers   is determined. If Z1 and Z2 are Z-numbers  with aggregating segments δ11 , δ21 , δ12 , δ22 accordingly, then a distance between them is defined as follows:   1 2  2 d (Z1 , Z2 ) = δ1 − δ12 + δ21 − δ22 (3)

3 Problem Formulation and Solution −

To evaluate the state of «Norway maple», three experts use a scale Al , l =1, 7: A1 - «old dead», A2 - «recently died», A3 - «drying up», A4 - «very weak», A5 - «mean weak», A6 - «moderately weak», A7 - «no signs of weakness» and to evaluate the reliability of −

information, experts use a scale Rk , k =1, 5: R1 - «Unlikely», R2 - «Not very likely», R3 - «Likely», R4 - «Very likely», R5 - «Extremely likely». The scale Al , l = 1, 7 is formalized on the basis of statistical information received from experts [4, 5]. Since the results of evaluation by experts may be different, the −

−

formalization of the scale by experts may also differ. Denote by A˜ il , l =1, 7, i =1, 3 the formalizations of the scale of three experts represented by full orthogonal semantic −

−

spaces with membership functions μil , l =1, 7, i =1, 3. The scale for evaluating the reliability of information with values R1 -«Unlikely», R2 - «Not very likely», R3 «Likely», R4 - «Very likely», R5 - «Extremely likely» is represented by full orthogonal semantic space with fuzzy numbers R1 = (0, 0, 0.25), R˜ 2 = (0.25, 0.25, 0.25), R˜ 3 = (0.5, 0.25, 0.25), R˜ 4 = (0.75, 0.25, 0.25), R˜ 5 = (1, 0.25, 0), which correspond to the _

−

values Rk , k =1, 5. Then the evaluation criterion of the species «Norway maple» of the ith expert, i

−

=1, 3 is presented as a set of seven Z-numbers Zi

=

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 − − − − ˜ ˜ Zil = Ail , Ril , l =1, 7 , i =1, 3, where R˜ ij = (ril1 , ril2 , ril3 ), l =1, 7, i =1, n equals −

to one of fuzzy number Rk , k =1, 5 ril1 = maxm (rmil1 1 ), il2 = maxm (rmil 2 ), ril3 = maxm (rmil3 ), if an expert evaluated M plants of the species «Norway maple» by the −

−

−

−

level Al , l =1, 7, with reliability R˜ iml = (riml1 , riml2 , riml3 ), i =1, n, m =1, M , l =1, 7. −

−

The membership functions μil , l =1, 7, i =1, 3 of the full orthogonal semantic −

−

−

spaces A˜ il , l =1, 7, i =1, 3 of three experts formalizing the scale Al , l =1, 7 and reliability of its levels are presented in Tables 1, 2, and 3. Table 1. Membership functions and reliability of the first expert. μ11 , R

μ12 , R

μ13 , R

μ14 , R

μ15 , R

μ16 , R

μ17 , R

(0, 0.011, 0, 0.024), R5

(0.035, 0.035, 0.024, 0.024), R3

(0.059, 0.059, 0.024, 0.024), R5

(0.083, 0.113, 0.024, 0.075), R3

(0.188, 0.275, 0.075, 0.260), R4

(0.535, 0.738, 0.260, 0.176), R4

(0.914, 1.000, 0.176, 0), R4

Table 2. Membership functions and reliability of the second expert. μ21 , R

μ22 , R

μ23 , R

μ24 , R

μ25 , R

μ26 , R

μ27 , R

(0, 0.022, 0, 0), R5

(0.022, 0.022, 0, 0), R3

(0.022, 0.050, 0, 0.050), R4

(0.100, 0.100, 0.050, 0.060), R4

(0.160, 0.275, 0.060, 0.300), R5

(0.575, 0.778, 0.300, 0.153), R4

(0.931, 1.000, 0.153, 0), R5

Table 3. Membership functions and reliability of the third expert. μ31 , R

μ32 , R

μ33 , R

μ34 , R

μ35 , R

μ36 , R

μ37 , R

(0, 0.012, 0, 0.026), R5

(0.038, 0.038, 0.026, 0.026), R2

(0.064, 0.064, 0.026, 0.026), R5

(0.090, 0.090, 0.026, 0.026), R3

(0.116, 0.263, 0.026, 0.324), R4

(0.587, 0.852, 0.324, 0.100), R3

(0.952, 1.000, 0.100, 0), R4

segments of the expert evaluation criteria Zi

We denote aggregating

− − − −   Zil = A˜ il , R˜ il , l =1, 7 , i =1, 3 as zil1 , zil2 , l =1, 7, i =1, 3.

=

Using formula (3), we determine the distance between the i-th and j-th expert criteria by the formula:   7  2  2     1  z1 − z1 + z2 − z2 d Zi , Zj = dij = (4) il jl il jl 7 l=1

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−

Let dmax = maxdij , i =1, 3, j =1, 3. We define for the expert evaluation criteria i,j

 − − − − ˜ ˜ Zi = Zil = Ail , Ril , l =1, 7 , i =1, 3, a difference index δij , i =1, 3, j =1, 3 and a similarity index ρii , i = 1, 3, j = 1, 3: δij =

− − dij , i =1, 3, j =1, 3 dmax −

−

ρij = 1 − δij , i =1, 3, j =1, 3 .

(5)

(6)

 ∼ It is easy to prove that B with membership Z , Z function μ i j B   = ρij defines a fuzzy − − ∼ A˜ il , R˜ il , l =1, 7 , i =1, 3 [19]. Using B, binary similarity relation on the set Zi = its transitive closure was constructed   and used for cluster analysis of expert evaluation − − criteria Zi = A˜ il , R˜ il , l =1, 7 , i =1, 3 [19]. The matrix elements of the fuzzy binary similarity relation and the matrix elements of the transitive closure of fuzzy binary similarity relation are presented in Tables 4 and 5. Table 4. The matrix elements of fuzzy binary similarity relation. 1

0.724

0.832

0.724

1

0.811

0.832

0.811

1

Table 5. The matrix elements of the transitive closure of fuzzy binary similarity relation. 1

0.811

0.832

0.811

1

0.811

0.832

0.811

1

For α = 0.811 we get one cluster {1, 2, 3}, for α = 0.832 we get two clusters {1, 3}, {2}, for α = 1 we get three clusters {1}, {2}, {3}. We can see from the matrix of the fuzzy binary similarity relation and, accordingly, from the results of the fuzzy cluster analysis, the evaluation criteria of the first and third experts are the most similar. Let us determine the significance of each individual criterion using weight coefficients using the results of cluster analysis. At α = 0.811, all criteria belong to the same cluster, so their weight coefficients will be considered equal. At α = 0.832, the criteria fall into two clusters. The criteria of the first and third experts fell into the same cluster, so their weight coefficients are equal, and the

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weight coefficient of the second expert is less than the weight coefficients of the first and third experts. We rank the criteria: Z1 = Z3 > Z2 . After that we apply the Fishburn scale to find the weight coefficients: ωi = −

2(n−i+1) n(n+1) , i

−

=1, n. In our particular case, we

obtain: ωi = 2(4−i) 12 , i =1, 3. Substitute i = 3, we get the weight coefficient of the second expert ω2 = 16 . Since the weight coefficients of the first and third experts are 5 equal, we get ω1 = ω3 = 12 . At α = 1, we get three clusters. Let us find the sum − 3 j=1 ρij , i =1, 3 for each criterion and rank the criteria according to the principle: the larger the greater the weight coefficient. We the rank and, accordingly,  the sum, the higher get 3j=1 ρ1j = 2.556, 3j=1 ρ2j = 2.535, 3j=1 ρ3j = 2.643. From here and Fishburn scale we get ω1 = 13 , ω2 = 16 , ω3 = 21 . Let us find a group expert criterion for ω1 = 13 , ω2 = 16 , ω3 = 21 . Then corresponds to, Z = ω1 Z1 + ω2 Z2 + ω3 Z3 . To determine which value the reliability  ˜ ˜ we determine the aggregating segments for Z-numbers Zl = Al , Rl = ω1 Z1l + −

−

ω2 Z2l + ω3 Z3l l =1, 7 and for Z-numbers with fuzzy numbers A˜ l , l =1, 7 and ∼ fuzzy numbers R˜ 1 = (0, 0, 0.25), R˜ 2 = (0.25, 0.25, 0.25), R3 = (0.5, 0.25, 0.25), R˜ 4 = (0.75, 0.25, 0.25), R˜ 5 = (1, 0.25, 0). Let us denote the aggregating segments  − −   of Zl = A˜ l , R˜ l , l =1, 7 as zl1 , zl2 , l =1, 7 and the aggregating segments of Zl1 =      − − A˜ l , R˜ 1 , Zl2 = A˜ l , R˜ 2 , . . . , Zl7 = A˜ l , R˜ 7 as zlj1 , zlj2 , l =1, 7, j =1, 5. Determine   2  2  − − zl1 − zlj1 + zl2 − zlj2 , j =1, 5. If dpl = minj djl , j =1, 5, the distances: djl =  − − then Zl = A˜ l , R˜ p , l =1, 7, p =1, 5. Similarly, the second components are determined  − for all Z-numbers Zl = A˜ l , R˜ l , l =1, 7 that are elements of the group expert criterion

 − Z = Zl = A˜ l , R˜ l , l =1, 7 . After calculating the membership functions of the group expert criterion are presented in Table 6. Table 6. Membership functions and reliability of the group expert criterion. μ1 , R

μ2 , R

μ3 , R

μ4 , R

μ5 , R

μ6 , R

μ7 , R

(0, 0.013, 0, 0.021), R5

(0.034, 0.034, 0.021, 0.021), R3

(0.055, 0.060, 0.021, 0.021), R5

(0.081, 0.099, 0.021, 0.048), R3

(0.147, 0.269, 0.048, 0.299), R4

(0.568, 0.802, 0.299, 0.134), R4

(0.936, 1.000, 0.134, 0), R4

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4 Conclusion In the paper, a group expert criterion for evaluating the state of «Norway maple», growing in Moscow, is constructed. Individual expert criteria are formalized with help of a set of Z-numbers, which makes it possible to consider the reliability of expert evaluations. The number of Z-numbers corresponds to the number of levels on the scale used by experts to carry out evaluation procedures. For the formalization of expert criteria, linguistic Z-numbers are used, the components of which are the values of semantic spaces with the properties of completeness and orthogonality. To construct a group expert criterion, the weight coefficients of individual expert criteria are determined based on fuzzy cluster analysis and the formulated rules. Creation of group expert opinions and criteria has always been an urgent task, but under Z-information, such methods are currently not developed enough, and for continuous linguistic Z-numbers there are practically none. This gap significantly limits the possibilities of analyzing expert information, taking into account its reliability, given that linguistic variables with continuous membership functions are used everywhere to formalize both components of Z-numbers. The author in this paper partially fills this gap and provides new opportunities for modeling expert criteria, their analysis and the creation of a group expert criterion, considering the reliability of expert evaluations. Future research is expected to focus on creating systems of fuzzy inference rules using group expert criteria to determine aggregating evaluations of green ecosystems services.

References 1. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning. Inf. Sci. 8, 199–249 (1975). https://doi.org/10.1016/0020-0255(75)90036-5 2. Ryjov, A.P.: The concept of a full orthogonal semantic scope and the measuring of semantic uncertainty. In: Proceedings of the Fifth International Conference Information Processing and Management of Uncertainty in Knowledge-Based Systems, pp. 33–34 (1994) 3. Zadeh, L.A.: A note on Z-numbers. Inf. Sci. 14(181), 2923–2932 (2011). https://doi.org/10. 1016/j.ins.2011.02.022 4. Darwish, A., Poleshchuk, O.: New models for monitoring and clustering of the state of plant species based on semantic spaces. J. Intell. Fuzzy Syst. 26(3), 1089–1094 (2014) 5. Poleshchuk, O., Komarov, E.: The determination of rating points of objects and groups of objects with qualitative characteristics. In: Proceedings of the North American Fuzzy Information Processing Society (NAFIPS-2009), p. 5156416 (2009) 6. Aliev, R.A., Huseynov, O.H., Zeinalova, L.M.: The arithmetic of continuous Z-numbers. Inf. Sci. 373, 441–460 (2016). https://doi.org/10.1016/j.ins.2016.08.078 7. Wang, F., Mao, J.: Approach to multicriteria group decision making with Z-numbers based on Topsis and power aggregation operators. Math. Prob. Eng. 2019, 1–18 (2019) 8. Aliyev, R.R., Talal Mraizid, D.A., Huseynov, O.H.: Expected utility based on decision making under Z-information and its application. Comput. Intell. Neurosci. 3, 364512 (2015). https:// doi.org/10.1155/2015/364512 9. Kang, B., Wei, D., Li, Y., Deng, Y.: A method of converting Z-number to classical fuzzy number. J. Inf. Comput. Sci. 9(3), 703–709 (2012)

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10. Poleshchuk, O.M.: Novel approach to multicriteria decision making under Z-information. In: Proceedings of the International Russian Automation Conference, (RusAutoCon-2019), p. 8867607 (2019). doi: https://doi.org/10.1109/RUSAUTOCON.2019.8867607 11. Jamal, M., Khalif, K., Mohamad, S.: The implementation of Z-numbers in fuzzy clustering algorithm for wellness of chronic kidney disease patients. J. Phys. Conf. Ser. 1366, 012058 (2018) 12. Aliev, R.A., Pedrycz, W., Guirimov, B.G., Huseynov, O.H.: Clustering method for production of Z-numbers based if-then rules. Inform. Sci. 520, 155–176 (2020) 13. Poleshchuk, O.M.: Clustering Z-information based on semantic spaces. In: Kahraman, C., Cebi, S., Cevik Onar, S., Oztaysi, B., Tolga, A.C., Sari, I.U. (eds.) INFUS 2021. LNNS, vol. 308, pp. 888–894. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-85577-2_102 14. Wang, J.-Q., Cao, Y.-X., Zhang, H.-Y.: Multicriteria decision making method based on distance measure and Choquet integral for linguistic Z-numbers. Cogn. Comput. 9(6), 827–842 (2017) 15. Sari, I.U., Kahraman, C.: Intuitionistic fuzzy Z-numbers. Adv. Intell. Syst. Comput. 1197, 1316–1324 (2020) 16. Aliev, R.K., Huseynov, O.H., Aliyeva, K.R.: Aggregation of an expert group opinion under Z-information. In: Proceedings of the Eighth International Conference on Soft Computing, Computing with Words and Perceptions in System Analysis, Decision and Control (ICSCW2015), pp. 115–124 (2015) 17. Domrachev, V.G., Poleshuk, O.M.: A regression model for fuzzy initial data. Autom. Rem. Control. 64(11), 1715–1723 (2003) 18. Poleshchuk, O.M.: Expert group information formalization based on Z-numbers. J. Phys: Conf. Ser. 1703, 012010 (2020). https://doi.org/10.1088/1742-6596/1703/1/012010 19. Averkin, A.N., Batyrshin, I.Z., Blishun, A.F., Tarasov, V.B.: Fuzzy Sets in Models of Control and Artificial Intelligence. Nauka, Moscow (1986)

Data Envelopment Analysis with Z-Numbers – An Application to Project Selection Dorota Kuchta(B)

and Barbara Gładysz

Wroclaw University of Science and Technology, Wybrze˙ze Wyspia´nskiego 27, 50-370 Wrocław, Poland [email protected]

Abstract. Data Envelopment Analysis in its fuzzy version is used to rank projects on the basis of their, in the general case, fuzzy inputs and outputs. The possibility of a biased evaluation of the inputs and outputs is taken into account. To eliminate bias influence, Z-numbers are applied. Although there exist attempts to integrate them in Data Envelopment Analysis, the known approaches are too simplistic, as they do not distinguish between biases concerning project inputs from those concerning project outputs. In this paper we propose a modified (addressing the above issue) Data Envelopment Analysis model with project inputs and outputs represented by Z-numbers and show its usefulness in the area of project portfolio management. The approach is illustrated by means of an example. Keywords: Project portfolio · Z-number · Data Envelopment Analysis

1 Introduction Practically in each organisation today, projects are present in a clearly noticeable way. They are necessary to achieve strategic, tactical, and operational objectives of the organisation. Today, no organisation can operate without projects. Even organisations with no particular growth ambitions have to implement compliance projects – those required to meet regulatory conditions needed to operate or emergency projects, which have to be implemented to repair a damage or solve a problem caused by a critical situation. To support current operations (to reduce cost or improve performance), organisational projects are implemented. And strategical projects (e.g., new product development) are those that support the long-term mission of the organisations. They are a must for any organisation that plans to survive for a longer time [1]. Some projects do not require high budgets, and they are initiated after a simple manager approval. However, many projects cannot be implemented without a considerable budget. As the resources of each organisation are limited, projects from the projects proposal portfolio are subject to a ranking procedure, and only the projects from the top of the list are accepted and assigned a budget. This is a delicate and conflicting procedure that must be performed with the highest possible care, objectivity, and transparency [1]. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 460–467, 2022. https://doi.org/10.1007/978-3-031-09173-5_55

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Here we assume that this procedure is based on planned inputs and outputs for each project. The inputs and outputs cannot always be described as crisped numbers – partly because the projects are only in the proposal stage, not even accepted for realization, and partly because a high degree of imprecision is inherent to any project [2]. We consider here project inputs and outputs being triangular fuzzy numbers. The problem consists in the difficulty in collecting reliable information about candidate projects. Apart from the obvious lack of knowledge resulting from the fact that the projects being considered belong totally to the future, as they are only competing to be approved, the problem of subjectivity or other biases in project presentation and evaluation is omnipresent in project management. The objective of this paper is to propose a model to be applied to the project selection process (from a portfolio of project candidates) which allows to take various biases into account and make the project selection procedure as objective and transparent as possible. The model is based on the Data Envelopment Analysis (DEA) approach combined with Z-numbers [3]. In Sect. 2 we discuss the problem of biases in project management. In Sect. 3 we present basic information on fuzzy DEA, as well the motivation for using DEA in this problem. In Sect. 4 we describe Z-numbers and their application to reducing subjectivity and other biases. In Sect. 5 we present our model against the background of the state of art concerning Z-number-based DEA models. Section 6 contains a project selection example taken from the literature, where our results are compared with those generated using a model from the literature.

2 Biases in Project Management ‘There are no facts about the future’ [4]: before a project starts, or even before it is finished, there are mainly unknowns about its features and parameters. When project managers, team members, or project owners are asked to give their estimation of project input or outputs, they do this without knowing the future, in the context of their organisation, their position within it, and subject to their personal features, experiences, constraints, and limitations. In [5] two groups of biases in project features assessment are distinguished: cognitive biases and motivational biases. Cognitive biases are caused by how the human mind microprocesses information (e.g., overconfidence in one’s abilities or knowledge). Motivational biases occur when people are influenced by what they want to happen (e.g., ‘wishful thinking’) or by external pressures or circumstances (e.g., the desire to ‘sell’ the project even by distorting some of its features). A widely discussed subject in project management literature is optimism bias [6], although other types of project feature estimators are also distinguished [7]: pessimistic, optimistic, and hesitant ones. This means that the information about future projects has to be verified and possibly adjusted, taking into account the features of information source.

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3 DEA Application to the Project Selection Problem When an organisation is facing the problem of selecting projects for implementation within a predestined budget, they have to decide about the criteria and a method of aggregating the criteria into a total scoring. The selection criteria include financial ones, but recently also, to a higher and higher degree, non-financial ones [1]. Usually a simple weighted total is used, but the problem of setting the weights is delicate, and it is generally difficult to arrive at a compromise. For this reason, among the different models used to rank individual projectcandidates, we find crisp [8] and fuzzy [9–11] DEA models. l , x m , x u (a positive fuzzy triangular number with the support Let us suppose that xjp jp jp   l u m ) represents the j − th input of the p − th project equal to xjp , xjp and the core xjp   l , x m , x u for the p = 1, . . . , n; j = 1, . . . , t, and a positive triangular fuzzy number xrp rp rp r − th output of the p − th project, p = 1, . . . , n; r = 1, . . . , s. The idea of DEA is to consider the efficiencies of the p − th project defined as   s l , xm , xu x v r=1 r rp rp rp   , p = 1, . . . , n Ep =  (1) t l m u j=1 wj xjp , xjp , xjp For each po = 1, . . . , n a mathematical programming problem is solved, where Ep0 is the objective function being maximized, equalities Ep ≤ 1 for p = po are the constraints, and the weights vr , r = 1, . . . , s; wj , j = 1, . . . , t are decision variables,   fulfilling the conditions sr=1 vr = 1 and tj=1 wj = 1. Ep0 is used as the basis for the evaluation of project po = 1, . . . , n. DEA models are suitable for the project selection problem, as they allow us to avoid the delicate discussion about the weights of different inputs and outputs: they permit each ‘project owner’ to present their project in the best light, choosing their own weights. If in spite of this possibility the project is ranked low, the result will be hard to undermine. Of course, the mathematical programming problems described above have to be “translated” into crisp versions according to a selected concept, and then they are transformed to linear programming problems. In fact, any existing fuzzy DEA model could be used here, e.g., the one from [11]. The problem lies in the biases described in the previous section. Project ‘owners’ will tend to underestimate project inputs and/or overestimate project outputs. On the other hand, there might also occur pessimistic, hesitant, or externally conditioned experts who might be characterized by another type of behaviours (overestimating the inputs and/or underestimating the outputs). The bias type and size will be individual, but its existence is highly probable, and their influence may be substantial.

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This aspect has been taken into account in [10], where the project selection problem is solved using a DEA model based on Z-numbers. Z-numbers give the possibility to adjust original information about project inputs and outputs to more objective and comparable data. Theoretically, any Z-number-based DEA model could be used in this context, e.g., [12, 13]. However, we identified a substantial inadequacy of those models for the project selection problem. The inadequacy is related to the transformation of a Znumbers based DEA model to a fuzzy mathematical programming model with adjusted fuzzy parameters. This problem will be discussed in the following section.

4 Z-Numbers and Their Application to Decision Making   ˜ Z˜ , where A˜ and Z˜ are fuzzy A Z-fuzzy number or a Z-number [3] is a couple A, numbers. In this paper, we will limit ourselves to triangular fuzzy numbers. Z˜ represents the credibility of the expert opinion A˜ or the possibility that evaluation A˜ is correct. The need for Z-fuzzy numbers is a consequence of the problems depicted in Sect. 2: the original evaluation A˜ of some magnitude (cost, duration, satisfaction degree, etc.) may be biased, and Z˜ represents the corresponding bias. In most papers in which Z-numbers are used, the support of Z˜ is included in the interval [0,1] and a certain “dictionary” of possible values of Z˜ is used. For example, in [14] the following dictionary is used: unlikely (0.1, 0.2, 0.3), fairly impossible (0.3, 0.4, 0.5), maybe (0.4, 0.5, 0.6), fairly (0.5, 0.6, 0.7), (0.7, 0.8, 0.9), most likely (0.8, 0.9, 1), certainly (1, 1, 1). A Z-fuzzy number is eventually expressed as a classical fuzzy number. The result of this transformation should represent the adjusted evaluation. In the literature, there exist two basic approaches to this transformation. Both share the first phase: fuzzy number Z˜ is defuzzied using a selected defuzzification method (e.g., the gravity method [10]) and represented by means of a crisp number α ∈ [0, 1]. The second stage takes two forms, depending on the source. In our opinion, both forms are inadequate for the project selection process and generally for the DEA approach. • The first approach, proposed in [15] andapplied  to the DEA method in [13], proposes ˜ ˜ This approach ˜ to choose as the final representation of A, Z the fuzzy number α A. assumes that each reliability degree other than ‘certainly’ (1,1,1) means that evaluation A˜ is too high and has to be reduced, so the corresponding membership function should be moved to the left. Such a procedure is correct only for certain types of data and biases: e.g., in the case when revenues are evaluated and the expert asked is an optimist. In the DEA method, this approach may be correct for outputs and optimistic experts. If, however, cost or inputs are evaluated and the expert is an optimist, this type of expert opinion adjustment is incorrect, and it even deepens the bias effect. This approach would also be incorrect in case of a pessimistic bias. The problem is that it uses the same type of adjustment to both inputs and outputs, which is essentially incorrect. Any type of bias will probably have a different effect on inputs and on outputs. • The second approach, proposed in the context of DEA and the project selection problem in [10], will be illustrated by means of Fig. 1.

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Fig. 1. Illustration of methods of adjusting A˜ on the basis of Z˜

The method proposed in [10] has a similar drawback as the one from [15]: it does not differ for project inputs and outputs. However, it is less limiting than the other one and can be easily adjusted to the needs of the project selection problem. This approach is based on the following assumption: if the reliability of the estimation A˜ is not complete, the ˜ By enlarging support of the adjusted fuzzy number should be greater than the one of A. the support, we admit that, of the limited reliability, other values than just those   because included in the interval a, a (that was given by the not completely reliable  expert) ˜ ˜ have to be considered. Thus, the authors of [10] transform the Z-number A, Z to the  − triangular fuzzy number a , a, a (see Fig. 1), where α is the crisp number (mentioned

_

− ˜ and a = a − a−a , a = a + a−a . The sides of the above) representing the reliability Z, α α _      triangles determined by nodes a , 0 , M , a , 0 and a, 0 , N , (a, 0) (Fig. 1)







_

are parallel. We propose to modify this approach, in order to differentiate the biases for inputs and outputs. Here, we assume optimism bias, omnipresent in the project management reality, or a situation (also extremely likely) in which the ‘project owner’ presents the project deliberately in such a way that it has higher chances to get accepted, embellishing the reality. Our proposal consists in the following transformations:    −  ˜ ˜ • for inputs: from Z-number A, Z to triangular fuzzy number a, a, a (triangle     a, 0 , M , a , 0 in Fig. 1);     ˜ ˜ • for outputs: from Z-number A, Z to triangular fuzzy number a , a, a (triangle _

 a , 0 , M , (a, 0) in Fig. 1).



_

These transformations allow to make input and output information about the projects more realistic. The two approaches - ours (in which inputs and outputs are treated

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differently) and that proposed in [10] (where inputs and outputs are subject to identical transformation) – will be applied to an example in the next section.

5 Application to a Project Portfolio In [10] (after [9]) 16 IT project candidates are considered. Each of them is assumed to have one input – the cost of the project (expressed in a monetary unit), and three outputs: number of potential subsequent projects being a consequence of the one in question (Output 1, expressed as absolute number), contribution of the project to the workflow improvement (Output 2, expressed as a number between 0 and 1, 0 standing for no contribution at all, and 1 for a very high contribution), percentage of end users considerably improving their Internet capacities as a result of the project (Output 3). The input and the outputs of the projects are estimated as triangular fuzzy variable, see Table 1. For each value, respective reliabilities (denoted with R in Table 1) were set (based on the experts features). They could be chosen among three possibilities: likely - L (0.5, 0.6, 0.7), usually – U (0.65, 0.75, 0.85), and sure - S (0.8, 1, 1). Table 1. Data for projects from [10] (the column couples: (Input, R), (Output 1, R), (Output 2, R) and (Output 3, R) form Z-numbers) Nb

Input

R

Output 1

R

Output 2

R

Output 3

R

1

(412, 435, 458) L

(128, 132, 136)

L

(0.73, 0.865, 0.95)

L

(42, 46, 50)

L

2

(174, 178, 182) L

(69, 75, 81)

S

(0.05, 0.16, 0.29)

S

(6, 9, 12)

L

3

(225, 242, 259) U

(27, 28, 29)

S

(0.68, 0.74, 0.91)

L

(36, 41, 46)

U

4

(308, 323, 338) S

(85, 90, 95)

S

(0.55, 0.7, 0.85)

U

(87, 90, 93)

S

5

(175, 189, 203) S

(73, 75, 77)

S

(0.37, 0.55, 0.68)

U

(71, 75, 79)

U

6

(84, 93, 102)

(66, 70, 74)

S

(0.07, 0.17, 0.31)

S

(45, 47, 49)

U

7

(349, 370, 391) S

(123, 130, 137)

U

(0.95, 0.99, 0.99)

S

(39, 44, 49)

L

8

(245, 271, 297) S

(41, 43, 45)

U

(0.31, 0.45, 0.59)

L

(32, 37, 42)

S

L

9

(151, 154, 157) U

(58, 60, 62)

L

(0.35, 0.45, 0.65)

U

(25, 27, 29)

L

10

(265, 281, 297) S

(49, 52, 55)

S

(0.68, 0.79, 0.94)

U

(37, 41, 45)

U

11

(345, 362, 379) L

(21, 24, 27)

L

(0.15, 0.18, 0.21)

U

(54, 58, 62)

S

12

(215, 222, 229) U

(4, 6, 8)

L

(0.19, 0.2, 0.21)

S

(56, 59, 62)

S

13

(385, 391, 397) S

(6, 8, 10)

L

(0.33, 0.34, 0.35)

S

(34, 36, 38)

S

14

(454, 474, 494) S

(7, 9, 11)

L

(0.44, 0.47, 0.5)

L

(11, 13, 15)

U

15

(384, 390, 396) S

(7, 8, 9)

S

(0.2, 0.22, 0.24)

S

(48, 51, 54)

L

16

(384, 391, 398) U

(9, 11, 13)

S

(0.16, 0.18, 0.2)

U

(52, 54, 56)

L

In [10] the approach to Z-numbers proposed by the authors of [10] was used, and then the fuzzy DEA problem was solved following [11]. We transformed the Z-numbers

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according to the approach proposed in Sect. 4 and also used the concept of the DEA solution from [11]. The results from [10] and ours are compared in Table 2. Table 2. Project efficiencies and rankings according to [10] and to our approach to Z-numbers Nb

Project efficiency [10]

Ranking position [10]

Project efficiency our approach

Ranking position our approach

1

0.9059

8

0.8348

7

2

0.7975

10

0.7640

8

3

1.4033

4

1.1678

4

4

1.0579

7

0.7372

9

5

1.4762

3

1.3536

2

6

1.6205

1

1.4841

1

7

1.0971

6

1.0785

6

8

0.8502

9

0.7117

10

9

1.4877

2

1.3115

3

10

1.2192

5

1.0894

5

11

0.4009

12

0.3809

12

12

0.6493

11

0.6334

11

13

0.3641

14

0.3472

14

14

0.3923

13

0.3491

13

15

0.3415

15

0.3297

15

16

0.3373

16

0.3245

16

We can see that in our approach all the project efficiencies are lower and the rankings are slightly different. In our approach, the inputs and outputs were adjusted based on the optimism assumption, whose influence is obviously reverse in case of inputs and outputs. Our approach is therefore bound to represent more objective information than that of [10], where it was ignored that ‘project owners’ would usually try to underestimate inputs and overestimate outputs. The IT company would accept the projects with the highest ranking positions, till the project portfolio budget is exhausted. The approach used may have a significant influence on the composition of the finally accepted portfolio, as we can see differences already on the 2nd position of the ranking.

6 Conclusions We have discussed the problem of project selection, performed on the basis of planned project inputs and project outputs. The decision to which projects assign budgets is not an easy task for organisations. The problems linked to this process follow not only from

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the obvious fact of incomplete knowledge about yet un-started projects, but also from human features and interpersonal and intergroup conflicts of interests and incompatible objectives. These soft factors cause biases in the information about project inputs and outputs the decision makers receive as the basis for their project selection decision. We propose a modification of a method to reduce biases and to make the project selection process more objective. The method is based on Data Envelopment Analysis and Znumbers. More research is needed to explore the usage of Z-numbers for different types of bias. Here we assume the optimism (or equivalently, the embellishing of reality) bias. In addition, methods of identifying biases (on the basis of historical records or questionnaires) should be developed. Funding. This research was funded by the National Science Centre (Poland), grant number 484071, 2020/37/B/HS4/03125, Grant title: Non-parametric approaches for the performance measurement of units with complex internal structure.

References 1. Larson, E.W., Gray, C.F.: Project Management: The Managerial Process. McGraw-Hill Irwin International Edition, New York (2011) 2. Kuchta, D., Despotis, D., Fr˛aczkowski, K., Stanek, S.: Applications of data envelopment analysis for the evaluation of IT project success. Oper. Res. Decis. 29, 17–36 (2019) 3. Zadeh, L.A.A.: Note on Z-numbers. Inf. Sci. 181(14), 2923–2932 (2011) 4. Hulett, D.T.: Integrated Cost-Schedule Risk Analysis. Gower (2011) 5. Schuyler, J.: Risk and Decision Analysis in Projects. Planning PressTM (2001) 6. Prater, J., Kirytopoulos, K., Tony, M.: Optimism bias within the project management context: a systematic quantitative literature review. Int. J. Manag. Proj. Bus. 10, 370–385 (2017) 7. Marchwicka, E.D., Kuchta, D.: Critical path method for Z-fuzzy numbers. In: Intelligent and Fuzzy Techniques for Emerging Conditions and Digital Transformation: Proceedings of the INFUS 2021 Conference, held 24–26 August 2021, vol. 2, pp. 871–878 (2022) 8. Eilat, H., Golany, B., Shtub, A.: Constructing and evaluating balanced portfolios of R&D projects with interactions: a DEA based methodology. Eur. J. Oper. Res. 172, 1018–1039 (2006) 9. Ghapanchi, A., Tavana, M., Khakbaz, M.H., Low, G.A.: Methodology for selecting portfolios of projects with interactions and under uncertainty. Int. J. Proj. Manag. 30, 791–803 (2012) 10. Azadeh, A., Kokabi, R.: Z-number DEA: a new possibilistic DEA in the context of Z-numbers. Adv. Eng. Inf. 30, 604–617 (2016) 11. Saati, S., Memariani, A., Jahanshahloo, G.: Efficiency analysis and ranking of DMUs with fuzzy data. Fuzzy Optim. Decis. Mak. 1, 255–267 (2002) 12. Sotoudeh-Anvari, A., Najafi, E., Soheil, S.-N.: A new data envelopment analysis in fully fuzzy environment on the base of the degree of certainty of information. J. Intell. Fuzzy Syst. 30, 3131–3142 (2016) 13. Namakin, A., Fallah, M., Javadi, M.: A new evaluation for solving the fully fuzzy data envelopment analysis with Z-numbers. Symmetry (Basel) 10, 384 (2018) 14. Hendiani, S., Bagherpour, M., Mahmoudi, A., Liao, H.: Z-number based earned value management (ZEVM): a novel pragmatic contribution towards a possibilistic cost-duration assessment. Comput. Ind. Eng. 143, 106430 (2020) 15. Kang, B., Wei, D., Li, Y., Deng, Y.A.: Method of converting Z-number to classical fuzzy number. J. Inf. Comput. Sci. 9, 703–709 (2012)

Picture Fuzzy Sets

Risk Analysis of Digital Transformation with an Integrated Picture Fuzzy QFD and FMEA Methodology Elif Haktanır(B) Altinbas University, Bagcilar, 34217 Istanbul, Turkey [email protected]

Abstract. Digital transformation takes more place in our lives day by day and changes both our individual lives and the way we do business. In addition to the numerous benefits it provides, it also has some risks that are accepted by everyone. In this study, these risks are analyzed with an integrated QFD (Quality Function Deployment) and FMEA (Failure Mode and Effects Analysis) methodology. The indecisiveness of the decision makers is handled with picture fuzzy sets. The novelty that the developed method adds to the literature is that it analyzes risk connectivity, one of the risk parameters, with the correlation matrix of QFD. The integrated approach uses nine risk parameters instead of the three risk parameters used in the classical FMEA method. In this way, the relationship pattern between the risks is included in the calculation and a more appropriate approach to real-life applications is suggested. Keywords: Failure Mode and Effects Analysis · Quality Function Deployment · Risk priority number · Picture Fuzzy Sets · Digital transformation

1 Introduction In today’s world, it is obvious that companies can only sustain their existence and growth by working under great stress, competition, and a very high tempo. Whether these companies are in the field of production, service or both, their success can only be achieved by reducing their costs and increasing their earnings. One of the biggest expense items of companies is the share they allocate from their budgets to detect and prevent possible failures. Those failures encountered in production processes can cause disruptions in the production plans as well as lead to much more serious consequences. Figure 1 compares the actual failure costs to an iceberg [1]. While the easily measurable and observable failure costs are at the tip of the iceberg, most of the failure costs are hidden below the surface. For all these reasons, it is of great importance for companies to detect failures before they occur. Failure Mode and Effects Analysis (FMEA) is one of the most frequently used methods in the literature and in real case applications to rank these failures. Although FMEA is one of the most valid risk assessment methods in the literature, it has also been © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 471–480, 2022. https://doi.org/10.1007/978-3-031-09173-5_56

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Fig. 1. Illustrative representation of hidden failure costs [1].

criticized in many studies [2–4]. The most common criticism for the classical FMEA method is the calculation of the risk priority number (RPN). RPN is the product of three parameters, Severity (S), Occurrence (O) and Detection (D), used for the numeric assessment of risk assigned to a process as part of the classical FMEA approach. But even if the value of each of these risk parameters is different, the multiplication result may be the same in the classical approach. To overcome this inadequacy, Haktanır and Kahraman [5] introduced a comprehensive FMEA method that allows to assign different weights to the risk parameters. The FMEA model they proposed includes nine risk parameters each having a different weight obtained from CRiteria Importance Through Intercriteria Correlation method. In this study, those same nine risk parameters (Risk Urgency, Risk Proximity, Risk Dormancy, Risk Manageability, Risk Controllability, Risk Detectability, Risk Connectivity, Strategic Impact, and Risk Propinquity) will be used to prioritize the risks in the FMEA approach. One of the nine new risk parameters, Risk Connectivity, will be analyzed under Quality Function Deployment (QFD) approach with a correlation matrix. Haktanır and Kahraman’s study [6] showed that one of the parts that is often overlooked due to financial and time constraints in the QFD method, but which is of great importance for obtaining more realistic results, is the correlation matrix between the defined criteria. Since both QFD and FMEA methods depend on decision makers’ subjective evaluations, they contain vagueness and impreciseness. In this study, these uncertainties are handled by using picture fuzzy (PF) sets. The rest of the study is organized as follows. Section 2 gives a brief literature review on fuzzy FMEA and QFD methodologies. Section 3 presents the preliminaries of Picture Fuzzy Sets (PFSs). Section 4 introduces the proposed integrated PF QFD and FMEA methodology. Section 5 demonstrates the application of the proposed methodology for digital transformation risks assessment. The last section concludes the paper with future directions.

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2 Literature Review on Fuzzy QFD and FMEA Methodologies FMEA and QFD methods are integrated in the literature in various studies under a fuzzy environment. Chen and Ko et al. [7] developed fuzzy linear programming models for new product design using QFD with FMEA. Chen and Ko [8] incorporated FMEA and fuzzy approaches into QFD for new product design. Liu [9] extended fuzzy QFD from product planning to part deployment and conducted FMEA for high importance group of part characteristics through the fuzzy inference approach. Yang et al. [10] presented a method integrating fuzzy QFD, frequency-cost FMEA, and gray relation analysis considering the fuzziness and uncertainty. Liu and Tsai [11] used two-stage QFD tables to represent the relationships among construction items, hazard types and hazard causes and performed FMEA to assess the risk value of hazard causes based on the fuzzy inference approach. Lin et al. [12] proposed a new product development framework integrating fuzzy analytic network process, QFD, and FMEA with an application on green and low-carbon products. Bhuvanesh Kumar and Parameshwaran [13] presented a fuzzy integrated QFD, FMEA framework for the selection of lean tools in a manufacturing organization. Senthilkannan and Parameshwaran [14] a performance analysis and quality improvement using fuzzy MCDM and lean tools in a paper industry. Ma et al. [15] proposed a fuzzy integrated approach to identify function components for product redesign based on an analysis of customer requirements with QFD and failure risk with FMEA. Ma et al. [16] identified to-be-improved components for the redesign of complex products and systems based on fuzzy QFD and FMEA. Li et al. [17] proposed a systematic and semi-quantitative decision support framework for risk management of hazmats road transportation based on the combination of QFD, fuzzy analytic hierarchy process, fuzzy FMEA, and non-linear goal programming. Bhuvanesh Kumar and Parameshwaran [18] presented a comprehensive fuzzy FMEA, analytic hierarchy process and QFD based approach to prioritize lean tools for manufacturing industries. Pourmadadkar et al. [19] developed an integrated QFD and FMEA approach under fuzzy environment for healthcare services risk assessment and quality enhancement. Efe and Efe [20] proposed a QFD based FMEA approach for risk evaluation. Reda and Dvivedi [21] Decision-making on the selection of lean tools using fuzzy QFD and FMEA approach in the manufacturing industry.

3 Preliminaries: Picture Fuzzy Sets Some definitions and operations about PFSs are given below [22]. Definition 1. A PFS on a A˜ P of the universe of discourse U is given by Eq. (1).     A˜ P = u, (μA˜ P (u), ηA˜ P (u), νA˜ P (u))u ∈ U

(1)

where μA˜ P (u) : U → [0, 1], ηA˜ P (u) : U → [0, 1], νA˜ P (u) : U → [0, 1]

(2)

0 ≤ μA˜ P (u) + ηA˜ P (u) + νA˜ P (u) ≤ 1∀u ∈ U

(3)

and

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E. Haktanır

For each u, μA˜ p (u), ηA˜ P (u), and νA˜ P (u) are called the degree of positive membership, ˜ the degree of neutral membership, and the degree of   negative membership of u to AP , respectively. ρ = 1 − μA˜ P (u) + ηA˜ P (u) + νA˜ P (u) is called as the degree of refusal membership of u in the PFS A˜ P . Definition 2. Some basic operations of PFSs are given in Eqs. (4–7) [22].   ˜ P ⊕ B˜ P = μ ˜ + μ ˜ − μ ˜ μ ˜ , η ˜ η ˜ , ν ˜ ν ˜ A AP BP AP BP AP BP AP BP   ˜ P ⊗ B˜ P = μ ˜ μ ˜ , η ˜ + η ˜ − η ˜ η ˜ , ν ˜ + ν ˜ − ν ˜ ν ˜ A AP BP AP BP AP BP AP BP AP B P λ · A˜ P =

 λ  , ηAλ˜ , νAλ˜ for λ > 0 1 − 1 − μA˜ P P

P

   λ  λ

 A˜ λP = μλA˜ , 1 − 1 − ηA˜ P , 1 − 1 − νA˜ P for λ > 0 P

(4) (5) (6) (7)

∼  Definition 3. Wang et al. [23] defined the score function S AP and the accuracy ∼  function H AP of a PFS as in Eqs. (8) and (9), respectively.   S A˜ P = μ ∼ − νA˜ P

(8)

AP

  H A˜ P = μ ∼ + νA˜ P + η ∼ AP

AP

(9)

∼  ∼  where S AP ∈ [−1, 1] and H AP ∈ [0, 1].

4 Picture Fuzzy QFD and FMEA Methodology In this section integrated PF QFD and FMEA methodology will be presented in steps. Step 1: Let the decision makers determine the risk factors and then assign their joint PF evaluations about these risks’ connectivity as a correlation matrix of QFD. Fill a cell with cross sign (X) if corresponding two risk factors has no correlation. Step 2: Sum the PF risk assessments associated with each risk factor separately by using Eq. (5). Use the total connectivity values of the risk factors obtained as a result of this summation as PF evaluations of the parameter “Risk Connectivity” in the FMEA. Step 3: Let the same experts jointly fill the FMEA matrix with PF values according to nine risk parameters for each risk factor. Nine risk parameters are presented with their explanations in Table 1.

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Table 1. Risk parameters and their explanations. Risk parameters

Meaning interpretations

Interpretations

Risk urgency

Time period within which the risk is to be implemented

Short time period = High urgency

Risk proximity

Time period within which the risk will have an impact

Short time period = High proximity

Risk dormancy

Time period after risk has occurred

Short time period = Low dormancy

Risk manageability

Ease with which the risk can be managed

Easy management = High manageability

Risk controllability

Degree to which outcome of the risk Easy control = High controllability can be controlled when it occurs

Risk detectability

Ease with which the risk can be detected

Easy detection = High detectability

Risk connectivity

Extend to which a risk is connected to other risks

More connection with other risks = High connectivity

Strategic impact

Severity degree to which a risk can have impact on organization’s strategic goal

High effect/impact = High impact on strategy

Risk propinquity

Degree to which the risk is perceived Significant for many stakeholders = to matter by one or more High propinquity stakeholders

Step 4: Calculate the PF RPNs by multiplying the PF values assigned to nine risk parameters by using Eq. (5) for each risk factor. Then defuzzify these numbers with the score function in Eq. (8). Higher risk scores mean higher risk priorities.

5 Application: Digital Transformation Risk Analysis Although digital transformation has continued to be effective for years, it has gained tremendous momentum with the Covid-19 pandemic. While digital transformation offers numerous individual and sectoral advantages, it also brings some risks. Some of the most important and common digital transformation risks are listed below with their explanations [24]. • Data Insecurity: Leakage of personal information about the person or the data of the organizations • Social Disconnect: The lack of human contact because of the excessive use of social media • Manipulation of Digital Data: Fake photographs, videos, audio, etc. with smart editing tools

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• Copyrights and Plagiarism: Copied content (e.g., students copy their homework from the internet without learning) • Fake Accounts and Anonymity: Stalking, bullying, or threatening other people • Excessive Reliance on Gadgets: Over-reliance of people on gadgets, decline in memory, laziness • Addiction: People busy on their phones at casual gatherings, social media and online games addiction In the following the proposed integrated PF QFD and FMEA approach is applied to a digital transformation risk analysis is steps. Step 1: Five digital transformation experts have determined the most common risks of digital transformation and then assigned their joint PF evaluations about the digital transformation risks’ connectivity as a correlation matrix of QFD (Fig. 2). If a cell is filled with cross sign (X), it represents that the corresponding two risk factors has no correlation.

x (0.9, 0.0, 0.2)

x (0.3, 0.4, 0.2) (0.6, 0.2, 0.2) (0.7, 0.1, 0.1) x

Data Insecurity

(0.3, 0.2, 0.4)

x

x

x

(0.8, 0.2, 0.0)

x

x

Social Disconnect

(0.8, 0.1, 0.1)

(0.2, 0.2, 0.3)

Manipulation of Digital Data

(0.3, 0.2, 0.2)

Copyrights and Plagiarism

(0.4, 0.4, 0.2)

x

Fake Accounts and Anonymity

(0.9, 0.0, 0.1)

x

Excessive Reliance on Gadgets

Addiction

Fig. 2. Risk factors’ connectivity on QFD’s correlation matrix.

Step 2: The PF risk assessments associated with each risk factor were summed separately for that risk factor by using Eq. (4). The total connectivity values of the risk factors obtained as a result of this summation are given in Table 2.

Risk Analysis of Digital Transformation with an Integrated Picture Fuzzy QFD

477

Table 2. The total PF connectivity values of the risk factors.

Risk connectivity

Data insecurity

Social disconnect

Manipulation Copyrights of digital data and plagiarism

Fake accounts and anonymity

Excessive reliance on gadgets

Addiction

(0.916, 0.008, 0.004)

(0.986, 0.000, 0.008)

(0.952, 0.004, 0.000)

(0.971, 0.000, 0.010)

(0.980, 0.001, 0.000)

(0.994, 0.000, 0.004)

(0.776, 0.008, 0.012)

Step 3: The same five experts jointly filled the FMEA matrix with PF data according to nine risk parameters for each risk factor. Only the data of the risk connectivity parameter is taken by Table 2 that constructed in Step 2. Table 3 presents the PF FMEA matrix. Table 3. PF FMEA evaluations of the experts. Risk

Risk

Risk

Risk

Risk

Risk

Strategic

Risk

Risk

urgency

proximity

dormancy

manageability

controllability

detectability

impact

propinquity

connectivity

Data insecurity

(0.3, 0.4, 0.2)

(0.7, 0.2, 0.0)

(0.6, 0.2, 0.2)

(0.8, 0.1, 0.1)

(0.7, 0.1, 0.2)

(0.6, 0.1, 0.2)

(0.7, 0.0, 0.2)

(0.6, 0.1, 0.3)

(0.916, 0.008, 0.004)

Social disconnect

(0.4, 0.3, 0.3)

(0.9, 0.0, 0.1)

(0.5, 0.0, 0.3)

(0.6, 0.2, 0.1)

(0.3, 0.2, 0.4)

(0.3, 0.3, 0.3)

(0.3, 0.2, 0.4)

(0.6, 0.2, 0.1)

(0.986, 0.000, 0.008)

Manipulation of digital data

(0.4, 0.2, 0.4)

(0.5, 0.2, 0.3)

(0.7, 0.1, 0.2)

(0.6, 0.3, 0.1)

(0.7, 0.1, 0.1)

(0.8, 0.0, 0.1)

(0.7, 0.0, 0.2)

(0.4, 0.4, 0.2)

(0.952, 0.004, 0.000)

Copyrights and plagiarism

(0.7, 0.1, 0.2)

(0.6, 0.1, 0.2)

(0.3, 0.3, 0.3)

(0.4, 0.4, 0.2)

(0.3, 0.4, 0.2)

(0.7, 0.2, 0.0)

(0.6, 0.0, 0.3)

(0.5, 0.2, 0.2)

(0.776, 0.008, 0.012)

Fake accounts and anonymity

(0.7, 0.1, 0.1)

(0.8, 0.0, 0.1)

(0.3, 0.2, 0.4)

(0.6, 0.2, 0.1)

(0.4, 0.3, 0.3)

(0.9, 0.0, 0.1)

(0.6, 0.2, 0.2)

(0.8, 0.1, 0.1)

(0.971, 0.000, 0.010)

Excessive reliance on gadgets

(0.3, 0.4, 0.2)

(0.7, 0.2, 0.0)

(0.7, 0.1, 0.2)

(0.8, 0.2, 0.0)

(0.6, 0.0, 0.3)

(0.5, 0.2, 0.2)

(0.3, 0.3, 0.3)

(0.6, 0.3, 0.1)

(0.980, 0.001, 0.000)

Addiction

(0.7, 0.1, 0.2)

(0.5, 0.2, 0.3)

(0.4, 0.3, 0.3)

(0.9, 0.0, 0.1)

(0.6, 0.2, 0.2)

(0.8, 0.1, 0.1)

(0.3, 0.2, 0.4)

(0.9, 0.0, 0.2)

(0.994, 0.000, 0.004)

Step 4: PF RPN was calculated by multiplying the PF values assigned to nine risk parameters by using Eq. (5) for each risk factor. These numbers were then defuzzified with the score function in Eq. (8). Both PF RPNs and risk scores are presented in Table 4. Since higher risk scores mean higher risk priorities, “Data Insecurity” is the risk factor with the highest priority.

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E. Haktanır Table 4. PF RPNs and risk scores. Data Social Manipulation Copyrights Fake insecurity disconnect of and accounts digital data plagiarism and anonymity

Excessive Addiction reliance on gadgets

(0.016, 0.750, 0.794)

(0.002, 0.799, 0.911)

(0.013, (0.002, 0.783, 0.843) 0.870, 0.841)

(0.017, 0.710, 0.804)

(0.006, 0.865, 0.774)

(0.016, 0.710, 0.879)

Risk −0.634 scores

−0.909

−0.831

−0.824

−0.768

−0.863

RPN

−0.839

6 Conclusions While digital transformation continues to increase its impact in all areas of life, it also brings some risks. In this study, digital transformation risks are prioritized with FMEA method. Contrary to the classical FMEA approach nine extended risk factors are used. One of these risk parameters, risk connectivity, was evaluated with the help of the correlation matrix of QFD [25–27]. It is aimed to obtain more consistent and realistic results in examining the relationship between risk factors with the correlation matrix of QFD. In addition, since the subjective opinions of decision makers are included in both QFD and FMEA methods, PFSs were used to handle the ambiguity. For further research, it is suggested to test the robustness of the method with sensitivity analysis and make a comparative analysis using other latest extensions of ordinary fuzzy sets such as Pythagorean fuzzy sets, spherical fuzzy sets or q-rung orthopair fuzzy sets.

References 1. Wood, D.: Principles of Quality Costs: Financial Measures for Strategic Implementation of Quality Management (4. b.). American Society for Quality, Quality Press, Milwaukee (2013) 2. Haktanır, E., Kahraman, C.: Interval-valued neutrosophic failure mode and effect analysis. J. Intell. Fuzzy Syst. 39(5), 6591–6601 (2020) 3. Haktanır, E., Kahraman, C.: Failure mode and effect analysis using interval valued neutrosophic sets. In: Kahraman, C., Cebi, S., Cevik Onar, S., Oztaysi, B., Tolga, A.C., Sari, I.U. (eds.) INFUS 2019. AISC, vol. 1029, pp. 1085–1093. Springer, Cham (2020). https://doi.org/ 10.1007/978-3-030-23756-1_128 4. Haktanir, E., Kahraman, C.: A literature review on fuzzy FMEA and an application on infant car seat design using spherical fuzzy sets. In: Kahraman, C., Cebi, S. (eds.) Customer Oriented Product Design. SSDC, vol. 279, pp. 429–449. Springer, Cham (2020). https://doi.org/10. 1007/978-3-030-42188-5_22 5. Haktanır, E., Kahraman, C.: A novel CRITIC based weighted FMEA method: application to COVID-19 blood testing process. J. Multip. Value. Log. Soft Comput. 37(3/4), 247–275 (2021)

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6. Haktanır, E., Kahraman, C.: A novel interval-valued Pythagorean fuzzy QFD method and its application to solar photovoltaic technology development. Comput. Ind. Eng. 132, 361–372 (2019) 7. Chen, L.H., Ko, W.C.: Fuzzy linear programming models for new product design using QFD with FMEA. Appl. Math. Model. 33(2), 633–647 (2009) 8. Chen, L.H., Ko, W.C.: Fuzzy approaches to quality function deployment for new product design. Fuzzy Sets Syst. 160(18), 2620–2639 (2009) 9. Liu, H.T.: The extension of fuzzy QFD: from product planning to part deployment. Expert Syst. Appl. 36(8), 11131–11144 (2009) 10. Yang, M., Li, Y., Liu, Y., Gao, X.: A method for problem selection in the 6σ definition stage. Adv. Mater. Res. 139–141, 1485–1489 (2010) 11. Liu, H.T., Tsai, Y.L.: A fuzzy risk assessment approach for occupational hazards in the construction industry. Saf. Sci. 50(4), 1067–1078 (2012) 12. Lin, C.Y., Lee, A.H.I., Kang, H.Y.: An integrated new product development framework-an application on green and low-carbon products. Int. J. Syst. Sci. 46(4), 733–753 (2015) 13. Bhuvanesh Kumar, M., Parameshwaran, R.: Fuzzy integrated QFD, FMEA framework for the selection of lean tools in a manufacturing organisation. Product. Plan. Control 29(5), 403–417 (2018) 14. Senthilkannan, N., Parameshwaran, R.: Performance analysis and quality improvement using fuzzy MCDM and lean tools in a paper industry. Int. J. Integrat. Supply Manag. 12(3), 205–229 (2019) 15. Ma, H., Chu, X., Li, Y.: An integrated approach to identify function components for product redesign based on analysis of customer requirements and failure risk. J. Intell. Fuzzy Syst. 36(2), 1743–1757 (2019) 16. Ma, H., Chu, X., Xue, D., Chen, D.: Identification of to-be-improved components for redesign of complex products and systems based on fuzzy QFD and FMEA. J. Intell. Manuf. 30(2), 623–639 (2016) 17. Li, Y.L., Yang, Q., Chin, K.S.: A decision support model for risk management of hazardous materials road transportation based on quality function deployment. Transp. Res. Part D: Transp. Environ. 74, 154–173 (2019) 18. Bhuvanesh Kumar, M., Parameshwaran, R.: A comprehensive model to prioritise lean tools for manufacturing industries: a fuzzy FMEA, AHP and QFD-based approach. Int. J. Serv. Oper. Manag. 37(2), 170–196 (2020) 19. Pourmadadkar, M., Beheshtinia, M.A., Ghods, K.: An integrated approach for healthcare services risk assessment and quality enhancement. Int. J. Qual. Reliab. Manag. 37(9–10), 1183–1208 (2020) 20. Efe, B., Efe, Ö.F.: Quality function deployment based failure mode and effect analysis approach for risk evaluation. Neural Comput. Appl. 33(16), 10159–10174 (2021) 21. Reda, H., Dvivedi, A.: Decision-making on the selection of lean tools using fuzzy QFD and FMEA approach in the manufacturing industry. Expert Syst. Appl. 192, 116416 (2022) 22. Cuong, B.C.: Picture fuzzy sets. J. Comput. Sci. Cybernet. 30(4), 409–420 (2014) 23. Wang, C., Zhou, X., Tu, H., Tao, S.: Some geometric aggregation operators based on picture fuzzy sets and their application in multiple attribute decision making. Italian J. Pure Appl. Math. 37, 477–492 (2017) 24. The Enterprise World. Negative effects of digitalization on society (2022). https://theenterp riseworld.com/negative-effects-of-digitalization/ 25. Haktanır, E., Kahraman, C.: New product design using Chebyshev’s inequality based intervalvalued intuitionistic Z-fuzzy QFD method. Informatica 33(1), 1–33 (2022)

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26. Haktanır, E., Kahraman, C., Kutlu Gündo˘gdu, F.: Delivery drone design using spherical fuzzy quality function deployment. In: Kahraman, C., Kutlu Gündo˘gdu, F. (eds.) Decision Making with Spherical Fuzzy Sets. SFSC, vol. 392, pp. 399–430. Springer, Cham (2021). https://doi. org/10.1007/978-3-030-45461-6_17 27. Haktanır, E.: Prioritization of competitive suppliers using an interval-valued Pythagorean fuzzy QFD & COPRAS methodology. J. Multip. Valued Log. Soft Comput. 34(1–2), 177–199 (2020)

ARAS Method in Picture Fuzzy Environment for the Selection of Catering Firm Nihan Tirmikcioglu(B) Faculty of Arts and Sciences, Department of Mathematics, Kirklareli University, Kayali Campus, Kirklareli, Turkey [email protected]

Abstract. Catering is a term used to mean food service. It has become an attractive sector in recent years and is also used in the sense of supplier of food. Companies that provide catering services are called by this name. In other words, it is the general name of the companies that provide catering and food production. Collective catering services provided to firms, schools, hospitals, small and large scale institutions, organizations and even to meetings with a small number of participants are considered under the term catering. It is very important that the catering service offers quality and professional solutions. For this reason, it is necessary to determine the best alternative considering certain criteria. Therefore multi criteria decision making methods are preferred for the selection. In this research, a decision model is proposed including five criteria and four alternatives for a catering firm selection. Considering the fuzziness of the process and as a novel approach, ARAS method is preferred and applied in picture fuzzy sets. Hygiene conditions and taste are determined as the two most important criteria and the fourth alternative is the best selection. Keywords: MCDM · Fuzzy sets · Picture fuzzy sets · Picture fuzzy ARAS

1 Introduction ARAS (Additive Ratio Assessment) method is proposed by [11]. The method evaluates decision alternatives considering various criteria. In this method, a utility function determines the relative effectiveness of an alternative with respect to the other alternative. The utility function values of alternatives are compared to the optimal utility function value. Evaluating the performances of each alternative, it determines their similarities to the ideal solution. ARAS method is also developed for multi criteria decision problems in fuzziness: [8] developed fuzzy ARAS method for supply chain management performance measurement. [2] used IVF ARAS method for the project evaluation. [7] proposed IF ARAS method for IT personnel selection. In this research, ARAS method is proposed developed in picture fuzzy environment for a catering firm. For the mathematical expression of decision makers’ evaluations, a picture fuzzy linguistic scale is used. In Sect. 2, literature review is given. Section 3 © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 481–488, 2022. https://doi.org/10.1007/978-3-031-09173-5_57

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defines the picture fuzzy sets. In Sect. 4, ARAS method is developed in picture fuzzy sets is presented. Section 5, the method developed is applied to decision problem. The last section gives the conclusion of the research.

2 Literature Review Catering is the business of providing food and service. It can be defined as preparing or providing food for someone to serve and also preparing, delivering and serving food in the places of another person, company or event [4]. For the selection a potential catering firm, the decision maker/s should make right and timely decisions. In this selection, the decision makers determine the criteria considering their needs. A decision maker may prefer to get food service from a catering firm with low cost, minimum food quality and high hygiene; for another decision maker the quality of food is more considered than the cost and the hygiene. Then, it’s clear that various and complex criteria are taken into account. In cases where they are multiple and conflicting criteria, using multi criteria decision techniques are effective to determine the best alternative. In literatıre, some papers about catering firm selection considering multi criteria decision making methods under mentioned criteria can be considered: In [3], the most appropriate alternative is determined by an integrated AHP-ARAS model where service quality, delivery time, company image and food safety are taking into account. In [4], a decision model using fuzzy AHP where service quality, hygiene and food quality are determined as the main criteria is proposed. [5] proposes Potential Method for a catering firm selection and service quality is observed as the most important criteria.

3 Picture Fuzzy Sets [1] defines a picture fuzzy set (PFS) on the universe as: PF = {{μPF (x), ρPF (x), νPF (x)|x ∈ X }}

(1)

μPF (x)[0, 1] represents the “degree of positive membership of PF”, ρPF (x)[0, 1] represents the “degree of neutral membership of PF”, νP (x) represents the “degree of negative membership of PF and ∀x ∈ X , 0 ≤ μPF (x) + ρPF (x) + vPF (x) ≤ 1. For x ∈ X , πPF (x) = 1 − (μPF (x) + ρPF (x) + vPF (x)) is defined as the “degree of refusal membership of x in PF. Definition 1 For two picture fuzzy numbers. Y = (μY , ρY , νY ) and Z = (μZ , ρZ , νZ ), following formula are given as follows [1]: Y ⊕ Z = (μY + μZ − μY μZ , ρY ρZ , νY vZ )

(2)

Y ⊗ Z = (μY μZ , ρY + ρZ − ρY ρZ , νY + νZ − νY νZ )

(3)

  kY = 1 − (1 − μY )k , ρYk , νYk , k > 0

(4)

ARAS Method in Picture Fuzzy Environment for the Selection of Catering Firm

  Y k = μkY , 1 − (1 − ρY )k , 1 − (1 − νY )k , k > 0

483

(5)

The operation formula has the properties [1]: Y ⊕ Z = Z ⊕ Y , Y ⊗ Z = Z ⊗ Y , (Y k1 )k2 = Y k1 k2

(6)

k(Y ⊕ Z) = kY ⊕ kZ, (Y ⊗ Z)k = (Y )k ⊗ (Z)k

(7)

k1 Y ⊕ k2 Y = (k1 + k2 )Y , (Y )k1 ⊗ (Y )k2 = (Y )(k1 +k2 )

(8)

Definition 2 Let Y = (μY , ρY , ϑY ) be a picture fuzzy number. The score and accuracy functions are calculated as follows [9]: S(Y ) = μY +

(1 − μY − νY ) ρY − (1 − π ) 2 2

(9)

H (Y ) = μY + ρY + νY

(10)

Definition 3 The picture fuzzy weighted averaging operator and the picture fuzzy weighted geometric operator are defined as [9]:   n  ωj n  ωj n  ωJ PFWAω (Y1 , . . . , Yn ) = 1 − 1 − μYj , ρYj , νYJ j=1

PFWGω (Y1 , . . . , Yn ) =



n j=1

j=1

n  ωj μYj , 1 −

j=1

j=1

n  ω 1 − ρYj j , 1 −

j=1

(11)   ωJ νYJ (12)

T where n ω = (ω1 , ω2 , . . . , ωn ) is the weight vector of Yj (j = 1, . . . , n) and ωj > 0, j=1 ωj = 1.

4 Picture Fuzzy ARAS Let m alternatives by {ALT 1 , ALT 2 , . . . , ALT m }, n criteria by {C1 , C2 , . . . , Cn } and r decision makers. λ = {λ1 , . . . , λk } (λk ≥ 0 (k = 1, 2, . . . , r) is the importance degrees of decision makers and lk=1 λk = 1. Step 1 The criteria of the decision model are evaluated by each decision maker DM r ⎞ ⎛ x˜ 11 x˜ 12 . . . x˜ 1k ⎜ x˜ 21 x˜ 22 . . . x˜ 2k ⎟ ⎟ (13) X˜ (k) = (˜xik )nxr = ⎜ ⎝ . . . . . . . . . . . . ⎠(i = 1, . . . , n, k = 1, . . . , r) x˜ i1 x˜ i2 . . . x˜ ik

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Step 2 Considering the importance degree of decision makers in the model, the evaluations are aggregated with PFWA operator (11) and picture fuzzy weights of the criteria are calculated [10]:   r  λ n  λk n  λk (14) 1 − μx˜ ik k , ρx˜ ik , νx˜ ik ω˜ i = 1 − k=1

j=1

j=1

∼ ∼  ∼ W = ω1 , ω2 , . . . , ωj (i = 1, . . . , n), (k = 1, , , .r) In this step, depending on the preference, picture fuzzy values can be defuzzified by (9) and the defuzzified values are normalized as follows to obtain the crisp values of the criteria weights: ωi ω i = n

j=1 ωi

0 < ωi < 1;

(i = 1, . . . , n)

n j=1

(15)

ωi = 1

Step 3 The evaluations of ALT j with respect to criteria Ci by r decision maker are aggregated with PFWA operator (11) and the decision matrix of the model constructed is: ALT 1 . . . ALT m   ˜ = d˜ ij D

nxm

⎡ ˜ C1 d11 ⎢ .. = . ⎣ . Cn d˜ n1

⎤ · · · d˜ 1m . . .. ⎥ . . ⎦(i = 1, . . . , n; j = 1, .., m) · · · d˜ nm

(16)

Step 4 Optimal picture fuzzy performance value is determined in the decision matrix as:      For benefit criteria R˜ OPTi = max d˜ ij = max μij , ρij , min νij (17) j

     For cost criteria R˜ OPTi = min d˜ ij = min μij , ρij , max νij j

(18)

A new column where the optimal picture fuzzy performance values calculated are placed is added to the decision matrix as a first column. Step 5 The decision matrix is normalized: ROPT ALT1 . . . ALTm   N˜ = n˜ ij nxm

⎡ C1 n˜ OPT1 ⎢ = ... ⎣ ... Cn

n˜ OPTn

⎤ n˜ 11 · · · n˜ 1m .. . . .. ⎥ . . ⎦ . n˜ n1 · · · n˜ nm

(19)

ARAS Method in Picture Fuzzy Environment for the Selection of Catering Firm

485

(i = 1, . . . , n; j = 1, .., m)   For benefit criteria n˜ ij = d˜ ij = μij , ρij , νij

(20)

  For cost criteria n˜ ij = (d˜ ij )c = νij , ρij , μij

(21)

Step 6 Using (3), the weighted normalized decision matrix is constructed: ROPT ALT 1 . . . ALT m   F˜ = f˜ij

nxm

⎡ C1 f˜OPT 1 ⎢ = ... ⎣ ... Cn f˜OPT n

f˜11 .. . f˜n1

⎤ · · · f˜1m . . .. ⎥ . . ⎦ · · · f˜nm

∼ f˜ij = ωi ∗ n˜ ij (i = 1, . . . , n; j = 1, .., m)

(22)

Step 6 The score values of weighted normalized decision matrix are calculated:    1 − μij − νij ρij  ∗ − 1 − πij (23) S (FIJ ) = μij + 2 2 Step 7 The optimality functions of the alternatives are obtained by: m OF j = S ∗ (Fij ) j=1

(24)

Step 8 For each alternative, the utility degree is obtained by the following formula where OF 0 indicates the best optimality function value: Uj =

OF j OF o

(25)

The utility degrees are ordered increasly. The best alternative has the highest score.

5 Application The proposed method determines the best catering firm. Four alternatives and five criteria are considered for the decision model: price (C1 ), hygiene conditions (C2 ), taste (C3 ), service quality (C4 ) and food variety (C5 ). For the evaluation, three decision makers (DM 1 , DM 2 , DM 3 ) are preferred and their importance degrees are (0.35; 0.35; 0.30). Picture fuzzy linguistic scale is presented in Table 1 [6]: The criteria evaluations, the picture fuzzy weights of the criteria obtained by (14) and their crisp values obtained by (9) and (15) are in Table 2: In the decision model, hygiene conditions and taste are observed as the two most important criteria. These criteria are followed by food variety, price and service quality.

486

N. Tirmikcioglu Table 1. Picture fuzzy linguistic terms for the evaluations

LT

PFN

Very Poor/Very Bad (VP/VB)

0.10, 0.00, 0.85

Poor/Bad (P/B)

0.25, 0.05, 0.60

Moderately Poor/Moderately Bad (MP/MB)

0.30, 0.00, 0.60

Fair (F)

0.50, 0.10, 0.40

Moderately Good/Moderately High (MG/MH)

0.60, 0.00, 0.30

Good/High (G/H)

0.75, 0.05, 0.10

Very Good/Very High (VG/VH)

0.90, 0.00, 0.05

Table 2. Criteria evaluations, picture fuzzy weights and crisp values DM1

DM2

DM3

Picture fuzzy weight

Crisp values of the weights

C1

VH

H

H

(0.82,0.00,0.08)

0.201

C2

VH

VH

VH

(0.90,0.00,0.05)

0.203

C3

VH

VH

VH

(0.90,0.00,0.05)

0.203

C4

H

H

H

(0.75,0.05,0.1)

0.190

C5

VH

H

VH

(0.86,0,0.16)

0.202

Table 3. Aggregated picture fuzzy decision matrix RO

ALT1

ALT2

ALT3

ALT4

C1 (0.50,0.10,0.40) (0.50,0.10,0.40) (0.75,0.05,0.10) (0.87,0.00,0.06) (0.75,0.05,0.10) C2 (0.90,0.00,0.05) (0.50,0.10,0.40) (0.81,0.00,0.08) (0.75,0.05,0.10) (0.90,0.00,0.05) C3 (0.90,0.00,0.05) (0.50,0.10,0.40) (0.68,0.06,0.16) (0.75,0.05,0.10) (0.90,0.00,0.05) C4 (0.82,0.00,0.08) (0.50,0.10,0.40) (0.45,0.00,0.45) (0.50,0.10,0.40) (0.82,0.00,0.08) C5 (0.68,0.06,0.16) (0.50,0.10,0.40) (0.61,0.08,0.25) (0.61,0.08,0.25) (0.68,0.06,0.16)

Table 4. Weighted normalized picture fuzzy decision matrix RO

ALT1

ALT2

ALT3

ALT4

C1 (0.71,0.00,0.14) (0.33,0.10,0.54) (0.60,0.05,0.17) (0.71,0.00,0.14) (0.61,0.05,0.17) C2 (0.81,0.00,0.09) (0.36,0.10,0.53) (0.73,0.00,0.13) (0.68,0.05,0.15) (0.81,0.00,0.09) C3 (0.81,0.00,0.09) (0.36,0.10,0.53) (0.61,0.06,0.20) (0.68,0.05,0.15) (0.81,0.00,0.09) C4 (0.61,0.05,0.17) (0.30,0.15,0.55) (0.34,0.05,0.51) (0.38,0.15,0.46) (0.61,0.05,0.17) C5 (0.76,0.00,0.12) (0.34,0.10,0.53) (0.52,0.08,0.29) (0.52,0.08,0.29) (0.76,0.00,0.12)

ARAS Method in Picture Fuzzy Environment for the Selection of Catering Firm

487

The evaluations of the alternatives are aggregated by PFWA operator (11) and picture fuzzy decision matrix given in Table 3 is obtained: Price (C1 ) is the cost criteria then the decision matrix is normalized by (20)–(21) and weighted by (22) using the picture fuzzy weights of the criteria. The results are given in Table 4: Using Table 3 and Eq. (23), the score values of weighted normalized picture fuzzy decision matrix are presented in Table 5: Table 5. Score values RO

ALT1

ALT2

ALT3

ALT4

C1

0.9091

0.4072

0.8411

0.9091

0.8411

C2

0.9355

0.4238

0.9161

0.8645

0.9355

C3

0.9025

0.4250

0.7638

0.8300

0.9025

C4

0.8411

0.3769

0.4592

0.4667

0.8411

C5

0.9223

0.4160

0.6784

0.6784

0.9223

  The optimality function values (OF j ) and the alternatives’ utility degrees Uj are calculated using (24) and (25). Table 6 presents the results obtained: Table 6. Optimality function values and utility degrees RO

ALT1

ALT2

ALT3

ALT4

OFj

4.5104

2.0488

3.6585

3.7486

4.4424

Uj

–

0.5600

0.9760

0.8438

0.9849

The fourth alternative is the best alternative for catering firm selection.

6 Conclusion The aim of this research is to propose a decision model for catering firm selection. ARAS is a decision making method based on the comparison of the utility function values of the alternatives with the optimal. Taking into account the conflicting structure of the criteria and the fuzziness of personal evaluations, the method is extended to fuzzy environment and this research proposes a picture fuzzy extension of ARAS. The fourth alternative is determined as the best choice considering the selection criteria among which the hygiene conditions and taste are the most considered. Future researches may be the comparison of this study’s results with those obtained using the other picture fuzzy methods.

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References 1. Cuong, B., Kreinovich, V.: Picture fuzzy sets-a new concept for computational intelligence problems. In: Third World Congress Information and Communication Technologies, pp. 1–6. IEEE (2013). https://doi.org/10.1109/WICT.2013.7113099 2. Dahooie, J.H., Zavadkas, K.E., Abolhasani, M., Vanaki, A., Turskis, Z.: A novel approach for evaluation of projects using on interval valued fuzzy ARAS method: a case study of oil and gas well drilling projects. Symetry 10(2), 1–32 (2018) 3. Fu, Y.K.: An integrated approach to catering supplier selection using AHP-ARAS MCGP methodology. J. Air Transp. Manag. 75, 164–169 (2019) 4. Kahraman, C., Cebeci, U., Ruan, D.: Multi attribute comparison of catering service companies using fuzzy AHP: the case of Turkey. Int. J. Prod. Econ. 87(2), 171–184 (2004) 5. Mamat, S.S., Ahmad, T., Awang, S.R.: The application of potential method in decision making for multi attribute of catering service companies. Int. J. Pure Appl. Math. 114(3), 537–551 (2017) 6. Meksavang, P., Shi, H., Lin, S.-M., Liıu, H.-C.: An extended picture fuzzy VIKOR approach for sustainable supplier management and its application in the beef industry. Symmetry 11(468), 3–19 (2019) 7. Misshra, A.R., Sisadia, G., Pardasani, K.R., Sharma, K.: Multi criteria IT personnel selection on intuitionistic fuzzy information measures and ARAS methodology. Iran. J. Fuzzy Syst. 17(4), 55–68 (2020) 8. Rostamzadeh, R., Esmaeli, A., Nia, A.S., Saparauskas, J., Ghorabaee, M.K.: A fuzzy ARAS method for supply chain management performance measurement in SMEs under uncertainity. Transform. Bus. Econ. 16(2A), 319–338 (2017) 9. Son, L.H.: Measuring analogousness in picture fuzzy sets: from picture distance measures to picture association measures. Fuzzy Optim. Decis. Mak. 16, 359–378 (2017) 10. Wei, G.W.: Picture fuzzy aggregation operators and their application to multiple attribute decision making. J. Intell. Fuzzy Syst. 33, 713–724 (2017) 11. Zavadkas, K.E., Turskis, Z.: A new additive ratio assessment (ARAS) method in multi criteria decision making. Technol. Econ. Dev. Econ. 16(2), 159–172 (2010)

Working Environment Selection After Pandemic Using Picture Fuzzy Sets Mustafa Bal and Irem Ucal Sari(B) Industrial Engineering Department, Istanbul Technical University, Macka, Istanbul, Turkey [email protected]

Abstract. After 2020, the behaviors of many industries about the working environment have changed rapidly, and remote working has become chosen significantly by many companies. The reason behind this behavior change is pandemic conditions. In current days, the most frequently asked question from a managerial perspective is whether to return to traditional working conditions or not. Even though a traditional working environment is still preferable for manufacturing industries, the service industry prefers remote-working such as banking, finance, software, and technology companies. In this paper, this question is considered and it is tried to answer for mentioned industries. Working environment change decision is not easy to answer when some criteria such as rent of office, efficiency, and usage of resources are considered; therefore, from a managerial perspective, decision making for working environment change is highly important. When the uncertainty of our world’s pandemic condition is taken into account, making a decision gets more difficult. Analytical Hierarchy Process (AHP) with picture fuzzy sets is used to evaluate criteria to make the best decision under uncertainty. Software and technology companies are considered in the study to make evaluations by picture fuzzy AHP process. Based on the results of the analysis, performance-related factors and cost are determined as the most important criteria in the working environment selection. Keywords: Fuzzy AHP · Picture fuzzy sets · Working environment

1 Introduction COVID-19 pandemic has many types of effects on human life in addition to the medical side. So many people have changed their behaviors according to pandemic conditions. One of these behaviors is the working conditions. The traditional working environment is abandoned and remote working becomes a new trend in current days. Adaptation to remote working is realized rapidly and sharply. Although many types of industries have adapted easily, the traditional working environment cannot be abandoned entirely. Working environment change has effects on several perspectives which are managerial, employee, medical and environmental. From traditional working to remote working cannot be gone over by managerial level people in some industries or it can be an indispensable opportunity by employees. This change is a type of prevention of to spread of © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 489–497, 2022. https://doi.org/10.1007/978-3-031-09173-5_58

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illness, so it can be considered as this change is necessary. In addition to these, remote working reduces transportation. As a result of transportation reduction, the environmental effect appears by decreasing fuel consumption. When these several perspectives are considered, it is not easy to decide to select the best working environment. Even though the concept of remote working and hybrid working models have entered our lives with the COVID-19 pandemic, it has been a topic that has been discussed and talked about for many years. The impact of remote or hybrid working models on productivity has been continually investigated. Most of these studies provide a definition of remote working. The most suitable definition for our conditions is stated 15 years ago by [4] “Telecommuting is an alternative work arrangement in which employees perform tasks elsewhere that are normally done in a primary or central workplace, for at least some portion of their work schedule, using electronic media to interact with others inside and outside the organization”. According to the definition, it overlaps pandemic conditions’ working conditions. In this point of view, remote working debates traditional working in some sectors. Therefore, from a managerial perspective, working type selection is significantly important because it determines employees living standards. Employees working conditions affect productivity and then, the firm’s existence has influenced all consequences of this selection. Analytical Hierarchy Process (AHP) is one of the used methods based on criteria hierarchy and weighting of them for each alternative. Evaluating an alternative such as remote working or working in an office concerning several criteria in a hierarchical manner is the main interest area of this study. At that point, the uncertain environment of the era to decide or chose one of the alternatives should be considered. There is certain evidence not to face a new epidemic or pandemic again and not to lockdown to home. On the other hand, manager evaluations cannot be certain to evaluate an alternative based on criteria. Also, risks on the alternatives such as infection risk, are another uncertain subject. With the gathering of these uncertainty elements, the decision-making method should work under a fuzzy environment to results precisely; therefore, fuzzy AHP will be used method to select an alternative. When work environment selection is discussed, it should be thought differentiation of conditions before the COVID-19 pandemic and after it. According to [1] before the pandemic, approximately 5% of workdays of employees are supplied from home, but after the pandemic, it will be 4 times 5%. Therefore, for a company it is a crucial decision to select the appreciative option which is remote-working, working at an office, or hybrid by considering pandemic environment conditions. This study aims to determine the importance of criteria used in working environment selection. According to the literature review of criteria for the working environment selection, the main 5 criteria that are cost, performance-related factors, organizational factors, environmental factors, and individual factors, are determined. To handle the uncertainty in the decision-making process picture fuzzy analytic hierarchy process is used in the analysis. The paper is organized as follows: In the second section, the methodology is summarized, then the analysis of working environment selection is given. Finally, the paper is concluded with the conclusion section.

Working Environment Selection After Pandemic Using Picture Fuzzy Sets

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2 Literature Review In the literature about remote working, the main interesting area of the researchers is productivity and performance of employees. Remote working is clearly triggered for employees and organizations at an incredible level after the COVID-19 pandemic. Serious impacts of remote working are ambiguous in the middle and long term. In the literature, a lot of factors and criteria are mentioned positively or negatively. The most asserted one is the performance of employees and its assessment. [7] stated that stress, technological challenges, level of relationship between supervisors and colleagues, social connection shortages and vagueness of work-home boundaries can role negatively on remote working productivity. On the other hand, some factors are declared by several studies to show remote working benefits. These factors are categorized into three main subjects which are organizational, individual, and societal motivators. Security considerations, cost savings, productivity gaining, and flexibility increasing are listed under organizational motivators. Reduction of travel time, flexible working hours, more leisure activities, and more productivity are placed under individual motivators; and air pollution quality, energy consumption, and transportation demand are determined as societal motivators [9]. To determine the criteria for working environment selection, several types of papers are assessed from different disciplines. Each of them has mentioned and evaluated working environment conditions from distinctive perspectives. By [2] three main categories are stated with pandemic conditions about working environment changes are personenvironment fitness, disproportionate work-family effects, and disproportion of alternative family structures. When people are working from outside of the office environments such as home or other places, home life distractions, time-wasting activities by electronic devices and social media will influence the tasks and productivity of employees [6]. According to [4] remote working can cause delaying of some tasks because it vanishes the communication of employees and the social life of employees by never knowing some colleagues in the same firm. Loss of interaction is frequently a minded criterion to assess for remote working in the literature. Creativeness and efficiency decrease are a result of loss of interaction and it should be measured to prevent total loss for working from home concept [14]. In another study, remote working is effective in several subjects at a high level. It is considerably efficient positively or negatively on environmental factors, the productivity of employees, absenteeism, cost issues, and communication skills [8].

3 Methodology In our era, even though the COVID-19 pandemic is the most enormous outbreak, it is obvious that it is not the latest one. Disasters, pandemics, outbreaks, economic crises, wars, and similar events are not inevitable. Unless these have vanished from human life, deaths and loss of properties will not be finished. Therefore, their possible risks will exist and it is so clear that there is always uncertainty in human life. Under uncertainty such as our pandemic conditions, it is hard to make a selection for any kind of topic in our daily life. At that point, fuzzy logic and fuzzy sets are the best to evaluate uncertainty. There

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are many types of extensions of the fuzzy sets. One of them is picture fuzzy sets (PFS) that are proposed by [3]. PFS is more efficient for human thoughts involving abstain and refusal in addition to yes and no being considered. These four situations are explained by “degree of positive membership” “degree of neutral membership” “degree of negative membership” and “degree of refusal membership” [3]. PFS involves decision-making, clustering algorithms, and information fusion as an innovative information tool [15]. Also, the success of PFS with decision-making is referred to and mentioned in the literature with several studies [11–13, 16]. According to the literature review of criteria of working environment selection, the main 5 criteria that are cost, performance-related factors, organizational factors, environmental factors, and individual factors, are determined. Due to the hierarchical structure of the criteria, this study uses the picture fuzzy analytic hierarch process (PFAHP). The steps of the PFAHP can be summarized as follows [10]: Step 1. Definition of the problem and construction of the hierarchical structure. Step 2. Establishing pairwise comparison matrices using linguistic statements that ˜ are  determined in Table  1 where a picture fuzzy number is denoted as Ap = μA˜ p (u), νA˜ p (u), πA˜ p (u) . Table 1. Linguistic statement and picture fuzzy scale [10]. Linguistic terms

Picture fuzzy scale

Linguistic terms

Picture fuzzy scale

AM: Absolutely More Importance

(0.9, 0.05, 0)

SL: Slightly Low Importance

(0.35, 0.6, 0.05)

VH: Very High Importance

(0.8, 0.15, 0.05)

L: Low Importance

(0.2,0.7,0.1)

H: High Importance

(0.7, 0.2, 0.1)

VL: Very Low Importance

(0.15,0.8, 0.05)

SM: Slightly More Importance

(0.6, 0.35, 0.05)

AL: Absolutely Low Importance

(0.05,0.9,0)

E: Equally Importance

(0.5, 0.5, 0)

Step 3. Construction of picture fuzzy comparison matrices: Pairwise comparison matrices are formed for each decision-maker using the given picture fuzzy scale. Step 4. Checking the consistency of each fuzzy pairwise comparison matrix using classical AHP. Step 5. Computation of aggregated picture fuzzy comparison matrix: The evaluations of decision-makers for each criterion can be aggregated using picture fuzzy weighted geometric mean  operator by Eq. (1) where wk represents the weight of the decision-maker that satisfies sk=1 wk = 1.  s     s  s  (k) wk (k) wk (k) wk μij νij 1 − πij (1) , ,1 − w˜ pij = k=1

k=1

k=1

Working Environment Selection After Pandemic Using Picture Fuzzy Sets

493

Step 6. Calculation of the local and global weights of criteria: The picture fuzzy local weights of each criterion are obtained by using the picture fuzzy weighted average mean operator and given in Eq. (2). 

 n

w

wj s wj s (2) 1 − μj j , νj · πj w˜ pj = 1 − j=1

k=1

k=1

where wj = 1/n. To compute the global weights,

 the local weight of each criterion is defuzzified by a modified score function (S w˜ pj ) using Eq. (3) and normalized using Eq. (4).

 1 + 2μj − νj − S w˜ pj = 2

 S w˜ pj

. wpj = n ˜ pj j=1 S w

πj 2

(3) (4)

Step 7. Computation of final picture fuzzy weights: Final picture fuzzy weights for each criterion and sub-criterion are obtained by multiplying the picture fuzzy global weights at the first level by each related sub-criterion global weight for each sub-criterion.

4 Working Environment Selection Using PFAHP The hierarchy of the criteria is shown in Fig. 1. The main criteria used in the paper are; C: Cost, P: Performance Related Factors, O: Organizational Factors, E: Environmental Factors, and I: Individual factors. The sub-criteria used in the paper are; C1: Rental cost of office for companies, C2: Remote working setup and maintenance cost for companies, C3: Indirect costs such as transportation services, electricity, and an internet connection, C4: Individual expenses such as wearing for employees, P1: Reducing absenteeism, P2: Productivity of the employee, P3: Less control and evaluation mechanism of employees by their managers, P4: Keeping employees in safe and productive, O1: Missing overlapping between organizational culture and employee’s expectation, O2: Easy recruitment, O3: Organizational flexibility, O4: Isolation of the employees, E1: Effect on air pollution, E2: Effect on traffic, E3: Effect on energy consumption, I1: Leisure time, I2: Being healthy and isolated from pandemic effects, I3: Ergonomic working environment, I4: Confliction and interrupts by family members, I5: Performance-related individual cases, I51: Overloaded tasks, I52: Working hours, I53: Pressure of being more productive.

Fig. 1. Hierarchy of Criteria and Sub-criteria

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Three experts made the pairwise evaluations of the criteria using the linguistic scale that is given in Table 1. Tables containing the calculations cannot be given due to the page limit, but expert evaluations are given in Table 2 to repeat the operations by the readers. Table 2. Expert evaluations for the criteria Expert 1 C

Expert 2

C

P

O

E

I

C

P

O

E

I

C

P

O

E

I

E

VL

E

VL

E

E

SL

SM

E

E

E

E

SM H

E

E

VH

SM H

E

H

SM

H

E

H

VH SM

E

VL

SM

E

SL

E

E

VH E

E

H

E

VH

P O E I C1

E C4

C1

C2

C3

C4

C1

C2

E

E

E

H

E

SL

E

SM

E

VH SM VH

E

E

SM

E

SM

SM

E

SM

E

E

E

E

E

VH

E

E

P2

P3

P4

P1

P2

P3

P4

P1

P2

P3

L

AL

E

AL

AL

AL

E

VL

SM AL

E

H

SM

E

H

SM

E

VH SL

E

SL

E

E

E

E

E

P4

AL E

O1

O2

O3

O4

O1

O2

O3

O4

O1

O2

O3

O4

E

AL

VL

SL

E

VL

L

E

E

E

L

E

E

SM

VH

E

H

H

E

SL

SM

E

SM

E

SM

E

H

O2 O3 O4

E

E

E1

E2

E3

E1

E2

E

E

E

E

VH E

E

E

E2 E3

I3

L

VL

P4

I2

C4

P1

P3

I1

E

C3

E

P2

E

E

E

E3

E1

E2

E

VH E

L

E

E I4

I5

VL E

C3

C4

E1

E

C2

C3

O1

E

C1 C2

P1

Expert 3

E3 L E

I1

I2

I3

I1

I2

I3

I1

I2

I3

I4

E

H

AM VH VH E

H

AM AM AM E

I4

H

E

VH E

E

H

H

VH

E

AM H

H

E

E

H

E

E

E

E

E

E

I5

E

I5 E

VH E (continued)

Working Environment Selection After Pandemic Using Picture Fuzzy Sets

495

Table 2. (continued) Expert 1

Expert 2

I4

E

I5

Expert 3

SM

E

E I51 I52

I53

I51 E

VH AM

I52

E

I53

E E

SM

E

E

E

I51 I52

I53

I51 I52

I53

E

E

H

E

VL

SL

E

H

E

E

E

VL

E

Local and global criteria weights were obtained by applying the steps of the PFAHP method and the defuzzified values of these weights are shown in Table 3. Table 3. The fuzzy local and global weights of the criteria and their defuzzified values Criteria

Local weights

Global weight of subcriteria

Normalized

(0.2024,0,0.5097)

0.197986

C1

(0.5695,0,0.3844)

(0.076,0,0.7903)

0.050035

C2

(0.4595,0,0.4935)

(0.0691,0,0.8078)

0.049397

C3

(0.5202,0,0.4438)

(0.0728,0,0.7984)

0.049738

C4

(0.3614,0,0.5951)

(0.0629,0,0.8239)

0.048816

C

P

(0.2919,0,0.2871)

defuzzified

0.224715

P1

(0.2318,0,0.7253)

(0.0633,0,0.7895)

0.054091

P2

(0.6745,0,0.2518)

(0.0954,0,0.6959)

0.057559

P3

(0.4012,0,0.5355)

(0.0758,0,0.752)

0.055461

P4

(0.6816,0,0.2515)

(0.0958,0,0.6948)

0.057603

O

(0.1456,0,0.5485)

0.185733

O1

(0.3379,0,0.6276)

(0.0334,0,0.8782)

0.045897

O2

(0.6204,0,0.3355)

(0.0433,0,0.8446)

0.046927

O3

(0.5763,0,0.3554)

(0.0419,0,0.8492)

0.046786

O4

(0.3997,0.0,0.5664)

(0.0356,0,0.8708)

E

(0.1893,0,0.4925)

weights

0.046122 0.196365

E1

(0.5709,0,0.4159)

(0.0724,0,0.7759)

0.066084

E2

(0.3437,0,0.6168)

(0.0591,0,0.814)

0.064368 (continued)

496

M. Bal and I. Ucal Sari Table 3. (continued)

Criteria

Local weights

Global weight of subcriteria

E3

(0.546,0,0.4291)

(0.0711,0,0.7797)

I

(0.1898,0,0.5198)

Normalized

defuzzified

weights

0.065912 0.195201

I1

(0.7147,0,0.235)

(0.0499,0,0.8528)

0.039748

I2

(0.5788,0,0.3574)

(0.045,0,0.8666)

0.039351

I3

(0.4015,0,0.5752)

(0.0382,0,0.8861)

0.038793

I4

(0.3173,0,0.6364)

(0.0352,0,0.8946)

0.038551

I5

(0.3882,0,0.5801)

(0.0377,0,0.8873)

0.038758

I51

(0.5062,0,0.4511)

(0.0134,0,0.959)

0.012939

I52

(0.4882,0,0.4881)

(0.0131,0,0.9597)

0.012931

I53

(0.363,0,0.5956)

(0.0117,0,0.9641)

0.012888

When the defuzzified weights of the main criteria are examined, it is seen that the most important main criterion is performance-related factors. However, the weights of the other main criteria are quite close to each other. When the defuzzified global weights of the sub-criteria are examined, it is seen that the most important sub-criteria belong to environmental factors. This is because the number of sub-criteria of environmental factors is less than the number of sub-criteria of other main criteria.

5 Conclusion In this paper, the criteria of working environment selection are determined in a hierarchical structure and analyzed using the picture fuzzy analytic hierarchy process. Although main criteria weights differ from each other, the global weights of the sub-criteria are found very closer to each other. Another interesting result is that the global weights of the sub-criteria belonging to the main criteria with relatively lower importance were higher than the other sub-criteria. The effect of this situation on the choice of alternative working environments will be examined in future studies. In the continuation of this study, a case study for a software and technology company will be conducted using one of the multi-criteria decision-making methods such as fuzzy WASPAS, fuzzy TOPSIS, or fuzzy CODAS using the weighted gathered in this study.

References 1. Barrero, J.M., Bloom, N., Davis, S.J.: Why Working from Home Will Stick (No. w28731). National Bureau of Economic Research (2021) 2. Carnevale, J.B., Hatak, I.: Employee adjustment and well-being in the era of COVID-19: implications for human resource management. J. Bus. Res. 116, 183–187 (2020)

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3. Cuong, B.C., Kreinovich, V.: Picture fuzzy sets-a new concept for computational intelligence problems. In: 2013 Third World Congress on Information and Communication Technologies (WICT 2013), pp. 1–6. IEEE (2013) 4. Elshaiekh, N.E.M., Hassan, Y.A.A., Abdallah, A.A.A.: The impacts of remote working on workers performance. In: 2018 International Arab Conference on Information Technology (ACIT), pp. 1–5. IEEE (2018) 5. Gajendran, R.S., Harrison, D.A.: The good, the bad, and the unknown about telecommuting: meta-analysis of psychological mediators and individual consequences. J. Appl. Psychol. 92(6), 1524 (2007) 6. Golden, T.D., Veiga, J.F., Dino, R.N.: The impact of professional isolation on teleworker job performance and turnover intentions: does time spent teleworking, interacting face-to-face, or having access to communication-enhancing technology matter? J. Appl. Psychol. 93(6), 1412 (2008) 7. Graves, L.M., Karabayeva, A.: Managing virtual workers—strategies for success. IEEE Eng. Manag. Rev. 48(2), 166–172 (2020) 8. Greer, T.W., Payne, S.C.: Overcoming telework challenges: outcomes of successful telework strategies. Psychol. Manag. J. 17(2), 87 (2014) 9. Ismail, F.D., Hamsa, A.A.K., Mohamed, M.Z.: Analysis of literature review on factors influencing the adoption of telecommuting. In: International Technical Conference (2012) 10. Kahraman, C., Ucal Sari, I., Cevik Onar, S.: Strategic multi-criteria decision making against pandemics using picture and spherical fuzzy AHP&TOPSIS. In: New Perspectives in Operations Research and Management Science (in press). Springer (2022) 11. Khan, S., Abdullah, S., Ashraf, S.: Picture fuzzy aggregation information based on Einstein operations and their application in decision making. Math. Sci. 13(3), 213–229 (2019) 12. Lin, M., Huang, C., Xu, Z.: MULTIMOORA based MCDM model for site selection of car sharing station under picture fuzzy environment. Sustain. Cities Soc. 53, 101873 (2020) 13. Liu, P., Zhang, X.: A novel picture fuzzy linguistic aggregation operator and its application to group decision-making. Cognit. Comput. 10(2), 242–259 (2018) 14. Mohite M.D., Kulkarni R.V.: Job satisfaction factors of employee in virtual workplace. Int. J. Trend Sci. Res. Develop. 38–42 (2019) 15. Rong, Y., Liu, Y., Pei, Z.: A novel multiple attribute decision-making approach for evaluation of emergency management schemes under picture fuzzy environment. Int. J. Mach. Learn. Cybern. (2021). https://doi.org/10.1007/s13042-021-01280-1 16. Wei, G.: Picture fuzzy cross-entropy for multiple attribute decision making problems. J. Bus. Econ. Manag. 17(4), 491–502 (2016)

Cloud Service Provider Selection Using Interval-Valued Picture Fuzzy TOPSIS Cengiz Kahraman(B) , Sezi Cevik Onar, and Basar Oztaysi Department of Industrial Engineering, Istanbul Technical University, 34367 Macka, Besiktas, Istanbul, Turkey [email protected]

Abstract. Cloud Service Provider selection is a multi-criteria decision making problem involving many criteria, which some of them may be conflicting. Alternatives under these criteria are generally assessed by using linguistic terms such as very high, excellent and absolutely low, which includes vagueness and impreciseness. In this paper, the uncertainties in the assessments are handled by intervalvalued picture fuzzy sets, and alternative cloud service providers are evaluated by TOPSIS method. Comparative and sensitivity analyses are also applied to show the validity of the proposed method and the robustness of the given decisions. Finally, the paper is completed by conclusions including discussions and future research suggestions. Keywords: Supplier selection · Picture fuzzy sets · TOPSIS · Interval-valued · Multi-criteria

1 Introduction Cloud service selection is a multiple criteria group decision-making problem. The technique for order preference by similarity to an ideal solution (TOPSIS) can be used to select the best cloud service providers by consumers using linguistic terms. Web services are tremendously interactive software components that can be published, located, and invoked practically anywhere on the web. The increasing number of web services available raises new challenges related to service discovery, selection, and composition. The most used criteria for cloud service provider selection are speed, bandwidth, price, security, and availability. TOPSIS method is one of the most used MCDM methods in the literature. In this paper, we employ the interval-valued picture fuzzy (IVPF) TOPSIS method for the selection of the best cloud service provider under uncertainty. Figure 1 illustrates the publication frequencies of fuzzy TOPSIS method by years. There is a large acceleration in the usage of fuzzy TOPSIS methods. Type-2 fuzzy TOPSIS method, intuitionistic fuzzy TOPSIS method, spherical fuzzy TOPSIS method, Pythagorean fuzzy TOPSIS method, and neutrosophic TOPSIS method are some extensions of fuzzy TOPSIS in the literature. The originality of this paper is the first time usage of IVPF TOPSIS method in a cloud service provider selection problem. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 498–507, 2022. https://doi.org/10.1007/978-3-031-09173-5_59

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Fig. 1. Fuzzy TOPSIS publications by years

The rest of this paper is organized as follows. Section 2 includes a literature review on cloud service providers and fuzzy TOPSIS methods. Section 3 presents the preliminaries of IVPF sets. Section 4 gives the steps of IVPF TOPSIS method. Section 5 presents the application of the proposed method to cloud service provider selection problem. 1.1 Literature Review on Cloud Service Cloud service providers are third-party companies offering a cloud-based platform, infrastructure, application, or storage services. They also give businesses a wide range of benefits such as scalability and flexibility by not being limited to physical constraints of on-premises servers, the reliability of multiple data centers with multiple redundancies, customization by configuring servers to companies’ preferences, and responsive load balancing that can easily respond to changing demands (Paul et al. 2020). Security considerations of storing information in the cloud is another highly important criterion. Figure 2 presents the frequencies of cloud service publications by years. After 2009, there is a strong acceleration up to 2014 and then this acceleration stops and slightly go downward. Figure 3 shows the source universities of publications on cloud service, who published more than 100 papers up to now. China, India and USA are the leading countries publishing on cloud service, respectively. China gives a special importance on research areas such as cloud computing, cloud service, and cloud security.

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450 400 350 300 250 200 150 100 50 0 2008

2010

2012

2014

2016

2018

2020

Fig. 2. Publication frequencies on cloud service

250 200 150 100 50 0

Fig. 3. Source universities of publications on cloud service

2022

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2 Interval-Valued Picture Fuzzy Sets (IVPFS) Definition 1. A picture fuzzy set (PFS) on the universe X is an object of the form ˜ ˜ A={x,μ A˜ (x),ηA˜ (x),vA˜ (x) x ∈ X}, Let A be an interval valued picture fuzzy number ˜ (IVPFN), where μA˜ (x)[0, 1] is named as the “degree of positive membership of A, ηA˜ (x)[0, 1] is named as the “degree of neutral membership of A˜ and vA˜ (x)[0, 1] is ˜ and μ ˜ (x),η ˜ (x), and v ˜ (x) satisfy named as the “degree of negative membership of A, A A A the following condition: 0 ≤ μ  A˜ (x)+ηA˜ (x)+vA˜ (x) ≤ 1, ∀ x ∈ X. Then for x ∈ X, πA (x) =  1 − μA˜ (x) + ηA˜ (x) + vA˜ (x) could be named as the degree of refusal membership of x in A (Naeem et    al. 2021).  Let A˜ = μA˜ , ηA˜ , υA˜ and B˜ = μB˜ , ηB˜ , υB˜ be two single valued picture fuzzy numbers. The operations with these numbers are as follows   A˜ ⊕ B˜ = μA˜ + μB˜ − μA˜ μB˜ , ηA˜ ηB˜ , vA˜ vB˜ (1)   A˜ ⊗ B˜ = μA˜ μB˜ , ηA˜ + ηB˜ − ηA˜ ηB˜ , vA˜ + vB˜ − vA˜ vB˜

(2)

  λ  λA˜ = 1 − 1 − μA˜ , ηAλ˜ , vAλ˜ , λ > 0

(3)

 λ λ    , λ>0 A˜ λ = μλA˜ , 1 − 1 − ηA˜ , 1 − 1 − vA˜

(4)

 L U   L U   L U  Definition 2. Let A˜ = μA , μA , ηA , ηA , vA , vA be an interval-valued PF U U U (IVPFN). It must satisfy the condition:  0 ≤ μ A + ηA +vA ≤ 1. The degree of refusal  U U where π L˜ = 1 − μU membership is defined as an interval π L˜ , π U A + ηA + vA and ˜ A A A   L L L πU ˜ = 1 − μA + ηA + vA (Naeem et al. 2021). A

  L U   L U     L U  and B˜ = μLB , μU Definition 3. Let A˜ = μLA , μU B , ηB , η B , A , ηA , ηA , vA , vA  L U  vB , vB be two interval-valued picture fuzzy numbers (IVPFNs). The operations with these numbers are as follows (Naeem et al. 2021). Multiplication A˜ ⊗ B˜ =

  U L L L L U U U U μLA μLB , μU A μB , ηA + ηB − ηA ηB , ηA + ηB − ηA ηB ,          1 − ηBL )vAL + 1 − ηAL vBL − vAL vBL , 1 − ηBU )vAU + 1 − ηAU vBU − vAU vBU

(5) Addition

A˜ ⊕ B˜ =

  U U U L L U U μLA + μLB − μLA μLB , μU A + μB − μA μB , ηA ηB , ηA ηB ,          U U U U U 1 − μLB )vAL + 1 − μLA vBL − vAL vBL , 1 − μU B )vA + 1 − μA vB − vA vB

(6)

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Multiplication by a Constant λ > 0 λ.A˜ =

λ λ  λ  λ   , ηAL , ηAU , 1 − 1 − μLA , 1 − 1 − μU A





1 − μLA

λ

λ  λ    U − vU λ − 1 − μLA − vAL , 1 − μU − 1 − μ A A A

(7)

Power Operation ˜ λ>0 λth Power of A; ˜λ = A

         λ λ L λ , 1 − 1 − ηU λ , , 1 − 1 − η μLA , μU A A A  λ  λ  λ  λ 1 − ηAL − 1 − ηAL − vAL , 1 − ηAU − 1 − ηAU − vAU

(8)

   L U   L U     L U Definition 4. Let A˜ = μLA , μU and B˜ = μLB , μU B , ηB , η B , A , ηA , ηA , vA , vA  L U  vB , vB . Then the Euclidean distance between these PFNs is given by Eq. (9):

(9) Definition 5. Aggregation Operator Let A˜ 1 , A˜ 2 , . . . ., and A˜ n be IVPFNs, which are the corresponding numbers in the linguistic scale. Aggregation of these IVPFNs assigned by experts with respect to each criterion. Are made by using IVPFWG operator given in Eq. (10).   IVPFWG A˜ 1 , A˜ 2 , . . . ., A˜ n  n      n  n  n  λi  λi λi λi    L U L U μ˜ μ˜ 1 − ηAi 1 − ηAi , = , 1− , 1− , i=1

Ai

 n 

L 1 − ηAi

i=1

Ai

i=1

λi

−

i=1

n  

L − vL 1 − ηAi Ai

i=1

λi

i=1

  n  n  λi  λi  U U U 1 − ηAi 1 − ηAi − vAi − , i=1

i=1

(10) Definition 6. Score and Accuracy Functions The score function (S) and accuracy function (A) for the IVPFN is given by Eqs. (11) and (12), respectively: S=

μL + μU − ϑ L − ϑ U − ηL /2 − ηU /2 2

(11)

μL + μU + ϑ L + ϑ U + ηL + ηU 2

(12)

A=

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3 IVPF TOPSIS The steps of the proposed IVPF TOPSIS method are presented in this section. The experts use the following linguistic scale for the evaluation of both alternatives and criteria. Table 1. Interval valued picture fuzzy scales Evaluations for alternatives

Abb

Evaluations for criteria

Abb

IVPFN

Absolutely high

AH

Absolutely high important

AHI

([0.7,0.85],[0,0.05],[0.05,0.1])

Very high

VH

Very high important

VHI

([0.6,0.75],[0.05,0.15],[0.05,0.1])

High

H

High Important

HI

([0.5,0.65],[0.1,0.25],[0.05,0.1])

Slightly high

SH

Slightly high important

SHI

([0.4,0.55],[0.2,0.35],[0.05,0.1])

Moderate

M

Moderate important

MI

([0.3,0.45],[0.3,0.45],[0.05,0.1])

Slightly low

SL

Slightly low important

SLI

([0.2,0.35],[0.4,0.55],[0.05,0.1])

Low

L

Low important

LI

([0.1,0.25],[0.5,0.65],[0.05,0.1])

Very low

VL

Very low important

VLI

([0.05,0.15],[0.6,0.75],[0.05,0.1])

Absolutely low

AL

Absolutely low important

ALI

([0,0.05],[0.7,0.85],[0.05,0.1])

Step 1. Define the alternatives (i = 1, .., n) and criteria (j = 1, .., m). (di, j, k ) Step 2. Collect the linguistic evaluations from the experts by using the scale given in Table 1 for decision matrices (Eq. 13) and criteria weights for each expert from experts (Eq. 14) where K is the number of experts (k = 1, .., K). Experts can have different weights based on their experiences (λk , k = 1, . . . , K). ⎤ ⎡ x˜ 11k · · · x˜ 1mk . . ⎥ ˜k = ⎢ (13) D ⎣ .. . . . .. ⎦, k = 1, . . . , K x˜ n1k · · · x˜ nmk   ˜ k = w˜ 1, k , . . . , w˜ m, k , k = 1, . . . , K W

(14)

Step 3. Aggregate the decision matrices and criteria evaluations by using the aggregation operator given in Eq. (10). Obtain the aggregated decision matrix in Eq. (15) and aggregated criteria weights vector in Eq. (16).

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⎤ x˜ 11 · · · x˜ 1m ⎥ ⎢ = ⎣ ... . . . ... ⎦ x˜ n1 · · · x˜ nm

(15)

˜ agg = (w˜ 1 , . . . , w˜ m ) W

(16)

⎡

˜ agg D

Step 4. Obtain the weighted decision matrix by using multiplication operation in Eq. (5) and obtain weighted aggregated decision matrix given in Eq. (17). ⎤ ⎡ r˜11 · · · r˜1m . . ⎥ ˜ w, agg = D ˜ agg ⊗ W ˜ agg = ⎢ (17) D ⎣ .. . . . .. ⎦ r˜n1 · · · r˜nm

  + as in Eq. (18) ˜ = r˜ + , r˜ + , . . . r˜m Step 5. Determine the positive ideal solution PIS 1 2  − −  − as in Eq. (19) by using the ˜ = r˜ , r˜ , . . . , r˜m and the negative-ideal solution NIS 1 2 score function defined in Eq. (11). ⎧ ⎫    ⎨ max Score rij , if fj ∈ F1 ⎬ 1≤i≤n    rj+ = (18) ⎩ min Score rij , if fj ∈ F2 ⎭ 1≤i≤n

and

⎧ ⎫    ⎨ min Score rij , if fj ∈ F1 ⎬   rj− = 1≤i≤n ⎩ max Score rij , if fj ∈ F2 ⎭

(19)

1≤i≤n

  L   L     U U and r˜j− = μLNISj , μU where r˜j+ = μLPISj , μU PISj , ηPISj , ηPISj , vPISj , vPISj NISj ,    L U L , vU , vNISj are associated fuzzy value of rj+ andrj− . F1 = {f1 , .., fb } ηNISj , ηNISj NISj denotes the set of benefit attributes, F2 = {f1 , .., fc } denotes the set of cost attributes and b + c = m,1 ≤ j ≤ m. ˜ and NIS ˜ by using Eqs. (20) Step 6. Compute the distance of each alternative to PIS and (21) respectively. #⎛ $  2  2  2 ⎞ $ L − μL U − μU L − ηL   $ " μ + μ + η m Aj PISj Aj PISj Aj PISj + ⎟ $⎜ ! = 1 d A˜ i , PIS 2  2  2 ⎠  ⎝ % j=1 m U − ηU L − vL U − vU ηAj + vAj + vAj PISj PISj PISj (20) #⎛ $  2  2  2 ⎞ $ L − μL U − μU L − ηL   $ " μ + μ + η m 1 Aj NISj Aj NISj Aj NISj + ⎟ $⎜ NIS = d A˜ i ,  2  2  2 ⎠  ⎝ % j=1 m U − ηU L − vL U − vU ηAj + vAj + vAj NISj NISj NISj (21)

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where i = 1, . . . , n Step 7. Compute closeness coefficients (C) for each alternative using Eq. (22).   ˜ d A˜ i , NIS    , 0 ≤ Ci ≤ 1, i = 1, . . . n Ci =  (22) ˜ + d A˜ i , NIS ˜ d A˜ i , PIS Step 8. Rank the alternatives in descending order. The largest closeness coefficient indicates the best alternative.

4 Application Cloud service providers have data centers in various locations, which makes them faster and more reliable. The top cloud service providers in the world are Microsoft, Amazon, Google, Oracle, IBM, Apple, Adobe, DigitalOcean, Citrix and Alibaba Cloud. A multicriteria selection problem among the five alternatives are realized based on five criteria: speed, bandwidth, price, security, and availability. IVPF TOPSIS given in Sect. 4 is used for this aim. There are three experts whose weights are 0.4, 0.3, and 0.3, respectively. Table 2 presents the three expert’s decision matrices including the linguistic terms whose corresponding meanings and values are given in Table 1. Table 2. Decision matrices of three experts Expert 1

Speed

Bandwidth

Price

Security

Availability

Alternative 1

H

SH

VH

SL

H

Alternative 2

AH

SL

L

H

VH

Alternative 3

L

H

VH

L

SL

Alternative 4

VL

SH

AH

VH

SL

Alternative 5

H

VH

SH

SH

L

Criteria weight

H

VH

SH

H

H

Expert 2

Speed

Bandwidth

Price

Security

Availability

Alternative 1

VH

SH

H

SL

H

Alternative 2

VH

H

L

H

H

Alternative 3

SL

H

H

SH

SL

Alternative 4

L

H

VH

VH

SL

Alternative 5

H

VH

SL

SH

SL

Criteria weight

VH

VH

SL

VH

SH

Expert 3

Speed

Bandwidth

Price

Security

Availability

Alternative 1

AH

H

SH

L

SH

Alternative 2

VH

H

SL

H

VH (continued)

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Expert 1

Speed

Bandwidth

Price

Security

Availability

Alternative 3

SH

SH

VH

AH

SH

Alternative 4

L

H

AH

VH

SL

Alternative 5

H

H

SH

SH

SH

Criteria weight

AM

H

SH

H

H

Table 3. Weighted aggregated decision matrix Speed

Bandwidth

Alternative 1 0.34 0.54 0.11 0.30 0.09 0.16 0.24 0.42 0.23 0.44 0.09 0.14 Alternative 2 0.37 0.58 0.09 0.26 0.09 0.16 0.20 0.36 0.28 0.50 0.08 0.14 Alternative 3 0.11 0.26 0.43 0.62 0.08 0.12 0.27 0.44 0.19 0.41 0.09 0.14 Alternative 4 0.04 0.15 0.57 0.74 0.07 0.11 0.26 0.44 0.20 0.42 0.09 0.14 Alternative 5 0.29 0.48 0.15 0.37 0.09 0.15 0.32 0.52 0.13 0.33 0.09 0.15 Price

Security

Alternative 1 0.16 0.31 0.35 0.56 0.08 0.13 0.09 0.21 0.48 0.68 0.07 0.11 Alternative 2 0.04 0.13 0.61 0.78 0.06 0.09 0.26 0.44 0.18 0.42 0.09 0.14 Alternative 3 0.18 0.35 0.31 0.52 0.08 0.13 0.14 0.31 0.35 0.56 0.08 0.13 Alternative 4 0.22 0.39 0.28 0.47 0.08 0.14 0.32 0.51 0.13 0.34 0.09 0.15 Alternative 5 0.11 0.23 0.46 0.66 0.07 0.11 0.21 0.37 0.27 0.49 0.08 0.13 Availability Alternative 1

0.22

0.38

0.25

0.48

0.08

0.13

Alternative 2

0.27

0.44

0.19

0.41

0.09

0.14

Alternative 3

0.12

0.25

0.43

0.64

0.07

0.11

Alternative 4

0.09

0.22

0.48

0.68

0.07

0.11

Alternative 5

0.09

0.22

0.47

0.67

0.07

0.11

The weighted aggregated decision matrix given in Table 3. Bold numbers indicate the minimum and maximum solutions for each criterion. Table 4 gives the distances to PIS and NIS for each alternative and the ranking of the alternatives. Cloud service provider 2 is the best alternative.

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Table 4. Ranking of the alternatives Distance to PIS

Distance to NIS

RI

Rank

Alternative 1

0.231333

0.3379453

0.5936381

2

Alternative 2

0.1975682

0.3709827

0.6525058

1

Alternative 3

0.3402406

0.2293714

0.4026801

5

Alternative 4

0.3030038

0.2648624

0.4664169

4

Alternative 5

0.2544254

0.316534

0.5543897

3

5 Conclusion Cloud services presents a wide range of services delivered on demand to companies and customers over the internet. These services are designed to provide easy, affordable access to applications and resources, without the need for internal infrastructure or hardware. Cloud services are fully managed by cloud computing vendors and service providers. We presented an IVPF TOPSIS method which can capture the vagueness in the linguistic evaluations of cloud service providers. Different experts weights, different decision matrices, and different criteria weights have been considered in the model. Defuzzification has been cancelled to the last step of the method in order to keep the fuzzy application. For future studies, we suggest the components of cloud service such infrastructure as a service (IaaS), software as a service (SaaS) or platform as a service (PaaS) to be multi-criteria evaluated under fuzziness. Alternatively, other fuzzy set extensions such as spherical fuzzy sets or neutrosophic sets can be used for comparison. Other multi-criteria decision making methods such as spherical fuzzy VIKOR (Kutlu Gundogdu and Kahraman 2019), intuitionistic fuzzy information axiom (Kahraman et al. 2018), fuzzy COPRAS methods (Turanoglu Bekar et al. 2016) or Pythagorean fuzzy AHP (Karasan et al. 2019).

References Kahraman, C., Cebi, S., Cevik Onar, S., Oztaysi, B.: A novel trapezoidal intuitionistic fuzzy information axiom approach: an application to multicriteria landfill site selection. Eng. Appl. Artif. Intell. 67, 157–172 (2018) Kara¸san, A., ˙Ilbahar, E., Kahraman, C.: A novel pythagorean fuzzy AHP and its application to landfill site selection problem. Soft Comput. 23(21), 10953–10968 (2019) Kutlu Gündo˘gdu, F., Kahraman, C.: A novel VIKOR method using spherical fuzzy sets and its application to warehouse site selection. J. Intell. Fuzzy Syst. 37, 1197–1211 (2019) Naeem, M., Qiyas, M., Abdullah, S.: An approach of interval-valued picture fuzzy uncertain linguistic aggregation operator and their application on supplier selection decision-making in logistics service value concretion. Math. Prob. Eng. 2021, 8873230 (2021) Paul, P.K., Ricardo, S., Aithal, P.S., Bashiru, A., Baby, P.: CloudService providers: an analysis of some emerging organizations and industries. Int. J. Appl. Eng. Manag. Lett. 4(1), 172–183 (2020) Turanoglu Bekar, E., Cakmakci, M., Kahraman, C.: Fuzzy COPRAS method for performance measurement in total productive maintenance: a comparative analysis. J. Bus. Econ. Manag. 17(5), 663–684 (2016)

Picture Fuzzy Benefit/Cost Analysis in Digital Transformation for an IT Firm Eda Boltürk(B) Istanbul Settlement and Custody Bank Inc.-Takasbank, Re¸sitpa¸sa Mahallesi, Borsa ˙Istanbul Caddesi, Sarıyer, 34467 ˙Istanbul, Türkiye [email protected]

Abstract. With the coronavirus disease (COVID-19) pandemic, it has been seen that the importance of IT companies and digitalization investments has accelerated. Engineering economics techniques are frequently used in investments and provide use among alternatives. Although benefit/cost analysis is one of the important engineering economic techniques, it is seen that it is widely used in the literature. Engineering economics analyzes are made based on the opinions and experiences of experts. While human thoughts can contain uncertainty, these uncertainties should also be taken into account in the investment evaluation. Fuzzy sets come to the fore in the literature to eliminate the uncertainty in human opinions. Fuzzy sets represent human thoughts through membership functions. Since fuzzy sets were proposed in 1965, fuzzy sets have extended to their extensions. Some of these extensions are type 2 fuzzy sets, spherical fuzzy sets, hesitant fuzzy sets, q-rung fuzzy sets, picture fuzzy sets, Pythagorean fuzzy sets, fermatean fuzzy sets, circular intuitionistic fuzzy sets, decomposed fuzzy sets and etc. When the studies on the benefit/cost analysis method, which is one of the engineering economics approaches, are examined, it is seen that it is used with fuzzy sets and their extensions. In this study, benefit/cost analysis is extended with picture fuzzy sets, and the extended model is applied in the digital transformation investment assessment for an information technology. Future suggestions and recommendations are given in conclusion section. Keywords: Engineering economics · Benefit/cost analysis · Digital transformation · Picture fuzzy sets

1 Introduction It is known seen that the coronavirus disease (COVID-19) pandemic has brought changes in human life all over the world. A new term, social distance, has been added to our lives. With social distance, new rules entered our lives. Social distance rules have caused changes in many activities such as sports, business life, entertainment life, meeting outside, and it has become important for sustainability to adapt quickly to these changes. In particular, the employees who go to the company physically have followed the way of completing their jobs with the remote working method instead of working physically. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 508–516, 2022. https://doi.org/10.1007/978-3-031-09173-5_60

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With this change, it can be said that the digitalization transformation investment processes have accelerated in companies that have not gone through the digitalization process in order to advance their business. In addition to making these changes, it should be taken into account that being successful in digital transformation may not be easy. Successful digital transformation requires an organization to expand a wide-range of capabilities; their significance will vary depending on the business context and the needs of a particular organization [1]. Picture fuzzy sets, one of the extensions of fuzzy sets, were introduced by Cuong and Kreinovich in 2014 [2]. A picture fuzzy set number consists of membership, nonmembership, and hesitation parameters, and the sum of these parameters is between 0 and 1. Models with picture fuzzy sets, which are sufficient in situations where we encounter human ideas, include more types of responses such as “yes,”, “no”, “abstain” and “refusal” [2]. It has been observed that since 2014, picture fuzzy sets have been studied in fields such as engineering, business, management, compute science, economics, decision science, environmental science, chemistry and etc. One of the approaches used to evaluate the alternatives is the benefit/cost analysis method and provides information to investors about the feasibility of investments for engineering economics problems. It is seen that fuzzy sets are used while making the evaluations because there may be uncertainty in the ideas of the investors. Benefit/cost analysis has been used with other fuzzy extensions [3–7] in different areas. To our knowledge, picture fuzzy benefit/cost analysis has not been used in engineering economics in the literature. The contribution and the originality this paper is to introduce the picture fuzzy benefit/cost analysis method and show the method in digital transformation investment analysis evaluation. This study is organized as follows: A literature review on digital transformation investment analysis studies is given in Sect. 2. The preliminaries of picture fuzzy sets are given in Sect. 3 with formulas. Picture fuzzy benefit/cost analysis with formulas is given in Sect. 4. In Sect. 5, a digital transformation application for a financial information technology firm is given. In Sect. 6, conclusion is given, along with future recommendations.

2 Literature Review It is seen that studies on digital transformation investment analysis have been in the literature since 1994. In this section, these digital transformation investment papers have been tried to be summarized from different perspectives. Figure 1 shows that the distribution of digital transformation investment analysis papers with respect to years. It is seen that most of the studies have been published in 2021 with a rate of 27%. Also, the number of studies increased sharply after 2017. Figure 2 shows the distribution of digital transformation investment analysis papers by country. Most of the papers on digital transformation investment analysis have been published by Russia. It can be seen that Russia is followed by America, Italy and China, respectively. In Fig. 3, the publication percentages of digital transformation investment analysis papers are given. It is seen that most of the studies are published as article at

510

E. Boltürk

a rate of 44.7%. It is seen that conference paper studies follow with a very high rate after the article with a rate of 35.9%. When we look at other types of studies related to digital transformation investment analysis, there are conference summary, book chapter review, book, data paper and editorial. In Fig. 4, distribution of subject area of papers is illustrated. The top three subject areas are in digital transformation investment analysis are computer science with 18.5%, engineering with 13.8% and social science 13.4%, respectively.

27% 24%

15%

8% 6% 4% 3%

3%

1% 1%

2% 0%

1% 1% 1% 1% 0% 0% 0%

2022202120202019201820172016201520142013201220112010200820072006200419981994

Fig. 1. Distribution of papers published on digital transformation investment analysis by yearly.

18%

12% 7%

6%6% 3% 3%

2%2%2% 2%2%2%2%

1% 1%1%1%1%1%1% 1%1%1%1%1%

1%

Fig. 2. Distribution of countries published digital transformation investment analysis.

Picture Fuzzy Benefit/Cost Analysis in Digital Transformation

44.7%

511

35.9% 8.1%

7.0%

Article ConferenceConference Book Paper Review Chapter

3.2%

0.4%

Review

Book

0.4%

0.4%

Data Paper Editorial

Fig. 3. Distribution of published digital transformation investment analysis publication types.

18.5% 13.8%13.4% 11.1%

Veterinary

Pharmacology, Toxicology and…

Chemistry

Health Professions

Psychology

Multidisciplinary

Arts and Humanities

Chemical Engineering

Agricultural and Biological…

Physics and Astronomy

Medicine

Materials Science

Earth and Planetary Sciences

Environmental Science

Mathematics

Energy

Economics, Econometrics and…

Decision Sciences

Business, Management and…

Engineering

Social Sciences

Computer Science

7.9% 6.4% 6.1% 4.4% 4.0% 3.2% 2.5%2.4%1.7% 1.2% 1.0%0.7%0.5%0.5%0.3% 0.2% 0.2% 0.2%

Fig. 4. Distribution of papers published digital transformation investment analysis by subject areas.

3 Picture Fuzzy Sets Preliminaries of picture fuzzy sets are given by definitions in Eqs. (1–7): Definition 1: [2] A picture fuzzy set on an A˜ P of the universe of discourse, U, is illustrated in Eqs. (1–2):     (1) A˜ p = u, (μA˜ p (u), νA˜ p (u), πA˜ p (u))u ∈ U , where μA˜ p (u) : U → [0, 1], νA˜ p (u) : U → [0, 1], πA˜ p (u) : U → [0, 1]

512

E. Boltürk

and 0 ≤ μA˜ p (u) + νA˜ p (u) + πA˜ p (u) ≤ 1 ∀u ∈ U .

(2)

Degrees of membership, non-membership, and hesitancy of u areμA˜ P (u),vA˜ P (u), and πA˜ P (u) for A˜ P , respectively. Refusal degree formulation of picture fuzzy sets is shown in Eq. (3) [2].   (3) ρ = 1 − μA˜ p (u) + νA˜ p (u) + πA˜ p (u) Definition 2: [2] Let A˜ P and B˜ P are single-valued picture fuzzy sets. The basic operators of A˜ P and B˜ P are given in Eqs. (4–5).   (4) A˜ p ⊕ B˜ p = μA˜ p + μB˜ p − μA˜ p μB˜ p , πA˜ p πB˜ p , vA˜ p vB˜ p   A˜ p ⊗ B˜ p = μA˜ p μB˜ p , πA˜ p + πB˜ p − πA˜ p πB˜ p , vA˜ p + vB˜ p − vA˜ p vB˜ p

(5)

Definition 3: [8] A single-valued picture fuzzy weighted averaging (PFWA) operator which is proposed by Wei, for picture fuzzy sets with respect to is presented in Eq. (6); PFWAw (A˜ 1 , ......., A˜ n ) = w1 A˜ 1 + w2 A˜ 2 + ...... + wn A˜ n 

n n n wi wi wi = 1− (1 − μA˜ i ) , v˜ , π˜ i=1

where w = (w1, w2 , . . . , wn ); wi ∈ [0, 1];

n

i=1 wi

i=1

Ai

i=1

Ai

(6)

= 1.

Definition 4: [9] Score functions for sorting picture fuzzy numbers is given in Eq. (7). Score function formula can be used to defuzzify the picture fuzzy numbers.   1  1 + 2μA˜ p − vA˜ p − πA˜ p /2 Score A˜ p = (7) 2

4 Picture Fuzzy Benefit/Cost Analysis In this section, extended picture fuzzy benefit/cost analysis is explained and formulations are given. The parameters which are used in picture fuzzy benefit/cost analysis are given ∼

∼

as follows: Picture fuzzy first cost = FCp , picture fuzzy annual cost = ACp , picture ∼

∼

fuzzy annual benefit = ABp , picture fuzzy useful life = n p , picture fuzzy interest rate = ∼ ∼ i p , picture fuzzy salvage value = SVp . Each picture fuzzy parameter formulas given by

experts/investors are shown in Eqs. (8–13). Benefit cost ratio formula for picture fuzzy sets is given in Eq. (14). If the result of this ratio is greater than 1, it means investment is feasible.

fc1 , PFN 1 , . . . , PFN m , fc2 , PFN 1 , . . . , PFN m , ˜ (8) FC P = . . . , fck , PFN 1 , . . . , PFN m

Picture Fuzzy Benefit/Cost Analysis in Digital Transformation

˜ P= AC



ac1 , PFN 1 , . . . , PFN m , ac2 , PFN 1 , . . . , PFN m , . . . , ack , PFN 1 , . . . , PFN m



ab1 , PFN 1 , . . . , PFN m , ab2 , PFN 1 , . . . , PFN m , . . . , abk , PFN 1 , . . . , PFN m

n1 , PFN 1 , . . . , PFN m , n2 , PFN 1 , . . . , PFN m , . . . , n˜ P = nk , PFN 1 , . . . , PFN m



˜iP = i1 , PFN 1 , . . . , PFN m , i2 , PFN 1 , . . . , PFN m , . . . , ik , PFN 1 , . . . , PFN m

sv1 , PFN 1 , . . . , PFN m , sv 2 , PFN 1 , . . . , PFN m , . . . , ˜ SV P = svk , PFN 1 , . . . , PFN m

˜ P= AB



513

˜ P ( P , ˜iP , n˜ P ) AB B˜ p A = P ˜ ˜ ˜ ˜ ˜ P ( P , ˜iP , n˜ P ) Cp FC P + AC P ( A , iP , n˜ P ) − SV F

(9) (10) (11) (12) (13)

(14)

5 Application 4 experts are trying to evaluate a digital transformation tool for an IT company to be faster and more effective among its competitors. Experts are software developer and business analysis manager (Expert 1), Strategy, R&D and Project Management Manager (Expert 2), IT Infrastructure Manager (Expert 3) and IT Architecture Manager (Expert 4). Experts have worked on software and data transformation projects and are familiar with implementation processes. The weights of these four experts are given as 0.2, 0.2, 0.3 and 0.3 for the digital transformation tool, respectively. Table 1 shows the possible values of the alternative given by the experts. First, the membership functions for each parameter are summed and defuzzified. After defuzzification process, the defuzzified values are normalized. The normalized values are used to aggregate the parameter values. Table 2 presents defuzzified values of the alternative parameters to obtain benefit/cost ratio. The benefit/cost ratio is obtained as 2.88 and it means this investment is feasible. The calculations based on Table 1 are given as follows: Aggregation membership for first row of FC in Table 1 is calculated by Eq. (6) as follows: → First row value of FC =          1 − (1 − 0.2)0.2 × (1 − 0.4)0.2 × (1 − 0.5)0.3 × (1 − 0.7)0.3 ,         0.30.2 × 0.50.2 × 0.40.3 × 0.10.3 ,         0.50.2 × 0.10.2 × 0.10.3 × 0.20.3 = 0.5113, 0.2605, 0.1699

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E. Boltürk

The defuzzification value of 0.5113, 0.2605, 0.1699 is calculated by Eq. (7) as follows:   0.1699 1 1 + 2 × 0.5113 − 0.2605 − = 0.839 Score = 2 2 ∼

∼

∼

∼

p

P, ABP ( A i P, nP)

1579230.56( A , i, n) p  = ∼ = ∼ ∼ ∼ ∼ ∼ ∼ ∼ 9651517.55 + 775.74 A , i, n − 0 P, Cp FCP + ACP ( A i P , n P ) − SVP ( FP , i P , n P ) Bp

=

22, 108, 280.6 22, 108, 280.6 = = 2.288 9, 651, 517.55 + 10, 859.895 9, 662, 377.44

Table 1. Opinions of experts for the alternative. Parameters

FC

AB

AC

SV

i

Values

Picture fuzzy membership values for expert 1

Picture fuzzy membership values for expert 2

Picture fuzzy membership values for expert 3

Picture fuzzy membership values for expert 4

Experts’ weight W = 0.2

Experts’ weight W = 0.2

Experts’ weight W = 0.3

Experts’ weight W = 0.3

e9, 500, 000

0.2, 0.3, 0.5

0.4, 0.5, 0.1

0.5, 0.4, 0.1

0.7, 0.1, 0.2

e9, 600, 000

0.7, 0.1, 0.2

0.5, 0.4, 0.1

0.3, 0.3, 0.4

0.1, 0.1, 0.3

e9, 700, 000

0.1, 0.1, 0.3

0.6, 0.1, 0.2

0.7, 0.1, 0.2

0.5, 0.4, 0.1

e9, 800, 000

0.3, 0.3, 0.4

0.5, 0.4, 0.1

0.3, 0.3, 0.4

0.7, 0.1, 0.2

e1, 300, 000

0.6, 0.1, 0.2

0.1, 0.1, 0.3

0.6, 0.1, 0.2

0.3, 0.3, 0.4

e1, 600, 000

0.5, 0.4, 0.1

0.3, 0.3, 0.4

0.5, 0.4, 0.1

0.7, 0.1, 0.2

e1, 500, 000

0.4, 0.5, 0.1

0.3, 0.3, 0.4

0.1, 0.1, 0.3

0.7, 0.1, 0.2

e1, 900, 000

0.1, 0.2, 0.3

0.4, 0.5, 0.1

0.7, 0.1, 0.2

0.5, 0.4, 0.1

e950

0.4, 0.5, 0.1

0.2, 0.3, 0.5

0.5, 0.4, 0.1

0.3, 0.3, 0.4

e550

0.7, 0.1, 0.2

0.3, 0.3, 0.4

0.1, 0.1, 0.3

0.1, 0.1, 0.3

e850

0.2, 0.3, 0.5

0.7, 0.1, 0.1

0.5, 0.4, 0.1

0.5, 0.4, 0.1

e750

0.7, 0.1, 0.2

0.5, 0.4, 0.1

0.1, 0.1, 0.3

0.3, 0.3, 0.4

0

0.4, 0.5, 0.1

0.3, 0.3, 0.4

0.4, 0.5, 0.1

0.5, 0.4, 0.1

0

0.7, 0.1, 0.2

0.5, 0.4, 0.1

0.1, 0.1, 0.3

0.3, 0.3, 0.4

0

0.5, 0.4, 0.1

0.4, 0.5, 0.1

0.3, 0.3, 0.4

0.4, 0.5, 0.1

0

0.2, 0.3, 0.5

0.4, 0.5, 0.1

0.2, 0.3, 0.5

0.1, 0.1, 0.3

2.3%

0.4, 0.5, 0.1

0.6, 0.1, 0.2

0.7, 0.1, 0.2

0.4, 0.5, 0.1

2.4%

0.1, 0.1, 0.3

0.7, 0.1, 0.2

0.2, 0.3, 0.5

0.4, 0.5, 0.1

(continued)

Picture Fuzzy Benefit/Cost Analysis in Digital Transformation

515

Table 1. (continued) Parameters

n

Values

Picture fuzzy membership values for expert 1

Picture fuzzy membership values for expert 2

Picture fuzzy membership values for expert 3

Picture fuzzy membership values for expert 4

Experts’ weight W = 0.2

Experts’ weight W = 0.2

Experts’ weight W = 0.3

Experts’ weight W = 0.3

2.6%

0.4, 0.5, 0.1

0.1, 0.1, 0.3

0.3, 0.3, 0.4

0.7, 0.1, 0.2

2.9%

0.7, 0.1, 0.2

0.3, 0.3, 0.4

0.1, 0.1, 0.3

0.3, 0.3, 0.4

20 years

0.4, 0.5, 0.1

0.5, 0.4, 0.1

0.1, 0.1, 0.3

0.5, 0.4, 0.1

17 years

0.1, 0.1, 0.3

0.7, 0.1, 0.2

0.5, 0.4, 0.1

0.7, 0.1, 0.2

15 years

0.1, 0.1, 0.3

0.2, 0.3, 0.5

0.5, 0.4, 0.1

0.5, 0.4, 0.1

18 years

0.7, 0.1, 0.2

0.4, 0.5, 0.1

0.7, 0.1, 0.2

0.1, 0.1, 0.3

Table 2. Defuzzified values of parameters. Parameters

Defuzified values

Parameters

Defuzified values

FC

e9,651,517.55

SV

0

AB

e1,579,230.56

i

2.53%

AC

e775.74

n

17.50 year

6 Conclusion Digital transformation has become a necessary investment for companies that want to be more agile and robust in recent years. Picture fuzzy sets have been used in many fields since 2014. Picture fuzzy sets are useful for evaluating decision makers in a fuzzy environment. In this study, benefit/cost analysis is extended using picture fuzzy sets to evaluate a tool alternative for digital transformation. The digital transformation tool alternative for the technology company is evaluated by 4 experts experienced in IT processes. Picture fuzzy benefit/cost analysis model is resulted with picture fuzzy sets operations. This model shows that the inflows of investment are wholly greater than the outflows of investments. This means that the digital investment tool can be implemented. In other words, the result of picture fuzzy benefit cost analysis showed that the investment is feasible. For further studies, the benefit/cost analysis can be extended with q-rung fuzzy orthopair sets or decomposed fuzzy sets in digital transformation tool evaluations and comparison analysis can be done.

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References 1. Carcary, M., Doherty, E., Conway, G.: A dynamic capability approach to digital transformation– a focus on key foundational themes. In: 10th European Conference on Information Systems Management, pp. 20–28. Academic Conferences and Publishing Limited, Portugal (2016) 2. Cuong B.C., Kreinovich, V.: Picture fuzzy sets-a new concept for computational intelligence problems. In: 2013 Third World Congress on Information and Communication Technologies (WICT 2013), pp. 1–6. IEEE, Hanoi (2013) 3. Kahraman, C., Cevik Onar, S., Oztaysi, B.: A comparison of wind energy investment alternatives using interval-valued intuitionistic fuzzy benefit/cost analysis. Sustainability 8(2), 118 (2016) 4. Wang, M.J., Liang, G.S.: Benefit/cost analysis using fuzzy concept. Eng. Econ. 40(4), 359–376 (1995) 5. Kahraman, C., Kaya, ˙I: Fuzzy benefit/cost analysis and applications. In: Kahraman, C. (ed.) Fuzzy Engineering Economics with Applications. Studies in Fuzziness and Soft Computing, vol. 233, pp. 129–143. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-708 10-0_8 6. Kahraman, C., Tolga, E., Ulukan, Z.: Justification of manufacturing technologies using fuzzy benefit/cost ratio analysis. Int. J. Prod. Econ. 66(1), 45–52 (2000) 7. Kahraman, C.: Fuzzy versus probabilistic benefit/cost ratio analysis for public work projects. Int. J. Appl. Math. Comput. Sci. 11(3), 705–718 (2001) 8. Wei, G.: Picture fuzzy aggregation operators and their application to multiple attribute decision making. J. Intell. Fuzzy Syst. 33(2), 713–724 (2017) 9. Wei, G.: Picture fuzzy Hamacher aggregation operators and their application to multiple attribute decision making. Fund. Inform. 157(3), 271–320 (2018)

Intuitionistic Fuzzy Sets

On the Temporal Intuitionistic Fuzzy Sets Krassimir T. Atanassov1,2(B) 1 Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Acad. G. Bonchev Street Bl. 105, 1113 Sofia, Bulgaria [email protected] 2 Intelligent Systems Laboratory, Prof. Asen Zlatarov University, 8010 Bourgas, Bulgaria

Abstract. The Temporal Intuitionistic Fuzzy Sets (TIFSs) are one of the essential extensions of the ordinary Intuitionistic Fuzzy Sets (IFSs). For them different operations, relations and operators (from modal, topological and level-types) have been defined and their basic properties have been studied. In all the research by this moment, TIFSs have been defined over one time-scale, or, whenever they have been defined over different time-scales the formulas of the operations over them have been described in the simplest form. In the present paper, essentially more detailed formulas for the operations over TIFSs with different time-scales are introduced. Moreover, ideas for some new operators that can be defined over TIFSs are introduced and their basic properties are established. Some possible applications of the TIFSs are discussed. Keywords: Intuitionistic fuzzy operator · Intuitionistic Fuzzy Set · Temporal intuitionistic fuzzy operator · Temporal Intuitionistic Fuzzy Set AMS Classification: 03E72

1

Introduction

The Intuitionistic Fuzzy Sets (IFSs, see [1,3,6]) were introduced in 1983 as extensions of the Zadeh’s fuzzy sets (see [10]). Over IFSs different operations, relations and operators (from modal, topological and level-types) have been defined and it is important to mention that the majority of them do not have archetype in the standard fuzzy set case. For example, now there are more than 200 intuitionistic fuzzy implications and more than 50 intuitionistic fuzzy negations. Firstly, in Sect. 2, we give the definition of the TIFSs and short remark for the operations and operators that can be defined over them. In the next Section, we give the new results over TIFSs, extending the definitions of the operations, relations and operators over them. The operations, relations and operators over ordinary IFSs are given in [3,6] and by this reason, they are not given here, but in the end of Sect. 3 we show how they can be obtained from the new definitions. Finally, short comments over some possible applications will be presented. c The Author(s), under exclusive license to Springer Nature Switzerland AG 2022  C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 519–528, 2022. https://doi.org/10.1007/978-3-031-09173-5_61

520

2

K. T. Atanassov

Short Remarks over TIFSs

The TIFSs were introduced in [2] in 1991 and the next results were published in [3–5]. Here, following [6], we give the definition of TIFS. Let E be a universe, and T be a non-empty set. We call the set T - time-scale and its elements - “time-moments”. Based on the definition of IFS, we define the TIFS as the following: A(T ) = {x, μA (x, t), νA (x, t)|x, t ∈ E × T }, where (a) A ⊂ E is a fixed set, (b) μA (x, t) + νA (x, t) ≤ 1 for every x, t ∈ E × T , (c) μA (x, t) and νA (x, t) are the degrees of membership and non-membership, respectively, of the element x ∈ E at the time-moment t ∈ T . Obviously, every ordinary IFS over some universe E can be regarded as a TIFS for which the set T is a given time-scale. On the other hand, each TIFS A(T ) can be interpreted as an ordinary IFS, but over universe E × T . In [6] was written that all operations and operators on the IFSs can be defined for the TIFSs. Suppose that we have two TIFSs: A(T  ) = {x, μA (x, t), νA (x, t)|x, t ∈ E × T  }, and

B(T  ) = {x, μB (x, t), νB (x, t)|x, t ∈ E × T  },

where T  and T  are two time-scales that have finite number of distinct timeelements or they are time-intervals. Then we can re-define the IFS-operations (∩, ∪, etc.) and the topological (C and I) and modal ( and ♦) operators for the TIFS-case. For example, A(T  ) ∪ B(T  ) = {x, μA(T  )∪B(T  ) (x, t), νA(T  )∪B(T  ) (x, t)|x, t ∈ E × (T  ∪ T  )},

where x, μA(T  )∪B(T  ) (x, t), νA(T  )∪B(T  ) (x, t) ⎧ x, μA (x, t ), νA (x, t ), if t = t ∈ T  − T  ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ x, μB (x, t ), νA (x, t ), if t = t ∈ T  − T  ⎪ ⎪ ⎨ =

x, max(μA (x, t ), μB (x, t )), min(νA (x, t ), νA (x, t )), ⎪ ⎪ ⎪ ⎪ if t = t = t ∈ T  ∩ T  ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ x, 0, 1, otherwise

On the Temporal Intuitionistic Fuzzy Sets

521

In [6] was mentioned also that the specific operators over TIFSs are: C ∗ (A(T )) = {x, sup μA(T ) (x, t), inf νA(T ) (x, t)|x ∈ E}, t∈T

t∈T

I ∗ (A(T )) = {x, inf μA(T ) (x, t), sup νA(T ) (x, t)|x ∈ E}. t∈T

t∈T

In the next Section, we will introduce new forms of the operations and operators over the TIFS and will add the definitions of the relations over them, because in [6] it was mentioned only that these relations are full analogues of the standard IFS relations. Now, it is clear that this assertion is not valid fully here, in the definitions of the relations new components arise.

3

Main Results

Let us have two time-scales T  and T  and let us define for the them and for t ∈ T  : τmax (t , T  ) = max{t|t ∈ T  & t ≤ t }, τmin (t , T  ) = min{t|t ∈ T  & t ≥ t }. 3.1

Relations over TIFSs

For every two TIFSs A(T  ) and B(T  ) over two time-scales the following relations can be defined A(T  ) ⊂ B(T  ) iff T  = T  & (∀x ∈ E)(∀t ∈ T  )((μA (T  )(x, t) < μB (T  )(x, t) & νA (T  )(x, t) > νB (T  )(x, t)) ∨ (μA (T  )(x, t) < μB (T  )(x, t) & νA (T  )(x, t) ≥ νB (T  )(x, t)) ∨ (μA (T  )(x, t) ≤ μB (T  )(x, t) & νA (T  )(x, t) > νB (T  )(x, t)))   A(T ) ⊆ B(T ) iff T  = T  & (∀x ∈ E)(∀t ∈ T  )(μA (T  )(x, t) ≤ μB (T  )(x, t) & νA (T  )(x, t) ≥ νB (T  )(x, t))   A(T ) = B(T ) iff T  = T  & (∀x ∈ E)(∀t ∈ T  )(μA (T  )(x, t) = μB (T  )(x, t) & νA (T  )(x, t) = νB (T  )(x, t))   A(T ) ⊂τ B(T ) iff T  ⊂ T  & (∀x ∈ E)(∀t ∈ T  )((μA (T  )(x, t) < μB (T  )(x, t) & νA (T  )(x, t) > νB (T  )(x, t)) ∨ (μA (T  )(x, t) < μB (T  )(x, t) & νA (T  )(x, t) ≥ νB (T  )(x, t)) ∨ (μA (T  )(x, t) ≤ μB (T  )(x, t) & νA (T  )(x, t) > νB (T  )(x, t)))   A(T ) ⊂τ B(T ) iff T  ⊆ T  & (∀x ∈ E)(∀t ∈ T  )(μA (T  )(x, t) ≤ μB (T  )(x, t) & νA (T  )(x, t) ≥ νB (T  )(x, t))

If by analogy with equivalence A(T  ) = B(T  ) iff A(T  ) ⊂ B(T  ) & B(T  ) ⊂ A(T  ) we define A(T  ) =τ B(T  ) iff A(T  ) ⊂τ B(T  ) & B(T  ) ⊂τ A(T  ),

522

K. T. Atanassov

we obtain that A(T  ) =τ B(T  ) iff T  = T  & (∀x ∈ E)(∀t ∈ T  )(μA (T  )(x, t) = μB (T  )(x, t) &νA (T  )(x, t) = νB (T  )(x, t)), i.e., relations “=τ ” and “=” coincide. 3.2

Operations over TIFSs

The above operation ∪ can have the following new forms:     A(T  ) ∪← 1 B(T ) = {x, max(μA (x, t ), μB (x, τmin (t , T ))),     min(νA (x, t ), νB (x, τmin (t , T )))|x, t ∈ E × T },     A(T  ) ∪→ 1 B(T ) = {x, max(μA (x, t ), μB (x, τmax (t , T ))), min(νA (x, t ), νB (x, τmax (t , T  )))|x, t ∈ E × T  },     A(T  ) ∪← 2 B(T ) = {x, max(μA (x, τmin (t , T ), μB (x, t ))),     min(νA (x, τmin (t , T ), νB (x, t )))|x, t ∈ E × T },     A(T  ) ∪→ 2 B(T ) = {x, max(μA (x, τmax (t , T ), μB (x, t ))),

min(νA (x, τmax (t , T  ), νB (x, t )))|x, t ∈ E × T  }. Similarly, we can introduce the remaining basic operations     A(T  ) ∩← 1 B(T ) = {x, min(μA (x, t ), μB (x, τmin (t , T ))), max(νA (x, t ), νB (x, τmin (t , T  )))|x, t ∈ E × T  },     A(T  ) ∩→ 1 B(T ) = {x, min(μA (x, t ), μB (x, τmax (t , T ))),

max(νA (x, t ), νB (x, τmax (t , T  )))|x, t ∈ E × T  },     A(T  ) ∩← 2 B(T ) = {x, min(μA (x, τmin (t , T ), μB (x, t ))), max(νA (x, τmin (t , T  ), νB (x, t )))|x, t ∈ E × T  },     A(T  ) ∩→ 2 B(T ) = {x, min(μA (x, τmax (t , T ), μB (x, t ))), max(νA (x, τmax (t , T  ), νB (x, t )))|x, t ∈ E × T  };        A(T  ) +← 1 B(T ) = {x, μA (x, t ) + μB (x, τmin (t , T )) − μA (x, t )μB (x, τmin (t , T )),

νA (x, t )νB (x, τmin (t , T  ))|x, t ∈ E × T  },        A(T  ) +→ 1 B(T ) = {x, μA (x, t ) + μB (x, τmax (t , T )) − μA (x, t )μB (x, τmax (t , T )),

νA (x, t )νB (x, τmax (t , T  ))|x, t ∈ E × T  }, 

+← 2



+→ 2

A(T )



B(T ) = {x, μA (x, τmin (t , T  ) + μB (x, t )) − μA (x, τmin (t , T  )μB (x, t )), νA (x, τmin (t , T  )νB (x, t ))|x, t ∈ E × T  },

A(T )



B(T ) = {x, μA (x, τmax (t , T  ) + μB (x, t )) − μA (x, τmax (t , T  )μB (x, t )), νA (x, τmax (t , T  )νB (x, t ))|x, t ∈ E × T  };

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    A(T  ).← 1 B(T ) = {x, μA (x, t )μB (x, τmin (t , T )), νA (x, t ) + νB (x, τmin (t , T  )) − νA (x, t )νB (x, τmin (t , T  ))|x, t ∈ E × T  },     A(T  ).→ 1 B(T ) = {x, μA (x, t )μB (x, τmax (t , T )), νA (x, t ) + νB (x, τmax (t , T  )) − νA (x, t )νB (x, τmax (t , T  ))|x, t ∈ E × T  },     A(T  ).← 2 B(T ) = {x, μA (x, τmin (t , T )μB (x, t )), νA (x, τmin (t , T  ) + νB (x, t )) − νA (x, τmin (t , T  )νB (x, t ))|x, t ∈ E × T  },     A(T  ).→ 2 B(T ) = {x, μA (x, τmax (t , T )μB (x, t )), νA (x, τmax (t , T  ) + νB (x, t )) − νA (x, τmax (t , T  )νB (x, t ))|x, t ∈ E × T  };

μA (x, t ) + μB (x, τmin (t , T  )) , 2 νA (x, t ) + νB (x, τmin (t , T  )) |x, t ∈ E × T  }, 2 μA (x, t ) + μB (x, τmax (t , T  ))  , A(T  )@→ 1 B(T ) = {x, 2 νA (x, t ) + νB (x, τmax (t , T  )) |x, t ∈ E × T  }, 2 μA (x, τmin (t , T  ) + μB (x, t ))  , A(T  )@← B(T ) = {x, 2 2 νA (x, τmin (t , T  ) + νB (x, t )) |x, t ∈ E × T  }, 2 μA (x, τmax (t , T  ) + μB (x, t ))  , A(T  )@→ 2 B(T ) = {x, 2 νA (x, τmax (t , T  ) + νB (x, t )) |x, t ∈ E × T  }. 2  A(T  )@← 1 B(T ) = {x,

The four operations from each one of the five groups above correspond to the cases, when there is a priority between TIFSs or between their time-scales. The number (1 or 2) that is an index of the operation, determines which set or scale has higher priority, while the arrow shows the direction of the searching of the necessary time-moment from the time-scale with lower priority. Now, we see that the commutative law has more complex form. Theorem 1. For every two TIFSs A(T  ) and B(T  ) over two different timescales it follows   →  (a) A(T  ) ◦← 1 B(T ) = B(T ) ◦2 A(T ),  ←   → (b) A(T ) ◦2 B(T ) = B(T ) ◦1 A(T  ),

where ◦ ∈ {∪, ∩, +, ., @}.

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Proof. First, we see that if t = τmin (t , T  ) (see Fig. 1), then

t = τmax (t , T  )

(see Fig. 2)

T

t



T 

T

t = τmin (t , T  )

T 

Fig. 1. Time-scale T1

Also, if

t = τmax (t , T  )



t Fig. 2. Time-scale T2

t = τmax (t , T  )

(see Fig. 3), then

t = τmin (t , T  )

(see Fig. 4)

T



T 

t t = τmax (t , T  ) Fig. 3. Time-scale T3

T

t = τmin (t , T  )



T 

t Fig. 4. Time-scale T4

Now, for (a), for “ ◦ ” equal to “∪”, we obtain:     A(T  ) ∪← 1 B(T ) = {x, max(μA (x, t ), μB (x, τmin (t , T ))),

min(νA (x, t ), νB (x, τmin (t , T  )))|x, t ∈ E × T  } = {x, max(μB (x, τmin (t , T  )), μA (x, t )), min(νB (x, τmin (t , T  )), νA (x, t ))|x, t ∈ E × T  } = {x, max(μB (x, t )), μA (x, τmax (t , T  ))), min(νB (x, t ), νA (x, τmax (t , T  )))|x, t ∈ E × T  }  = B(T  ) ◦→ 2 A(T ).

On the Temporal Intuitionistic Fuzzy Sets

525

The remaining nine equalities (for ∪← 2 and when ◦ ∈ {∩, +, ., @}) are checked in the same manner. The same is valid for the following assertion, too. We recall that the classical negation over an IFS (and in the particular case TIFS) is ¬A(T ) = {x, νA (x, t), μA (x, t)|x, t ∈ E × T }. Theorem 2. For every two TIFSs A(T  ) and B(T  ) over two different timescales it follows (a) ¬(¬A(T  ) ◦ ¬B(T  )) = B(T  ) ∗ A(T  ), (b) ¬(¬A(T  ) ◦ ¬B(T  )) = B(T  ) ∗ A(T  ), ← → → ← ← → → ← ← where ◦, ∗ ∈ {∪← i , ∩1 , ∪i , ∩1 , ∩i , ∩1 , ∩i , ∩1 , +i , ∩1 , → → ← ← → → ← ← → → +i , ∩1 , .i , ∩1 , .i , ∩1 , @i , ∩1 , @i , ∩1 |i = 1, 2}.

3.3

Topological Operators over TIFSs

Following [6] and having in mind, e.g., [8,9], we introduce two operators defined over a TIFS A(T ) that are simultaneously topological and temporal: C ∗ (A(T )) = {x, sup μA(T ) (x, t), inf νA(T ) (x, t)|x ∈ E}, t∈T

t∈T

I ∗ (A(T )) = {x, inf μA(T ) (x, t), sup νA(T ) (x, t)|x ∈ E}. t∈T

t∈T

There, it is formulated and proved a theorem that we will improve here. Theorem 3. For every two TIFSs A(T  ) and B(T  ): (a) (b) (c) (d) (e) (f) (g) (h)

 ∗  ← ∗  C ∗ (A(T  ) ∩← i B(T )) ⊆ C (A(T )) ∩i C (B(T )),  ∗  ← ∗  C ∗ (A(T  ) ∪← B(T )) = C (A(T )) ∪ C (B(T )), i i ∗  ←  ∗  ← ∗ I (A(T ) ∩i B(T )) = I (A(T )) ∩i I (B(T  )),  ∗  ← ∗  I ∗ (A(T  ) ∪← i B(T )) ⊇ I (A(T )) ∪i I (B(T )), ∗  →  ∗  → ∗  C (A(T ) ∩i B(T )) ⊆ C (A(T )) ∩i C (B(T )),  ∗  → ∗  C ∗ (A(T  ) ∪→ i B(T )) = C (A(T )) ∪i C (B(T )), ∗  →  ∗  → ∗ I (A(T ) ∩i B(T )) = I (A(T )) ∩i I (B(T  )),  ∗  → ∗  I ∗ (A(T  ) ∪→ i B(T )) ⊇ I (A(T )) ∪i I (B(T )),

where i = 1, 2. Proof. First, we will mention that for every ai , bi ∈ [0, 1], where i ∈ I - finite or infinite set of natural numbers we can define sup min(ai , bi ) = min(as , bs ) i∈I

sup ai = ap , i∈I

sup bi = bq i∈I

for some s ∈ I.

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Then min(as , bs ) ≤ as ≤ ap , min(as , bs ) ≤ bs ≤ bq , i.e. min(as , bs ) ≤ min(ap , bq ) and sup min(ai , bi ) ≤ min(sup ai , sup bi ). i∈I

i∈I

i∈I

Now, for (a), for i = 1, we obtain  ∗    C ∗ (A(T  ) ∩← 1 B(T )) = C ({x, min(μA (x, t ), μB (x, τmin (t , T ))),

max(νA (x, t ), νB (x, τmin (t , T  )))|x, t  ∈ E × T  }) = {x, sup (min(μA (x, t ), μB (x, τmin (t , T  )))), t ∈T 

inf (max(νA (x, t ), νB (x, τmin (t , T  ))))|x, t  ∈ E × T  }

t ∈T 

⊆ {x, min( sup μA (x, t ), sup μB (x, τmin (t , T  ))), t ∈T  

t ∈T 

max( inf  νA (x, t ), inf  νB (x, τmin (t , T  )))|x, t ∈ E × T  } t ∈T

t ∈T

= {x, sup μA (x, t ), inf  νA (x, t )|x, t ∈ E × T  } t ∈T

t ∈T 

∩← 1 {x,





sup μB (x, τmin (t , T )), inf  νB (x, τmin (t , T  ))|x, t  ∈ E × T  } t ∈T

t ∈T 

= {x, sup μA (x, t ), inf  νA (x, t )|x, t ∈ E × T  } t ∈T

t ∈T 

∩← 1 {x,



sup μB (x, t )), inf  νB (x, t ))|x, t  ∈ E × T  } t ∈T

t ∈T 

∗

∗  = C (A(T  )) ∩← 1 C (B(T )).

The remaining equalities and inequalities are checked in the same manner. The same is valid for the following assertions, too. 3.4

Modal Operators over TIFSs

By the moment, in the IFS theory there are four types of modal operators. Here, we will discuss only the operators from the first (standard) type of them, giving to these operators new forms. The possibility for this is mentioned in [6], having in mind, e.g., [7], but the present form of the modal operators is more extended, because it is related to the existence of two different time-scales, while in [6] the scale is one. It is related to the given TIFS, while now, we will associate another time-scale to each one of the operators.

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Let A(T  ) be a TIFS over time-scale T  and let T  be another time-scale. Then we define: ←

T  A(T → T  A(T



) = {x, μA (x, τmin (t , T  ), 1 − μA (x, τmin (t , T  )|x ∈ E},



) = {x, μA (x, τmax (t , T  ), 1 − μA (x, τmax (t , T  )|x ∈ E},

     ♦← T  A(T ) = {x, 1 − νA (x, τmin (t , T ), νA (x, τmin (t , T )|x ∈ E},

     ♦→ T  A(T ) = {x, 1 − νA (x, τmax (t , T ), νA (x, τmax (t , T )|x ∈ E}.

Theorem 4. For each TIFS A(T  ) and a time-scale T  : (a) (b) (c) (d) (e) (f) (g) (h) (i) (j)

←

←

←   T  A(T ) = T  A(T ), →  →  T  ♦T  A(T ) = ♦T  A(T ), ← ←   ♦← T  A(T ) = T  A(T ), T  → →  →  ♦T  ♦T  A(T ) = ♦T  A(T ), ←  ¬ T  ¬A(T  ) = ♦← T  A(T ), →  ¬ T  ¬A(T  ) = ♦→ T  A(T ), ← ←  ¬♦T  ¬A(T ) = T  A(T  ), →   ¬♦→ T  A(T ), T  ¬A(T ) = ←   ←  T  A(T ) ⊆ A(T ) ⊆ ♦T  A(T ), →   →  T  A(T ) ⊆ A(T ) ⊆ ♦T  A(T ). T  →

The checks of these equalities are similar to the above ones.

4

Conclusion: Remarks for Future Research

In the present paper, we introduced a new point of view over the TIFSs. The above definitions and assertions are the basis of the next research in which we will discuss the definitions and properties of the extended modal operators of the first type, of the modal operators of the next three types and of the leveloperators. Another direction for next research is related to introducing a new type of negation and a new type of time-scales. Acknowledgement. This research was funded by Bulgarian National Science Fund, grant number KP-06-N22/1/2018 “Theoretical research and applications of InterCriteria Analysis”.

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References 1. Atanassov, K.: Intuitionistic fuzzy sets. In: VII ITKR’s Session, (Deposed in Central Science & Technology Library of the Bulgarian Academy of Sciences, 1697/84), Sofia, June 1983 (in Bulg.), Reprinted: Int. J. Bioautomation, Vol. 20, S1-S6 (2016) (in English) (1983) 2. Atanassov, K.: Temporal intuitionistic fuzzy sets. Comptes Rendus de l’Academie bulgare des Sciences, Tome 44(7), 5-7 (1991) 3. Atanassov, K.: Intuitionistic Fuzzy Sets. Springer, Heidelberg (1999). https://doi. org/10.1007/978-3-7908-1870-3 4. Atanassov, K.: On the temporal intuitionistic fuzzy sets. In: Proceedings of the Ninth International Conference IPMU 2002, Annecy, France, vol. III, pp. 1833– 1837, 1-5 July 2002 5. Atanassov, K.: Temporal intuitionistic fuzzy sets (review and new results). In: Proceeding of the Thirty Second Spring of the Union of Bulgarian Mathematicians, Sunny Beach, pp. 79-88, 5–8 April 2003 6. Atanassov, K.: On Intuitionistic Fuzzy Sets Theory. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-29127-2 7. Feys, R.: Modal logics. Gauthier, Paris (1965) 8. Kuratowski, K.: Topology, Vol. 1. Acad. Press, New York (1966) 9. Kˆ osaku, Y.: Functional Analysis. CM, vol. 123. Springer, Heidelberg (1995). https://doi.org/10.1007/978-3-642-61859-8 10. Zadeh, L.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

Intuitionistic Fuzzy Generalized Net Model of the Humanoid Service Robot Functionalities Simeon Ribagin1,2(B) , Sotir Sotirov2 , Evdokia Sotirova2 , Iasen Hristozov3 , and Krassimir Atanassov1,2 1 Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and

Biomedical Engineering, Bulgarian Academy of Sciences, Sofia, Bulgaria [email protected], [email protected] 2 Intelligent Systems Laboratory, University “Prof. D-R Asen Zlatarov”, Burgas, Bulgaria {ssotirov,ssotirova}@btu.bg 3 European Soft Design, Ltd., Sofia, Bulgaria [email protected]

Abstract. This paper presents an approach to model the humanoid service robot functionalities based on the apparatuses of one of the extensions of the Generalized Nets (GNs) and the Intuitionistic Fuzzy Sets (IFSs), called Intuitionistic Fuzzy GNs of the first type (IFGN1). Here, an IFGN1-model of humanoid robot is developed, which describes the main functionalities of the service and the feedback of the embedded sensors the intuitionistic fuzzy estimations of the IFGN1transition condition predicates give information for the possible risks to the robot when performing various tasks. The so described IFGN1-model will permit the development of a more detailed and complex model allowing optimization and improvement of the robot functioning in different environment. Keywords: Humanoid robot · Intuitionistic fuzzy estimation · Intuitionistic fuzzy generalized net of first type

1 Introduction Service robots (SRs) are an extensive category of robots which perform services related to the well-being of human population, which include all non-industrial applications. According to the International Organization for Standardization (ISO) a SR is as a robot “that performs useful tasks for humans or equipment excluding industrial automation applications” [20]. These robots have the ability to perform intended tasks based on current state and sensing, without human intervention. As robots are able to perform complex tasks, they are able to advance from the industrial to the service context [16]. The major areas of application are public relations and logistics and most of the robots are being used to reduce operational expenses while improving the customer’s overall experience. Customer SRs (CSRs) represent a specific group of professional SRs intended to interact with customers in order to assist in finding an item or completing a task. CSRs possibilities to physically replace human service employees [13, 17] and thus © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 529–536, 2022. https://doi.org/10.1007/978-3-031-09173-5_62

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increase the level of customer service while decreasing costs [2, 12]. These robots come in humanoid and non-humanoid forms and automate much of the most basic of tasks in customer service. Most of these robots are built to mimic human motion and interaction, designed to optimize relations both with customers and between company employees. Since SRs have to operate and communicate in an unconstraint, human-centered environment, a high degree of autonomy is an inherent characteristic of them [14]. The degree of autonomy of SRs ranges from partial autonomy (including human-robot interaction) to full autonomy (without operational human-robot intervention). The main functionalities of such robots are autonomous navigation, person detection and recognition, speech synthesis and recognition etc. allowing smart and efficient interactions with end users. These robots are equipped with a wide variety of sensors to ensure smooth movement through its environment and thanks to advances in sensor technology, Humanoid SRs (HSRs) can operate in unconstrained environments of everyday life [1]. Sensors are the key to making a robot-perceived environment a reality and sensing the environment is the first step when a robot performs a specific task. The proper function, the level of accuracy of the sensors, as well as the analyzed sensory information is one of the most important factors for reaching the full potential of HSRs. For the purpose of the present study we will briefly describe the main functionalities and sensor specifications of a HSR, namely the UBTECH’s humanoid Cruzr robot [21]. The robot itself has anthropomorphic features, such as head and body, two upper limbs and chassis. The design of the robot, the multi-modal synergies and coordination make the interaction more fluid and more human-like, which greatly enhances the user experience. The information and interaction with the surrounding environment is possible thanks to the embedded sensors in the different parts of the robot. Cruzr is equipped with variety of sensors: cliff sensor, RGBD depth-sensing camera, e-Skin, infrared and sonar sensor, IMU sensor, laser radar, geomagnetic sensor, temperature and humidity sensors. In some cases, when performing a task, especially in those with high level of uncertainty, there are a number of limitations and restrictions, related to the sensors (input and output data) affecting the overall functioning of the robot in specific environment and situation. Most of the sensor signals are ineffective against glass, stainless steel, pure black materials, black light absorbing materials, wave absorbing materials and complex surfaces. Moreover, the battery of the robot provides predefined time limit (5–8 h of active use and 24 h in standby mode) so when the battery is low, the robot must automatically return to the nearest self-charging dock. In an unexpected scenario or in complex dynamic environment these limitations may lead to a significant reduction in the efficiency of the robot or even to threats its safety and security. In a view of this it is important to develop models or strategies that include and take into account the degree of uncertainty during the robot activities.

2 Materials and Methods In the present paper we construct a reduced IFGN1-model of humanoid service robot functionalities. The model is based on the information and the feedback from the embedded sensors and the mechanical construction of the robot. The proposed model gives the possibility of development of more complex and detailed model of the humanoid service

Intuitionistic Fuzzy Generalized Net Model of the Humanoid Service

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robot. The described here IFGN1-transitions contain only input and output places and transition condition predicates. Generalized Nets (GNs, [4, 7, 8] were introduced as an extension of Petri Nets (see [18]) and the other their modifications and extensions. Similarly, to all other Petri nets type, they have places (here denoted by l), transitions (here denoted by Z), and tokens. In GNs the transitions are characterized with more complex structure, having input and output places, moment of activation, duration of the active status, a special matrix, called index matrix (IM, see [6, 10]) of transition condition predicates (here marked by r), IM of the capacities of transition arcs and type of the transition. The full definition of a GN contains a set of transitions, functions determining the priorities of the transitions and places, the capacities of the places, of the truth-values of the transition condition predicates, the moments of the transition activations and the duration of them; a set of tokens, their priorities and the moments in which they must enter the net; time-moment in which the GN will start function, the duration of its work and the elementary time-step with which the time will grow; a set of initial token characteristics, a function that give new characteristics of the tokens when they transfer from an input to an output place of a some transition and the maximal number of characteristics that token can have. As it is mentioned in [7, 8], a part of the GN-components can be omitted in respect of the aims of each one concrete model and a such net is called a reduced GN. Intuitionistic Fuzzy Sets (IFSs) [3, 9] were introduced as an extension of fuzzy sets of L. Zadeh [19]. For each universe E and for each its subset A, they have two degrees – of membership (denoted by μA ) and of non-membership (denoted by ν A ), so that for each element x ∈ E: μA (x), ν A (x), μA (x) + ν A (x) ∈ [0,1]. In [5], in 1985, i.e., three years before C. Looney’s paper [15], for a first time the objects of Petri net type and fuzziness were united in an GN-extension, called an Intuitionistic Fuzzy GNs of the first type (IFGN1). In it, the transition condition predicates are evaluated by intuitionistic fuzzy pairs a, b, where a, b, a + b ∈ [0,1]. The GNs and IFSs have a lot of applications in the area of Artificial Intelligence and Data Mining, described in [11]. There, the possible applications of both apparatuses for modelling of robots have been discussed. In the present paper we construct a reduced IFGN1-model of HSR’ functionalities. The model is based on the information and the feedback from the embedded sensors and the mechanical construction of the robot. The proposed model gives the possibility of development of more complex and detailed model of the HSR. The transitions in described here IFGN1-model contain only input and output places and transition conditions predicates.

3 The IFGN1-Model of Humanoid Service Robot Functionalities As we mentioned above, in a standard GN, each transition condition predicate W i,j corresponds to the i-th input and j-th output places. When its truth value is “true”, a token from the i-th input place transfers to j-th output place, otherwise this is not possible. In the IFGN1-case, each transition condition predicate W i,j is evaluated by a pair μi,j , ν i,j  such that μi,j , ν i,j , μi,j + ν i,j ∈ [0,1]. For each one of these predicates we

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can determine two thresholds – lower (t l ∈ [0,1]) and higher (t h ∈ [0,1]), so that t l + t h ≤ 1. The token from place li will go to place l j if the following conditions hold:     μ Wi,j > tl and ν Wi,j < 1 − th The proposed IFGN1-model (Fig. 1) has 7 transitions, 34 places and it contains seven types of tokens: α, β, σ, γ, τ, ϕ and ψ. The seven transitions have the following meaning: Z 1 represents the self-charging dock station and the battery of the robot; Z2 - the data storage (cloud server); Z 3 - the control module of the robot; Z 4 - the body of the robot; Z5 - the head of the robot; Z6 - the upper limbs of the robot; Z7 - the robot chassis. The seven transitions of the GN model have a so called “special place”, where a token stays and collects information about the specific part of the robot, represents as follows: In place l5 , token α stays permanently and collects information about the level of battery and the self-charging dock station. In place l8 , token β stays permanently and collects information about in the cloud server, In place l19 , token σ stays permanently and collects information from the embedded sensors and the control module of the robot, In place l24 , token γ stays permanently and collects information about the body of the robot, In place l28 , token τ stays permanently and collects information about the head of the robot, In place l31 , token ϕ stays permanently and collects information about the upper limbs of the robot, In place l34 , token ψ stays permanently and collects information about the chassis of the robot. At the time of duration of the IFGN1-model functioning, some of these tokens can split, generating new tokens, that will transfer in the net obtaining respective characteristics, and also in some moments they will unite with some of tokens α, β, σ , γ , τ , ϕ and ψ. Initially the following tokens enter the IFGN1 in places l1 , l 2 , l 9 , l 10 , l 11 , l 12 , l 13 , l 14 , l15 and l 25 with charactreristics: token with a characteristic: “the robot is turned on”, token β ’ with a characteristic: “the robot network connection is on”, token σ 1 with a characteristic: “signal from the cliff sensor”, token σ 2 with a characteristic: “signal from the RGBD depth-sensing camera”, token σ 3 in with a characteristic: “signal from the e-skin sensors”, token σ 4 in with a characteristic: “signals from the infrared and sonar sensors”, token σ 5 with a characteristic: “signal from the IMU sensor”, token σ 6 with a characteristic: “signal from the laser radar sensor”, token σ 7 in with a characteristic: “signals from the temperature and humidity sensors”, token τ in with a characteristic: “signals from the microphone and the touchscreen display”. In order to ease the understandings of the actual formalism in use we shall not describe the transition condition predicates fully formally. We will give a formal description only for the transition Z1 and the first three predicates “W 5,3 ”, “W 5,4 ”, “W 5,5 ”. The rest of the transitions and predicates in our model can be described formally in an identical way and the threshold values can be chosen accordingly to the specific values obtained from the embedded sensors, quality of the network connection and the effects of the surrounding environment. The transition Z 1 of the IFGN1-model has the following form: Z1 = {l1 , l5 , l16 }, {l3 , l4 , l5 }, r1 ,

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where:

• W 5,3 = “the battery of the robot is charged” • W 5,4 = “the robot cannot be turned on” • W 5,5 = “the battery of the robot is charging” These predicates can be estimated by their intuitionistic fuzzy degrees of the charging and discharging parameters due to the current state of the battery life (battery ageing) and the battery sensor.

Fig. 1. An IFGN1-model of HSR’ functionalities

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We must mention that the predicate P is valid if for f (P) = a, b holds a > Let     Ecu − Etol Emax − Ecu f W5,3 = , , Emax Emax     Emax − Ecu Ecu − Etol f W5,4 = , , Emax Emax

1 2

> b.

W5,5 = ¬W5,3 ∧ ¬W5,4 . where E max , E cu and E tol , are the maximal quantity of the electric charge in the battery, the current quantity of the electric charge in the battery and the tolerance of the sensor that evaluates the quantity of the electric charge in the battery, respectively. Token α 1 obtains a characteristic: “set the basic settings of the robot” in place l3 , “check the battery life” in place l4 , “wait until the robot is charged (standby mode)” in place l 5 . Below, for brevity, we’ll give only short and informal descriptions of the next transitions, mentioning the token characteristics and the transition condition predicates. The predicates of the transition Z2 are as follows: W 8,6 = “there is an established network connection between the robot and the server”, W 8,7 = “the robot cannot connect to the network server” and W 8,8 = “the robot is still connecting to the network server”. These predicates can be estimated by their intuitionistic fuzzy degrees of accuracy and non-accuracy of the transferred data due to the quality of the internet connection. Depending on the degree of validity of these predicates, token β 1 will obtain a characteristic: “link the robot to the server, select the desired working mode of the robot” in place l6 “check the network quality” in place l7 and “wait until the robot is connected to the network server” in place l8 . The predicates of the transition Z3 are as follows: W 19,16 = “the robot needs battery recharging or the information from the embedded sensors is corrupted” and W 19,17 = “there is a normal flow of information coming from the embedded sensors of the robot and the current working mode is set”. These predicates can be estimated by their intuitionistic fuzzy degrees of correctness and non-correctness of the sensory signal due to the surrounding environment. Depending on the degree of validity of these predicates, token σ  will obtain a characteristic: “send the currently controlled robot to go recharge” in place l 16 and “give the robot a specific command or set the current task” in place l17 .  In place l18 token σ obtains a characteristic: “current data information for the cloud server”. The tokens from all input places of transition Z 4 enter place l 24 and unite with token γ that obtains the characteristic, as mentioned above. On the other hand, token γ splits to five tokens – the same token γ that stays permanently in the place l24 and tokens γ 1, γ 2 , γ 3 and token γ 4 . Token γ 1 enters in place l 20 with a characteristic: “power supply and signal to the head of the robot”. Token γ 2 enters in place l 21 with a characteristic: “power supply and signal to the upper limbs of the robot”. Token γ 3 enters in place l 22 with a characteristic: “power supply and signal to the chassis of the robot”. Token γ 3 enters in place l23 with a characteristic: “the robot is off ”.

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The predicates of the transition Z5 are as follows: W 28,26 = “the display and the microphone of the robot are in active interaction mode” and W 28,27 = “the display or the microphone of the robot is off ”. These predicates can be estimated by their intuitionistic fuzzy degrees of the correctness and non- correctness of the sound signal due to the surrounding environment or to the degree of the touchscreen display sensitivity. Depending on the degree of validity of these predicates, token τ 1 will obtain a characteristic: “interact with the robot and choose the desired task from the current mode” in place l26 and “check and/or adjust the display of the robot” in place l27 . The predicates of the transition Z6 are as follows: W 31,29 = “the robot can freely perform movements with its upper limbs according to the current task” and W 31,30 = “¬W 31,29 ”. These predicates can be estimated by their intuitionistic fuzzy degrees of the complete or incomplete movement of the upper limbs of the robot, due to the motors, different objects or to the surrounding environment. Depending on the degree of validity of these predicates, token ϕ 1 will obtain a characteristic: “check for the objects or the surrounding environment that jammed the upper limb joints, check the motors of the joints” in place l29 and “information for the current position of the upper limbs of the robot” in place l 30 . The predicates of the transition Z7 are as follows: W 34,32 = “the robot can move freely through the selected path” and W 31,33 = “¬W 34,32 ”. These predicates can be estimated by their intuitionistic fuzzy degrees of correctness and non-correctness of the navigation sensors signal due to the surrounding environment or to the mobility and immobility of the omni wheels of the robot. Depending on the degree of validity of these predicates, token ψ1 will obtain a characteristic: “information for the current position of the robot” in place l 32 and “check for the objects, changes in the surrounding environment, check the omni wheels” in place l33.

4 Conclusions The developed IFGN1 model describes the main functionalities of the humanoid robot and the feedback of the embedded sensors. Moreover, the applied intuitionistic fuzzy estimations in the model describe the possible risks to the robot when performing various tasks. The so described IFGN1 model will permit the development of a more detailed and complex model allowing optimization and improvement of the robot functioning in different environment. Acknowledgments. This work is partially supported by the grant: BG05M20P001-1.002-0011 “Centre of Competence MIRACle - Mechatronics, Innovation, Robotics, Automation, Clean technologies”.

References 1. Akdim, K., Belanche, D., Flavián, M.: Attitudes toward service robots: analyses of explicit and implicit attitudes based on anthropomorphism and construal level theory. Int. J. Contemp. Hosp. Manag. (2021). https://doi.org/10.1108/IJCHM-12-2020-1406

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2. Allmendinger, G., Lombreglia, R.: Four strategies for the age of smart service. Harvard Bus. Rev. 83(10), 131–143 (2005) 3. Atanassov, K.: Intuitionistic fuzzy sets, VII ITKR’s Session, Sofia, June 1983 (Deposed in Central Sci. - Techn. Library of Bulg. Acad. of Sci., 1697/84) (in Bulg.). Reprinted: Int. J. Bioautomat. 20(S1), S1–S6 (2016) 4. Atanassov, K.: Theory of Generalized nets (an algebraic aspect). Adv. Model. Simulat. 1(2), 27–33 (1984) 5. Atanassov, K.: Generalized nets and their fuzzings. AMSE Rev. 2(3), 39–49 (1985) 6. Atanassov, K.: Generalized index matrices. Comp. Rend. L’Acad. Bulg. Sci. 40(11), 15–18 (1987) 7. Atanassov, K.: Generalized Nets. World Scientific, Singapore (1991) 8. Atanassov, K.: On Generalized Nets Theory. Prof. M. Drinov Academic Publishing House, Sofia (2007) 9. Atanassov, K.: On Intuitionistic Fuzzy Sets Theory. Spirnger, Cham (2012) 10. Atanassov, K.: Index Matrices: Towards an Augmented Matrix Calculus. Springer, Cham (2014) 11. Atanassov, K.: Generalized Nets and Intuitionistic Fuzziness in Data Mining. Prof. M. Drinov Academic Publishing House, Sofia (2020) 12. Bitner, M.J.: Self-service technologies: what do customers expect? Market. Manag. 10(1), 10–11 (2001) 13. Edwards, R.: Robot butler piloted at California hotel (2014). www.telgraph.co.uk/travel/des tinations/northamerica/usa/11031447/Robot-butler-piloted-at-California-hotel.html 14. Haidegger, T., et al.: Applied ontologies and standards for service robots. Robot. Auton. Syst. 61(11), 1215–1223 (2013) 15. Looney, C.G.: Fuzzy Petri nets for rule–based decision making. IEEE Trans. Syst. Man Cybern. 18(1), 178–183 (1988) 16. Sprenger, M., Tobias, M.: Service robots. Bus. Inf. Syst. Eng. 57(4), 271–274 (2015) 17. Oh, H., Jeong, M., Baloglu, S.: Tourists’ adoption of self-service technologies at resort hotels. J. Bus. Res. 66(6), 692–699 (2013) 18. Petri, C.A.: Kommunication mit Automaten, Ph.D. dissertion, University of Bonn, 1962; Schriften des Inst. Fur Instrument. Math., No. 2, Bonn (1962) 19. Zadeh, L.: Fuzzy sets. Inf. Control 8, 338–353 (1965) 20. ISO. https://www.iso.org/obp/ui/#iso:std:iso:8373:ed-3:v1:en 21. UBTECH. http://www.ubtrobot.com/Cruzr/index.aspx

The Initial Value Problem of Intuitionistic Fuzzy Differential Equations and the Economic Growth Models Nguyen Dinh Phu(B) , Nguyen Nhut Hung, and Le Thi Ngoc Quynh Faculty of Engineering Technology , Quang Trung University, Quy Nhon City, Vietnam {ndphu,nnhung,ltnquynh}@qtu.edu.vn Abstract. The objective of this study is to prove the existence and uniqueness of solutions of initial value problems of intuitionistic fuzzy differential equations on ordered semi-linear spaces. We also build economic growth models that depend on capital investment in production capacity and operating capital. In addition, we give some examples to illustrate the results of the presented theory. Keywords: The intuitionistic fuzzy numbers (ifns) · The ordered semi-linear space of ifns. The intuitionistic fuzzy differential equation The economic growth models

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Introduction

In 1983, Atanassov introduced the concept of the intuitionistic fuzzy sets ([2,3]). It is a generalization of Zadeh’s fuzzy sets that it could be an important idea when describing a problem with a variable language (fuzzy) and was pretty useful in situations when describing a problem. Because of the flexibility of Intuitionistic fuzzy sets in handling uncertainty, they are a tool for a more human consistent reasoning under the undefined event perfect and vague. In [11] the author have used the same terminology “intuitionistic fuzzy set” as Atanassov but different in meaning to build the concept of intuitionistic fuzzy logic and IFSs. In the present time, the IFS theory has been applied to many different fields, for example, in [5] the author discussed intuitionistic fuzzy medical diagnosis consisting of three major steps: symptom identification, formulation of medical knowledge. In [10] the author had discussed an application of intuitionistic fuzzy multiset in medical diagnosis, in [4] proposed method of many measurement tools and multi-criteria decision making. As we all know, the most real-world problems are studied through differential equations, since the structure of solutions of differential equations can explain many natural phenomena. One specific example is the fuzzy sets were introduced in 1965. However, more than 20 years later, people began to pay attention to its analytic structure, By launched the concept of the addition between two fuzzy sets and the scalar multiplication between a fuzzy set and a non-negative real number, these two operations along with Zadeh’s c The Author(s), under exclusive license to Springer Nature Switzerland AG 2022  C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 537–555, 2022. https://doi.org/10.1007/978-3-031-09173-5_63

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extended principle have been the basis for the development of semi-linear metric spaces of fuzzy sets, which has led to studies of fuzzy differential equations thrive. In recent years, there have been many studies revolving around the concept of “fuzzy differential equations”. As for the intuitionistic fuzzy sets (IFSs), which K.A. Atanassov introduced in his researched since 1983. But until 1999, he began to present the operators on IFSs, so far there have been extensive research articles on these operators. Based on this ideas, Xu and Yager [12] defined the intuitionistic fuzzy numbers which are considered as the basic elements of the intuitionistic fuzzy sets. Most recently, In [1] the authors gave the definition of derivative operations for IFNs and their limited character analysis. In [7] - [9], the authors presented new concepts of geometric lattice intuitionistic fuzzy functions, geometric discriminantity and IVP for GLIFDE. In those works, the authors have built a semi-linear space for intuitionistic fuzzy numbers; monotony and differentiability of intuitionistic fuzzy functions. However, there are still some issues that the authors have not mentioned such as the diversity of derivatives of intuitionistic fuzzy functions, such as existence and uniqueness of solutions of IVP for GLIFDE,... Therefore, in this study, we will present the existence and uniqueness of a solution for the IVP for IFDEs in L∗ . Simultaneously, we continue to expand the results in [7] by adding another order relation on L∗ and create a new ordered set. With this result, we can simulate the growth process in the economy when the object depends closely on the working capital and capital of production. This paper includes: In second section, we collect the basic concepts of intuitionistic fuzzy numbers, semi-linear spaces L∗ of intuitionistic fuzzy functions. In Sect. 3, we give the monotony and the differentialble of intuitionistic fuzzy functions in ordered semi-linear space L∗GS and all types of derivatives of intuitionistic fuzzy functions for use in the sequel, the IVP models for IFDE types, proving the existence and uniqueness of this modeling solution. In addition, in this section we also introduce economic growth models and give some examples to illustrate the results of the presented theory.

2 2.1

Preliminaries The Intuitionistic Fuzzy Numbers

Definition 1 ([13]) Let U be a universe of discourse, then a fuzzy set (FS) A = {(u, μA (u)) |u ∈ U } that is characterized by membership function: μA : U → [0, 1] ,

(1)

that means membership function μA (u) is continuous on [0, 1]. Definition 2 ([3]) Let U be a universe of discourse, then an intuitionistic fuzzy set (IFS) A = {(u, μA (u), νA (u))|u ∈ U }

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that is characterized by membership function: μA : U → [0, 1] ,

(2)

and by non-membership function: νA : U → [0, 1] ,

(3)

that means membership function μA (u), and non-membership function νA (u) = μA¯ (u) are continuous on [0, 1] and satisfy 0  μA (u) + νA (u)  1. Based on Atanassov’s ideas, Xu and Yager [12] defined the intuitionistic fuzzy numbers which are considered as the basic elements of the intuitionistic fuzzy sets. In detail (can see in [6] or [12]) Definition 3 Let A = {(u, μA (u), νA (u))|u ∈ U } be an intuitionistic fuzzy set as in Definition 2, then an intuitionistic fuzzy number (IFN) α is an ordered pair of nonnegative real numbers α = (μα , να ) ∈ [0, 1]×[0, 1] such that 0 ≤ μα +να ≤ 1. Two nonnegative real numbers μα and να are the membership degree and the non-membership degree of A, respectively. Definition 4 [6] Let  = {α = (μα , να )|0 ≤ μα + να ≤ 1} be called the set of all intuitionistic fuzzy numbers (IFNs), where α is the IFN as in Definition 3. In this study, we also consider the concept of the IFNs as in Definition 3, but we use different a symbol of the set of all IFNs from its notation in Definition 4. Definition 5 (can see [7]). L∗ = {x = (x1 , x2 ) ∈ [0, 1] × [0, 1]|0  x1 + x2  1} , which corresponds to each element x ∈ L∗ , we put x = (x1 , x2 ) = (μA (u), νA (u)) where x1 and x2 are defined respectively, the membership degree and nonmembership degree of the element u ∈ U to the intuitionistic fuzzy set A. Next, we provide some definitions and theorems, which are presented in detail in [7]. These will be useful for the following studies. At the same time, we will also expand the results for these definitions and theorems. Definition 6 [7] Let L∗ be the set of all IFNs as in Definition 5, we denote that: (i) θ = (0, 0) ∈ L∗ is called a zero element of L∗ ; (ii) if x = (x1 , x2 ) ∈ L∗ then x = (x1 , x2 ) = (x2 , x1 ) ∈ L∗ is called a complement element (or reverse element) of x ∈ L∗ . In [7] the authors proved that L∗ is the semi-linear space of intuitionistic fuzzy numbers.

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The Differentialble of Intuitionistic Fuzzy Functions in Ordered Semi-linear Space L∗

The results of the intuitionistic functions can be consulted through the works [7,9]: Definition 7 Let [t0 , T ] ⊂ R be a non-empty set, we denote f : [t0 , T ] −→ L∗ t −→ f (t) = (f1 (t), f2 (t)) , where [t0 , T ] is the domain of f and f1 , f2 satisfy the conditions 0 ≤ f1 (t) ≤ 1, 0 ≤ f2 (t) ≤ 1 and 0 ≤ f1 (t) + f2 (t) ≤ 1 for any t ∈ [t0 , T ]. f : [t0 , T ] → L∗ is called a intuitionistic fuzzy function with real domain. Example 1 Let f (t) = (e−t , 1 − e−t ) ∈ L∗ with t ∈ [0, +∞), f (t) = (1 − cos2 (t), cos2 (t)) ∈ L∗ with t ∈ R, and so on. Definition 8 [7] Let x : [t0 , T ] → L∗ and h > 0 with x(t) = (x1 (t), x2 (t)) in L∗ and t, t + h ∈ [t0 , T ]. We say that (i) the intuitionistic fuzzy function x(t) is strictly monotone increasing by t iff x(t) G x(t + h) in L∗ with x1 (t)  x1 (t + h), x2 (t) ≥ x2 (t + h), ∀t ∈ [t0 , T ]; (ii) there exists a geometric difference under first type x(t) G1 y(t) = z(t) iff y(t) G x(t) in L∗ and y1 (t)  x1 (t), y2 (t) ≥ x2 (t), ∀t ∈ [t0 , T ], where (z1 (t), z2 (t)) = (x1 (t) − y1 (t), y2 (t) − x2 (t)) = (x1 (t) − y1 (t), −(x2 (t) − y2 (t))) . Definition 9 [7] Let x : [t0 , T ] → L∗ and h > 0 with x(t) = (x1 (t), x2 (t)) in L∗ and t, t + h ∈ [t0 , T ]. We say that (i) the intuitionistic fuzzy function x(t) is strictly monotone decreasing by t if x(t + h) G x(t) in L∗ , with x1 (t + h)  x1 (t), x2 (t + h) ≥ x2 (t), ∀t ∈ [t0 , T ]; (ii) there exists a geometric difference under second type x(t) G2 y(t) = z(t) iff x(t) G y(t) in L∗ and x1 (t)  y1 (t), x2 (t) ≥ y2 (t), ∀t ∈ [t0 , T ] where (z1 (t), z2 (t)) = (y1 (t) − x1 (t), x2 (t) − y2 (t)) = (−(x1 (t) − y1 (t)), x2 (t) − y2 (t)) .

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Definition 10 Let x : [t0 , T ] → L∗ and h > 0 with x(t) = (x1 (t), x2 (t)) ∈ L∗ and t, t + h ∈ [t0 , T ]. We say that the intuitionistic fuzzy function x(t) is continuous at t iff   lim x(t + h) = lim x1 (t + h), lim x2 (t + h) h→0

h→0

h→0

= (x1 (t), x2 (t)) = x(t) Definition 11 [7] Let x : [t0 , T ] → L∗G and h > 0. We say that a intuitionistic fuzzy function x(t) is geometric differentiable at t ∈ (t0 , T ), if there are exist the geometric differences x(t + h) G1 x(t), x(t) G1 x(t − h) and DG x(t) ∈ L∗G , such that x(t + h) G1 x(t) x(t) G1 x(t − h) = lim = DG x(t); lim h h h→0+ h→0+ or if there exists geometric differences x(t + h) G2 x(t), x(t) G2 x(t − h) and DG x(t) ∈ L∗G , such that lim

h→0+

x(t + h) G2 x(t) x(t) G2 x(t − h) = lim = DG x(t), + h h h→0

where denote DG x(t) is geometric derivative in L∗G . Theorem 1 [7] The geometric derivative of the intuitionistic fuzzy function x(t) ∈ L∗G will have the following form:   dx1 dx2 ,− a/ DG x(t) = if the intuitionistic fuzzy function x(t) is strictly dt dt monotone increasing by  t;  dx1 dx2 , b/ DG x(t) = − if the intuitionistic fuzzy function x(t) is strictly dt dt monotone decreasing by t. Proof Can see in [7]. Definition 12 Let x : [t0 , T ] → L∗ with x(t) = (x1 (t), x2 (t)) ∈ L∗ and two functions x1 (t) and x2 (t) are measurable and Lebesgue integrable on [t0 , T ]. We define a definite integral of x by  t   t  t x(s)ds = x1 (s)ds, x2 (s)ds , t0

t0

t0

with t ∈ [t0 , T ]. Definition 13 [7,9] Let x and y be two intuitionistic fuzzy numbers. Then a geometric distance between two intuitionistic fuzzy numbers x = (x1 , x2 ) and y = (y1 , y2 ) and L∗ denote by HL∗ (x, y) = sup {|x1 − y1 | , |x2 − y2 |} .

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Definition 14 Let x = (x1 , x2 ) and y = (y1 , y2 ) be two IFNs. Then, two order relations between them are defined as the following forms: (i) A G order in L∗ : y G x ⇔ y1 ≤ x1 and y2 ≥ x2 , (ii) A S order in L∗ : y S x ⇔ y1 ≤ x1 and y2 ≤ x2 , (iii) if y1 = x1 and y2 = x2 then y = x.

Fig. 1. A geometrical interpretation of y G x in L∗ .

Fig. 2. A geometrical interpretation of y S x in L∗ .

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Remark 1 The concepts of ordering as a comparison in Definitions 11-17 allow the same evaluation for the intuitioniistic fuzzy functions x(t), y(t) and the same for a function for x(t) and x(t + h) as below concept: Definition 15 Let x : [t0 , T ] → L∗ and h > 0 with x(t) = (x1 (t), x2 (t)) ∈ L∗ and t, t + h ∈ [t0 , T ]. We say that – the intuitionistic fuzzy function x(t) is regular monotone increasing by t iff x(t) S x(t + h) in L∗ with x1 (t)  x1 (t + h), x2 (t)  x2 (t + h), ∀t ∈ [t0 , T ]; – there exists a geometric difference under third type x(t) S1 y(t) = z(t) iff y(t) S x(t) in L∗ and y1 (t)  x1 (t), y2 (t)  x2 (t), ∀t ∈ [t0 , T ] where (z1 (t), z2 (t)) = (x1 (t) − y1 (t), x2 (t) − y2 (t)). Definition 16 Let x : [t0 , T ] → L∗ and h > 0 with x(t) = (x1 (t), x2 (t)) ∈ L∗ and t, t + h ∈ [t0 , T ]. We say that – the intuitionistic fuzzy function x(t) is regular monotone decreasing by t iff x(t + h) S x(t) in L∗ , with x1 (t + h)  x1 (t), x2 (t + h)  x2 (t), ∀t ∈ [t0 , T ]; – there exists a geometric difference under fourth type x(t) S2 y(t) = z(t) iff x(t) S y(t) in L∗ and x1 (t)  y1 (t), x2 (t)  y2 (t), ∀t ∈ [t0 , T ] where (z1 (t), z2 (t)) = (y1 (t) − x1 (t), y2 (t) − x2 (t)) = (−(x1 (t) − y1 (t)), −(x2 (t) − y2 (t))) . Definition 17 Let x : [t0 , T ] → L∗S . We say that a intuitionistic fuzzy function x(t) is geometric differentiable at t ∈ (t0 , T ), if there exist the geometric differences x(t + h) S1 x(t), x(t) S1 x(t − h) and DS x(t) ∈ L∗S , such that lim

h→0+

x(t + h) S1 x(t) x(t) S1 x(t − h) = lim+ = DS x(t); h h h→0

or if there exist the geometric differences x(t + h) S2 x(t), x(t) S2 x(t − h) and DS x(t) ∈ L∗S , such that lim

h→0+

x(t + h) S2 x(t) x(t) S2 x(t − h) = lim = DS x(t), h h h→0+

where denote DS x(t) is geometric derivative in L∗S .

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Theorem 2 The geometric derivative of the intuitionistic fuzzy function x(t) ∈ L∗S will have the following form:  dx dx  1 2 , a/ DS x(t) = if the intuitionistic fuzzy function x(t) is regular monodt dt tone increasing by t;  dx dx2  1 ,− , if the intuitionistic fuzzy function x(t) is regular b/ DS x(t) = − dt dt monotone decreasing by t. Proof Can see in [9]. The next definition, we introduce a construct for building a new ordered set that it may include L∗G partially ordered set and L∗S partially ordered set. by definition of G order relation and S order relation, we can realize that L∗G = (L∗ , G ) and L∗S = (L∗ , S ) are disjoint.

3 3.1

Main Results The Monoton Ess and Differentialble of Intuitionistic Fuzzy Functions in Ordered Semi-linear Space L∗G S .

Definition 18 Let L∗G = (L∗ , G ) and L∗S = (L∗ , S ) be two (disjoint) ordered sets. we denote the disjoint union set of L∗G and L∗S as L∗GS = L∗G ∪ L∗S , which is the ordered set formed by defining x GS y in L∗GS if and only if x, y ∈ L∗G and x G y in L∗G , or x, y ∈ L∗S and x S y in L∗S . Remark 2 Definition 19 gives us a new ordered set, which is formed from a union of two ordered sets (L∗G and L∗S ). Therefore, L∗GS can inherit the properties that L∗G and L∗S have. Specifically, L∗GS = (L∗ , GS ) is a partially ordered set because both L∗G and L∗S are two partially ordered set. Moreover, we will get the following results, which are inherited from L∗G and L∗S . Let x(t), y(t) and z(t) be the IFFs with t ∈ [t0 , T ]. If there exist x(t) G1 y(t) = z(t), x(t) G2 y(t) = z(t), x(t) S1 y(t) = z(t) or x(t) S2 y(t) = z(t), then we say that there exists x(t) GS y(t) and is called a geometric difference (with symbol GS ). Definition 19 Let x : [t0 , T ] → L∗GS . We say that a intuitionistic fuzzy function x(t) is geometric differentiable at t ∈ (t0 , T ), if there are exist the geometric differences x(t + h) G1 x(t), x(t) G1 x(t − h) and DGS x(t) ∈ L∗GS , such that lim

h→0+

x(t + h) G1 x(t) x(t) G1 x(t − h) = lim+ = DGS x(t); h h h→0

or if there exists geometric differences x(t + h) G2 x(t), x(t) G2 x(t − h) and DGS x(t) ∈ L∗GS , such that lim+

h→0

x(t + h) G2 x(t) x(t) G2 x(t − h) = lim+ = DGS x(t); h h h→0

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or if there exist the geometric differences x(t + h) S1 x(t), x(t) S1 x(t − h) and DGS x(t) ∈ L∗GS , such that lim+

h→0

x(t + h) S1 x(t) x(t) S1 x(t − h) = lim+ = DGS x(t); h h h→0

or if there exist the geometric differences x(t + h) S2 x(t), x(t) S2 x(t − h) and DGS x(t) ∈ L∗GS , such that lim

h→0+

x(t + h) S2 x(t) x(t) S2 x(t − h) = lim = DGS x(t), + h h h→0

where denote DGS x(t) is geometric derivative in L∗GS . Theorem 3 The geometric derivative of the intuitionistic fuzzy function x(t) ∈ L∗GS will have the following form:   dx1 dx2 , a/ DGS x(t) = if the intuitionistic fuzzy function x(t) is regular dt dt monotone increasing by t;   dx2 dx1 ,− b/ DGS x(t) = − , if the intuitionistic fuzzy function x(t) is regular dt dt monotone decreasing by t.   dx1 dx2 ,− c/ DGS x(t) = if the intuitionistic fuzzy function x(t) is strictly dt dt monotone increasing by t;  dx1 dx2 , d/ DGS x(t) = − if the intuitionistic fuzzy function x(t) is strictly dt dt monotone decreasing by t. Proof It is the direct result of Theorem 1 - 2 and the finitions . Remark 3 when a specific ordered space has been identified, we can define some concepts such as closed, open, Ideals, Bands, subspace on it. This helps to study the subset structures, as well as the topological structures for of it, becoming more abundant. However, in this study, we will present an important tool on L∗GS that is the differential equation, which has many applications in many areas and will be presented in the following section. 3.2

The Initial Valued Problem for Intuitionistic Fuzzy Differential Equations

Let D ⊂ [t0 , T ] × L∗GS and x = (x1 , x2 ) denote elements of L∗GS . At the same time, let elements of D be denoted as (t, x). When x is a vector-valued function of t, we denote   dx1 dx2 , DGS x = . dt dt where DGS x satisfies Theorem ??, that means we have four kinds of derivatives of the intuitionistic fuzzy functions.

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For two given functions f1 : D → [0, 1] and f2 : D → [0, 1] such that 0 ≤ f1 + f2 ≤ 1, let f = (f1 , f2 ). We consider a system of first-order ordinary differential equations given by dxi = fi (t, x1 , x2 ), dt

i = 1, 2.

(4)

Eq. (4) can be written more compactly as DGS x = f (t, x).

(5)

For f ∈ C 1 [(t0 , T ), L∗GS ] , which means that f : (t0 , T ) → L∗GS and f is continuous and differentiable, a solution of Equation (5) is a vector-valued differentiable function y defined on (t0 , T ) such that (t, y(t)) ∈ D for all t ∈ (t0 , T ) and DGS y(t) = f (t, y(t)) for all t ∈ (t0 , T ). When t ∈ [t0 , T ], then DGS y(t0 ) is interpreted as the right-side derivative and DGS y(T ) is interpreted as the left-side derivative. For (t0 , x0 ) ∈ D, the initial value problem (IVP) corresponding to Eq. (5) is given by (6) DGS x(t) = f (t, x(t)), x(t0 ) = x0 And so, according to the Theorem 2, we have 04 initial value problems for the intuitionistic fuzzy differential equation. Definition 20 Let the function f : D → L∗GS be continuous, a function y is a solution of IVP (6) if and only if y satisfies the integral equation  y(t) GS x0 =

t

f (s, y(s))ds

(7)

t0

where t ∈ [t0 , T ], (t0 , x0 ) ∈ D, and  t   t  t f (s, y(s))ds = f1 (s, y(s))ds, f2 (s, y(s))ds . t0

t0

t0

Corollary 1 The solution of the initial value problem (6) depends on the function f on the right side of the differential equation in IVP (6). Proof Assuming that y is a solution of the initial value problem (6), by Definition 20, we get  y(t) GS x0 =

t

f (s, y(s))ds. t0

If initial data x(t0 ) = x0 ∈ L∗GS is given, clearly that y depends on f. Next, we will state and demonstrate the existence and uniqueness of the solution for the initial value problem (6).

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Definition 21 Let a function f (t, x) be defined on a domain D ⊂ [t0 , T ] × L∗GS . we say that f satisfies Lipschitz condition by x on D, if there exists a positive constant L > 0 (often called Lipschitz constant) such that HL∗ (f (t, x), f (t, y)) ≤ L.HL∗ (x, y),

∀(t, x), (t, y) ∈ D.

Theorem 4 Let a function f (t, x) in (8) be continuous and satisfying Lipschitz condition by x on a domain B = {(t, x) ∈ [t0 , T ] × L∗GS | |t − t0 | ≤ δ, HL∗ (x, x0 ) ≤ ε} with δ > 0 and ε > 0, when the initial value problem (6) has a unique ε solution defined on an interval [t0 , t0 + k] with k = min(δ, M ) and M = ∗ max HL∗ (f (t, x), θ) (θ is zero element of L in Definition 8).

(t,x)∈B

Proof For existence: Let (xn )n∈N is a sequence on [t0 , t0 + k], it is defined as follows ⎧ 0 = x0 , with n ∈ N ⎨x  t (8) ⎩xn+1 GS x0 = f (s, xn (s))ds, t0

The sequence (8) is called a Picard sequence. Now, we will prove this sequence converges uniformly on [t0 , t0 + k] to a solution of IVP (6). To do this, we need to prove the following inequality is true n+1

 |t − t0 | , HL∗ xn+1 (t) GS x0 , xn (t) GS x0 ≤ M.Ln (n + 1)!

∀t ∈ [t0 , t0 + k]. Indeed, we will prove this inequality by inductive method. For n = 0, the inequality is

 HL∗ x1 (t) GS x0 , x0 (t) GS x0   t = HL∗ f (s, x0 (s))ds, θ ≤ M |t − t0 | t0

and this inequality is true. Next, assuming that this is also true with n − 1, when with t ∈ [t0 , t0 + k] we have

 HL∗ xn+1 (t) GS x0 , xn (t) GS x0  t n n+1 |t − t0 | |t − t0 | ds = M.Ln . ≤ M.Ln n! (n + 1)! t0 Now, considering the sequence (xn )n∈N on [t0 , t0 + k], with p ≥ 1 we have

 HL∗ xn+p (t) GS x0 , xn (t) GS x0 k M (L |t − t0 |) . ≤ L k! k≥n+1

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The series

∞ k (L |t − t0 |)

k=0

(L|t−t0 |)k , k≥n+1 k!

k!

is convergence, so its remainder, which is

can be arbitrarily small when n is large enough. This implies that the sequence (xn )n∈N converges uniformly on [t0 , t0 + k] to a function x(t). To prove x(t) is the solution of of IVP (6), we just need to take the limit n → ∞ in the equation  xn+1 GS x0 =

t

f (s, xn (s))ds.

t0

Because (xn )n∈N is uniformly convergent and f is continuous on B, the sequence {f (s, xn (s))} converges uniformly on [t0 , t0 + k] to a function f (t, x(t)). Therefore,it is possible to take limit n → ∞ to get Eq. (6). So x(t) is a solution of IVP (6). For Uniqueness: Assuming that IVP (6) has a solution y(t), when we have HL∗ (x(t) GS x0 , y(t) GS x0 )   t  t = HL∗ f (s, x(s))ds, f (s, y(s))ds t0

t0

≤ 2M. |t − t0 | . Thus HL∗ (x(t) GS x0 , y(t) GS x0 )   t  t = HL∗ f (s, x(s))ds, f (s, y(s))ds  ≤ L.

t0 t

t0 2

HL∗ (x(s), y(s)) ds ≤ 2M L.

t0

|t − t0 | . 2

Repeating this process with n ∈ N, we get HL∗ (x(t) GS x0 , y(t) GS x0 ) ≤ 2M Ln

n+1

|t − t0 | (n + 1)!

with t ∈ [t0 , t0 + k], for n → ∞ we obtain HL∗ (x(t) GS x0 , y(t) GS x0 ) = HL∗ (x(t), y(t)) = 0 on [t0 , t0 + k]. Therefore, the solution x(t) is uniqueness. Remark 4 for proof of Theorem 3, which is the theorem of the existence and uniqueness of the solution of the initial value problem for intuitionistic fuzzy differential equations in L∗GS , we use the Picard approximation with the assumption of Lipschitz condition. Specifically, under Lipschitz condition we show that the Picard sequence converges to a solution of the initial value problem. From this, we obtained the existence and uniqueness of this solution, which is a local solution of the initial value problem.

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Next, we will provide illustrative examples corresponding to the four types of functions in Theorem 2. Example 2 Let us consider the following problem:  DGS x(t) = (x1 (t), e−t ), ∀t ∈ [0, 20],

 x(0) = (x1 (0), x2 (0)) = 12 , 0 ∈ L∗ ,

(9)

where the function x(t) is strictly monotonic decreasing by t.  is strictly monotonic decreasing by t, we have DGS x(t) =  Since x(t) dx1 dx2 , from Theorem ??. Therefore, The IVP for IFDE (9) is equiva− dt dt lent to a following system of first-order ordinary differential equations ⎧ dx − dt1 = x1 (t), ∀t ∈ [0, 20], ⎪ ⎪ ⎪ ⎨ dx2 = e−t , dt (10) 1 ⎪ x 1 (0) = 2 , ⎪ ⎪ ⎩ x2 (0) = 0. Solving the system (10), we obtain  x1 (t) = 2e1t , x2 (t) = 1 − e−t and for all t ∈ [0, 20]  x(t) = (x1 (t), x2 (t)) =

 1 −t , 1 − e . 2et

(11)

we see that the function x(t) in (11) is strictly monotonic increasing by t in L∗GS . Therefore, it is a solution of the IVP for IFDE (9). Illustrative images of two functions x1 (t) and x2 (t) are shown in Fig. 3, where the function x1 (t) is blue and the function x2 (t) is red. At the same time, the solution x(t) = (x1 (t), x2 (t)) in L∗ is shown in Fig. 4 with a red function. 3.3

The Economic Growth Models

In [9] the authors considered models for processes with two closely related states. In this paper, we try to propose an economic growth model that depends on working capital in cash Q1 , on investment capital for production power Q2 , for example factories, machinery, people,... Then economic growth Y will be a function of Q1 , Q2 , that means Y = f (Q1 , Q2 ), that satisfies the following conditions:  Y = f (Q1 , Q2 ), (12) df df dQ1 > 0. dQ2 > 0

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In model 12, we find that the economic growth function Y depends on the volatility of investment Q(t) = (Q1 (t), Q2 (t)), that means dQ(t) dt = Y ⎧ dQ(t) ⎪ ⎨ dt = f (Q1 , Q2 ), df df dQ1 > 0. dQ2 > 0 ⎪ 2 ⎩ df d2 f (dQ1 )2 < 0. (dQ2 )2 < 0

(13)

1

x2(t)

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

x1(t) 0 0

2

4

6

8

10

12

14

16

18

20

t

Fig. 3. The real functions x1 (t) and x2 (t) belong to C([0, 20], [0, 1]).

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2

x(t)=(x 1(t),x 2(t))

0.1 0

0

0.2

0.4

0.6

0.8

1

Fig. 4. The solution x(t) = (x1 (t), x2 (t)) in L∗ .

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3.3.1 Linear Model for Economic Growth Assume that Q(t) = (Q1 (t), Q2 (t)) ∈ L∗GS are the investments, and S is the growth plan coefficient, the problem model (13) can be rewritten in linear form - the linear model for economic growth depends on this investments:  DGS Q(t) = Sf (Q(t)), (14) Q(t0 ) = (Q1 (t0 ), Q2 (t0 )) ∈ L∗ , and the linear model for economic growth depends on this investments with the control parameters λ : ⎧ ⎪ ⎨DGS Q(t) = Sf (Q(t)) − λQ(t), (15) Q(t0 ) = (Q1 (t0 ), Q2 (t0 )) ∈ L∗ , ⎪ ⎩ λ − control parameters Example 3 Let us consider the following problem: 

 DGS Q(t) = 12 Q1 (t), Q1 (t)Q2 (t) GS λ Q(t), ∀t ∈ [0, 6], Q(0) = (Q1 (0), Q2 (0)) = (0.3, 0.7) ∈ L∗ ,

(16)

By direct calculation with λ = 23 , we obtain a solution of the problem (16), Q(t) = (Q1 (t), Q2 (t))   3 −t/6 7 −2t/3−(9/5)e−t/6 9/5 e e , e . = 10 10 Illustrative images of two functions Q1 (t) and Q2 (t) are shown in Fig. 5, where the function Q1 (t) is blue and the function Q2 (t) is red. At the same time, the solution Q(t) = (Q1 (t), Q2 (t)) in L∗ is shown in Fig. 6 with a red function. 1 0.9 0.8 0.7 0.6 0.5 Q 2 (t)

0.4 Q 1 (t)

0.3 0.2 0.1 0

0

1

2

3

4

5

6

t

Fig. 5. The real functions Q1 (t) and Q2 (t) belong to C([0, 6], [0, 1]).

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0.2 0.1 0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Fig. 6. the solution Q(t) = (Q1 (t), Q2 (t)) in L∗ .

3.3.2 Nonlinear Model for Economic Growth Assume that Q(t) = (Q1 (t), Q2 (t)) ∈ L∗GS are the investments, and S is the market volatility, problem model (11) can be rewritten in nonlinear form - nonlinear model for economic growth depends on this investments with the control function R(Q(t), U (t)): ⎧ ⎪ ⎨DGS Q(t) = Sϕ(Q(t)) + R(Q(t), U (t)), (17) Q(t0 ) = (Q1 (t0 ), Q2 (t0 )) ∈ L∗ , ⎪ ⎩ U (t) − control f unctions. Example 4 Let us consider the following problem: 

 DGS Q(t) = 13 Q1 (t), Q1 (t)Q2 (t) + −5t 2 Q(t), ∀t ∈ [0, 6], Q(0) = (Q1 (0), Q2 (0)) = (0.2, 0.6) ∈ L∗ , By direct calculation with U (t) = (18),

−5t 2 ,

(18)

we obtain a solution of the problem

Q(t) = (Q1 (t), Q2 (t))  1 −t(3t−8)/24 e , = 5  3 (erf(√2/3)e2/9 √2√π)/5 (erf(√2t/4−√2/3)e2/9 √2√π)/5−t2 /8 e e . 5 x 2 where erf(x) = √2π 0 e−t dt. Illustrative images of two functions Q1 (t) and Q2 (t) are shown in Fig. 7, where the function Q1 (t) is blue and the function Q2 (t) is red. At the same time, the solution Q(t) = (Q1 (t), Q2 (t)) in L∗ is shown in Fig. 8 with a red function.

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1 0.9 0.8 0.7 0.6 0.5 0.4 Q 2 (t)

0.3 Q 1 (t)

0.2 0.1 0

0

1

2

3

4

5

6

t

Fig. 7. The real functions Q1 (t) and Q2 (t) belong to C([0, 6], [0, 1]). 1 0.9 0.8 0.7 0.6 0.5 0.4 Q(t)=(Q 1 (t),Q2 (t))

0.3 0.2 0.1 0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Fig. 8. The solution Q(t) = (Q1 (t), Q2 (t)) in L∗ .

Remark 5 Putting the function Q∗ (t) = Q1 (t)/Q2 (t)) is the rate of investment capital and assume that the function on the right is homogeneous f (Q1 (t), Q2 (t) = Q2 (t).f (Q1 (t)/Q2 (t), 1), we can take the nonlinear model for economic growth depends on this rate of investment capital Q∗ (t): ⎧ ∗ ∗ ∗ ⎪ ⎨DGS Q (t) = Sϕ(Q (t)) + R(Q (t), U (t)), (19) Q∗ (t0 ) = (Q1 (t0 ), Q2 (t0 )) ∈ L∗ , ⎪ ⎩ U (t) − control f unctions.

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Conclusions

In the ordered semi-linear space L∗GS the intuitionistic fuzzy functions have four different types of derivatives, so the initial value problem (IVP) for the intuitionistic fuzzy differential equation (IFDEs) is also very diverse. We give the model of the initial value problem of the intuitionistic fuzzy differential equations (IVP for IFFDEs) on this ordered semi-linear space L∗GS . Simultaneously, we provide and prove the theorem of the existence and uniqueness of the solution of this initial value problem, we use the Picard approximation with the assumption of the Lipschitz condition. In detail, under the Lipschitz condition, we show that the Picard sequence converges to a solution of the initial value problem. From this, we obtained the existence and uniqueness of this solution, which is a local solution to the initial value problem. In addition, we give four examples corresponding to four types of functions defined in this ordered space. For the application of IVP for IFFDEs, we also give the economic growth models. Acknowledgments. The authors are deeply grateful to the ...

References 1. Ai, Z., Xu, Z., Lei, Q.: Limit properties and derivative operations in the metric space of intuitionistic fuzzy numbers. Fuzzy Optim. Decis. Making 16, 71–87 (2017). https://doi.org/10.1007/s10700-016-9239-7 2. Atanassov, K.T.: Intuitionistic fuzzy sets. VII ITKR’s Session, Sofia (1983) 3. Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986) 4. Atanassov, K.T., Pasi, G., Yager, R.: Intuitionistic fuzzy interpretations of multicriteria multi-person and multi-measurement tool decision making. Int. J. Syst. Sci. 36, 859–868 (2005) 5. De, S.K., Biswas, R., Roy, A.R.: An application of intuitionistic fuzzy sets in medical diagnostic. Fuzzy Sets Syst. 117, 209–213 (2001) 6. Lei, Qian, Xu, Zeshui: Intuitionistic Fuzzy Calculus. SFSC, vol. 353. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-54148-8 7. Phu, N.D., Hung, N.N.: The geometric lattice intuitionistic fuzzy functions and applications. J. Int. Fuzzy Syst. 35, 1–12 (2018). https://doi.org/10.3233/IFS172027 8. Phu, N.D., Ahmadian, A., Hung, N.N., Salahshour, S., Senu, N.: Narrow Metric Semi-linear Space of Intuitionistic Fuzzy Numbers: application to AIDS Model. Int. J. Fuzzy Syst. 21(6), 1738–1754 (2019). https://doi.org/10.1007/s40815-01900649-3 9. Phu, Nguyen Dinh, Hung, Nguyen Nhut, Quynh, Le Thi Ngoc.: Some new ordered semi-linear spaces of intuitionistic fuzzy processes and the pair of closely related states. In: Kahraman, Cengiz, Cevik Onar, Sezi, Oztaysi, Basar, Sari, Irem Ucal, Cebi, Selcuk, Tolga, A. Cagri. (eds.) INFUS 2020. AISC, vol. 1197, pp. 397–411. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-51156-2 47 10. Shinoj, T.K., Sunil, J.J.: Intuitionistic fuzzy multisets and its application in medical diagnosis. Int. J. Math. Comput. Phys. Elect. Comput. Eng. 6, 34–38 (2012)

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11. Takeuti, G., Titani, S.: Intuitionistic fuzzy logic and intuitionistic fuzzy set theory. J. Symbolic Logic 49, 851–866 (1984) 12. Xu, Z., Yager, R.R.: Some geometric aggregation operators based on intuitionistic fuzzy sets. Int. J. Gen. Syst. 35, 417–433 (2006) 13. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

Second Order Intuitionistic Fuzzy Time Series Forecasting Model via Crispification Nik Muhammad Farhan Hakim Nik Badrul Alam(B)

and Nazirah Ramli

Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA Pahang, 26400 Bandar Tun Abdul Razak Jengka, Pahang, Malaysia {farhanhakim,nazirahr}@uitm.edu.my

Abstract. Forecasting is one of the valuable tools in making decisions for proper planning. However, the classical statistical forecasting method cannot cater to data in linguistic variables. The evolvement of the fuzzy set has made forecasting for data in natural language possible. The fuzzy set has been generalized into the intuitionistic fuzzy set (IFS), which can better handle uncertainty. This paper proposes a fuzzy time series (FTS) forecasting model based on the second order intuitionistic fuzzy logical relationships (IFLR). The IFS were converted into crisp values using the crispification method before calculating the forecasted data. The historical data of students’ enrollment at the University of Alabama was adopted to illustrate the proposed model. Two main findings were obtained. Here, the forecasting model based on IFS has shown a better performance than the models based on the fuzzy set, while the second-order IFLR has produced better forecasting results than the first order IFLR. Keywords: Fuzzy time series · Intuitionistic fuzzy set · Crispification · Second order intuitionistic fuzzy logical relationship

1 Introduction Forecasting time series data can be challenging since the data may fluctuate and are unpredictable. However, many industries need to forecast future data so that decisionmakers can do proper planning to minimize the probable risks. In statistics, many models have been developed for forecasting time series data, such as ARMA, ARIMA, GARCH and ARAR [1]. The statistical methods of forecasting time series data are insufficient to handle historical data in linguistic variables [2]. Thus, Song and Chissom [3] proposed the concept of fuzzy time series (FTS), in which the data in linguistic variables can be forecasted using Zadeh’s [4] fuzzy set. The FTS is powerful due to its ability to process both the crisp and fuzzy values [5]. Furthermore, Song and Chissom [6] proposed the FTS model for forecasting students’ enrollment at the University of Alabama using seven intervals length, max-min composition operation and centroid defuzzification method. Since then, various FTS forecasting models have been developed employing various interval lengths, data fuzzification and defuzzification methods. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 556–565, 2022. https://doi.org/10.1007/978-3-031-09173-5_64

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Atanassov [7] developed an intuitionistic fuzzy set (IFS). It is an extended form of the classical fuzzy set. In addition, the degree of non-membership is incorporated to signify how much the components do not belong to the fuzzy set with a particular degree of hesitant. In IFS theory, both the degrees of belongingness and non-belongingness are considered, while in fuzzy sets, only the belongingness of an element to a set is considered. Many FTS forecasting models based on IFS have been developed, but most used the first-order intuitionistic fuzzy logical relationships (IFLR). Hence, this paper proposed a novel FTS forecasting model based on the second-order IFLR and crispification approach. In the crispification formula, both the membership and non-membership values of IFS are considered to convert the IFS into crisp numbers. The nature of IFS is preserved since their features are used in the formula. The organization of this paper is as follows: Sect. 1 presented the introduction; some literature is reviewed in Sect. 2; Sect. 3 reviewed some related preliminaries; Sect. 4 proposed the second order intuitionistic FTS forecasting model and Sect. 5 implemented the model with a numerical example; Sect. 6 discussed the result and Sect. 7 concluded the paper.

2 Literature Review Fuzzy time series (FTS) was first proposed by Song and Chissom [3] to deal with time series data in natural language. The proposed model was implemented in [6, 8] to forecast the students’ enrollment at the University of Alabama. Moreover, Chen [9] and Hwang et al. [10] further simplified the max-min composition operation used in [6, 8] and replaced it with arithmetic rules considering the midpoints of intervals for the defuzzification. Furthermore, Lee and Chou [11] modified Chen’s [9] method by defining the supports of fuzzy sets, representing the linguistic values more appropriately. In addition, Singh [12] improved the rules for calculating the forecasted enrollment by considering data for consecutive previous three years to predict the enrollment for the next year. Instead of using fuzzy sets, Liu [13] developed an FTS forecasting model based on trapezoidal fuzzy numbers. More information is provided by the fuzzy numbers instead of only the single-point forecasted values. Subsequently, Kuo et al. [14] proposed a hybrid forecasting model that integrated particle swarm optimization with the FTS. Utilizing Atanassov’s intuitionistic fuzzy set (IFS) [7], many intuitionistic FTS forecasting models have been developed. A novel FTS forecasting model was proposed by Joshi and Kumar [15], in which they utilized the hesitation degree for fuzzification based on IFS theory. Moreover, Joshi and Kumar’s [15] work was refined by Gangwar and Kumar [16], who used the interval partitioning technique based on the cumulative probability distribution approach. The score function-based method was then proposed in [17, 18] to measure the IFS. The previously mentioned models used the first order IFLR. Recently, Abhisekh et al. [19] proposed an FTS forecasting model on the basis of IFS using the second order IFLR. However, the defuzzification method used the midpoints of intervals, in which the degrees of belongingness and non-belongingness of IFS were ignored entirely.

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3 Preliminaries This section reviews some fundamental concepts related to the intuitionistic fuzzy set (IFS) and fuzzy time series (FTS). The IFS consists of membership and non-membership functions. The membership function represents how much the element belongs to the set, while the non-membership function is the degree of non-belongingness. The IFS can be defined as follows: Definition 1 [7]. An IFS I is a set in the universe of discourse ξ that is defined as I = { (θ, μθ , νθ )|θ ∈ ξ },

(1)

where μθ and νθ are the degrees of belongingness and non-belongingness, respectively. Zadeh’s classical fuzzy set [4] can be generalized into an IFS using Atanassov’s conversion method, which is shown in Definition 2. Definition 2 [20]. Let AF be in the collection of all fuzzy sets in ξ . Let δmin : ξ → [0, 1] and δmax : ξ → [0, 1]. f : [0, 1]2 ×[0, 1] → L∗ [0, 1]→ L∗ , where f (u, δmin , δmax ) = fμ (u, δmin , δmax ), fν (u, δmin , δmax ) whereby fμ (u, δmin , δmax ) = u(1 − δmin δmax ),

(2)

fν (u, δmin , δmax ) = 1 − u(1 − δmin δmax ) − δmin δmax .

(3)

and

Chen and Tan [21] defined the score function to compare within IFS. The IFS with a higher score value is greater than the IFS with a lower score value. The definition of the score function of IFS is presented in the following.   Definition 3 [21]. Let I˜ = μI˜ , νI˜ be an intuitionistic fuzzy value. Then, the score function I˜ is given by   S I˜ = μI˜ − νI˜ . (4)

4 Second Order Intuitionistic Fuzzy Time Series Forecasting Model This section proposes a second order fuzzy time series (FTS) forecasting model based on an IFS using a novel crispification method as a means of defuzzification. The proposed model is described in the following steps: Step 1. Collect the historical data and define its universe of discourse using the following formula. ξ = [χL − δ1 , χU + δ2 ],

(5)

where χL and χU are the smallest and largest historical data, respectively, while δ1 and δ2 are two proper non-negative numbers.

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Step 2. Divide the universe of discourse into several intervals using the frequency densitybased method [22]. Hence, define the triangular fuzzy number (TFN) for each interval. Step 3. Transform the historical data into fuzzy sets using the defined TFN. Step 4. Convert each fuzzy set obtained from Step 3 into an IFS using Atanassov’s conversion formula [20]. Step 5. Calculate the score function of each element in the IFS. Based on the score function, each datum is assigned the IFS, in which the IFS with a higher score value is chosen. Step 6. Construct second order IFLR and group them. If the data of years n, n + 1 and n + 2 are assigned with I i , I j and I k , then the IFLR can be constructed as I i , I j → I k . Step 7. Defuzzify each IFS defined in Step 4 using the following crispification formula

θ˜ =

k     μθ − νθ  · θi i i

i=1

k    i=1

 μθi − νθi 

,

(6)

where θi i = 1, 2, ..., k are all elements (historical data) included in the IFS while μθi and νθi are their degrees of belongingness and non-belongingness, respectively. Step 8. Calculate the forecasted data based on the second order IFLR and crisp values obtained from Step 6 and Step 7, respectively. The following rules are used to calculate the forecasted data: 1. If Ii1 , Ii2 → Ii3 is the second order IFLR for the previous year, then the forecasted value of the next year is given by θ˜i3 , which is the defuzzified value of IFS Ii3 . 2. If Ii1 , Ii2 → Ii3 , Ii4 , ..., Iip is the second IFLR for the previous year, then the forecasted value for the next year is given by θ˜i3 + θ˜i4 + ... + θ˜ip p−2 where θ˜i3 , θ˜i4 , ..., θ˜ip are the defuzzified values of Ii3 , Ii4 , ..., Iip , respectively. 3. If Ii1 , Ii2 → φ is the second order IFLR for the previous year, then the forecasted value of the next year is given by the average of θ˜i1 and θ˜i2 , where θ˜i1 and θ˜i2 are defuzzified values of Ii1 and Ii2 , respectively.

5 Numerical Example The student enrollment data at the University of Alabama extracted from [6] are adopted to illustrate the proposed second order intuitionistic fuzzy time series (FTS) forecasting model. The student enrollment data are shown in Fig. 1.

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N. M. F. H. N. B. Alam and N. Ramil Student Enrollments at the University of Alabama (1971-1992) 20000 19000

Number of Students

18000 17000 16000 15000 14000 13000 12000 11000 1991

1992

1990

1989

1988

1987

1986

1985

1983

1984

1982

1981

1980

1979

1978

1976

1977

1975

1974

1972

1973

1971

10000 Year

Fig. 1. Student enrollments at the University of Alabama (1971–1992).

Step 1. The smallest and largest number of students are 13055 and 19337, respectively. Hence, the universe of discourse ξ is defined as [13050, 19350], in which δ1 = 5 and δ2 = 13 are chosen. Step 2. Utilizing the frequency-density-based interval partitioning method, the universe of discourse is partitioned into 14 intervals. The intervals with their corresponding triangular fuzzy numbers (TFN) are listed in Table 1.

Table 1. TFN corresponds to each interval. Interval

TFN

Interval

TFN

[13000, 13500]

(13000, 13500, 14000)

[16000, 16333]

(16000, 16333, 16667)

[13500, 14000]

(13500, 14000, 15000)

[16333, 16667]

(16333, 16667, 17000)

[14000, 15000]

(14000, 15000, 15250)

[16667, 17000]

(16667, 17000, 18000)

[15000, 15250]

(15000, 15250, 15500)

[17000, 18000]

(17000, 18000, 18500)

[15250, 15500]

(15250, 15500, 15750)

[18000, 18500]

(18000, 18500, 19000)

[15500, 15750]

(15500, 15750, 16000)

[18500, 19000]

(18500, 19000, 20000)

[15750, 16000]

(15750, 16000, 16333)

[19000, 20000]

(19000, 20000, 20000)

Step 3. Using the TFN in Table 1, the membership degrees for the fuzzy sets are defined. Hence, 14 fuzzy sets are formed.

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561

Step 4. The fuzzy sets are then transformed into IFS. Hence, the following intuitionistic fuzzy set (IFS) is formed. I1 = {(13055, 0.099, 0.804), (13563, 0.790, 0.114), (13867, 0.240, 0.663)} I2 = {(13563, 0.114, 0.793), (13867, 0.666, 0.241), (14696, 0.276, 0.632)} I3 = {(14696, 0.527, 0.230), (15145, 0.318, 0.440), (15163, 0.264, 0.494)}  (15145, 0.575, 0.416), (15163, 0.646, 0.345), (15311, 0.749, 0.242), I4 = 0.266, 0.725), (15460, 0.159, 0.832), (15497, 0.012, 0.979)  (15433, (15311, 0.185, 0.574), (15433, 0.556, 0.203), (15460, 0.637, 0.121), I5 = (15497, 0.750, 0.009), (15603, 0.446, 0.313) I6 = {(15603, 0.397, 0.567), (15861, 0.536, 0.428), (15984, 0.062, 0.903)} I7 = {(15861, 0.259, 0.325), (15984, 0.547, 0.037)} I8 = {(16388, 0.252, 0.050)}  (16388, 0.149, 0.756), (16807, 0.524, 0.380), (16859, 0.383, 0.522), I9 = (16919, 0.220, 0.685) I10 = {(16807, 0.287, 0.395), (16859, 0.393, 0.289), (16919, 0.516, 0.166)} I11 = {(18150, 0.357, 0.153)} I12 = {(18150, 0.295, 0.687), (18876, 0.244, 0.738), (18970, 0.059, 0.923)}  (18876, 0.283, 0.093), (18970, 0.354, 0.023), (19328, 0.253, 0.124), I13 = (19337, 0.250, 0.127) I14 = {(19328, 0.292, 0.598), (19337, 0.300, 0.590)} Step 5. The score function for each IFS is calculated. Then, the historical data are fuzzified using the IFS, as shown in Table 2.

Table 2. Fuzzification of historical data using IFS. Data

IFS

Data

IFS

Data

IFS

Data

IFS

13055

I1

15603

I5

15497

I5

18970

I 13

13563

I1

15861

I6

15145

I4

19328

I 13

13867

I2

16807

I9

15163

I4

19337

I 13

14696

I3

16919

I 10

15984

I7

18876

I 13

15460

I5

16388

I8

16859

I 10

15311

I4

15433

I5

18150

I 11

Step 6. Next, the second order IFLR is constructed and grouped as presented in Table 3.

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N. M. F. H. N. B. Alam and N. Ramil Table 3. Second order IFLR groups.

Group

Second Order IFLR

Group

Second Order IFLR

I1 , I1 → I 2 I1 , I2 → I 3

11

I6 , I9 → I10 I7 , I10 → I11

13

4

I2 , I3 → I 5 I3 , I5 → I 4

14

I 8 , I5 → I 5 I9 , I10 → I8

5

I4 , I4 → I 7

15

I10 , I8 → I5

6

16

7

I4 , I5 → I 6 I4 , I7 → I10

17

I10 , I11 → I13 I11 , I13 → I13

8

I5 , I4 → I 4 , I5

18

I13 , I13 → I13

9

I5 , I5 → I 4 I 5 , I6 → I 9

19

I13 , I13 → φ

1 2 3

10

12

Step 7. Each IFS is defuzzified into a crisp value. For example, the IFS I1 is defuzzified using Eq. (6) as follows:

θ˜1 =

|0.099 − 0.804|13055 + |0.790 − 0.114|13563 + |0.240 − 0.663|13867 = 13435.76. |0.099 − 0.804| + |0.790 − 0.114| + |0.240 − 0.663|

The rest of the IFS are defuzzified similarly; hence we obtained θ˜2 = 13927.68, θ˜3 = 14945.78, θ˜4 = 15397.53, θ˜5 = 15450.19, θ˜6 = 15914.32, θ˜7 = 15970, θ˜8 = 16388, θ˜9 = 16662.98, θ˜10 = 16886.29, θ˜11 = 18150, θ˜12 = 18759.59, θ˜13 = 19065.14 and θ˜14 = 19332.38. Step 8. The forecasted data are calculated using the proposed rules. The IFS for 1972 and 1973 are I1 and I2 , respectively, hence it follows Group 2 that the IFLR is I1 , I2 → I3 . Therefore, the forecasted data for 1974 is θ˜3 = 14946. The IFS for 1983 and 1984 are I5 and I4 , respectively, hence it follows Group 8 that the IFLR is I5 , I4 → I4 , I5 . Thus, for 1985, the forecasted data is the average of θ˜4 = 15397.53 and θ˜5 = 15450.19, which is 15424.

6 Results and Discussion The following figure presents students’ actual and predicted enrollment using the proposed model (Fig. 2). The difference between the actual and forecasted enrollments is calculated to measure the errors produced by the forecasting model. In this research, the mean square error (MSE), root mean square error (RMSE) and mean absolute error (MAE) calculated in the proposed model are calculated and compared with the existing models.

Second Order Intuitionistic Fuzzy Time Series

563

Actual and Forecasted Enrollment of Students at the University of Alabama (1971-1993)

Actual

1993

1991

1992

1990

1989

1988

1987

1985

1986

1984

1983

1982

1981

1980

1979

1978

1977

1975

1976

1974

1973

1972

1971

20000 19000 18000 17000 16000 15000 14000 13000 12000 11000 10000

Forecasted

Fig. 2. Actual and forecasted enrollments at the University of Alabama (1971–1993).

Table 4. MSE, RMSE and MAE of the proposed and existing models. Order of FLR

Type of fuzzy set

MSE

RMSE

MAE

First order [9]

Fuzzy set

407507.29

638.36

498.81

First order [23]

IFS

132016.00

363.34

257.38

First order [24]

IFS

130282.00

360.95

254.70

Third order [25]

Fuzzy set

86693.63

294.44

255.95

Third order [26]

Fuzzy set

76509.42

276.60

235.32

Second order [19]

IFS

24443.40

156.34

132.70

Second order (proposed model)

IFS

22700.85

150.67

112.75

In reference to Table 4, forecasting time series data using an intuitionistic fuzzy set (IFS) gives a better performance than the model that uses the classical fuzzy set since IFS can better handle the non-determinism and vagueness [7]. The order of fuzzy logical relationships (FLR) and intuitionistic fuzzy logical relationships (IFLR) also influence forecasting performance. The results show that the higher-order FLR and IFLR have more minor errors than the lower-order. The second-order IFLR proposed in this study outperforms other studies by [9, 19, 23–25] and [26] in terms of accuracy. Furthermore, the proposed model has improved the defuzzification method, in which the absolute score functions were used to crispify the IFS instead of using the midpoints of intervals as considered in [19]. Therefore, the nature of IFS in handling uncertainty is preserved.

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7 Conclusion This paper discusses the role of an intuitionistic fuzzy set (IFS) in handling uncertain data. A fuzzy time series (FTS) forecasting model was proposed based on IFS using the second order intuitionistic fuzzy logical relationships (IFLR). During the defuzzification process, a new crispification formula was used to convert the IFS into crisp values applying the degrees of belongingness and non-belongingness to preserve the nature of IFS in handling the uncertainty. The proposed model was implemented to predict the student enrollments at the University of Alabama. The results showed that forecasting using the proposed model had produced a better performance than the existing models. Since the IFS generalizes the classical fuzzy set, it was also proven that FTS forecasting models based on IFS had performed better than those using the classical fuzzy set. Another finding of this study is that the second order IFLR has controlled the forecasting models to reduce the errors between the actual and predicted data compared to the first order IFLR. In the future, different defuzzification methods will be applied so that the degree of non-determinacy contained in the uncertain data can be carefully considered in crispifying the IFS. The higher order IFLR can also be further developed to investigate if it helps produce a better performance of the intuitionistic FTS forecasting. Acknowledgement. The authors would like to thank Universiti Teknologi MARA for supporting this research under UiTM Lestari Covid Research Grant 600-RMC/LESTARI COVID/5/3 (038/2020).

References 1. Brockwell, P.J., Davis, R.A.: Introduction to Time Series and Forecasting. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-29854-2 2. Phil, S.: Statistics in Linguistics. Annu. Rev. Anthropol. 20, 377–393 (1991) 3. Song, Q., Chissom, B.S.: Fuzzy time series and its models. Fuzzy Sets Syst. 54, 269–277 (1993) 4. Zadeh, L.: Fuzzy sets. Inf. Control. 8, 338–353 (1965) 5. Bose, M., Mali, K.: Designing fuzzy time series forecasting models: a survey. Int. J. Approx. Reason. 111, 78–99 (2019). https://doi.org/10.1016/j.ijar.2019.05.002 6. Song, Q., Chissom, B.S.: Forecasting enrollments with fuzzy time series - part I. Fuzzy Sets Syst. 54, 1–9 (1993). https://doi.org/10.1016/0165-0114(93)90355-L 7. Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986). https://doi.org/ 10.1016/S0165-0114(86)80034-3 8. Song, Q., Chissom, B.S.: Forecasting enrollments with fuzzy time series - part II. Fuzzy Sets Syst. 62, 1–8 (1994). https://doi.org/10.1016/0165-0114(93)90355-L 9. Chen, S.-M.: Forecasting enrollments based on fuzzy time series. Fuzzy Sets Syst. 81, 311–319 (1996). https://doi.org/10.1016/0165-0114(95)00220-0 10. Hwang, J.R., Chen, S.M., Lee, C.H.: Handling forecasting problems using fuzzy time series. Fuzzy Sets Syst. 100, 217–228 (1998). https://doi.org/10.1016/s0165-0114(97)00121-8 11. Lee, H.S., Chou, M.T.: Fuzzy forecasting based on fuzzy time series. Int. J. Comput. Math. 81, 781–789 (2004). https://doi.org/10.1080/00207160410001712288 12. Singh, S.R.: A simple method of forecasting based on fuzzy time series. Appl. Math. Comput. 186, 330–339 (2007). https://doi.org/10.1016/j.amc.2006.07.128

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Internally Stable Set in Intuitionistic Fuzzy Graph Cengiz Kahraman1

, Alexander Bozhenyuk2(B)

, and Margarita Knyazeva2

1 Department of Industrial Engineering, Istanbul Technical University, Besiktas, 34367 Istanbul,

Turkey 2 Southern Federal University, Nekrasovsky Street 44, 347922 Taganrog, Russia

[email protected]

Abstract. In this paper, the idea of maximum intuitionistic internally stable vertex subset of graph with fuzzy intuitionistic stability degree is considered. The notion of an internally stable set is introduced as some invariant of an intuitionistic fuzzy graph. Here an intuitionistic fuzzy graph is considered as a pair consisting of a crisp set of vertices and an intuitionistic fuzzy set of undirected edges. The paper considers an approach for finding all maximal intuitionistic internally stable subsets of vertices, as a method extension for calculating all maximal internally stable subsets in a crisp graph. The method that allows estimating all maximal internally stable subsets in a fuzzy graph with the highest degree of stability is considered. An example illustrating the operation of the method for finding the internally stable set of the intuitionistic fuzzy graph is also represented in this article. Keywords: Intuitionistic fuzzy graph · Invariant · Fuzzy subgraph · Maximum intuitionistic internally stable subset · Intuitionistic separability degree

1 Introduction Graph theory is an important tool for solving many problems in various fields, including computer science, optimization methods, operations research, social network analysis, etc. Crisp graphs are made up of vertices and edges, which are all deterministic. However, the adjacency between vertices is not always completely defined, since in a real situation the system describing the connections between elements (graph vertices) can be much more complicated. Therefore, such a system cannot be represented by a classical crisp graph, and therefore we need a tool to deal with various uncertainties. In 1965, L. Zadeh proposed to consider non-deterministic phenomena using fuzzy set theory [1]. After that, some researchers used fuzzy set theory to process fuzzy phenomena in graph theory. In 1973, in the paper [2], a fuzzy graph with a crisp set of vertices and a fuzzy set of edges was proposed. In 1975, in the paper [3], fuzzy graph structures were considered, which are fuzzy graphs with a fuzzy set of vertices and a fuzzy set of edges. In 1983, in [4], the idea of fuzzy sets with intuitionistic components was considered as another form of fuzzy sets representation. A new component has been added to © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 566–572, 2022. https://doi.org/10.1007/978-3-031-09173-5_65

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the definition of a fuzzy set - the degree of non-membership. Unlike traditional fuzzy sets, intuitionistic aspects of fuzzy sets both define the degree of membership and nonmembership independently of each other. Thus, intuitionistic fuzzy sets are higher-order sets than traditional fuzzy sets. In [5, 6], the concept of an intuitionistic fuzzy graph was introduced in the form of a structure consisting of intuitionistic sets of vertices and edges. In papers [7–9] the characteristics of intuitionistic fuzzy graphs were introduced - dominating set, regular independent set, dominance number of dominating edges. In [10, 11], the concepts and methods for finding the dominating set and the set of bases of an intuitionistic fuzzy graph with a crisp set of vertices were considered. The paper aims to propose the notions of a maximum internally stable subset of vertices, its intuitionistic stability degree, and the set of internal stability of an intuitionistic fuzzy graph. These notions are a generalization the maximum internally stable subset of traditional and fuzzy graphs [12, 13]. This paper has the follow structure: In the second section of the paper, we observe preliminaries. The third section describes the internal stability set for intuitionistic fuzzy graphs. The fourth section studies a proposed method and an algorithm of internal stability set calculation. Finally, findings and future scope section concludes the paper.

2 Preliminaries Let’s consider X be a non-empty set. The fuzzy set A˜ on the set X is defined as the set of pairs A˜ = {< μA (x), x > |x ∈ X } [1]. Here μA : X → [0, 1] is a membership function that associates each element x with some value from the interval [0,1]. The intuitionistic fuzzy set B˜ on the set X can be formalized as the following set of triples: B˜ = {< μB (x), νB (x), x > |x ∈ X } [4]. Here μB : X → [0, 1] is also a membership function, νB : X → [0, 1] is a non-membership function, and the functions μB and νB are such that they satisfy the condition (∀x ∈ X)[μA (x) + νA (x) ≤ 1]. Denote by p˜ and q˜ the intuitionistic fuzzy variables having the form: p˜ = (μp , νp ) and q˜ = (μq , νq ), where μp + νp ≤ 1 and μq + νq ≤ 1. Then the operations “&” and “∨” are defined respectively [14]:     p˜ &˜q = (min μp , μq , max νp , νq ), (1)     p˜ ∨ q˜ = (max μp , μq , min νp , νq ).

(2)

    We assume that p˜ ≤ q˜ if the inequalities μp ≤ μq and νp ≥ νq hold. ˜ = (V , R), ˜ with V being a traditional crisp set of A fuzzy graph [15, 16] is a pair G ˜ vertices and R being a fuzzy relation on the set V × V , where the edges connecting the vertices V have the membership function μR : V × V → [0, 1]. ˜ = (V , U˜ ). Here set V is a set of crisp An intuitionistic fuzzy graph [5, 6] is a pair G ˜ graph vertices, set U =< V × V , μ, ν > is a set of intuitionistic fuzzy edges for which (∀x, y ∈ V )[0 ≤ μ(x, y) + ν(x, y) ≤ 1].

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3 Internal Stability Set ˜ = (V , U˜ ). Denote by p(x, y) = (μ(x, y), ν(x, y)) Consider an intuitionistic fuzzy graph G the intuitionistic fuzzy variable and it corresponds to the degree of adjacency and degree of non-adjacency of vertices x, y ∈ X. In what follows, we will consider an undirected graph for which: (∀x, y ∈ V )p(x, y) = p(y, x). Definition 1. The quantity δ(x, y) = (ν(x, y), μ(x, y)) is called the intuitionistic separability degree of the vertices x and y. The intuitionistic separability degree of vertices is a kind of extension nonadjacency idea of vertices for a crisp graph [13] and the degree of separability of vertices for a fuzzy graph [12, 16]. ˜ Let ψ ⊆ V be an arbitrary subset of vertices of the graph G. Definition 2. The quantity γ (ψ) = degree of subset ψ.

& δ(x, y) is called the intuitionistic separability

∀x,y∈ψ

˜ is called a maximal internally Definition 3. A subset ψ of an intuitionistic fuzzy graph G stable subset if for any subset of vertices X ⊃ ψ the degree of separability is less than that of the subset ψ: (∀X ⊆ V )[ψ ⊂ X → γ (ψ) > γ (X )]. ˜ 1 shown in Fig. 1. The subset of Example 1. Consider the intuitionistic fuzzy graph G vertices ψ 1 = {x 1 , x 2 } has the intuitionistic separability degree γ (ψ 1 ) = (0.3, 0.6), but is not maximal internally stable, since the set V = {x 1 , x 2 , x 3 } has the same degree of separability - γ (V ) = (0.3, 0.6) & (0.7, 0.2) & (1,0 ) = (0.3, 0.6). The subset ψ 2 = {x 1 , x 3 } is maximal internally stable with degree γ (ψ 2 ) = (1, 0).

x2 . ,0 7)

(

)

.2 (0

3 ,0. 6 . 0

x1

x3

˜ 1. Fig. 1. Intuitionistic fuzzy graph G

Consider the family {ψk1 , ψk2 , ..., ψkl } of all maximal internally stable subsets, including k vertices and having degrees of internal stability γk1 , γk2 , ..., γkl , respectively. Denote by γk0 = γk1 ∨ γk2 ∨ ... ∨ γkl the value that means that the graph has a maximum internally stable subset that includes k vepxin vertices, and it has a degree of internal stability γk0 . In addition, there is no other maximal internally stable subset ∼

with k vertices graph G whose degree is greater than γk0 .

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Let T1 = {ψ11 , ψ12 , ..., ψ1N1 } and T2 = {ψ21 , ψ22 , ..., ψ2N2 } be families of maximal internally stable sets with degrees of internal stability γ1 and γ2 respectively. Let the inequality γ1 < γ2 be satisfied, then lets consider the following properties: Property 1. N 1 ≥ N 2 ; Property 2. (∀ψ2 ∈ T2 )[∃ψ1 ∈ T1 |ψ2 ⊆ ψ1 ]. Definition 4. An intuitionistic fuzzy set ∼  = {< γ10 /1 >, < γ20 /2 >, ..., < γn0 /n >} ˜ is the internal stability set of the graph G. ˜ is its invariant, that is, it The internal stability set of the intuitionistic fuzzy graph G is not going to be changed within the different structural transformations of the graph itself. ˜ presented in Fig. 1, the internal stability set will look like: Example 2. For the graph G ∼

 = {< (1, 0)/1 >, < (1, 0)/2 >, < (0.3, 0.6)/3 >}.

4 Internal Stability Set Calculation Method Let us now consider an approach to finding all maximal internally stable subsets of vertices of an intuitionistic fuzzy graph with a computed internal stability degree. The internal stability set is directly determined from the computed maximum internally stable subsets. Let ψ ∈ V be some internally stable subset with an intuitionistic degree of internal stability γ (ψ). Then, for arbitrary vertices xi , xj ∈ V , one of the three conditions is / ψ; xj ∈ / ψ; or xi ∈ ψ &xj ∈ ψ. satisfied: xi ∈ In the latter case, the intuitionistic degree of internal stability does not exceed the separability degree of vertices x i and x j : γ (ψ) ≤ δ(xi , xj ). From this it will follow that the following expression is true: / ψ ∨ xj ∈ / ψ ∨ (γ (ψ) ≤ δ(xi , xj ))]. (∀xi , xj ∈ V )[xi ∈

(3)

We associate with each vertex xi ∈ V a Boolean variable p(xi ), hat takes the value 1 / ψ. if xi ∈ ψ and 0 if xi ∈ Constructing the Eq. (3) to manage i and j indices, we will get the following statement:  = & & (p(xi ) ∨ p(xj ) ∨ δ(xi , xj )). i j =i

(4)

After that opening the brackets and applying the absorption rules for the same terms, we get the following equation: p1 ∨ p1 &p2 = p1 ; p1 &γ 1 ∨ p1 &p2 &γ 2 = p1 &γ 1 .

(5)

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Here p1 , p2 ∈ {0, 1}; γ1 , γ2 - intuitionistic fuzzy variables for which the inequality γ1 ≥ γ2 is satisfied. As a result, the expression (4) will be presented as the expression (6):  = ∨ (p(x1i )&p(x2i )&...&p(xki )&γi ).

(6)

i=1,l

Property 3. If considering the expression (6) the further steps of simplification based on rules (5) are not possible, then the expression (6) determines all maximal internally stable subsets of vertices. Namely, each i-th disjunctive term defines the maximum internally stable subset, which includes those vertices whose variables are not included in the considered disjunctive term. In this case, the value γi will be the intuitionistic degree of internal stability of the computed maximum internally stable subset. Using the property 3, the following algorithm for constructing an internally stable set of an intuitionistic fuzzy graph is proposed: 1. We determine all the maximum internally stable sets of a subset of vertices, with calculated degrees of internal stability; 2. By enumeration of all maximal internally stable sets with the same number of vertices, we calculate the greatest degree of internal stability; 3. According to the greatest degrees of internal stability found, we write down the internally stable set of the considered graph.

5 Example of Calculating an Internally Stable Set Consider an example of finding an internally stable set for the fuzzy intuitionistic graph ˜ 2 , shown in Fig. 2: G

x2 2) ,0. .5 (0

) 0.3 , 6 (0. (0.3,0.6)

x1

x3

(0 ) .3 ,0 .7

x4

˜ 2. Fig. 2. Intuitionistic fuzzy graph G

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The adjacency matrix for the considered graph will look like:

Using the adjacency matrix, we write expression (4):

We multiply brackets 1 and 2, brackets 3 and 4, and applying the rules (5) we get:

Multiplying the resulting brackets, we finally get:

Further simplification based on rules (5) is impossible. Therefore, it follows from ˜ 2 has 10 maximal internally stable the resulting expression that the considered graph G subsets - {x 3 , x 4 }, {x 2 , x 4 }, {x 1 } with degree (1,0); {x 2 , x 3 , x 4 }, {x 1 , x 2 , x 3 } with degree (0.2,0.5); {x 1 , x 3 , x 4 }, {x 1 , x 2 , x 4 } with degree (0.3, 0.7); {x 1 , x 3 } with degree (0.6,0.3); {x 1 , x 2 } with degree (0.3,0.6); {x 1 , x 2 , x 3 , x 4 } with degree (0.2, 0.7). Hence, the internally stable set of the graph will look like: ∼

 = {< (1, 0)/1 >, < (1, 0)/2 >, < (0.2, 0.5)/3 >, < (0.2, 0.7)/4 >}.

6 Findings and Future Scope In this article, the concepts of the maximum internally stable subset of vertices and the internally stable set of an intuitionistic fuzzy graph were introduced. The approach and the method for finding the family of all maximal internally stable subsets of vertices with computed degree are proposed. This approach is a generalization of the approach for crisp and fuzzy graphs. This approach can be applied to handle different graphbased problems on intuitionistic fuzzy graphs. It should be noted that the proposed method can be effectively applied for analysis of intuitionistic fuzzy graphs with nonhomogeneous structure and sufficiently small and medium problem dimensions. An example was carried out to illustrate the proposed method. In the future, the proposed method of finding all the maximum internally stable subsets will allow us to propose an approach for considering the coloring problems for these graphs. Acknowledgments. The reported study was funded by RFBR, the research project N20-0100197.

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References 1. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965). https://doi.org/10.1016/S0019-995 8(65)90241-X 2. Kaufmann, A.: Introduction a la theorie des sous-ensembles flous. Masson, Paris 1, 41–189 (1973) 3. Rosenfeld, A.: Fuzzy graphs. In: Zadeh, L.A., Fu, K.S., Shimura, M. (eds.) Fuzzy Sets and Their Applications, pp. 77–95. Academic Press, New York (1975). https://doi.org/10.1016/ B978-0-12-775260-0.50008-6 4. Atanassov, K.T.: Intuitionistic fuzzy sets. In: Proceedings of VII ITKR’s Session, Central Science and Technical Library, vol. 1697/84, pp. 6–24. Bulgarian Academy of Sciences, Sofia (1983) 5. Shannon, A., Atanassov K.T.: A first step to a theory of the intuitionistic fuzzy graphs. In: Lakov, D. (ed.) Proceeding of the FUBEST, pp. 59–61. Sofia, Bulgaria (1994) 6. Shannon, A., Atanassov, K.T.: Intuitionistic fuzzy graphs from α-, β- and (α, b)-levels. Notes Intuit. Fuzzy Sets 1(1), 32–35 (1995) 7. Karunambigai, M.G., Sivasankar, S., Palanivel, K.: Different types of domination in intuitionistic fuzzy graph. Ann. Pure Appl. Math. 14(1), 87–101 (2017). https://doi.org/10.22457/ apam.v14n1a11 8. Parvathi, R., Thamizhendhi, G.: Domination in intuitionistic fuzzy graphs. Notes Intuit. Fuzzy Sets 16, 39–49 (2010) 9. Velammal, S.: Edge domination in intuitionistic fuzzy graphs. Int. J. Comput. Sci. Math. 4(2), 159–165 (2012) 10. Bozhenyuk, A., Belyakov, S., Knyazeva, M., Rozenberg, I.: On computing domination set in intuitionistic fuzzy graph. Int. J. Comput. Intell. Syst. 14(1), 617–624 (2021). https://doi.org/ 10.2991/ijcis.d.210114.002 11. Bozhenyuk, A., Belyakov, S., Kacprzyk, J., Knyazeva, M.: The method of finding the base set of intuitionistic fuzzy graph. In: Kahraman, C., Cevik Onar, S., Oztaysi, B., Sari, I.U., Cebi, S., Tolga, A.C. (eds.) INFUS 2020. AISC, vol. 1197, pp. 18–25. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-51156-2_3 12. Bershtein, L.S., Bozhenuk, A.V.: Maghout method for determination of fuzzy independent, dominating vertex sets and fuzzy graph kernels. Int. J. General Syst. 30(1), 45–52 (2001). https://doi.org/10.1080/03081070108960697 13. Ore, O.: Theory of Graphs. American Mathematical Society, Providence, USA (1962) 14. Atanassov, K., Gargov, G.: Elements of intuitionistic fuzzy logic. Part I. Fuzzy Sets Syst. 95, 39–52 (1998). https://doi.org/10.1016/S0165-0114(96)00326-0 15. Trillas, E., Eciolaza, L.: Fuzzy relations. In: Fuzzy Logic. SFSC, vol. 320, pp. 117–129. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-14203-6_4 16. Bershtein, L., Bozhenyuk, A.: Fuzzy graphs and fuzzy hypergraphs. In: Dopico, J., de la Calle, J., Sierra, A. (eds.) Encyclopedia of Artificial Intelligence, Information SCI, pp. 704–709. Hershey, New York, (2008). https://doi.org/10.4018/978-1-59904-849-9.ch105

Investigation of Employer Attractiveness from an University Students Perspective by Application of Intuitionistic Fuzzy Assessments Milen Todorov, Gergana Avramova-Todorova, and Sotir Sotirov(B) “Prof. Dr. Assen Zlatarov” University, “Prof. Yakimov” Blvd., Burgas 8010, Bulgaria {mtodorov,ssotirov}@btu.bg, [email protected]

Abstract. The employer brand has a range of dimensions which can be specified as a product of a variety of influencing factors. The combination of those factors are closely related to the level of ‘employer attractiveness’, defined as “the envisioned benefits that a potential employee sees in working for a specific organization”. The paper identifies the significant factors which attract students from national university in south-east Bulgaria “Prof. Dr. Asen Zlatarov” to potential employers, both on a general basis and for specific student segments. Data was gathered from the students through a self-completion electronic questionnaire which includes a total of 35 items in four directions - social value, development value, application values and economic value. A generalized net model to analyze employer attractiveness from perspective of job seekers represented by university students. Intuitionistic fuzzy assessments for evaluation the attractiveness μ, unattractiveness ν of an employer and the degree of uncertainty π were proposed. Keywords: Intuitionistic fuzzy sets · Modelling · Employer attractiveness

1 Introduction From marketing point of view any product that can provoke attraction could be valuable for a certain customer. In general, each product can be presented as a set specific characteristics precisely selected to attract the attention of specific target group. Besides the group of “touchable” products that can be found on market shelves there is another group that could be advertised based on “untouchable attractiveness” such as job position in a business company or organization. Nowadays, the prosperity of business company is related to a complex mix of internal and external factors. These factors should be taken into account in order to achieve specific goals as well as to survive in current situation of business competition. Considering the internal marketing concept [7] one should mention the understanding that the organisation’s personnel are the first market of any company. Thus, one of the main goals of the management should include analysis of job seekers attitudes toward the company. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 573–580, 2022. https://doi.org/10.1007/978-3-031-09173-5_66

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Berthon, Ewing, and Hah [3] have related employer brand attractiveness set of factors based on focus groups responses. Following standard procedures in developing scales, the authors identify five factors: economic value (e.g. salary), interest value (e.g. interesting work), social value (e.g. enjoyable working environment), development value (e.g. advancement opportunities) and application value (e.g. opportunities to implement own knowledge). Several additional studies have identified job attributes as an aggregated measure to be important for employer brand attractiveness [10]. The employer attractiveness is discussed in [2, 4–6]. Dynamic changes that influence the labour markets on national or international level require continuous monitoring of both available and potential labour resources. Potential job seekers could be segmented based on different criteria. A specific group that is of special interest are university students. The key aspect that can be attributed to this group is that they normally have limited or no job experience. However, university students constantly shape their prospective vision about their forthcoming professional development. On a national (or even regional) level it will be valuable to survey the university student’s attitudes toward employers. The obtained information could be used successfully in collaborative activities between academic career centers and human resources departments [8]. The aim of this work is to identify the employee benefits that students from University “Prof. Dr. Asen Zlatarov”, Burgas relate to companies, for which they will work. A generalized net model with intuitionistic fuzzy evaluation the attractiveness μ, unattractiveness ν of an employer and the degree of uncertainty π as a results of student responses is proposed. The theory of intuitionistic fuzzy sets is used as a decision making tool for evaluation of a Human Factor [9]. The paper is organized as follows. Section 2 presents the methodology for data collection. In Sect. 3 an intuitionistic fuzzy assessments of the attractiveness μ, unattractiveness ν of an employer and the degree of uncertainty π are proposed. In Sect. 4 a constructed generalized net model is shown, Sect. 5 presents our conclusions. Section 5 and Sect. 6 are acknowledgments and references.

2 Data Collection For data collection, an electronic questionnaire has been sent to the students with active institutional profile. The questionnaire contained 35 questions related to economic value, interest value, social value, development value and application. The return rate was about 35% (clicked/responded by data from e-mail campaign), with a final number of 92 responses. The survey was attended by 36% (33) of students (1st, 2nd and 3rd year of education) and 64% (59) of graduates (4th year of education and masters). 77% of women and 23% of men participated in the study. The structure of the respondents does not differ from the structure of the University’s students, who are mostly female.

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3 Intuitionistic Fuzzy Evaluations Intuitionistic fuzzy sets represent an extension of the concept of fuzzy sets, showing the function μA (X) defining the presence of an element x to the set A, graded in the interval [0; 1]. The difference between fuzzy sets and intuitionistic fuzzy sets (IFSs, see [1]) is in the presence of a second function ν A (x) defining the non-membership of the element x to the set A, where μA (x) ∈ [0; 1], ν A (x) ∈ [0; 1], under the condition of μA (x) + ν A (x) ∈ [0; 1]. In addition to constructing a model, here we will define an assessment of the attractiveness μ, unattractiveness ν of an employer and the degree of uncertainty π. μ=

ai − Ak B−A

(1)

where μ ∈ [0; 1]; ai – current value; Ak – local minimum; Bk – local maximum; B – global maximum; A - global minimum; non-affiliation coefficient – ν, reflecting the degree of saturation of the nutrient medium, ν=

Bk − ai B−A

(2)

where ν ∈ [0; 1]; and a coefficient of uncertainty reflecting the degree of inertia and inaccurate measurement of the parameters by the measuring instruments π =1−μ−ν

(3)

μk+1 , νk+1  = max μall , min νall 

(4)

Optimistic formula:

where: μall = (μ0 , μ1 , ..., μk ), k ∈ [0, 1, 2, ..., l − 1], νall = (ν0 , ν1 , ..., νk ), k ∈ [0, 1, 2, ..., l − 1] Strongly optimistic formula: μk+1 , νk+1  = μk+1 + μk − μk+1 .μk , νk. .νk+1. 

(5)

Pessimistic formula: μk+1 , νk+1  = min μall , max νall  where: μall = (μ0 , μ1 , ..., μk ), k ∈ [0, 1, 2, ..., l − 1], νall = (ν0 , ν1 , ..., νk ), k ∈ [0, 1, 2, ..., l − 1]

(6)

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Strongly pessimistic formula: μk+1 , νk+1  = μk+1 .μk , νk+1 + νk − νk .νk+1 

(7)

4 A Generalized Net Model In our investigation we work with n responders, i = 1, 2,…, n; q electronic questionnaires, l = 1, 2,…, q, and m questions in the electronic questionnaire, k = 1, 2,…, m. The GN-model is presented on Fig. 1. It contains 6 transitions and 21 places. In the beginning, α and β tokens stay in places l3 and l 7 , and they will be there during the whole time of the functioning the GN. This tokens may split into two or three tokens that will pass through transitions Z 1 and Z 2 respectively. The original α and β tokens have the following initial and current characteristics:

Z3

Z1 l2

l1

l8

l3

l4

Z2

Z6

Z5

Z4 l10

l16

l11

l17

l12

l18 l19

l5

l20

l13

l6 l7

l9

l14

l20

Fig. 1. Structure of a MLP

– token α: “data base with electronic questionnaires” (in place l3 ), – token β: “list of the respondents” (in place l7 ), The forms of the transitions are the following.

Investigation of Employer Attractiveness from an University Students Perspective

where: w3,2 = “The questionnaire is chosen”.

where: w7,5 = “The respondents are determined”, w7,6 = “The questionnaire is estimated”.

where: w9,8 = “The electronic questionnaire l is fill out”.

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where: w14,10 = “The degree of satisfaction for question k in the questionnaire is evaluated”, w14,11 = “The degree of non-satisfaction for question k in the questionnaire is evaluated”, w14,12 = “The degree of uncertainty for question k in the questionnaire is evaluated”, w14,13 = “There are no another questions in the questionnaire”. The γ1 , γ2 , …, γn tokens that enter place l14 do not obtain new characteristic. The ϕ tokens that enter place l 15 from place l 20 merge in δ token with characteristic. “current status of the intuitionistic fuzzy estimations of the electronic questionnaire l”. In every step δ token extends its previous characteristic with the next evaluated question k in the electronic questionnaire l. When there are no another questions in the questionnaire (predicate w14,13 has value “true”), the δ token enters place l 13 without new characteristic. The δ1 , δ2 and δ3 tokens that enter places l 10 , l 11 , and l12 obtain characteristics respectively:

where:

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  o according optimistic formula w19,15 = “The intuitionistic fuzzy estimation μol,k , ηl,k for question k in the questionnaire l is evaluated”,   so according strong optimistic w19,16 = “The intuitionistic fuzzy estimation μso , η l,k l,k formula for question k in the questionnaire l is evaluated”,  p p w19,17 = “The intuitionistic fuzzy estimation μl,k , ηl,k according pessimistic formula for question k in the questionnaire l is evaluated”,   sp sp w19,18 = “The intuitionistic fuzzy estimation μl,k , ηl,k according strong pessimistic formula for question k in the questionnaire l is evaluated”. The δ1 , δ2 and δ3 tokens that enter place l19 merge in new ϕ token with characteristic “Questionnaire l, question k, μAll = (μ0 , μ1 , …, μk ), ν All = (ν 0 , ν 1 , …, ν k )”. The ϕ1 , ϕ2 , ϕ3 and ϕ4 tokens that enter places l15 , l 16 , l 17 and l 18 obtain characteristic respectively:

The ϕ1 , ϕ2 , ϕ3 or ϕ4 tokens that enter place l20 do not obtain new characteristic.

5 Conclusion In this study, a generalized net model for analysis of employer attractiveness based on data obtained by responses from university students in University “Prof. Dr. Asen Zlatarov” located in Burgas, Bulgaria is proposed. It is expected that the results will supports employers to adapt their job offer proposition to attract the attention of recently university graduates.

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As part of previous presented generalized net model [10] which includes three components this article describes the role of first one – employer (company) attractiveness. The second one - emotional intelligence and the third that’s is concept of “work-life balance” will be investigated in further research work. Acknowledgment. The authors are grateful for the support provided by the Bulgarian National Science Fund under Grant Ref. No. KP-06-N22/1/2018 “Theoretical research and applications of InterCriteria Analysis”. The authors declare that there is no conflict of interest regarding the publication of this paper.

References 1. Atanassov, K.T.: On Intuitionistic Fuzzy Sets Theory. Springer, Heidelberg (2012). https:// doi.org/10.1007/978-3-642-29127-2 2. Ariyanto, R., Kustini, K.: Employer branding and employee value proposition: the key success of startup companies in attracting potential employee candidates. Ann. Hum. Resour. Manage. Res. 1(2), 113–125 (2021). https://doi.org/10.35912/ahrmr.v1i2.728 3. Berthon, P., Ewing, M., Hah, L.L.: Captivating company: dimensions of attractiveness in employer branding. Int. J. Advert. 24(2), 151–172 (2005) 4. Dauth, T., Schmid, S., Baldermann, S., Orban, F.: Nationality diversity in the executive suite: does it influence employer attractiveness for foreign job seekers? Eur. Manage. J. (2021). Elsevier.https://doi.org/10.1016/j.emj.2021.10.007 5. Gradinarova, B., Bakardjieva, T., Gradinarova, M.: Some aspects of application of software agents in information retrieval in virtual-based educational environments. In: Kumar, D., Turner, J. (eds.) Education for the 21st Century — Impact of ICT and Digital Resources, pp. 315–319. Springer US (2006). https://doi.org/10.1007/978-0-387-34731-8_37 6. Kapu´sci´nski, G., Zhang, N., Zeng, L., Cao, A.: Effects of crisis response tone and spokesperson’s gender on employer attractiveness. Int. J. Hosp. Manage. 94, 102884 (2021). https:// doi.org/10.1016/j.ijhm.2021.102884 7. Kotler, P.: Marketing Management: Analysis, Planning, Implementation and Control, 8th edn. Prentice-Hall Inc., Englewood Cliffs, NJ (1994) 8. Todorov, M., Avramova-Todorova. G., Sotirov S.: Generalized network model for career guidance using emotional intelligence, self-assessment and attitudes toward the employer. In: Big Data, Knowledge and Control Systems Engineering (BdKCSE), pp. 1–4 ((2021)) 9. Traneva, V., Tranev, S.: InterCriteria analysis of the human factor assessment in a mobile company. In: Georgiev, I., Kostadinov, H., Lilkova, E. (eds.) BGSIAM 2018. SCI, vol. 961, pp. 381–392. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-71616-5_34 10. Wilden, R., Gudergan, S., Lings, I.: Employer branding: strategic implications for staff recruitment. J. Mark. Manag. 26(1–2), 56–73 (2010)

Digital Interpretation of Movie Sales Revenue Through Intuitionistic Fuzzy Analysis of Variance Velichka Traneva(B)

and Stoyan Tranev

“Prof. Asen Zlatarov” University, “Prof. Yakimov” Blvd, Bourgas 8000, Bulgaria [email protected], [email protected] http://www.btu.bg Abstract. The Covid-19 pandemic has accelerated the digital transformation of the industry with the rapid adoption of digital technologies and created a digital economy. As a consequence of digitalization, business intelligent systems have been created that analyze data in order to support management decisions. Analysis of variance (ANOVA) is a basic method in data analysis. The galloping inflation and the pandemic lead to accumulation of unclear data in business. The classical methods for analysis cannot handle their processing. To solve the problem, we extended ANOVA to the intuitionistic fuzzy IFANOVA so that it can process intuitionistic fuzzy observations rather than clear numbers. The proposed new approach combines the advantages of ANOVA and the concepts of intuitionistic fuzzy logic and index matrices. A software utility for IFANOVA was created in order to digitize the calculations. The paper applies IFANOVA on a unique set of data from a Cinema City Bulgaria multiplex to analyze the dependencies of ticket sales for the premieres of the films “Heights” and “Avengers” by the factor “day of the week”. The proposed IFANOVA can be used to modernize intelligent business systems in uncertainty. Keywords: IFANOVA Management

1

· Index matrix · Intuitionistic fuzzy logic ·

Introduction

In the context of a pandemic and rising inflation, there is a need to improve decision-making algorithms so that they can be applied to unclear or inaccurate data. ANOVA is a popular method in the data analysis, developed by Fisher [12]. There are some unavoidable cases in the experiments, which could be the cause for the vagueness in the recorded data due to human errors in measuring, information noise, etc. The classical apparatus of ANOVA cannot analyze unclear numbers. The fuzzy logic [32] and its extensions are used as an artificial intelligence tool for modelling. Intuitionistic fuzzy sets (IFSs, [2]) are an extension of Supported by the Asen Zlatarov University under Project NIX-440/2020 “Index matrices as a tool for knowledge extraction”. c The Author(s), under exclusive license to Springer Nature Switzerland AG 2022  C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 581–588, 2022. https://doi.org/10.1007/978-3-031-09173-5_67

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fuzzy sets that have a degree of hesitancy compared to them. In this research work, the dependencies of movie sales of the premieres “Heights” and “Avengers” by “day of the week” factor will be studied using the one-way IFANOVA [31] over a Cinema City Bulgaria multiplex data. The dependencies between the studied factors and the ticket sales are compared and analyzed through the classical variation analysis and IFANOVA. The originality of the research is caused by an intuitionistic fuzzy interpretation of ANOVA through the use of the IMs tools on the one hand, and on the other - the application of IFANOVA on real data to determine the dependencies of ticket sales of the premieres of the films “Heights” and “Avengers” “day of the week” factor. The remaining paper has the following structure: Sect. 2 presents a short literature review. Section 3 describes some basic definitions of the formalisms of IMs and intuitionistic fuzzy logic. Section 4 describes the classical ANOVA and analyze its application over the ticket sales of the premieres of “Heights” and “Avengers” on “day of the week” factor. Section 5 introduces the indexed-matrix IFANOVA. The proposed algorithm of IFANOVA is applied over the intuitionistic fuzzy data about the ticket sales of the movies “Avengers” and “Heights” to find the dependencies of ticket sales “day of the week” factor and also compares the results of IFANOVA with those obtained from classical ANOVA. Section 6 offers the conclusion and marks aspects for future research.

2

Literature Review

In the current section we presents some current works on ANOVA in fuzzy and intuitionistic fuzzy environment. Two different approaches to one-way ANOVA are developed in [19], based on fuzzy random variables [24]. A method for ANOVA using the data including vagueness is proposed in [18], based on removing the influence of vagueness for sum of squares using the moment correction. A bootstrap approach to FANOVA is described in [13]. FANOVA is considered in [9] using the confidence intervals for variance parameter. An algorithm for testing of one-way FANOVA is proposed by [15,16] using triangular fuzzy data. One-way FANOVA, by applying of Zadeh’s extension principle, is studied in [20]. An ANOVA test, based on least squares approach for fuzzy variables is provided in [14]. Another method for FANOVA is presented in [22] over normal fuzzy numbers, extending the classical ANOVA. In [17], the application of IFSs to find the homogeneity among students using ANOVA by transforming IFSs to fuzzy sets is proposed. One-way FANOVA model is described through transformation of intuitionistic fuzzy data into crisp [1]. FANOVA over triangular fuzzy numbers was proposed in [15,16]. Extending the classical one-factor analysis of variance [21] through the view of index matrices (IMs, [3]) and intuitionistic fuzzy logic of Atanassov [4], we have proposed intuitionistic fuzzy ANOVA (IFANOVA) [31] to analyze the intuitionistic fuzzy data caused by high inflation and the changeable epidemic situation. The digital transformation of IFANOVA has been realized through the developed software application in [30].

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Short Remarks on IMs and Intuitionistic Fuzzy Logic

3.1

Intuitionistic Fuzzy Pairs

An intuitionistic fuzzy pair (IFP) has the form a, b = μ(p), ν(p), where a, b ∈ [0, 1] and a + b ≤ 1, that are used as evaluation of a proposition p [4,8]. Let us have two IFPs x = a, b and y = c, d. Basic operations are described in [4,6,8,10,25]. Let Ra,b = 0.5(2 − a − b)(1 − a) [26]. Then, as per [4,31]: x ≥ y iff b ≤ d; x ≥R y iff Ra,b ≤ Rc,d . 3.2

(1)

Definition of Intuitionistic Fuzzy Index Matrix

Let I be a fixed set. By two-dimensional intuitionistic fuzzy index matrix (2-D IFIM) with index sets K and L (K, L ⊂ I), we denote the object [5]: l1 k1 μk1 ,l1 , νk1 ,l1  [K, L, {μki ,lj , νki ,lj }] ≡ . .. .. . km μkm ,l1 , νkm ,l1 

... lj . . . μk1 ,lj , νk1 ,lj  .. .. . . . . . μkm ,lj , νkm ,lj 

... ln . . . μk1 ,ln , νk1 ,ln  , .. .. . . . . . μkm ,ln , νkm ,ln 

where for every 1 ≤ i ≤ m, 1 ≤ j ≤ n: 0 ≤ μki ,lj , νki ,lj , μki ,lj + νki ,lj ≤ 1. On 2-D IFIMs A and B are defined operations similar to those with the classical matrices, but there are also specific ones such as addition, transposition, multiplication, projection, substitution, aggregation operations, internal subtraction of IMs’ components, term-wise multiplication and subtraction, defined in [5,27– 29,31].

4

One-Way ANOVA to the Movie Sales of “Heights” and “Avengers”

In this section, the classical one-way ANOVA is applied to the real movie sales of the premiere films “Heights” and “Avengers” of Cinema City Bulgaria, a part of Cineworld PLC Group, to investigate the relationships between their sales and “day of the week” factor. The ANOVA approach were proposed by Fisher [12]. Let yki ,lj (i = 1, 2, ..., m and j = i1 , i2 , ...iI (1 ≤ iI ≤ n)) are the data from the ki −th level of the factor and lj −th observation. Let N is the number of observations. ANOVA has been applied to accept/reject hypothesis H0 : all Mki are equal, against H1 : not all Mki are equal, where Mki (i = 1, 2, ..., m) are the level means of A. The mean sums of squares for error M SE, the mean sums of squares for treatment M SC and the mean sum of squares M ST , are calculated according to [21]. The decision rule is F =

M SC 1 M SE 1 = F(1−α,N −m,m−1) , ≥ F(α,m−1,N −m) or = ≤ M SE F M SC F(α,m−1,N −m)

(2)

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V. Traneva and S. Tranev Table 1. ANOVA table by “day of the week” factor for “Heights” Source

SS

Between groups 169588,86

df MS

F

p-value F crit

6 28264,81 3,66 0,012

Within groups

162356

21 7731.24

Total

331945

27

2,57

Table 2. ANOVA table by “day of the week” factor for “Avengers” Source

SS

Between groups 4889514

df MS

F

p-value F crit

6 720824,33 0,89 0,52

Within groups

22813553,6 28 814769,77

Total

27138499,6 34

2,45

where F(α,m−1,N −m) is α−quantile of F −distribution with m − 1 and N − m degrees of freedom, then hypothesis H0 is a false null hypothesis on significance level α [11,12]. We verify the normality of the data distribution by the Kolmogorov-Smirnov test [11] at the significance level of 5%. The “day of the week” factor has seven levels – from Monday to Sunday. The one-way ANOVA using the software SPSS is applied on the monthly sales of the two premiere films “Heights” (2-D) and “Avengers” (3-D). The results from ANOVA by “day of the week” factor for the movies “Heights” and “Avengers” are presented in Table 1 and Table 2 at a significance level of 5%: Then we compare the ANOVA test statistics with the critical values of ANOVA test. The conclusions of ANOVA are that the “day of the week” factor has influence over the amount of ticket sales for the premiere movie “Heights”, but for the movie “Avengers” – this factor does not affect the amount of ticket sales. The Fig. 1 compares the ticket sales of the movies “Heights” and “Avengers” for a month: The conclusions after the application of ANOVA are as follows: – The ticket sales for the movie “Avengers” are the highest on Tuesday (the price is the lowest compared to the other days of the week) and for the movie “Heights” - on Thursday, which is due to the lowest price. – The ticket sales for the movie “Avengers” for a month are 4, 5 times higher than those for the movie “Heights”. Customers prefer three-dimensional projection over two-dimensional projection due to the effects of projection. – On Monday and Wednesday, customers have less motivation to go to the cinema. – On Tuesday, increased cinema attendance was due to the reduced ticket price of movie “Avengers”. On Thursday, the increased attendance at the cinema

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Fig. 1. Number of tickets on “day of the week” factor for a month.

is explained by the reduced ticket price for the movie “Heights”. On Saturday and Friday, attendance is the highest compared to the other days of the week. The conclusions can help the manager in the decision-making process on revenue growth of the multiplex by increasing the price of the tickets on Friday and Saturday and reducing it on Monday and Wednesday.

5

Intuitionistic Fuzzy Approach to One-Way ANOVA by “Day of the Week” Factor

In [31], we have proposed one-way IFANOVA, combining the advantages of classical variational analysis and the concepts of intuitionistic fuzzy logic and IMs. In this section, IFANOVA is applied to explore the dependence between the levels of “day of the week” factor for the ticket sales of the movies “Avengers” and “Heights” for a month using the same values as these in the section (4). The data values about the ticket sales for the two movies need to be transformed into intuitionistic fuzzy using the method specified in [4] before the algorithm starts. We obtain two IFIM Y [K, L/{Sr1 , Sr}] and Z[K, L/{Sr1 , Sr}] without the last two columns with monthly sales by the “day of the week” factor respectively for the premiere films “Avengers” and “Heights”:

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M onday T uesday W ednesday Y = T hursday F riday Saturday Sunday

l1 l2 l3 l4 l5 0, 31; 0, 69 0, 19; 0, 81 0, 11; 0, 89 0, 01; 0, 99 0; 1 0, 89; 0, 11 0, 56; 0, 44 0, 17; 0, 83 0, 10; 0, 90 0, 08; 0, 67 0, 25; 0, 75 0, 18; 0, 82 0, 07; 0, 93 0, 02; 0, 98 0, 02; 0, 98 0, 36; 0, 64 0, 16; 0, 84 0, 03; 0, 97 0, 01; 0, 99 0, 01; 0, 99 1; 0 0, 33; 0, 67 0, 23; 0, 77 0, 06; 0, 94 0, 05; 0, 95 0, 58; 0, 42 0, 49; 0, 51 0, 22; 0, 78 0, 02; 0, 98 0, 04; 0, 96 0, 55; 0, 45 0, 43; 0, 57 0, 16; 0, 84 0, 01; 0, 99 0, 01; 0, 99

M onday T uesday W ednesday Z= T hursday F riday Saturday Sunday

l1 l2 l3 l4 0, 21; 0, 78 0, 24; 0, 75 0, 09; 0, 90 0, 05; 0, 94 0, 43; 0, 56 0, 31; 0, 6 0, 17; 0, 82 0, 10; 0, 90 0, 11; 0, 88 0, 06; 0, 93 0, 04; 0, 95 0, 17; 0, 82 0, 92; 0, 07 0, 76; 0, 23 0, 42; 0, 57 0, 27; 0, 72 0.51; 0.48 0, 28; 0, 71 0, 17; 0, 82 0, 03; 0, 96 0, 62; 0, 37 0, 46; 0, 53 0, 37; 0, 62 0, 22; 0, 77 0, 55; 0, 44 0, 52; 0, 47 0, 29; 0, 70 0, 17; 0, 82

The software utility “Test1”, which performs IFANOVA, was developed in [30]. The computational results from the “Test1” by “day of the week” factor for the ticket sales of the movies “Avengers” and “Heights”, printed on the console are: M SCAvengers = 0.03, 0.566, M SEAvengers = 0.001, 0.97 M SCHeights = 0.014, 0.9856 and M SEHeights = 0.005, 0.985. The fuzzy estimators of the IFANOVA key statistics FAvengers and FHeights are obtained applying Pietraszek’s approach [23]. The classic variation analysis key statistic FAvengers (0, 95; 28; 6) = 0, 41 is transformed in the fuzzy indicator Ff uzzy,Avengers(0,95;28;6) = 0, 92; 0 and the classic key statistic FHeights (0, 95; 21; 6) = 0, 39 is transformed in the fuzzy criterion Ff uzzy,Heights(0,95;21;6) = 0, 92; 0. Therefore 0, 043; 0.936 =

1 ≤ Ff uzzy,Avengers(0,95;28;6) = 0, 92; 0 and FAvengers

0, 36; 0 =

1 ≤ Ff uzzy,Heights(0,95;21;6) = 0, 90; 0 FHeights

The “day of the week” factor has an influence the amount of the ticket sales for both premieres. When we compare the results of IFANOVA with those obtained by ANOVA by “day of the week” factor for both movies, it can be concluded that the results are disagree in the influence of the “day of the week”

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factor for the film “Heights”, which due to the high degree of the hesitancy of the test statistic 1 = 0.36, 0. FHeights

6

Conclusion

In this research work, one-way IFANOVA [31] is proposed as a tool for intuitionistic fuzzy transformation of the classical method for variation analysis over a unique data from a Cinema City Bulgaria multiplex, to analyze the dependency of the movie sales from the premieres of “Heights” and “Avengers” by “day of the week” factor. The dependencies between the levels of the studied factor and IFP values of the ticket sales were obtained. The results of IFANOVA and ANOVA about the studied factor for the two movies shows that they differ in the influence of “day of the week” factor for “Heights”, due to the high degree of the hesitancy of the test statistic 1/FHeights . In future, the proposed IFANOVA will be digitized and integrated into intelligent business decision-making systems in a vague environment. IFANOVA’s proposed approach will be extended so that it can be applied to interval-valued intuitionistic fuzzy data [7].

References 1. Anuradha, D., Kalpanapriya, D.: Intuitionistic fuzzy ANOVA and its application in medical diagnosis. Res. J. Pharm. Technol. 11(2), 653–656 (2018) 2. Atanassov, K.: Intuitionistic fuzzy sets. In: Proceedings of VII ITKR’s Session, Sofia (1983). (in Bulgarian) 3. Atanassov, K.: Generalized index matrices. Comptes rendus de l’Academie Bulgare des Sciences 40(11), 15–18 (1987) 4. Atanassov, K.: On Intuitionistic Fuzzy Sets Theory. STUDFUZZ. 283. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29127-2 5. Atanassov, K.T.: Index Matrices: Towards an Augmented Matrix Calculus. SCI, vol. 573. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10945-9 6. Atanassov, K.: Remark on an intuitionistic fuzzy operation “division”. Issues in IFS and GNs, vol. 14, 2018/19, pp. 113–116 (2018) 7. Atanassov, K., Gargov, G.: Interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst. 31(3), 343–349 (1989) 8. Atanassov, K., Szmidt, E., Kacprzyk, J.: On intuitionistic fuzzy pairs. Notes Intuitionistic Fuzzy Sets 19(3), 1–13 (2013) 9. Buckley, J.J.: Fuzzy Probability and Statistics. Springer, Heidelberg (2006). https://doi.org/10.1007/3-540-33190-5 10. De, S.K., Bisvas, R., Roy, R.: Some operations on IFSs. Fuzzy Sets Syst. 114(4), 477–484 (2000) 11. Doane, D., Seward, L.: Applied Statistics in Business and Economics. McGraw-Hill Education, New York (2016) 12. Fisher, R.: Statistical Methods for Research Workers, London (1925) 13. Gil, M.A., Montenegro, M., Gonz´ alez-Rodr´ıguez, G., Colubi, A., Casals, M.R.: Bootstrap approach to the multi-sample test of means with imprecise data. Comput. Stat. Data Anal. 51, 148–162 (2006)

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14. Jiryaei, A., Parchami, A., Mashinchi, M.: One-way ANOVA and least squares method based on fuzzy random variables. Turk. J. Fuzzy Syst. 4(1), 18–33 (2013) 15. Parchami, A., Mashinchi, M., Kahraman, C.: A case study on vehicle battery manufacturing using fuzzy analysis of variance. In: Kahraman, C., Cevik Onar, S., Oztaysi, B., Sari, I.U., Cebi, S., Tolga, A.C. (eds.) INFUS 2020. AISC, vol. 1197, pp. 916–923. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-51156-2 106 16. Kalpanapriya, D., Pandian, P.: Fuzzy hypotesis testing of ANOVA model with fuzzy data. Int. J. Mod. Eng. Res. 2(4), 2951–2956 (2012) 17. Kalpanapriya, D., Unnissa, M.M.: Intuitionistic fuzzy ANOVA and its application using different techniques. In: Madhu, V., Manimaran, A., Easwaramoorthy, D., Kalpanapriya, D., Mubashir Unnissa, M. (eds.) Advances in Algebra and Analysis. TM, pp. 457–468. Springer, Cham (2018). https://doi.org/10.1007/978-3-03001120-8 50 18. Konishi, M., Okuda, T., Asai, K.: Analysis of variance based on fuzzy interval data using moment correction method. Int. J. Innov. Comput. Inf. Control 2(1), 83–99 (2006) 19. Montenegro, M., Gonzalez-Rodriguez, G., Gil, M.A., Colubi, A., Casals, M.R.: Introduction to ANOVA with fuzzy random variables. In: Lopez-Diaz, M., Gil, M.A., Grzegorzewski, P., Hryniewicz, O., Lawry, J. (eds.) Soft Methodology and random information systems, pp. 487–494. Springer, Heidelberg (2004). https:// doi.org/10.1007/978-3-540-44465-7 60 20. Nourbakhsh, M.R., Parchami, A., Mashinchi, M.: Analysis of variance based on fuzzy observations. Int. J. Syst. Sci. 44(4), 714–726 (2013) 21. Ostertagov´ a, E., Ostertag, O.: Methodology and application of one-way ANOVA. Am. J. Mech. Eng. 1(7), 256–261 (2013) 22. Parchami, A., Nourbakhsh, M., Mashinchi, M.: Analysis of variance in uncertain environments. Complex Intell. Syst. 3(3), 189–196 (2017) 23. Pietraszek, J., Kolomycki, M., Szczotok, A., Dwornicka, R.: The fuzzy approach to assessment of ANOVA results. In: Nguyen, N.-T., Manolopoulos, Y., Iliadis, L., Trawi´ nski, B. (eds.) ICCCI 2016. LNCS (LNAI), vol. 9875, pp. 260–268. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-45243-2 24 24. Puri, M., Ralescu, D.: Fuzzy random variables. J. Math. Anal. Appl. 114, 409–422 (1986) 25. Riecan, B., Atanassov, A.: Operation division by n over intuitionistic fuzzy sets. NIFS 16(4), 1–4 (2010) 26. Szmidt, E., Kacprzyk, J.: Amount of information and its reliability in the ranking of Atanassov intuitionistic fuzzy alternatives. In: Rakus-Andersson, E. (eds.) Recent Advances in Decision Making, SCI, vol. 222, pp. 7–19. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02187-9 2 27. Traneva, V.: Internal operations over 3-dimensional extended index matrices. Proc. Jangjeon Math. Soc. 18(4), 547–569 (2015) 28. Traneva, V., Tranev, S.: Index Matrices as a Tool for Managerial Decision Making. Publ. House of the Union of Scientists, Bulgaria (2017). (in Bulgarian) 29. Traneva, V., Tranev, S., Stoenchev, M., Atanassov, K.: Scaled aggregation operations over 2- and 3-dimensional IMs. Soft. Comput. 22(15), 5115–5120 (2018) 30. Traneva, V., Mavrov, D., Tranev, S.: Software Utility of One-Way Intuitionistic Fuzzy ANOVA (2022, in press) 31. Traneva, V., Tranev, S.: Inuitionistic fuzzy analysis of variance of ticket sales. In: Kahraman, C. (ed.) Intelligent and Fuzzy Techniques for Emerging Conditions and Digital Transformation, Proceedings of the INFUS 2021 Conference, August 24–26 (2021). https://doi.org/10.1007/978-3-030-85577-2 8 32. Zadeh, L.: Fuzzy Sets. Inf. Control 8(3), 338–353 (1965)

Circular Intuitionistic Fuzzy Analytic Hierarchy Process for Remote Working Assessment in Covid-19 Esra Çakır1(B) and Mehmet Ali Ta¸s2 1 Department of Industrial Engineering, Galatasaray University, Ortakoy,

34349 Istanbul, Turkey [email protected] 2 Department of Industrial Engineering, Turkish-German University, Beykoz, 34820 Istanbul, Turkey [email protected]

Abstract. The Covid-19 pandemic has caused many revolutionary changes in business life. Thanks to the remote working opportunity in some sectors and limited areas, some leading companies were able to continue their activities and aimed to prevent the spread of the epidemic in the business environment. Although remote working is very advantageous due to economic and health conditions, some challenges can also be mentioned in terms of efficient and effective business management. Evaluation of these challenges may enable the pursuit of a holistic management strategy. In this study, the challenges of the remote working method for businesses are evaluated. Circular Intuitionistic Fuzzy Sets (C-IFS), which is a fairly new fuzzy set concept, and the Analytic Hierarchy Process (AHP), which is a widely used multi-criteria decision making (MCDM) method, are proposed as a novel hybrid methodology. IFS is used to reflect linguistic expressions of decision makers’ assessments. The proposed methodology is implemented to investigate the compliance of tourism enterprises with the concept of remote work and to increase the use of the C-IFS AHP methodology. Keywords: Circular Intuitionistic Fuzzy Sets · Analytic Hierarchy Process · Remote working · Fuzzy multi criteria decision making

1 Introduction Due to the pandemic that emerged in the first quarter of 2020, the modern world had to reconsider the concepts, until recently, were considered “unchangeable” [1]. The imperative of revolution in the working order is one of the most striking [2]. After the initial shocking shutdown, companies outside of service industries such as security, healthcare, and transportation had to find ways to work remotely until governments relaxed or lifted restrictions. Although some companies have introduced options to employees such as flexible working hours and working from home on certain days since the beginning of

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 589–597, 2022. https://doi.org/10.1007/978-3-031-09173-5_68

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the new century, a process in which remote working is the only alternative has not been experienced before for almost all companies [3]. Thanks to the developing technological opportunities, it has been possible to manage the activities without interruption and simultaneously [4]. Businesses want to discover the benefits of working remotely and continue to focus on these benefits [5]. Reduction in workplace costs such as rent, air conditioning, and transportation is a strong factor for businesses [6]. The fact that it is an important part of modern working life and therefore human life makes it essential to examine. By analyzing the benefits of remote working for employees, it can be possible for employees to choose the most suitable business. Fuzzy logic and multi-criteria decision-making approaches can be one of the appropriate tools for assessing remote working and its advantages. After Zadeh [7] presented fuzzy set theory, many fuzzy sets have been introduced [8– 11]. Atanassov’s Circular intuitionistic fuzzy set (C-IFS), which is based on intuitionistic fuzzy sets [12], are defined by the circle of radius r, centered on the membership and non-membership degrees [13]. Since the C-IFS concept is relatively new, there are few applications containing C-IFS and MCDM methods in the literature. Applications of C-IFS MCDM methodologies include supplier selection [14, 15], site selection [16, 17], health tourism center appraisement [18], and industrial symbiosis evaluation [19]. It has been observed that the C-IFS concept has not yet been used in the AHP method within the studies. AHP approach is a multi-criteria decision-making method introduced by Saaty [20]. It is one of the widely-used methods in the literature and uses a hierarchy based on pairwise comparisons. This ensures that it is an approach that has a context suitable for fuzzy logic evaluations [21]. AHP method is integrated with ordinary, intuitionistic, interval type-2, hesitant, Pythagorean, spherical, q-rung orthopair, and so on. This paper contributes to the literature by suggesting C-IFS usage on AHP procedure. C-IFS is in a form suitable for combining views in group decision making. In addition to the applications of AHP, which is a multi-criteria decision-making technique, in fuzzy environments, a new integration has been proceed. Alternatives are evaluated thanks to the fuzzy linguistic IFS decisions of the decision makers and the structure of C-IFS. The proposed approach is applied in a ranking of several businesses to assess their adaptation to remote work during the Covid-19 pandemic. The rest of the paper is designed as follows. Section 2 gives the preliminaries of circular intuitionistic fuzzy sets. The procedure of newly integrated C-IFS AHP is introduced step by step in Sect. 3. Section 4 applies the proposed approach on evaluation of alternative businesses to assess their adaptation to remote working in the Covid-19 pandemic. Finally, Sect. 5 concludes the study and suggest the future directions.

2 Circular Intuitionistic Fuzzy Sets Circular intuitionistic fuzzy set is the extension of the IFS and differs from IFS by including a circle of the number consisting of membership and non-membership degrees [14].

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Definition 1: [18, 22] Let E be a fixed universe, and a generic element a C-IFS Cr in E is denoted by x; Cr = {, x ∈ E} is the form of an object that is the C-IFS, where the functions “u, v: E → [0, 1]” define respectively the membership function and the non-membership function of the element x ∈ E to the set C-IFS with condition:  √  (1) 0 ≤ uC (x) + vC (x) ≤ 1 and r ∈ 0, 2 where r is the radius of the circle around each element x ∈ E. The indeterminacy function can be also defined as πC (x) = 1 − uC (x) − vC (x). Geometrical presentation of C-IFS is in Fig. 1.

Fig. 1. Geometrical representation of circular intuitionistic fuzzy numbers.

When r = 0, a C-IFS is reduced to a standard IFS. the Atanassov discussed in  As √  the article [22], the region of the r values should be 0, 2 to allow the point and cover IFIT [17, 19]. Unlike Atanasov’s suggestion of the arithmetic mean [13] for use in the weighted environment, here we propose to use the IF weighted averaging (IFWA) operator to also take into account the weights of each element:      Definition 2: [23] Let mi,1 , ni,1 , mi,2 , ni,2 , . . . is a set of IF pairs. Then, their aggregated value which is the center of Ci by using the IF weighted averaging (IFWA) operator is also an IF value: Ci = IFWAWi



n n

    wi,j

w mi,1 , ni,1 , mi,2 , ni,2 , . . . =< 1 − 1 − mi,j , ni,ji,j > (2) j=1



j=1



where Wi = wi,1 , . . . , wi,n is the weighting vector of IF pairs with wi,j ∈ [0, 1] and n  wi,j = 1. j=1

The radius ri of the Ci is obtained by the maximum of the Euclidean distances as follows [13]:  2  2 ri = max uC (Ci ) − mi,j + vC (Ci ) − ni,j (3) 1≤j≤ki

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Definition 3: [13] Let L∗ = {a, b|a, b ∈ [0, 1] & a + b ≤ 1}. Therefore Cr can be rewritten in the form Cr∗ = {, x ∈ E} where “Or (uC (x), vC (x)) = {a, b|a, b ∈ [0, 1], (uC (x) − a)2 + (vC (x) − b)2 ≤ r, a +b ≤ 1}” is a function of circle representation. Definition 4: [17] A score function SC−IFS and an accuracy function HC−IFS of the CIFV c is defined as follows with respect to the decision-maker’s (or manager’s) preference information λ ∈ [0, 1]: √ uc − vc + 2r(2λ − 1) where SC−IFS (c) ∈ [−1, 1] SC−IFS (c) = (4) 3 HC−IFS (c) = uc + vc where HC−IFS (c) ∈ [0, 1]

(5)

As discussed in [17–19], “λ reflects the decision-maker’s perspective to the model. If λ is equal to zero, it shows the full pessimistic point of view, and if λ is equal to one, it shows the optimistic point of view. In general acceptance, λ ∈ [0, 0.5) indicates a pessimistic point of view, and λ ∈ (0.5, 1] indicates an optimistic point of view. λ = 0.5 reflects indifferent attitude of decision-maker”. Definition 5: [13] Let C1 =< uC1 (x), vC1 (x); r1 > be a C-IFSs. The complement of this number is as follows:    C1 = x, vC1 (x), uC2 (x); r1 |x ∈ E (6)

3 Circular Intuitionistic Fuzzy Analytic Hierarchy Process The circular intuitionistic fuzzy AHP (C-IFS AHP) methodology is given step by step as follows: Step 1: Define the case, determine the decision makers “D = {D1 , D2 , . . . , Dk }” and construct the hierarchical structure by determining the levels. For a three-level hierarchy, Level 1 is the best option for the problem according to the score. Level 2 consists of sub-criteria by defining the set “C = {C1 , C2 , . . . , Cn }” for any criterion C. In the Level 3, alternatives are placed at the bottom of the hierarchy by defining the set “A = {A1 , A2 , . . . , Am }”. For each level repeat from Step 2 to Step 6 to obtain weights. Step 2: Construct intuitionistic fuzzy decision matrix ||DM || from decision-makers using linguistic scales in Table 1 [24]. Step 3: Check the consistency of IFS decision matrix by experts. The consistency test of IFS judgements is carried out according to the Algorithm I on the study [25] exist in the literature. The threshold of consistency is 0.1. If this threshold is exceeded, experts should reconsider their decisions based on Algorithm II on the study [25]. Step 4: Obtain the aggregated IF decision matrix ||DMaggr || using IFWA operator Eq. (2). These values are also the center of each aggregated decision.

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Table 1. Intuitionistic fuzzy linguistic terms Linguistic terms

Code

IFS

Very low

VL

Low

L

Equal

E

Medium

M

High

H

Very high

VH

Step 5: Calculate the maximum radius lengths of each aggregated decision ||DMaggr || by Eq. (3) from IF decision matrix ||DM || and revise the aggregated decision ||DM || with radius (C-IFS). Step 6: The priority vector “w = {w1 , w2 , . . . , wk }” of each C-IFS preference relation by Eq. (7) as follows: n n   μik (1 − vik ) k=1 k=1 (7) wi = n n , n n ; max(rik ) i=1 k=1 (1 − vik ) i=1 k=1 μik The idea using the max(rik ) in calculation of weight comes from a C-IF number of circles of radius r has at least one element around it, and its radius must not be smaller to take this decision into account. Step 7: Combine the calculated weights at all levels of the hierarchy from Level n to Level 1. The final matrix consists entirely of C-IFS numbers. First, defuzzify only the criterion weights by score function. The revised IFWA operator for C-IFS (called C-IFWA) is used as in Eq. (8) to obtain values for alternative order. n n

     w

w 1 − mi,j i,j , ni,ji,j ; max(ri ) > C − IFWAWi mi,1 , ni,1 , mi,2 , ni,2 , . . . =< 1 − j=1

j=1

(8) √

Scores of these values is obtain by S(wi ) = uc −vc +6 2r+3 where WCi ∈ [0, 1] and then normalize. (We recommend here to set λ = 0.5 unless you have a special point of view on Eq. (4)). Step 8: Rank the score of alternatives and the alternative with the highest score is the best option.

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4 Case Study Due to the Covid 19 pandemic, many institutions encouraged their employees to work remotely. This development, which was positive in order to reduce the spread and risk of the disease, also positively affected the way companies work. The C-IFS AHP method proposed in this study was used to evaluate adaptation to remote working conditions for four companies in the tourism sector in Turkey. A1, A2, A3 and A4 companies are evaluated according to the criteria C1: Communication level with distance workers, C2: Compliance with official hours, C3: Development of organizational culture, C4: Usage rate of technological devices and software. The hierarchical structure of the case is shown in Fig. 2.

Fig. 2. The hierarchy process of the case study.

Three experts from the tourism sector expressed their linguistic views according to the scale in Table 1. The steps of the method suggested in the previous section are applied on the case. Not all information is included due to page limit, but some application data are as in Tables 2, 3, 4, 5 and 6. Table 2. IF decisions of three DM on weighting criteria DM1 1

2

DM2

3

4

1

2

DM3

3

4

1

2

3

4

1 2

′

′

′

3 4

′

′

′

′

′

′

′

′

′

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Table 3. C-IFS matrix and weight results for criteria C1 C2 C3 C4

C1



C2



C3



C4



Weight



Score 0.631 0.730 0.672 0.654

Norm. 0.235 0.272 0.250 0.243

Table 4. IF decisions of three DM on weighting alternatives based on criterion 1. C1

DM1 1

2

DM2

3

4

1

2

DM3

3

4

1

2

3

4

1

′

′

2

′ ′

3

′

4

′

′

′

′

′

′

′

′

Table 5. C-IFS matrix and weight results for alternatives based on criterion 1. C1 A1 A2 A3 A4

A1



A2



A3



A4



Weight



Table 6. Final Matrix of combined weights of levels

A1 A2 A3 A4

C1

C2

C3

C4













Ranking Value

Score



0.649 0.672 0.704 0.765

Norm. Score 0.233 0.241 0.252 0.274

As a result of the methodology, the ranking of tourism companies on their remote working process is as A4 > A3 > A2 > A1. The most adapted company as a result of remote working evaluation is A4 and the least adapted one is A1. A1 should work to increase its compatibility on distance working.

5 Conclusion Circular intuitionistic fuzzy set is an extension of intuitionistic fuzzy sets that group IFS decisions in a new uncertainty. Thanks to Atanassov [13], as a different form of expression in fuzzy group decision making, C-IFS, which includes all decisions and

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creates a new circular uncertainty cloud, is therefore suitable for use in MCDM methods. Beyond the previously developed C-IFS functions by the authors of this study, the C-IFS AHP procedure is proposed for adaptation to group decision making approaches in fuzzy environment. AHP is a multi-level procedure in nature and has been practiced many times in an uncertain environment. In the light of the IFS opinions received from the decision makers, the group decision making results are compared with the C-IFS figures and the alternatives are ordered. This study was carried out in the case of evaluating companies that adapt to remote work during the Covid-19 process, using the C-IFS AHP technique, which it successfully developed. As a result, the proposed C-IFS AHP procedure, with the help of fuzzy linguistic expressions of experts, ranked the adapted alternatives as A4 > A3 > A2 > A1. For further benefits, newly introduced circular intuitionistic fuzzy AHP methodology can be applied for the cases that have already been covered in the literature. Thus, the comparison of the proposed methodology with existing fuzzy MCDM approaches is examined. On the other hand, circular intuitionistic fuzzy sets can take their place in MCDM methods by suggesting advance variations and extensions.

References 1. Hodder, A.: New technology, work and employment in the era of COVID-19: reflecting on legacies of research. N. Technol. Work. Employ. 35(3), 262–275 (2020) 2. Lund, S., et al.: The future of work after COVID-19. McKinsey Global Institute, vol. 18 (2021) 3. Bick, A., Blandin, A., Mertens, K.: Work from home before and after the Covid-19 outbreak. Available at SSRN 3786142 (2021). https://papers.ssrn.com/sol3/papers.cfm?abstract_ id=3786142 4. Ting, D.S.W., Carin, L., Dzau, V., Wong, T.Y.: Digital technology and COVID-19. Nat. Med. 26(4), 459–461 (2020) 5. Ferreira, R., Pereira, R., Bianchi, I.S., da Silva, M.M.: Decision factors for remote work adoption: advantages, disadvantages, driving forces and challenges. J. Open Innov. Technol. Mark. Complexity 7(1), 70 (2021) 6. Mohapatra, B., Tripathy, S., Singhal, D., Saha, R.: Significance of digital technology in manufacturing sectors: examination of key factors during Covid-19. Res. Transp. Econ. 93, 101134 (2021) 7. Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965) 8. Zadeh, L.A.: The concept of a linguistic variable and its application. Inf. Sci. 8(3), 199–249 (1975) 9. Smarandache, F.: Neutrosophy: Neutrosophic Probability, Set, and Logic: Analytic Synthesis & Synthetic Analysis (1998) 10. Yager, R.R.: Pythagorean fuzzy subsets. In: 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), pp. 57–61. IEEE (2013) 11. Yager, R.R.: Generalized orthopair fuzzy sets. IEEE Trans. Fuzzy Syst. 25(5), 1222–1230 (2016) 12. Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986) 13. Atanassov, K.: Circular intuitionistic fuzzy sets. J. Intell. Fuzzy Syst. 39(5), 5981–5986 (2020) 14. Kahraman, C., Alkan, N.: Circular intuitionistic fuzzy TOPSIS method with vague membership functions: supplier selection application context. Notes Intuitionistic Fuzzy Sets 27(1), 24–52 (2021)

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15. Otay, ˙I, Kahraman, C.: A novel circular intuitionistic fuzzy AHP&VIKOR methodology: an application to a multi-expert supplier evaluation problem. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi 28(1), 194–207 (2022) 16. Kahraman, C., Otay, I.: Extension of VIKOR method using circular intuitionistic fuzzy sets. In: Kahraman, C., Cebi, S., Cevik Onar, S., Oztaysi, B., Tolga, A.C., Sari, I.U. (eds.) INFUS 2021. LNNS, vol. 308, pp. 48–57. Springer, Cham (2022). https://doi.org/10.1007/978-3-03085577-2_6 17. Çakır, E., Ta¸s, M.A., Ulukan, Z.: A new circular intuitionistic fuzzy MCDM: a case of Covid19 medical waste landfill site evaluation. In: 2021 IEEE 21st International Symposium on Computational Intelligence and Informatics (CINTI), pp. 000143–000148. IEEE (2021) 18. Çakır, E., Ta¸s, M.: Circular intuitionistic fuzzy multi-criteria decision making methodology. Avrupa Bilim ve Teknoloji Dergisi 28, 900–905 (2021) 19. Çakır, E., Ta¸s, M.A., Ulukan, Z.: Circular intuitionistic fuzzy sets in multi criteria decision making. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 34–42. Springer, Cham (2022). https://doi. org/10.1007/978-3-030-92127-9_9 20. Saaty, T.L.: How to make a decision: the analytic hierarchy process. Eur. J. Oper. Res. 48(1), 9–26 (1990) 21. Chang, D.Y.: Applications of the extent analysis method on fuzzy AHP. Eur. J. Oper. Res. 95(3), 649–655 (1996) 22. Atanassov, K., Marinov, E.: Four distances for circular intuitionistic fuzzy sets. Mathematics 9(10), 1121 (2021) 23. Zeshui, X.: Intuitionistic fuzzy aggregation operators. IEEE Trans. Fuzzy Syst. 15(6), 1179– 1187 (2007) 24. Efe, B., Efe, Ö.F.: Intuitionistic fuzzy number based group decision making approach for personnel selection. Uluda˘g Univ. J. Fac. Eng. 23(3), 11–26 (2018) 25. Xu, Z., Liao, H.: Intuitionistic fuzzy analytic hierarchy process. IEEE Trans. Fuzzy Syst. 22(4), 749–761 (2013)

Weighting ESG Criteria of Banks by Using Interval Valued Intuitionistic Fuzzy Best Worst Method Burcu Simsek Yagli1(B)

, Nuri Ozgur Dogan1

, and Ibrahim Yagli2

1 Department of Quantitative Methods, Nevsehir Haci Bektas Veli University,

50300 Nev¸sehir, Turkey [email protected] 2 Department of Finance, Nevsehir Haci Bektas Veli University, 50300 Nev¸sehir, Turkey

Abstract. Even though the ESG-financial performance relationship is well addressed with the ambiguous results, the literature lacks to determine the relative importance of individual ESG criteria regarding sustainability. To fill this gap, the study aims to determine the relative weights of ESG criteria for the banking industry from the perspective of scholars. To reach the aim of the paper, we employ Interval Valued Intuitionistic Fuzzy Best Worst Method and reveal that Governance (C 3 ) is the most significant criteria among the main criteria, followed by Social (C 2 ) and Environment (C 1 ) criteria. Regarding sub-criteria, Management (G1 ), Shareholders (G2 ) and Workforce (S 1 ) are the most significant sub-criteria whereas Product responsibility (S 4 ), Resource Use (E 1 ) and Emissions (E 2 ) are the least significant sub-criteria, respectively. These results do not fully represent real weights because of the subjective judgments of decision makers but it gives banking sector practitioners to comparable reference to allocate their scarce resources. Keywords: Banking industry · ESG · Interval valued intuitionistic fuzzy sets · Best Worst Method

1 Introduction Sustainability is defined as a “development that meets the needs of the present without compromising the ability of future generations to meet their own needs” [1]. Sustainability corresponds to corporate sustainability at the company-level and aims to create value for all stakeholders by considering Environment, Social and Governance (ESG) issues as well as financial performance. The aim of the company is to achieve sustainable development by balancing these criteria. The aim of the paper is to weight the ESG criteria for the banking industry considering that sustainability of the banking sector affects other sectors via their economic relationship. Several factors drive us to prioritize the ESG criteria. First, studies addressing corporate sustainability and financial performance provide conflicting outcomes [2]. A bulk of papers find a positive relationship between corporate sustainability and financial © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 598–605, 2022. https://doi.org/10.1007/978-3-031-09173-5_69

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performance while others report neutral or negative impacts of sustainability on financial performance. Second, several studies also reveal that individual ESG criteria have divergent impacts on financial performance. Third, recent studies indicate the non-linear relationship between ESG and financial performance [3], indicating overinvestment in ESG is harmful to corporate financial performance. Even though the relationship between ESG performance and financial performance is well-studied, the weighting of ESG criteria is not adequately addressed, with the exception of Aras et al. [4]. The study contributes literature by determining the relative importance of ESG criteria for the banking sector. Our study, however, differs from their study in three aspects. First, we focus on non-financial sustainability criteria while they address financial and economic factors with ESG. Second, we utilize relatively new Multi-Criteria Decision Making (MCDM) method, Best-Worst Method (BWM), to determine the weights of ESG criteria. BWM provides not only consistent and reliable results but also requires less data collection and calculation effort [5]. We integrate BWM with interval valued intuitionistic fuzzy (IVIF) sets since they efficiently cope with the uncertainty of decision makers’ judgment [6]. Third, ESG criteria are evaluated in the perspective of scholars. The rest of the paper is organized as follows. Section 2 reviews the literature, Sect. 3 introduced basic concept of IVIF-BWM, Sect. 4 provides case study and results, Sect. 5 gives concluding remarks.

2 Literature Review Bank performance is the common area of interest for bank managers, investors, and policymakers. Parallel to this interest, bulks of academic research have been conducted to evaluate the performance of banks with different evaluation criteria and different methods. The earlier studies only focus on financial indicators to assess bank performance while recent literature considers sustainability indicators along with financial criteria. Performance evaluation is required to consider multiple criteria at the same time. Thereby, MCDM methods are suitable tools to evaluate bank performance criteria. For instance, Aras et al. [4] evaluated sustainability performance of Turkish banking industry in the framework of financial, economic, environmental, social and governance by using content analysis, entropy weight and TOPSIS method. Seyfi-Shishavan [7] focused also on banking performance assessment in pandemic process employing IFBWM. But, there is not an ESG orientation in this study. On the other hand, Ecer [8] studied corporate sustainability performance of bank with economic, environment and social non-subjective data by using Entropy-ARAS integrated method. In a similar vein, Akın and Yılmaz [9] assessed the bank performance focused on economic, environment, social, financial, governance disclosures objectively. The literature shows that, there is a need for a study in which ESG criteria are subjectively prioritized in the context of the banking sector. In the literature, the BWM that newly proposed by Rezaei [10] used in different sectors for generally weighting the factors. For instance, the BWM is employed in problems such as sustainability assessment [11], supplier selection [5, 12, 13], banking industry performance [7], circular economy adoption barriers [14] and digitalization of quality management [15]. Furthermore, the method is extended into many

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fuzzy environments such as Intuitionistic fuzzy sets [7], IVIFSs [15, 16], hesitant fuzzy sets [17].

3 Interval Valued Intuitionistic Fuzzy Best Worst Method 3.1 Interval Valued Intuitionistic Fuzzy Sets IVIFSs are efficient sets to deal with uncertainty since they address membership and nonmembership functions in an interval [6]. In a complex real life problem, it can be applied. First of all, some definitions about IVIF sets should be given before proceeding with the IVIF-BWM steps. The main concepts of IVIFSs are briefly introduced. Please refer to [18, 19] for details. Definition 1. Let X = ∅ be given set, an IVIFS in X is an object A˜ given as in Eq. (1).   (1) A˜ = x, μA˜ (x), vA˜ (x); x ε X where μA˜ (x) : X , vA˜ (x) : X → [0, 1] and 0 ≤ μA˜ (x) + vA˜ (x) ≤ 1 for all x ε X . Definition 2. An IVIF number A˜ is defined in X (Eq. 2):       + ; x ε X , v A˜ = x, μ−˜ , μ+˜ , v− ˜ ˜ A

A

A

A

(2)

− − where 0 ≤ μ+˜ + v+ ˜ ≤ 1and μ ˜ ≥ 0, v ˜ ≥ 0. A

A

A

A

4 Interval Valued Intuitionistic Fuzzy Best Worst Method The five steps of the IVIF Best Worst Method algorithm are discussed below [12, 16]: Step 1. Determine the most significant (or the best-C B ) criterion and the least significant (or the worst-C W ) criterion from a predetermined set of criteria (C j , j = 1,2,…,n) based on the DMs’ perspective. Step 2. Compare the most significant criterion with the other criteria (Best-to-Others vector), assessed by each decision maker (DMk ) employing a linguistic term set:  (k) (k) (k) (k) (3) R˜ B = r˜B1 , r˜B2 , . . . , r˜Bn     (k) (L) (U ) (L) (U ) where r˜Bj = shows the IVIF preference of the most μ˜ Bj , μ˜ Bj , v˜ Bj , v˜ Bj significant criterion C B over the other criteria C j provided by each DMk . Step 3. Compare the other criteria with the least significant criterion (Others-to-Worst vector), evaluated by each decision maker (DMk ) adopting a linguistic term set:  (k) (k) (k) (k) (4) R˜ W = r˜1W , r˜2W , . . . , r˜nW     (k) (L) (U ) (L) (U ) where r˜jW = μ˜ jW , μ˜ jW , v˜ jW , v˜ jW indicates the IVIF preference of the other criteria C j over the least significant criterion C W provided by each DMk .

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Step 4. Calculate the optimal weights for each   DMk :     (k) (L) (U ) (L) (U ) (k) (L) (U ) (L) (U ) , ω˜ W = μ˜ W , μ˜ W , v˜ W , v˜ W Assume ω˜ B = μ˜ B , μ˜ B , v˜ B , v˜ B     (k) (L) (U ) (L) (U ) and ω˜ j = μ˜ j , μ˜ j , v˜ j , v˜ j . The optimal weight for the criteria is the one

(k)



(k) (k) (k)

ω˜

ω˜ ω˜ ω˜ (k)

(k)

where, for each pair of B(k) and j(k) , we have

B(k) − r˜Bj

and

j(k) − r˜jW

. For the ω˜ j ω˜ W ω˜ j ω˜ W decision maker DMk , to fulfill the requirements for all C , we should j

(k)

find a solution

(k)

ω˜ j



ω˜ (k) (k) where the maximum absolute differences

B(k) − r˜Bj

and

(k) − r˜jW

for all C j are ω˜ j

ω˜ W

minimized. Moreover, the non-negativity and sum condition of the weights should be considered. Then, the following optimization model (Eq. 3) can be derived and optimal weights of criteria and ε∗ for each DMk can be obtained [16]: minε s.t.

(k)

(k) (k) (k) (k)

L

μB + vjL − μLB .vjL − μLBj ≤ ε, for all Cj

(k)

(k) (k) U (k)

U U (k)

.v − μ

μB + vjU − μU B j Bj ≤ ε, for all Cj

(k)

(k)

L L(k)

vB + μLj − vBj

≤ ε, for all Cj

(k)

(k)

U U (k)

− v

vB + μU j Bj ≤ ε, for all Cj

(k)

(k) L(k) (k)

L L(k) − μLj .vW − μLjW ≤ ε, for all Cj

μj + vW

(k)

(k) U (k)

U U (k) U (k)

+ vW − μU .v − μ

μj j W jW ≤ ε, for all Cj

(k)

(k)

L L(k)

vj + μLW − vjW

≤ ε, for all Cj

(k)

(k)

U U (k)

+ μU − v

vj W jW ≤ ε, for all Cj

(5)

n   (k) =1 S ω˜ j j=1

 (k) S ω˜ j ≥ 0, for all Cj By solving the optimization model (3), the optimal weights of each criteria, ε∗ and ω˜ (k) = (ω˜ 1 , ω˜ 2 , . . . , ω˜ n )(k) obtained by DMk can be determined. ε∗ refers the consistency ratio of the comparison system and value close to zero shows that DMk ’s comparisons are quite consistent [5]. Step 5. Defuzzification of the optimal weights of each criteria [12]: ω˜ j = ([a, b], [c, d ]); ωj =

a + a(1 − a − c) + b + b(1 − b − d ) , for all Cj 2

(6)

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5 A Case Study: Weighting ESG Criteria for Banking Industry As an important component of the financial system, banks have a major role in sustainable development [4]. It is not enough to focus only on financial performance indicators to ensure sustainability in banking industry. For this reason, the performance of the banking industry is also evaluated within the framework of environment, social and governance (ESG) which comprises of sub-criteria those relative importance vary across industries. The current study, therefore, aims to reveal the relative importance weights of the main and sub-criteria of ESG (Environment-C1 : Resource Use-E 1 , EmissionsE 2 , Innovation-E 3 ; Social-C2 : Workforce-S 1 , Human rights-S 2 , Community-S 3 , Product responsibility-S 4 ; Governance-C3 : Management-G1 , Shareholders-G2 , CSR strategyG3 ) using IVIF-BWM in the context of the banking industry. The criteria are weighted within the perspective of 4 scholars who have a minimum 9 years of experience in the field of banking sector and sustainability reporting. The brainstorming method is adopted to create a consensus among scholars in filling the prepared questionnaire. In the first stage, the experts are asked to identify the most and the least significant criteria (Table 1). In this regard, governance and environment are determined as the most and least significant criteria, respectively. Table 1. The most and least significant criteria. Criteria

The most significant

The least significant

Main criteria

ESG

Governance (C3 )

Environment (C1 )

Sub-criteria

Environment

Innovation (E3 )

Emissions (E2 )

Social

Workforce (S1 )

Product responsibility (S4 )

Governance

Management (G1 )

CSR strategy (G3 )

Then, the scale in Table 2 is used for pairwise linguistic evaluations. Next, these linguistic evaluations are converted into IVIF numbers (Table 3 and 4). Table 2. Linguistic terms for pairwise comparisons [16]. Linguistic terms

IVIF numbers

Equally important_(EI)

([1.0,1.0],[0.0,0.0])

Very important_(VI)

([0.7,0.8],[0.1,0.2])

Weakly important_(WI)

([0.5,0.6],[0.3,0.4])

Absolutely important

([0.8,0.9],[0.1,0.2])

Strongly important_(SI)

([0.6,0.7],[0.2,0.3])

(AI)

Table 3 reports the IVIF-best-to-others vectors for main and sub-criteria determined using linguistic scale. In this regard, C3 is the most significant one among main criteria while E3 , S1 , and G1 are the most significant criteria in environment, social and governance dimensions, respectively.

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Table 3. The IVIF best-to-others vectors. (a) ESG

C1

C2

Best: C3

([0.6,0.7],[0.2,0.3]) ([0.5,0.6],[0.3,0.4]) ([1.0,1.0],[0.0,0.0])

(b) Environment E1 Best: E3

C3

E2

E3

([0.5,0.6],[0.3,0.4]) ([0.6,0.7],[0.2,0.3]) ([1.0,1.0],[0.0,0.0])

(c) Social

S1

Best: S1

([1.0,1.0],[0.0,0.0]) ([0.6,0.7],[0.2,0.3]) ([0.6,0.7],[0.2,0.3]) ([0.5,0.6],[0.3,0.4])

S2

S3

(d) Governance

G1

Best: G1

([1.0,1.0],[0.0,0.0]) ([0.6,0.7],[0.2,0.3]) ([0.7,0.8],[0.1,0.2])

G2

S4

G3

To make the IVIF others-to-worst vectors, the other criteria are compared with the least significant criteria in Table 4. In this regard, C1 is the least significant main criteria whereas E2 , S4 , and G3 are the least significant criteria in environment, social and governance dimensions, respectively. Table 4. The IVIF others-to-worst vectors. (a) ESG Worst: C1 C1

(b) Environment Worst: E2

C2

([1.0,1.0],[0.0,0.0]) E1 ([0.6,0.7],[0.2,0.3]) E2

C3

([0.7,0.8],[0.1,0.2]) E3

([0.8,0.9],[0.1,0.2])

(c) Social

Worst: S4

Worst: G3

S1

([0.7,0.8],[0.1,0.2]) G1

([0.7,0.8],[0.1,0.2])

S2

([0.6,0.7],[0.2,0.3]) G2

([0.6,0.7],[0.2,0.3])

S3

([0.6,0.7],[0.2,0.3]) G3

([1.0,1.0],[0.0,0.0])

S4

([1.0,1.0],[0.0,0.0])

(d) Governance

([0.5,0.6],[0.3,0.4]) ([1.0,1.0],[0.0,0.0])

To calculate the weights of the ESG criteria, we apply following steps: (Step 1) we construct the optimization model (Eq. 3) employing the data in Tables 3 and 4. (Step 2) the constructed model is solved in the LINGO 19 software and (Step 3) the IVIF optimal weights of criteria are determined. (Step 4) Then, defuzzified optimal weights of criteria are calculated employing Eq. (4). (Step 5) All criteria are ranked according to the defuzzified optimal weights of criteria. Table 5 reports the ranking results, optimal weights and ε∗ value. According to the obtained results, Governance (ωj = 0,4566) is on the first rank among main criteria followed by Social (ωj = 0,3524) and Environment (ωj = 0,1910). Then the ranking result of the all sub-criteria is derived as G1 > G2 > S1 > G3 > E3 > S2 > S3 > S4 > E1 > E2. These results are consistent since ε∗ value is close to zero.

604

B. Simsek Yagli et al. Table 5. Weights of ESG criteria (ωj ) and the value of ε∗ .

Main criteria ε∗ = 0,084

Sub-criteria

Local_weights

Global_weights

Rank

Environment

E1

0,3110

0,0594

9

ωj = 0,1910

E2

0,2068

0,0395

10

ε∗ = 0,107

E3

0,4821

0,0921

5

Social

S1

0,3325

0,1172

3

ωj = 0,3524

S2

0,2476

0,0873

6

ε∗ = 0,121

S3

0,2476

0,0873

7

S4

0,1722

0,0607

8

Governance

G1

0,4944

0,2258

1

ωj = 0,4566

G2

0,2988

0,1364

2

ε∗ = 0,116

G3

0,2068

0,0944

4

6 Conclusions Covid-19 pandemic once again shows that sustainability is not a fashionable trend; instead it is the permanent mission for both individuals and companies. Companies attempt to make their business model sustainable. However, companies should prioritize alternative sustainability investments among the ESG investments since their resources are limited. Given the limited company resources and ambiguous relationship between corporate sustainability and financial performance, the current paper aims to determine weights of ESG criteria for the banking industry from the perspective of scholars by using IVIFBWM integrated approach. The results show that Governance (C 3 ) and its sub-criteria are the most significant criteria for the banking industry from scholars’ perspectives, while Environment (C 1 ) is the least significant one. The findings are not parallel with Aras et al. [4], who finds the environment criterion more important than the others. Moreover, Management (G1 ), Shareholders (G2 ), Workforce (S 1 ) are the most significant sub-criteria but Emissions (E 2 ) is the least significant because of not so much emissions generated in the banking industry. These results may provide significant implication for bank managers in ESG investment. For future research, the relative importance of ESG may be evaluated from different perspectives. Furthermore, the weights of ESG can be determined for other industries. Other extensions of fuzzy sets like Neutrosophic fuzzy sets, Spherical fuzzy sets and/or integrate with other MCDM methods are also employed to determine the weights of ESG.

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Watson Crick Intuitionistic Fuzzy Automata N. Jansirani1

, N. Vijayaraghavan2(B)

, and V. R. Dare3

1 Queen Mary’s College, University of Madras, Chennai 600004, India 2 KCG College of Technology, Chennai 600097, India

[email protected] 3 Madras Christian College, University of Madras, Chennai 600059, India

Abstract. Fuzzy Automata are simply nondeterministic Finite State Automata with inaccurate information of the machine’s next state. Fuzzy Automata are capable computational tools for modelling Discrete Event Dynamic Systems with crisp input alphabets but fuzzy transitions. Traditional Fuzzy Automata, on the other hand, are insufficient to model complicated real-world applications, thereby giving rise to Intuitionistic Fuzzy Automata. Watson Crick Finite Automata was introduced as a computational model to examine DNA molecules for computational purposes, and it operates on Double Stranded tapes. Watson Crick Fuzzy Automata got introduced and researched the concept of Fuzziness in Watson Crick Automata theory. Watson Crick Fuzzy Automata theory can be viewed as a useful computational model for DNA computing challenges involving inadequate knowledge and ambiguity. The Watson Crick Intuitionistic Fuzzy Automata are introduced in this research work in order to efficiently manage the concept of Uncertainty in Automata Theory. Watson Crick Intuitionistic Fuzzy Automata have several applications in real-world difficult situations across a wide range of areas. Here, Watson Crick Intuitionistic Fuzzy Automata’s transition map has been extended and the Languages accepted by these Automata are also discussed. Keywords: Intuitionistic · Fuzzy · Watson Crick

1 Introduction One of the first computational models proposed in the context of DNA computing was the Watson-Crick finite automaton, a type of finite state abstract machine that takes its input tape from the DNA double strand and considers complementarity relationships between symbols as they occur in nature with respect to the DNA nucleotides [2]. The fuzzy approach is based on the assumption that the main elements in human mind aren’t just numbers, but may be approximated as tables of fuzzy sets, or classes of objects with a gradual rather than abrupt transition from membership to non-membership. As an uncertainty approach, Zadeh invented the concept of a fuzzy subset of a set. Fuzzy set theory has gained a lot of attention from scientists all over the world since Zadeh’s groundbreaking 1965 article [8]. A field like formal languages and automata theory is an example of this. In practice, this means that in order to recognize a language, a machine must compute the characteristic function. To take things a step further, a machine can only recognise a fuzzy language if and only if it can compute its membership function. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 606–615, 2022. https://doi.org/10.1007/978-3-031-09173-5_70

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Atanassov presented intuitionistic fuzzy sets in 1983 as a generalization of fuzzy sets [1]. It has recently been discovered to be extremely effective in coping with ambiguity. Jun [3] introduced intuitionistic fuzzy finite state machines as a generalization of fuzzy finite state machines, based on the concepts of intuitionistic fuzzy sets and fuzzy finite automata. The concept of Watson Crick intuitionistic fuzzy Automata is introduced in this study. The remainder of the paper is laid out as follows. The second section recaps the necessary preliminaries and definitions. The Penultimate section introduces Watson Crick Intuitionistic Fuzzy Automata and their corresponding languages. The conclusion and future work are presented in the final part.

2 Literature Review Rosenberg et al. [7] Proposed Watson Crick finite automaton as part of DNA computing. This is a kind of abstract finite state machine that takes a double stranded input tape. Wee and Fu [6] presented the mathematical model of fuzzy finite automata in 1969. A fuzzy language notion has also been developed by Mordeson and Malik in 2002. Because classical automata cannot deal with system uncertainty, fuzzy automata are utilized to solve it. Jun Y.B introduced the concept of Intuitionistic Fuzzy Finite machine and studied it in 2006 [3, 4]. In 2021, Jansirani et al. studied Watson Crick Fuzzy Automata and the languages accepted by them [5].

3 Preliminaries In this section, the definitions of Intuitionistic Fuzzy set, Intuitionistic Fuzzy Automaton and Watson Crick Finite Automaton are recalled. “An intuitionistic fuzzy set on the universal set X is an object of the form H = {< a, μH (a), γH (a) > |a ∈ X} where μH : X → [0, 1] and γH : X → [0, 1] are called the membership and non-membership functions respectively and the condition that 0 ≤ μH (a) + γH (a) ≤ 1 for all a ∈ X [1]. An Intuitionistic Fuzzy Automaton is a 3-tuple M = (Q, , A), where Q and  are finite non empty sets called the set of states and set of Inputs respectively, A = (μA , γA ) is an Intuitionistic fuzzy set in Q ×  × Q [3]. A Watson Crick Finite Automaton is a 6-tuple M = (Q, , ρ, δ, q0 , F), Where Q, , q0 , F ⊆ Q are the same as in the definition  ofFinite Automaton with ρ ⊆  ×     is the complimentary relation and δ : Q × → Q 2Q , is called the transition     w1 = φ, only for finitely many triples (q, w1 , w2 ) ∈ Q × function, such thatδ q, w2 ∗ ∗  ×  [2].

4 Watson Crick Intuitionistic Fuzzy Automata Definition 4.1. A Watson Crick Intuitionistic Fuzzy Machine is a 4-tuple M = (Q, , ρ, A), where Q and  are finite non empty sets called the set of states and set of

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Inputs respectively,  ρ∗is the complementarity relation, A = (μA , γA ) is an Intuitionistic  × Q. fuzzy set in Q × ∗ Definition 4.2. Let M = (Q, , ρ, A) be a Watson Crick Intuitionistic  ∗ Fuzzy Machine.  × Q by Then define an Intuitionistic Fuzzy set A* = (μA ∗, γA ∗) in Q × ∗       λ 1, ifq = p (i) μA q, ,p = λ 0, ifq = p              a x x1 a 1 1 ∗ ∗ , p = r∈Q μA q, , r ∩ μA r, 1 , p (ii) μA q, x2 a2 x2 a2       λ 0, ifq = p (iii) γA ∗ q, ,p = λ 1, ifq = p             x a x a (iv) γA ∗ q, 1 1 , p = r∈Q γA ∗ q, 1 , r ∪ γA r, 1 , p x2 a2 x2 a2          ∗ λ  a  x ∀p, q ∈ Q, ∀ 1 , ∈ ,∀ 1 ∈ a2 x2 ∗ λ  ∗

Theorem 4.1 (Transition Map Extension Theorem): Let M = (Q, be a  ,ρ,A)  y1 x1 , ∈ Watson Crick Intuitionistic Fuzzy Machine, then ∀p, q ∈ Q, ∀ x2 y2  ∗        a λ  ,∀ 1 , ∈ ∗ a2 λ               x y x y (i) μA ∗ q, 1 1 , p = r∈Q μA ∗ q, 1 , r ∩ μA ∗ r, 1 , p and x2 y2 x2 y2             x y x y (ii) γA ∗ q, 1 1 , p = r∈Q γA ∗ q, 1 , r ∪ γA ∗ r, 1 , p x2 y2 x2 y2  Proof: (i) Let p, q ∈ Q,

    ∗ y  x1 , 1 ∈ .We prove this theorem by induction x2 y2 ∗

on |y1 | = |y2 | =n.          λ x1 λ y1 x1 x1 y1 = = . Let n = 0, then = and hence y2 x2 y2 x2 λ x2 λ              x y x Therefore r∈Q μA ∗ q, 1 , r ∩ μA ∗ r, 1 , p = μA ∗ q, 1 , p x2 y2 x2     x y = μA ∗ q, 1 1 , p , by the definition. Hence Basis is true. x2 y2    ∗ z  Suppose that the result is true for all for all 1 ∈ with |z1 | = |z2 | = n − 1, z2 ∗ n > 0.

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      ∗     z1 a1 z1   a1 y1 = with ∈ , |z1 | = |z2 | = n− and ∈ let , y2 z2 a2 z2 ∗ a2          x y x z a now μA ∗ q, 1 1 , p = μA ∗ q, 1 1 1 , p x2 y2 x2 z2 a2 

        x1 z1 a ∗ q, , r ∩ μA r, 1 , p = x2 z2 a2              x z a ∩ μ∗A r, 1 , p = ∪r∈Q (∪s∈Q μ∗A q, 1 , s ∩ μ∗A s, 1 , r x2 z2 a2              z a x ∩ μ∗A q, 1 , s = ∪s∈Q ∪r∈Q (μ∗A s, 1 , r ) ∩ μ∗A r, 1 , p z2 a2 x2         x1 z1 a1 ∗ ∗ , s ∩ μA s, ,p = ∪s∈Q (μA q, x2 z2 a2         x y = ∪s∈Q (μ∗A q, 1 , s ∩ μ∗A s, 1 , p x2 y2 ∪r∈Q (μ∗A

Thus the result is true for |y1 | = |y2 | = n.  (ii) Let p, q ∈ Q, |y1 | = |y2 | = n. 

    ∗ x1 y  , 1 ∈ .We prove this theorem by induction on x2 y2 ∗

        λ x1 λ x1 x1 y1 Let n = 0, then = = . = and hence x y x λ x λ      2 2   2  2   x y x Therefore r∈Q γA ∗ q, 1 , r ∪ γA ∗ r, 1 , p = γA ∗ q, 1 , p x2 y2 x2     x y = γA ∗ q, 1 1 , p , by the definition. Hence Basis is true. x2 y2    ∗  z with |z1 | = |z2 | = n − 1, Suppose that the result is true for all for all 1 ∈ z2 ∗ n > 0.        ∗     z1 a1 z1   a1 y1 = with ∈ , |z1 | = |z2 | = n− and ∈ let , y2 z2 a2 z2 ∗ a2          x y x z a now γA ∗ q, 1 1 , p =γA ∗ q, 1 1 1 , p x2 y2 x2 z2 a2         x z a = r∈Q γA ∗ q, 1 1 , r ∪ γA ∗ r, 1 , p x2 z2 a2             x1 z1 a ∗ ∗ ∗ = r∈Q ( s∈Q (γA q, , s ∪ γA s, , r ) ∪ γA r, 1 , p x z a2    2    2       z a x1 1 1 ∗ ∗ ∗ ,r ∪ γA r, , p ) ∪ γA q, ,s = s∈Q ( r∈Q γA s, z2 a2 x2 y1 y2



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        x1 z1 a1 ∗ , s ∪ γA s, ,p = r∈Q γA q, x z a   2    2 2  x y = r∈Q γA ∗ q, 1 , s ∪ γA ∗ s, 1 , p x2 y2 Thus the result is true for |y1 | = |y2 | = n. Hence the proof.

∗

Theorem 4.2: Let = (Q, , ρ, be a Watson    Crick  Intuitionistic   Fuzzy  Machine,  M A)  λ a a a  then ∀p, q ∈ Q, ∀ 1 , ∈ (i) μA ∗ q, 1 , p = μA q, 1 , p and a2 a2 a2 λ          a a (ii) γA ∗ q, 1 , p = γA q, 1 , p a2 a2

μA ∗ q,



 

 

   x1 a1 x1 a1 ∗ , p = r∈Q μA q, , r ∩ μA r, ,p x2 a2 x2 a2

Proof: (i) Consider              λ λ a1 λ x1 ∗ ∗ = , p = r∈Q μA q, If , then we have μA q, ,r ∩ x λ λ a2 λ  2       a λ , r = 1, if q = r. μA r, 1 , p , But by the definition, we have μA ∗ q, a2 λ             λ a1 a a , p = μA ∗ q, 1 , p = 1 ∩ μA q, 1 , p Therefore μA ∗ q, a2 a2 λ a2             a a a = μA q, 1 , p . Hence μA ∗ q, 1 , p =μA q, 1 , p . a2 a2 a2             x a x a (ii) γA ∗ q, 1 1 , p = r∈Q γA ∗ q, 1 , r ∪ γA r, 1 , p x2 a2 x2 a2

            x1 λ λ a1 λ If = , p = r∈Q γA ∗ q, , then we have γA ∗ q, ,r ∪ x2 λ λ a2 λ         a λ , r = 0, if q = r. γA r, 1 , p , But by the definition, we have γA ∗ q, a2 λ             λ a1 a1 a ∗ ∗ , p = γA q, , p = 0 ∪ γ A q, 1 , p Therefore γA q, a a λa     2   2     2 a1 a a 1 1 = γA q, , p . Hence γA ∗ q, , p = γA q, , p . Hence the a2 a2 a2 proof. Definition 4.3. A Watson Crick Intuitionistic Fuzzy Automaton (Recognizer) is a 6tuple M = (Q, , ρ, A, I , F), where Q and  are finite non empty sets called the set of states and set of Inputs respectively,  ∗ρis the complementarity relation, A = (μA , γA ) is  × Q, I = (μI , γI ) is a intuitionistic fuzzy subset an Intuitionistic fuzzy set in Q × ∗ of Q called the Intuitionistic initial Fuzzy state of Q, F = (μF , γF ) is a intuitionistic fuzzy subset of Q called the Intuitionistic fuzzy subset of Final states of Q.

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Let M = (Q, , ρ, A, I , F) be a Watson Intuitionistic Fuzzy  Crick     Automaton.   a b b a M is called Commutative if and only if μA p, 1 1 , q = μA p, 1 1 , q a b b2 a2         2 2 a1 b1 b1 a1 ,q = γA p, ,q and for all p, q in Q and γA p, a b b2 a2    2 2   a1 b  , 1 in . a2 b2  Theorem 4.3: Let M = (Q, , ρ, A, I , F) be a Watson Crick  Intuitionistic   x a ∗ = Fuzzy Automaton. If M is called Commutative, then μA p, 1 1 , q x a            2 2 a x x a a x μA ∗ p, 1 1 , q and γA ∗ p, 1 1 , q = γA ∗ p, 1 1 , q for all p, q a x x a a2 x2  2 2      2∗ 2 a1   x1 in Q and ∈ ∈ . a2 x2 ∗        ∗   a1 x ∈ Proof: (i) Let p, q be in Q and . 1 ∈ a2 x2 ∗  | |x | |x = = n. We prove this theorem by induction on 1 2           λ λ a1 a1 a1 λ x1 x1 a1 = = = = Let n = 0, then , and hence x2 x2 a2 a2 a2 λ λ λ a2   a1 x1 = a2 x2 Therefore



 



 

  

x a λ a1 μA ∗ p, 1 1 , q = μA ∗ p, = μA ∗ p, ,q x2 a2 λ a2





    a1 λ a1 x1 μA ∗ p, , q Hence the basis is true. , q = μA ∗ p, a2 λ a2 x2

a1 ,q a2

=

   ∗  z1 ∈ with |z1 | = |z2 | = n − 1, Assume that the result is true for all z2 ∗             b1  z1 b1 x a x1 n > 0. Let ∈ = , then μA ∗ p, 1 1 , q = , Let b2 x2 z2 b2 x2 a2      b a z μA ∗ p, 1 1 1 , q z2 b2 a2       z b = ∪r∈Q (μ∗A q, 1 , r ∩ μ∗A r, 1 z2 b2       z a = ∪r∈Q (μ∗A q, 1 , r ∩ μ∗A r, 1 z2 a2     z1 a1 b1 ∗ ,q = μA p, z2 a2 b2

  a1 ,p a2   b1 ,p b2

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        z a b = ∪r∈Q (μ∗A q, 1 1 , r ∩ μ∗A r, 1 , p z2 a2 b2         a1 z1 b ∗ ∗ , r ∩ μA r, 1 , p = ∪r∈Q (μA q, a2 z2 b2         a z b a x = μA ∗ p, 1 1 1 , q = μA ∗ p, 1 1 , q . Therefore the result is true for a2 z2 b2 a2 x2 every n.        ∗   a1 x ∈ (ii) Let p, q be in Q and . 1 ∈ a2 x2 ∗  | |x | |x = = n. We prove this theorem by induction on 1          2 λ λ a1 a1 x1 x1 a1 = = = = Let n = 0, then , and hence x2 x2 a2 a2 λ λ a2     a1 λ a1 x1 . = a2 λ a2 x2 Therefore             x a λ a1 a = γA ∗ p, ,q = γA ∗ p, 1 , q = γA ∗ p, 1 1 , q x2 a2 a2 λ a2         a λ a x γA ∗ p, 1 , q = γA ∗ p, 1 1 , q Hence the basis is true. a2 λ a2 x2  ∗    z1 ∈ with|z1 | = |z2 | = n − Assume that the result is true for all z2 ∗              z1 b1 x1 a1 b1 x1 ∗ ∈ = , then γA p, ,q = 1, n > 0. Let .Let b2 x2 z2 b2 x2 a2      z b a γA ∗ p, 1 1 1 , q z2 b2 a2         z1 b1 a1 ∗ ∗ , r ∪ γA r, ,p = ∩r∈Q γA q, z2 b2 a2         z a b = ∩r∈Q γA∗ q, 1 , r ∪ γA∗ r, 1 1 , p z2 a2 b2             z1 a1 b1 z1 a1 b ∗ ∗ ∗ , q = ∩r∈Q γA q, , r ∪ γA r, 1 , p = γA p, z2 a2 b2 z2 a2 b2         a z b = ∩r∈Q γA∗ q, 1 1 , r ∪ γA∗ r, 1 , p a2 z2 b2     a1 z1 b1 ∗ ,q = γA p, a2 z2 b2     a x = γA ∗ p, 1 1 , q a2 x2 Therefore the result is true for every n.

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Definition 4.4. Let  =(Q,∗ ,  ρ, A,I , F) be a Watson Crick Intuitionistic Fuzzy  M  x1 x1 ∈ , then is said to be recognised by M if Automaton. Let y1 ∗ y1     ∗ p, x1 , q ∧ μ (q)) > 0. (μ ∧ μ (p) I A F p,q∈Q y   1 

∗ p, x1 , q ∨ γ (q) < 1. (ii) F p,q∈Q (γI (p) ∨ γA y1 (i)



Theorem 4.4: Let , F) be a Watson Crick Intuitionistic Fuzzy (Q, ,  ρ, A, I  M =  ∗ x1 x1 ∈ , then is recognised by M if and only if there Automaton. Let y1 ∗ y1 exists p, q in Q such  that        x1 x ∗ ∗ p, , q ∧μ p, 1 , q ∨γF (q) < 1. > 0 ii) γ (i)μI (p)∧μA F (q) I (p)∨γA y1 y1 Proof:  Let M (Q, ,  =  ρ, A, I , F) be a Watson  Crick  Intuitionistic Fuzzy Automaton. ∗ x1 x1 ∈ , Let us suppose that is recognised by M. Let y1 ∗ y  1   x This implies that (i) p,q∈Q (μI (p) ∧ μA ∗ p, 1 , q ∧ μF (q)) > 0. y1    

x (ii) p,q∈Q (γI (p) ∨ γA ∗ p, 1 , q ∨ γF (q) < 1. y1     x ∗ Since Q is a finite set, there exists p and q in Q such that μI (p)∧μA p, 1 , q ∧ y1     x μF (q) > 0 and γI (p) ∨ γA ∗ p, 1 , q ∨ γF (q) < 1. y1     x Conversely let us suppose that μI (p) ∧ μA ∗ p, 1 , q ∧ μF (q) > 0 and γI (p) ∨ y1     x γA ∗ p, 1 , q ∨ γF (q) < 1 for p, q in Q, now y1          x1 x ∗ ∗ , q ∧ μF (q) ≤ (μI (p) ∧ μA p, 1 , q ∧ μF (q)) μI (p) ∧ μA p, p,q∈Q y1 y1     x i.e., 0 ≤ p,q∈Q (μI (p) ∧ μA ∗ p, 1 , q ∧ μF (q)) and y1          x x (γI (p) ∨ γA ∗ p, 1 , q ∨ γF (q) γI (p) ∨ γA ∗ p, 1 , q ∨ γF (q) ≥ p,q∈Q y1 y1      

x x1 is recognised by 1 ≥ p,q∈Q (γI (p) ∨ γA ∗ p, 1 , q ∨ γF (q). Therefore y1 y1 M.

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Definition 4.5. Let M =  A, I , F) Fuzzy (Q, ,  ρ,   be  a Watson Crick Intuitionistic  ∗  x1 x1 ∈ : isrecognisedbyM . Then L(M) is Automaton. Let L(M) = y1 ∗ y1 called the Language recognised by M. Let M = (Q, , ρ,

A, I ,F) be aWatson Crick Intuitionistic

  Fuzzy Automax

∗

x

1 ton. Then L(M) = ∈ : μI (p) ∧ μA ∗ p, 1 , q ∧ μF (q) > 0, γI (p) y1 ∗ y1      x ∨γA ∗ p, 1 , q ∨ γF (q) < 1forsomep, q ∈ Q . y1 Let M1 and M2 be two Watson Crick Intuitionistic Fuzzy Automata. We say that M1 and M2 are equivalent if they accept the same Languages, i.e., L(M1 ) = L(M2 ).

Theorem 4.5. Let Intuitionistic  A,∗ I, F) be a Watson Crick    Fuzzy   M = (Q,, ρ, y1  ∗ x1 x1 , ∈ . Define a relation ≡ on by ≡ Automaton. Let x2 y2 ∗ ∗ x2           y1 x y if and only if μA ∗ p, 1 , q > 0 ⇐⇒ μA ∗ p, 1 , q > 0 and y2 x2 y2         x y γA ∗ p, 1 , q < 1 ⇐⇒ γA ∗ p, 1 , q < 1 for all p, q in Q. Then ≡ is a x2 y2  ∗  . Congruence relation on ∗  Proof: Let

z1 z2



 ∈

∗ ∗



 and assume that

x1 x2



 ≡

 y1 . For all p, q in Q, we have y2

            z x z x μ∗A p, 1 1 , q > 0 ⇔ ∪r∈Q μ∗A p, 1 , r ∩ μ∗A r, 1 , q z2 x2 z2 x2         z1 x ∗ ∗ , r ∩ μA r, 1 , q > 0 ⇔ ∃r ∈ Q μA p, z2 x2         z y ⇔ ∃r ∈ Q μ∗A p, 1 , r ∩ μ∗A r, 1 , q > 0 z2 y2         z y ⇔ ∪r∈Q μ∗A p, 1 , r ∩ μ∗A r, 1 , q > 0 z2 y2     z1 y1 ∗ ⇔ μA p, ,q > 0 z2 y2             z x z x And γA ∗ p, 1 1 , q < 1 ⇐⇒ r∈Q γA ∗ p, 1 , r ∪ γA ∗ r, 1 , q z2 x2 z2 x2 < 1.         z x ⇔ ∃r ∈ Q γA∗ p, 1 , r ∪ γA∗ r, 1 , q < 1 z2 x2

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        z y ⇔ ∃r ∈ Q γA∗ p, 1 , r ∪ γA∗ r, 1 , q < 1 z2 y2         z1 y ∗ ∗ , r ∪ γA r, 1 , q < 1 ⇔ ∩r∈Q γA p, z2 y2     y ⇔ γA∗ p, 1 , q < 1 y2         z1 x1 z1 y1 x1 z1 y1 z1 Therefore ≡ , Similarly we can prove that ≡ . z2 x2 z2 y2 x2 z2 y2 z2  ∗  .” Hence ≡ is a Congruence relation on ∗

5 Application Ciliates are single-celled creatures having two types of nuclei: micronucleous and macronucleous nuclei. The DNA molecules are stored in the micronucleus, whereas the RNA is provided by the macronucleus. In the literature, gene assembly refers to the intramolecular process of transforming a micronucleous into a macronucleous. If this computation process involve imprecise and incomplete information, them Watson Crick Intuitionistic Fuzzy Automata will be very useful to apply.

6 Conclusion and Future Scope The concept of Watson Crick Intuitionistic Fuzzy Automata is introduced and their corresponding Intuitionistic Fuzzy Languages are also discussed. Some of the Algebraic and topological aspects of Watson Crick Intuitionistic Fuzzy Automata are discussed. The Future work intends to study Watson Crick Interval Valued Fuzzy Automata and Watson Crick Vague Automata using Watson Crick Complementarity relation.

References 1. Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986) 2. Czeizler, E., Czeizler, E.: A short survey on Watson-Crick automata. Bull. EATCS 88, 104–119 (2006) 3. Jun, Y.B.: Intuitionistic fuzzy finite state machines. J. Appl. Math. Comput. 17(1–2), 109–120 (2005) 4. Jun, Y.B.: Intuitionistic fuzzy finite switchboard state machines. J. Appl. Math. Comput. 20(1– 2), 315–325 (2006) 5. Vijayaraghavan, N., Jansirani, N., Dare, V.R.: Watson crick fuzzy automata with output. Adv. Math. Sci. J. 10(3), 1637–1654 (2021) 6. Wee, W.G., Fu, K.S.: A formulation of fuzzy automata and its application as a model of learning systems. IEEE Trans. Syst. Man Cybern. 5, 215–223 (1969) 7. Chen, J., Reif, J. (eds.): DNA 2003. LNCS, vol. 2943. Springer, Heidelberg (2004). https://doi. org/10.1007/b95518 8. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

Generalized Net Model of a Serial Composition of Services with Intuitionistic Fuzzy Estimations of Uncertainty Velin Andonov(B) , Stoyan Poryazov , and Emiliya Saranova Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Street, Block 8, 1113 Sofia, Bulgaria {velin andonov,stoyan,emiliya}@math.bas.bg Abstract. Generalized Nets (GNs) are used in the conceptual modelling of service systems. In the present paper, a GN model of a serial composition of services is proposed. The model includes intuitionistic fuzzy estimations of uncertainty in the form of intuitionistic fuzzy pairs. The intuitionistic fuzzy pairs are represented as characteristics of some tokens of the GN. A naming system for the places and the transitions of the GN is proposed which facilitates the analytical modelling. The proposed GN approach can be used in the construction of GNs representing more complex compositions of services. It can also be used to define new Quality of Service (QoS) indicators as a function of QoS indicators of the composed services. Keywords: Generalized nets · Conceptual modelling service characterization · Intuitionistic fuzzy pairs

1

· Quality of

Introduction

Generalized Nets (GNs, see [2]) are extensions of Petri nets. They are widely used for describing real-world sequential and parallel processes. In recent years, GNs have been used in the conceptual modelling of service systems and, in particular, of telecommunication systems. In [1], two GN models of the causal structure of a queuing system are constructed. In the paper, an overall approach to the conceptual modeling of service systems through GNs is described including a naming system of the places of the GN which enhances the analytical modelling. The models can be used in the study of the Quality of Service (QoS) of queuing systems. In particular, for the derivation of analytical expressions for QoS indicators. The work of Velin Andonov is supported by the research project Perspective Methods for Quality Prediction in the Next Generation Smart Informational Service Networks (KP-06-N52/2) financed by the Bulgarian National Science Fund. The work of S. Poryazov is partially supported by the Scientific Infrastructure Project (D01-222/22.10.2021), by the Bulgarian Ministry of Education and Science. c The Author(s), under exclusive license to Springer Nature Switzerland AG 2022  C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 616–623, 2022. https://doi.org/10.1007/978-3-031-09173-5_71

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In [7], the apparatus of the Intuitionistic Fuzzy (IF) sets is used to estimate the uncertainty of the service of requests by service devices. More specifically, for every virtual service device an Intuitionistic Fuzzy Pair (IFP, see [3]) is defined which evaluates the degree to which the requests are successfully serviced by the device. The study of the uncertainty estimation in service systems continues in [8] where three intuitionistic fuzzy characterizations of uncertainty in the service of requests by virtual service devices are proposed: IF traffic, IF flow and IF time characterization. The traffic characterizations are in compliance with ITU documents such as [4,5]. Each characterization is in the form of an IFP. The degrees of membership, non-membership and uncertainty are expressed as ratios of the parameters of the virtual service device. The proposed characterizations are evaluated for a serial composition of two virtual service devices as a part of a comprise service device. The degrees of membership, non-membership and uncertainty for the comprise device are expressed through the corresponding degrees of the embedded devices. The obtained results are important for the study of QoS composition in service systems. In the present paper, a GN model of a serial composition of services is constructed. It is based on the conceptual model of a serial composition of services described in [8].

2

Preliminaries

The overall approach to the modelling of service systems described in [6] is based on the notion of base virtual device. Every base virtual device x has the following parameters: intensity of the flow of requests (Fx ), probability of directing the flow of requests towards the device (Px ), service time in the device (Tx ), traffic intensity (Yx , measured in Erlang). Various types of base virtual devices are used (see [6]). Their graphical representation is shown in Fig. 1.

Fig. 1. Types of base virtual service devices.

Every type of base virtual device has a specific function (see [8]).

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Fig. 2. Causal decomposition of the traffic inside a virtual service device x (see [8]).

A conceptual model of the causal decomposition of the traffic inside a virtual service device x is shown in Fig. 2. Special qualifiers are used for characterization of the traffic: not served (nsr.), offered (ofr.), served (srv.), uncertain (unc.), abortive(abr.) and successful (scc.). For their explanation see [8]. The qualifiers may be two, one or none. If the parameter’s symbol is omitted, then the causal name is a name of a device (see Fig. 2). The devices’ names are in small or subscript letters. For example, scc.Fx is the intensity of the carried flow of requests of the device x (see Fig. 3). In the figures, only the names of causal devices may be present. The names of the device parameters are implicit. Now, the three intuitionistic fuzzy characterizations of the service of the requests by device x are defined as follows. 1) IF traffic characterization: μyx =

scc.Yx y nsc.Yx y unc.Yx ; νx = ; πx = . ofr .Yx ofr .Yx ofr .Yx

(1)

2) IF flow characterization: μfx =

scc.Fx f nsc.Fx f unc.Fx ;ν = ;π = . ofr .Fx x ofr .Fx x ofr .Fx

(2)

3) IF time characterization: μtx =

prt.scc.Tx t prt.abr .Tx t prt.unc.Tx ; νx = ; πx = . srv .Tx srv .Tx srv .Tx

(3)

For the definition of partial service time (qualifier prt.) see [8]. Using the conceptual model of the causal decomposition of the traffic inside a virtual service device above, a conceptual model of a serial composition of two service devices is proposed in [8]. The model is shown in Fig. 3.

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Fig. 3. Serial composition of services in a comprise virtual service device (see [8]).

3

Generalized Net Model of a Serial Composition of Services

We shall construct a GN model of a serial composition of services based on the conceptual model shown in Fig. 3. In the model, reduced GN is used (see [2]). The graphical representation of the GN model is shown in Fig. 4. Z1

Z2

Z3

Z4

Z5

Z6

Z7

Z8

Z9

Z10

l l2 l5 l7 l9 l11 l13 l15 l17  10                  

l1

l6

l8

lscc1

      lnsr1

lunc1

   

l3

  l4

  lof r1

 

l14

 

l16

lscc2

    l12 lnsr2 lunc2   lest1         lof r2 lestx      lsrv1      lest2    

lof rx

 

lsrv2

 

Fig. 4. Generalized net model of a serial composition of services.

The GN model consists of 10 transitions and 31 places. The labels of places corresponding to virtual devices from Fig. 3 are in the form lx where “x” is the name of the corresponding virtual device but the “.” symbol, if present in the name of the device, has been omitted. Fourteen types of tokens are used denoted by greek letters (α, β, ..., π).

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– Tokens of type α represent the requests. In the initial time moment of the GN functioning, token α stays in place l1 with initial characteristic “formula for generating the offered flow of requests to the comprise virtual device x”. – Token of type β stays in place lof r1 in the initial time moment with initial characteristic “initial values of Yof r1 , Pof r1 , Fof r1 , Tof r1 , Nof r1 ”. It accumulates data about the ofr.1 device. – Token of type γ stays in place lof rx in the initial time moment with initial characteristic “initial values of Yof rx , Pof rx , Fof rx , Tof rx , Nof rx ”. It accumulates data about the ofr.x device. – Token of type δ stays in place lnsr1 in the initial time moment with initial characteristic “initial values of Ynsr.1 , Pnsr.1 , Fnsr.1 , Tnsr.1 , Nnsr.1 ”. It accumulates data about the nsr.1 device. – Token of type  stays in place lunc1 in the initial time moment with initial characteristic “initial values of Yunc.1 , Punc.1 , Func.1 , Tunc.1 , Nunc.1 ”. It accumulates data about the unc.1 device. – Token of type ζ stays in place lscc.1 in the initial time moment with initial characteristic “initial values of Yscc.1 , Pscc.1 , Fscc.1 , Tscc.1 , Nscc.1 ”. It accumulates data about the scc.1 device. – Token of type η stays in place lest1 in the initial time moment with initial characteristic “initial values of μy1 , ν1y , μf1 , ν1f , μt1 , ν1t ”. It accumulates the uncertainty estimations in the form of IFPs. – Token of type θ stays in place lsrv1 in the initial time moment with initial characteristic “initial values of Ysrv.1 , Psrv.1 , Fsrv.1 , Tsrv.1 , Nsrv.1 ”. It accumulates data about the srv.1 device. – Tokens of types κ, λ, μ, ν, ξ, o, π stay in places lof r2 , lnsr2 , lunc2 , lscc2 , lestx , lest2 , lsrv2 respectively. Their initial characteristics are the same as the characteristics of the tokens in the corresponding places of the first device of the serial composition. The formal description of the GN transitions follows below. Z1 = {l1 , lof r1 , lof rx }, {l2 , l3 , l4 , lof r1 , lof rx }, r1 , where r1 =

l1

lof r1 lof rx

l2 l3 l4 lof r1 lof rx true f alse f alse true true . f alse true f alse true f alse f alse f alse true f alse true

Token α in place l1 splits into three identical tokens which enter respectively places l2 , lof r1 , lof rx . In places lof r1 and lof rx , they merge with the β and γ tokens. Tokens β and γ obtain the characteristics “current values of Yof r1 , Pof r1 , Fof r1 , Tof r1 , Nof r1 ” and “current values of Yof rx , Pof rx , Fof rx , Tof rx , Nof rx ”, respectively. At each time step, the β and γ tokens in places lof r1 and lof rx split into two identical tokens one of which remains in the original place while the other one enters places l3 and l4 without obtaining a new characteristic. Z2 = {l2 , lnsr1 }, {l5 , l6 , lnsr1 }, r2 ,

Generalized Net Model of a Serial Composition of Services

where r2 =

l1

lnsr1

621

l5 l6 lnsr1 true f alse true . f alse true true

The α token in place l2 splits into two identical tokens one of which enters place lnsr1 and merges with the δ token there. The other one enters place l5 without obtaining a new characteristic. Token δ in place lnsr1 splits into two identical tokens one of which remains in place lnsr1 and obtains the characteristic “current values of Ynsr.1 , Pnsr.1 , Fnsr.1 , Tnsr.1 , Nnsr.1 ”. The other one enters place l6 without obtaining a new characteristic. Z3 = {l5 , lunc1 }, {l7 , l8 , lunc1 }, r3 , where r3 =

l5

lunc1

l7 l8 lunc1 true f alse true . f alse true true

The α token in place l5 splits into two identical tokens one of which enters place lunc1 and merges with the  token there. The other one enters place l7 without obtaining a new characteristic. Token  in place lunc1 splits into two identical tokens one of which remains in place lunc1 and obtains the characteristic “current values of Yunc.1 , Punc.1 , Func.1 , Tunc.1 , Nunc.1 ”. The other one enters place l8 without obtaining a new characteristic. Z4 = {l7 , lscc1 }, {l9 , lscc1 }, r4 , where

l9 lscc1 r4 = l7 true true . lscc1 f alse true

The α token in place l7 splits into two identical tokens one of which enters place lscc1 and merges with the ζ token there. The other one enters place l9 with characteristic “current values of Yscc.1 , Pscc.1 , Fscc.1 , Tscc.1 , Nscc.1 ”. Token ζ in place lscc1 obtains the characteristic “current values of Yscc.1 , Pscc.1 , Fscc.1 , Tscc.1 , Nscc.1 ”. Z5 = {l3 , l6 , l8 , l9 , lest1 , lsrv1 }, {l10 , lest1 , lsrv1 }, r5 , where

l10 lest1 lsrv1 l3 f alse true f alse l6 f alse true f alse r5 = l8 f alse true f alse . l9 true true true lest1 f alse true f alse lsrv1 f alse f alse true

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Token α in place l9 splits into three identical tokens which enter places l10 , lest1 and lsrv1 and merge with the tokens there. Tokens β in place l3 , δ in place l6 ,  in place l11 enter place lest1 and merge with the η token there. Token η in place lest1 obtains the characteristic “current values of μy1 , ν1y , μf1 , ν1f , mut1 , ν1t ”. The values of the IFPs are evaluated using Eqs. (1), (2) and (3). Token θ in place lsrv1 obtains the characteristic “current values of Ysrv.1 , Psrv.1 , Fsrv.1 , Tsrv.1 , Nsrv.1 ”. Z6 = {l10 , lof r2 }, {l11 , l12 , lof r2 }, r6 , where

l11 l12 lof r2 r6 = l10 true f alse true . lof r2 f alse true true

The α token in place l10 splits into two identical tokens one of which enters place lof r2 and merges with the θ token there. The other one enters place l11 without obtaining a new characteristic. Token θ in place lof r2 splits into two identical tokens one of which remains in place lof r2 and obtains the characteristic “current values of Yof r.2 , Pof r.2 , Fof r.2 , Tof r.2 , Nof r.2 ”. The other one enters place l12 without obtaining a new characteristic. Transitions Z7 , Z8 and Z9 have the same formal description as transitions Z2 , Z3 and Z4 , respectively. That is why we omit their description. Z10 = {l4 , l12 , l14 , l16 , l17 , lestx , lest2 , lsrv2 }, {lestx , lest2 , lsrv2 }, r10 , where

r10

l4 l12 l14 = l16 l17 lestx lest2 lsrv2

lestx lest2 lsrv2 true f alse f alse f alse true f alse f alse true f alse f alse true f alse . f alse true true true f alse f alse f alse true f alse f alse f alse true

Token α in place l17 splits into two identical tokens which enter places lsrv2 , lest2 and merge with the tokens there. Token γ in place l4 enters place lestx and merges with the ν token there. Token ν in place lestx obtains the characteristic “current values of μyx , νxy , μfx , νxf , μtx , νxt  ”. The values of the IFPs are evaluated using Eqs. (1), (2) and (3). Tokens θ in place l12 , κ in place l14 and λ in place l16 enter place lest2 and merge with the ξ token there. Token ξ in place lest2 obtains the characteristic “current values of μy2 , ν2y , μf2 , ν2f , μt2 , ν2t  ”. The values of the IFPs are evaluated using Eqs. (1), (2) and (3). Token o in place lsrv2 obtains the characteristic “current values of Ysrv.2 , Psrv.2 , Fsrv.2 , Tsrv.2 , Nsrv.2 ”.

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4

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Conclusion

The proposed GN model of a serial composition of services can be used in the study of QoS compositions in service systems such as an overall telecommunication system and for derivation of analytical expressions of QoS indicators. With some minor changes, it can be easily included in more complex GN models of service systems in which serial composition of services is present. In future, GN models of other compositions of services such as parallel composition, cycle, etc., should be constructed.

References 1. Andonov, V., Poryazov, S., Saranova, E.: Generalized net representations of the causal structure of a queuing system. In: Proceedings of the 2020 IEEE 10th International Conference on Intelligent Systems (IS), Varna, Bulgaria, pp. 80–86 (2020) 2. Atanassov, K.: On Generalized Nets Theory. Prof. M. Drinov Academic Publ. House, Sofia, Bulgaria (2007) 3. Atanassov, K., Szmidt, E., Kacprzyk, J.: On intuitionistic fuzzy pairs. Notes Intuitionistic Fuzzy Sets 19(3), 1–13 (2013) 4. ITU-T E.501 (05/97): Estimation of traffic offered in the network 5. ITU-T Recommendation E.600 (03/93), Terms and definitions of traffic engineering 6. Poryazov, S., Saranova, E.: Models of Telecommunication Networks with Virtual Channel Switching and Applications. Prof. Marin Drinov Academic Publishing House (2012). (in Bulgarian) 7. Poryazov, S., Andonov, V., Saranova, E.: Intuitionistic fuzzy representation of uncertainty in biomedical operations. In: Sotirov, S.S., Pencheva, T., Kacprzyk, J., Atanassov, K.T., Sotirova, E., Staneva G. (eds.) Contemporary Methods in Bioinformatics and Biomedicine and Their Applications. BioInfoMed 2020. Lecture Notes in Networks and Systems, vol. 374. Springer, Cham (2022). https://doi.org/10.1007/ 978-3-030-96638-6 29 8. Poryazov, S., Andonov, V., Saranova, E.: Three intuitionistic fuzzy estimations of uncertainty in service compositions. In: Atanassov, K.T., et al. (eds.) Uncertainty and Imprecision in Decision Making and Decision Support: New Advances, Challenges, and Perspectives. IWIFSGN 2020, BOS/SOR 2020. Lecture Notes in Networks and Systems, vol. 338. Springer, Cham (2022). https://doi.org/10.1007/9783-030-95929-6 6

Intuitionistic Fuzzy Estimations of Uncertainty of a Parallel Composition of Services Stoyan Poryazov , Velin Andonov(B) , and Emiliya Saranova Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Street, Block 8, 1113 Sofia, Bulgaria {stoyan,velin andonov,emiliya}@math.bas.bg

Abstract. The problem for representation of uncertainty in service systems is studied in [6, 7] where the ITU traffic characterization is extended with the proposed three Intuitionistic Fuzzy (IF) characterizations: IF flow characterization, IF traffic characterization, IF time characterization. In this paper, a conceptual model of a parallel composition of services is proposed which includes the intuitionistic fuzzy characterizations. On the basis of this model, three estimations of the uncertainty of the parallel composition are obtained. They are Quality of Service (QoS) indicators of a parallel composition of services. Keywords: Conceptual modelling · Quality of service characterization · Intuitionistic fuzzy pairs

1

Introduction

The uncertainty representation problem in the service of requests in service systems, and more specifically in biomedical operations is studied in [6]. First a conceptual model of the causal decomposition of the service of requests inside a base virtual service device is proposed which is aimed at quantifying the uncertainty. The traffic inside the virtual service device is characterized through qualifiers: .srv (served), .ofr (offered), .scc (successful), .unc (uncertain), .nsr (not served). The definitions of these qualifiers are based on ITU documents such as [2,3]. A characterization of the uncertainty in the service of requests is proposed based on the conceptual model which uses the notion of intuitionistic fuzziness and more precisely the Intuitionistic Fuzzy Pair (IFP, see [1]). The study of the representation of the uncertainty in the service of requests is continued in [7], where three intuitionistic fuzzy estimations of uncertainty The work of Velin Andonov and Emiliya Saranova is supported by the research project Perspective Methods for Quality Prediction in the Next Generation Smart Informational Service Networks (KP-06-N52/2) financed by the Bulgarian National Science Fund. The work of S. Poryazov is partially supported by the Scientific Infrastructure Project (D01-222/22.10.2021), by the Bulgarian Ministry of Education and Science. c The Author(s), under exclusive license to Springer Nature Switzerland AG 2022  C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 624–631, 2022. https://doi.org/10.1007/978-3-031-09173-5_72

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are proposed: IF traffic characterization, IF flow characterization and IF time characterization. They are in the form of IFPs. The proposed characterizations are estimated for a comprise virtual service device containing a consecutive composition of two virtual service devices. In the present paper, a conceptual model of a parallel composition of services is proposed. The degrees of membership, non-membership and uncertainty of the IF characterizations of the comprise service device are expressed as linear combinations of the corresponding degrees of membership, non-membership and uncertainty of the embedded devices. The obtained analytical expressions can be used in the study of the dependence of the Quality of Service (QoS) of comprise devices on the QoS of embeded devices.

2

Preliminaries

For the conceptual modelling service systems, the approach described in [5] is used. At the lowest level, we have base virtual devices which do not contain other devices. Each base virtual device x has the following parameters: intensity of the flow of requests (Fx ), probability of directing the flow of requests towards the device (Px ), service time in the device (Tx ), traffic intensity (Yx , measured in Erlang). Different types of base virtual devices are used (see [5]). Their graphical representation is shown in Fig. 1.

Fig. 1. Types of base virtual service devices.

A conceptual model of the causal decomposition of the traffic inside a virtual service device x is shown in Fig. 2. For the definitions of not served, offered, served, uncertain and successful traffic see [7]. The qualifiers may be two, one or none. In case that the parameter’s symbol is omitted, the causal name is a name of a device (see Fig. 2). The names of the devices are in small or subscript letters. For example, scc.Fx is the intensity of the carried flow of requests of the device x (see Fig. 3). In the figures, only the names of causal devices may be present. The names of the device parameters are implicit.

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Fig. 2. Causal decomposition of the traffic inside a virtual service device x (see [7]).

Now, the three intuitionistic fuzzy characterizations of the service of the requests by device x are defined as follows. 1) IF traffic characterization: μyx =

scc.Yx y nsc.Yx y unc.Yx ;ν = ;π = . ofr .Yx x ofr .Yx x ofr .Yx

(1)

2) IF flow characterization: μfx =

scc.Fx f nsc.Fx f unc.Fx ; νx = ; πx = . ofr .Fx ofr .Fx ofr .Fx

(2)

3) The IF time characterization, considered in [6] and [7], is equivalent to the IF traffic characterization and we’ll not use it here.

3

Parallel Composition of Services

A conceptual model of a parallel composition of two services inside a comprise virtual service x is shown in Fig. 3. The composition of the two embeded service devices 1 and 2 is parallel alternative, i.e. every request is serviced by only one of the two devices. The type of service ending of the embeded devices is preserved (remains the same) for the comprise device. An example of a parallel alternative service is an office with two service places, of the same type. We shall derive analytical expressions for the intuitionistic fuzzy traffic characterization of the comprise device through the intuitionistic fuzzy characterizations of the embeded devices. For the degree of membership μyx we have: μyx =

scc.Y1 + scc.Y2 scc.Yx = . ofr .Yx ofr .Y1 + ofr .Y2

(3)

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Fig. 3. Conceptual model of a parallel composition of two services within a comprise virtual service device x.

Using the graphical representation in Fig. 3 and the Theorem of Little (see [4]), for the offered traffic to first embedded service device we have: of r.Y1 = of r.F1 srv.T1 = ofr .Fx P1 {unc.P1 unc.T1 + (1 − unc.P1 )scc.T1 }. (4) Similarly, for the offered traffic to the second embeded service device we have: of r.Y2 = of r.F2 srv.T2 = ofr .Fx P2 {unc.P2 unc.T2 + (1 − unc.P2 )scc.T2 }. (5) From (3), (4) and (5) we obtain ofr .Yx = ofr .Fx {P1 srv.T1 + P2 srv.T2 }.

(6)

In order to derive expressions for the successfully served traffic by the first (scc.Y1 ) and the second (scc.Y2 ) embeded service devices, first we notice that scc.Y1 = scc.F1 scc.T1 = ofr .Fx P1 (1 − nsc.P1 )(1 − unc.P1 )scc.T1 .

(7)

The degree of membership of the intuitionistic fuzzy traffic characterization of the first embeded service device is given by (1 − nsc.P1 )(1 − unc.P1 )scc.T1 . srv.T1 From (7) and (8) we obtain μy1 =

scc.Y1 = ofr .Fx P1 μy1 srv.T1 .

(8)

(9)

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In a similar way, we can verify that scc.Y2 = ofr .Fx P2 μy2 srv.T2 .

(10)

From (3), (6), (9) and (10) we obtain μyx =

ofr .Fx [P1 μy1 srv.T1 + P2 μy2 srv.T2 ] ofr .Fx [P1 srv.T1 + P2 srv.T2 ] = k1 μy1 + k2 μy2 ,

(11)

where k1 and k2 do not depend from the input flow intensity ofr .Fx : k1 =

P1 srv.T1 P2 srv.T2 ; k2 = . P1 srv.T1 + P2 srv.T2 P1 srv.T1 + P2 srv.T2

(12)

Now, we shall derive expression for the degree of non-membership of the intuitionistic fuzzy traffic characterization of the comprise virtual service device x through the degrees of non-membership of the intuitionistic fuzzy traffic characterizations of the embeded devices. From the definition of νxy we have νxy =

nsc.Y1 + nsc.Y2 nsc.Yx = . ofr .Yx of r.Y1 + of r.Y2

(13)

From (6) we have ofr .Yx = ofr .Fx (P1 srv.T1 + P2 srv.T2 ). nsc.Y1 = ofr .Fx P1 nsc.P1 nsc.T1 .

(14)

nsc.Y2 = ofr .Fx P2 nsc.P2 nsc.T2 .

(15)

From (6), (13), (14) and (15) we obtain νxy =

P1 nsc.P1 nsc.T1 + P2 nsc.P2 nsc.T2 . P1 srv.T1 + P2 srv.T2

(16)

For the degrees of non-membership of the intuitionistic fuzzy traffic characterizations of the embeded devices we have nsc.P1 nsc.T1 ; srv.T1 nsc.P2 nsc.T2 ν2y = . srv.T2 ν1y =

(17)

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Following the definition of equivalent offered traffic (see [3]), where nsc.T = srv.T , the two expressions above are equivalent respectively to nsc.P1 nsc.T1 = srv.T1 ν1y and

nsc.P2 nsc.T2 = srv.T2 ν2y .

After substitution of the above two equalities in (16) and using(12), we obtain νxy = k1 ν1y + k2 ν2y .

(18)

Finally, we shall express the degree of uncertainty of the intuitionistic fuzzy traffic characterization of the comprise service device x. πxy =

unc.Yx . ofr .Yx

(19)

From the graphical representation we have: unc.Yx = unc.Y1 + unc.Y2 .

unc.Y1 = unc.F1 + unc.T1 = ofr .Fx P1 (1 − nsc.P1 )unc.P1 unc.T1 .

(20)

(21)

The degree of uncertainty of the first embeded device is given by π1y =

(1 − nsc.P1 )unc.P1 unc.T1 . srv.T1

(22)

From (21) and (22) we obtain unc.Y1 = ofr .Fx P1 srv.T1 π1y .

(23)

unc.Y2 = ofr .Fx P2 srv.T2 π2y .

(24)

Analogously,

Combining (19), (20), (21), (24) and using (12) we obtain πxy = k1 π1y + k2 π2y .

(25)

For the degree of membership of the intuitionistic fuzzy flow characterization of the comprise service device we have: μfx =

scc.F1 + scc.F2 scc.F x = . of r.F x of r.F1 + of r.F2

(26)

From the graphical representation of the conceptual model it is clear that ofr .Fx = of r.F1 + of r.F2 .

(27)

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scc.F1 = ofr .Fx P1 (1 − nsc.P1 )(1 − unc.P1 ).

(28)

μf1 = (1 − nsc.P1 )(1 − unc.P1 ).

(29)

From (28) and (29) we have scc.F1 = ofr .Fx P1 μf1 .

(30)

scc.F2 = ofr .Fx P2 μf2 .

(31)

Analogously,

From (26), (28), (31) we obtain μfx = P1 μf1 + P2 μf2 .

(32)

For the degree of non-membership of the intuitionistic fuzzy flow characterization of the comprise virtual service device x we have νxf = nsc.Px =

ofr .Fx (P1 nsc.P1 + P2 nsc.P2 ) = P1 nsc.P1 + P2 nsc.P2 . ofr .Fx ν1f = nsc.P1 ,

ν2f = nsc.P2 .

(33) (34)

From (33) and (34) we obtain νxf = P1 ν1f + P2 ν2f .

(35)

Finally, for the degree of uncertainty of the intuitionistic fuzzy flow characterization of the comprise service device x we have πxf = (1 − nsc.Px )unc.Px =

ofr .Fx (1 − nsc.P1 )unc.P1 + P2 (1 − nsc.P2 )unc.P2 ofr .Fx

‘ = (1 − nsc.P1 )unc.P1 + P2 (1 − nsc.P2 )unc.P2 .

(36)

π1f = (1 − nsc.P1 )unc.P1 , π2f = (1 − nsc.P2 )unc.P2 .

(37)

From (36) and (37) we obtain πxf = P1 π1f + P2 π2f .

(38)

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Conclusion

The IF traffic degrees are expressed respectively through the degrees of membership, non-membership and uncertainty of the intuitionistic fuzzy traffic characterizations of the embeded devices. The degrees of membership, non-membership and uncertainty of the comprise service device are linear combinations of the corresponding degrees of membership, non-membership and uncertainty of the embeded devices with coefficients k1 and k2 . The sum of the coefficients is equal to 1. Therefore, these coefficients are weights. Another important observation is that the coefficients k1 and k2 do not depend on the load. The degrees of membership, non-membership and uncertainty of the intuitionistic fuzzy flow characterization of the comprise virtual service device x are expressed as linear combinations of the degrees of membership, non-membership and uncertainty of the embeded devices in a parallel composition of two services. The coefficients P1 and P2 in (32), (35) and (38) do not depend on the load of the system and P1 + P2 = 1. Therefore, they are weights. The obtained expressions are homogenous as the degrees of membership of the comprised device (μyx and μfx ) depend on the corresponding degrees of membership of the embeded devices (μy1 ,μy2 and μf1 ,μf2 ); the degrees of nonmembership of the comprised device (νxy and νxf ) depend on the degrees of nonmembership of the embeded devices (ν1y ,ν2y and ν1f ,ν2f ); the degrees of uncertainty of the comprised device (πxy and πxf ) depend on the degrees of uncertainty of the embeded devices (π1y ,π2y and π1f ,π2f ).

References 1. Atanassov, K., Szmidt, E., Kacprzyk, J.: On intuitionistic fuzzy pairs. Notes Intuitionistic Fuzzy Sets 19(3), 1–13 (2013) 2. ITU-T E.501 (05/97): Estimation of traffic offered in the network 3. ITU-T Recommendation E.600 (03/93), Terms and definitions of traffic engineering 4. Little, J.D.C.: A proof of the queueing formula L = λW . Oper. Res. 9, 383–387 (1961) 5. Poryazov, S., Saranova, E.: Models of Telecommunication Networks with Virtual Channel Switching and Applications. Prof. Marin Drinov Academic Publishing House, Sofia (2012). (In Bulgarian) 6. Poryazov, S., Andonov, V., Saranova, E.: Intuitionistic fuzzy representation of uncertainty in biomedical operations. In: Sotirov, S.S., Pencheva, T., Kacprzyk, J., Atanassov, K.T., Sotirova, E., Staneva, G. (eds.) Contemporary Methods in Bioinformatics and Biomedicine and Their Applications. BioInfoMed 2020. LNNS, vol. 374. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-96638-6 29 7. Poryazov, S., Andonov, V., Saranova, E.: Three intuitionistic fuzzy estimations of uncertainty in service compositions. In: Atanassov, K.T., et al. (eds.) Uncertainty and Imprecision in Decision Making and Decision Support: New Advances, Challenges, and Perspectives. IWIFSGN 2020, BOS/SOR 2020. LNNS, vol. 338. Springer, Cham (2022)

Intuitionistic Fuzzy Model for Franchisee Selection Velichka Traneva(B)

and Stoyan Tranev

“Prof. Asen Zlatarov” University, “Prof. Yakimov” Blvd, 8000 Bourgas, Bulgaria [email protected], [email protected] http://www.btu.bg

Abstract. In today’s dynamic market environment, accompanied by galloping inflation and the epidemic caused by Covid-19, the franchise business model is an effective choice for companies to expand and strengthen their business. The process of digital transformation of the business under unclear conditions requires updating the multicriteria methods for decision making regarding the selection of the most suitable franchisee. The selection of the most suitable franchisee applicant in an uncertain environment is a key decision for a franchisor and the success of a franchising business. In this research, a generalized problem for optimal franchisee selection is formulated and a new approach for solution of this problem is proposed by the theories of index matrices and intuitionistic fuzzy logic. The priorities of the evaluation criteria and the rating of the experts are taken into account in the proposed algorithm. The intelligent decision support model is applied on a franchisee selection in the first Bulgarian franchise patisserie with entirely Bulgarian know-how, leading to winning results. In the future, a software application will be developed to transform the process of selection of a franchisee into digital in an uncertain environment.

Keywords: Franchising

1

· Index matrix · Intuitionistic fuzzy sets

Introduction and Literature Review

Social distance, lockdown and the new normal are the consequences of the global pandemic crisis caused by Covid-19. To avoid the economic collapse, companies look for new ways to expand and digitally transform their business. Franchising is an effective business strategy for entering new markets. The franchisor gives the right to its franchisees to use the business brand, the concept and the products (services) for a certain period of time [10]. Developing an effective smart franchisee model in a rapidly changing environment with a galloping inflation is a challenge for the franchisor. Selecting the most appropriate franchisee is Supported by the Asen Zlatarov University under Project NIX-440/2020 “Index matrices as a tool for knowledge extraction”. c The Author(s), under exclusive license to Springer Nature Switzerland AG 2022  C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 632–640, 2022. https://doi.org/10.1007/978-3-031-09173-5_73

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a key moment for the brand effectiveness at both a national and an international market [12,17] and belong to the algorithms of Group Decision Making (GDM) [4]. Decision-making models need to be extended in view of their application to unclear or missing data. Fuzzy logic [24] and its extensions are an artificial intelligence tool for creating such models. The study [13] presents a fuzzy franchisee selection model from the franchisor’s perspective using the Analytic Hierarchy Process (AHP). [18] describes a fuzzy cloud-based responsive system to propose decision help in franchised businesses. In [23] is proposed a fuzzy franchising decision support system for future development planning. In [16] is considered the selection of franchise convenience store location by applying AHP and neural network in an uncertain environment. Fuzzy AHP was used in [11] in order to locate a franchise in Colombia. Intuitionistic fuzzy sets (IFSs) [4], which are an extension of fuzzy sets of Zadeh, have a degree of hesitation. They are a stronger tool for presenting ambiguity in the environment. In the face of the contemporary rapid inflation and pandemics, it is necessary to expand franchisee selection models so that they can be applied to unclear or missing data. In our study is formulated an intuitionistic fuzzy problem for finding the most effective franchise candidate and is proposed a new approach to its solution (IFIMFr), using the concepts of index matrices (IMs, [2]) and intuitionistic fuzzy sets (IFSs, [1,4]). The rank coefficients of the experts and the priorities of the evaluation criteria according to the franchising services are used in the solution algorithm for this problem. The contributions of the research are: its proposal for an intuitionistic fuzzy approach to selecting the most suitable candidates for franchising in conditions of unclear parameters and its application to a real case - a franchise chain of patisseries in Bulgaria. The rest of our study includes 4 sections as follows: Sect. 2 describes some theoretical statements from the theory of IMs and IF logic. Section 3 formulates a type of generalized IF problem for the selection of a franchisee and describe the IF methodology for its solution. In the Sect. 4, the proposed approach is applied on a real case study in the first Bulgarian franchise patisserie. Section 5 sets out the conclusions and aspects for future research.

2

Remarks on IMs and Intuitionistic Fuzzy (IF) Logic

This section marks some definitions of the concepts of IF logic [4] and IMs [3]. 2.1

Intuitionistic Fuzzy Pair (IFP)

IFP is in the form of μ(p), ν(p), where μ(p), ν(p) ∈ [0, 1] and μ(p) + ν(p) ≤ 1 are the degrees of membership and non-membership of a proposition p [7]. The basic operations and relations with IFPs x = a, b and y = c, d are described in [4,7,19]. Let Ra,b = 0.5(2 − a − b)(1 − a) [19]. Then, as per [4,21]: x ≥ y iff b ≤ d; x ≥R y iff Ra,b ≤ Rc,d .

(1)

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Three-Dimensional Intuitionistic Fuzzy Index Matrices (3-D IFIM)

The definition of a 3-D IFIM [K, L, H, {μki ,lj ,hg , νki ,lj ,hg }], (K, L, H ⊂ I) with IF elements, we denote the object [3,20]: hg ∈ H l1 ... lj ... ln k1 μk1 ,l1 ,hg , νk1 ,l1 ,hg  . . . μk1 ,lj ,hg , νk1 ,lj ,hg  . . . μk1 ,ln ,hg , νk1 ,ln .hg  .. .. .. .. . ... . ... . . km μkm ,l1 ,hg , νkm ,l1 ,hg  . . . μkm ,lj ,hg , νkm ,lj ,hg  . . . μkm ,ln ,hg , νkm ,ln ,hg  (2) In [3,20,22], were proposed operations with 3-D IFIMs, analogous to those with the classical matrices, but there are also specific ones such as projection, substitution, aggregation operations, internal subtraction of IMs’ components, term-wise multiplication and subtraction. Let us remind some of them, which have an application in the algorithm of IFIMFr. Aggregation Operation by One Dimension [22] l1 αK,#q (A, k0 ) =

...

ln

m

m

i=1

i=1

k0 #q μki ,l1 , νki ,l1  . . . #q μki ,ln , νki ,ln 

, (1 ≤ q ≤ 3)

(3)

If we use #∗1 = min, max we accept super pessimistic aggregation operation, with #∗2 = average, average we assume averaging aggregation operation and with #∗3 = max, min we accept super optimistic aggregation operation. Projection: Let M ⊆ K, N ⊆ L and U ⊆ H. Then, prM,N,U A = [M, N, U, {bki ,lj ,hg }], and for each ki ∈ M, lj ∈ N and hg ∈ U, bki ,lj ,hg = aki ,lj ,hg . Substitution: A substitution over the IM B is defined for the pair of indices (p, ki ) by   p ; ⊥; ⊥ B = [(K − {ki }) ∪ {p}, L, H, {bki ,l,h }] (4) ki

3

An Intuitionistic Fuzzy Index-Matrix Model for Selection of a Franchisee

In this section a type of IF problem for selecting the most effective candidate for franchising in an uncertain environment will be presented. The problem is: A franchise company has planned to expand its business by choosing a franchisee. Three experts have participated in the discussion for selection of the most optimal candidate. Each of the experts has a rating according to their participation in the number of procedures for selection of a franchisee. The evaluations are based on criteria that also have priority coefficients according to their importance from the franchisor’s point of view. The company

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has a criterion system for evaluating franchise candidates {k1 , . . . , ki , . . . , km } (for i = 1, ..., m) for its brand ve , containing criteria {c1 , . . . , cj , . . . , cn } (for j = 1, ..., n). The experts {d1 , . . . , ds , . . . , dD } (for s = 1, ..., D) assess the IF priorities pk cj ,ve of the criteria cj (for j = 1, ..., n) in the evaluation system of the candidates for the franchise chain ve . The ratings of the experts {r1 , . . . , rs , . . . , rD } in the form of IFPs δs , s (1 ≤ s ≤ D) are defined on the basis of their participation in γs (s = 1, ..., D) evaluating franchise procedures respectively and given to the experts. All candidates for a franchisee have been evaluated by the experts in a time-moment hf and their evaluations ev ki ,cj ,ds (for 1 ≤ i ≤ m, 1 ≤ j ≤ n, 1 ≤ s ≤ D) are intuitionistic fuzzy data. The aim of the problem is to select the most eligible franchisee for this brand. The solution procedure, which we denote as IFIMFr, includes the following steps: Step 1. A 3-D IFIM EV [K, C, E, {ev ki ,cj ,ds }] is built with the dimensions K = {k1 , k2 , . . . , km }, C = {c1 , c2 , . . . , cn } and E = {d1 , d2 , . . . , dD } . The elements {ev ki ,cj ,ds } = μki ,cj ,ds , νki ,cj ,ds  (for 1 ≤ i ≤ m, 1 ≤ j ≤ n, 1 ≤ s ≤ D) of the IM EV , are the valuation of the ds -th expert for the ki -th candidate by the cj -th criterion. Expert assessments are uncertain due to galloping inflation and the existing pandemic. First we need to transform the data values into IFPs as in [4,21]. Then we go to Step 2. Step 2. Let the score coefficient rs of each expert (s ∈ E) is defined by an IFP δs , s , which elements can be interpreted respectively as his degree of competence and of incompetence. The IM EV ∗ [K, C, E, {ev ∗ ki ,cj ,ds }] = r1 prK,C,d1 EV ⊕(max,min) r2 prK,C,d2 EV . . . ⊕(max,min) rD prK,C,dD EV. EV := EV ∗ (evki ,lj ,ds = evk∗i ,lj ,ds , ∀ki ∈ K, ∀lj ∈ L, ∀ds ∈ E) is constructed. The total assessment of the ki -th candidate on the cj -th criterion in a moment / E is calculated by an⎧application of the αE -th aggregation hf ∈ ⎫ operation as fol-

cj hf ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ D ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ k1 #q μk1 ,cj ,ds , νk1 ,cj ,ds  ⎬ lows R = αE,#q (EV, hf ) = | cj ∈ C , (1 ≤ q ≤ 3), then s=1 . . ⎪ ⎪ .. .. ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ D ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ # k μ , ν  ⎪ ⎪ q m k ,c ,d k ,c ,d m j s m j s ⎪ ⎪ ⎩ ⎭ s=1

go to Step 3. If we use #∗1 = min, max, then we accept super pessimistic aggregation operation, with #∗2 = average, average we assume averaging aggregation operation and with #∗3 = max, min we accept super optimistic aggregation operation for the assessment of the applicant. Step 3. This step creates a 3-D IFIM P K with the coefficients determining the importance of the evaluation criteria for the franchisor ve by :

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ve hf c1 pk c1 ,ve ,hf .. .. . . P K[C, ve , hf {pk cj ,ve ,hf }] = , cj pk cj ,ve ,hf .. .. . . cn pk cn ,ve ,hf where C = {c1 , c2 , . . . , cn } . Then we calculate the transposed IM of R RT [K, C, hf ]. The evaluation IFIM B[K, ve , hf {bki ,ve ,hf }] = RT (◦,∗) P K is calculated, containing the total estimates of the ki -th candidate (for 1 ≤ i ≤ m) for the brand ve , where ◦, ∗ is an operation from (3). Go to Step 4. Step 4. In this step, the most optimal franchisee of the franchise chain ve is selected by the aggregation operation αK,#q (B, k0 ) using pessimistic or optimistic scenarios ve alK,#q (B, k0 ) =

m

k0 #q μki ,ve , νki ,ve 

,

(5)

i=1

where k0 ∈ / K, 1 ≤ q ≤ 3. Go to Step 5. Step 5. After selecting the most effective franchisee, it is advisable to optimize the evaluation system for franchise candidates with a view to using it in a future selection. We propose the intercriteria analysis (ICrA, [6,8]) to optimize the evaluation system by eliminating slower or more expensive criteria that have been found to be strongly correlated to other criteria [15] in intuitionistic fuzzy conditions to optimize the franchisee rating system. The digital transformation of this process in conditions of vagueness requires the application of an intuitionistic fuzzy approach to the correlation analysis from point of view of ICrA. Let α, β is an IFP. The criteria Ck and Cl are in (α, β)-positive consonance, if μCk ,Cl > α and νCk ,Cl < β; (α, β)-negative consonance, if μCk ,Cl < β and νCk ,Cl > α; (α, β)dissonance, otherwise. The ICrA algorithm is applied over the matrix R to find the criteria, which are in a consonance. More expensive, slower or more complex criteria are reduced from the evaluation franchise system using the IM reduction operation over R. Go to Step 6. Step 6. This step obtains the new rating coefficients of the experts. Let the expert ds (s = 1, ..., D) has participated in γs evaluation procedures for the selection of a franchisee, on the basis of which his score rs = δs , s  is determined, then after his participation in the next procedure, his new score will be changed by [4]: ⎧ δγ+1 γ ⎪ if the expert has assessed correctly ⎨  γ+1 , γ+1 ,   δγ γ  γ+1 , γ+1 , if the expert had not given any estimation (6) δs , s  = ⎪ ⎩  δγ , γ+1 , if the expert has assessed incorrectly γ+1 γ+1

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The proposed IFIMFr algorithm has the complexity O(Dm2 n2 ), based on the complexity of ICrA [9]).

4

A Real Case Study of IFIMFr to a Patisserie

In this section, the proposed IFIMFr model from the Sect. 3 is demonstrated with a real case study for choosing a franchisee for a chain of patisseries in Bulgaria. The following problem is formulated for successful selection of a franchisee: The first Bulgarian franchise chain of patisseries has planned to expand its business through the selection of a franchisee. For this purpose, the franchisor decides to invite a team of experts d1 , d2 and d3 to participate in the evaluation of the candidates ki (for 1 ≤ i ≤ 4). The evaluation system for selection of a franchisee consists 4 groups of criteria as follows: C1 - management capability and entrepreneurial spirit; C2 - business concept for successful brand development; C3 - financial capability and store size; C4 - location conditions, level of competition, purchasing power of the population, traffic and parking opportunities. The intuitionistic fuzzy coefficients pk cj ,ve determining the priorities of the criteria cj (for j = 1, ..., 5) for choosing a franchisee for the researched franchisor ve and the rank coefficients of the experts {r1 , r2 , r3 } are given. The problem is how to optimally select the most suitable franchisee candidate. Solution of the Problem: Step 1. At this step, we create the 3-D expert evaluation IFIM EV [K, C, E, {eski ,cj ,ds }] with the estimates of the ds -th expert for the ki -th candidate by the cj -th criterion (for 1 ≤ i ≤ 4, 1 ≤ j ≤ 5, 1 ≤ s ≤ 3) and its form is: ⎧ d1 ⎪ ⎪ ⎪ ⎪ ⎨ k1 k2 ⎪ ⎪ k ⎪ ⎪ ⎩ 3 k4

c1 c2 c3 c4 0.3, 0.3 0.2, 0.5 0.6, 0.2 0.2, 0.5 0.1, 0.6 0.4, 0.4 0.4, 0.5 0.4, 0.4 , 0.4, 0.2 0.1, 0.7 0.2, 0.4 0.6, 0.2 0.1, 0.7 0.2, 0.7 0.2, 0.8 0.4, 0.5

d3 k1 k2 k3 k4

d2 k1 k2 k3 k4

c1 c2 c3 c4 0.4, 0.4 0.1, 0.7 0.7, 0.1 0.3, 0.5 0.2, 0.8 0.3, 0.5 0.6, 0.2 0.6, 0.1 , 0.3, 0.4 0.3, 0.6 0.1, 0.7 0.4, 0.4 0.2, 0.6 0.3, 0.3

⎫ c1 c2 c3 c4 ⎪ ⎪ ⎪ 0.1, 0.7 0.2, 0.7 0.4, 0.4 0.4, 0.4 ⎪ ⎬ 0.1, 0.8 0.3, 0.6 0.2, 0.6 0.5, 0.2 ⎪ 0.3, 0.5 0.2, 0.7 0.3, 0.6 0.4, 0.5 ⎪ ⎪ ⎪ ⎭ 0.1, 0.8 0.3, 0.5 0.1, 0.7 0.3, 0.6

Step 2. The rating coefficients of the experts are: {r1 , r2 , r3 } = {0.8, 0.1, 0.7, 0.1, 0.9, 0.1}. The IM EV ∗ [K, C, E, {ev ∗ }] is created by EV ∗ = r1 prK,C,d1 EV ⊕(max,min) r2 prK,C,d2 EV ⊕(max,min) r3 prK,C,d3 EV ; EV := EV ∗

(7)

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Then we apply the optimistic aggregation operation αE,(max,min) (EV, hf ) = R[K, hf , C] to calculate the aggregated value of the ki -th applicant about cj -th criterion in / D in line with the optimistic economic scenario. a current time-moment hf ∈ Step 3. At this step, a 3-D IFIM P K of the weight coefficients of the assessment criterion according to its antecedence is created from the franchisor ve : hf c1 P K[C, V, hf , {pk cj ,ve ,hf }] = c2 c3 c4 hf k1 and B = RT (◦,∗) P K = k2 k3 k4

ve 0.9, 0.1 0.8, 0.1 0.6, 0.2 0.8, 0.1

(8)

ve 0.678, 0.047 0.689, 0.040 0.694, 0.048 0.539, 0.170

(9)

Step 4. The optimistic aggregation operation αK,#3 (B, k0 ) finds that k3 is the optimal franchisee for the researched franchise chain of patisseries in Bulgaria ve with the maximum degree of acceptance 0.694 and the minimum degree of rejection 0.048 in an optimistic scenario. If the future is pessimistic and the decision-making environment is uncertain, decision-makers prefer a pessimistic strategy and will choose a candidate k4 with the minimum degree of membership 0.539 and the maximum degree of non-membership 0.17 in a pessimistic scenario. Step 5. At this step, we was applied the ICrA with α = 0.85 and β = 0.10 over R. The conclusion is that there are no criteria that are consonantally dependent. The results, obtained from the application of the software that implements ICrA [14], are in the form of IM in μ - ν view result matrix (see Fig. 1)

Fig. 1. Membership and non-membership parts of the IFPs, giving the InterCriteria correlations.

Step 6. At last step, we assume that the experts’ assessments are correct from the point of view of intuitionistic fuzzy logic [4] and their new rating coefficients are equal to {0.82, 0.09, 0.73, 0.09, 0.91, 0.09}.

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Conclusion

In the study, we have defined a new IFIMFr business model for the most effective selection of franchisee by intuitionistic fuzzy evaluations from independent experts, based on the theories of IFSs and IMs. The proposed approach is demonstrated on real life data, namely, the choice of a franchisee in a chain of patisseries in Bulgaria. In the future, the researches will continue with the development of interval-valued IFIMFr approach [5] and the digitalization of the IFIMFr through a software utility.

References 1. Atanassov, K.: Intuitionistic fuzzy sets. In: Proceedings of VII ITKR’s Session, Sofia, (1983) (Deposed in Centr. Sci.-Techn. Library of the Bulg. Acad. of Sci. 1697/84) (1983) 2. Atanassov, K.: Generalized index matrices. Comptes rendus de l’Academie Bulgare des Sciences 40(11), 15–18 (1987) 3. Atanassov, K.T.: Index Matrices: Towards an Augmented Matrix Calculus. SCI, vol. 573. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10945-9 4. Atanassov, K.: On Intuitionistic Fuzzy Sets Theory. STUDFUZZ, vol. 283. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29127-2 5. Atanassov, K.: Interval-Valued Intuitionistic Fuzzy Sets. World Scientific (2018) 6. Atanassov, K., Mavrov, D., Atanassova, V.: Intercriteria decision making: a new approach for multicriteria decision making, based on index matrices and intuitionistic fuzzy sets. Issues IFSs Generalized Nets 11, 1–8 (2014) 7. Atanassov, K., Szmidt, E., Kacprzyk, J.: On intuitionistic fuzzy pairs. Notes Intuitionistic Fuzzy Sets 19(3), 1–13 (2013) 8. Atanassov, K., Szmidt, E., Kacprzyk, J., Atanassova, V.: An approach to a constructive simplication of multiagent multicriteria decision making problems via ICrA. Comptes rendus de lAcademie bulgare des Sciences 70(8), 1147–1156 (2017) 9. Atanassova, V., Roeva, O.: Computational complexity and influence of numerical precision on the results of intercriteria analysis in the decision making process. Notes Intuitionistic Fuzzy Sets 24(3), 53–63 (2018) 10. Elango, B.: A bibliometric analysis of franchising research (1988–2017). J. Entrepreneurship 28(2), 223–249 (2019). https://doi.org/10.1177/ 0971355719851897 11. Escorcia, C., Daniel, C., Perez, L., Valle, R., Orozco, W.: Use of the multicriteria method “Fuzzy Analytic Hierarchy Process (Fuzzy AHP)” to locate a Starbucks franchise in a Barranquilla mall. In: SSRN, pp. 1–9 (2018) 12. Ghantous, N., Das, S.S.: International franchising and performance: a resource based perspective. Int. J. Retail Distrib. Manage. 46(8), 744–763 (2018) 13. Hsu, P., Chen, B.: Developing and implementing a selection model for bedding chain retail store franchisee using Delphi and Fuzzy AHP. Qual. Quantity 41, 275–290 (2007) 14. Ikonomov, N., Vassilev, P., Roeva, O.: ICrAData - software for InterCriteria analysis. Int. J. Bioautomation 22(1), 1–10 (2018). https://doi.org/10.7546/ijba.2018. 22.1.1-10

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¨ 15. Kahraman, C., Onar, S.C., Oztay¸ si, B.: A novel spherical fuzzy CRITIC method and its application to prioritization of supplier selection criteria. JIFS 42(1), 29–36 (2022) 16. Kuo, R.J., Chi, S.C., Kao, S.S.: A decision support system for selecting convenience store location through integration of fuzzy AHP and artificial neural network. Comput. Ind. 47(2), 199–214 (2002) 17. Lafontaine, F., Zapletal, M., Zhang, X.: Brighter prospects? Assessing the franchise advantage using census data. J. Econ. Manage. Strategy 28(2), 175–197 (2019). https://doi.org/10.1111/jems.12289 18. Lee, K.L., Choy, G., Ho, L., Canhong, L.: A cloud-based responsive replenishment system in a franchise business model using a fuzzy logic approach. Expert Syst. 33(1), 14–29 (2016). https://doi.org/10.1111/exsy.12117 19. Szmidt, E., Kacprzyk, J.: Amount of information and its reliability in the ranking of Atanassov intuitionistic fuzzy alternatives. In: Rakus-Andersson, E., Yager, R.R., Ichalkaranje, N., Jain, L.C. (eds.) Recent Advances in Decision Making. SCI, vol. 222, pp. 7–19. Springer, Heidelberg (2009). https://doi.org/10.1007/9783-642-02187-9 2 20. Traneva, V., Tranev, S.: Index Matrices as a Tool for Managerial Decision Making. Publ. House of the Union of Scientists, Bulgaria (2017). (in Bulgarian) 21. Traneva, V., Tranev, S.: Intuitionistic fuzzy analysis of variance of movie ticket sales. In: Kahraman, C., Cevik Onar, S., Oztaysi, B., Sari, I.U., Cebi, S., Tolga, A.C. (eds.) INFUS 2020. AISC, vol. 1197, pp. 363–371. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-51156-2 43 22. Traneva, V., Tranev, S., Stoenchev, M., Atanassov, K.: Scaled aggregation operations over 2- and 3-dimensional IMs. Soft Comput. 22(15), 5115–5120 (2018) 23. Wu, C., Ho, G., Lam, C., Ip, W.: Franchising decision support system for formulating a center positioning strategy. Industr. Manage. Data Syst. 115(5), 853–882 (2015) 24. Zadeh, L.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)

Software Selection for IT Industry Using Complex q-Rung Orthopair Fuzzy MCDM Model D. Ajay1(B) , J. Aldring2 , and T. S. Jaganath3 1

Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur 635601, India [email protected] 2 Department of Mathematics, Panimalar Institute of Technology, Chennai 600123, India 3 Wellsfargo, Chennai, India

Abstract. The selection of software in IT industry involves various parameters and requires an evaluation of performance against a variety of criteria. So, a multicriteria decision making model is very suitable to handle the situation. In this paper, the main objective is to develop an aggregation operator under complex q-Rung Orthopair fuzzy sets (CqROFSs). Also novel grey similarity measure and score function are proposed on Cq-ROFSs. Then this study intends to present a fuzzy intelligent system for the selection of software with the help of Techniques for Order of Preference by Similarity to Ideal Solution (TOPSIS), and Evaluation Based on Distance from Average Solution (EDAS) methods. Finally, a case study for an IT industry is presented to verify the validity of the proposed method. Keywords: Complex q-rung orthopair fuzzy sets models · Aggregation operators · IT industry

1

· Decision making

Introduction

There are some decision situations in which the information cannot be evaluated precisely and quantitatively, but can be evaluated in linguistic terms and to rectify this kind of situations, the concept of fuzzy sets (FSs) [1] introduced by Zadeh is more appropriate. This notion is based on grades of membership of uncertain information. To overcome the limitations of fuzzy sets, many researchers developed different type of fuzzy sets which are extensions of FSs such as intuitionistic fuzzy sets (IFSs) [2], Pythagorean fuzzy sets (PFSs) [3], Spherical Fuzzy Sets (SFSs) [4] and q-Rung Othropair Fuzzy Sets [5]. Fuzzy sets were taken forward into the complex field by Ramot et al. in 2002. First they initiated a complex fuzzy set (CFSs) [6] in which the range of membership function is extended from real to the complex numbers within the unit disc. Later on, Ullah et al. [7] proposed complex Pythagorean fuzzy sets c The Author(s), under exclusive license to Springer Nature Switzerland AG 2022  C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 641–648, 2022. https://doi.org/10.1007/978-3-031-09173-5_74

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(CPyFSs) and their applications in pattern recognition. Also, the CPyFS have been implemented to multi criteria decision making method (MCDM) based on complex projection measure [8]. Furthermore, Liu et al. combined CFSs and qROFSs to develop complex q-rung orthopair fuzzy sets (Cq-ROFSs) and studied their fundamental properties [9]. Many novel research works have emerged in MCDM scenario. For example, the application of entropy MCDM techniques used in IT industry [10], the complex spherical fuzzy MCDM method used in aviation industry 4.0 [11] and the assessment of cyber security technologies have been executed by Fermatean fuzzy sets [12]. So in this research, we have further developed grey similarity measure and verified their properties. Meanwhile, we study two decision making approach such as TOPSIS and EDAS method using Cq-ROFS and compared the final results with a numerical illustration. The remaining part of the paper is organized as follows. Section 2 describes basic definitions in complex Cq-ROFS and their operations. The weighted Grey Similarity Measure (WGSM) has been developed for Cq-ROFN in Sect. 3 and also their operations are discussed. In Sect. 4, two complex fuzzy aggregation operators are developed for Cq-ROFSs. An MCDM approach such TOPIS and EDAS method has been illustrated in Sect. 5. Then, a cased study have been conducted to select best software for IT industry.

2

Preliminaries

˘ ˜ Definition 1. A fuzzyset F defined on a universe of discourse  has the form:  ˘ ˘ ˜ ˙ : (r) ˙ ∈  , where ξF˜ (r) ˙ :  → [0, 1]. Here ξF˜ (r) ˙ denotes the memF = ξF˜ (r) bership function of each r. ˙ Definition 2. An intuitionistic fuzzy set I˜F is defined as a setof ordered  pairs ˘ where ˘ and is given by I˜F = ξI˜F (r), ˙ ψI˜F (r) ˙ : r˙ ∈  over a universal set  ˘ → [0, 1], ψ ˜ (r) ˘ ˙ :  ˙ + ψI˜F (r) ˙ ≤ 1 ξI˜F (r) IF ˙ :  → [0, 1] with the condition ξI˜F (r) ˘ ˙ and ψI˜F (r) ˙ denotes the membership and for each element r˙ ∈ . Here ξI˜F (r) non-membership grades respectively. ˘ be a universe of discourse. A q-Rung orthopair fuzzy sets Definition 3. Let  ˘ ˘ (q-ROFS) Q in  is an object having the form    ˘ , ˘ Q = r, ˙ ξ˘q (r), ˙ ψ˘q (r) ˙ : r˙ ∈  ˘ → [0, 1] and ψ˘q (r) ˘ → [0, 1], with the condition that ˙ : ˙ : where ξ˘q (r)  q  q ˘ 0 ≤ ξ˘q (r) ˙ + ψ˘q (r) ˙ ≤ 1, ∀r˙ ∈ . ˙ and ψ˘q (r) ˙ denote, respectively, the degree of membership and The numbers ξ˘q (r) the degree of non-membership of the element r˙ in the set ˘ Q. For any q-ROFS  q  q  ˘ ˘ and r˙ ∈ , π˘q (r) Q ˙ = 1 − ξ˘q (r) ˙ − ψ˘q (r) ˙ is identified as the degree of ˘ indeterminacy  of r˙ in Q. In the interest  of simplicity,  we shall  mention the symbol  ˘ . ˘ Q = r, ˙ ξ˘q (r), ˙ ψ˘q (r) ˙ : r˙ ∈  Q = ξ˘q , ψ˘q for the q-ROFS ˘

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Definition 4. A complex q-Rung orthopair fuzzy set (Cq-ROFS) EQ defined on ˘ is represented by the degree of membership ξ and a universe of discourse , Eq ˘ the degree of non membership ψ Eq that take complex valued grades for any r˙ ∈  and is defined as

 ˘ r, ˙ ξ Eq (r), ˙ ψ Eq (r) ˙ : r˙ ∈  (1) EQ =     ˘ → z1 : z1 ∈ Eq , |z1 | and ψ :  ˘ → z2 : z2 ∈ Eq , |z2 | such that where ξ Eq :  Eq ξ Eq = z1 = a1 + ib1 and ψ Eq = z2 = a2 + ib2 provided that 0 ≤ |z1 |q + |z2 |q ≤ 1. A simple form of Cq-ROFS is defined as

 j2π(Θμ (r)) ˙ j2π(Θν (r)) ˙ ˘ ξ Eq (r) , ψ Eq (r) EQ = : r˙ ∈  ˙ .e ˙ .e √ where j = −1. The amplitude terms of membership and non-membership functions are ξ Eq (r) ˙ and ψ Eq (r) ˙ respectively which lie in [0, 1], and the phase terms of membership and non-membership functions are denoted respectively as ˙ , and Θν ( r) ˙ whose Θμ (r)  real part lie in [0, 1] satisfying the conditions that 0 ≤

ξ Eq (r) ˙

q

+ ψ Eq (r) ˙

q

q

q

≤ 1 and 0 ≤ (Θμ (r)) ˙ + (Θν (r)) ˙ ≤ 1. Moreover, j2π(Θη (r)) ˙ ˘ for any C-PyFSs EQ and r˙ ∈ , the term π Eq = π Eq (r) is such that ˙ .e  q q

 q q + ψ Eq (r) and Θη (r) ˙ = 1 − (Θμ (r)) ˙ + (Θν (r)) ˙ is π Eq (r) ˙ = 1 − ξ Eq (r) ˙ ˙ identified as the degree of indeterminacy of r˙ in EQ . 2.1

Set Operations on C-PyFSs 



Definition 5. Let EQ = ξ Eq .ej2π(Θμ ) , ψ Eq .ej2π(Θν ) , EQ1 = ξ E1q .ej2π(Θμ 1 ) ,  

ψ E1q .ej2π(Θν 1 ) and EQ2 = ξ E2q .ej2π(Θμ 2 ) , ψ E2q .ej2π(Θν 2 ) be three Cq-ROFSs. Then the following operations are defined: (i). Algebraic sum of Cq-ROFS  ⎫  ⎧  q q q q  ⎪ ⎬ ⎨ ξ q + ξ q − ξ q .ξ q .ej2π Θμ 1 +Θμ 2 −Θμ 1 .Θμ 2 ,⎪ E1q E2q E1q E2q EQ1  EQ2 =   ⎪ ⎪ ⎭ ⎩ ψ E1q .ψ E2q .ej2π[Θν 1 .Θν 2 ] (ii). Algebraic product of Cq-ROFS   ⎧ ⎫ ⎨ ⎬ ξ E1q .ξ E2q .ej2π[Θμ 1 .Θμ 2 ] ,    EQ1  EQ2 =  q q q 2 ⎩ ψ q 1 + ψ q 2 − ψ q 1 .ψ 2 2 .ej2π Θν 1 +Θν 2 −Θν 1 .Θν 2 ⎭ Eq E E E q

q

q

(iii). Scalar multiplication of a Cq-ROFS      κ  j2π 1−1−Θq κ  

κ μi κEQi = 1 − 1 − ξ qEi , ψ κEiq .ej2π[Θν i ] .e q

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(iv). Exponent of a Cq-ROFS        κ 

κ j2π Θμκ i j2π 1−(1−Θ q i ) κ q κ ν [EQi ] = ξ Ei .e , 1 − 1 − ψ Ei .e q q

Definition 6. The score ℘ (E Q ) and accuracy H (EQ ) of Cq-ROFS EQ = 

j2π(Θμ ) j2π(Θν ) , ψ Eq .e = ξ Eq , ψ Eq are defined as ξ Eq .e 

q q (2) ℘ (EQ ) = ξ qEq − ψ qEq · ej2π(Θμ −Θν ) 

q q (3) H (EQ ) = ξ qEq + ψ qEq · ej2π(Θμ +Θν ) where ℘ (EQ ) , H (EQ ) will be a complex fuzzy number. Definition 7. Comparison q-Rung othropair fuzzy set (Cq between complex 

ROFS) EQ1 = ξ E1q , ψ E1q and EQ2 = ξ E2q , ψ E2q , (i). If |℘ (EQ1 )| > |℘ (EQ2 )|, then EQ1 > EQ2 (EQ1 is superior to EQ2 ) (ii). If |℘ (EQ1 )| = |℘ (EQ2 )|, then EQ1 = EQ2 (EQ1 is equivalent to EQ2 )

3

Weighted Grey Similarity Measure of Cq-ROFS



Definition 8. Let EQi = ξ Eiq .ej2π(Θμ i ) , ψ Eiq .ej2π(Θν i ) and 

DQi = ξ Diq .ej2π(Θμ i ) , ψ Diq .ej2π(Θν i ) ∀i = 1, 2, 3, . . . , n be two collection of Cq-ROFNs. Using the extension of grey relational analysis, the weighted grey similarity measure (WGSM) of Cq-ROFN is given as follows: " # n + Λξ Emax + Λψ Emax Λψ Emin Λξ Emin 1 ! q q q q w SGSM (EQi , EDi ) = wi + 2n i=i Λξ Eiq + Λξ Emax Λψ Eiq + Λψ Emax q q

$

(4) min max n min max  ΛΘ +ΛΘ j2π

.e

1 2n

i=i

wi

μ μ i +ΛΘ max ΛΘμ μ

+

ΛΘν +ΛΘν i +ΛΘ max ΛΘν ν

% % % % % % % % where, Λξ Eiq = %ξ Eiq − ξ Diq % , Λξ Emin = min − ξ i i %ξ Eq D % , q % % q % % % % % % Λξ Emax = max %ξ Eiq − ξ Diq % , Λψ Eiq = %ψ Eiq − ψ Diq % , q % % % % % % % % Λψ Emin = min i − ψ Di % , and Λψ Emax = max i − ψ Di % . Similarly %ψ %ψ E E q q q q q q we can find the values of ΛΘμi , ΛΘμmin , ΛΘμmax , ΛΘνi , ΛΘνmin , and ΛΘνmax that is the phase terms of Cq-ROFNs. It satisfy the conditions:

w (EQi , EDi )| ≤ 1. (i). 0 ≤ |SGSM w w (EDi , EQi )| (ii). |SGSM (EQi , EDi )| = |SGSM w (iii). |SGSM (EQi , EDi )| = 1 if EQi = EDi T

Remark 1. If we take wi = w11 , w12 , w13 , . . . w1n , then the WGSM for Cqw ROFN reduced to GSM for Cq-ROFN. i.e. SGSM (EQi , EDi ) = SGSM (EQi , EDi ).

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4

645

Complex Cq-ROF Aggregation Operators

In this section, Cq-ROF Yager Hybird Weighted Arithmetic (Cq-ROFYHWA) and Cq-ROF Yager Hybird Weighted Geometric (Cq-ROFYHWG) aggregation Operators have been developed on Cq-ROF Numbers (Cq-ROFN). 

Theorem 1. Let EQi = ξ Eiq .ej2π(Θμ i ) , ψ Eiq .ej2π(Θν i ) for i = 1, 2, . . . , n be a collection of Cq-ROFN, then the aggregate values of Cq-ROFN by CqROFYHWA operator is also an Cq-ROFN and the operator is as follows: Cq − ROF Y HW Aw

=

⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩



E 1 , E 2 , . . . , EQn Q Q



n

=

i=1

wi E i Q

 ⎫ ⎞ ⎛   

qη  1 ⎪ ⎪ n

 ⎪  η⎟ ⎪  q min⎜ ⎪ ⎞ j2π  ⎛ wi Θ i ⎪ ⎠ ⎝1,  ⎪       1 μ  ⎪ qη ⎪ i=1 n  ⎪  η⎟ ⎪ q min ⎜  ⎪ ⎪ w ξ , ⎠.e ⎝1,  ⎪ i i ⎪ E ⎪ i=1 Q ⎬  ⎛ ⎞ ⎪    1 ⎪  ⎪    n   η⎟ ⎪ q η ⎪ ⎜  q ⎞ j2π  ⎛ ⎪ wi 1− Θ i ⎠ ⎪  ⎪ 1−min⎝1,     q η  1 ⎪ ν  ⎪ i=1 ⎪ n  ⎪  η ⎟ ⎪ q 1 − min ⎜  ⎪ w 1 − ψ ⎠.e ⎝1, ⎪  i i ⎪ E ⎭ i=1 Q

Cq − ROF Y HW Gw



E 1 , E 2 , . . . , EQn Q Q



=

n

E i Q

(5)

w i

i=1  ⎧ ⎞ ⎫ ⎛   



q η  1 ⎪ ⎪ ⎪ n

 ⎪ ⎪  η⎟ ⎪ ⎪ ⎪  q 1−min⎜  ⎪ ⎛ ⎞ w 1− Θ j2π  ⎪ ⎪ ⎠ ⎪ ⎝1,  i i ⎪ ⎪    q η  1  μ ⎪  ⎪ ⎪ ⎪ i=1 n  ⎪ ⎪  η ⎪ ⎪ ⎜ ⎟ q ⎪ 1 − min ⎝1, ⎪ ⎪ wi 1 − ξ i , ⎪ ⎠.e  ⎪ ⎪ ⎪ ⎪ EQ ⎪ ⎪ i=1 ⎨ ⎬  = ⎞ ⎛  ⎪ ⎪  1 ⎪ ⎪  ⎪ ⎪  qη η ⎪ ⎪ n    ⎪ ⎪ ⎟  q min⎜ ⎪ ⎪  ⎞ j2π  ⎛ ⎪ ⎪ wi Θ i ⎠ ⎝1,  ⎪ ⎪    qη  1 ⎪ ⎪ ν  ⎪ ⎪ i=1 ⎪ ⎪ n  ⎪ ⎪  η⎟ ⎜ ⎪ ⎪ q  ⎪ ⎪ wi ψ i min ⎝1, ⎠.e ⎪ ⎪  ⎪ ⎪ EQ ⎩ ⎭ i=1

(6) T

where w = (w1 , w2 , . . . wn ) be the weight vector of EQi , wi > 0 and

n & i=1

wi = 1.

The properties of the developed Cq-ROFYHWA and Cq-ROFYHWG aggregation operators are mentioned as follows: 

Theorem 2. Let EQi = ξ Eiq .ej2π(Θμ i ) , ψ Eiq .ej2π(Θν i ) for i = 1, 2, . . . , n be a collection of Cq-ROFNs which are identical, i.e. EQi = EQ ∀i. Then (i). Cq − ROF Y HW Aw (EQ1 , EQ2 , . . . , EQn ) = EQ (ii). Cq − ROF Y HW Gw (EQ1 , EQ2 , . . . , EQn ) = EQ . 

Theorem 3. Let EQi = ξ Eiq .ej2π(Θμ i ) , ψ Eiq .ej2π(Θν i ) for i = 1, 2, . . . , n be a

collection of Cq-ROFNs. Let EQ+ = max (EQ1 , EQ2 , . . . , EQn ) and EQ− = min (EQ1 , EQ2 , . . . , EQn ). Then (i). EQ− ≤ Cq − ROF Y HW Aw (EQ1 , EQ2 , . . . , EQn ) ≤ EQ+ (ii). EQ− ≤ Cq − ROF Y HW Gw (EQ1 , EQ2 , . . . , EQn ) ≤ EQ+ .

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 Theorem 4. Let EQi = ξ Eiq .ej2π(Θμ i ) , ψ Eiq .ej2π(Θν i ) and

 DQi = ξ Diq .ej2π(Θμ i ) , ψ Diq .ej2π(Θν i ) ∀i = 1, 2, 3, . . . , n be two collection of Cq-ROFNs, and EQi ≤ DQi . Then, (i). Cq − ROF Y HW Aw (EQn ) ≤ Cq − ROF Y HW Aw (DQn ) (ii). Cq − ROF Y HW Gw (EQn ) ≤ Cq − ROF Y HW Gw (DQn ). Proof. The proof of the above Theorems (2), (3) and (4) are obvious.

5

Application of the Software Selection for IT Industry

Five ETL softwares that are R1 - Ab Initio, R2 - Informatica Power Center, R3 - IBM Infosphere Datastage, R4 -Talend Open Studio, R5 - Pentaho Data Integration for IT industry have been taken as alternatives and their performance is evaluated using the following criteria: S1 - Type, S2 - Cost, S3 - Performance, S4 - User Friendly, S5 - Security and Reliability, and S6 - Flexibility. The weight vecT tor of the criteria are respectively, wi = 0.15, 0.15, 0.2, 0.15, 0.2, 0.15 . Then a decision maker evaluated the alternatives on criteria using given fuzzy linguistic terms with their corresponding Cq-ROFN   that is given in the following Table 1. where Eij The Cq-ROF decision matrix M = Eij Q Q denotes the fuzzy linm×n

guistic terms of alternative Ri on Sj is given and convert the linguistic terms to Cq-ROFNs. R1

⎛

S1

S2

S3

S4

S5

S6

ES

VE

H

H

H

M

LE

H

M

H

LE

M

M

H

F

M

L

M

F

M

L

L

⎜ R2 ⎜ ⎜ ES ⎜ M 1 = R3 ⎜ ES ⎜ R4 ⎜ ⎝ OS R5 OS

⎞

⎟ M⎟ ⎟ ⎟ L⎟ ⎟ H⎟ ⎠ H

Table 1. Linguistic terms Variables

Cq-ROFN  0.4.ej2π(0.5) , 0.6.ej2π(0.5) Enterprise Software (ES)  0.9.ej2π(0.6) , 0.2.ej2π(0.3) Free (F)  Open Source Software (OS) 0.8.ej2π(0.7) , 0.2.ej2π(0.3)  0.9.ej2π(0.7) , 0.1.ej2π(0.2) High (H)  0.1.ej2π(0.2) , 0.7.ej2π(0.8) Very Expensive (VE)  0.5.ej2π(0.4) , 0.4.ej2π(0.6) Medium (M)  0.8.ej2π(0.7) , 0.2.ej2π(0.3) Less Expensive (LE)  0.1.ej2π(0.2) , 0.8.ej2π(0.7) Less (L)

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After using score function that is Eq.(2) when q = 1, we derived the following complex fuzzy decision matrix. ⎛ R1 R2 R3 R4 R5

S1

j2π(0) ⎜ −0.2.e ⎜ ⎜ ⎜ −0.2.ej2π(0) ⎜ ⎜ ⎜ j2π(0) ⎜ ⎜ −0.2.e ⎜ ⎜ j2π(0.4) ⎜ 0.6.e ⎝ 0.6.ej2π(0.4)

S2

S3

S4

S5

−0.6.ej2π(−0.6)

0.8.ej2π(0.5)

0.8.ej2π(0.5)

0.8.ej2π(0.5)

0.6.ej2π(0.4)

0.8.ej2π(0.4)

0.1.ej2π(−0.2)

0.8.ej2π(0.5)

0.6.ej2π(0.4)

0.1.ej2π(−0.2)

0.1.ej2π(0.2)

0.8.ej2π(0.5)

0.7.ej2π(0.3)

0.1.ej2π(−0.2)

−0.7.ej2π(−0.5)

0.1.ej2π(−0.2)

0.7.ej2π(0.3)

0.1.ej2π(−0.2)

−0.7.ej2π(−0.5)

−0.7.ej2π(−0.5)

S6 ⎞ 0.1.ej2π(−0.2) ⎟ ⎟ ⎟ 0.1.ej2π(−0.2) ⎟ ⎟ ⎟ ⎟ j2π(−0.5) ⎟ −0.7.e ⎟ ⎟ ⎟ j2π(0.5) ⎟ 0.8.e ⎠ 0.8.ej2π(0.5)

The process of decision making using TOPSIS [13] and EDAS [14] methods are executed after finding the absolute values for the complex fuzzy decision matrix. Then the performance score of the alternatives using TOPSIS method is given as follows: R1 = 0.6268, R2 = 0.5360, R3 = 0.4097, R4 = 0.4498, R5 = 0.5408. Similarly, the average score of the alternatives using EDAS method is as follows: R1 = 0.6914, R2 = 0.3351, R3 = 0.1760, R4 = 0.5764, R5 = 0.76384. Finally the ranking order of the alternatives is given the following Table 2. Table 2. Ranking order of the alternatives Methods Ranking order

6

TOPSIS

R 1 > R5 > R 2 > R 4 > R 3

EDAS

R 5 > R1 > R 4 > R 2 > R 3

Conclusion

In this paper, the notion of Cq-ROFS has been studied with TOPSIS and EDAS methods. Also, the weighted grey similarity measure is developed for Cq-ROFS. Then, Yager hybird weighted arithmetic and geometric aggregation operators are developed under Cq-ROFNs. Some of the properties of similarity measure and aggregation operators are verified. Furthermore, a case study has been conducted to select the best software for IT industry with the help of TOPSIS and EDAS methods. The score function of Cq-ROFS plays a vital role in decision making methods. So in this direction, the future research can explore this theory in order to obtain different score functions for the extension of complex fuzzy sets.

References 1. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965) 2. Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986) 3. Yager, R.R.: Pythagorean fuzzy subsets. In: 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), Edmonton, Canada, pp. 57–61 (2013) 4. Kutlu Gundogdu, F., Kahraman, C.: Spherical fuzzy sets and spherical fuzzy TOPSIS method. J Intell. Fuzzy Syst. 36(1), 337–352 (2019)

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5. Yager, R.R.: Generalized orthopair fuzzy sets. IEEE Trans. Fuzzy Syst. 25(5), 1222–1230 (2017). https://doi.org/10.1109/TFUZZ.2016.2604005 6. Ramot, D., Milo, R., Friedman, M., Kandel, A.: Complex fuzzy sets. IEEE Trans. Fuzzy Syst. 10, 171–186 (2002) 7. Ullah, K., Mahmood, T., Ali, Z., Jan, N.: On some distance measures of complex Pythagorean fuzzy sets and their applications in pattern recognition. Complex Intell. Syst. 6(1), 15–27 (2019). https://doi.org/10.1007/s40747-019-0103-6 8. Aldring, J., Ajay, D.: Multicriteria group decision making based on projection measures on complex Pythagorean fuzzy sets. Granul. Comput. (2022). https:// doi.org/10.1007/s41066-022-00321-6 9. Liu, P., Mahmood, T., Ali, Z.: Complex q-rung orthopair fuzzy aggregation operators and their applications in multi-attribute group decision making. Information 11, 5 (2020) 10. Chodha, V., Dubey, R., Kumar, R., Singh, S., Kaur, S.: Selection of industrial arc welding robot with TOPSIS and entropy MCDM techniques. Mater. Today Proc. 50, 709–715 (2022) 11. Ajay, D., Aldring, J.: Complex spherical fuzzy sets and an application to catering services in aviation 4.0. In: Kahraman, C., Aydın, S. (eds.) Intelligent and Fuzzy Techniques in Aviation 4.0. SSDC, vol. 372, pp. 87–121. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-75067-1 5 12. Aldring, J., Ajay, D.: MABAC method for assessment of cyber security technologies under fermatean fuzzy sets. In: Bhateja, V., Tang, J., Satapathy, S.C., Peer, P., Das, R. (eds.) Evolution in Computational Intelligence. Smart Innovation, Systems and Technologies, vol. 267. Springer, Singapore (2022). https://doi.org/10.1007/ 978-981-16-6616-2 43 13. N˘ gd˘ gban, S., Dzitac, S., Dzitac, I.: Fuzzy topsis: a general view. Procedia Comput. Sci. 91, 823–831 (2016) 14. Keshavarz Ghorabaee, M., Zavadskas, E.K., Olfat, L., Turskis, Z.: Multi-criteria inventory classification using a new method of evaluation based on distance from average solution (EDAS). Informatica 26(3), 435–451 (2015)

Internet of Things Fermatean Fuzzy CRITIC Testing Procedure for New Normal Mehmet Kabak1

, Serhat Aydın2(B)

, and Ahmet Akta¸s3

1 Gazi University, 06570 Ankara, Turkey 2 National Defence University, 34149 Istanbul, Turkey

[email protected] 3 University of Turkish Aeronautical Association, 06790 Ankara, Turkey

Abstract. Digital disruption was crucial to corporate success even before COVID-19 pandemic. The need for speed digitization has grown even more pressing since the pandemic broke out, exposing firms’ digital inadequacies and jeopardizing their operational performance. If firms in all industries are to survive and prosper in the new normal, they must undergo a significant transition. Domestic manufacturers aim to embrace Industry 4.0 technology to close the labor price gap and to be cost competitive. Internet of things (IoT) is one of the key factors in adapting to the new normal. In this study, we determine the criteria for evaluating whether IoT devices are safe and ready to adapt to the new normal. We evaluated eight different criteria and determined their impacts on evaluation process with a Fermatean fuzzy CRITIC procedure. Finally, we determined the weights of criteria. Keywords: Fermatean fuzzy sets · Internet of Things · CRITIC method · Industry 4.0

1 Introduction Information technologies (IT) and globalization have already advanced significantly in the past decades and these advancements have affected the processes in many firms. The effects of the developments in IT and business models have led to some disruptive changes for companies. With the proposal of the Industry 4.0 concept, cyber-physical systems have become extremely important for companies, especially devices with Internet of Things (IoT). The disruptive changes within the Industry 4.0 transformation in business are called the new normal [1]. IoT is a fundamental component within the infrastructure of Industry 4.0, which consists of several data gathering connected and smart sensors for processing. Transformation of these data are based on needs and these data are shared with other devices or people to help achieve the goals of a user or system [2]. It is expected that more than 80 billion devices will be connected to people and each other and will be in constant communication until 2027. The rapid development of IoT technologies will affect our lives in both positive and negative ways [3]. Some positive impacts of IoT technologies on life can be listed as: © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 649–655, 2022. https://doi.org/10.1007/978-3-031-09173-5_75

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• • • • • • •

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Efficiency increase in resource utilization Productivity improvement Better life quality Delivery cost reduction Emergence of new businesses Products with digital services Additional knowledge generation

Although IoT technologies have many positive benefits to people, they also have some negative aspects, which can be counted as: • • • •

Privacy of personal data Security Handling of complexity within systems Unemployment risk for unskilled people

Different types of cyber threats and attacks may affect IoT devices [4]. Ignoring security issues during the construction phase of IoT device networks could cause various problems like confidence, integration, etc. For this reason, security and readiness assessment of IoT devices is vital in placing them in digitalization processes within the period of the new normal. There are several studies in the literature about the assessment of IoT devices. Khan et al. [5] indicated that the security of IoT devices is variable for each device, compared the performances of several cryptographic security algorithms that can be implemented on IoT devices and provided a graphical overview of the results. Test of IoT devices was made using an extended framework of IoT Open Web Application Security Project (OWASP) by Lally and Sgandurra [6]. The framework consists of two main requirements: (i) identification of suitable attack surfaces and (ii) providing a set of guidelines describing how to test the vulnerabilities. A testing framework for IoT devices was proposed by Kim et al. [7]. The benefits of their framework against the traditional testing approach were presented along with examples from several case studies. Wang et al. [4] modeled the security evaluation process of Internet of Health Things systems as a multi-criteria decision-making process and proposed an evaluation framework based on AHP and TOPSIS methods. In a similar manner, Verma and Chandra [8] indicated the security of Fog based IoT paradigm is affected by different factors, and the prioritization of these factors can be made by a multi-criteria analysis. By taking the uncertainty of decision elements within the process into account, they proposed an Interval Valued Intuitionistic Fuzzy Analytic Hierarchy Process based security evaluation approach. Based on the mentioned information in previous studies, IoT device testing is a decision-making process with a number of conflicting criteria. In order to take various criteria in the evaluation process simultaneously, a multi-criteria decision-making technique can be useful in this process. In some situations, decision-making can be more difficult because of the imprecise and uncertain elements related to criteria and alternatives. Fuzzy decision-making models have been proposed in a wide range of applications for such situations so far. In this study, Fermatean Fuzzy Sets [9], which is a recent extension of q-rung Orthopair Fuzzy Sets [10], were used in order to handle

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the uncertainty of decision elements better within the assessment process. A Fermatean fuzzy Criteria Importance Through Intercriteria Correlation (FF-CRITIC) based approach was proposed to determine the impacts of eight criteria on the assessment of IoT devices. The rest of the paper is organized as follows: Sect. 2 presents the FF-CRITIC method. Application steps of IoT device assessment by using the method are given in Sect. 3. The paper is concluded in Sect. 4 by providing possible extensions of the studies in further research.

2 FF-CRITIC Method In this step, The FF-CRITIC approach is explained in detail. The experts evaluate the alternatives through the linguistic terms shown in Table 1 [11, 12]. Table 1. The linguistic terms and FFNs Linguistic terms

FFNs

Linguistic terms

FFNs

Extremely High (EH)

(0.9,0.1)

Medium Low (ML)

(0.4,0.5)

Very High (VH)

(0.8,0.1)

Low

(0.25,0.6)

High

(0.7,0.2)

Very Low (VL)

(0.1,0.75)

Medium High (MH)

(0.6,0.3)

Extremely Low (EL)

(0.1,0.9)

Medium (M)

(0.5,0.4)

Step 1. The decision matrix’s construction: Assume that {N1 , N2 , . . . , Nm } is a set of alternatives, {C1 , C2 , . . . , Cn } is a set of criteria, and  {E  1 , E2 , . . . , Er } is a group of experts. The decision matrix (D) is explained k by D = dij , for i = i,…,m; j = i,…,n, and dijk indicates the assessment of the kth  experts. Wk is the significance degree of the kth experts and rk=1 Wk = 1. Step 2. Aggregate the individual opinions of experts:  In this step, the decision matrices by experts are aggregated by using Eq. (1). R = rij m×n be the aggregated Fermatean fuzzy decision matrix, ⎛ rij = ⎝ 1 − 3

r k=1



 3 Wk r 1 − bkij ,

k=1

⎞   Wk 3 ⎠ nkij

(1)

Step 3. Establish the score matrix:   In step 3, score matrix S = kij m×n is established by using Eq. (2). kij =

   1  3 bj − n3j − ln 1 + πj3 + 1 , for i = 1, 2, . . . , m 2

Step 4. Normalize the score matrix:

(2)

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  Then, normalized score matrix N = nij m×n is established by using Eq. (3).

nij =

⎧ ⎪ ⎨ ⎪ ⎩

kij −kj−

kj+ −kj− kj+ −kij

, j ∈ Nb

kj+ −kj−

j ∈ Nn

where kj− = mini kij and kj+ = maxi kij . Step 5. Calculate the standard deviation of the criteria:    m i=1 nij − nj σj = m m where nj = i=1 nij /m. Step 6. Calculate the correlation between criteria:  m  i=1 nij − nj (nit − nt ) rjt =  2 m m  2 i=1 nij − nj i=1 (nit − nt ) Step 7. Calculate the quantity of information of each criterion by Eq. (6). n   1 − rjt vj = σj t=1

(3)

(4)

(5)

(6)

Step 8. Calculate the weights of the criteria by Eq. (7). vj ωj = m

i=1 vj

(7)

3 Prioritizing Internet of Things Criteria by FF-CRITIC Method In the application section, we determine the weights of the criteria by using FF-CRITIC method. To that end, we defined eight different criteria: Data security (C1 ), Security threats (C2 ), Access management (C3 ), 3rd-party data sharing (C4 ), Compliance requirements (C5 ), Hardware challenges (C6 ), Validation (C7 ), and Integration management (C8 ). There are four different alternative firms, (A1 ), (A2 ), (A3 ), (A4 ). There are three different experts who used Fermatean fuzzy linguistic scale shown in Table 1. The aggregated matrix was established with the joint decision of the experts. The joint decision matrix is shown in Table 2.

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Table 2. The joint decision matrix. A1

A2

A3

A4

C1

(0.70,0.20,0.87)

(0.80,0.10,0.79)

(0.80,0.10,0.79)

(0.60,0.30,0.91)

C2

(0.50,0.40,0.93)

(0.70,0.20,0.87)

(0.10,0.90,0.65)

(0.70,0.20,0.87)

C3

(0.40,0.50,0.93)

(0.60,0.30,0.91)

(0.10,0.75,0.83)

(0.60,0.30,0.91)

C4

(0.80,0.10,0.79)

(0.10,0.90,0.65)

(0.60,0.30,0.91)

(0.70,0.20,0.87)

C5

(0.40,0.50,0.93)

(0.50,0.40,0.93)

(0.10,0.75,0.83)

(0.10,0.75,0.83)

C6

(0.60,0.30,0.91)

(0.50,0.40,0.93)

(0.10,0.90,0.65)

(0.50,0.90,0.53)

C7

(0.25,0.60,0.92)

(0.50,0.40,0.93)

(0.40,0.50,0.93)

(0.40,0.50,0.93)

C8

(0.50,0.40,0.93)

(0.40,0.50,0.93)

(0.40,0.50,0.93)

(0.50,0.50,0.91)

Then, the score matrix was constructed and normalized by using Eq. (2). The score matrix is shown in Table 3. Table 3. The score matrix. A1

A2

A3

A4

C1

0.417

0.557

0.557

0.313

C2

0.234

0.417

0.016

0.417

C3

0.173

0.313

0.062

0.313

C4

0.557

0.016

0.313

0.417

C5

0.173

0.234

0.062

0.062

C6

0.313

0.234

0.016

0.130

C7

0.115

0.173

0.173

0.173

C8

0.234

0.115

0.173

0.115

After constructing the score matrix, Eq. (3) was used to establish a normalized score matrix. In addition, the standard deviation, information quantity, and criteria weights were calculated by using Eqs. (4–7). All the calculation results are shown in Table 4. According to Table 4, the highest criterion weight is 0.164 and belongs to Validation (C7 ) and the lowest one 0.091 belongs to hardware challenges (C6 ).

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M. Kabak et al. Table 4. The Fermatean fuzzy CRITIC results A1

A2

A3

A4

σj

vj

wj

Rank

C1

0.428

1.000

1.000

0.000

0.421

3.402

0.144

2

C2

0.541

1.000

0.000

1.000

0.412

2.579

0.109

6

C3

0.442

1.000

0.000

1.000

0.420

2.684

0.113

5

C4

1.000

0.000

0.548

0.742

0.367

3.168

0.134

4

C5

0.645

1.000

0.000

0.000

0.430

2.472

0.104

7

C6

1.000

0.733

0.000

0.383

0.376

2.153

0.091

8

C7

0.000

1.000

1.000

1.000

0.433

3.888

0.164

1

C8

1.000

0.000

0.486

0.000

0.414

3.328

0.141

3

4 Conclusion In this study, we utilized FF-CRITIC method to determine the weights of criteria evaluating IoT devices. The criteria were determined by a detailed literature survey, and the superiority of the criteria over each other was calculated by the FF-CRITIC method. First, decision matrix was established by experts using Fermatean fuzzy linguistic scale. Then, the normalized score matrix was constructed and standard deviation, correlation between criteria, information quantity, and finally criteria weights were calculated. The results indicated that the used method can be taken as an appropriate method to determine the weights. In future studies, the number of criteria can be enhanced; moreover, different alternatives can be determined, and ranking of alternatives can be obtained by using Fermatean fuzzy Multi Criteria Decision Making methods. Acknowledgments. The authors would like to thank Gazi University Academic Writing Application and Research Center for proofreading the article.

References 1. Ochs, T., Riemann, U.: Industry 4.0: how to manage transformation as the new normal. In: Ellermann, H., Messner, W., Kreutter, P. (eds.) The Palgrave Handbook of Managing Continuous Business Transformation, pp. 245–272. Palgrave Macmillan UK, London (2017). https://doi.org/10.1057/978-1-137-60228-2_11 2. Schwab, K.: Shaping the Future of the Fourth Industrial Revolution: A Guide to Building a Better World. Currency, New York (2018) 3. Nankervis, A., Connell, J., Montague, A., Burgess, J. (eds.): The Fourth Industrial Revolution. Springer, Singapore (2021). https://doi.org/10.1007/978-981-16-1614-3 4. Wang, L., Ali, Y., Nazir, S., Niazi, M.: ISA evaluation framework for security of internet of health things system using AHP-TOPSIS methods. IEEE Access 8, 152316–152332 (2020) 5. Khan, N., Sakib, N., Jerin, I., Quader, S., Chakrabarty, A.: Performance analysis of security algorithms for IoT devices. In: 2017 IEEE Region 10 Humanitarian Technology Conference (R10-HTC), pp. 130–133, Dhaka, Bangladesh (2017)

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6. Lally, G., Sgandurra, D.: Towards a framework for testing the security of IoT devices consistently. In: Saracino, A., Mori, P. (eds.) ETAA 2018. LNCS, vol. 11263, pp. 88–102. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-04372-8_8 7. Kim, H., et al.: IoT-TaaS: towards a prospective IoT testing framework. IEEE Access 6, 15480–15493 (2018) 8. Verma, R., Chandra, S.: Interval-valued intuitionistic fuzzy-analytic hierarchy process for evaluating the impact of security attributes in fog based Internet of Things paradigm. Comput. Commun. 175, 35–46 (2021) 9. Senapati, T., Yager, R.R.: Fermatean fuzzy sets. J. Ambient. Intell. Humaniz. Comput. 11(2), 663–674 (2019). https://doi.org/10.1007/s12652-019-01377-0 10. Yager, R.R.: Generalized orthopair fuzzy sets. IEEE Trans. Fuzzy Syst. 25, 1222–1230 (2017) 11. Mishra, A.R., Rani, P., Pandey, K.: Fermatean fuzzy CRITIC-EDAS approach for the selection of sustainable third-party reverse logistics providers using improved generalized score function. J. Ambient. Intell. Humaniz. Comput. 13, 1–17 (2021). https://doi.org/10.1007/s12 652-021-02902-w 12. Saraji, M.K., Streimikiene, D., Kyriakopoulos, G.L.: Fermatean fuzzy CRITIC-COPRAS method for evaluating the challenges to industry 4.0 adoption for a sustainable digital transformation. Sustainability 13, 9577 (2021)

IoT Platform Selection Using Interval Valued Intuitionistic Fuzzy TOPSIS Sezi Çevik Onar(B) , Cengiz Kahraman, and Ba¸sar Öztay¸si Industrial Engineering Department, Istanbul Technical University, 34367 Maçka, Istanbul, Turkey {cevikse,kahramanc,oztaysib}@itu.edu.tr

Abstract. The Internet of Things (IoT) platform selection is one of the important steps that leads to digital transformation. The companies should consider multiple factors such as return of investment, the flexibility to change the IoT platform, the future performance, sustainability of the platform, the maturity level of IoT platform, security of the IT platform, the support services provided by the platform, previous relations with the IoT platform provider company, the strength of IoT ecosystem, the scope of the services, and usability of the IoT platform. Evaluating these factors is a complex process that requires ambiguous and subjective judgments. Interval valued intuitionistic fuzzy sets enable dealing with ambiguous and subjective evaluations. In this study we developed an interval valued intuitionistic fuzzy TOPSIS method for evaluating IoT Platforms. In order to show the applicability of the proposed methodology, an illustrative example is provided. Keywords: IoT platform selection · MCDM · Interval valued intuitionistic fuzzy sets · TOPSIS · Digital transformation

1 Introduction The role of the IoT in business in the world is increasing, the market value of IoT is growing more than two digits every year with an acceleration. The advances in IoT technologies makes it easier for the firms to utilize IoT technologies. The main challenge for an IoT system adoption is to use the solutions that are safe and adaptive to the other systems of the firm. While considering an IoT solution, not only problem specific issues but also the future challenges such as adaptation and scalability should be taken into account. In the world, many companies are starting their first IoT projects. The projects can be a part of many subjects such as designing a smart plant, autonomous car, or smart energy system. In most of these companies using a modular IoT platform for managing the data is considered for supporting the application development process and providing analytics. IoT platforms usually provide lower costs, a fast application opportunity with professional support. The different layers of IoT platforms provide various solutions to the customers. The layers of IoT platforms are Connectivity Service, Device Management Services, Data Storage Services, Data Processing Services, Visualization Services, © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 656–664, 2022. https://doi.org/10.1007/978-3-031-09173-5_76

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Integration Services, and Security Services. Although it may provide these befits, some IoT projects are not successful due to the problems such as lack of match with the platform and the companies’ needs, problems due to scaling and adaptation to the other systems. In the market there not only big IoT platform providers such as Microsoft Azure IoT, Amazon AWS IoT, PTC Thingworx, or Siemens Mindsphere. There are also the small players, new startups that provide various solutions to the companies. Thus, despite its potential benefits selecting the right IoT platform is a complex process that involves multiple criteria and necessitates subjective evaluations of the alternatives based on these criteria. Interval valued intuitionistic fuzzy sets enable us to define membership and nonmembership values independently as an interval (Kahraman et al. 2016, 2019; Oztaysi et al., 2019a, 2019b, 2017). This flexibility in defining the uncertainty and imprecision enable decision makers represent their hesitancy in the evaluation of a concept. Especially, when the decision makers struggle evaluating subjective aspects of complex problems interval valued intuitionistic fuzzy sets can be utilized. In this study, we have used interval valued intuitionistic fuzzy TOPSIS approach for evaluating IoT platforms. The rest of the paper is organized as follows: In Sect. 2, a literature review on IoT platforms and IoT platform evaluation criteria based on the literature review is give. Section 3 summarizes the utilized methodology. In Sect. 4 an illustrative case study is provided. Last section concludes and gives further suggestions.

2 Literature Review and the IoT Platform Evaluation Criteria IoT Platforms does not only attract industry but also the academicians. In the Scopus database we have search “IoT Platforms” in the abstract, keywords and title, a total of 2667 paper have focused on IoT platforms. Figure 1 shows the number of studies that focus on IoT per year.

600 500 400 300 200 100 0 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021

Fig. 1. The number of studies that focus on IoT (based on Scopus Database)

Figure 2 shows the top 5 articles that publish studies based on IoT platforms. The papers in Sensors Switzerland, Sensors, IEEE Access, and Electronics Switzerland are the articles that mainly focus on technical aspects of IoT Platforms. In IEEE Internet of

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Things Journal not only just the technical aspects the other implications of IoT are also evaluated.

Fig. 2. Top 5 articles that publish studies based on IoT platforms

In the literature, several studies focus on the IoT project evaluation. Some of the studies analyzed just one of the aspects. For instance, Hasan et al. (2022) try to reveal the threats that could weaken the integrity, privacy, and security of internet of medical things systems. The results show that of internet of medical things systems are vulnerable to the security attacks. Bharathi (2019) evaluate the security risks of IoT platforms by using analytical hierarchy process. The second group tries to evaluate IoT platforms with a holistic perspective. De Nardis et al. (2022) conduct a review on the existing IoT platforms. The platforms are evaluated based on communication protocols, data visualization, data processing, integration with external services and security. Based on this review, authors develop a framework for IoT project selection by using seven criteria. Famideh et al. (2021) develop a framework for analyzing IoT platforms. They applied this framework in the IoT platform selection for smart cities. Mijuskovic et al. (2021) design a comparison frameworks for IoT platforms by considering both functional and nonfunctional requirements. The authors applied a AHP based methodology for evaluating five different IoT platforms namely, Azure, AWS, SaS; Thingworx; Kaa IoT are studied to evaluate the performance of the framework. Mijuskovic et al. (2021) claim that while selecting IoT platforms comparative analysis methods should be used. In this study, five IoT platforms namely Azure, AWS, SaS, ThingWor and Kaa IoT are evaluated by using analytical hierarchy process. Mijaˇc et al. (2021) utilized Promethee method for selecting an IoT platform for smart cities. Lin et al. (2020) develop a new probabilistic linguistic best-worst method for defining the criteria weights for IoT platform evaluation. They combined this methodology with probabilistic linguistic TODIM method for evaluating IoT platforms. Kondratenko et al. (2019) utilize Mamdani-type fuzzy rule based system for evaluating IoT platforms. The criteria are selected as reliability, dependability, safety, and security of IoT platforms. Based on the literature review the criteria for evaluating IoT alternatives can be gathered as return of investment (RIO), the flexibility to change the IoT platform (flexibility),

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the future performance (future), sustainability of the platform (sustainability), the maturity level of IoT platform (maturity), security of the IT platform (security), the support services provided by the platform (support), previous relations with the IoT platform provider company (relations), the strength of IoT ecosystem (strength) the scope of the services (scope), usability of the IoT platform (usability).

3 Interval Valued Intuitionistic Fuzzy TOPSIS IVIF be Interval-valued intuitionistic fuzzy set with a membership function μX (x) Let X and non-membership function vX (x) are closed intervals where the starting and ending + − + points are shown by μ−  (x), μX  (x), υX (x) and υV  (x), respectively (Cevik Onar 2015). X       IVIF = < x, μ− (x), μ+ (x) , υ − (x), υ + (x) >|x ∈ X , X     X X X X

(1)

+ − − where 0 ≤ μ+  (x) + υX  (x) ≤ 1, μX  (x) ≥ 0, υX  (x) ≥ 0. X The hesitancy degree πX (x) can be obtained as in Eq. (2).

    + + − − l u πX  (x) = 1 − μX  (x) − vX  (x) = 1 − μ (x) − υ (x), 1 − μ (x) − υ (x) = πX  (x), πX  (x) X

X

X

X

(2) 

 − 



+ , v − , v + be two  = μX − , μX + , vX − , vX + and  Y = μ Let X   Y , μ Y Y Y  and  interval-valued intuitionistic fuzzy numbers. The operations on X Y can be defined as follows:     − − − + + + + − − + + ⊕ , v , (3) + μ − μ μ , μ + μ − μ μ v , v v X Y = μ−            X Y X Y X Y X Y X Y X Y ⊗ X Y =

    − + + − − − − + + + + , v . μ , μ μ + v − v v , v + v − v v μ−             X Y X Y X Y X Y X Y X Y

(4)

IVIF can be given in Eq. (5). The score function of X − + − + μX + μX −v X − vX  S XIVIF = 2



(5)

IVIF can be given in Eq. (6). The accuracy function of X − + − + μX + μX +v X + vX  A XIVIF = 2

(6)

Interval valued intuitionistic fuzzy weighted aggregation operator can be given in Eq. (7) 

n IVIFWAw ( x2 , . . . , xn ) = 1 − x1 ,

i=1

n wi 1 − μ− ,1 − i

i=1

wi   n , 1 − μ+ i

i=1

(vi− )wi ,

n i=1

(vi+ )wi



(7)

− + − + where  xi =  μi , μi , vi , vi  (i = 1, 2, . . . , n) and the weights are w =  (w1 , w2 , . . . , wn )T , wi ∈ [0, 1], ni=1 wi = 1.

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The steps of Interval Valued Intuitionistic Fuzzy TOPSIS can be given as follows (Oztaysi et al. 2017):   Step 1. Define the decision matrix  DM k for each decision maker (k = 1, .., K) by using the scale in Table 1. A Am A   1    2  · · ·   , μ+ , v − , v+ μ− , μ+ , v − , v + μ− , μ+ , v − , v + · · · μ−  11k 11k   11k 11k   12k 12k   12k 12k   1mk 1mk   1mk 1mk  + − + + − + + − + μ− μ− · · · μ− C  21k , μ21k , v21k , v 21k 22k , μ22k , v22k , v 22k 2mk , μ2mk , v2mk , v 2mk DM k = 2 . . . . .. . . . . . .  .    .    .   − + − + − + − + − + − , v+ Cn μn1k , μn1k , vn1k , v n1k μn2k , μn2k , vn2k , v n2k · · · μnmk , μnmk , vnmk nmk C1

(8)

where n denotes the number of criteria (i = 1, …, n) and m denotes the number of alternatives (j = 1, …, m). Table 1. Interval valued intuitionistic fuzzy linguistic scale Linguistic terms

Membership & non-membership values

Absolutely Low (AL)

([0.10, 0.25], [0.65, 0.75])

Very Low (VL)

([0.15, 0.30], [0.60, 0.70])

Low (L)

([0.20, 0.35], [0.55, 0.65])

Medium Low (ML)

([0.25, 0.4]), [0.50, 0.60])

Approximately Equal (AE)

([0.45, 0.55], [0.30, 0.45])

Medium High (MH)

([0.50, 0.60], [0.25, 0.40])

High (H)

([0.55,0.65], [0.20, 0.35])

Very High (VH)

([0.60,0.70], [0.15,0.30])

Absolutely High (AH)

([0.65,0.75], [0.10,0.25])

 xk ) and fuzzy negative ideal Step 2. Define the fuzzy positive ideal solution (PIS  solution (NIS xk ) for each decision maker by using Eq. (5) and (6).              xk = PIS μ− , μ+ , v1−∗ k , v + , μ+ , v2−∗ k , v+ , μ+ , vn−∗ k , v + (9) , μ− , · · · , μ− 1∗ k 1∗ k 1∗ k 2∗ k 2∗ k 2∗ k n∗ k n∗ k n∗ k             − + − + − + − + − + − +  xk = NIS μ − ,μ − , v − ,v − , μ − ,μ − , v − ,v − ,··· , μ − ,μ − , v − ,v − 1 k

1 k

1 k

1 k

2 k

2 k

2 k

2 k

n k

n k

n k

n k

(10) − 

 − + where μi∗ k , μ+ is the interval valued intuitionistic fuzzy evaluai∗ k , vi∗ k , v i∗ k tion of the i th criterion associated with the highest score and accuracy functions.  − − +  , v is the interval valued intuitionistic fuzzy evaluation of the i , v μi− k , μ+ i− k i− k i− k th criterion associated with the minimum score and accuracy functions. Step 3. Calculate the distances between the j th alternative to positive and negative ideal solutions by using Eq. (11) and (12). Dj∗k

   n 2  2  2  2  2  2  1  − + l − πl u − πu = wiT μ− − μ− + μ+ − μ+ + vijk − vi−∗ k + vijk − vi+∗ k + πijk + πijk ∗k ∗k ∗k ∗k i i ijk i ijk i 2 i=1

(11)

IoT Platform Selection

−k

Dj

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   n 2  2  2  2  2  2  1  − + − + l − πl u − πu = wiT μ− + μ+ + vijk − vi−− k + vijk − vi+− k + πijk + πijk ijk − μi− k ijk − μi− k i− k i− k 2 i=1

(12) Step 4. Aggregate the distances for the decision makers by using Eq. (13) and (14) for each alternative j.  K  ∗ Dj∗ = λk Dj k (13) k=1

Dj− =

K k=1

  − λk Dj k

(14)

where j = 1, 2, …, m; k = 1, 2, …, K, and λk is the weight of decision maker k and 0 ≤ λk ≤ 1, K k=1 λk = 1. Step 5. Obtain the CC j closeness coefficient of each alternative by using Eq. (15) and rank the alternatives based on closeness coefficient values. CCj =

Dj− Dj− + Dj∗

, j = 1, 2, . . . , m

(15)

4 Evaluation of IoT Platforms by Using Interval Valued Intuitionistic Fuzzy TOPSIS In this study, in order to illustrate the applicability of the proposed methodology, we have evaluated five IoT platforms by using the criteria namely, return of investment (RIO), the flexibility to change the IoT platform (flexibility), the future performance (future), sustainability of the platform (sustainability), the maturity level of IoT platform (maturity), security of the IT platform (security), the support services provided by the platform (support), previous relations with the IoT platform provider company (relations), the strength of IoT ecosystem (strength) the scope of the services (scope), usability of the IoT platform (usability). Table 2 shows the linguistic evaluations of IoT platform alternatives.

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S. Ç. Onar et al. Table 2. Linguistic evaluations of IoT platform alternatives Alt 1

Alt 2

Alt 3

Alt 4

Alt 5

RIO

MH

VH

H

AE

AH

Flexibility

ML

VL

H

AL

ML

Future

MH

VL

EE

MH

VH

Sustainability

VH

L

AH

H

MH

Maturity

VL

L

AL

VH

AH

Security

VL

H

VL

VH

H

Support

VL

AH

VH

AE

EE

Relations

L

L

EE

AL

AE

Strength

VH

H

L

VL

VL

Scope

AE

H

AE

AH

MH

Usability

ML

MH

L

VH

VH

Table 3 shows the interval valued intuitionistic fuzzy evaluations of IoT platform alternatives. Table 3. Interval valued intuitionistic fuzzy evaluations of IoT platform alternatives Alt 1

Alt 2

Alt 3

Alt 4

Alt 5

RIO

([0.5,0.6],[0.25,0.4])

([0.6,0.7],[0.15,0.3])

([0.55,0.65],[0.2,0.35])

([0.45,0.55],[0.3,0.45])

([0.65,0.75],[0.1,0.25])

Flexibility

([0.25,0.4],[0.5,0.6])

([0.15,0.3],[0.6,0.7])

([0.55,0.65],[0.2,0.35])

([0.1,0.25],[0.65,0.75])

([0.25,0.4],[0.5,0.6])

Future

([0.5,0.6],[0.25,0.4])

([0.15,0.3],[0.6,0.7])

([0.5,0.5],[0.5,0.5])

([0.5,0.6],[0.25,0.4])

([0.6,0.7],[0.15,0.3])

Sustainability

([0.6,0.7],[0.15,0.3])

([0.2,0.35],[0.55,0.65])

([0.65,0.75],[0.1,0.25])

([0.55,0.65],[0.2,0.35])

([0.5,0.6],[0.25,0.4])

Maturity

([0.15,0.3],[0.6,0.7])

([0.2,0.35],[0.55,0.65])

([0.1,0.25],[0.65,0.75])

([0.6,0.7],[0.15,0.3])

([0.65,0.75],[0.1,0.25])

Security

([0.15,0.3],[0.6,0.7])

([0.55,0.65],[0.2,0.35])

([0.15,0.3],[0.6,0.7])

([0.6,0.7],[0.15,0.3])

([0.55,0.65],[0.2,0.35])

Support

([0.15,0.3],[0.6,0.7])

([0.65,0.75],[0.1,0.25])

([0.6,0.7],[0.15,0.3])

([0.45,0.55],[0.3,0.45])

([0.5,0.5],[0.5,0.5])

Relations

([0.2,0.35],[0.55,0.65])

([0.2,0.35],[0.55,0.65])

([0.5,0.5],[0.5,0.5])

([0.1,0.25],[0.65,0.75])

([0.45,0.55],[0.3,0.45])

Strength

([0.6,0.7],[0.15,0.3])

([0.55,0.65],[0.2,0.35])

([0.2,0.35],[0.55,0.65])

([0.15,0.3],[0.6,0.7])

([0.15,0.3],[0.6,0.7])

Scope

([0.45,0.55],[0.3,0.45])

([0.55,0.65],[0.2,0.35])

([0.45,0.55],[0.3,0.45])

([0.65,0.75],[0.1,0.25])

([0.5,0.6],[0.25,0.4])

Usability

([0.25,0.4],[0.5,0.6])

([0.5,0.6],[0.25,0.4])

([0.2,0.35],[0.55,0.65])

([0.6,0.7],[0.15,0.3])

([0.6,0.7],[0.15,0.3])

The results of the analysis and the ranking of alternatives are given in Table 4. The results show that Alternative 5 is the best alternative whereas Alternative 2 is the worst alternative.

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Table 4. Evaluation results for IoT platform alternatives Alt 1

Alt 2

Alt 3

Alt 4

Alt 5

D(PIS)

0.37

0.52

0.38

0.31

0.2

D(NIS)

0.33

0.12

0.42

0.42

0.49

CC

0.47

0.18

0.53

0.57

0.71

Rank

4.00

5.00

3.00

2.00

1.00

5 Conclusion and Further Suggestions Among various IoT platforms, it is very hard for the companies to select the appropriate IoT platform. The success of these projects effects the digital transformation journey of the firms. IoT platform selection process involve many criteria that can only be evaluated by human judgements. Thus, evaluating IoT alternatives based on subjective judgements is a complex process. In this study, we have proposed an interval valued intuitionistic TOPSIS approach for evaluating IoT platforms. We have utilized eleven criteria for evaluating the alternatives. In the illustrative example we show how the proposed methodology can be applied for evaluating IoT platforms. For the future studies, the proposed methodology should be applied to a real case problem. A sensitivity analysis and comparing the methodology with other MCDM methods will be beneficial. Other extensions of fuzzy sets such as Type 2, hesitant, Pythagorean, spherical and picture fuzzy TOPSIS methods can be applied and the results can be compared.

References Bharathi, S.V.: Forewarned is forearmed: assessment of IoT information security risks using analytic hierarchy process. Benchmarking 26(8), 2443–2467 (2019) De Nardis, L., Mohammadpour, A., Caso, G., Ali, U., Di Benedetto, M.-G.: Internet of Things platforms for academic research and development: a critical review. Appl. Sci. (Switzerland) 12(4), 2172 (2022) Fahmideh, M., Yan, J., Shen, J., Mougouei, D., Zhai, Y., Ahmad, A.: A comprehensive framework for analyzing IoT platforms: a smart city industrial experience. Smart Cities 4(2), 588–622 (2021) Hasan, M.K., et al.: A review on security threats, vulnerabilities, and counter measures of 5G enabled Internet-of-Medical-Things. IET Commun. 16(5), 421–432 (2022) Kondratenko, Y., Kondratenko, G., Sidenko, I.: Multi-criteria decision making and soft computing for the selection of specialized IoT platform. In: Chertov, O., Mylovanov, T., Kondratenko, Y., Kacprzyk, J., Kreinovich, V., Stefanuk, V. (eds.) ICDSIAI 2018. AISC, vol. 836, pp. 71–80. Springer, Cham (2019). https://doi.org/10.1007/978-3-319-97885-7_8 Lin, M., Huang, C., Xu, Z., Chen, R.: Evaluating IoT platforms using integrated probabilistic linguistic MCDM method. IEEE Internet Things J. 7(11), 11195–11208 (2020). Art. no. 9099246 Mijaˇc, T., Pašali´c, I.N., Tomat, L.: Selection of IoT platforms in smart cities: multicriteria decision making. In: Proceedings of the 16th International Symposium on Operational Research in Slovenia, SOR 2021, pp. 35–40 (2021)

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Mijuskovic, A., Ullah, I., Bemthuis, R., Meratnia, N., Havinga, P.: Comparing apples and oranges in IoT context: a deep dive into methods for comparing IoT platforms. IEEE Internet Things J. 8(3), 1797–1816 (2021). Art. no. 9169714 Kahraman, C., Oztaysi, B., Cevik Onar, S.: Interval-valued intuitionistic fuzzy confidence intervals. J. Intell. Syst. 28(2), 307–319 (2019) Oztaysi, B., Onar, S.C., Kahraman, C.: Performance measurement model for software development teams using interval-valued intuitionistic fuzzy analytic hierarchy process. J. Multiple-Valued Logic Soft Comput. 33(4–5), 321–339 (2019) Oztaysi, B., Onar, S.C., Goztepe, K., Kahraman, C.: A multi-expert interval-valued intuitionistic fuzzy location selection for the maintenance facility of armored vehicles. J. Multiple-Valued Logic Soft Comput. 32(1–2), 149–173 (2019) Oztaysi, B., Cevik Onar, S., Kahraman, C., Yavuz, M.: Multi-criteria alternative-fuel technology selection using interval-valued intuitionistic fuzzy sets. Transp. Res. Part D: Transp. Environ. 53, 128–148 (2017) Oztaysi, B., Onar, S.C., Goztepe, K., Kahraman, C.: Evaluation of research proposals for grant funding using interval-valued intuitionistic fuzzy sets. Soft. Comput. 21(5), 1203–1218 (2015). https://doi.org/10.1007/s00500-015-1853-8 Kahraman, C., Onar, S.C., Oztaysi, B.: A comparison of wind energy investment alternatives using interval-valued intuitionistic fuzzy benefit/cost analysis. Sustainability (Switzerland) 8(2), 118 (2016) Cevik Onar, S., Oztaysi, B., Otay, I., Kahraman, C.: Multi-expert wind energy technology selection using interval-valued intuitionistic fuzzy sets. Energy 90, 274–285 (2015)

A Hybrid Algorithm for Multilayer Perceptron Design with Intuitionistic Fuzzy Logic Using Malignant Melanoma Disease Data Sotir Sotirov1(B) , Yaroslava Petrova1,2 , Hristo Bozov1,2 , and Evdokia Sotirova1 1 Prof. Assen Zlatarov University, 1 Prof. Yakimov Blvd., Burgas 8010, Bulgaria

{ssotirov,esotirova}@btu.bg, [email protected] 2 Oncology Complex Center - Burgas, 86 Demokratsiya Blvd., Burgas 8000, Bulgaria

Abstract. In the article a method for reducing the input data coming to the input of a neural network of the Multilayer Perceptron type is proposed. The data that was used for the analysis are related to one of the most malignant tumors - malignant melanoma. They refer to patients with malignant melanoma that were registered in Oncology Complex Center in Burgas town. The data and contain information about age, sex, marital status of the patient, date of diagnosis, name of the disease according to the International statistical classification of diseases and health problems. The InterCriteria Analysis (ICA) approach was used to analyze the relationships between these parameters. A new improved structure and algorithm for increasing the learning speed of the Multilayer Perceptron (MLP) neural network are proposed. The algorithm is hybrid and includes determining the degrees of consonance and dissonance between the observed parameters. From the pairs of parameters (from ICA) with the highest consonance and with the lowest dissonance, one parameter is removed. For the purposes of MLP training, one of the values of the fuzzy pair of parameters is redundant because it does not carry additional information, and its removal reduces the number of neurons in the input layer of the neural network. In turn, this reduces the total error generated by each neuron. Another positive part is the faster learning of the neural network due to the lightweight architecture. Keywords: InterCriteria analysis · Malignant melanoma · Intuitionistic Fuzzy Logic · Multilayer Perceptron

1 Introduction Malignant melanoma is a malignant tumor and is the most serious oncological problem in dermatology. In recent years, the annual incidence of malignant melanoma has increased significantly [6, 14]. This tumor affects younger people and can metastasize in the early stages of the disease [10]. Early diagnosis leads to cure in over 91% of low-risk melanomas [9]. In this investigation a data for patients at the time of diagnosis were analyzed. The patients are registered in Burgas region during an 8-year period (2014–2021). The analysis and evaluation of the data connected with oncological diseases has been receiving © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 665–672, 2022. https://doi.org/10.1007/978-3-031-09173-5_77

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significant importance over the past years, because it reflects the trend in optimizing the effectiveness of the treatment of the patients. The data contains information about different parameters: age of patients, name of the disease, according to International statistical classification of diseases and health problems, gender, marital status, data of the registration of the patient, etc. As an instrument of analysis a InterCriteria Analysis (ICA) method is used [4]. It is based on the intuitionistic fuzzy sets (IFSs, [3]) and index matrices (IMs, [2]). The ICA approach is especially designed for decision support of multicriteria decision making problems. By applying the ICA method, the relationships between and among indicators of the patients (marital status, gender, age, name of the melanoma, according to International statistical classification of diseases, year of registration) were identified. The obtaining degree of correlation between all possible pairs of indicators are in the form of intuitionistic fuzzy pairs (IFPs, [5]) with values in the [0, 1] interval. The dependences between the indicators are called “positive consonance”, “negative consonance” or “dissonance”. The ICA method has been used by the authors for analysis an oncological data for Burgas region for 2014–2018. In [18] 1772 patients with malignant neoplasms of the digestive organs were observed. In [17] 100 patients with malignant melanoma were investigated and the obtained by ICA method results are confirmed by statistical analysis according to Pearson, Kendall and Spearman. The ICA method has been used successfully in the fields of medicine and neural networks [7, 11, 13, 16, 17, 19], and etc. The paper is organized as follows. Section 2 is the application of the InterCriteria Analysis approach. The investigated data connected the patient with malignant melanoma registered for period 2014–2021 are explained. The application of the ICA method is shown. In Sect. 3 a new improved structure and algorithm for increasing the learning speed of the MPL neural network are proposed. Section 4 presents our conclusions. Section 5 and Sect. 6 are acknowledgments and references.

2 The ICA Approach The ICA approach is applied to real data connected with age, gender, marital status, name of the disease, according to International statistical classification of diseases, year of registration the patient, etc. For our observation a data for 164 patients registered in registered in Oncology Complex Center in Burgas town with malignant melanoma disease in period 2014–2021 were collected. For the purposes of the study, the observed data are grouped as follows: • 7 malignant melanoma of skin, group C43 classified according to the International Statistical Classification of Diseases and Health Problems (ICD) [12] with following number of patients: 6 patients (4 men, 2 women) in group “C43.2”; 14 patients (7 men, 7 women) in group “C43.3”; 8 patients (6 men, 2 women) in group “C43.4”; 67 patients (44 men, 23 women) in group “C43.5”; 22 patients (12 men, 10 women) in group “C43.6”; 40 patients (16 men, 24 women) in group “C43.7”; 9 patients (6 men, 3 women) in group “C43.9”;

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• 7 age groups with following number of patients: 8 patients in group “up to 30 years” (3 men, 5 women); 15 patients in group “31–40” (10 men, 5 women); 21 patients in group “41–50” (9 men, 12 women); 21 patients in group “51–60” (15 men, 6 women); 53 patients in group “61–70” (26 men, 27 women); 23 patients in group “71–80” (15 men, 8 women); and 25 patients in group “over 80” (17 men, 8 women); • 8 years with following number of patients: 19 patients for 2014 (8 men, 11 women); 20 patients for 2015 (14 men, 6 women); 27 patients for 2016 (15 men, 12 women); 21 patients for 2017 (11 men, 10 women); 13 patients for 2018 (9 men, 4 women); 19 patients for 2019 (14 men, 5 women); 25 patients for 2020 (12 men, 13 women); 22 patients for 2021 (13 men, 9 women). For our study, the data are summarized in a table with 7 rows and 14 columns, containing information on for ICD for malignant melanoma of the skin (by rows) and age groups, 7 groups for men, 7 groups for women (by columns). After data processing with ICA software we obtain two tables with membership part and non-membership part of the intuitionistic fuzzy pairs respectively (see Table 1 and Table 2). In this way we obtain an IFS assessment of the relations between every pair of criteria. Table 1. Membership parts of the Intuitionistic fuzzy pairs of the relations between “ICD groups”

µ C432 C433 C434 C435 C436 C437 C439

C432 1,000 0,418 0,791 0,440 0,451 0,363 0,923

C433 0,418 1,000 0,385 0,396 0,352 0,242 0,451

C434 0,791 0,385 1,000 0,516 0,352 0,407 0,813

C435 0,440 0,396 0,516 1,000 0,484 0,527 0,451

C436 0,451 0,352 0,352 0,484 1,000 0,626 0,451

C437 C439 0,363 0,923 0,242 0,451 0,407 0,813 0,527 0,451 0,626 0,451 1,000 0,385 0,385 1,000

Table 2. Non-membership parts of the Intuitionistic fuzzy pairs of the relations between “ICD groups”

C432 C433 C434 C435 C436 C437 C439

C432 0,000 0,099 0,022 0,154 0,099 0,143 0,011

C433 0,099 0,000 0,143 0,286 0,242 0,330 0,088

C434 0,022 0,143 0,000 0,132 0,187 0,176 0,022

C435 0,154 0,286 0,132 0,000 0,275 0,209 0,165

C436 0,099 0,242 0,187 0,275 0,000 0,110 0,121

C437 C439 0,143 0,011 0,330 0,088 0,176 0,022 0,209 0,165 0,110 0,121 0,000 0,165 0,165 0,000

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After applying the ICA method one pair of criteria in positive consonance is obtained: C43.2 (Malignant melanoma of ear and external auricular canal) – C43.9 (Malignant melanoma of skin, unspecified) with evaluation 0.923077; 0.010989. This shows the same tendency of morbidity of these two types of melanoma depending on gender and age group. Two pairs of criteria are in weak positive consonance: “C43.4 (Malignant melanoma of scalp and neck)” - C43.9 (Malignant melanoma of skin, unspecified)” and “C43.2 (Malignant melanoma of ear and external auricular canal)” - “C43.4 (Malignant melanoma of scalp and neck)”, that means very similar tendency. The other eighteen couples do not show a consistent trend of finding a specific type of malignant melanoma depending on gender and age group. Nine pairs are in dissonance; eight pairs are in strong dissonance; one pair is in weak negative consonance.

3 Structure and Algorithm for Increasing the Learning Speed of the Multilayer Perceptron Neural Network Neural networks [8] are one of the models that can be used to recognize, classify, identify objects and predict the behavior of different objects (see Fig. 1).

Fig. 1. Structure of a MLP

Fig. 2. Learning process of a MLP

Multilayer perceptron’s can be thought of as a set of individual neurons [8] that deal with part of a problem, and then their individual outputs combine the source layer to form a global solution to the full problem. The basic idea is that the complex problem can be divided into simpler subtasks that can be solved by MLPs, and then the overall solution will be a combination of the outputs of the simple neurons. In the Fig. 1 the structure of a neural network is shown. The Levenberg-Marquard method was used to train the MLP. The learning process is shown Fig. 2 for one of the experiments.

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The objective of the preparation of the two matrices is to remove one or more columns of parameters such repetitive (with the corresponding index of the positive consonance). Testing is done as in the first step all values of the ICD for type of malignant melanoma of skin against the age groups for men and women are analyzed in order to make a comparison of the obtained results thereafter. For this comparison to be possible, the predefined weight coefficients and offsets that are normally random values between –1 and 1, are now established and are the same in all studies of the various attempts. For the learning process, we set the following parameters: Performance (MSE) = 0.00001; Validation check = 15. The input vector is divided into three different parts: Training (70/100); Validation (10/100) and Testing (20/100). The following parameters are given at the seven neural network inputs as follows: ICD C43.2, C43.3, C43.4, C43.5, C43.6, C43.7, C43.9. For tagret of the neural newtork is number, coresponded to a gender and ages (Table 3). Table 3. Target of a multilayer perceptron Age and sex

Men

Women

0–30 31–40 41–50 51–60 61–70 71–80 ≥81 0–30 31–40 41–50 51–60 61–70 71–80 ≥81

Target 1

2

3

4

5

6

7

8

9

10

11

12

13

14

At the first step of the process, we use all the 7 data for the melanome, in order to train the neural network. After the training process on the MLP all input values are simulated. The average deviation of the all 151 samples is 0.0198. The number of the weight coefficients is 96. At the next step of the process, we use a fork and try independently to remove one of the columns, and experiment with data from the rest six columns. We make a reduction of column 7 (with maximal intercriteria intuitionistic fuzzy pair (0.923077; 0.010989)) and use this data as a training set of the neural network. After the training process all input values are simulated. The average deviation of all the 151 samples is 0.0179. The number of the weight coefficients is 84. At the next step, we alternatively experiment with the reduction of one different column, column 1 (with maximal intercriteria intuitionistic fuzzy pair (0.923077; 0.010989)), and put the data on the input of the neural network. The average deviation after the training of the neural network of the all 151 samples is 0.0181. The number of the weight coefficients is 84. At the next step, we proceed with feeding the neural network with 5 inputs, with the reduction of both columns, 1 and 3, simultaneously, their maximal intercriteria intuitionistic fuzzy pair given above (Table 4). The average deviation of all the 151 samples is 0.0178%. The number of the weight coefficients is 72. At the fifth step, we reduce the number of inputs with one more, i.e. we put on the input of the neural network experimental data from 4 inputs, with removed columns 1, 3, and 7, which maximal intercriteria intuitionistic fuzzy pair is giben above. The average deviation of the all 151 samples is 0.0186 and the number of the weight coefficients is 60.

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Finally, at the sixth step, we experiment with the reduction of a fourth column, feeding the neural network with only 3 inputs. After the reduced columns 1, 3 and 7, the fourth reduced column is column 6, which maximal intercriteria intuitionistic fuzzy pair is (0.791209, 0.021978). The average deviation of the all 151 samples is 0.0256 and the number of the weight coefficients is 48. Table 4. Results from the simulations Number of inputs

Maximal value for μ per column

Respectivevalue for ν per column

7 inputs

–

–

0.0198

96

6 inputs without column 7

0.95601

0.04193

0.0179

84

6 inputs without column 1

0.95601

0.04193

0.0181

84

5 inputs without columns 1 and 3

0.95601 0.813187

0.04193 0.02197

0.0178

72

4 inputs without 0.95601 columns 1, 3 and 7 0.813187 0.791209

0.04193 0.02197 0.021978

0.0186

60

3 inputs without columns 1, 3, 6 and 7

0.04193 0.02197 0.021978 0.10989

0.0256

48

0.95601 0.813187 0.791209 0.626374

Average deviation

Number of the weight coefficients

4 Conclusion In the article an approach for reducing the number of parameters of a predictable process is presented. Reducing the number of parameters on the input of the neural network reduces the size of the weight matrices of the MLP and thus speeds up computation time and resources. This also decreases the required memory by the system. The number of neurons is one of the main parameters that must be determined during the implementation of MLP. For finding the dependences between parameters an ICA method is used. To check the accuracy and effectiveness of the proposed approach, average deviation is used and the number of weights in the network is described. The training and testing was carried out using real data for the registered patients with malignant melanoma in Burgas region for 2014–2021. In the next observations we will apply the ICA approach to patients with early postoperative urological and surgical complications [12], patients with panayiotopoulos syndrome [1] and KCNQ2 mutations [15].

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Acknowledgment. The authors are grateful for the support provided by the Bulgarian National Science Fund under Grant Ref. No. KP-06-N22/1/2018 “Theoretical research and applications of InterCriteria Analysis”. The authors declare that there is no conflict of interest regarding the publication of this paper.

References 1. Aleksandrova, I., Bojinova, V., Dimova, P.: Panayiotopoulos syndrome – a clinical and EEG study of 40 patients. Comptes rendus de l’Académie bulgare des Sciences 70(3), 435–442 (2017) 2. Atanassov, K.: Index matrices: towards an augmented matrix calculus. Studies. In: Computational Intelligence Series, vol. 573. Springer, Cham (2014). https://doi.org/10.1007/978-3319-10945-9 3. Atanassov, K.: On Intuitionistic Fuzzy Sets Theory. Springer, Heidelberg (2012). https://doi. org/10.1007/978-3-642-29127-2 4. Atanassov, K., Mavrov, D., Atanassova, V.: Intercriteria decision making: a new approach for multicriteria decision making, based on index matrices and intuitionistic fuzzy sets. Issues Intuitionistic Fuzzy Sets Generalized Nets 11, 1–8 (2014) 5. Atanassov, K., Szmidt, E., Kacprzyk, J.: On intuitionistic fuzzy pairs. Notes Intuitionistic Fuzzy Sets 19(3), 1–13 (2013) 6. Garbe, C., Leiter, U.: Clinics in Dermatology, vol. 27, issue 1, pp. 3–9, January–February 2009. Elsevier. https://doi.org/10.1016/j.clindermatol.2008.09.001 7. Jekova, I., Vassilev, P., Stoyanov, T., Pencheva, T.: InterCriteria analysis: application for ECG data analysis. Mathematics 9(8), 854 (2021). https://doi.org/10.3390/math9080854 8. Hagan, M., Demuth, H., Beale, M.: Neural Network Design. PWS Publishing, Boston (1996) 9. Karimkhani, C., et al.: The global burden of melanoma: results from the Global Burden of Disease Study 2015. Br. J. Dermatol. 177(1), 134–140 (2017) 10. Markovic, S., et al.: Malignant melanoma in the 21st century, part 1: epidemiology, risk factors, screening, prevention, and diagnosis. In: Mayo Clinic Proceedings, pp. 364–380. Elsevier (2007) 11. Krumova, S., et al.: Intercriteria analysis of calorimetric data of blood serum proteome. BBA-Gen. Subjects 1861(2), 409–417 (2017) 12. Melanoma and other malignant neoplasms of skin (C43-C44), International Statistical Classification of Diseases and Related Health Problems 10th Revision (ICD-10)-WHO Version for 2019-covid-expanded. https://icd.who.int/browse10/2019/en#/C43-C44 13. Mladenov, V.l., et al.: Risk factors for the occurrence of early postoperative urological and surgical complications after kidney transplantation from a living and cadaveric donor. Comptes rendus de l’Académie bulgare des Sciences (2022). ISSN (online) 2367-5535 14. National Center of Public Health and Analyses, Annual information. http://ncpha.govern ment.bg/index.php?lang=en 15. Peycheva, V., et al.: Impact of KCNQ2 mutations in Bulgarian patients with electroclinical syndromes with onset in the first year of life. Biotechnol. Biotechnol. Equip. 31(1), 138–142 (2017). Impact Factor (2015) 16. Sotirov, S., et al.: Application of the intuitionistic fuzzy InterCriteria analysis method with triples to a neural network preprocessing procedure. Computat. Intell. Neurosci. (2017). https://doi.org/10.1155/2017/2157852. 9 pages, Article ID 2157852

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17. Sotirov, S., Atanassova, V., Sotirova, E., Bureva, V., Mavrov, D.: Application of the intuitionistic fuzzy InterCriteria analysis method to a neural network preprocessing procedure. In: 9th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), 30 June–03 July 2015, Gijon, Spain, pp. 1559–1564 (2015). https://doi.org/10.2991/ifsa-eus flat-15.2015.222 18. Sotirova, E., Vasilev, V., Bozova, G., Bozov, H., Sotirov, S.: Application of the InterCriteria analysis method to a dataset of malignant neoplasms of the digestive organs for the Burgas Region for 2014–2018. In: 2019 Big Data, Knowledge and Control Systems Engineering (BdKCSE), pp. 1–6 (2019). https://doi.org/10.1109/BdKCSE48644.2019.9010609 19. Sotirova, E., Bozova, G., Bozov, H., Sotirov, S., Vasilev, V.: Application of the InterCriteria analysis method to a data of malignant melanoma disease for the Burgas Region for 2014– 2018. In: Atanassov, K.T., et al. (eds.) IWIFSGN 2019 2019. AISC, vol. 1308, pp. 166–174. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-77716-6_15

Generalized Net Model of Balanced Iterative Reducing and Clustering Using Hierarchies (Birch) with Intuitionistic Fuzzy Evaluations Veselina Bureva1(B)

, Petar Petrov1,2

, and Stanislav Popov1

1 Laboratory of Intelligent Systems, “Prof. Dr. AssenZlatarov” University, “Prof. Yakimov”

Blvd., Burgas 8010, Bulgaria [email protected] 2 Vocational School of Electrical Engineering and Electronics, “Konstantin Fotinov”, Burgas, Bulgaria

Abstract. Balanced Iterative Reducing and Clustering using Hierarchies (BIRCH) is a method for agglomerative cluster analysis. A Generalized net (GN) model of the BIRCH is constructed. The clustering procedure is estimated using intuitionistic fuzzy evaluations. The process monitoring is explained using the constructed GN model and calculated IFEs. The GN model of BIRCH with IFEs optimizes and estimates the standard clustering algorithm. The proposed method is implemented using Python programming language. Keywords: Big data analytics · Data science · Generalized Nets · Intuitionistic Fuzzy Sets

1 Introduction Generalized Nets (GNs) are presented in [4, 6, 8, 9, 12]. The transitions description in the GN model is made using index matrices R [7]. Intuitionistic Fuzzy Sets (IFS) theory is presented in [5, 10, 11, 13]. These three tools are used in the presented research to describe and optimize the clustering procedure. GN model of the BIRCH clustering procedure is constructed. It allows us to simulate and optimize the steps of the algorithm. The GN model performance is estimated using the defined intuitionistic fuzzy evaluations. The current research work is part of series of papers related to GN modeling of the data mining processes [5, 6]. In the literature, different data methods are modeled. Part of them are the following: GN models in the field of cluster analysis [14, 15], GN models of neural networks [2, 3], GN models of genetic algorithms [1]. The paper has the following structure: Sect. 1 presents the notation of the study; Sect. 2 introduces the constructed GN model of Balanced Iterative Reducing and Clustering using Hierarchies (Birch) with Intuitionistic Fuzzy Evaluations; Sect. 3 presents an example of the implementation of BIRCH with IFE using Python language. In Sect. 4 some concluding remarks are discussed.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 673–680, 2022. https://doi.org/10.1007/978-3-031-09173-5_78

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2 Generalized Net Model of Balanced Iterative Reducing and Clustering using Hierarchies (Birch) with Intuitionistic Fuzzy Evaluations In the field of big data analytics, BIRCH is applied using the single machine approach [16]. BIRCH procedure contains four phases. In the first step, Birch scans the database and loads data into the memory to build a CF-tree. If the resource is not enough, the CF-tree is rebuilt. Initial parameters for the CF-Tree are selected: threshold for minimum number of data in a sub-cluster, branching factor, distance calculation, splitting nodes, merging nodes. The second step of the algorithm resizes the data and is optional. It builds a smaller CF tree by removing extreme values (outliers). The third step is for global clustering using classic clustering algorithm. The fourth optional step specifies the clusters. It works on allocating the data points to the different leaf nodes in the CF trees [18]. In the current research work a Generalized Net (GN) Model of Balanced Iterative Reducing and Clustering using Hierarchies (Birch) with Intuitionistic Fuzzy Evaluations is presented (Fig. 1). The GNDraw software is used for GN model construction [17]. The GN model is constructed by following transitions: A = {Z1 , Z2 , Z3 , Z4 , Z5 , Z6 , Z7 }, where the transitions describe the processes: • • • • • • •

Z1 Z2 Z3 Z4 Z5 Z6 Z7

– Data sources; – Data preprocessing; – Scanning data into memory; – Compress data; – Global clustering; – Concentrate clusters; – Intuitionistic fuzzy evaluations.

Initially, there is one token that is located in place L 28 with initial characteristic: “data warehouse”. In the next time-moments this token is split into two. The original token will continue to stay in place L 28 , while the other tokens will move to the next transitions. A token enters the net via place l1 with initial characteristics: “new data”. Transition Z 1 has the form: Z1 = {l1 , l27 , l28 }, {l2 , l3 , l28 }, R1 , ∨(l1 , l27 , l28 ), where

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Fig. 1. Generalized net model of the process of cluster analysis using BIRCH algorithm using intuitionistic fuzzy evaluations

and • W 28,2 = “there is appropriate data for segmentation using BIRCH algorithm”; • W 28,3 = “there is appropriate data for preprocessing”; • W 28,28 = ¬(W 28,2 ∧ W 28,3 ). The tokens that enter the places l2 and l 3 have the following characteristics: “selected data for cluster analysis using BIRCH algorithm” in place l2 and “selected data for preprocessing” in place l3 . A token enters the net via place l4 with initial characteristics: “methods and parameters for data preprocessing”. Transition Z 2 has the form: Z2 = {l3 , l4 , l6 }, {l5 , l6 , l27 }, R2 , ∨(∧(l3 , l4 ), l6 ), where

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and • W 6,5 = “there is preprocessed training set for segmentation using BIRCH algorithm”; • W 6,6 = “there is preprocessed training set for storing”; • W 6,6 = ¬(W 6,5 ∧ W 6,6 ). The tokens that enter places l5 and l 6 have the following characteristics: “preprocessed data for cluster analysis using BIRCH algorithm” in place l2 and “preprocessed data for storing” in place l3. A token enters the net via place l7 with initial characteristics: “parameters and metrics for cluster analysis”. Transition Z 3 has the form: Z3 = {l2 , l5 , l7 , l12 , l13 , l21 }, {l8 , l9 , l10 , l11 , l12 , l13 }, R3 , ∨(∧(∨(l2 , l5 , l21 ), l7 ), l12 , l13 ), where

and • • • • • • •

W 13,12 = “there are constructed clustering features - CFs”; W 13,13 = ¬W 13,12 ; W 12,8 = “there is a copy of data for clusters specifying”; W 12,9 = “there is a CF-Tree for global clustering”; W 12,10 = “there is a CF-Tree for allocating data (resizing the received CF-Tree)”; W 12,11 = “there are outliers”; W 12,12 = ¬(W 12,8 ∧W 12,9 ∧W 12,10 ∧W 12,11 ).

The token that enters in place l12 has the following characteristic: “constructed clustering features - CFs”. At the second activation of the transition, the token from place l12 generates four new tokens that enter in places l8 , l 9 , l 10 and l11 with characteristics respectively: “copy of data for clusters specifying” in place l8 , “CF-Tree for global clustering” in place l9 , “CF-Tree for data allocating” in place l10 , “extreme values” in place l11 . Transition Z 4 has the form: Z 4 = {l 10 , l 16 }, {l 14 , l 15 , l 16 }, R4 , ∨(l10 , l 16 ), where

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and • W 16,14 = “there are resized CF-Tree”; • W 16,15 = “there are outliers after the step of data allocating”; • W 16,16 = = ¬(W 16,14 ∧ W 16,15 ). The tokens that enter in places l14 and l 15 have the following characteristics: “resized CF-Tree” in place l14 and “outliers after the step of data condensing” in place l15. A token enters the net via place l17 with initial characteristics: “standard clustering algorithm”. Transition Z 5 has the form: Z5 = {l9 , l14 , l17 , l20 }, {l18 , l19 , l20 }, R5 , ∨(∧(∨(l9 , l14 ), l17 ), l20 ), where

and • W 20,18 = “there are clustered data”; • W 20,19 = “there are outliers after the step of global clustering”; • W 20,20 = ¬(W 20,18 ∧ W 20,19 ). The tokens that enter places l18 and l19 have the following characteristics: “clustered data” in place l18 and “outliers after the step of global clustering” in place l19. Transition Z 6 has the form: Z 6 = {l 8 , l 18 , l 23 }, {l 21 , l 22 , l 23 }, R6 , ∨(l 8 , l 18 , l 23 ), where

and • W 23,21 = “there is a need of data”;

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• W 23,22 = “there are refined clusters”; • W 23,23 = ¬(W 23,21 ∧ W 23,22 ). The tokens that enter places l21 and l 22 have the following characteristics: “need of data” in place l21 and “refined clusters” in place l22. A token enters the net via place l24 with initial characteristics: “formulas for intuitionistic fuzzy evaluations”. Transition Z 7 has the form: Z7 = {l11 , l15 , l19 , l22 , l24 , l26 }, {l25 , l26 }, R7 , ∨(∧(l11 , l15 , l19 , l22 , l24 ), l26 ), where

and • W 26,25 = “there are intuitionistic fuzzy evaluations”; • W 26,26 = ¬ W 26,25 . The token that enters in place l25 has the following characteristics: “intuitionistic fuzzy evaluations”. The following notation is used for calculating the IFEs: all data points – m, clustered points – k, points on the border of the cluster – b, extreme values – l. Then, we can find the degree of membership and the degree of non-membership for the clustering procedure. The uncertainty is also calculated. k −b l , νcl = , πcl = 1 − μcl − νcl . m m The threshold values are presented as follows: X max , X min , V max , V min . The received results have to satisfy the following conditions: μcl =

• μcl > X max and ν cl < V min - good performance of the procedure is achieved. • μcl < X min and ν cl > V max - the results are not satisfactory. • μcl ≤ X max and ν cl ≥ V min - the result is unknown and new iterations of the cluster procedure are necessary.

3 Results of the BIRCH with IFE Implementation The BIRCH algorithm with IFEs is implemented using Python programming language. Depending on the input data and clustering parameters different IFEs are calculated.

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An example using random data is presented in Fig. 2. The input parameters distance and centers of the clusters are set. Separate functions are used to derive the data points related to clusters, boundaries and outliers.

Fig. 2. BIRCH with IFEs

4 Conclusion In the current paper a GN model of BIRCH with IFEs is made. It allows us to better monitor the clustering procedure. The presented GN model and IFEs can be used for optimizing the method of cluster analysis. Practical examples on different datasets can be performed using the Python implementation. In future research works, GN models of clustering algorithms as OPTICS and DBSCAN will be created. The intuitionistic fuzzy evaluations will be applied and the performance of the clustering procedures will be compared. Acknowledgments. The authors are grateful for the support provided by the European Regional Development Fund and the Operational Program “Science and Education for Smart Growth” under contract UNITe No. BG05M2OP001-1.001-0004-C01 (2018–2023).

References 1. Atanassov, K., Roeva, O., Pencheva, T., Shennon, A.: Generalized nets in artificial intelligence. In: Volume 7: Generalized Nets and Genetic Algorithms. Prof. Marin Drinov Academic Publishing House, Sofia (2013)

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2. Atanassov, K., Sotirov, S.: Generalized nets as tools for modelling of the neural networks. In: 2020 IEEE 10th International Conference on Intelligent Systems, pp. 521–525 (2020) 3. Atanassov, K., Sotirov, S.: Generalized nets in artificial intelligence. In: Volume 6: Generalized Nets and Supervised Neural Network. Prof. Marin Drinov Academic Publishing House, Sofia (2012) 4. Atanassov, K., Sotirova, E.: Generalized Nets. Professor Marin Drinov Publishing House of Bulgarian Academy of Sciences, Sofia (2017). (in Bulgarian) 5. Atanassov, K.: Generalized Nets and Intuitionistic Fuzziness in Data Mining. Professor Marin Drinov Publishing House of Bulgarian Academy of Sciences, Sofia (2020) 6. Atanassov, K.: Generalized nets as a tool for the modelling of data mining processes. In: Sgurev, V., Yager, R.R., Kacprzyk, J., Jotsov, V. (eds.) Innovative Issues in Intelligent Systems. SCI, vol. 623, pp. 161–215. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-272 67-2_6 7. Atanassov, K.: Index Matrices: Towards an Augmented Matrix Calculus. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10945-9 8. Atanassov, K.: Theory of generalized nets (an algebraic aspect). AMSE Rev. 1(2), 27–33 (1984) 9. Atanassov, K.: Generalized Nets. World Scientific, Singapore (1991) 10. Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986) 11. Atanassov, K.: Intuitionistic Fuzzy Sets: Theory and Applications. Physica-Verlag, Heidelberg (1999) 12. Atanassov, K.: On Generalized Nets Theory. “Prof. M. Drinov” Academic Publ. House, Sofia (2007) 13. Atanassov, K.: On Intuitionistic Fuzzy Sets Theory. Springer, Berlin (2012). https://doi.org/ 10.1007/978-3-642-29127-2 14. Bureva, V., Sotirova, E., Popov, S., Mavrov, D., Traneva, V.: Generalized net of cluster analysis process using STING: a statistical information grid approach to spatial data mining. In: Christiansen, H., Jaudoin, H., Chountas, P., Andreasen, T., Legind Larsen, H. (eds.) FQAS 2017. LNCS (LNAI), vol. 10333, pp. 239–248. Springer, Cham (2017). https://doi.org/10. 1007/978-3-319-59692-1_21 15. Bureva, V., Traneva, V., Zoteva, D., Tranev, S.: Generalized net model simulation of cluster analysis using CLIQUE: clustering in quest. In: Dimov, I., Fidanova, S. (eds.) HPC 2019. SCI, vol. 902, pp. 48–60. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-55347-0_5 16. Hassanien, A.E., Azar, A.T., Snasael, V., Kacprzyk, J., Abawajy, J.H. (eds.): Big Data in Complex Systems. SBD, vol. 9. Springer, Cham (2015). https://doi.org/10.1007/978-3-31911056-1 17. Ikonomov, N.: GNDraw – software application for creating generalized nets. Issues Intuitionistic Fuzzy Sets Generalized Nets 13, 61–71 (2017) 18. Zhang, T., Ramakrishnan, R., Livny, M.: BIRCH: an efficient data clustering method for very large databases. In: Proceedings of the 1996 ACM SIGMOD International Conference on Management of Data – SIGMOD’96, pp. 103–114 (1996)

Software Utility of One-Way Intuitionistic Fuzzy ANOVA Velichka Traneva(B) , Deyan Mavrov , and Stoyan Tranev Prof. Dr. Asen Zlatarov University, 1 Prof. Y. Yakimov Blvd., 8000 Burgas, Bulgaria [email protected], [email protected], [email protected] http://www.btu.bg/ Abstract. The post-COVID-19 era will bring forward a new normal one that will accelerate digital transformation in many areas as one solution to avoid severe economic consequences. Many factors have been considered as a possible influence on the diffusion of COVID-19 around the world - one such factor being the geographic location of each country. One-way Analysis of Variance (ANOVA) studies the influence of a single factor on a variable. In a previous publication, we proposed one-way intuitionistic fuzzy ANOVA (1-D IFANOVA), based on the formalisms of Index Matrices (IMs) and Intuitionistic Fuzzy Sets (IFSs), which is a modification of classical ANOVA. In this paper, we will introduce a command-line utility for the calculation of IFANOVA results which performs the algorithm using Intuitionistic Fuzzy Pairs (IFPs). Then we will apply IFANOVA to clarify how the number of daily reported cases in European countries depends on their geographic location, using the dataset of ECDPC daily cases from January 1 to December 31, 2021. We will also analyze the data with classical ANOVA and will perform a comparative analysis of the results obtained from that and from IFANOVA. Keywords: ANOVA · COVID-19 Intuitionistic fuzzy sets

1

· IFANOVA · Index matrix ·

Introduction

Coronavirus disease 2019 (COVID-19) was first arisen in Wuhan, Hubei province, China at the end of 2019 (see [14,31]). Over the following months it spread across the world, forcing many countries to implement preventative measures. These measures have had a strong effect on the economy and on public life, in the light of which many recent papers have attempted to analyze the movement of the number of new COVID-19 cases and to predict how it will change in the future. One-way and two-way ANOVA were used to analyze the COVID-19 infection rate in India in [1]. This work is supported by the Asen Zlatarov University through project Ref. No. NIX440/2020 “Index matrices as a tool for knowledge extraction”. c The Author(s), under exclusive license to Springer Nature Switzerland AG 2022  C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 681–689, 2022. https://doi.org/10.1007/978-3-031-09173-5_79

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Analysis of variance, or ANOVA, is a popular method for analysis, originally developed by Fisher [12], which investigates whether certain factors exert significant influence on the data. The input data used in analysis such as ANOVA, may often come with certain irregularities, such as gaps in the data or irregular changes in consecutive number values, caused by e.g. delayed or incomplete reporting of numbers. Fuzzy logic [33] is a concept which may used to represent such irregularities. Fuzzy logic has already been used to create modified variants of ANOVA, known as Fuzzy ANOVA (FANOVA): A bootstrap approach to FANOVA was introduced in [13]; a confidence-interval based FANOVA was explored in [9]; a FANOVA using triangular fuzzy data was proposed in [15,20]; a FANOVA based on Zadeh’s extension principle is described in [18,19]. Intuitionistic fuzzy sets (IFSs) [2,4] take the idea of fuzzy logic further by adding a degree of falsity, which subtracted from the degree of truth gives the degree of hesitancy for an element. An Intuitionistic Fuzzy ANOVA (IFANOVA) is a modified ANOVA which uses intuitionistic fuzzy values. One example of the IFANOVA was proposed in [16], where IFSs are converted to fuzzy sets. In previous publications [27,28] we proposed one-way and two-way IFANOVA without replications, based on the classical analysis of variance [11] and the apparatuses of IFSs and index matrices (IMs) [3], in which the input data consists of IFPs) rather than real numbers. We also developed two-way IFANOVA, which we later used to investigate how the COVID-19 data depend on demographic and climatic factors [29]. In this work, we aim to apply one-way IFANOVA to analyse the effect of the “geographic location” factor on the number of cases in Europe, as reported in the dataset of daily cases provided by the European Centre for Disease Prevention and Control [34] for the period from January 1 to December 31, 2021. To facilitate the analysis, we have created a new command-line utility which performs one-way IFANOVA over an IM of pre-prepared IFPs. Later in this paper, we will show the results we obtained from one-way IFANOVA using the utility and compare them with those of regular ANOVA. The remainder of this paper is divided in the following way: Sect. 2 gives some basic definitions of IM and IFS theory; Sect. 3 defines classical one-way ANOVA and shows the results from its application on the number of COVID-19 cases; in Sect. 4 we define the algorithm of one-way (1-D) IFANOVA, describe the software implementation and give the final results; and finally in Sect. 5 we draw our inferences from the results and outline possible ideas for further research.

2

Basic Definitions

The IFP is an object of the form a, b = μ(p), ν(p), where a, b ∈ [0, 1] and a+b ≤ 1, that is used as an evaluation of a proposition p [7]. μ(p) and ν(p) respectively determine the degrees of membership and non-membership. Let us have two IFPs x = a, b and y = c, d. Basic operations are described in [4,7,8,10,22].

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Let Ra,b = 0.5(2 − a − b)(1 − a) [24]. Then, as per [4,27]: x ≥ y iff b ≤ d; x ≥R y iff Ra,b ≤ Rc,d .

(1)

Let I be a set. By two-dimensional IF index matrix (2-D IFIM) A = [K, L, {μki ,lj , νki ,lj }] with index sets K and L (K, L ⊂ I), we denote [5]: l1 k1 μk1 ,l1 , νk1 ,l1  A≡ . .. .. . km

... lj ... ln . . . μk1 ,lj , νk1 ,lj  . . . μk1 ,ln , νk1 ,ln  , .. .. .. .. . . . . μkm ,l1 , νkm ,l1  . . . μkm ,lj , νkm ,lj  . . . μkm ,ln , νkm ,ln 

where for every 1 ≤ i ≤ m, 1 ≤ j ≤ n: 0 ≤ μki ,lj , νki ,lj , μki ,lj + νki ,lj ≤ 1. In [5,25,26,30], were defined operations with 2-D IFIMs, similar to those with the classical matrices, but there are also specific ones such as addition, transposition, multiplication, projection, substitution, aggregation operations, internal subtraction of IMs’ components, termwise multiplication and subtraction.

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Application of ANOVA to the COVID-19 Cases in Europe

3.1

Classical One-Way ANOVA

The original approach of ANOVA for analysing the variance of the means of several independent populations, was developed by Fisher [12]. The simplest case is one-way ANOVA [11], which is performed as follows: Let xki ,lj for i = 1, 2, ..., m and j = i1 , i2 , ...iI (1 ≤ iI ≤ n) denote the data from the ki −th level and lj −th observation. Let N is the number of observations. The ANOVA has been contemplate to accept/reject hypothesis H0 : Mk1 = Mk2 = ... = Mkm , against H1 : not all Mki are equal, where Mki are the factor level means. The total mean sum of squares M ST , the mean sums of squares for error M SE and the mean sums of squares for treatment M SC are calculated according to [11]. If the test statistic F =

1 1 M SC ≥ F(α,m−1,N −m) or ≤ = F(1−α,N −m,m−1) , M SE F F(α,m−1,N −m)

(2)

where F(α,m−1,N −m) is α−quantile of F −distribution with m − 1 and N − m degrees of freedom, then H0 is rejected on significance level α [11,12].

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Application of One-Way ANOVA Over COVID-19 Cases in Europe

Let us apply one-way ANOVA using Excel on the same data on COVID-19 cases (see [34–36]). The data are normally distributed according to the KolmogorovSmirnov test [11] at the 5% significance level. The “geographical location” factor for the European countries has five different values - Northern Europe, Eastern Europe, Southern Europe, Western Europe and Central Europe. The following Table 1 presents the results of one-way ANOVA by the factor “geographical location” for the European countries with α = 0.05: Table 1. ANOVA table by the factor “geographical location” for the European countries. Source

SS

df MS

F

p-value F crit

Between groups 14842910334 4 3710727584 5,81 0,00056 2,54 Within groups 35100123176 55 638184057,7 Total 49943033510 59

Grouping of the European countries: We can conclude from the Northern Europe: Belarus, Denmark, Estonia, ANOVA’s results that the value of Faeroe Islands, Finland, Latvia, Liechtenstein, Lithuania, Norway, Russia and Sweden; the “geographical location” factor Eastern Europe: Albania, Bulgaria, Georgia, does have a statistically significant Kosovo, Macedonia, Moldova, Romania, Serbia and Ukraine; effect on the number of COVID-19 Southern Europe: Andorra, Azerbaijan, Bosnia cases. and Herzegovina, Croatia, Cyprus, Greece, Italy, Malta, Montenegro, Portugal, San Marino, Spain The average COVID-19 number and Vatican; of cases per 100 000 people for 2021 Western Europe: Belgium, France, Germany, Gibraltar, Guernsey, Iceland, Ireland, Isle of Man, is the highest in the Central EuroJersey, Luxembourg, Monaco, Netherlands and pean countries (104309 cases), and United Kingdom; Central Europe: Austria, Czech Republic, Hunthey the lowest in Northern Eurogary, Poland, Slovakia, Slovenia and Switzerland pean countries (62346 cases per 100 000 people) and Eastern Europe (67631 cases per 100 000) (see Table 2 and Fig. 1).

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Table 2. Average COVID-19 case notification rates of the European countries on the location Northern Europe Eastern Europe

Southern Europe

Western Europe

Central Europe

62346

94076

81190

104309

67631

Fig. 1. Cases of Covid-19 per million from January 1, 2021 to December 31, 2021 depending on the “location” factor

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Intuitionistic Fuzzy One-Way ANOVA

In [27], we introduced a way to combine the advantages of classical variational analysis with the means of intuitionist fuzzy logic and IMs. In order to facilitate the efficient application of the 1-D IFANOVA algorithm on real data, a C++ based command-line utility has been developed. It is implemented with the index matrix template class (IndexMatrixT ) from [17], which implements the basic IM operations. For the analysis described in this paper, we make use of the same work done for the application of 2-D IFANOVA [29]. The program manipulates IM objects consisting of IFIMs. As the code operates with objects representing IMs and IFPs, it helps to further analyse the algorithm and find any mistakes made in its theoretical description (Fig. 2).

Fig. 2. An extract from the IFANOVA utility’s code

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The program opens a user-specified tab-separated text file with the contents of one IFIM. The original data need to be converted to IFPs using the method from [4]. When finished, the program prints the resulting M SE, M SC, and F1 values. Enabling the “verbose” option makes it print the interim matrices (Fig. 3).

Fig. 3. A snippet from an input file of IFPs and the results from the utility after processing the file

We will apply 1-D IFANOVA to analyse the effect the “geographic location” factor has on the number of COVID-19 cases from the same ECDPC dataset [34] which we used for classical ANOVA. First we need to transform the data values with COVID-19 cases into IFPs as in [4,27]. The expert approach presented in detail in [4] can be use to convert the data to IFPs. The IFIM X[K, L] is created, the elements of which are the values measured according to the different levels of the studied factor. The original arrangement of the matrix X without the last two rows and columns is: X[K/{Sr2 , Sr}, L/{Sr1 , Sr}] = January

F ebruary

M arch

...

October

N ovember December

Northern Europe 0.008, 0.99 0.05, 0.94 0.09, 0.90 . . . 0.33, 0.66 0.44, 0.55 0.56, 0.43 Eastern Europe 0.03, 0.96 0.07, 0.92 0.13, 0.86 . . . 0.41, 0.59 0.48, 0.51 0.52, 0.47 . Southern Europe 0.15, 0.84 0.23, 0.75 0.30, 0.69 . . . 0.59, 0.40 0.65, 0.34 0.78, 0.21 Western Europe 0.10, 0.88 0.16, 0.82 0.20, 0.79 . . . 0.50, 0.49 0.60, 0.39 0.78, 0.21 Central Europe 0.18, 0.81 0.27, 0.72 0.14, 0.85 . . . 0.61, 0.38 0.75, 0.24 0.97, 0.02

After applying IFANOVA on X (as described in Sect. 4, we obtained the following results: M SC = 0.004, 0.995, M SE = 0.006, 0.994. We need to use Pietraszek’s approach ([21], 2016), which led to the obtaining of fuzzy estimator of ANOVA key statistics F value. The classic value F (0.95, 55, 4) = 0.39 corresponds to the fuzzy assessment Ff uzzy(0.95,55,4) = 0.92, 0. Therefore 1 M SE = ≤ Ff uzzy(0.95,55,4) = 0.92, 0. 0.627, 0.159 = M SC F Thus, we can say IFANOVA does find a dependency on the studied factor.

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5

687

Conclusion

In this work we have presented a software utility implementing the 1-D IFANOVA algorithm. After analysing data on the number of COVID-19 cases in European countries for the period from January 1 to December 31, 2021, we can conclude that the “geographical location” factor has a statistically significant effect on the COVID-19 notification rate per 100 000 people. Thus we can see that both classical ANOVA [11] and IFANOVA register its influence on the number of cases. In the future, the research will continue through index matrix interpretation of the classical two-factor variational analysis with replications on intuitionist fuzzy data, as well as with the development of a software application for its implementation.

References 1. Anwla, P.: Introduction to ANOVA for Statistics and Data Science (with COVID19 Case Study using Python). Analtics Vidhua. https://www.analyticsvidhya.com/ blog/2020/06/introduction-anova-statistics-data-science-covid-python. Accessed 21 Jan 2022 2. Atanassov, K.: Intuitionistic fuzzy sets. In: Proceedings of VII ITKR’s Session, Sofia (1983) (in Bulgarian) 3. Atanassov, K.: Generalized index matrices. Comp. Rend. l’Acad. Bulg. Sci. 40(11), 15–18 (1987) 4. Atanassov, K.: On Intuitionistic Fuzzy Sets Theory. STUDFUZZ. vol. 283. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29127-2 5. Atanassov, K.T.: Index Matrices: Towards an Augmented Matrix Calculus. SCI, vol. 573. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10945-9 6. Atanassov, K.: On index matrices, Part 2: Intuitionistic fuzzy case. Proc. Jangjeon Math. Soc. 13(2), 121–126 (2010) 7. Atanassov, K., Szmidt, E., Kacprzyk, J.: On intuitionistic fuzzy pairs. Notes Intuitionist. Fuzzy Sets 19(3), 1–13 (2013) 8. Atanassov, K.: Remark on an intuitionistic fuzzy operation “division”. In: Issues in IFS and GNs 14 (2018–2019), pp. 113–116 9. Buckley, J.J.: Fuzzy Probability and Statistics. Springer, Heidelberg (2006). https://doi.org/10.1007/3-540-33190-5 10. De, S.K., Bisvas, R., Roy, R.: Some operations on IFSs. Fuzzy Sets Syst. 114(4), 477–484 (2000) 11. Doane, D., Seward, L.: Applied Statistics in Business and Economics. McGraw-Hill Education, New York (2016) 12. Fisher, R.: Statistical Methods for Research Workers. London (1925) 13. Gil, M.A., Montenegro, M., Gonz´ alez-Rodr´ıguez, G., Colubi, A., Casals, M.R.: Bootstrap approach to the multi-sample test of means with imprecise data. Computer Statistics and Data Analysis 51, 148–162 (2006) 14. Khan, M., Kazmi, S., Bashir, A., Siddique, N.: COVID-19 infection: origin, transmission, and characteristics of human coronaviruses. J. Adv. Res. 24, 91–98 (2020). https://doi.org/10.1016/j.jare.2020.03.005 15. Kalpanapriya, D., Pandian, P.: Fuzzy hypotesis testing of ANOVA model with fuzzy data. Int. J. Mod. Eng. Res. 2(4), 2951–2956 (2012)

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16. Kalpanapriya, D., Unnissa, M.: Intuitionistic fuzzy ANOVA and its application using different techniques. In: Madhu, V., Manimaran, A., Easwaramoorthy, D., Kalpanapriya, D., Mubashir Unnissa, M. (eds.), Advances in Algebra and Analysis. Trends in Mathematics, pp. 457–468. Birkh¨ auser, Cham (2017) 17. Mavrov, D.: An application for performing operations on two-dimensional index matrices. In: Annual of “Informatics” Section, Union of Scientists in Bulgaria, vol. 10, pp. 66–80 (2019/2020) 18. Nourbakhsh, M.R., Parchami, A., Mashinchi, M.: Analysis of variance based on fuzzy observations. Int. J. Syst. Sci. 44(4), 714–726 (2013) 19. Parchami, A., Nourbakhsh, M., Mashinchi, M.: Analysis of variance in uncertain environments. Complex Intell. Syst. 3 (3), 189-196 (2017) 20. Parchami, A., Mashinchi, M., Kahraman, C.: A Case Study on Vehicle Battery Manufacturing Using Fuzzy Analysis of Variance. In: Kahraman, C., Cevik Onar, S., Oztaysi, B., Sari, I.U., Cebi, S., Tolga, A.C. (eds.) INFUS 2020. AISC, vol. 1197, pp. 916–923. Springer, Cham (2021). https://doi.org/10.1007/978-3-03051156-2 106 21. Pietraszek, J., Kolomycki, M., Szczotok, A., Dwornicka, R.: The fuzzy approach to assessment of ANOVA results. In: Nguyen, N.-T., Manolopoulos, Y., Iliadis, L., Trawi´ nski, B. (eds.) ICCCI 2016. LNCS (LNAI), vol. 9875, pp. 260–268. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-45243-2 24 22. Riecan, B., Atanassov, A.: Operation division by n over intuitionistic fuzzy sets. NIFS 16(4), 1–4 (2010) 23. Soto-Acosta, P.: COVID-19 pandemic: shifting digital transformation to a highspeed gear. Inf. Syst. Manag. 37(4), 260–266 (2020) 24. Szmidt, E., Kacprzyk, J.: Amount of information and its reliability in the ranking of Atanassov intuitionistic fuzzy alternatives, In: Rakus-Andersson (eds.) Recent Advances in Decision Making, vol. 222, pp. 7–19. SCI, Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02187-9 2 25. Traneva, V.: Internal operations over 3-dimensional extended index matrices. Proc. Jangjeon Math. Soc. 18(4), 547–569 (2015) 26. Traneva, V., Tranev, S.: Index Matrices as a Tool for Managerial Decision Making. Publishing House of the Union of Scientists, Bulgaria (2017). (in Bulgarian) 27. Traneva, V., Tranev, S.: Intuitionistic fuzzy analysis of variance of movie ticket sales. In: Kahraman, C. Cevik Onar, S., Oztaysi, B., Sari, I.U., Cebi, S., Tolga, A.C. (eds.) INFUS 2020. AISC, vol. 1197, pp. 363–371. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-51156-2 43 28. Traneva, V., Tranev, S.: Intuitionistic fuzzy two-factor variance analysis of movie ticket sales. J. Intell. Fuzzy Syst. 42(1), 563–573 (2022). https://doi.org/10.3233/ JIFS-219212 29. Traneva, V., Mavrov, D., Tranev, S: Fuzzy two-factor analysis of COVID-19 cases in Europe. In: 2020 IEEE 10th International Conference on Intelligent Systems (IS), pp. 533–538. Varna, Bulgaria (2020) 30. Traneva, V., Tranev, S., Stoenchev, M., Atanassov, K.: Scaled aggregation operations over 2- and 3-dimensional IMs. Soft Comput. 22(15), 5115–5120 (2018) 31. Wang, H., et al.: Phase-adjusted estimation of the number of Coronavirus Disease 2019 cases in Wuhan, China. Cell Discov. 6(1), 4–11 (2020). https://doi.org/10. 1038/s41421-020-0148-0 32. Westerman, G., Bonnet, D.: Revamping your business through digital transformation. MIT Sloan Manag. Rev. 56(3), 10 (2015) 33. Zadeh, L.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)

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34. www.ecdc.europa.eu/en/publications-data/download-todays-data-geographicdistribution-covid-19-cases-worldwide. Accessed 25 Jan 2022 35. https://github.com/owid/covid-19-data/tree/master/public/data. Accessed 25 Jan 2022 36. https://www.ecdc.europa.eu/en/geographical-distribution-2019-ncov-cases. Accessed 25 Jan 2022

Spherical Fuzzy Sets

Analyzing Critical Criteria of Spaceport Site Selection Based on Spherical Fuzzy AHP Method Melike ˙Ilhan1

, Fatma Kutlu Gündo˘gdu2(B)

, and Ali Kara¸san3

1 Department of Industrial Engineering, Hezârfen Aeronautics and Space Technologies,

National Defence University, Istanbul 34149, Turkey 2 Department of Industrial Engineering, Turkish Air Force Academy, National Defence

University, Istanbul 34149, Turkey [email protected] 3 Department of Industrial Engineering, Yıldız Technical University, Istanbul 34347, Turkey

Abstract. Spaceport site selection is an essential phase of the spacecraft program since it consists of many essential work steps and requirements for the success of the constructed system. Most of the criteria are related to the system’s total cost, but some technical requirements and social conditions are also taken into account for aggregated performance. Based on that, in this study, we present a comprehensive decision-making structure for evaluating the spaceport, considering both international applications the Turkey’s individual ecosystem. Through that, a decisionmaking method, the spherical fuzzy AHP method, is applied to determine the importance of the weights. Spherical fuzzy sets are an extension of intuitionistic fuzzy sets that offer to involve the evaluations’ impreciseness and the hesitancy of the experts in the mathematical formulation of the problem to better reflect the input data to the outcomes. As a result of the application, we found that technical requirements, cost and economy, and infrastructure are the most important main criteria for the success of the spaceports based on the desired objectives. Related to the main criteria, technical factors, population density, operational cost, and transportation cost are determined as the most important sub-criteria. When considering the constructed decision-making structure, the results are mostly related to the investments and other cost-based parameters, which are in line with Turkey’s condition as a developing country. Keywords: Spaceport site selection · Spherical fuzzy sets · Analytical Hierarchy Process (AHP) · MCDM · Space technology

1 Introduction Space technologies have been rapidly developed and utilized multi-functionally, such as defense, aviation, and advanced communication technologies, since the launch of Sputnik-1 in 1957. Recently, the scope of space technologies has been expanded into constellation technology, interplanetary transport systems, reusable launch systems, © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 693–701, 2022. https://doi.org/10.1007/978-3-031-09173-5_80

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space mining, and air launch. These projects involve advanced technology and high-cost processes and are being conducted at a special facility called a spaceport. A spaceport is a facility where spacecraft and their associated equipment are launched into or beyond orbit. The activities that are carried out at a spaceport are usually conducted by governments and have commercial and military purposes. Recently, with the incentives for civil companies to enter the field of space technologies and sciences, the scope of space technologies has been varied and differentiated as well. At this point, for the launch of different types of orbit, projects, goals, and approaches, the site selection process gains prominence. The success of a spacecraft in its mission is determined by reaching and entering into orbit. Although the launch of the spacecraft is the main step that causes high cost and is a decisive factor for its success, new techniques are being developed to decrease the cost of the launch systems. Depending on some technical requirements and social conditions, the evaluations of the alternative locations become more important to consider. For the launches to have a high success rate and to be carried out at a low cost, the locations that are close to the equator may be prioritized. Besides this, spaceports also serve the scope of space tourism, which has a rising trend recently, and the space tourism sector has different features than traditional spaceports regarding the user experience, such as being accessible by the user and training center. Therefore, the location alternatives can differ depending on the purpose of the usage. In order to provide a structure to decrease the cost and increase the success rate of space activities, the location of the spaceport needs to have some specific criteria. Hence, the assessment of these criteria is a significant issue for accessing determined goals. Since the very beginning of the developments in the field of space sciences, different techniques and strategies have been provided by several countries, such as the USA, Russia, Japan, and China. Aside from that, some countries, such as South Korea, Ukraine, Brazil, Australia, and the South African Republic, have recently created content for their space programs.pioneer studies, which have been performed for the evaluation of different locations for different purposes of usage, similar techniques and methods have been used, such as AHP, multi-criteria value analysis, and descriptive statistics. Balakrishnan et al. [1] evaluated the site location of the Satish Dawan spaceport. Baxter et al. [2] improved the location choices for a spaceport that would be used for space tourism in Australia by using qualitative research methods. Perwitasari [3] selected a proper location by using AHP for the spaceport of Indonesia. Additionally, Dachyar and Purnomo [4] conducted a study for the site selection of the Indonesian spaceport. Diana and Ibrahim [5] also investigated the spaceport of Indonesia from the aspect of economic contributions. Demiralay et al. [6] examined the alternative available spaceports for Turkey to use for its space activities by suggesting a hybrid PF-AHP-PF-TOPSIS method. In addition, most of the methods mentioned in the mentioned studies do not consider the high uncertainty that is caused by the decision-making process. Thus, the results may not be truly correct and satisfactory. Turkey is one of the countries that has a space program. According to the Turkey Space Program introduced by a space agent, Turkey aims to develop a new concept to conduct its space activities. The program has some specific goals, such as designing the

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launch systems, testing of the space platforms, lunar missions, and satellite projects. Having a spaceport has been assigned as one of the main purposes of Turkey’s space program in order to gain access to space. Some uncertainties have arisen in expert judgments because of space research being new for Turkey. To deal with this kind of uncertainty, fuzzy set theory is an efficient tool. For this reason, in this study, one of the recent extensions of the Fuzzy Set Theory, spherical fuzzy sets, has been used. To the best of our knowledge, there is not any study on the spaceport site selection in Turkey based on spherical fuzzy sets. Spherical fuzzy sets allow decision-makers to define hesitancy degrees as well as membership and non-membership degrees [7]. AHP is a comprehensive technique in terms of evaluating all alternatives by making pairwise comparisons in a hierarchical order according to objective and subjective criteria. Kutlu Gündodu and Kahraman [8] developed and applied the Spherical Fuzzy AHP (SF-AHP) method to renewable energy problems in 2019. Hence, to define and prioritize the critical criteria for site selection of the spaceport of Turkey, the spherical fuzzy AHP method has been employed to overcome the level of hesitancy of decision-makers and consider the uncertainties. The rest of this paper is organized as follows. Section 2 presents the preliminaries of spherical fuzzy sets and the proposed methodology. Section 3 includes an application for prioritizing the critical criteria of spaceport site selection. Finally, the study is concluded in Sect. 4.

2 Preliminaries of Spherical Fuzzy Sets and Spherical Fuzzy AHP Method Spherical fuzzy sets have been introduced by Kutlu Gündo˘gdu and Kahraman in 2019 [7]. This theory considers the degree of hesitancy in an expert judgment. It proposes a larger preference domain to decision-makers so that they can express their evaluations. The definition of spherical fuzzy sets is given as follows; A˜ s = {x, μA˜ s (x), ϑA˜ s (x), πA˜ s (x)|x ∈ X }

(1)

where μA˜ s (u), ϑA˜ s (u), πA˜ s (u) : U → [0, 1] are the degree of membership, nonmembership, and hesitancy of x to A˜ S , respectively, and ϕ (μ, ϑ, π ) 0 ≤ μ2A˜ (x) + ϑA2˜ (x) + π2A˜ (x) ≤ 1 s

 Then,

s

s

(2)

  1 − μ2˜ (x) + ϑ 2˜ (x) + π2˜ (x) is defined as the refusal degree of x in X . The As

As

As

proposed SF linguistic scale is given in Table 1.

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M. ˙Ilhan et al. Table 1. Linguistic terms for SF-AHP

Spherical Fuzzy AHP The steps of the methodology are given in pseudo-code as follows:

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697

3 Application The proposed methodology has been employed to prioritize the criteria and find the weights of them to be used for the site selection process of the spaceport of Turkey. The criteria have been gathered based on the literature review. The study involves five main criteria and 20 sub-criteria as given in Table 2. Table 2. The definitions of the critical criteria for spaceport site selection Main criteria C1: Technical requirements

Sub-criteria

Explanation

References

C11

Distance to the equator

The definition of the distance between spaceport and equator

[3, 9, 10]

C12

Flight trajectory

The azimuth angle required for launching a payload

[1, 4, 9–11]

C13

Technical factors

The technical needs for [3, 4, 12–14] launch vehicle, type of orbit, altitude, latitude, and velocity

C14

Flight safety/cruise route

The preference for a location that’s near to the water resources to prevent possible dangers

[11, 12, 15]

(continued)

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M. ˙Ilhan et al. Table 2. (continued)

Main criteria C2: Infrastructure

C3: Environment

C4: Cost and economy

Sub-criteria

Explanation

References

C21

Main and support infrastructure

The infrastructure of the spaceport’s land and launch pads

[4, 12–14, 16, 17]

C22

Scheduling flexibility

The flexibility in scheduling for the canceled launch

[17]

C23

Reliability

The successful launch ratio

[12]

C24

Accessibility

The accessibility of the [1, 2, 4, 12, 16–18] spaceport by the different transportation units

C25

Operational factors

The flight rates, reusable pads, integration of the components, and vehicle orientation

[4, 9, 12]

C26

Site area

The facility should be long enough to satisfy runway and flight requirements

[13]

C31

Spaceport security

The level of security conditions

[3, 9, 11, 18, 19]

C32

Meteorology

The meteorological conditions based on mist, wind, and the annual temperature in the area

[1, 2, 4, 11, 15, 17]

C33

Potential disasters

The risk of the natural disasters that can happen in the area

[4]

C34

Risk of environmental threat

The preference for a location that is far away to the facilities that produces fatal waste

[3, 13]

C41

Operational cost

Total cost of all operations conducted in the spaceport

[9, 17]

C42

Transportation cost The transportation [17] costs depending on the distance (continued)

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Table 2. (continued) Main criteria

C5: Social

Sub-criteria

Explanation

References

C43

Economic contribution

The relation between [3, 5, 9, 14, 17] the location and industrial areas to support each other’s need and contribute the economic growth

C51

Population density

The density of the human settlement in the area

C52

Social and legal situation

The ability of the local [3, 12] partners to handle with social and political conflict

C53

Environment

The cooperation [12] between the owners of the spaceport and local partners

[2, 4, 13, 19]

The expert evaluation for the main criteria is given in Table 3. Based on Step 1.1, linguistic terms have been converted to spherical fuzzy numbers and consistency analyses have been performed. According to these analyses, the consistency index of all matrices has been obtained to be less than 0.1. The calculations that are computed based on Steps 1.3 and 1.4 have been shared in Table 3. Due to the page limitation, the rest of the pairwise comparison tables have not been shared. Table 3. Results of the application Main criteria

C1

C2

C3

C4

C5

Aggregated values

Normalized values

Rank

C1

EI

SMI

VHI

EI

VHI

(0.68, 0.30, 0.26)

0.297

1

C2

SLI

EI

HI

SLI

EI

(0.52, 0.44, 0.33)

0.205

3

C3

VLI

LI

EI

SLI

SLI

(0.38, 0.60, 0.29)

0.099

5

C4

EI

SMI

SMI

EI

SMI

(0.56, 0.40, 0.34)

0.228

2

C5

VLI

EI

SMI

SLI

EI

(0.47, 0.50, 0.33)

0.171

4

Table 4 indicates the global weights of sub-criteria for spaceport site selection in Turkey.

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M. ˙Ilhan et al. Table 4. Global weights of sub-criteria

Technical factors

Global weights

Infrastructure

Global weights

Environment

Global weights

Cost and economy

Global weights

Social

Global weights

C11

0.05

C21

0.06

C31

0.01

C41

0.09

C51

0.11

C12

0.11

C22

0.00

C32

0.04

C42

0.09

C52

0.05

C13

0.07

C23

0.00

C33

0.02

C43

0.04

C53

0.03

C14

0.07

C24

0.06

C34

0.02

C25

0.06

C26

0.03

Based on Table 3, the most important main criteria are technical requirements, cost and economy, and infrastructure, respectively. According to Table 4, the most important sub-criteria are technical factors, population density, operational cost, and transportation cost. At least important sub-criteria are “scheduling flexibility” and “reliability”.

4 Conclusion Considering launching of a spacecraft, there are many essential work steps and requirements for the success of the constructed system. Since most of the criteria are related to the system’s cost, there are also some technical requirements and social conditions for an aggregated performance. Based on that, in this study, we present a comprehensive decision-making structure for evaluating the spaceport, considering both international applications the Turkey’s individual ecosystem. Through that, a decision-making method, which aims to the pairwise comparison of the evaluation criteria, is applied to determine the importance weights. Since the input data of the model is based on expert knowledge, some uncertainties such as impreciseness of the evaluations and hesitancy of the expert have been observed during the assessment process. To involve the mentioned uncertainties, we extended the AHP method with spherical fuzzy sets, which is an extension of intuitionistic fuzzy sets to better reflect the input data to the outcomes. Through that, we aimed to obtain more applicable and meaningful results as a result of the study. As a result of the application, we found that technical requirements, cost and economy, and infrastructure are the most important main criteria for the success of the spaceports based on the desired objectives. Related to the main criteria, technical factors, population density, operational cost, and transportation cost are determined as the most important sub-criteria. When considering the constructed decision-making structure, the results are mostly related to the investments and other cost-based parameters, which are in line with Turkey’s condition as a developing country. Since Turkey has many investments in both energy and industry sectors, current investments are mostly cost-dependent strategies considering not only governmental incentives but also the build-operate-transfer model.

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As for further studies, the dataset can be extended by considering the involvement of experts from the field, academy, and policymakers. Through that, a comprehensive data set can be used as the input data, and results can be compared. Moreover, the locations for the spaceport can be determined and prioritized based on an integrated methodology.

References 1. Balakrishnan, S.S., Moorthi, D.N., Venkateswara Rao, P., et al.: Satish dhawan space centre SHAR - Spaceport of India. In: International Astronautical Federation - 55th International Astronautical Congress 2004, pp. 8206–8216 (2004) 2. Baxter, G., Wild, H., Ogawa, H.: Optimising the potential location of spaceport australia based on current suborbital space tourism requirements. In: 30th International Symposium on Space Technology and Science, pp. 7–12 (2015) 3. Perwitasari, I.: Indonesia spaceport selection based on multicriteria analysis: a study on relative importance and priority regarding spaceport selection location attributes utilizing AHP. In: Proceedings of the 3rd International Conference on Indonesian Social and Political Enquiries (ICISPE 2018). Semarang, Indonesia, pp. 41–45 (2018) 4. Dachyar, M., Purnomo, H.: Spaceport site selection with analytical hierarchy process decision making. Ind. J. Sci. Technol. 11, 1–8 (2018). https://doi.org/10.17485/ijst/2018/v11i10/96506 5. Diana, S.R., Farida, F., Musdafia, I.: Selection of spaceport site in indonesia: good economic efficiency and contribution to local economic development. Res. World J. Arts Sci. Commer. IX, 65 (2018). https://doi.org/10.18843/rwjasc/v9i4/09 6. Demiralay, E., Çopur, E.H., Paksoy, T.: Spaceport Selection Using a Novel Hybrid Pythagorean Fuzzy AHP and TOPSIS Based Methodology: A Case Study of Turkey (2022) 7. Kutlu Gündoˇgdu, F., Kahraman, C.: Spherical fuzzy sets and spherical fuzzy TOPSIS method. J. Intell. Fuzzy Syst. 36, 337–352 (2019). https://doi.org/10.3233/JIFS-181401 8. Kutlu Gündo˘gdu, F., Kahraman, C.: A novel spherical fuzzy analytic hierarchy process and its renewable energy application. Soft. Comput. 24(6), 4607–4621 (2019). https://doi.org/10. 1007/s00500-019-04222-w 9. Nolek, D.D., Finger, G.W.: Attracting “new space” to your spaceport. In: AIAA Space 2009 Conference and Exposition, pp. 1–5 (2009). https://doi.org/10.2514/6.2009-6691 10. Finger, G.W., Gulliver, B.S.:Economic factors for launch complex development in current economy. In: 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, pp. 1–8 (2010). https://doi.org/10.2514/6.2010-1345 11. Hayward, T.B.: Spaceport Hawaii: environmental issues. In: AIAA Space Programs and Technologies Conference (1992). https://doi.org/10.2514/6.1992-1302 12. Gulliver, B.S., Finger, G.W.: Spaceport infrastructure cost trends. In: AIAA SPACE 2014 Conference and Exposition, pp. 1–8 (2014). https://doi.org/10.2514/6.2014-4397 13. Selvidge, P.: From airport to spaceport: designing for an aerospace revolution (2010) 14. Webber, D.: Designing the Orbital Space Tourism Experience, Rockville (2006) 15. Floyd, K.K., Welti, T.G.: Commercial Spacepotts: A New Frontier of Infrastructure Law, Washington, DC (2020) 16. Finger, G.W., Keller, D.L., Gulliver, B.S.: Public-private spaceport development. SpaceOps 2008 Conference 1–8 (2008). https://doi.org/10.2514/6.2008-3584 17. Cass, S., Schooff, R.M.: Alternative launch site selection. In: Space Congress Proceedings: Countdown to the Millennium, vol. 36, pp. 1–9 18. Adams, C.M., Petrov, G.:Spaceport master planning: principles and precedents. Collection of Technical Papers - Space 2006 Conference, vol. 2, pp. 1488–1511 (2006). https://doi.org/ 10.2514/6.2006-7325 19. Wayne Finger, G., Kercsmar, J.C., Gulliver, B.: Evolution of the commercial aerospaceport. In: SpaceOps 2010 Conference, pp. 1–11 (2010). https://doi.org/10.2514/6.2010-2149

Fuzzy Analytic Hierarchy Process Using Spherical Z-Numbers: Supplier Selection Application Nur¸sah Alkan(B) and Cengiz Kahraman Department of Industrial Engineering, Istanbul Technical University, Macka, Besiktas, 34367 Istanbul, Turkey [email protected]

Abstract. Z-numbers are expressed by a restriction function and a reliability function. In the literature, Z-numbers have been extended by intuitionistic fuzzy sets but not by other fuzzy sets. This paper extends Z-numbers by using single valued spherical fuzzy sets. Later, spherical fuzzy Z-numbers are used in the development of Z fuzzy AHP methods. These methods are applied to a supplier selection problem. Keywords: Fuzzy sets · AHP · Spherical fuzzy sets · Z-numbers · MCDM

1 Introduction Multi criteria decision making (MCDM) methods to overcome complex decision problems aim to find the most appropriate solution by evaluating existing alternatives according to many conflicting criteria. In the MCDM literature, methods such as Analytic Hierarchy Process (AHP) and Analytic Network Process (ANP) based on pairwise comparisons are often used in the literature. The AHP method divides a large and complex problem into smaller and easier problems that can be easily solved, and then combines these sub-solutions to obtain the final solution of the main problem. Ordinary fuzzy sets are represented by degree of membership and help to reduce modeling complexity by using with fuzzy numbers corresponding to linguistic terms rather than exact/integer numbers [1]. Different extensions of ordinary fuzzy sets such as intuitionistic fuzzy sets (IFSs) [2] and spherical fuzzy sets (SFSs) [3] have been proposed in the literature to obtain more accurate solution in complex decision-making problems. SFSs, an extension of picture fuzzy sets, allow decision makers (DMs) to assign their uncertainties separately, provided that the squared sum of the degrees of membership, non-membership, and hesitation must be at most one. On the other hand, Z numbers, which better reflect real-world information and allow to include the evaluation of the reliability level of information, are employed in many application areas in decisionmaking processes. While Z numbers are important because they consider the reliability and restriction of membership degrees, SFSs are also important because they consider the membership, non-membership and hesitancy degrees of DMs’ judgments together. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 702–713, 2022. https://doi.org/10.1007/978-3-031-09173-5_81

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The combination of Z-numbers and SFSs should be used to obtain more realistic results in decision making problems. To achieve the above-mentioned main goal, this study develops novel approaches on the spherical fuzzy (SF) Z-AHP method, based on a combination of Z-numbers and SFSs. Thus, this paper is the first study proposed the SF Z-AHP method. In the study, different approaches of the proposed method are presented and implemented to supplier selection problem. The rest of this study is organized as follows. The principles of SFSs are given in Sect. 2. The steps of Z-numbers and spherical Z-numbers are presented in Sect. 3. The steps of the developed SF Z-AHP methods are presented in Sect. 4. The SF Z-AHP methods is implemented for the supplier selection problem in Sect. 5. Finally, the study ends with the conclusion and suggestions for further research in Sect. 6.

2 Spherical Fuzzy Sets SFSs, an extension of Pythagorean and picture fuzzy sets, reflect the DMs’ information more comprehensively, handling each DM’s hesitancy information independently in the SF environment. Definition 1. A Single-valued spherical fuzzy set (SVSFSs) of the universe X which given by [3]:    (1) A˜ s = x, μA˜ s (x), ϑA˜ s (x), πA˜ s (x)x ∈ X } where μA˜ s (u), ϑA˜ s (u), πA˜ s (u) : U → [0, 1] are the degrees of membership, nonmembership, and indeterminacy of x to A˜ S , respectively, and 0 ≤ μ2A˜ (x) + ϑA2˜ (x) + πA2˜ (x) ≤ 1 s

Then,

s

(2)

s

   1 − μ2˜ (x) + ϑ 2˜ (x) + π 2˜ (x) is described as the refusal degree of x in As

As

As

X. Definition 2. Assume that A˜ s and B˜ s be any two SFSs. The basic operations of SFSs can be defined as follows [3]: A˜ s ⊕ B˜ s =   



 1 − μ2˜ π 2˜ + 1 − μ2˜ π 2˜ − π 2˜ π 2˜ μ2˜ + μ2˜ − μ2˜ μ2˜ , ϑA˜ s ϑB˜ s , As

Bs

As

Bs

Bs

As

Bs

As

As Bs

(3) A˜ s ⊗ B˜ s =   



 (4) 2 2 2 2 2 2 2 2 2 2 1 − ϑ˜ π˜ + 1 − ϑ˜ π˜ − π˜ π˜ μA˜ s μB˜ s , ϑ ˜ + ϑ ˜ − ϑ ˜ ϑ ˜ , As

Bs

As Bs

Bs

As

As

Bs

As Bs

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 k A˜ s =

1− 

A˜ ks

=



 μkA˜ , s

1 − μ2˜ As

k

 ,

ϑAk˜ , s



k

k 1 − μ2˜ − 1 − μ2˜ − π 2˜ As

As

As



 

k

k

k 2 2 2 2 1 − ϑ˜ 1 − 1 − ϑ˜ , − 1 − ϑ˜ − π˜ As

As

As

As

(5) (6)

Definition 3. Spherical Fuzzy Weighted Arithmetic Mean (SFWAM ) with respect to, w = (w1 , w2 , . . . , wn ); wi ∈ [0, 1]; ni=1 wi = 1, is specified as [3]:

SFWAMw A˜ S1 , A˜ S2 , . . . , A˜ Sn = w1 A˜ S1 + w2 A˜ S2 + . . . + wn A˜ Sn ⎧ ⎫   n n n n ⎨

wi 

wi 

wi ⎬     1 − μ2As , 1 − μ2As 1 − μ2As − πA2s = 1 − ϑAwsi ,  − ⎩ ⎭ i=1

i=1

i=1

i=1

(7) Definition 4. Spherical Fuzzy Weighted Geometric Mean (SFWGM ) with respect to, w = (w1 , w2 , . . . , wn ); wi ∈ [0, 1]; ni=1 wi = 1, is proofed as [3]:

i ˜ wi ˜ wi SFWGMw A˜ S1 , A˜ S2 , . . . , A˜ Sn = A˜ w S1 + AS2 + . . . + ASn ⎧ ⎫    n n n n ⎨

wi 

wi 

wi ⎬     i  1 − ϑA2s ,  1 − ϑA2s 1 − ϑA2s − πA2s = μw 1− − As , ⎩ ⎭ i=1

i=1

i=1

i=1

(8)

3 Z-Numbers and Spherical Z-Numbers The numbers introduced by Zadeh [4] are an ordered pair of fuzzy numbers, Z-fuzzy

˜ B˜ as shown in Fig. 1. The first component A˜ is a restriction function while the Z A, second component B˜ is a measure of reliability for the first component.



˜ B˜ Fig. 1. A simple Z-fuzzy number, Z A,

A Z-fuzzy number aim to provide a basis for computation with fuzzy numbers which are not reliable. Fuzzy expectation of a fuzzy set, transformation from Z-numbers to fuzzy Z-numbers can be found in [5].

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        Let A˜ δ1 ,δ2 ,δ3 = x, μA˜ (x); δ1 , ϑA˜ (x); δ2 , πA˜ (x); δ3 |μ(x) ∈ [0, 1]         and R˜ β1 ,β2 ,β3 = x, μR˜ (x); β1 , ϑR˜ (x); β2 , πR˜ (x); β3 |μ(x) ∈ [0, 1] , μδ˜1 (x), A

ϑ δ˜ 2 (x),π δ˜ 3 (x) are spherical membership, non-membership, and hesitancy degrees for A

A

β

β

β

restriction function, respectively, μ ˜ 1 (x), ϑ ˜ 2 (x),π ˜ 3 (x) are spherical membership, R R R non-membership, and hesitancy degrees for reliability function, respectively.



Fig. 2. A simple Z˜ ((δ ,β ),(δ ,β ),(δ ,β )) number, Z˜ A˜ (δ1 ,δ2 ,δ3 ) , R˜ (β1 ,β2 ,β3 ) 1 1 2 2 3 3



˜ R˜ A SF Z-number is an ordered pair of spherical fuzzy numbers (SFNs), SFZ A, as shown in Fig. 2. The first component A˜ is a restriction function while the second component R˜ is a measure of reliability for the first component.

Z˜ ((δ1 ,β1 ),(δ2 ,β2 ),(δ3 ,β3 )) =  ⎧     ⎫ β β  ⎪ ⎪ ∫ μ ˜ 1 (x)dx ∫ ϑ ˜ 2 (x)dx  ⎪ ⎪ δ δ δ δ δ δ δ 1 2 3 1 1 2 2 R R ⎪ ⎪ ⎪ ⎬ ⎨ x, μz˜ (x), ϑz˜ (x), πz˜ (x)μz˜ (x) = μA˜ x ∫ xμβ1 (x)dx , ϑz˜ (x) = ϑA˜ x ∫ xϑ β2 (x)dx , ⎪ R˜ R˜   β3 ⎪ ⎪ ∫ π ˜ (x)dx ⎪ ⎪ δ3 δ3 R ⎪ ⎪ ⎪ ⎪ ⎭ ⎩ πz˜ (x) = πA˜ x ∫ xπ β3 (x)dx μ(x), ϑ(x), π (x) ∈ [0, 1] R˜

(9)

4 Spherical Fuzzy Z-AHP Method The AHP method is a very useful and easy method that allows to obtain the final weights of the features by dividing a large and complex problem into smaller problems that can be easily solved. On the other hand, SF Z-numbers will enable to better define experts’ information with a reliability function. In this study, a new approach based on SF Znumbers, the SF Z-AHP method is developed. Four different modeling approaches to the SF Z-AHP are presented in the following.

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4.1 SF Z-AHP with Defuzzified Restriction and Reliability Functions Step 1. Define the hierarchy of the problem. The alternatives, and relevant criteria to construct the framework of the application are determined as given Fig. 3. The set Ai = {A1 , A2 , ....., Am } having i = 1, 2, ...., m alternatives, is assessed by n decision criteria of set Cj = {C1 , C2 , ....., Cn }, with j = 1, 2, ...., n. Let w = (w1 , w 2 , . . . ., wn ) be the vector set used for defining the criteria weights, where wj > 0 and nj=1 wj = 1. Step 2. Construct the pairwise comparison matrices using SF restriction and reliability functions based on Tables 1 and 2, respectively.

Table 1. Linguistic scale for restriction Linguistic restriction

Spherical fuzzy Z scale μ

ϑ

π

Absolutely More Strong − (AMS)

1

0

0

Very High Strong − (VLS)

0.9

0.1

0

High Strong − (HS)

0.8

0.1

0.1

Quite More Strong − (QMS)

0.7

0.2

0.2

Fairly More Strong − (FMS)

0.6

0.3

0.3

Slightly More Strong − (SMS)

0.5

0.4

0.4

Exactly Equal − (EE)

0.5

0.5

0.5

Slightly Low Strong − (SLS)

0.4

0.5

0.4

Fairly Low Strong − (FLS)

0.3

0.6

0.3

Quite Low Strong − (QLS)

0.2

0.7

0.2

Low Strong − (LS)

0.1

0.8

0.1

Very Low Strong − (VLS)

0.1

0.9

0

Absolutely Low Strong − (ALS)

0

1

0

Step 3. Defuzzify the reliability SF Z-numbers in each pairwise comparison matrix using Eq. (10) and normalize the obtained values using Eq. (11).   !  2    πA˜ s 2 ϑA˜ s  s 3μA˜ s − (10) − πA˜ s − S w˜ j = 100 ×    2 2

S w˜ js

w˜ js = n S w˜ js j=1

(11)

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Table 2. Linguistic scale for reliability Linguistic reliability

Spherical fuzzy Z scale μ

ϑ

π

Absolutely Reliable − (AMS)

0.9

0.1

0

Strongly Reliable − (VLS)

0.8

0.2

0.1

Very Highly Reliable − (HS)

0.7

0.3

0.2

Highly Reliable − (QMS)

0.6

0.4

0.3

Fairly Reliable − (FMS)

0.5

0.5

0.4

Weakly Reliable − (SMS)

0.4

0.6

0.3

Very Weakly Reliable − (EE)

0.3

0.7

0.2

Strongly Unreliable − (SLS)

0.2

0.8

0.1

Absolutely Unreliable − (FLS)

0.1

0.9

0

Step 4. Multiply the SF restriction values in each pairwise comparison matrix by the square root of normalized reliability values using Eq. (5). Step 5. Aggregate the values in pairwise comparison matrices obtained in Step 4 using Eq. (7). Step 6.1 Multiply the pairwise comparison matrix obtained in Step 5 by aggregated SF criteria weights using Eq. (4). Alternatively, you can apply Step 6.2 instead of Step 6.1. Step 6.2 Multiply the pairwise comparison matrix obtained in Step 5 by aggregated and defuzzified SF criteria weights. Step 7. Find the weighted SF score value for each alternative by applying Eq. (3). Step 8. Defuzzify the SF vector obtained in Step 7 using Eq. (10). 4.2 SF Z-AHP with Aggregated and Defuzzified Reliability Function Step 1. Define the hierarchy of the problem. Step 2. Construct the pairwise comparison matrices using SF restriction and reliability functions based on Tables 1 and 2, respectively. Step 3. Aggregate and defuzzify the reliability SF Z- numbers in each pairwise comparison matrix using Eqs. (7) and (10), respectively, and normalize the obtained values using Eq. (11). Step 4. Aggregate the SF restriction values in pairwise comparison matrices using Eq. (7). Step 5. Multiply the aggregated restriction vector by the square root of normalized reliability values using Eq. (5). Step 6.1. Multiply the aggregated SF vector obtained in Step 5 by aggregated SF criteria weights using Eq. (4). Alternatively, you can apply Step 6.2 instead of Step 6.1. Step 6.2. Multiply the aggregated SF vector obtained in Step 5 by aggregated and defuzzified SF criteria weights using Eq. (5).

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Step 7. Find the weighted SF score value for each alternative by applying Eq. (3). Step 8. Defuzzify the SF vector obtained in Step 7 using Eq. (10). 4.3 Complete SF Z-AHP Step 1. Define the hierarchy of the problem. Step 2. Construct the pairwise comparison matrices using SF restriction and reliability functions based on Tables 1 and 2, respectively. Step 3. Compute the square root of each SF number in reliability matrix. Step 4. Multiply the SF restriction values in pairwise comparison matrices by the obtained values in Step 3 using Eq. (4). Step 5. Aggregate the SF values in each row using Eq. (10). Step 6.1. Multiply the aggregated SF vector obtained in Step 5 by aggregated SF criteria weights using Eq. (4). Alternatively, you can apply Step 6.2 instead of Step 6.1. Step 6.2. Multiply the aggregated SF vector obtained in Step 5 by aggregated and defuzzified SF criteria weights using Eq. (5). Step 7. Find the weighted SF score value for each alternative by applying Eq. (3). Step 8. Defuzzify the SF vector obtained in Step 7 using Eq. (10). 4.4 SF Z-AHP with Aggregated Restriction and Reliability Functions Step 1. Define the hierarchy of the problem. Step 2. Construct the pairwise comparison matrices using SF restriction and reliability functions based on Tables 1 and 2, respectively. Step 3. Aggregate the reliability and restriction SF Z- numbers in each pairwise comparison matrix using Eq. (7). Step 4. Multiply the aggregated restriction vector by the square root of aggregated reliability values using Eq. (5). Step 5.1. Multiply the aggregated SF vector obtained in Step 4 by aggregated SF criteria weights using Eq. (4). Alternatively, you can apply Step 5.2 instead of Step 5.1. Step 5.2. Multiply the aggregated SF vector obtained in Step 4 by aggregated and defuzzified SF criteria weights using Eq. (5). Step 6. Find the weighted SF score value for each alternative by applying Eq. (3). Step 7. Defuzzify the SF vector obtained in Step 6 using Eq. (10).

5 Application MCDM methods are used successfully in supplier selection problems in the literature. In this section, the supplier selection process of a company operating in the production area is evaluated by using the developed SF Z-AHP methods and it is aimed to select the best among various supplier alternatives. Four criteria have been identified according to a comprehensive literature review and expert opinions to evaluate three supplier alternatives (A1, A2, A3), as presented in the hierarchy in Fig. 3.

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Fig. 3. Hierarchical structure of the problem

After checking the consistency ratios, the matrices obtained for restriction and reliability are presented in Tables 3 and 4, respectively. Normalized reliability matrix for criteria is given in Table 5. SFNs converted from SF Z-numbers based on the first method are given in Table 6. Defuzzified weights and final rankings of the first method are presented in Table 7. In our second developed method, aggregated, defuzzified, and normalized values of the SF reliability Z- numbers are given in Table 8. After SF restriction Z-numbers of each pairwise comparison matrix of criteria are aggregated, the values obtained by multiplying the normalized reliability values by the square root are given in Table 9.

Table 3. Linguistic restriction comparison matrix for criteria

Table 4. Linguistic reliability comparison matrix for criteria

Goal

C1

C2

C3

C4

Goal

C1

C2

C3

C4

C1

EE

LS

FLS

QLS

C1

C2

HS

EE

HS

HS

C2

FR

VWR

WR

WR

VHR

FR

VHR

HR

C3

FMS

LS

EE

SLS

C3

HR

VWR

FR

WR

C4

QMS

LS

SMS

EE

C4

HR

WR

HR

FR

Table 5. Normalized reliability matrix for criteria C1

C2

C3

C4

C1

0.196

0.201

0.175

0.208

C2

0.304

0.330

0.334

0.327

C3

0.250

0.201

0.216

0.208

C4

0.250

0.268

0.275

0.256

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N. Alkan and C. Kahraman Table 6. SFNs converted from SF Z-numbers based on the first method C1

C2

μ

ϑ

π

C3

μ

ϑ

π

μ

C4 ϑ

π

μ

ϑ

π

C1 0.346 0.736 0.380 0.067 0.905 0.067 0.197 0.807 0.203 0.136 0.849 0.137 C2 0.656 0.281 0.094 0.390 0.672 0.420 0.668 0.264 0.095 0.665 0.268 0.094 C3 0.447 0.548 0.242 0.067 0.905 0.067 0.354 0.725 0.388 0.276 0.729 0.291 C4 0.535 0.447 0.169 0.072 0.891 0.072 0.374 0.618 0.319 0.368 0.704 0.401

Table 7. Defuzzified weights and final rankings according to the first method First approach

Second approach

Deff. weights

Deff. weights

Ranking

Ranking

A1

3.91

3

7.36

3

A2

12.52

1

17.47

1

A3

6.08

2

10.22

2

Table 8. Aggregated, defuzzified, and normalized values of the SF reliability Z- numbers Aggregated weights

Defuzzified weights

Normalized weights

μ

ϑ

π

C1

0.409

0.596

0.316

10.676

0.193

C2

0.637

0.366

0.277

17.693

0.320

C3

0.471

0538

0.316

12.536

0.227

C4

0.536

0.468

0.328

14.406

0.260

Table 9. SF weights converted from aggregated SF Z-number based on second method Aggregated weights

Defuzzified weights

Normalized weights

μ

ϑ

π

C1

0.215

0.822

0.239

4.981

0.122

C2

0.614

0.341

0.204

17.409

0.427

C3

0.321

0.715

0.282

8.210

0.201

C4

0.385

0.645

0.277

10.163

0.249

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Defuzzified weights and final rankings based on second method are given in Table 10. Table 10. Defuzzified weights and final rankings according to second method First approach

Second approach

Deff. weights

Deff. weights

Ranking

Ranking

A1

3.787

3

6.778

3

A2

12.619

1

17.899

1

A3

6.081

2

10.198

2

In our third developed method, SFNs converted from SF Z-number of pairwise comparison matrix of criteria according to the third method are given in Table 11. After the SF values are aggregated, two different approaches can be applied to obtain the final ranking of the alternatives, as applied to other methods. The deffuzified weights and final ranking of the alternatives for the first and second approaches according to third method are presented in Table 12. Table 11. SFNs converted from SF Z-number of pairwise comparison matrix of criteria according to the third method C1 μ

C2 ϑ

π

μ

C3 ϑ

π

μ

C4 ϑ

π

μ

ϑ

π

C1 0.354 0.592 0.506 0.055 0.862 0.121 0.190 0.699 0.302 0.126 0.769 0.232 C2 0.669 0.236 0.173 0.354 0.592 0.506 0.669 0.236 0.173 0.620 0.304 0.241 C3 0.465 0.407 0.348 0.055 0.862 0.121 0.354 0.592 0.506 0.253 0.632 0.374 C4 0.542 0.347 0.286 0.063 0.844 0.164 0.387 0.480 0.419 0.354 0.592 0.506

Table 12. Defuzzified weights and final rankings according to third method of alternatives First approach

Second approach

Deff. weights

Ranking

Deff. weights

A1

3.433

2

6.456

3

A2

9.073

1

15.468

1

A3

1.355

3

9.236

2

Ranking

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In our fourth proposed method, the restriction and reliability SF Z-numbers are aggregated in each pairwise comparison matrix. Aggregated SF restriction and reliability Z-number values are presented in Table 13. After the aggregated restriction vector is multiplied by the square root of the aggregated reliability values, two different approaches can be applied to obtain the final ranking of the alternatives, as applied to other methods. The defuzzified weights and final ranking of the alternatives for the first and second approaches according to fourth method are presented in Table 14. Table 13. Aggregated SF restriction and reliability Z-numbers Aggregated SF restriction Z-numbers

Aggregated SF reliability Z-numbers

μ

ϑ

π

μ

ϑ

π

C1

0.320

0.640

0.343

0.409

0.596

0.316

C2

0.753

0.150

0.223

0.637

0.366

0.277

C3

0.453

0.495

0.375

0.471

0.538

0.316

C4

0.520

0.423

0.351

0.536

0.468

0.328

Table 14. Defuzzified weights and final rankings according to fourth method of alternatives First approach

Second approach

Deff. weights

Deff. weights

Ranking

Ranking

A1

2.060

3

6.867

3

A2

12.538

1

15.071

1

A3

4.997

2

8.874

2

6 Conclusion Since real life problems bring many uncertainties, the crisp values assigned by the decision makers in decision-making problems are often insufficient in solving the problems and this causes errors in obtaining correct results. Since SFSs better reflect the uncertainty of the decision makers and Z numbers, unlike SFSs, allow the evaluation of the reliability level of the information, the importance of using both in the decision-making process has been revealed. In this study, the SF Z-AHP method has been developed considering the combined use of Z-numbers based on SFSs. Four different methods are proposed for the development SF Z-AHP and the results of these methods on the supplier selection problem have been shown. According to the results obtained from the methods, while the 1st alternative was the same in all proposed methods, only the 2nd and 3rd rank of the proposed 3rd method were different. The fact that the best alternative is the

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same has proven the accuracy and validity of the proposed methods. For further study, Z-numbers can be considered with different fuzzy set extensions such as Pythagorean fuzzy sets, neutrosophic sets, picture fuzzy sets. The developed methods can be used in different MCDM methods. Moreover, it can also applied on different decision-making problems.

References 1. Alkan, N., Kahraman, C.: Prioritization of factors affecting the digitalization of quality management using interval-valued intuitionistic fuzzy best-worst method. In: Intelligent and Fuzzy Techniques for Emerging Conditions and Digital Transformation, Proceedings of the INFUS 2021 Conference, 24–26 August 2021, Istanbul (2021) 2. Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986) 3. Kutlu Gündo˘gdu, F., Kahraman, C.: Spherical fuzzy sets and spherical fuzzy TOPSIS method. J. Intell. Fuzzy Syst. 36(1), 337–352 (2019) 4. Zadeh, L.A.: A note on Z-numbers. Inf. Sci. 181(14–15), 2923–2932 (2011) 5. Ucal Sari, I., Kahraman, C.: Intuitionistic fuzzy Z-numbers. In: Kahraman, C., Cevik Onar, S., Oztaysi, B., Sari, I.U., Cebi, S., Tolga, A.C. (eds.) INFUS 2020. AISC, vol. 1197, pp. 1316– 1324. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-51156-2_154

A Multi-attribute Decision Making Method for the Evaluation of Software Enterprise Based on T-Spherical Fuzzy Dombi Aggregation Information Kifayat Ullah1(B) , Zunaira Gul1 , Harish Garg2 , and Tahir Mahmood3 1 Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah

International University Lahore, Lahore 54000, Pakistan [email protected] 2 School of Mathematics, Thapar Institute of Engineering and Technology, Deemed University, Patiala 147004, Punjab, India [email protected] 3 Department of Mathematics, International Islamic University Islamabad, Islamabad 44000, Pakistan [email protected]

Abstract. Dealing with uncertain and incomplete information is a challenging task and several fuzzy frameworks have been established.. T-spherical fuzzy set (TSFS) is one of the freshly established models that associate human opinion with a membership grade (MG), abstinence grade (AG), and non-membership grade (NMG). Dombi aggregation operators (DAOs) are widely discussed in several fuzzy frameworks to deal with problems under uncertainty. This manuscript aims to develop the DAOs in a T-spherical fuzzy (TSF) environment. We introduce the notion of Dombi operators for TSFSs and explored their characteristics. The Dombi operations lead us to develop the concepts of DAOs including the TSF Dombi weighted averaging (TSFDWA) and TSF Dombi weighted geometric (TSFDWG) operator. The newly developed DAOs are exemplified numerically. A MADM method is introduced in view of proposed DAOs followed by an illustrative example where the impact of variable parameters and is analyzed on ranking results. A comparative survey of the proposed DWOs is set up with previously existing DAOs where the advantages of the newly developed DAOs are discussed. Keywords: Dombi operations · Picture fuzzy set · Dombi aggregation operators · T-spherical fuzzy set · MADM

1 Introduction Uncertainties and imprecision are involved in almost every event of the world especially where human opinion is involved. To manage data based on uncertainties, Zadeh © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 714–722, 2022. https://doi.org/10.1007/978-3-031-09173-5_82

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[1] proposed the notion of membership grades (MG) of elements or objects and presented the perception of a fuzzy set (FS). Atanassov [2] associated objects with nonmembership grade (NMG) alongside an MG and introduced the idea of intuitionistic FS (IFS). Atanassov’s notion of IFS allows only those pairs of information wherever the amount of both components (MG and NMG) lies in [0, 1]. This condition restricts the assigning of MG and the NMG to a certain range and hence does not give us the flexibility of choosing the MG and NMG. This leads Yager [3] to develop the framework of Pythagorean FS (PyFS) with the condition that the sum of squares of MG and NMG must lie in [0, 1]. This notion of PyFS is further generalized to q-rung orthopair FS (QROFS) [4] where these duplets are allowed whose sum of th power lies in [0, 1]. Cuong [5] realized that the representation of human opinion by using an MG and NMG may lead to some loss of information as a human opinion may also consist of some abstinence and refusal degree as well. Cuong [5] introduced the framework of picture FS (PFS) by associating the human opinion with an MG, abstinence grade (AG), and NMG with the condition that their sum lies in [0, 1]. Cuong’s PFS generalizes the notion of IFS and hence provides better grounds to deal with imprecise information. Cuong’s concept of PFS was further generalized by Mahmood et al. [6] to the concepts of spherical FS (SFS) and consequently T-spherical FS (TSFS). An SFS allows the sum of squares of MG, AG, and NMG in [0, 1] while the frame of TSFS allows the sum of th power of MG, AG, and NMG in [0, 1]. Aggregation of the information under uncertainties is a widely discussed topic that has been extensively used in multi-attribute decision making (MADM) problems for the selection of optimum alternatives. Several aggregation theories are developed in this regard based on several t-norms and t-conorms which can be seen in [7–27]. In the long list of t-norms and t-conorms, Dombi t-norm (DTN) and Dombi t-conorm (DTCN) [28] are also widely studied which leads to DAOs for MADM. Several studies on DAOs can be found in [29–41]. In our literature survey, it is found that the DAOs of IFSs, PyFSs and QROFSs fails to deal with situations where uncertain information has variation. Similarly, the DAOs of PFSs and SFSs are also unable to meet some specific information and hence show a limited behavior. Therefore, to overcome the drawbacks of the previous DAOs, we propose DAOs in the environment of TSFSs in this manuscript. The organization of this paper is based on 7 sections which are discussed with full details in the rest of the paper as follows.

2 Preliminaries The goal of this section is to discuss some previous concepts and to enlighten the gap between the current study and the previous study. Definition 1. [6] For any universal set X , a TSFS is of the from Where and are mappings from X → [0, 1] denoting the MG, AG and and NG respectively provided that for some least is known as the refusal grade (RG) of x in P.

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Definition 2. [42] The score value of a TSFN

is defined as:

Definition 3. [28] Let f , g ∈ R. Then, DTN and DTCN are defined as

3 Dombi Operations on TSFSs The aim of this section is to introduce the Dombi operations TSF environment. We propose Dombi sum, Dombi product, Dombi scalar multiplication, Dombi power operations. Some basic features of the Dombi AOs are also discussed. Definition 4. Let λ ≥ 0. Then Dombi operations are defined as follows:

1.

2.

3.

4.

be three TSFNs and

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4 DAOs for TSFSs In this section, we aim to develop some DAOs in the environment of TSFSs. Note that, T throughout this paper, ψj = (ψ1 , ψ2 , ψ 3n. . . ψn ) represents the weight vector of TSFNs Pj (j = 1, 2, 3 . . . n) with ψj > 0 and j=1 ψj = 1. Definition 5. Let defined as:

be TSFNs. Then TSFDWA operator is

Theorem 1. For TSF numbers gives us a TSF number given by:

Definition 6. Let defined as:

, The TSFDWA operator

be TSFNs. Then TSFDWG operator is n  ψ TSFDWG(P1 , P2 . . . .Pn ) = ⊕ Pj j j=1

Theorem 2. For TSF numbers gives us a TSF number given by:

, The TSFDWG operator

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5 Applications in Multi-attribute Decision Making MADM is a way of choosing the best alternative in view of some finite attributes using the Dombi AOs of TSFSs. The most favourable thing here is that the information is based on TSFNs which discusses the membership grades, abstinence, and non-membership grades of the information. Let the collection of alternatives be (k is finite) and attributes be where the terms Gj (j is finite) which form a decision matrix denoted by in triplet denote the membership grades, abstinence, and non-membership grades of the information. The  weight vector, in this case, be denoted by ψj = (ψ1 , ψ2 , ψ3 . . . ψn )T with ψj > 0 and nj=1 ψj = 1. A brief algorithm of the MADM process is illustrated as follows in Example 1. Example 1: An example of technology commercialization is adapted from [32] where the decision matrix is given in Table 1 and the weight vector chosen in this case is ψj = (0.15, 0.25, 0.41, 0.19)T .

Table 1. Information of decision makers provided in the form of TSFNs

Step 3: This step involves the aggregation of information given in Table 1 and the results are depicted in Table 2 as follows: Table 2. TSFDWA and TSFDWG operators-based aggregation information

Step 4: The scores of information given in Table 2 are computed and the results are given in Table 3. Step 5: Based on the scores obtained in Table 3, the alternatives are ranked, and the ranking results are given in Table 4 as follows: The analysis of score values of the information shows that is most reliable technology enterprise based on the aggregation of information using TSFDWA while is declared as best option using TSFDWG operator.

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Table 3. Scores of aggregated information

Table 4. Ranking results

5.1 Impact of q and R on Ranking Results There two parameters associated with TSFDWA and TSFDWG operators i.e., and and both have an impact on ranking results. In this section, we aim to see the impact of variation in both the parameters which can be seen in Table 5. Table 5. Effect of

on ranking results)

6 Comparative Study The aim of this section is to establish a comparison of the proposed Dombi AOs in TSF environment and operations that are already exists. We take the Example 1 and see the results by applying the existing aggregation operators. A detailed analysis of the results obtained by proposed study and existing study is given in Table 6 below. The observations presented in Table 6 clearly indicate that the existing Dombi AOs of IFSs, PyFSs, QROFSs, and PFSs failed to aggregate the information provided in TSF environment which shows the superiority of Dombi AOs of TSFSs.

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Operator

Environment

Results

TSFDWA (Proposed work)

TSFSs

TSFDWG (Proposed work)

TSFSs

A1 > A3 > A4 > A2 A1 > A3 > A4 > A2

TSFHWA [17]

TSFSs

TSFHWG [17]

TSFSs

A1 > A3 > A4 > A2 A1 > A3 > A4 > A2

TSFWA [42]

TSFSs

A1 > A4 > A3 > A2

TSFWG [42]

TSFSs

PFDWA [32]

PFSs

A1 > A3 > A4 > A2 Failed

QROFDWA [31]

QROFSs

Failed

PyFDWA [30]

PyFSs

Failed

IFDWA [29]

IFSs

Failed

7 Conclusion In this paper, the notion of DTN and DTCN is discussed in the TSF environment. Based on DTN and t-conorm, Dombi sum, Dombi product, scalar multiplication, and power operations are developed, and their properties are discussed. The Dombi operations are further utilized to introduce the notion of Dombi AOs based on TSFNs. The algorithm for the MADM problem is developed in view of TSFDWA and TSFDWG operators which is further clarified by a numerical example. The impact of parameters and is studied for their various values and a comparative study of the TSFDWA and TSFDWG operators is established with some existing studies to show the significance of proposed work.

References 1. Zadeh, L.A.: Information and control. Fuzzy Sets 8, 338–353 (1965) 2. Intanssov, K.T.: Intuitionistic fuzzy set. Fuzzy Sets Syst. 20, 87–96 (1986) 3. Yager, R.R.: Pythagorean Fuzzy Subsets. In Proceedings of the 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), pp. 57–61. Edmonton, Canada, 24–28 June 2013 4. Yager, R.R.: Generalized orthopair fuzzy sets. IEEE Trans. Fuzzy Syst. 25, 1222–1230 (2016) 5. Cu,o`,ng, B.C.: Picture fuzzy sets. J. Comput. Sci. Cybern. 30, 409 (2014) 6. Mahmood, T., Ullah, K., Khan, Q., Jan, N.: An approach toward decision-making and medical diagnosis problems using the concept of spherical fuzzy sets. Neural Comput. Appl. 31, 7041–7053 (2019) 7. Xu, Z.: Intuitionistic fuzzy aggregation operators. IEEE Trans. Fuzzy Syst. 15, 1179–1187 (2007) 8. Xu, Z., Yager, R.R.: Some geometric aggregation operators based on intuitionistic fuzzy sets. Int. J. Gen. Syst. 35, 417–433 (2006) 9. Wang, X.: Fuzzy number intuitionistic fuzzy arithmetic aggregation operators. Int. J. Fuzzy Syst. 10, 104–111 (2008)

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10. Wei, G.: Some arithmetic aggregation operators with intuitionistic trapezoidal fuzzy numbers and their application to group decision making. JCP 5, 345–351 (2010) 11. Ye, J.: Intuitionistic fuzzy hybrid arithmetic and geometric aggregation operators for the decision-making of mechanical design schemes. Appl. Intell. 47, 743–751 (2017) 12. Munir, M., Kalsoom, H., Ullah, K., Mahmood, T., Chu, Y.-M.: T-Spherical fuzzy einstein hybrid aggregation operators and their applications in multi-attribute decision making problems. Symmetry 12, 365 (2020) 13. Wang, W., Liu, X.: Intuitionistic fuzzy geometric aggregation operators based on einstein operations. Int. J. Intell. Syst. 26, 1049–1075 (2011) 14. Riaz, M., Athar Farid, H.M., Kalsoom, H., Pamuˇcar, D., Chu, Y.-M.: A robust Q-rung orthopair fuzzy einstein prioritized aggregation operators with Application towards MCGDM. Symmetry 12, 1058 (2020) 15. Zhang, S., Yu, D.: Some geometric choquet aggregation operators using einstein operations under intuitionistic fuzzy environment. J. Intell. Fuzzy Syst. 26, 491–500 (2014) 16. Tehrim, S.T., Riaz, M.: A novel extension of TOPSIS to MCGDM with bipolar neutrosophic soft topology. J. Intell. Fuzzy Syst. 37(4), 5531–5549 (2019) 17. Ullah, K., Mahmood, T., Garg, H.: Evaluation of the performance of search and rescue robots using T-spherical fuzzy hamacher aggregation operators. Int. J. Fuzzy Syst. 22, 570–582 (2020) 18. Jana, C., Pal, M.: Assessment of enterprise performance based on picture fuzzy hamacher aggregation operators. Symmetry 11, 75 (2019) 19. De, K.B.S.K., Decision making under intuitionistic fuzzy metric distances. Ann. Optim. Theory Pract. 3(2), 49–64 (2020) 20. Ullah, K., Hassan, N., Mahmood, T., Jan, N., Hassan, M.: Evaluation of investment policy based on multi-attribute decision-making using interval valued T-spherical fuzzy aggregation operators. Symmetry 11(3), 357 (2020) 21. Zeng, S.Z., Hu, Y.J., Balezentis, T., Streimikiene, D.: A multi-criteria sustainable supplier selection framework based on neutrosophic fuzzy data and entropyweighting. Sustain. Dev. 28(5), 1431–1440 (2020) 22. Zeng, S., Hu, Y., Xie, X.: Q-rung orthopair fuzzy weighted induced logarithmic distance measures and their application in multiple attribute decision making. Eng. Appl. Artif. Intell. 100, 104167 (2021) 23. Liu, P., Munir, M., Mahmood, T., Ullah, K.: Some similarity measures for interval-valued picture fuzzy sets and their applications in decision making. Information 10(12), 369 (2019) 24. Zhang, C.H., Su, W.H., Zeng, S.Z., Balezentis, T., Herrera-Viedma, E.: A two-stage subgroup decision-making method for processing large-scale information. Expert Syst. Appl. 171, 114586 (2021) 25. Mu, Z.M., Zeng, S.Z., Wang, P.Y.: Novel approach to multi-attribute group decision-making based on interval-valued Pythagorean fuzzy power Maclaurin symmetric mean operator. Comput. Ind. Eng. 155, 107049 (2021) 26. Riaz, M., Hashmi, M.R.: Linear Diophantine fuzzy set and its applications towards multiattribute decision-making problems. J. Intell. Fuzzy Syst. 37(4), 5417–5439 (2019) 27. Dombi, J.: A general class of fuzzy operators, the De Morgan class of fuzzy operators and fuzziness measures induced by fuzzy operators. Fuzzy Sets Syst. 8(2), 149–163 (1982) 28. Seikh, M.R., Mandal, U.: Intuitionistic fuzzy Dombi aggregation operators and their application to multiple attribute decision-making. Granular Comput. 6(3), 473–488 (2019) 29. Jana, C., Senapati, T., Pal, M.: Pythagorean fuzzy Dombi aggregation operators and its applications in multiple attribute decision-making. Int. J. Intell. Syst. 34(9), 2019–2038 (2019) 30. Jana, C., Muhiuddin, G., Pal, M.: Some Dombi aggregation of Q-rung orthopair fuzzy numbers in multiple-attribute decision making. Int. J. Intell. Syst. 34(12), 3220–3240 (2019)

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31. Jana, C., Pal, M., Wang, J.: Bipolar fuzzy Dombi aggregation operators and its application in multiple-attribute decision-making process. J. Ambient Intell. Human. Comput. 10(9), 3533–3549 (2019) 32. Shi, L., Ye, J.: Dombi aggregation operators of neutrosophic cubic sets for multiple attribute decision-making. Algorithms 11(3), 29 (2018) 33. He, X.: Typhoon disaster assessment based on Dombi hesitant fuzzy information aggregation operators. Nat. Hazards 90(3), 1153–1175 (2017) 34. Lu, X., Ye, J.: Dombi aggregation operators of linguistic cubic variables for multiple attribute decision making. Information 9(8), 188 (2018) 35. He, X.: Group decision making based on Dombi operators and its application to personnel evaluation. Int. J. Intell. Syst. 34(7), 1718–1731 (2019) 36. Liu, P., Liu, J., Chen, S.M.: Some intuitionistic fuzzy Dombi Bonferroni mean operators and their application to multi-attribute group decision making. J. Oper. Res. Soc. 69(1), 1–24 (2018) 37. Zhang, H., Zhang, R., Huang, H., Wang, J.: Some picture fuzzy Dombi Heronian mean operators with their application to multi-attribute decision-making. Symmetry 10(11), 593 (2018) 38. Talukdar, P., Goala, S., Dutta, P., Limboo, B.: Fuzzy multicriteria decision making in medical diagnosis using an advanced distance measure on linguistic Pythagorean fuzzy sets. Ann. Optim. Theory Pract. 3(4), 113–131 (2020) 39. Li, Z., Gao, H., Wei, G.: Methods for multiple attribute group decision making based on intuitionistic fuzzy Dombi Hamy mean operators. Symmetry 10(11), 574 (2018) 40. Mahmood, T., Ullah, K., Jan, N., Ahmad, Z.: Policy decision making based on some averaging aggregation operators of t-spherical fuzzy sets; a multi-attribute decision making approach. Ann. Optim. Theory Pract. 3(3), 69–92 (2020) 41. Wei, G., Jiang, W.U., Wei, C., Wang, J., Lu, J.: Models for MADM with 2-tuple linguistic neutrosophic Dombi Bonferroni mean operators. IEEE Access 7, 108878–108905 (2019)

A Decision Support System for Rheumatoid Arthritis (RA) Treatment Selection and Factor Prioritization by Using Spherical Fuzzy Sets Rana Ezgi Köse1 , Neriman Rençber2 , Tu˘gçe Beldek1 , and Aziz Kemal Konyalıo˘glu1(B) 1 Faculty of Management, Management Engineering Department, Istanbul Technical University,

Istanbul, Turkey {koser19,beldek,konyalioglua}@itu.edu.tr 2 Department of Physical Therapy and Rehabilitation, Eyup State Hospital, Istanbul, Turkey [email protected]

Abstract. Rheumatoid Arthritis, also abbreviated as RA, is an inflammatory and autoimmune disease that can be seen both in females and males. It is known that rheumatoid arthritis, which is an autoimmune disorder, is widely seen in joints and occurs when your immune system mistakenly attacks the body’s tissues and organs including lungs, kidneys, eyes and skin. As there exist many factors causing Rheumatoid Arthritis, it is not certain which factor is the most effecting factor and it is generally difficult to organize a treatment process. Also, because of many factors causing RA and many treatment methods, it is not easy to select the best treatment alternative based on the effecting factors such as obesity, family history, age and sex. In this paper, it is aimed to prioritize the factors causing Rheumatoid Arthritis by using Spherical Fuzzy AHP and to select the best treatment alternative based on Spherical Fuzzy Sets. Furthermore, this study will provide a general and an analytical view to medical doctors for how to plan a treatment process for the patients having RA. Keywords: Spherical sets · AHP · Rheumatoid Arthritis · Healthcare applications of fuzzy sets

1 Introduction Rheumatoid Arthritis, also abbreviated as RA, is an inflammatory and autoimmune disease that can be seen both in females and males. Because of hardness of illness and long process to treat, many patients have difficulties due to decreasing life standards. It is known that rheumatoid arthritis, which is an autoimmune disorder, is widely seen in joints and occurs when your immune system mistakenly attacks the body’s tissues and organs including lungs, kidneys, eyes and skin. As there exist many factors causing Rheumatoid Arthritis, it is not certain which factor is the most effecting factor and it is generally difficult to organize a treatment process. Also, because of many factors causing © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 723–732, 2022. https://doi.org/10.1007/978-3-031-09173-5_83

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RA and many treatment methods, it is not easy to select the best treatment alternative based on the effecting factors such as obesity, family history, age and sex. Medical doctors cannot always be certain which treatment should be chosen in order to avoid of accelerating the disease and which treatment will exactly fit. Thus, try and see method can sometimes be the best option to treat or decrease the side effects of RA. In this paper, it is aimed to prioritize the factors causing Rheumatoid Arthritis by using Spherical Fuzzy AHP and to select the best treatment alternative based on Spherical Fuzzy Sets. This study includes 5 main parts which are an introduction part to introduce RA, a literature review part to investigate the latest study about spherical fuzzy AHP, a methodology part to explain spherical fuzzy AHP approach, an application and results part to apply spherical fuzzy AHP for the selection of treatment for RA and RA’s factors prioritization and finally a conclusion part. Furthermore, this study will provide a general and an analytical view to medical doctors for how to plan a treatment process for the patients having RA by a fuzzy view.

2 Literature Review Kutlu Gündo˘gdu and Kahraman (2019) introduced three dimensional spherical fuzzy sets with its operations. They extended the classical Analytic Hierarchy Process (AHP) to Spherical Fuzzy Analytic Hierarchy Process (SF-AHP) (Kutlu Gündo˘gdu and Kahraman (2019). There is a comparison between neutrosophic AHP and SF-AHP at the location selection application part in another study to show the new methods’ validity (Kutlu Gündo˘gdu and Kahraman (2020). There are many articles in the literature that they used SF-AHP in their applications. Buyuk and Temur (2020) studied spherical fuzzy AHP in terms of food waste management. Today food waste management is very important for sustainability. Waste supply chain needs to have decision making tools. Spherical sets are used with AHP at their study to make a guide for the stakeholders for decision making (Buyuk and Temur 2020). Mathew et al. (2020) studied a combined method by using spherical fuzzy AHP and spherical fuzzy TOPSIS together. Spherical fuzzy weights are determined with SF-AHP and final ranking is found by SF-TOPSIS. This combined method is used in the case of a manufacturing system selection problem (Mathew et al. 2020). Another study is conducted by Jaller and Otay (2020) in freight transportation sector. Goods and services for both people and companies are very important to be brought on time. There are many different properties, technologies, that may be changed according to the needs and environmental issues such as the fuels being used. For this problem again, SF-AHP and SF-TOPSIS methods are combined. They defined five criteria, financial, market, environmental, maintenance and safety (Jaller and Otay 2020). Dogan used SF-AHP method for technology selection in terms of process mining under uncertainty (2021). Price, process discovery, process analysis and analytics are the most important criteria for process mining technology selection when the SF-AHP is applied (Dogan 2021). Another study written by Kieu et al. (2021), used the same method with Combined Compromise Solution Algorithm in logistics sector. Logistics is very important for companies for competitiveness. There are many qualitative and quantitative criteria for distribution center location selection problem. The results may

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be used in agricultural supply chain globally (Kieu et al. 2021). Nguyen et al. (2021) studied COVID-19 vaccination intention in Vietnam. They used three methods together, spherical fuzzy AHP, partial least squares-structural equation model and artificial neural network (Nguyen et al. 2021). Candan and Cengiz Toklu (2022) studied evaluation criteria of European Union countries’ sustainability performance. Social, economic and environmental main criteria and 16 sub-criteria were used. The weights were calculated with SF-AHP and the ranking is found by Grey Relational Analysis. According to the 2018 data, Germany, Luxembourg, Denmark, Sweden and Netherlands were the top ranked countries (Candan and Cengiz Toklu 2022). Another sustainability research is done by Unal and Temur (2022). They studied sustainable supplier selection with SF-AHP. Economic, quality, social and environmental criteria were the main ones. Prioritization of the main and sub-criteria were conducted by three experts via questionnaires (Unal and Temur 2022). Yilmaz et al. (2022) studied operational efficiency of Turkish civil airports between 2015–2018. They used SF-AHP with Data Envelopment Analysis together (Yilmaz et al. 2022).

3 Methodology In this section, Spherical Fuzzy Sets (SFS) and Spherical Analytic Hierarchy Process (SF-AHP) are explained respectively. In methodology section, SFS and SF-AHP methodologies has been defined by the study of Gündo˘gdu and Kahraman (2019). For explaining spherical fuzzy sets, firstly let us define U1 and U2 as two different universes and related spherical fuzzy sets for U1 and U2 as A˜ S and B˜ S respectively. In this case, let A˜ S be defined as given in (1) (Gündo˘gdu and Kahraman 2019).     (1) A˜ S = x, μA˜ S (x), νA˜ S (x), πA˜ S (x) |xU1 where, each of μA˜ S (x), νA˜ S (x), πA˜ S (x) has a domain in U1 and a range of [0,1] provided in (2) that 0 ≤ μ2A˜ (x) + νA2˜ (x) + πA2˜ (x) ≤ 1 S

S

S

∀uU1

(2)

And here note that μA˜ S (x), νA˜ S (x), πA˜ S (x) are respectively defined as membership, non-membership, and hesitancy of u to A˜ S and on the surface of the sphere, it can be written as given in (3). μ2A˜ (x) + νA2˜ (x) + πA2˜ (x) = 1 S

S

S

∀uU

(3)

The steps for Spherical Fuzzy AHP can be sequenced as follows (Gündo˘gdu and Kahraman 2019). Step 1. A hierarchical structure for the main selection problem is constructed. Step 2. Spherical fuzzy pairwise comparison matrices are formed. Step 3. Consistency Ratio for each pairwise comparison matrices of AHP, denoted also as CR, is checked.

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Step 4. If CR is less than 0.1, which means the matrices are consistent, fuzzy local weights of each criteria and criterion are calculated. If not, the pairwise comparisons should be readjusted. Step 5. In order to obtain spherical fuzzy global weights, hierarchical layer sequencings are constructed. Step 6. For each alternative, the score values are calculated. Step 7. The alternatives are ranked based on calculations. For the calculations, Fig. 1 shows the linguistic measures of importance which are used to compare pairwise calculation matrices (Gündo˘gdu and Kahraman 2019).

Fig. 1. Linguistic measures of importance which are used to compare pairwise calculation matrices (Gündo˘gdu and Kahraman 2019).

4 Application and Results In the application section, firstly, a hierarchical structure for the prioritizing of the factors causing Rheumatoid Arthritis by using Spherical Fuzzy AHP and the selection of the best treatment alternative based on Spherical Fuzzy Sets is constructed. Then, based on medical doctors’ views, pairwise comparisons have been done and SWAM operator has been used by weighted arithmetic mean for calculating fuzzy local weights SWAMw (AS1 , . . . , ASn ) = w1 AS1 + w2 AS2 + · · · + wn ASn  n  wi 1/2  2 1 − μASi , 1− i=1 n  i=1



vAwSii ,

n  n  wi  wi  1 − μ2ASi 1 − μ2ASi − πA2Si − i=1

1/2

(4)

i=1

where w = 1/n. Then, the score function given in (5) has been used for defuzzifying the criteria   2  2     π v ˜ ˜  A A s 3μA˜ s − s (5) − πA˜ s − S w˜ js = 100 ∗    2 2

A Decision Support System for Rheumatoid Arthritis (RA) Treatment Selection

In order to normalize the criteria weights, the Eq. (6) has been used.   S w˜ js   w¯ js =  n ˜ js J =1 S w

727

(6)

Finally, under spherical fuzzy multiplication, the Eq. (7) has been applied for final defuzzification.  A˜ Sij = w¯ js · A˜ Si =

 w¯ s 1/2 w¯ s  w¯ s 1/2

 w¯ js j j j 1 − μ2˜ 1 − 1 − μ2˜ , v˜ − 1 − μ2˜ − π 2˜ AS AS AS AS AS

(7)

Finally, in order to rank the factors and alternatives, final spherical fuzzy AHP score has been found by Eq. (8). F˜ =

n 

A˜ Sij = A˜ Si1 ⊕ A˜ Si2 · · · ⊕ A˜ Sin ∀i

j=1

i.e. A˜ S11 ⊕ A˜ S12 =



  πA2˜ , 1 − μ2A˜ s12

1/2

μ2A˜ S11

s11

+ μ2A˜ S12

− μ2A˜ μ2A˜ S11 S12

  πA2˜ + 1 − μ2A˜ s11

s12

− πA2˜ s

11

, vA¯ s vA˜ s 11

1/2

(8)

12

πA2˜ s

12

Table 1 shows the main criteria pairwise comparison and Fig. 2 shows the hierarchical structure. Consistency Ratio: 0 < 0.1, which is valid. Table 2 indicates patient related factors’ sub criteria pairwise comparison and consistency ratio is equal to 0.09, which is less than 0.1 Table 3 shows the disease related factors’ sub criteria pairwise comparison and the consistency ratio is equal to 0.08, which is less than 0.1. Table 4 shows the drug related factors’ sub criteria pairwise comparison matrix and the consistency ratio is equal to 0.096. Table 1. Main criteria pairwise comparison for the factor prioritization and treatment selection for RA 1. Patient related factors

2. Disease related factors

3. Drug related factors

1. Patient related factors

Equally importance

Absolutely low importance

Low importance

2. Disease related factors

Absolutely more Importance

Equally importance High importance

3. Drug related factors

High importance

Low importance

Consistency Ratio: 0 < 0.1, which is valid

Equally importance

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Paent Related Factors

Gender

Genec

Obesity

Disease Related Factors

Smoking

Diet

Comorbid disease

High AFR

Swollen Joint Count

Corcosteroids

Age/disease onset

Bone erosion

Drug Related Factors

High RF/CCP

Extra-arcular involvement

Therapeuc index

Structure

Delivery

Adverse effect grade

Frequent usage

Maximum usage

Efficiency

Paent compliance

Disease Modifying Anrheumac Drugs

NSAIDs

Fig. 2. Hierarchical structure for the selection of the best treatment of Rheumatoid Arthritis

Table 2. Patient related factors’ sub criteria pairwise comparison Age/Disease onset

Gender

Genetic

Obesity

Smoking

Diet

Comorbid disease

Age/Disease onset

EI

SMI

SLI

HI

VHI

HI

VHI

Gender

SLI

EI

LI

SHI

HI

SHI

HI

Genetic

SMI

HI

EI

VHI

AMI

VHI

AMI

Obesity

LI

SLI

VLI

EI

SMI

EI

SMI

Smoking

VLI

LI

ALI

SLI

EI

SLI

EI

Diet

LI

SLI

VLI

EI

SMI

EI

SMI

Comorbid Disease

VLI

LI

ALI

SLI

EI

SLI

EI

Table 3. Disease related factors’ sub criteria pairwise comparison AFR

SW

BE

RF

Ex-A

High AFR (AFR)

EI

SLI

LI

EI

SMI

Swollen Joint Count (SW)

SMI

EI

SLI

HI

VHI

Bone Erosion(BE)

HI

SMI

EI

VHI

AMO

High RF/CCP(RF)

EI

LI

VLI

EI

SMI

Extra-articular Involvement(Ex-A)

SLI

VLI

ALO

SLI

EI

After building pairwise comparison matrices, by using Eq. (4), fuzzy local weights have been calculated for each matrices. Table 5 shows the fuzzy local weights for main criteria for RA and the final score rankings of main criteria by using Eqs. (5), (6), (7), (8). Furthermore, Table 6 shows the local weights for patient related factors for RA the final score values and rankings of patient related factors criteria. Table 7 shows the local weights for disease related factors for RA the final score values and rankings of disease related factors criteria.

Muldrug use

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Table 4. Drug related factors’ sub criteria pairwise comparison Therapeutic Structure Delivery Adverse Frequent Maximum Efficiency Patient Multidrug Index effect usage usage compliance use grade Therapeutic EI Index

EI

SMI

SLI

SLI

LI

ALI

VLI

VLI

Structure

EI

EI

SMI

SLI

Delivery

SLI

SLI

EI

SLI

SLI

LI

ALI

LI

VLI

LI

VLI

ALI

ALI

Adverse effect Grade

SMI

SMI

SMI

VLI

EI

EI

SLI

ALI

VLI

LI

Frequent usage

SMI

SMI

HI

EI

EI

SLI

VLI

SLI

LI

Maximum usage

HI

HI

SMI

SMI

EI

EI

LI

SLI

SLI

Efficiency

AMI

AMI

AMI

VHI

HI

EI

EI

SMI

SMI

Patient compliance

VHI

VHI

AMI

VHI

HI

SMI

SLI

EI

SMI

Multidrug use

VHI

VHI

VHI

HI

SMI

SMI

SLI

SLI

EI

Table 5. Rankings and defuzzified score values for main criteria of prioritization of factors for RA Membership Non-membership Hesitancy 1. Patient related factors

0,34983953

Score Value

Ranking

0,63192623

0,28183963

2. Disease related 0,7631005 factors

0,22928062

0,20596594 21,84410285

1

3. Drug related factors

0,43831366

0,28436502 14,89440995

2

0,54435008

9,079577669 3

Table 6. Local Weights, Rankings and defuzzified score values for patient related factors’ prioritization of factors for RA Membership

Non-membership

Hesitancy

Score value

Ranking

Age/Disease onset

0,718558

0,285

0,1925

20,58799

2

Gender

0,6015124

0,399

0,2643

16,711581

3

Genetic

0,7447984

0,252

0,1905

21,381964

1

Obesity

0,5046981

0,477

0,3024

13,614015

4

Smoking

0,362592

0,628

0,2767

Diet

0,5046981

0,477

0,3024

Comorbid disease

0,3620468

0,653

0,2428

9,4869852 13,614015 9,6108033

5 4 6

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Table 7. Local Weights, Rankings and defuzzified score values for disease related factors’ prioritization of factors for RA Membership

Non-membership

Hesitancy

Score value

Ranking

High AFR

0,4769

0,645

0,34

12,6

3

Swollen Joint Count

0,6371

0,514

0,26

17,8

2

Bone erosion

0,6371

0,381

0,21

21,4

1

High RF/CCP

0,6371

0,663

0,32

12

4

Extra-articular involvement

0,6371

0,736

0,28

9,3

5

Table 8 shows the local weights for disease related factors for RA the final score values and rankings of disease related factors criteria. Table 8. Local weights, rankings and defuzzified score values for drug related factors’ prioritization of factors for RA Membership

Non-membership

Hesitancy

Score value

Ranking

Therapetic index

0,399

0,595

0,374

10,05826

8

Structure

0,405

0,586

0,379

10,21233

7

Delivery

0,325

0,681

0,323

8,14198

9

Advers effect grade

0,469

0,526

0,399

11,99143

6

Frequent usage

0,503

0,487

0,404

12,9679

5

Maximum usage

0,599

0,405

0,39

15,89517

4

Efficiency

0,808

0,194

0,337

22,42503

1

Patient compliance

0,718

0,285

0,371

19,55594

2

Multidrug use

0,666

0,336

0,38

17,94101

3

Table 9 shows the alternative rankings based on spherical fuzzy AHP. Table 9. Local weights, rankings and defuzzified score values for alternatives. Membership Non-membership Hesitancy

Score value

Ranking

NSAIDs

0,38140631

0,600307

0,307961971

9,90207143 3

Corticosteroids

0,46845659

0,524487

0,308878222 12,5006108

2

Disease modifying 0,83627807 antirheumatic drugs (DMARDs)

0,159033

0,151945587 24,3178303

1

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5 Conclusion Rheumatoid Arthritis has been always an uncertain disease to determine how to treat and which treatment is the most effective one. Thus, not only patients but also medical doctors cannot observe the effectiveness of treatment of RA. Thus, in terms of factors affecting RA, many treatment methods exist and the usage of these treatments can change according to the related factors. In this study, a spherical fuzzy AHP approach has been used to prioritize the related factors affecting RA and alternatives for treatment have been evaluated. According to these calculations, under main factors, disease related factors are the most important one, which affects RA. Furthermore, under patient related factors, genetic is the most important factor affecting RA while for disease related factors, bone erosion is the most powerful. Finally, drug related factors have been evaluated by using Spherical Fuzzy AHP and efficiency of drugs has been found as the most important factor. Combining these evaluations, it is found that disease modifying antirheumatic drugs (DMARDs) can be the most effective treatment for RA. For further researches, neutrosophic or Pythagorean sets can be applied in order to observe if the sets have an impact on ranking and evaluations.

References Buyuk, A.M., Temur, G.T.: A framework for selection of the best food waste management alternative by a spherical fuzzy AHP based approach. In: Kahraman, C., Cevik Onar, S., Oztaysi, B., Sari, I., Cebi, S., Tolga, A. (eds.) International Conference on Intelligent and Fuzzy Systems, AISC, vol. 1197, pp. 151–159. Springer, Cham (2020). https://doi.org/10.1007/978-3030-51156-2_19 Candan, G., Cengiz Toklu, M.: Sustainable industrialization performance evaluation of European Union countries: an integrated spherical fuzzy analytic hierarchy process and grey relational analysis approach. Int. J. Sustain. Develop. World Ecol. 1–14 (2022) Dogan, O.: Process mining technology selection with spherical fuzzy AHP and sensitivity analysis. Expert Syst. Appl. 178, 114999 (2021) Jaller, M., Otay, I.: Evaluating sustainable vehicle technologies for freight transportation using spherical fuzzy AHP and TOPSIS. In: Kahraman, C., Cevik Onar, S., Oztaysi, B., Sari, I., Cebi, S., Tolga, A. (eds.) International Conference on Intelligent and Fuzzy Systems, AISC, vol. 1197, pp. 118–126. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-51156-2_15 Kieu, P.T., Nguyen, V.T., Nguyen, V.T., Ho, T.P.: A spherical fuzzy analytic hierarchy process (SFAHP) and combined compromise solution (CoCoSo) algorithm in distribution center location selection: a case study in agricultural supply chain. Axioms 10(2), 53 (2021) Kutlu Gündo˘gdu, F., Kahraman, C.: Spherical fuzzy sets and spherical fuzzy TOPSIS method. J. Intell. Fuzzy Syst. 36(1), 337–352 (2019) Kutlu Gündo˘gdu, F., Kahraman, C.: A novel spherical fuzzy analytic hierarchy process and its renewable energy application. Soft. Comput. 24(6), 4607–4621 (2019). https://doi.org/10.1007/ s00500-019-04222-w Mathew, M., Chakrabortty, R.K., Ryan, M.J.: A novel approach integrating AHP and TOPSIS under spherical fuzzy sets for advanced manufacturing system selection. Eng. Appl. Artif. Intell. 96, 103988 (2020)

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Nguyen, P.H., Tsai, J.F., Lin, M.H., Hu, Y.C.: A hybrid model with spherical Fuzzy-AHP, PLSSEM and ANN to predict vaccination intention against COVID-19. Mathematics 9(23), 3075 (2021) Unal, Y., Temur, G.T.: Sustainable supplier selection by using spherical fuzzy AHP. J. Intell. Fuzzy Syst. (Preprint) 1–11 (2022) Yilmaz, M.K., Kusakci, A.O., Aksoy, M., Hacioglu, U.: The evaluation of operational efficiencies of Turkish airports: an integrated spherical fuzzy AHP/DEA approach. Appl. Soft Comput. 119, 108620 (2022)

Neuro-Fuzzy Systems

Active Power Control of a Natural Gas/Fuel Oil Turbine Power Plant with Adaptive Neuro-Fuzzy Inference System-Based on Modern Controllers Rahma Tabakh(B)

, Hasan Tiryaki , and Nevra Bayhan

Department of Electrical and Electronics Engineering, Istanbul University, Cerrahpa¸sa, 34320 Istanbul, Turkey [email protected]

Abstract. The settings of conventional controllers, which are commonly used in power plants, are determined based on system characteristics during the establishment phase, and, thus are unable to adjust to changing system dynamics over the life of the plant. To avoid this unsatisfactory state, the parameters of the controllers used in electric power plants should be self-adapting. As a result, the goal of this paper is to determine the optimal parameter settings using Ant Colony Optimization-based PI controller (ACO-PI), Fuzzy Gain Scheduled PI (FGPI), Adaptive Neuro-Fuzzy Inference System based PI (ANFIS-PI) and, conventional PI controller for proportional-integral (PI) controllers that will adapt to the changing dynamics of a natural gas/fuel oil turbine power plant’s system model and, comparing the system output signal’s transient responses. The results show that the ANFIS-PI controller outperforms the other methods. Keywords: Power systems · Active power control · Gas/Fuel oil turbine power plant · PI · FGPI · ACO-PI · ANFIS-PI

1 Introduction While energy is generally defined as the ability or potential to do work, it can also be defined as a factor that causes changes. Along with advancements in science and, technology, a big change is observed in living standards and, styles, significant changes occur in issues such as the production and, consumption patterns of goods and, services, their prices, demand, structures, market conditions, working conditions and, productivity, global products and, markets and, global giant organizations emerge. The speed and, direction of this development and, change largely depend on developments in energy supply, and, the issue of energy has become one of the focal points of studies in science and, technology [1]. Electrical energy consumption has increased over time, and, it has become one of the most important markers of a country’s development level. The best way to meet this increasing demand, is possible by making future plans in advance [2].

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 735–743, 2022. https://doi.org/10.1007/978-3-031-09173-5_84

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Consumers using electrical energy expect manufacturers to provide quality electrical energy. Uninterrupted electrical energy without fluctuations in voltage and, frequency meant a good quality of electrical energy. Furthermore, since it is difficult to store large-scale electrical energy, it has also become difficult to meet the changing consumer demands. Therefore, meeting the energy needed by the consumer at the desired time and, in the desired amount has become one of the main problems of electrical power systems [3]. Among electrical energy generating systems, natural gas turbine power plants stand, out with their ease of use and, high available capacity [4]. Natural gas turbine power plants, which rank second in terms of capacity with 29660 MW installed power (29%) and, rank first in meeting consumer demand, with 90705 GWh electricity generation (29.9%) are extremely important for Turkey [5]. Various studies on the control of natural gas turbine power plants have been undertaken to far. Some of these outstanding studies are discussed. Kavalerov et al. [6] employed an adaptive control program to control the speed of natural gas turbine power plants in their research. The sliding mode control method was introduced by Bonfiglio et al. [7] for generators used in natural gas turbine power plants. Stanescu et al. [8] studied how to regulate the temperature of compressed air utilized in natural gas turbine power plant’s combustion chambers. Ahmed [9] proposed the fuzzy logic control approach for speed management in natural gas turbine power plants in a report published in 2018. Traditional controllers are still in use for existing natural gas/fuel oil turbine power plants, and, because controller parameters are determined based on system features at the time of initial establishment, they are unable to adapt to changing system dynamics over the power plant’s lifetime, resulting in a loss of efficiency. To avoid this undesired circumstance, contemporary controllers should be utilized to build the parameters of power plant controllers so that they can self-adapt to the constantly changing system dynamics. In this study, conventional PI controller and, modern controllers such as ACO-PI controller, FGPI controller, and, ANFIS-PI controller were modeled and, optimized for the active power control of a natural gas/fuel oil turbine power plant model that is used in Istanbul Natural Gas Combined Cycle Power Plant A located in Beylikdüzü/IstanbulTurkey. The organization of this study is as follows: in Sect. 2, the investigated power plant model is given and the proposed control method is explained, the results are reviewed and discussed in Sect. 3 and, the paper is concluded in Sect. 4.

2 Materials and, Method 2.1 Modeling of a Natural Gas/Fuel Oil Turbine Power Plant In experimental modeling studies, it was observed that there was no difference in turbine and, generator systems when the energy source used for electricity generation was natural gas or fuel oil; however, there was a change in the transfer function coefficients of the speed regulator, burning, and, combustion chamber systems [4, 10, 11]. This study was based on working with fuel oil.

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2.2 Control Methods The block diagram used to provide the active power control of the natural gas/fuel oil turbine power plant was developed in MATLAB R2020a [12] program and, is given in Fig. 1.

Fig. 1. Generalized simple mathematical model for the natural gas/fuel oil turbine power plant [3].

PI, ACO-PI, FGPI, and, ANFIS-PI controllers were applied, respectively, for the controller block observed in Fig. 1, and, + 1 MW over the range of 0–100 s and, −1 MW over the range of 101–200 s were taken for the set value. As a result, it was anticipated to gain a better understanding of how controllers adjust to changing dynamics. Proposed ANFIS-PI Controller. Jang was the first to introduce the adaptive networkbased fuzzy inference system method. ANFIS is a simple data learning method that use fuzzy logic to turn provided inputs into desired outputs via densely interconnected neural network processing units and, information connections that are weighted to map numerical inputs to outputs [13]. To determine and, alter the structure and, parameters of fuzzy inference systems, the ANFIS system uses artificial neural network learning principles. The data presented to the machine can be learned using fuzzy rules [14]. Jang [13] created a hybrid neuro-fuzzy inference expert system that is based on the Takagi-Sugeno fuzzy inference system. The ANFIS architecture is comprised of five layers. Adaptive neurons are found in the first and, fourth layers, respectively. The second, third, and, fifth layers, on the other hand, are made up of fixed neurons. Fixed nodes lack any parameters, while adaptive neurons are coupled with their own parameters and, updated correctly with each of them in the next iteration [3, 15–20]. When two fuzzy rules based on a Sugeno model of the first order are considered: • Rule 1: (if x = A1) and, (if y = B1), then (f1 = p1x + q1y + r1) • Rule 2: (if x = A2) and, (if y = B2), then (f2 = p2x + q2y + r2) Ai and, Bi are fuzzy sets, and, x and, y are inputs. The outputs within the fuzzy zone are fi , and, the design parameters pi , qi , and, ri are calculated during the training phase. Figure 2 depicts the ANFIS architecture for implementing these two rules. Layer 1 is the fuzzification layer. Layer 1’s outputs are the input’s fuzzy membership degrees, which are as follows: Oi1 = µAi (x1 ); i = 1, 2

(1)

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Oi1 = µBi−2 (x2 ); i = 3, 4

(2)

where x and, y are the inputs of the layers, A and, B are linguistic labels, and, µA i (x) and, µB i−2 (y) functions can be selected as any fuzzy membership function.

Fig. 2. ANFIS architecture.

Layer 2’s output is a fixed node labeled M, which is the sum of all input signals. This layer’s outputs can be represented as follows: Oi2 = wi = µAi (x) × µB i (x); i = 1, 2

(3)

The normalization layer, which is a fixed node labeled N, is the Layer 3. Oi3 = w1 =

wi ; i = 1, 2 w1 + w2

(4)

where w1 represents the normalized output of layer 3. The defuzzification layer is the Layer 4. The product of normalized strength and, a first-order polynomial is the output of each node in this layer. Oi4 = wi fi = wi .(pi x1 + qi x2 + ri ); i = 1, 2

(5)

where (pi ,qi ,ri ) rule is the set-out output parameters for i, and, fi is the i order polynomial. The summation neuron, which is located in layer 5, is a fixed node that calculates the output as the sum of all input signals.   wi fi wi . fi = i=1 ; i = 1, 2 (6) Oi5 = y = i=1 wi As can be seen in Fig. 3, while the inputs of the ANFIS-PI controller are KI and, KP , the control signal processed sensitively to changes in the system dynamics with the help of the fuzzy logic rule base created by artificial neural networks is given to the system [3]. The flow diagram of the ANFIS structure is given in Fig. 3.

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Fig. 3. Flowchart of the ANFIS structure.

As can be seen in the flowchart in Fig. 3, uploading training and, test data to the system is the first step in developing an ANFIS controller. The next stage for ANFIS is to develop a fuzzy inference system. To accomplish this, the number and, type of membership functions for each input, as well as the type of membership function for the output, should be chosen. In addition, whether the output membership function is fixed or linear, as well as which grid or extraction partitioning method will be utilized, should be determined. It is necessary to determine the error tolerance and, epoch number of the optimization method to train the fuzzy inference system created. Training stops automatically when the training error reaches the specified error tolerance or when the specified number of epochs is reached. In the final step, the fuzzy inference system created is checked according to the test data. If satisfactory results are obtained, the structure and, rules of ANFIS are recorded to be used in the future [3]. Data collection and, Uploading To gather data for the ANFIS-PI controller used the time-varying KI and, KP parameters of the conventional PI controller applied to the active power output model of the natural gas/fuel oil turbine power plant used in this study were taken as inputs, and, the time-varying total output of the same controller was considered as the system output. 1 s was chosen as the sampling time to receive the data. This research employed a total of 6044 data. Approximately 75% of the data was utilized to train the Sugeno-based ANFIS model, with the remainder being used to test the system’s accuracy [3]. Determination of Membership Functions and, Architecture. The number of membership functions used in this study for each of the ANFIS-PI controller’s inputs was 6.

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The system selects which output to apply in which instance without enabling any interaction, using 36 rule bases automatically constructed for the output of the ANFIS-PI controller as a consequence of training and, validation studies by the ANFIS architecture. In an attempt to find the optimum structure, the mixed learning algorithm was used by selecting the dsigmf (used as the difference between two sigmoidal membership functions) function for the inputs and, selecting a linear type for the output. Training. Training is a learning process of the developed model. The model is trained until the results are achieved with minimum error. It is very important to select the appropriate dataset for good training and, validation. In this study, the number of epochs selected for the training of the ANFIS-PI controller was determined to be optimal 100. The minimum test error can be obtained in the first test. For a correct dataset, the test error decreases as training progress to a jump point. The parameters of memberships are updated during the learning process. In MATLAB, there are two methods for ANFIS parameter optimization, the backpropagation optimization method and, the hybrid optimization method which is a combination of least-squares and, backpropagation gradient descent methods. As a result of the tests done for this study, the hybrid method was chosen as the most suitable method for the model. In terms of error size, the error tolerance is applied as the training stopping condition. After the training data error remains within this tolerance, the training will be stopped. For each ANFIS-PI controller input, six membership functions were employed, and, the mean test error (Mean Squared Error-MSE) was found to be 0.00043217 [3]. Validation. The validation dataset is used to validate the fuzzy inference model created by the ANFIS and, to test its generalization potential. This validation is done by feeding the evaluation data into the model and then seeing how it answers. The mean test error (Mean Squared Error-MSE) for the validation dataset of the ANFIS-PI controller was found to be 0.00041822 [3].

3 Results and, Discussion Around the world, approximately 21% of electricity is generated from natural gas/fuel oil turbine power plants, although its share in the total generation changes every year. The size of the generated energy increases the importance of controlling these power plants. In this study, the simulation results of the reference system are shown in the same figure to make a more objective evaluation. Figure 4 and Table 1 show the outcomes of the simulation. A band, of 5% was used to make comparisons. When the results were generally examined, it was determined that the ANFIS-based PI controller gave much better results than the other controllers. The ACO-PI controller can be considered more successful than the conventional PI controller since it gave close results to the FGPI controller. When looking closely, it can be observed that the ANFISPI controller has the fastest settling compared to all the other controllers. Thus, the ANFIS-PI controller is easily the most successful controller among the others in terms of settling time and, overshoot value, demonstrating that ANFIS-based controllers adapt more quickly to altering system dynamics due to their structure.

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(a)

(b) Fig. 4. System response curves, (b) A zoomed-in at the positive part, (c) A zoomed-in at the negative part.

Table 1. Simulation results. Positive Part Settling time (sec) Overshoot (%)

ANFIS-PI FGPI 1.79 2.63 50

ACO-PI PI 3.39 4.59 7.63 0

Negative Part Settling time (sec) Overshoot (%)

2.82 3.85 8.05 15.25

3.86 5.96 22.16 0

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4 Conclusion The parameters of conventional controllers are determined based on the features in the initial establishment conditions of the power plant. However, as the lifespan of power plants increases, these parameters are unable to react to changes in system dynamics. The efficiency of the power plants suffers as a result of this. In general, energy losses are unacceptable; therefore, the parameters of controllers used in natural gas/fuel oil turbine power plants should be developed using current controllers to ensure that they self-adapt to changing system dynamics. ANFIS-based controllers beat other controllers in terms of settling time and, overshoot, according to simulation results. As a result, it is determined that in order to improve the efficiency of power plant equipment, new control approaches, such as ANFIS-based controllers, should be used instead of conventional controllers in active power control. Energy production from fossil fuels that are gradually becoming depleted and, cause dangers by polluting the environment will be reduced in this way. For more effective control of power plants, new generation control methods based on artificial intelligence can be considered for future works.

References 1. Bilen, H.: Combined cycle power plant design, MSC thesis, Gazi University, Turkey. (in Turkish) 2. Ba¸saran, Ü.: 380 kV interconnected power systems at various power flow distribution and, economic analysis. Ph.D. thesis, Anadolu University, Turkey (2004). (in Turkish) 3. Tabakh, R.: Application of modern control methods in power plants. MSC thesis, Istanbul University - Cerrahpa¸sa, Turkey (2020). (in Turkish) 4. Çiftkaya, B.: Investigation of heavy duty gas turbines and, their simulation. MSC thesis, Istanbul Technical University, Turkey (2010). (in Turkish) 5. Electricity Generation Company. Annual Report. Report for the Department of Press and, Public Relations. Report no. 2019, 31 December 2019, Ankara (2019) 6. Kavalerov, B.V., Bakhirev, I.V., Kilin, G.A.: An investigation of adaptive control of the rotation speed of gas turbine power plants. Russ. Electr. Eng. 87(11), 607–611 (2016). https://doi.org/ 10.3103/S1068371216110067 7. Bonfiglio, A., Cacciacarne, S., Invernizzi, M., Lanzarotto, D., Palmieri, A., Procopio, R.: A sliding mode control approach for gas turbine power generators. IEEE Trans. Energy Convers. 34(2), 921–932 (2018) 8. Stanescu, G., Barbu, E., Vilag, V., Andreescu, T.: Constructal approach on the feasibility of compressed air temperature control by evaporative cooling in gas turbine power plants. Proc. Romanian Acad. Ser. A Math. Phys. Techn. Sci. Inf. Sci. 19, 201–206 (2018) 9. Ahmed, F.H.A.: Gas turbine speed control using fuzzy logic. Ph.D. thesis, Sudan University of Science and, Technology, Sudan (2018) 10. Mehrpanahi, A., Arbabtafti, M., Payganeh, G.: Robust controller design for a three-shaft industrial gas turbine in the infinite grid power generation. Trans. Inst. Meas. Control. 42(1), 131–156 (2020) 11. Nail, B., Kouzou, A., Hafaifa, A.: Robust block roots assignment in linear discrete-time sliding mode control for a class of multivariable system: gas turbine power plant application. Trans. Inst. Meas. Control. 41(5), 1216–1232 (2019) 12. MATLAB R2020a, Reference Manual, Licence Number: 40827100 (2020)

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13. Jang, J.S.: ANFIS: adaptive-network-based fuzzy inference system. IEEE Trans. Syst. Man Cybern. 23(3), 665–685 (1993) 14. Gomaa Haroun, A.H., YinYa, L.: A novel optimized fractional-order hybrid fuzzy intelligent PID controller for interconnected realistic power systems. Trans. Inst. Meas. Control. 41(11), 3065–3080 (2019) 15. Abraham, A.: Adaptation of Fuzzy Inference System Using Neural Learning. In: Fuzzy systems engineering, pp. 53–83. Springer, Berlin (2005) 16. Alhanafy, T.E., Zaghlool, F., Moustafa, A.S.E.D.: Neuro-fuzzy modeling scheme for the prediction of air pollution. J. Am. Sci. 6(12), 605–616 (2010) 17. Milosavljevic, A., Stoimenov, L., Rancic, D.: An algorithm for automatic generation of fuzzy neural network based on perception frames. In: 9th WSEAS International Conference on Neural Networks Sofia, Bulgaria, 2–4 May 2008, pp. 215–220. WSEAS, Sofia (2008) 18. Nazmy, T., et al.: Adaptive neuro-fuzzy inference system for classification of ECG signals. J. Theor. Appl. Inf. Technol. 12(2), 71–76 (2010) 19. Zayoud, A.: Circulating Fluidized Bed Combustor Towards Third Generation of Oxy-Fuel Combustion. Ph.D. thesis, Indian Institute of Technology Guwahati, India (2016) 20. Flora, J., Auxillia, J.: Sensor failure management in liquid rocket engine using artificial neural network. J. Sci. Ind. Res. 79–11 (2020)

ANFIS-Based Determination of pH Level of Liquid Raw Materials with Image Processing Batuhan Atasoy1,2(B)

, Kadim Tasdemir1 , Mahmut Durmus3,4 Fatih Gucluer2 , and Emre Tosun2

, Ezgi Demir5

,

1 IND Information Technologies, Istanbul, Turkey

[email protected]

2 Istanbul Technical University, Istanbul, Turkey 3 Gebze Technical University, Kocaeli, Turkey 4 Nanovasyon Technological Researches, Kocaeli, Turkey 5 Sumer Robotics, Engineering and Consultancy Ltd., London, UK

Abstract. Determination of pH level in liquid materials are important phenomenon, especially to determine the quality of the raw material, and some mechanical features like abrasive characteristics, and so on. Today’s conventional methods are based on spectroscopic or non-spectroscopic methods, such as refractometric, diffractometric methods. These methods are quite useful and accurate for any defined feature such as acidity, organic/inorganic material content like alcohol or glucose content. However, main drawback of these methods are, they are mostly measurable for one feature, so the operational and maintenance costs are expensive. Image processing and Convolutional Neural Networks based methods are low-cost, but satisfactory results, however the main requirements of them are high computational power and this sometimes results overfitting problem. Moreover, some color tones are not detected correctly, hence they are detected and analyzed as crisp values. In this study, a hybrid methodology of computer vision and fuzzy inference systems has been proposed for a computationally effective, and accurate results for the determination of pH levels in liquid raw materials. The chemical sensor based color change has been detected by computer vision algorithms, then the required Red-Green-Blue (RGB) values have been transformed into Hue-Saturation-Value (HSV) space. These values are then input to Adaptive Network-based Fuzzy Inference Systems (ANFIS) to determine the pH level of any liquid material. During the first phase of the analyses, satisfactory results have been obtained and the research studies are ongoing within National Scientific and Technological Research Council of Turkey (TUBITAK) 1501-called R&D project. Keywords: Liquid materials · Chemical sensors · pH level · Computer vision · Neuro-fuzzy systems

1 Introduction Liquid raw materials are one of the important industrial products, which are sometimes better and easier for storage, processing, and manufacturing than the other type of © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 744–751, 2022. https://doi.org/10.1007/978-3-031-09173-5_85

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raw materials. Because of their physical and chemical status, some important features like acidity, organic/inorganic material content must be measured with online or offline methods. To detect or measure these features, electromagnetic methods such as spectroscopic, refractrometric, or diffractrometric methods have been widely used. They give accurate results by means of the light properties; however, they are quite expensive when considering the operational and maintenance costs, and additionally they enable to measure a single feature for any specimen at the same time. That is, one may require multiple measurement devices to analyse the specimen taken by the same sample. Recently, by means of developing camera and hardware technologies, deep learning based methods such as Artificial Neural Networks (ANN) and Convolutional Neural Networks (CNN) based methods have a potential to develop cheaper and versatile-use analyses. However, image processing-based methods are mainly dependent to the ambient light properties, and the developed AI models to have accurate results. In this study, image processing algorithms have been combined with Adaptive Network-based Fuzzy Inference Systems (ANFIS). Different from the literature, the proposed algorithm guarantees to see the changes in colour tones by means of first order Sugeno type fuzzy membership functions instead of crisp values and uses HueSaturation-Value (HSV) colour space to have a better tone detection rather than RedGreen-Blue (RGB) colour space. In the second chapter, the literature studies have been examined in detail. The methodology used to analyse the system to detect the pH level has been mentioned in Sect. 3, and result have been discussed and further studies have been explained in Sect. 4.

2 Literature Survey To analyse the chromatic features of the liquids, various conventional methods are widely used. These methods can be classified into spectroscopic and non-spectroscopic methods, depending on the type of analyses. In spectroscopic methods, the specimen is exposed to an electromagnetic radiation such as ultraviolet (UV), visible, or infrared (IR) spectrum. Then the specimen absorbs the light and reflects at a definite wavelength, depending on the type of electromagnetic energy (Kelly and Woodbury 2003). Main advantage of these methods is their accuracy, on the other hand, they are quite expensive considering the operational and maintenance costs. Due to those reasons, they are used mainly for special batch analyses. Apart from them, non-spectrocopic methods are cheaper alternatives. Such them include refractrometric or, diffractrometric methods based on the refraction or diffraction properties of the light. Widely used methods are Raman Spectroscopy, X-Ray Diffractrometry, Abbe Refractrometry, and Michelson Interferometry (Choosing a Refractometer | Labcompare.Com, n.d.). These methods are also accurate to detect any feature like heavy metals, ions, or organic materials inside the liquid materials, however, they are still expensive for maintenance and operational costs. One another drawback for the spectroscopic and non-spectroscopic methods are, it is possible to detect one feature at the same time, so for the detection of more than one feature, one also needs to use multiple spectrometers, refractrometers or diffractrometers concurrently.

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To overcome the cost and accuracy problem, image processing-based methods may be used alternatively. However, two important criteria which affects the model accuracy directly are, environmental properties such as light intensity and, the AI model can be used. Kim et al. in 2017 uses smartphone camera-based adaptive colorimetric pH detection algorithms, and satisfactory results have been obtained. However, the ambient light conditions also suffer to reduce the accuracy level (Kim et al. 2017). Puno et al in 2017 developed an Artificial Neural Networks (ANN) based image processing algorithms to obtain the nutrient quality of soil, such as pH level, amount of Phosporus and its derivatives, which gives accurate results. However, the accuracy level for ANN-based methods are mainly dependent on the hyperparameter tuning such as number of hidden layers, number of neurons inside any hidden layer, optimizer method, learning rate, etc. (Puno et al. 2017). Similarly, Babu et al. in 2016 developed to determine the chemical characteristics for soil, in which they also used digital image processing methods in combination with fractal dimensional analyses, such as Boxcount Dimension (D2). Their results are within 1% error level, however one main drawback for the fractal analyses are, they may be changed with respect to the same specimen, so statistical methods such as hypothesis testing, ANOVA analysis, or p-value tests are also highly required to construct a stable analysis (Manikandababu and Pandian 2016). Janardhan et al. in 2020 combined the digital image processing with ANN algorithms, in which Red-Green-Blue (RGB) colour space has been used to determine the pH level of soil. Their study gives satisfactory results, but the use RGB colour space sometimes disables to see the colour tones at similar specimens (Janardhan 2020). Craig et al. in 2018 used quantitative colorimetric image processing methods to determine the pH level in aerosols, which gives evidence to determine the pH level accurately. However, based on smartphone camera images, ambient light intensity is one of the important problems should be taken into account (Craig et al. 2018). Choudhary et al. in 2019 examined the quality of milk based on fluorophore-based pH sensors in combination with fibre optic spectrophotometers, in which they found accurate results by means of single and dual fluorophore based analyses, however the analyses is based on offline solutions with respect to the time (Choudhary et al. 2019).

3 Methodology Due to the detected advantages and disadvantages in the other literature studies, it is essential to address the basic problems: How may one overcome the light intensity problem? How may a neural network-based methods distinguish the pH level accurately considering the semi colour tones? To solve the problems, in this study, a novel and computationally cost-effective approach to determine the pH levels of liquid raw materials have been shown in detail. Rather than traditional ANN or CNN-based methods, this method includes a clustering-based object detection algorithms in combination with neural network methods. However, the desired accuracy level of the model for the traditional methods are based on hyperparameter tuning, such as determination of the number hidden layers and neurons located in each hidden layer.

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3.1 Image Processing Part As a starting point, the input features have been determined by means of image processing methods. All the analyses are based on the image masking processes, so it is important to determine not only the main colours of liquid raw materials, but also to determine the different tones. The input data for the ANFIS model is based on the 3-dimensional color matrix, in which the widely used one is Red-Green-Blue (RGB) space. However, to determine the required colour tones, coordinate transformation from cartesian to cylindirical is required. To do this, Hue-Saturation-Value (HSV) colour space has been used to determine the required input features, which is shown in Fig. 1.

Fig. 1. RGB color space (left) and HSV color space (right) (Popov et al. 2018)

To detect the required RGB values, firstly the RGB values of specimen has been detected from the constant pixel positions. This can be done by using the image maskingbased contour detection algorithms. The required contour can be found by the threshold values, in which they are detected by means of directional derivative-based clustering algorithms. By means of this algorithm, one does not have to assign a constant RGB values for thresholding, instead dramatic gradient changes can enable to determine required threshold values in Fig. 2.

Fig. 2. Directional derivative-based object detection (A. M. Saif et al. 2016)

After the detection of image masking, it is important to obtain the required HSV values inside the contour. To perform this, randomly selected 50 points inside of the contour have been prepared as the test data, which enables a pH value set rather than a single pH-value to handle the noisy data coming from the different light intensity values. The working principle of the analysis algorithm has been revealed in Fig. 3.

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Fig. 3. The proposed method to determine the pH levels of liquid raw materials

3.2 ANFIS Model Design After the construction of training data from 510 different data from 30 different samples, ANFIS structure has been designed. To perform this, the required model has been determined as 3 input membership functions. The model structure has been given in Fig. 4.

H-Value

S-Value

pH Value

V-Value

Fig. 4. ANFIS structure to determine the pH level

The input features have 3 membership functions, each has Gaussian type. For the output feature, the output membership function has been adjusted as the first order Sugeno-type fuzzy inference system. The optimization method of the weights in the ANFIS structure is based on backpropagation-type optimizer, so the weights of the model are optimized by means of stochastic gradient descent methods. The model error after 50 epochs have been given in Fig. 5. After 50 epochs, the error level is within 10−3 level for training data. Then the test results have been given in Fig. 6.

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Fig. 5. Error after 50 epochs

Fig. 6. Test Results

For the test data, the determined pH values (Blue dotted) are so nearby the test value (Red star) results, as within 10−3 level, so that HSV values can be applicable to determine the pH levels of liquid raw materials.

4 Results and Discussion 4.1 Discussion In this study, a novel approach to determine the pH-level of liquid raw materials has been studied. To do this, image processing-based features have been combined with Adaptive Network-based Fuzzy Inference Systems (ANFIS), which gives better results than Artificial Neural Networks (ANN) to see the similar tones of having different pH levels. In conventional use of determining any feature such as pH level, spectroscopic or non-spectroscopic methods have been used. Such non-spectrospoic methods like refractrometric or diffractrometric methods give satisfactory results, however these methods are quite expensive, and they are valid just only to measure one feature. To solve these drawbacks, image processing-based methods are cost-effective and enables to measure more than one feature concurrently. Some methods including Artificial Neural Networks (ANN) and Convolutional Neural Networks (CNN) may give satisfactory results, however CNN-based methods are sometimes computational costly and results overfitting and overgeneralization problems with respect to the input data. Whereas ANN-based methods are computationally cost-effective, however the success rate is dependent on the hyperparameter tuning.

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To perform the study, firstly Red-Green-Blue (RGB) space values have been obtained from image masking methods. Then these obtained values have been converted into HueSaturation-Value (HSV) space. To perform this, 510 Sample images from 30 samples have been exposed to the same light source for 17 days. Then the pH values have been determined day by day both with pH meter sensors and chemical sensors. After the data generation these values have been implemented through the ANFIS network to determine the pH level, which gives satisfactory results to determine the pH level of liquid raw materials with a Mean-Squared Error level of 10−3 s. 4.2 Further Studies Since the study is the first phase of the Scientific and Technological Research Council of Turkey (TUBITAK) 1507 R&D project, it gives important results to determine the pH-level of liquid raw materials. After that, the project is going on determining other features such as detection of heavy metals, alcohol level, glucose level, etc. of the liquid raw materials by means of chemical sensors in combination with image processing. Then the obtained data is going to be used to the digital twin design of the real physical system. This project is TUBITAK-granted 1501 R&D project of project number 3210209 and name “Developing the Sensor Technologies and Digitalization of the Manufacturing Process of Industrial Vinegars”.

References Saif, J.A.M., Hammad, M.H., Alqubati, I.A.A.: Gradient based image edge detection. Int. J. Eng. Technol. 8(3), 153–156 (2016). https://doi.org/10.7763/IJET.2016.V8.876 Babu, T., Tubana, B., Datnoff, L., Yzenas, J., Maiti, K.: Release and sorption pattern of monosilicic acid from silicon fertilizers in different soils of Louisiana: a laboratory incubation study. Commun. Soil Sci. Plant Anal. 47(12), 1559–1577 (2016) Choosing a Refractometer | Labcompare.com. (n.d.). https://www.labcompare.com/10-FeaturedArticles/19399-Choosing-a-Refractometer/. Accessed 28 Mar 2022 Choudhary, S., Joshi, B., Pandey, G., Joshi, A.: Application of single and dual fluorophore-based pH sensors for determination of milk quality and shelf life using a fibre optic spectrophotometer. Sens. Actuators B Chem. 298, 126925 (2019). https://doi.org/10.1016/J.SNB.2019.126925 Craig, R.L., et al.: Direct determination of aerosol pH: size-resolved measurements of submicrometer and supermicrometer aqueous particles. Anal. Chem. 90(19), 11232–11239 (2018). https:// doi.org/10.1021/ACS.ANALCHEM.8B00586/SUPPL_FILE/AC8B00586_SI_001.PDF Janardhan, K.: Determination of pH in soil using deep learning and digitalimage processing. Int. Res. J. Innov. Eng. Technol. (IRJIET), 4(3), 66–70 (2020). www.irjiet.com Kelly, M.L., Woodbury, D.J.: Advantage and disadvantages of patch clamping versus using BLM. Membr. Sci. Technol. 7(C), 699–721 (2003).https://doi.org/10.1016/S0927-5193(03)80049-9 Kim, S.D., Koo, Y., Yun, Y.: A smartphone-based automatic measurement method for colorimetric pH detection using a color adaptation algorithm. Sensors 17(7), 1604 (2017). https://doi.org/ 10.3390/S17071604 Manikandababu, C.S., Pandian, M.A.: Determination of physical and chemical characteristics of soil using digital image processing. Int. J. Emerg. Technol. Comput. Sci. Electron. (IJETCSE) 20, 976–1353 (2016)

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Popov, V., Ostarek, M., Tenison, C.: Practices and pitfalls in inferring neural representations. Neuroimage 174, 340–351 (2018). https://doi.org/10.1016/j.neuroimage.2018.03.041 Puno, J.C., Sybingco, E., Dadios, E., Valenzuela, I., Cuello, J.: Determination of soil nutrients and pH level using image processing and artificial neural network. In: 9th International Conference on Humanoid, Nanotechnology, Information Technology, Communication and Control, Environment and Management, HNICEM 2017, January 2018, pp. 1–6 (2017). https://doi.org/10. 1109/HNICEM.2017.8269472

Recurrent Neural Network Controller for Linear and Nonlinear Systems Saeid Sheikhmemari(B) Ardabil Branch, Islamic Azad University, 467 Ardabil, Iran [email protected]

Abstract. This paper aims to design deep recurrent neural network controllers for linear and non-linear systems. Design and comparison with two different controllers are considered. A pure recurrent neural network controller and self-tuning PID controller based on recurrent neural networks (PRNN), according to the influence of the object’s parameter on system output performance, The PRNN can auto-adjust its weights to vary kP , kI and kD The emulation results show that the presented control systems have quick response speed and strong adaptive capability. The PID self-tuning based on the recurrent neural network- has superior performance in tracking error and reached the reference model in both linear and nonlinear systems. The deep recurrent neural network is used to potentially improve control performances, such as reducing ripple and overshoot and excellent performance in the tracking reference model. Keywords: Recurrent neural network self-tuning PID controller · Deep learning recurrent neural network

1 Introduction The field of neural networks covers a very broad area. The neural network controllers have emerged as a tool for difficult control problems of unknown nonlinear systems. In this paper we used a recurrent neural network (RNN) for system identification for unknown nonlinear systems which is a recurrent neural network (Elman type), it is called Elman type because feedback connection comes from the hidden layer instead of the output layer, this caused weights and biases adjust better if feedback connection comes from output layer usually called (JORDAN type) which we used this type of neural network as a controller for linear and nonlinear systems control. There are several control Strategies for neural networks which some of them are: 1) Feedforward control, 2) Direct inverse control (extracting inverse dynamics), 3) Indirect adaptive control method based on NN identification, 4) direct adaptive control with guaranteed stability, 5) Feedback linearization, 6) Predictive control [1]. The direct adaptive control method can be used as an adaptive or non-adaptive controller, if the learning process continues, the controller will be an adaptive controller. In a non-adaptive controller, the process is accomplished © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 752–760, 2022. https://doi.org/10.1007/978-3-031-09173-5_86

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for a certain period of time. The proposed controller guarantees that all the closed-loop signals are uniform ultimate boundedness and that the tracking errors converge to a small neighborhood of the desired trajectory. Finally, simulation studies are given to show the effectiveness of the proposed approach. For the second controller, a multilayer recurrent neural network is used to auto-adjust three parameters that consist of three hidden layers and one output layer. The number of hidden neurons should be 2/3 the size of the input layer, plus the size of the output layer, for this controller we consider 7 neurons in the first and second hidden layers and only three neurons exist in the third hidden layer. This paper aims to improve the performance of the self-tuning PID controller which, the control input is limited, and compare it with the pure RNN controller. Section 2 introduces the Mathematics background of Recurrent neural networks, Sect. 2.1 is implementing back-propagation, direct model non-adaptive RNN is discussed in Sect. 3 also the linear and nonlinear systems to be used. Results are shown in Sect. 3, in the last section, the advantages of PID-RNN are discussed.

2 Recurrent Neural Network A recurrent neural network (RNN) is a type of artificial neural network which uses sequential data or time-series data. These deep learning algorithms are commonly used for ordinal or temporal problems, such as language translation. The output of recurrent neural networks depends on the prior elements within the sequence as shown in Fig. (1). While future events would also help determine the output of a given sequence, unidirectional recurrent neural networks cannot account for these events in their predictions [2].

Fig. 1. Recurrent Neural Network

The net inputs are Xn and delay term zn−1 that define as; zn−1 = f (wzn zn−1 + wxn xn + b) −1

(1)

where b is bias and f is the activation function. Two common activation functions are sigmoid and tangent hyperbolic functions that sigmoid function with the formula; f (x) = So zn−1 becomes;

1 1 + e(−x)

  −1 zn−1 = 1/1 + exp −(wzn zn−1 + wxn xn + b )

(2)

(3)

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The tangent hyperbolic activation function is defined as; h(x) =

(e−x − e−x ) (e−x + e−x )

(4)

The net outputs yn which is defined as;   −1 yn− = h wyn zn−1 + by

(5)

This can be rewritten as; −1 yn− = tanh(wyn zn−1 + by )

(6)

where wyn is outputs weights and by is bias and h is the hyperbolic activation function which is indicated in Eq. (3). the initial weights are random. Also, the back-propagation is used to apply for this training, since it is the most common and flexible algorithm. The connection weights are iteratively adjusted, and the error between the network output and the desired output is limited. Therefore, the error target, which is usually labeled as the mean squares errors (MSE), can be expressed as: MSE =

 1 T  yt − yt− t=1 T

(7)

2.1 Backpropagation Algorithm The main goal of the backpropagation algorithm is to deduce method/conditions for adjustment of weight factors based on the minimum value of energy function, For the output layer of the network, which has one neuron, the training rule for specialized back-propagation can be written as blow [3], consider the feed-forward neural network in Fig. 1, the total net input to each hidden layer neuron can be written as: nethi = xi wi +

k

z −1 wj n=1 n

+b

(8)

Then output nodes of hidden layers can be illustrated (we squash it using the logistic function to get the output node): outhi = 1/1 + exp(−(neth )) Repeat this process for the output layer; n neto =

i=1

outhi wjk

(9)

(10)

Linear activation function is considered for the output layer, so outo ; outo = neto

(11)

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755

After that, we calculate the error between actual output and model output which is represented in (Eq. 7). The main goal of the backpropagation algorithm is to adjust each of the weights in ∂E is the network so that they cause the actual output to be closer to the target output. ∂wi read as the partial derivative of E concerning wi . It can be called the partial derivative of E concerning wi . ∂E ∂E ∂outo ∂neto1 = × × ∂wkj ∂outo ∂neto1 ∂wkj

(12)

Often it can be seen as the delta rule: ∂E = (y − y− ) × outo (1 − outo ) × outhi ∂wkj And

∂outo ∂E ∂outo and ∂neto1

(13)

which can be written as δo , so the above calculation can be: ∂E ∂outo ∂E × = ∂outo ∂neto1 ∂neto1

(14)

δo = (y − y− ) × outo (1 − outo )

(15)

∂E = −δo outhi ∂wkj

(16)

δo = And it can be represented as

Therefore

To decrease the error, we then subtract this value from the current weight (optionally multiplied by some learning rate, alpha, which we set to 0.01): + wkj = wkj + α

∂E ∂wkj

(17)

2.2 Direct Model Non-adaptive RNN Controller The proposed recurrent neural network controller is shown in Fig. (2), which is designed to control both linear and non-linear systems. system identification can be applied by RNN for the non-linear system. The objective is to train the neural network in such a way that to obtain a controller to control the plant. The RNN must be trained well to produce control parameter u(t) to be applied to the plant to produce y(t). The backpropagation algorithm is the proposed method explained in the previous section is considered to train the RNN controller, in this method u(t) and y(t) are required to train the network. The reference model was applied to obtain an output signal from the system close to the reference model’s output by reducing the error’s square (Table 1).

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Fig. 2. Recurrent Neural Network Controller for Linear and Non-linear Systems

Table 1. Parameter for each input RNN/Parameters Inputs

Value 7

Outputs

1

Hidden-layers

3

Node in hidden layers

7

Sweeps of training

3500

To verify the applicability of the proposed method, the implementation is applied to linear and non-linear systems simulation and experiments to a temperature control system for a water bath. The linear and nonlinear models used in the simulation are: YN +1 = 0.998Yn + 0.232un

(18)

2 YN +1 = 0.9yn − 0.001Yn−1 + un + sin(un−1 )

(19)

where the linear model (a) is a model of a single input, single-output of a temperature control process for a water bath and the nonlinear model (b) is a nonlinear model. The result will compare with the PID self-tuning which is adjusted by RNN. The scheme of PID self-tuning is shown in the figure below (Fig. 3). RNN has 7 neurons in hidden layers and 3 neurons in the output layer. the simulations are implemented in two cases, namely when the control input and PID gains are not limited case and limited case. The range of control Input is limited between the defined values, namely, zero and 10 for minimum and maximum values of the control Input, respectively. The proposed simulation results show that the proposed method can be implemented conveniently in linear and nonlinear systems.

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Fig. 3. Self-tuning PID controller based on recurrent neural

3 Results This section presents and compares different methodologies for controlling linear and non-linear systems. as shown in Figs. 4, 5, 6, 7 and 8. Firstly, the temperature control system for the water bath is operated by the adaptive recurrent neural network controller and then auto-adjusted PID controller based on RNN applied to the linear system. Two case-control input is considered, the objective control inputs are limited once between 0 and 25 and again between 0 and 10 without input limiting control.

Fig. 4. Recurrent neural network controller for the linear system with limited control input

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Fig. 5. Self-tuning PID-controller for linear system with limited control input

Fig. 6. PID-based NN without limited control input

Recurrent Neural Network Controller

Fig. 7. RNN controller out limited control input

Fig. 8. PID-based RNN with limited control input

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4 Conclusion The paper investigates issues involved in applying pure recurrent neural networks and self-tuning PID controllers based on RNN. Figure 4 and 5 show the linear and nonlinear systems with control input limitation (between 0 and 25), It can be concluded that a satisfying performance of the linear and nonlinear system to tracking reference model in PID-RNN controller is better than a pure recurrent neural network, especially in a nonlinear system with a limited control signal Fig. 7 and 8. The resultant output never obtained overshoot and bad response like traditional PID controllers as shown in Figs. (4, 5, 6, 7 and 8), because the proportional (Kp ) the integral (Ki ), and (KD ) gains are adjusted instantly by the RNN. The artificial neural network is a powerful algorithm to apply for controlling the linear and nonlinear systems, because it is a high learning ability and is capable to deal with either non-linear or linear problems, in Fig. 6 a NN PID controller is used to control the linear system without input limitation. For future studies, I proposed to investigate fault detection in controlling systems with RNN. If a fault occurs in the system, RNN can be used as a fault detector and circuit breaker.

References 1. Song, Z., Liu, C., Song, X.: Application of self-tuning PID control based on diagonal recurrent neural network in crystallization process. In: 2006 International Conference on Machine Learning and Cybernetics, pp. 365–369 (2006) 2. Belov, M.P., Van Lanh, N., Khoa, T.D.: State observer-based Elman recurrent neural network for electric drive of optical-mechanical complexes. In: 2021 IEEE Conference of Russian Young Researchers in Electrical and Electronic Engineering (ElConRus), p. 802 (2021) 3. Rajawat, S., Jain, S.:Fusion deep learning based on back propagation neural network for personalization. In: 2nd International Conference on Data, Engineering and Applications (IDEA), pp. 1–7 (2020). https://doi.org/10.1109/IDEA49133.2020.9170693

Prediction of the Spatiotemporal Dynamics of von Kármán Vortices by ANFIS Cihan Bayindir1,2(B)

and Halid Akdemir1,3

1 ˙Istanbul Technical University, Sarıyer, 34469 ˙Istanbul, Turkey

{cbayindir,akdemirh20}@itu.edu.tr

2 Bo˘gaziçi University, Bebek, 34342 ˙Istanbul, Turkey 3 Antalya Bilim University, 07190 Antalya, Turkey

Abstract. Wakes and vortices are commonly observed in fluid flows around bluff bodies, a phenomenon which is called vortex shedding. Such vortices are named as von Kármán vortices since their first investigation is performed by the leading fluid dynamicist Theodore von Kármán. Although initially observed in the studies of fluid flows, the same phenomenon can also be observed in different branches of mediums such as condensates. It is possible to model these vortices using numerical techniques that solve the Navier-Stokes equations, however, some dynamic equations such as the complex Ginzburg-Landau (GL) equation is another frequently used model for these purposes. In this paper, we solve the GL equation using a spectral scheme and Runge-Kutta time integrator to simulate the dynamics of von Kármán vortices around a cylinder. The prediction of temporal dynamics is of crucial importance to avoid excessive shedding, resonance, and structural damage of the engineering structures. With this motivation, here we examine the predictability of the von Kármán vortices using the adaptive neuro-fuzzy inference system (ANFIS) which relies on a rule-based relationship between input values and output values that are learned adaptively by being trained with the data set analyzed. We show that the temporal dynamics of the von Kármán vortices can be adequately performed by ANFIS and we report the prediction success of the ANFIS in the solution of this complex prediction problem measured by the coefficient of determination (R2 ) and the root mean square error (RMSE) values. Our results can be used for predicting, interpolating, and extrapolating vortex data to analyze fluid dynamics problems and to develop control strategies for avoiding structural failures. Keywords: von Kármán vortices · Ginzburg-Landau equation · ANFIS

1 Introduction Flows around bluff bodies cause vortices to form downstream, which are called von Kármán vortex street or vortex shedding, after von Kármán, who was the first to discover it. It is initially observed in the studies of fluids but the same phenomenon can also be observed in different branches of mediums such as condensates [1] or in an atomic superfluid gas [2]. In the literature, the vortex street has been analyzed by researchers with © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 761–768, 2022. https://doi.org/10.1007/978-3-031-09173-5_87

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several methods such as numerically [3] or observationally [4] and for diverse purposes such as fishing problems [5], bubble wake analysis [6], or energy harvesting [7], etc. Even though it is mostly solved with Navier-Stokes equations, the complex GinzburgLandau (GL) equation can also be used to analyze and simulate it. On the other hand, artificial intelligence, efficient and soft computational techniques have become popular tools in predicting in a wide variety of branches in the last few decades. Finance [8], medical [9], computer sciences [10], civil engineering [11], and fluid mechanics [12] are just a few of them. The aim of this study is to contribute to the analysis of the dynamics of von Kármán vortices. In this scope, firstly, the amplitudes of von Kármán vortices in spatial series were solved with the complex GL equation. Thereafter, vortex amplitudes in the spatial series were predicted with ANFIS, and its prediction capability was evaluated. This paper is shaped by headings as ıntroduction, methodology, results and discussion, and conclusion. In Sect. 1, general information about the paper and its literature was shared. In Sect. 2, the methodology of this paper was introduced. The results of the study were discussed and it can be found in Sect. 3. Section 4 gives the implications of this paper.

2 Methodology 2.1 Review of the Ginzburg-Landau Equation The complex GL equation, named after Vitaly Ginzburg and Lev Landau, is a mathematical physical equation describing the dynamics of oscillations in physics. A dimensionless form of the GL equation is given as ∂A ∂A ∂ 2A +U = μ(x)A + (1 + iCD ) 2 − (1 + iCN )|A|2 A + F(x.t) ∂t ∂x ∂x

(1)



μ(x) = μ0 + μ x where x and t are space and time, A(x, t) denotes the complex amplitude and U , CD , CN are real constants expressing the advection speed, diffusion, and nonlinearity constants respectively. The F(x, t) is the forcing function and μ(x) is the wake growth parameter. Equation 1 is solved with 4th order Runge-Kutta time-stepping algorithm and Fourier spectral method which are summarized below m1 = g(An , tn , x)

(2)

m2 = g(An + 0.5m1 dt, t n + 0.5dt, x)

(3)

m3 = g(An + 0.5m2 dt, t n + 0.5dt, x)

(4)

m4 = g(An + m3 dt, t n + dt, x)

(5)

An = An−1 + dt(m1 + 2m2 + 2m3 + m4 )/6

(6)

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tn = tn−1 + dt

(7)

∂A = F −1 [ikF[A]] ∂x

(8)

∂ 2A = F −1 [−k 2 F[A]] ∂x2

(9)

here, F and F −1 symbolizes the Fourier and inverse Fourier transform, respectively, and k represents the wavenumber vector. The number n is the time index. The reader is referred to [13] for a more comprehensive discussion of the GL equation and [14–17] for a more detailed analysis of the Fourier spectral methods. 2.2 Review of the ANFIS A neural network (NN) is a system that works with an adaptive learning method inspired by the biological structure of the human brain. In this model, inputs and outputs, called neurons, are associated with connections. The connections of the neurons are weighted by using appropriate data in the process called training. In the training process, the outputs of the model are compared with the target values and the error is minimized by controlling it with iterative processes. Thus, a weighted relationship network emerges and becomes ready to predict. NN is divided into 3 types according to the movement of the network. These are as follows; feedforward neural network (FNN), convolutional neural network (CNN), recurrent neural network (RNN). The reader is referred to [18] more detailed and comprehensive explanation. Fuzzy inference system (FIS), contrary to Aristotelian logic, is the expression of situations with a rating method between 0 and 1. This algorithm returns one or more output values with one or more input associated with some conditional rules. Each variable is represented by membership functions. Membership functions have some linguistic expressions, which have mathematical equivalents. Membership functions operate to express linguistic conditions, and these conditions return an output value. In this period, the math process is nothing but taking the weights of the geometries in a general sense. A more detailed and comprehensive explanation can be seen in [19]. Adaptive neuro-fuzzy inference systems (ANFIS) is a combined model of fuzzy inference systems and neural networks. As in FIS, there is a rule-based relationship between input values and output values, but unlike FIS, the rules are learned adaptively by being trained with the data set, as in the neural network algorithm. In this structure, connections between neurons are associated with membership functions and rules rather than crisp weight numbers, unlike the NN structure. The reader is referred to [20] more detailed and comprehensive explanation.

3 Results and Discussion The flow field around a circular cylinder located at the origin was simulated with the complex GL equation. (see Fig. 1) Accordingly, the forcing function was taken as F(x.t) = 0,

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since no additional external forcing on vortices is considered. The time step was chosen as dt = 0.005 to ensure temporal instability. The length of the simulation space was set as L = 120 and it was divided into N = 512 equally spaced collocation points. The advection speed, diffusion, and nonlinearity constants were chosen as follows; U = 5, CD = 1, CN = 0. In order to compute the wake growth parameter, dimensionless  parameter μ0 and the slope of the wake growth rate parameter μ were selected as −4 3.57, −0.0434 respectively. A(x, 0) = 10 was chosen as the initial condition in our simulations.

Fig. 1. Flow field exhibiting vortices around a circular cylinder located at x = 0 at time t = 60.

The parameters A(x, t) and dA(x, t)/dt were selected as input variables of ANFIS in order to predict the spatial and temporal series vortex amplitudes. The training-to-test ratio of the series for ANFIS was chosen as 40%–60%.

Fig. 2. Modeled and predicted vortex amplitude spatial series in the training phase.

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The initial 40% of the vortex amplitude spatial series is subjected to the training phase in ANFIS and the comparison of the model and ANFIS predictions are depicted in Fig. 2. The remaining 60% of the same spatial series is subjected to blind testing and the result is depicted in Fig. 3.

Fig. 3. Modeled and predicted vortex amplitude spatial series in the blind testing phase.

The coefficient of determination (R2 ) and the root mean square error (RMSE) of ANFIS results depicted in Fig. 2 and Fig. 3 in comparison to the complex GL model results are 1.00 and 0.063 respectively in the training phase, and 0.99 and 0.067 in the blind testing phase.

Fig. 4. Modeled and predicted vortex amplitude temporal series in the training phase.

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Fig. 5. Modeled and predicted vortex amplitude temporal series in the blind testing phase.

Similarly, we investigate the prediction of the temporal dynamics of the von Kármán vortices by ANFIS in Figs. 4 and 5. The initial 40% of the vortex amplitude temporal series that is depicted in Fig. 4 is subjected to the training phase in ANFIS, and the comparison of the model and ANFIS predictions are illustrated therein. The remaining 60% of the same temporal series is subjected to blind testing and the result is depicted in Fig. 5. The coefficient of determination (R2 ) and the root mean square error (RMSE) of ANFIS predictions of the temporal series depicted in these figures in comparison to the complex GL model results are found out to be 1.00 and 3.21 × 10−5 respectively in the training phase, and 1.00 and 5.30 × 10−5 in the blind testing phase. In the frame of these findings, it is possible to state that both the spatial and the temporal dynamics of von Kármán vortices can be accurately predicted by ANFIS. The prediction time is limited to one time step in the current study, however it is possible to extend our findings for enhanced prediction times using downsampling techniques and/or other artificial intelligence techniques such as LSTM with no updates.

4 Conclusion In this paper, preliminary, the dynamics of von Kármán vortices were solved with the complex GL equation. ANFIS prediction capability of the dynamics of vortex street and shedding of the spatial and temporal series modeled in the frame of the complex GL equation are investigated. It is shown that vortex amplitudes in the spatial and temporal series as well as their dynamics can be predicted by ANFIS. Accordingly, it has been revealed that ANFIS can successfully predict such a complex event as a vortex street spatially even with limited data. The results of this study will contribute to related fields such as structural health monitoring and fluid dynamics, where flow-induced vibrations and sound can bring up challenging engineering problems. Our findings can also be extended for analysis of other vortex dynamics such as those observed in the BoseEinstein condensation. For future studies, the predictability of the dynamics of vortex

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streets by other soft computing and artificial intelligence techniques is planned to be investigated.

References 1. Sasaki, K., Suzuki, N., Saito, H.: Bénard-von kármán vortex street in a Bose-Einstein condensate. Phys. Rev. Lett. 104(15), 1–4 (2010). https://doi.org/10.1103/PhysRevLett.104. 150404 2. Kwon, W.J., Kim, J.H., Seo, S.W., Shin, Y.: Observation of von Kármán Vortex street in an atomic superfluid gas. Phys. Rev. Lett. 117(24), 245301 (2016). https://doi.org/10.1103/Phy sRevLett.117.245301 3. Fromm, J.E., Harlow, F.H.: Numerical solution of the problem of vortex street development. Phys. Fluids 6(7), 975–982 (1963). https://doi.org/10.1063/1.1706854 4. Pankanin, G.L., Kuli´nczak, A., Berli´nski, J.: Investigations of Karman vortex street using flow visualization and image processing. Sens. Actuators A Phys. 138(2), 366–375 (2007). https://doi.org/10.1016/j.sna.2007.05.005 5. Yan, L., Chang, X.-H., Wang, N.-H., Tian, R., Zhang, L.-P., Liu, W.: Computational analysis of fluid-structure interaction in case of fish swimming in the vortex street. J. Hydrodyn. 33(4), 747–762 (2021). https://doi.org/10.1007/s42241-021-0070-4 6. Rüttinger, S., Hoffmann, M., Schlüter, M.: Experimental analysis of a bubble wake influenced by a vortex street. Fluids 3(1), 8 (2018). https://doi.org/10.3390/fluids3010008 7. Wang, D.A., Chiu, C.Y., Pham, H.T.: Electromagnetic energy harvesting from vibrations induced by Kármán vortex street. Mechatronics 22(6), 746–756 (2012). https://doi.org/10. 1016/j.mechatronics.2012.03.005 8. Kumar, G., Jain, S., Singh, U.P.: Stock market forecasting using computational intelligence: a survey. Arch. Comput. Meth. Eng. 28(3), 1069–1101 (2020). https://doi.org/10.1007/s11 831-020-09413-5 9. Houssein, E.H., Emam, M.M., Ali, A.A., Suganthan, P.N.: Deep and machine learning techniques for medical imaging-based breast cancer: a comprehensive review. Exp. Syst. Appl. 167, 114161 (2021). https://doi.org/10.1016/j.eswa.2020.114161 10. Amin, I., Kumar Dubey, M.: An overview of soft computing techniques on review spam detection. In: 2021 2nd International Conference on Intelligent Engineering and Management, ICIEM-2021, pp. 91–96 (2021). https://doi.org/10.1109/ICIEM51511.2021.9445280 11. Akdemir, H., Alaybeyo˘glu, A., Mehr, A.D.: A new perspective to design phase of water supply systems from aspect of water demand using fuzzy automation. In: Kahraman, C., Cevik Onar, S., Oztaysi, B., Sari, I.U., Cebi, S., Tolga, A.C. (eds.) INFUS 2020. AISC, vol. 1197, pp. 1242–1249. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-51156-2_145 12. Bayındır, C., Namlı, B.: Efficient sensing of von Kármán vortices using compressive sensing. Comput. Fluids 226 (2021). https://doi.org/10.1016/j.compfluid.2021.104975 13. García-Morales, V., Krischer, K.: The complex Ginzburg-Landau equation: an introduction. Contemp. Phys. 53(2), 79–95 (2012). https://doi.org/10.1080/00107514.2011.642554 14. Bayındır, C.: Compressive split-step Fourier method. TWMS J. Appl. Eng. Math. 5(2), 298– 306 (2015) 15. Bayındır, C., Ozaydin, F.: Freezing optical rogue waves by Zeno dynamics. Opt. Commun. 413(2), 141–146 (2018) 16. Bayındır, C.: Self-localized solutions of the Kundu-Eckhaus equation in nonlinear waveguides. Results Phys. 14, 102362 (2019) 17. Bayındır, C.: Shapes and statistics of the rogue waves generated by chaotic ocean current. In: 26th International Ocean and Polar Engineering Conference (ISOPE), Rhodes, Greece (2016). arXiv preprint arXiv:1512.03584

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18. Dongare, A.D., Kharde, R.R., Kachare, A.D.: Introduction to artificial neural network (ANN) methods. Int. J. Eng. Innov. Technol. 2(1), 189–194 (2012). https://citeseerx.ist.psu.edu/vie wdoc/download?doi=10.1.1.1082.1323&rep=rep1&type=pdf 19. Zadeh, L.A.: Fuzzy logic. Computer 21(4), 83–93 (1988) 20. Kim, J., Kasabov, N.: HyFIS: adaptive neuro-fuzzy inference systems and their application to nonlinear dynamical systems. Neural Netw. 12(9), 1301–1319 (1999). https://doi.org/10. 1016/S0893-6080(99)00067-2

Two-Stage Rail Defect Classification Based on Fuzzy Measure and Convolutional Neural Networks Ilhan Aydın(B)

and Erhan Akın

Computer Engineering Department, Firat University, 23119 Elazig, Turkey {iaydin,eakin}@firat.edu.tr Abstract. Railway transportation has gained importance with the development of high-speed trains in recent years. Problems that occur especially on the rail surface and fasteners during railway operation affect the operating safety of the train. For this reason, it has gained importance to examine railway lines at certain intervals. In this study, a two-stage approach is proposed to detect defects on rail surfaces. In the first stage of the approximation, rail extraction is performed and the histogram of the rail surface image is modeled as a Gaussian function. In addition, the region that may be defective is modeled with a Gaussian membership function and the membership values of the pixels are calculated. According to the dependencies of the pixels, whether there is a rail surface defect is determined, and if there is a defect in the next step, the defect type is determined with the convolutional neural network model. The proposed method has been tested for different defect types and successful results have been obtained. Keywords: Fuzzy measurement · Image processing · Deep learning

1 Introduction In railway transportation, the rails are an important part of the railway, and their stability should be periodically inspected for railway working safety. With the increase in train speeds on railways, rail surface defects create traffic noise and cause serious accidents. In particular, rail surface defects that cannot be detected at an early stage can lead to more serious problems, causing trains to derail [1]. Rail surface defects occur in different types. These defects can be given as corrugation, rail collapse, flaking of the rail surface, and connection point problems [2]. Effective control for rail surface defects is essential for rail safety. The traditional method for detecting rail surface defects is to manually check the rail line at certain times with the human naked eyes. This approach is both timeconsuming and dependent on the experience of the controller. In addition, it is usually done at night because it occupies the train line, and false alarms are often generated due to human experience [3]. With the developments in information technologies, nondestructive analysis techniques have been used to determine rail defects. The spectrogram of the obtained signals was examined to determine the rail surface defects by acoustic signal measurement [4]. The principal component analysis extracts some features from the signals obtained with acoustic sensors placed at different points. Afterward, three types of rail surface defects were determined by evaluating the obtained © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 769–776, 2022. https://doi.org/10.1007/978-3-031-09173-5_88

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features with support vector machines [5]. Acoustic analysis is costly and needs to be placed at specific points on the rail to identify rail surface defects. Techniques using eddy currents for the detection of rail defects have also been proposed [6, 7]. However, this technique is not suitable for long-term use in outdoor environments and has only been tested in a laboratory environment. In recent years, with the developments in computer vision and deep learning, studies have been carried out to detect railway rail defects. The rail location was determined by edge extraction and then the defective regions were segmented by differential box-counting the and GrabCut method. Then, the locations of the defects were determined with the Yolov2 deep learning method. The features obtained from DenseNet and local binary patterning approaches were used to detect rail surface defects [8]. Aydin et al. [9] used the features obtained from the MobilenetV2 and SqueezeNet convolutional neural network models for the detection of rail surface defects and classified different rail defects. In the study, five different rail surface defects are detected. The method combining two deep methods is presented to detect rail surface defects in cases where there are not enough defective samples [10, 11]. The saliency detection [12], entropy and image processing [13], and morphology-based image processing [14] techniques have been proposed for the detection of rail surface defects. Determination of rail defects is an important task in the literature, and studies in this field have focused on the detection of defects. The proposed methods for determining the defect type are based on the combination of complex multiple deep learning methods. In addition, in some studies, healthy regions are determined as defects, and these noises are removed by morphological processes. In this study, a two-stage approach is presented for the detection and classification of rail surface defects. In the first stage, the histogram of the image representing the healthy rail surface is modeled with a Gaussian function, and the representing fuzzy membership function is created. In the same way, a fuzzy membership function is created for the defective region and the defects are segmented. If a defect is detected, the defect type is determined with a deep neural network in the second step. The advantages of the proposed method are given as follows. – Providing a real-time working method for defect detection, – Classification of different defect types by deep learning method, – Precise detection of defect regions with a noise-sensitive segmentation. The proposed approach combines fuzzy measurement, classical image processing, and deep learning to identify defect types. The approach offers high performance and real-time work for detecting and determining the type of defect.

2 The Proposed Approach for Two-Step Detection of Rail Surface Defects In this study, a two-stage method is presented for the detection of rail surface defects and the classification of the defect type. The proposed method for defect detection is based on fuzzy measurement-based background modeling. The background is modeled with a Gaussian function for the histogram obtained for the healthy rail. In addition, the

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region outside the background is modeled as a separate Gaussian function. Then, it is determined whether a pixel is defective or not, according to the membership function to which a pixel belongs. After the defect is detected, the defect type is classified by the MobileNetv2 convolutional neural network. The block diagram of the proposed algorithm is given in Fig. 1. Fuzzy membership construcon for healthy and defected parts

Convert RGB image to Grayscale

Membership Matrix Histogram calculaon Healthy rail image

Defect detecon by connected parts

800

A test image

700 600 500 400 300 200 100 0

50

100

150

200

250

Gaussian modelling

No

Transfer Learning Model Using MobilenetV2

Yes

Is a there a defect?

Defect classificaon

Fig. 1. The schematic diagram of the proposed method

In Fig. 1, the fuzzy measurement-based part is processed first to detect the surface defects. If the first module detects a defect, the trained deep neural network activates and determines the type of defect. 2.1 Fuzzy Measure Based Defect Detection For defect detection, firstly, the RGB image taken from the healthy rail is converted to a gray image. The gray histogram of the healthy image is then modeled as a Gaussian function. The Gaussian function is shown in the following Eq. (1). f (x, y) = √

2 y − (x−μ) e σ2 πσ

(1)

In the Gaussian function given in Eq. (1), the values of μ and σ show the mean and standard deviation values, respectively. The x and y values in Eq. (1) represent the input data and the amplitude of the data, respectively. In the histogram modeling, x and y values represent the pixel values and the occurrence frequency of each pixel value in the histogram, respectively. To model the histogram with the Gaussian function, the parameters μ and σ need to be estimated. The Nelder-Mead simplex method-based method was used for the estimation of these two parameters. This method uses n + 1

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points for an n-dimensional vector x. Initially, it starts with the lowest function value f(x1) and subtracts the worst value from the simplex, and adds a new point. It is started by giving the initial values for the amplitude, mean and standard deviation values of the Gaussian function, and then the optimum value is obtained. In Fig. 2, the Gaussian functions obtained for the solid and imperfect cases are given.

Fig. 2. The histogram modeling and membership construction

After obtaining the membership function representing the histogram for the healthy rail in Fig. 2, a membership function is created for the defective rail in the area outside the healthy histogram. In the next step, the membership function to which the pixel values of any test image belong is determined. Therefore, a pixel is labeled as a background or defect. Figure 3 represents the process of determining pixels as background or defect, depending on whether they belong to the membership function.

Fig. 3. The defect detection steps

In Fig. 3, membership values are calculated by first assigning the gray image matrix to two membership functions. Then, the membership values are determined by using the Gaussian fuzzy function, and a 3 × 3 filter is slid over the membership matrix to find the connected parts. If all pixels in the 3 × 3 neighborhood of a pixel belong to defect membership, it is labeled as a defect. Otherwise, the relevant pixel is taken as

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the background in the binary image. After the image is converted to a binary image, defective regions and their numbers are determined by blob analysis. The trained deep learning method is activated to determine the defect type if a defect is detected. 2.2 MobileNetv2 Based Classification of Defect Types After detecting the defect with fuzzy measurement, the transfer learning method is used to determine the type of defect. For this purpose, MobileNetvV2, a low-weight network, was used [15]. Although the MobileNetv2 model consists of 53 layers in total, it is preferred due to its low parameter number and high performance. Since this deep learning network uses depth-wise convolution layers and inverted residual blocks, the number of parameters is very low.

3 Experimental Results The proposed two-stage defect detection method was applied to a dataset containing one healthy and three defect types. In the data set, there are defects such as joint, light squat, and severe squat on the rail. Figure 4 represents examples for each class in the data set.

Fig. 4. Healthy and faulty images for each class

In Fig. 4, the solid, Joint, Light Squat and Severe Squat classes consist of 492, 408, 608, and 330 samples, respectively. Therefore, the dataset consists of 1838 samples. First, the Gaussian function, which models the solid rail, is obtained by taking a solid sample. The Gaussian function obtained is shown in Fig. 5.

Healthy rail image

Histogram and inial Gauss funcon

Opmized Gauss funcon

Fig. 5. The optimizing Gaussian function for modeling histogram

In Fig. 5, the Gaussian function is initialized with random parameters first, and then the mean and standard deviation parameters of the Gaussian function are optimized. The resulting Gaussian function is determined as a fuzzy membership function for the

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Gray image

Segmentation

Squat

Severe squat

Joint

Healthy

Gray image

Fig. 6. Fuzzy measure based defect detection

healthy state. A membership function for the defective state is then constructed in the remaining histogram space. In Fig. 6, the proposed fuzzy-based segmentation, and defect detection results for healthy and defective rail surfaces are given. Figure 6 shows how defects are detected on a sample for each defect. In Table 1, the number of samples that were found to be healthy and defective and the success rate for each class are given. Table 1. The defect detection performance. Class

Number of prediction Healthy

Healthy Light squat

Detection rate (%)

Defect

474

18

96.34

1

607

99.83

Joint

2

406

99.50

Severe squat

0

330

100.00

Overall detection rate

99.66

In Table 1, the average detection rate was 99.66%. The dataset contains different types of defects and a mask image was not created for the defects. The detection rate was based on the presence or absence of defective areas only. If a defect is detected on the surface, deep learning is activated to determine the type of defect. For this purpose, Table 2. The used parameters for MobilenetV2. Parameter

Value

Learning rate

0.001

Max epochs

20

Batch size

32

Validation frequency

20

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MobilenetV2 was used. The parameters of the network used are given in Table 2, the parameters used for training. According to the parameters given in Table 2, the MobileNetv2 network is trained and the defects are determined. The dataset is separated as 70% training and 30% validation. The accuracy and loss graphs for training and validation are given in Fig. 7.

Fig. 7. The training and loss graph for MobileNetV2

In Fig. 7, 95.46% validation accuracy was obtained. The performance of the proposed method was compared with other methods suggested in the literature and better results were obtained. Comparison results are given in Table 3. Table 3. The comparison results of the proposed method with other studies Ref

Method

# of classes

Accuracy rate (%)

[8]

Graph cut and faster RCNN

2

95.34

[9]

Image features + Deep feature extraction

4

93.80

[11]

Deep extractor

2

93.04

[12]

CNN + LST

2

94.27

Ours

Fuzzy measure based detection

4

99.66

MobileNetV2 based classification

95.46

In Table 3, instead of determining the type of defect in many studies, only whether there is a defect or not is determined. In this study, both defect detection and defect type were determined. The proposed method gives more accurate results than the literature.

4 Conclusions In this study, a two-stage approach is presented for the detection of defects on the rail surfaces and the recognition of the defect type. The proposed approach requires modeling the histogram of the healthy rail image as a Gaussian function to determine the defect type. After modeling, background and defective regions are obtained with fuzzy

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membership functions. If the fuzzy system detects a defect, MobileNetv2 determines the type of defect. The proposed approach was applied to a data set containing three different defects and successful results were obtained compared to the literature. Acknowledgments. This work was supported by the TUBITAK (The Scientific and Technological Research Council of Turkey) under Grant No: 120E097.

References 1. Tu, Z., Wu, S., Kang, G., Lin, J.: Real-time defect detection of track components: considering class imbalance and subtle difference between classes. IEEE Trans. Instrum. Measure. 70, 1–12 (2021) 2. Gan, J., Wang, J., Yu, H., Li, Q., Shi, Z.: Online rail surface inspection utilizing spatial consistency and continuity. IEEE Trans. Syst. Man Cybern. Syst. 50(7), 2741–2751 (2018) 3. Yu, H., et al.: A coarse-to-fine model for rail surface defect detection. IEEE Trans. Instrum. Measure. 68(3), 656–666 (2018) 4. Pieringer, A., Stangl, M., Rothhämel, J., Tielkes, T.: Acoustic monitoring of rail faults in the German railway network. In: Degrande, G., et al. (eds.) Noise and Vibration Mitigation for Rail Transportation Systems. NNFMMD, vol. 150, pp. 242–250. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-70289-2_24 5. Deng, F., Li, S.Q., Zhang, X.R., Zhao, L., Huang, J.B., Zhou, C.: An intelligence method for recognizing multiple defects in rail. Sensors 21(23), 8108 (2021) 6. Rajamäki, J., Vippola, M., Nurmikolu, A., Viitala, T.: Limitations of eddy current inspection in railway rail evaluation. Proc. Inst. Mech. Eng. Part F J. Rail Rapid Transit 232(1), 121–129 (2018) 7. Park, J.W., et al.: Rail surface defect detection and analysis using multi-channel Eddy current method based algorithm for defect evaluation. J. Nondestr. Eval. 40(3), 1–12 (2021). https:// doi.org/10.1007/s10921-021-00810-9 8. Yang, H., Wang, Y., Hu, J., He, J., Yao, Z., Bi, Q.: Deep learning and machine vision-based inspection of rail surface defects. IEEE Trans. Instrum. Meas. 71, 1–14 (2021) 9. Aydin, I., Akin, E., Karakose, M.: Defect classification is based on deep features for railway tracks in sustainable transportation. Appl. Soft Comput. 111, 107706 (2021) 10. Zhang, Z., Liang, M., Wang, Z.: A deep extractor for visual rail surface inspection. IEEE Access 9, 21798–21809 (2021) 11. Zhang, D., Song, K., Wang, Q., He, Y., Wen, X., Yan, Y.: Two deep learning networks for rail surface defect inspection of limited samples with line-level labels. IEEE Trans. Industr. Inf. 17(10), 6731–6741 (2020) 12. Niu, M., Song, K., Huang, L., Wang, Q., Yan, Y., Meng, Q.: Unsupervised saliency detection of rail surface defects using stereoscopic images. IEEE Trans. Industr. Inf. 17(3), 2271–2281 (2020) 13. Franca, A.S., Vassallo, R.F.: A method of classifying railway sleepers and surface defects in real environments. IEEE Sens. J. 21(10), 11301–11309 (2020) 14. Nieniewski, M.: Morphological detection and extraction of rail surface defects. IEEE Trans. Instrum. Meas. 69(9), 6870–6879 (2020) 15. Sandler, M., Howard, A., Zhu, M., Zhmoginov, A., Chen, L. C.: MobileNetV2: inverted residuals and linear bottlenecks. In: Proceedings of the conference on computer vision and pattern recognition, pp. 4510–4520. IEEE, Salt Lake City, Utah (2018)

Optimal Gene Selection and Classification of Microarray Data Using Fuzzy Min-Max Neural Network with LASSO Yashpal Singh and Seba Susan(B) Department of Information Technology, Delhi Technological University, Delhi, India [email protected]

Abstract. Microarray gene expression data is a small sample high-dimensional dataset in which each sample is attributed with thousands of genes. The gene expression dataset is therefore very hard to classify because we have to consider thousands of genes for each sample while training the dataset. In this paper, we propose to classify the lung cancer microarray gene expression data using the Fuzzy Min-Max (FMM) classifier that is seldom used for high-dimensional datasets due to the large computational overhead. To improve the accuracy and speed of the FMM classifier, we use Least Absolute Shrinkage and Selection Operator (LASSO) to select the optimal gene subset for classification of lung cancer. We compare the classification performance of FMM-LASSO with that of support vector machine (SVM), Random Forest, K-nearest Neighbor (KNN), Naïve Bayes and Logistic Regression classifiers, with and without LASSO. The results prove that FMM-LASSO performs better as compared to other approaches. Keywords: Microarray data · Gene expression · Lung Cancer · Fuzzy Min-Max neural network · LASSO

1 Introduction DNA microarrays are gene chips printed with microscopic spots in defined positions. These spots contain a known DNA sequence that can be used for the analysis of gene expression. With the help of microarrays, we can analyze different types of genes simultaneously [1]. Recently, many microarray gene expression datasets have become publicly available on the internet. There are many challenges we have to face when we are using microarray datasets, like having thousands of genes in each sample, and relatively smaller number of samples in the dataset. We also have to handle the noisiness of gene expression data [2]. A cancer diagnosis is difficult to achieve for various reasons, but recent studies have shown that the diagnosis becomes easy when it is achieved by classifying microarray gene expression data. There are many related works proposed since the early 2000s that rely on microarray data for cancer classification and gene function prediction [3]. BenDor et al. [4] performed classification on colon and ovarian cancer dataset in which they © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 777–784, 2022. https://doi.org/10.1007/978-3-031-09173-5_89

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used an unsupervised clustering algorithm, and for correlating with the cancer classes they have used supervised learning. But it is very challenging to perform classification on microarray data because each sample is attributed with thousands of genes to consider and evaluate. Most of the genes are irrelevant or redundant as asserted in a recent survey paper [5]. So in our work, we will address the issue on how to handle gene expression data by performing normalization and feature selection in order to get more accurate results. Specifically, we use Least Absolute Shrinkage and Selection Operator (LASSO) as the feature selection technique. We propose the application of the Fuzzy Min-Max (FMM) neural network classifier for the classification of the lung cancer dataset using an optimal gene subset constructed using LASSO. The rest of this paper is organized as follows. Section 2 presents a brief review of related works in literature, while Sect. 3 describes the methodology used for the classification of lung cancer using the FMM classifier and LASSO. In Sect. 4, we show a comparison of different classification approaches used on the lung cancer dataset, and in Sect. 5, we conclude our paper.

2 Background Different approaches have been followed for the classification of lung cancer. Kuruvilla et al. [6] used computed tomography (CT) images of lungs for the classification of cancer. Microarray gene expression data facilitates highly efficient cancer diagnosis [5]. Most of the related research involve some form of feature selection for selecting the most informative genes for cancer diagnosis, such as [7] that makes use of the Particle Swarm Optimization algorithm in a fuzzy multi-objective framework. Hu et al. [8] compared five classification approaches on seven different microarray cancer datasets with and without gene selection; they proved that data preprocessing improves the classification accuracy. Lee et al. [9] compared different feature selection methods for different microarray datasets. A fuzzy rough quick reduct method was proposed in [10] to find the most informative genes using a similarity measure for the classification of lung cancer. Fuzzy classifiers have proved to perform well in the past due to the computation of fuzzy decision boundaries for classifying the difficult-to-classify samples [11, 12]. A simple fuzzy system was devised in [13] for classifying tumors. In this paper, we propose a Fuzzy Min-Max (FMM) neural network for the classification of the microarray gene expression data for lung cancer diagnosis. We used LASSO feature selection technique for extracting the important features (i.e. genes) [14], prior to classification. LASSO automatically selects those genes which are useful for the lung cancer classification, and discards the redundant genes. LASSO has proved to be very effective for highdimensional datasets [15–17], and hence is deemed suitable for the microarray gene expression dataset where each sample is represented by thousands of genes.

3 Methods and Implementation In this section, we give an explanation about the methods and the implementation details used in our experiment. Firstly, we explain the feature selection process, then the FMM classifier, and in the end, the methodology is explained.

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3.1 Feature Selection As we know, in microarray data, a large number of features (i.e. genes) are present, and not all these genes are relevant for the cancer classification task. So, with the help of feature selection, we shortlist all those genes which make an impact on cancer classification. We have used LASSO for feature selection [14]. LASSO has been proved to provide a skewed feature subset that leads to good classifications scores, in the shortest possible time [17]. Basically, LASSO regression is used to minimize the cost function, so for achieving this aim LASSO will reduce the coefficient values of all features. In this way, LASSO will make the coefficient value equal to zero for those features which are useless and unwanted [18]. So, the main idea is we fit LASSO regression on a scaled version of our cancer dataset, and select only those features which do not have coefficient value equal to 0. Then we used all these selected features called the optimal gene subset for the classification task. 3.2 FMM Classifier The Fuzzy Min-Max (FMM) neural network was proposed as a classifier by Simpson in 1992 [19]. It stands apart from all the other classifiers it has the ability to learn from a single pass through the data by constructing fuzzy hyperboxes for different input patterns [20, 21]. Simpson [19] proved that the FMM classifier performs better in case of overlapping classes by finding rational decision boundaries. In general, in FMM classification, the training set F contains N ordered pairs {Ih , ch }, where Ih = (ih1 , ih2 , . . . ., ihn ) ∈ I n is the input string and ch ∈ {1, 2, . . . , m} is the index of one of the m classes. The learning process starts with selecting an ordered pair from the set F and finding a hyperbox for the same class (if present). If no hyperbox is found for an ordered pair, then one is created and added to the neural network. The FMM classification learning process has three phases: 1. Hyperbox Expansion: For a given ordered pair {Ih , ch } ∈ F, the aim is to find a hyperbox Bj which provides the highest degree of membership, and can be expanded to include the input pattern. There is a hyperparameter 0 ≤ ϑ ≤ 1 which bounds the size of the hyperbox. For expanding the hyperbox Bj to includeIh , these are the conditions that have to met: n      max wjk , ihk − min vjk, ihk (1) nϑ ≥ k=1

If the inequality in (1) gets satisfied, we expand the hyperbox Bj , and the min and max points of the hyperbox are updated as per (2) and (3), respectively.   new old ∀k = 1, 2, ..., n (2) vjk = min vjk , ihk   new old wjk ∀k = 1, 2, ..., n = max wjk , ihk

(3)

2. Hyperbox Overlap Test: After successful hyperbox expansion, we move to the next step which is hyperbox overlap test. Expansion of the hyperbox may create an overlap

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with other hyperboxes. Overlapping of two hyperboxes creates a problem only if the other hyperbox is from a different class. A dimension-by-dimension comparison between hyperboxes is performed for determining whether an expansion creates an overlap or not. 3. Hyperbox contraction: After the testing, we obtain the dimension where the overlap is minimal between two hyperboxes belonging to different classes. Now we contract the expanded box in such a way that the contraction size is as small as possible and the overlap is removed. 3.3 Methodology In our experiments, we are performing lung cancer classification using microarray gene expression data for six different classification methods (FMM, support vector machine (SVM), Random Forest, K-nearest Neighbor (KNN), Naïve Bayes and Logistic Regression classifiers). Figure 1 shows the process flow for the learning process.

Fig. 1. Process flow for the learning process averaged over multiple runs

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Five-fold cross-validation is used for different choices of train and test sets, as shown in Fig. 1, keeping the train-test split ratio as 70:30 in each run. All the classifiers are trained on both the original gene set and the optimal gene subset constructed by LASSO. Table 1 shows the hyperparameters of all the classifiers which are used in our experiments. Table 1. Hyperparameters of all the classification methods. Classifier

Hyperparameter

Values

Fuzzy Min-Max (FMM) Classifier [19]

Hyper box coefficient (ϑ) Sensitivity (ω)

0.7 1 [0.0018 with LASSO]

Support vector Machine (SVM) [22]

Regularization parameter (c), Gamma

1 [0.126 with LASSO]

K-Nearest Neighbor [23]

No. of neighbors

7

Logistic Regression [24]

C Penalty Solver

1 l2 lbfgs

Naïve Bayes [25]

Var_smoothing

1e−9

Random Forest [26]

N_estimators Max_depth

100 2

4 Results 4.1 Experimental Setup The experiments were performed on Jupyter notebook version 4.4.0 on a 2.00 GHz Intel core™ i3 PC. The device specifications are: Processor: Intel® Core™ i3-5005U CPU @2.00 GHz, Memory: RAM 8.00 GB DDR3L, System type: 64-bit Operating System, x64-based processor, Graphics Card: AMD Radeon™ R5 M430 2GB. 4.2 Dataset We perform all the classification experiments on the microarray lung cancer dataset sourced from the Dana-Farber Cancer Institute; this dataset contains 203 samples characterized by 12600 genes [27]. There are five types of classes with an unbalanced class distribution. We have used random 70:30 train and test split with five-fold cross validation. Among the 12,600 genes only a few of them make an impact on the classification, and the rest are either irrelevant or redundant. LASSO extracted 176 genes out of 12600 which are important for the classification task; we call this subset of selected genes as the optimal gene subset. If we use these extracted genes for the classification task, the whole process becomes faster and accuracy is also improved.

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4.3 Result Analysis Table 2 compares the test accuracies and F1-scores of all the six classifiers used in our experiment, with and without feature selection using LASSO. The classes in the dataset are unbalanced, so we conducted the F1-score test for all the classifiers. The proposed combination of FMM classifier with LASSO performs the best as compared to all other methods with 95.08% accuracy and the highest F1-score of 0.92. After analyzing the classification scores, we note that the FMM classifier performs best with LASSO feature selection and SVM performs better in the case of without feature selection. In Table 3, we have shown the comparison of execution times for all six classifiers (with and without LASSO), and we observe that FMM takes more time to execute as compared to the other classifiers. LASSO make a major impact, since we note that the accuracies are comparatively very less without LASSO, and the same observation is made for F1-score and the execution time. The execution time is drastically reduced for the FMM classifier when LASSO feature selection is used. Table 2. Test accuracy and F1-score for lung cancer classification using different methods. (LASSO – optimal gene subset; w/o LASSO – original gene set). Classifiers

Test accuracy

F1-score

LASSO

w/o LASSO

LASSO

w/o LASSO

Fuzzy Min-Max Classifier

95.08%

89.5%

0.92

0.70

SVM

94.09%

92.45%

0.86

0.83

K-Nearest Neighbor

93.77%

89.18%

0.77

0.63

Random Forest

83.31%

80.32%

0.55

0.51

Logistic Regression

92.13%

90.81%

0.86

0.78

Naïve Bayes

92.78%

89.18%

0.73

0.70

Table 3. Execution time of classifiers (in seconds) (LASSO – optimal gene subset; w/o LASSO – original gene set). Classifiers

LASSO

w/o LASSO

Fuzzy Min-Max Classifier

13.77

963.31

SVM

0.40

17.74

K-Nearest Neighbor

0.37

0.37

Random Forest

1.98

2.90

Logistic Regression

0.66

8.51

Naïve Bayes

0.32

1.39

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5 Conclusion and Future Work In this paper, a novel combination of Fuzzy Min-Max (FMM) classifier with LASSO is proposed for the classification of the lung cancer microarray dataset that is characterized by small number of samples and high dimensions. Significant gene features are ranked and selected using LASSO, which reduces the dimensionality of the dataset and also maintains the informative genes. We compare the results with other classifiers, and the proposed method gives the highest scores in terms of accuracy and F1-score. Computationally faster architectures of FMM would be further explored in our future work to make the automated cancer diagnosis system more efficient in terms of both execution time and accuracy. Enhanced FMM neural networks with enhanced learning algorithms such as in [28] would be explored in the next stage of our work for the classification of the gene expression data for cancer diagnosis.

References 1. Schena, M., Shalon, D., Davis, R.W., Brown, P.O.: Quantitative monitoring of gene expression patterns with a complementary DNA microarray. Science 270(5235), 467–470 (1995) 2. John, Q.: Computational analysis of microarray data. Nat. Rev.Ggenet. 2(6), 418–427 (2001). (Author, F., Author, S., Author, T.: Book title. 2nd edn. Publisher, Location (1999)) 3. Brazma, A., Vilo, J.: Gene expression data analysis. FEBS Lett. 480(1), 17–24 (2000) 4. Ben-Dor, A., Bruhn, L., Friedman, N., Nachman, I., Schummer, M., Yakhini, Z.: The Fourth Annual International Conference on Computational Molecular Biology RECOMB-2000, pp. 54–64. ACM Press, Tokyo (2000) 5. Abd-Elnaby, M., Alfonse, M., Roushdy, M.: Classification of breast cancer using microarray gene expression data: a survey. J. Biomed. Inform. 117, 103764 (2021) 6. Jinsa, K., Gunavathi, K.: Lung cancer classification using neural networks for CT images. Comput. Methods Programs. Biomed. 113(1), 202–209 (2014) 7. Saleh, S., Rahideh, A., Helfroush, M.S., Kazemi, K.: Gene selection from large-scale gene expression data based on fuzzy interactive multi-objective binary optimization for medical diagnosis. Biocybern. Biomed. Eng. 38(2), 313–328 (2018) 8. Hong, H., Li, J., Plank, A., Wang, H., Daggard, G.: A comparative study of classification methods for microarray data analysis. In: Proceedings of the 5th Australasian Data Mining Conference (AusDM 2006): Data Mining and Analytics 2006, pp. 33–37. ACS Press (2006) 9. Won, L.J., Lee, J.B., Park, M., Song, S.H.: An extensive comparison of recent classification tools applied to microarray data. Comput. Statist. Data Anal. 48(4), 869–885 (2005) 10. Arunkumar, C., Ramakrishnan, S.: Attribute selection using fuzzy roughset based customized similarity measure for lung cancer microarray gene expression data. Future Comput. Inf. J. 3(1), 131–142 (2018) 11. Seba, S., Sharma, S.: A fuzzy nearest neighbor classifier for speaker identification. In: 2012 Fourth International Conference on Computational Intelligence and Communication Networks, pp. 842–845. IEEE (2012) 12. Seba, S., Chandna, S.: Object recognition from color images by fuzzy classification of gabor wavelet features. In: 2013 5th International Conference and Computational Intelligence and Communication Networks, pp. 301–305. IEEE (2013) 13. Ohno-Machado, L., Vinterbo, S., Weber, G.: Classification of gene expression data using fuzzy logic. J. Intell. Fuzzy Syst. 12(1), 19–24 (2002)

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14. Tibshirani, R.: Regression shrinkage and selection via the lasso. J. Roy. Stat. Soc.: Ser. B (Methodol.) 58(1), 267–288 (1996) 15. Zena, M.H., Gillies, D.F.: A review of feature selection and feature extraction methods applied on microarray data. Adv. Bioinform. 2015, 1–13 (2015) 16. Kıvanç, G., Cantürk, I., Özyilmaz, L.: Dna microarray gene expression data classification using SVM, MLP, and RF with feature selection methods relief and LASSO. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 23(1), 126–132 (2019) 17. Susan, S., Hanmandlu, M.: Smaller feature subset selection for real-world datasets using a new mutual information with Gaussian gain. Multidimension. Syst. Signal Process. 30(3), 1469–1488 (2018). https://doi.org/10.1007/s11045-018-0612-2 18. Kang, C., Huo, Y., Xin, L., Tian, B., Bin, Y.: Feature selection and tumor classification for microarray data using relaxed Lasso and generalized multi-class support vector machine. J. Theor. Biol. 463, 77–91 (2019) 19. Simpson, P.K.: Fuzzy Min—MaX Neural NetWorks—part 1: classification. IEEE Trans. on Neural Networks 3(5), 776–786 (1992) 20. Seba, S., Khowal, S.K., Kumar, A., Kumar, A., Yadav, A.S.: Fuzzy min-max neural networks for business intelligence. In: 2013 International Symposium on Computational and Business Intelligence, pp. 115–118. IEEE (2013) 21. Zhang, H., Liu, J., Ma, D., Wang, Z.: Data-core-based fuzzy min–max neural network for pattern classification. IEEE Trans. Neural Networks 22(12), 2339–2352 (2011) 22. Vladimir, V.: The Nature of Statistical Learning Theory. Springer Science & Business Media (1999). https://doi.org/10.1007/978-1-4757-2440-0 23. Guo, G., Wang, H., Bell, D., Bi, Y., Greer, K.: KNN model-based approach in classification. In: Meersman, R., Tari, Z., Schmidt, D.C. (eds.) OTM 2003. LNCS, vol. 2888, pp. 986–996. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-39964-3_62 24. Joanne, P.C.-Y., Lee, K.L., Ingersoll, G.M.: An introduction to logistic regression analysis and reporting. J. Educ. Res. 96(1), 3–14 (2002) 25. Wickramasinghe, I., Kalutarage, H.: Naive Bayes: applications, variations and vulnerabilities: a review of literature with code snippets for implementation. Soft. Comput. 25(3), 2277–2293 (2020). https://doi.org/10.1007/s00500-020-05297-6 26. Breiman, L.: Random forests. Mach. Learn. 45(1), 5–32 (2001) 27. Arindam, B., et al.: “Classification of human lung carcinomas by mRNA expression profiling reveals distinct adenocarcinoma subclasses. Proc. National Acad. Sci. 98(24), 13790–13795 (2001) 28. Falah, M.M., Lim, C.P.: An enhanced fuzzy min–max neural network for pattern classification. IEEE Trans. Neural Networks Learn. Syst. 26(3), 417–429 (2014)

Interval Type-3 Fuzzy Aggregators for Ensembles of Neural Networks in Time Series Prediction Oscar Castillo(B)

, Martha Pulido , and Patricia Melin

Tijuana Institute of Technology, Tijuana, Mexico {ocastillo,pmelin}@tectijuana.mx, [email protected]

Abstract. In this article we are presenting an approach for fuzzy aggregation in ensembles of neural networks for forecasting. The aggregator in an ensemble is used to combine the outputs of the networks forming the ensemble, in such a way that the total output is better than the outputs of the individual modules. In our approach a fuzzy system is used to estimate the weights that will be assigned to the outputs in the process of combining them in a weighted average calculation. The uncertainty in the process of aggregation is modeled with interval type-3 fuzzy, which in theory can outperform type-2 and type-1. Results of the Dow Jones time series show the potential of the approach to outperform other aggregators. Keywords: Interval type-3 fuzzy logic · Aggregation · Time series prediction

1 Introduction Fuzzy logic has become very important in different disciplines of study, one of the areas in which we focus for this work is the control area, it has been shown in the literature that the use of fuzzy logic helps in the optimization of problems of control [1]. Type-1 fuzzy systems evolved to type-2 fuzzy systems with the works by Mendel in 2001 [2]. Initially, interval type-2 fuzzy systems were studied and applied to several problems [3]. These systems were applied to many problems in areas such as: robotics, intelligent control and others [4, 5]. Simulation and experimental results show that interval type-2 outperform type-1 fuzzy systems in situations with higher levels of noise, dynamic environments or highly nonlinear problems [6–8]. Later, general type-2 fuzzy systems were considered to manage higher levels of uncertainty, and good results have been achieved in several areas of application [9–11]. Recently, it is becoming apparent that type-3 fuzzy systems could help solve even more complex problems. For this reason, in this paper we are putting forward the basic constructs of type-3 fuzzy systems by extending the ideas of type-2 fuzzy systems [12–14]. The key contribution is the proposal of mathematical definitions of interval type-3 fuzzy theory, which were obtained by using the extension principle on the type-2 fuzzy sets definitions. In addition, interval type-3 fuzzy in aggregation of ensemble outputs for © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 785–793, 2022. https://doi.org/10.1007/978-3-031-09173-5_90

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prediction has not been presented before in the literature, and it is shown that interval type-3 has the potential to be better. We consider that these are important contributions to the frontier knowledge in soft computing. The structure of this article is defined as: Sect. 2 introduces basic terminology of interval type-3 fuzzy sets, Sect. 3 outlines the proposed type-3 prediction method, Sect. 4 summarizes the results, and Sect. 5 outlines the conclusions and future works.

2 Interval Type-3 Fuzzy Logic Interval type-3 can be viewed as an extension of type-2 models. We offer basic terminology of interval type-3 fuzzy sets to give an idea of the difference with respect to their type-2 counterparts. Definition 1. A type-3 fuzzy set (T3 FS) [15, 16], denoted by A(3) , is represented by the plot of a trivariate function, called membership function (MF) of A(3) , in the Cartesian product X × [0, 1] × [0, 1] in [0, 1], where X is the universe of the primary variable of A(3) , x. The MF of µA(3) is formulated by µA(3) (x, u, v) (or µA(3) for short) and it is called a type-3 membership function (T3 MF) of the T3 FS, µA(3) : X × [0, 1] × [0, 1] → [0, 1] A(3) =

   x, u(x), v(x, u), µA(3) (x, u, v) |x ∈ X , u ∈ U ⊆ [0, 1], v ∈ V ⊆ [0, 1] (1)

where U is the universe for the secondary variable u and V is the universe for tertiary variable v. If the tertiary MF is uniformily equal to 1 then we have an Interval type-3 fuzzy set (IT3 FS) with interval type-3 MF (IT3MF). ∼ Figure 1 illustrates and IT3 FS with IT3MF µ (x, u), where µ(x, u) is the LMF and 

_

µ(x, u) is the UMF. The embedded secondary T1 MFs in x of A and A are f x (u) and _

f x (u).

∼

Fig. 1. Fuzzy set with an IT3 MF µ (x, u)

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3 Proposed Method The method consists of utilizing an ensemble of two neural networks and then combine their outputs with a weighted average in which the weights are computed with an interval type-3 fuzzy system. The fuzzy rules for aggregating the results with two modules are: 1. 2. 3. 4. 5. 6. 7. 8. 9.

If (e1 If (e1 If (e1 If (e1 If (e1 If (e1 If (e1 If (e1 If (e1

is small) and (e2 is small), then (w1 is high)(w2 is high). is small) and (e2 is medium), then (w1 is high)(w2 is medium). is small) and (e2 is high), then (w1 is high)(w2 is low). is medium) and (e2 is small), then (w1 is medium)(w2 is high). is medium) and (e2 is medium), then (w1 is medium)(w2 is medium). is medium) and (e2 is high), then (w1 is medium)(w2 is low). is high) and (e2 is small), then (w1 is low)(w2 is high). is high) and (e2 is medium), then (w1 is low)(w2 is medium). is high) and (e2 is high), then (w1 is low)(w2 is low).

The interval type-3 system (seen in Fig. 2) has as inputs the error values of each neural network, e1 and e2 , respectively. In this case, the errors have been granulated with three terms and the rules reflect that when error is small the weight is higher. After the defuzzification, the Type-3 system has as outputs the corresponding weights (w1 and w2 ) for each neural network according to its prediction errors to obtain a final prediction P (combining P1 and P2 , the prediction of the neural networks) given by: P=

w1 P1 + w2 P2 w1 + w2

Fig. 2. Interval type-3 system to compute the weights

(2)

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In Figs. 3 and 4 we show the input MFs for both errors, respectively. In Figs. 5 and 6 we illustrate the output MFs for both weights, respectively.

Fig. 3. MFs of input e1

Fig. 4. MFs of input e2

Interval Type-3 Fuzzy Aggregators for Ensembles

Fig. 5. MFs of output w1

Fig. 6. MFs of output w2

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Fig. 7. Nonlinear surface representing the fuzzy model

In Fig. 7 we show two views of the nonlinear surface representing the fuzzy model. In Fig. 8 we illustrate the computation for a particular value of one of the inputs, showing the inference and then type-reduction and defuzzification.

1 0.9 0.8 0.7

B

(y)

0.6 0.5 0.4 0.3 0.2 0.1 0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

y

Fig. 8. Surfaces representing the interval type-3 fuzzy model

4 Simulation Results Table 1 summarizes the resulting errors of training the two modules of the ensemble (e1 and e2 ) and the corresponding weights obtained by the interval type-3 system of the previous section. In Table 2 we illustrate the results of combining the predicted values of modules with the weighted average equations using the weights produced by the fuzzy system. The modules of the neural network were trained with the Dow Jones time series from January of 2020 to 2022, and the last 15 days are used for testing (shown in Table 2) and comparing with the real values. Recurrent neural networks were used, with three delays, 300 epochs of training, and backpropagation with momentum learning and adaptive learning rate. There are 3 layers in each of the networks.

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Table 1. Results of the modules of ensemble and the weights from the IT3 fuzzy system

DowJones

e1

e2

w1

w2

0.2385

0.7615

0.6126

0.4039

Table 2. Results of the prediction with weighted average and comparison with real values P1

P2

Weighted average

Real

36059.9347

35175.3895

35708.4661

36231.53

36030.7713

35149.4544

35680.5855

36067.75

35943.6384

35024.5185

35578.4318

36251.7

36013.2786

35140.6072

35666.528

36290.71

36059.8116

35190.2179

35714.2839

36114.94

35974.6501

35063.2385

35612.5064

35911.28

35834.1682

34881.356

35455.5741

35369.39

35464.4451

34397.7438

35040.5979

35029.17

35111.1058

34004.3777

34671.3542

34714.14

34786.2538

33645.8939

34333.1388

34265.5

34322.6213

33141.6617

33853.3743

34366.67

34291.048

33166.3647

33844.162

34296.74

34253.4593

33110.0748

33799.1426

34166.84

34113.8333

32962.433

33656.3315

34160.51

34069.9295

32931.3725

33617.5309

34396.39

5 Conclusions In this article a new approach for fuzzy aggregation in ensembles of neural networks has been outlined. The aggregator in an ensemble is used to combine the outputs of the networks forming the ensemble, in such a way that the total output is better than the outputs of the individual modules. In our approach a fuzzy system is used to estimate the weights that will be assigned to the outputs in the process of combining them in a weighted average calculation. The uncertainty in the process of aggregation is modeled with interval type-3. Results show the potential of the approach to outperform other methods. As future work we plan to use our approach in other applications, like in [18– 21]. Also, we plan to optimize the type-3 system with metaheuristics for improving the results. Finally, we plan to combine type-3 with other intelligent techniques for build strong hybrid models.

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References 1. Zadeh, L.A.: Knowledge representation in Fuzzy Logic. IEEE Trans. Knowl. Data Eng. 1, 89 (1989) 2. Novák, V.: Fuzzy logic. In: Smets, P. (ed.) Quantified Representation of Uncertainty and Imprecision. HDRUMS, vol. 1, pp. 75–109. Springer, Dordrecht (1998). https://doi.org/10. 1007/978-94-017-1735-9_3 3. Mendel, J.M.: Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions. Prentice-Hall, Upper-Saddle River, NJ (2001) 4. Mendel, J.M.: Uncertain Rule-Based Fuzzy Systems: Introduction and New Directions, 2nd Edition. Springer International Publishing, Cham (2017). https://doi.org/10.1007/978-3-31951370-6 5. Karnik, N.N., Mendel, J.M.: Operations on type-2 fuzzy sets. Fuzzy Sets Syst. 122(2), 327– 348 (2001). https://doi.org/10.1016/S0165-0114(00)00079-8 6. Moreno, J.E., et al.: Design of an interval Type-2 fuzzy model with justifiable uncertainty. Inf. Sci. 513, 206–221 (2020) 7. Mendel, J.M., Hagras, H., Tan, W.-W., Melek, W.W., Ying, H.: Introduction to Type-2 Fuzzy Logic Control. Wiley and IEEE Press, Hoboken (2014) 8. Olivas, F., Valdez, F., Castillo, O., Melin, P.: Dynamic parameter adaptation in particle swarm optimization using interval type-2 fuzzy logic. Soft. Comput. 20(3), 1057–1070 (2014). https://doi.org/10.1007/s00500-014-1567-3 9. Sakalli, A., Kumbasar, T., Mendel, J.M.: Towards systematic design of general type-2 fuzzy logic controllers: analysis, interpretation, and tuning. IEEE Trans. Fuzzy Syst. 29(2), 226–239 (2021) 10. Ontiveros, E., Melin, P., Castillo, O.: High order α-planes integration: a new approach to computational cost reduction of general type-2 fuzzy systems. Eng. Appl. Artif. Intell. 74, 186–197 (2018) 11. Castillo, O., Amador-Angulo, L.: A generalized type-2 fuzzy logic approach for dynamic parameter adaptation in bee colony optimization applied to fuzzy controller design. Inf. Sci. 460–461, 476–496 (2018) 12. Cao, Y., Raise, A., Mohammadzadeh, A., et al.: Deep learned recurrent type-3 fuzzy system: Application for renewable energy modeling/prediction. Energy Reports 7, 8115–8127 (2021) 13. Mohammadzadeh, A., Castillo, O., Band, S.S., Mosavi, A.: A novel fractional-order multiplemodel type-3 fuzzy control for nonlinear systems with unmodeled dynamics. Int. J. Fuzzy Syst. 23(6), 1633–1651 (2021). https://doi.org/10.1007/s40815-021-01058-1 14. Qasem, S.N., Ahmadian, A., Mohammadzadeh, A., Rathinasamy, S., Pahlevanzadeh, B.: A type-3 logic fuzzy system: optimized by a correntropy based Kalman filter with adaptive fuzzy kernel size Inform. Sci. 572, 424–443 (2021) 15. Rickard, J.T., Aisbett, J., Gibbon, G.: Fuzzy subsethood for fuzzy sets of type-2 and generalized type-n. IEEE Trans. Fuzzy Syst. 17(1), 50–60 (2009) 16. Mohammadzadeh, A., Sabzalian, M.H., Zhang, W.: An interval type-3 fuzzy system and a new online fractional-order learning algorithm: theory and practice. IEEE Trans. Fuzzy Syst. 28(9), 1940–1950 (2020) 17. Cervantes, L., Castillo, O.: Type-2 fuzzy logic aggregation of multiple fuzzy controllers for airplane flight control. Inf. Sci. 324, 247–256 (2015) 18. Melin, P., Castillo, O.: An intelligent hybrid approach for industrial quality control combining neural networks, fuzzy logic and fractal theory. Inf. Sci. 177, 1543–1557 (2007)

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19. Castillo, O., Castro, J.R., Melin, P., Rodriguez-Diaz, A.: Application of interval type-2 fuzzy neural networks in non-linear identification and time series prediction. Soft. Comput. 18(6), 1213–1224 (2013). https://doi.org/10.1007/s00500-013-1139-y 20. Rubio, E., Castillo, O., Valdez, F., Melin, P., Gonzalez, C.I., Martinez, G.: An extension of the fuzzy possibilistic clustering algorithm using type-2 fuzzy logic techniques. Adv. Fuzzy Syst. (2017). https://doi.org/10.1155/2017/7094046

Brain Signal Classification Using Self-tuning Assisted Fuzzy Structure Uncertain Indirect Observer Shahnaz TayebiHaghighi, Young-Doo Lee, and Insoo Koo(B) Department of Electrical, Electronics and Computer Engineering, University of Ulsan, Ulsan, South Korea [email protected], [email protected]

Abstract. Sleep staging is a critical step that can help to identify sleep disturbances. Recently, sleep stages classification is accomplished a serious issue in preserving people’s lives. Tiredness and drowsiness in driving can endanger the lives of many people in vehicle accidents. Thus, identifying sleep disorders, which include the identification and classification of various sleep stages is an important subject. Biomedical signals such as an electroencephalogram (EEG) are used to recognize sleep disorders. In this research, a self-tuning indirect estimation approach along with a nonlinear modeling technique is proposed for brain signal classification with high accuracy. This proposed approach consists of five steps. In the first stage, the brain signals are resampled, and the root means square (RMS) feature is extracted from resampled brain signals. After that, in the second step, the resampled RMS brain signals are modeled using Gaussian autoregressiveLaguerre approach. To improve the accuracy and robustness, in the next step, the proposed self-tuning fuzzy technique along with structure uncertain observer is recommended. In the fourth step, the RMS resampled residual brain signal is generated. Based on the difference in the levels of the RMS resampled residual brain signals and based on support vector machine (SVM), the brain signals will be classified into alertness, ambiguous, drowsiness, and sleep modes. According to the results, the classification accuracy using the proposed method is around 98%. Keywords: Brain signal classification · Sleep stage classification · Self-tuning approach · Fuzzy technique · Structure uncertain observer

1 Introduction Sleep stage classification can help identify sleep disturbances. Sleep disorders are important issues as they are a significant role in tiredness and drowsiness among drivers, and cause about 15% of the whole vehicle accidents which lead to death each year. Thus, identifying sleep disorders, which include the identification and classification of various sleep stages is very important for improving road safety and reducing the danger to thousands of human lives. Research about sleep disorders carries out by data collection from various sources employing some techniques such as electroencephalogram (EEG) [1]. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 794–801, 2022. https://doi.org/10.1007/978-3-031-09173-5_91

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An EEG is the information of electrical signals which illustrates human brain activity and neurological disturbance through the electrodes output signal. Analysis, feature extraction, and classification of EEG signals are always challenging subjects for researchers because of the brain signals variations. Also, some methods for the classification of various sleep steps are based on time or frequency features and as, EEG signals, in essence, are non-stationary and uncertain, some single approaches are not enough for the classification of sleep various states for EEG signals [1, 2]. There are several approaches for classifying brain signals that can be grouped into four classes, such as signal processing-based methods, mathematical model-based approach, artificial intelligence-based techniques, and hybrid-based methods [3, 4]. Signalbased methods have used signal processing approaches to filter and optimally classify brain signals. The accuracy of these methods decreases in conditions of uncertainty [3]. Mathematical model-based methods use classical techniques to classify brain signals. The challenge of these methods is to model complex signals with high uncertainty [3]. In recent years, intelligent techniques have been widely used to classify brain signals. The main advantage of these approaches is high flexibility, and the most important challenge is the need for a huge dataset for training and testing [4]. Hybrid techniques have been proposed to address challenges signal processing-based methods, mathematical modelbased approach, and artificial intelligence-based techniques. These approaches used by combining above methods together to reduce constraints. The main focus of this research is the use of modern control techniques and mathematical model-based approaches to classify brain signals. Mathematical model-based schemes include various algorithms. The observation technique is one of the main algorithms in the model-based method. The principal part of the observation techniques is signal modeling [5]. Although different methods have been introduced for signal modeling, they can be divided into two main groups, including mathematical-based modeling and data-driven-based approaches [6]. Data-driven-based signal modeling consists of several techniques including regressors, neural network, fuzzy logic, machine learning, and deep learning [5, 6]. In this research the nonlinear regression technique is suggested for brain signal modeling. Observers are used to estimating signals. Linear estimators generally have low efficiencies in conditions of uncertainty and nonlinear complex signals. In this case, nonlinear estimating techniques are suggested. These techniques are divided into three categories: classical observers, intelligent observers, and hybrid observers [7]. Classical nonlinear observers such as sliding mode and backstepping observers are robust and reliable. Intelligent nonlinear observers such as fuzzy observers and neural network estimators are flexible. To improve the effectiveness of classical and intelligent observers, hybrid algorithms have been introduced [7, 8]. In this work, the hybrid observer based on self-tuning assisted fuzzy structure uncertain indirect observer is suggested for brain signal estimation. To classification, the brain signals various machine-learning techniques such as support vector machine (SVM), decision trees, and convolution neural network (CNN) [9] have been suggested. In this research, the SVM is used for brain signal classification.

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This research has the following contributions: brain signal modeling using indirect resampled RMS auto-Laguerre Gaussian regressor algorithm, and brain signal estimation and classification using the combination of proposed self-tuning assisted fuzzy structure uncertain indirect observer and SVM. This research work has the following sections. The proposed self-tuning assisted fuzzy structure uncertain indirect observer is presented in the next Section. In the third Section, experimental results are explained. The conclusion is represented in the fourth Section.

2 Self-tuning Assisted Fuzzy Structure Uncertain Indirect Observer Figure 1 illustrates the sleep stage brain signal classification using proposed self-tuning assisted fuzzy structure, indirect observer. The proposed algorithm has five steps. First, the brain signals are resampled, and the RMS feature of the signals are extracted. Next, the resampled RMS brain signal in the known condition is modeled using the autoLaguerre Gaussian regressor algorithm. Third, the brain signals in known and unknown conditions are estimated using self-tuning assisted fuzzy structure uncertain indirect observer integrated with auto-Laguerre Gaussian regressor algorithm. Moreover, the residual of resampled RMS brain signals is generated using the difference between resampled RMS brain signals and estimated ones in the fourth step. In the last step, the SVM is used for the residual brain signal classification.

Fig. 1. Brain sleep stage condition using proposed self-tuning assisted fuzzy structure uncertain indirect observer.

Step 1: According to Fig. 1, in the first stage, the brain signals are resampled, and the RMS feature is extracted. In this work, brain signals were collected in four different states, including alertness, ambiguity, drowsiness, and sleep modes. According to Fig. 2, each state has 20,000 samples. Modeling the signals with the volume of signal density complicates the model function. To solve this challenge, we resampled the brain signal and extract the RMS feature from the brain signal.

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Fig. 2. Original brains signal for alertness, ambiguous, drowsiness, and sleep conditions.

Wrms

  k 1   = Wresample j 2 . k

(1)

j=1

Here, Wrms , k and Wresample j are the resampled RMS value of the brain signal for every window, number of windows, and resampled brain signal, respectively. Figure 3 illustrates the resampled RMS brain signal.

Fig. 3. Resampled RMS brains signal for alertness, ambiguous, drowsiness, and sleep conditions.

According to Fig. 3, the number of samples in each case is changed from 20,000 samples to 100 samples and the RMS feature is extracted from it. Step 2: According to the above description and Fig. 1, after resampling and extracting the RMS feature from brain signals, in the second stage, the brain signal must be modeled. Thus, the auto-Laguerre gaussian regressor (ALGR) technique is suggested for resampled RMS brain signal modeling in known condition. First, the brain signal in alertness condition is modeled using the gaussian regressor (GR) algorithm and the state space function is extracted as follows.  PGR (k + 1) = [ωGR PGR (k) + ωB B(k)] + eGR (k) + αGR (k) (2) WGR (k) = (ωW −GR )T PGR (k) Here, PGR (k), ωGR , B(k), eGR (k), αGR (k), WGR (k), and (ωB , ωW −GR ) are the state of alertness condition using GR technique, the covariance matrix of GR algorithm, the resampled RMS alertness signal, the error of the alertness signal modeling using GR

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method, the uncertainty of alertness signal calculated by GR approach, the result of alertness signal modeling using GR technique, and coefficients in GR approach, respectively. To reduce the effect of uncertainties and error the Laguerre approach is suggested. The auto-Laguerre filter is used to increase the robustness of the GR technique. The statespace equation for combination of auto-Laguerre technique and GR approach, ALGR, is introduced as follows. ⎧ ⎨ PALGR (k + 1) = [ωALGR PALGR (k) + ωB B(k) + ωW WALGR (k)] + eALGR (k) + αALGR (k) (3) ⎩ WALGR (k) = (ωW −ALGR )T PALGR (k) where PALGR (k), ωALGR , eALGR (k), αALGR (k), WALGR (k), and (ωW , ωW −ALGR ) are the state of alertness condition using ALGR technique, the covariance matrix of ALGR algorithm, the error of the alertness signal modeling using ALGR method, the uncertainty of alertness signal calculated by ALGR approach, the result of alertness signal modeling using ALGR technique, and coefficients in ALGR approach, respectively. Figure 4 demonstrates the error of the alertness signal modeling using the proposed ALGR approach and GR technique. Based on this figure, the error of alertness signal modeling using the proposed ALGR technique is lower than the GR approach. Thus, in this research, the proposed ALGR technique is suggested for alertness signal modeling. Step 3: Based on Fig. 1, in the third step, the brain signals in all conditions should be estimated by the self-tuning assisted fuzzy structure uncertain indirect observer (SFSU) integrated with the auto-Laguerre Gaussian regressor algorithm. First, the brain signals are estimated using the structure uncertain indirect (SU) observer. This technique is a robust estimation algorithm. The state-space definition of the SU observer to estimation the brain signals is represented as follows.  PSU (k + 1) = [ωALGR PSU (k) + ωB B(k) + ωW WSU (k)] + eALGR (k) + βSU (k) (4) WSU (k) = (ωa )T PSU (k) + ωb sgn(βSU (k) − αALGR (k)) Moreover, the unknown condition based on SU technique, βSU (k), can be estimated using following definition. βSU (k + 1) = ω1 βSU (k) + ω2 [βSU (k) − αALGR (k)] + ω3 sgnβSU (k) − αALGR (k)

(5)

where PSU (k), βSU (k), WSU (k), and (ωa , ωb , ω1 , ω2 , ω3 ) are the state estimation of brain signals using SU method, the estimation of unknown condition of brain signals using SU approach, the estimator’s result for brain signals using SU approach, and coefficients to estimate the brain signal using SU approach, respectively. To improve the accuracy of the estimation of unknown condition of brain signals the assisted fuzzy approach is integrated with the SU approach and represented as the following equation. ⎧ PFSU (k + 1) = [ωALGR PFSU (k) + ωB B(k) + ωW WFSU (k)] ⎪ ⎪ ⎨ +eALGR (k) + βFSU (k) ⎪ ⎪ ⎩ WFSU (k) = (ωa )T PFSU (k) + ωb sgn(βFSU (k) − αALGR (k))

(6)

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Fig. 4. Error of resampled RMS alertness signal modeling using ALGR and GR approaches.

βFSU (k + 1) = ω1 βFSU (k) + ω2 [βFSU (k) − αALGR (k)] + ω3 sgnβFSU (k) − αALGR (k) + ω4 ∅F

(7)

Here, PFSU (k), βFSU (k), WFSU (k), ∅F , and (ω4 ) are the state estimation of brain signals using FSU method, the estimation of unknown condition of brain signals using FSU approach, the estimator’s result for brain signals using FSU approach, the fuzzy estimator output, and coefficients to estimate the brain signal using FSU approach, respectively. The self-tuning approach is combined with FSU to improve the reliability of the proposed algorithm and represented as follows. ωb−Update = ωb × ∅F

(8)

⎧ ⎨ PSFSU (k + 1) = [ωALGR PSFSU (k) + ωB B(k) + ωW WSFSU (k)] + eALGR (k) + βSFSU (k) ⎩ WSFSU (k) = (ωa )T PSFSU (k) + ωb−Update sgn(βSFSU (k) − αALGR (k))

(9)

βSFSU (k + 1) = ω1 βSFSU (k) + ω2 [βSFSU (k) − αALGR (k)] + ω3 sgnβSFSU (k) − αALGR (k) + ω4 ∅F

(10)

Here, PSFSU (k), βSFSU (k), WSFSU (k), and (ωb−Update ) are the state estimation of brain signals using SFSU method, the estimation of unknown condition of brain signals using SFSU approach, the estimator’s result for brain signals using SFSU approach, and updated coefficient to estimate the brain signal using SFSU approach, respectively. Step 4: Based on Fig. 1, the residual of resampled RMS brain signal using proposed SFSU technique, γSFSU (k), is generated using the following definition. γSFSU (k) = WSFSU (k) − B(k)

(11)

Step 5: To classify the resampled RMS residual brain signal, the SVM is suggested in this research.

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3 Experimental Results Figure 5 shows the residual of resampled RMS brain signal using proposed SFSU algorithm. Based on the comparison of Figs. 3 and 5, it is clear that, the proposed SFSU algorithm has greatly improved the brain signal classification capability. Moreover, Table 1 shows the accuracy of brain signals in four conditions using proposed SFSU, FSU, and SU techniques. According to this Table, the classification accuracy in SFSU, FSU, and SU approaches are 98.75%, 95.25%, and 86%, respectively.

Fig. 5. Residual of resampled brain signal using SFSU approach.

Table 1. Accuracy of brain signal classification using SFSU, FSU, and SU approaches. Conditions

SFSU & SVM (%)

FSU & SVM (%)

SU & SVM (%)

Alertness

100

100

96

Ambiguous

100

94

90

Drowsiness

98

93

78

Sleep

97

94

80

Average

98.75

95.25

86

4 Conclusion Sleep disorders are important issues as they are significant roles in fatigue and drowsiness among drivers. In this regard, EEG brain signal analysis is very effective. In this research, the combination of self-tuning assisted fuzzy structure uncertain indirect observer, autoLaguerre Gaussian regressor modeling algorithm, and SVM is suggested for brain signal classification. The proposed method consisted of five steps. In the first step, the brain signals were resampled, and the RMS features were extracted from them. After that, the alertness signal was modeled using the proposed auto-Laguerre Gaussian regressor algorithm. Next, the brain signal was estimated by the proposed self-tuning assisted

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fuzzy structure uncertain indirect observer, and their residual signals were calculated in the fourth step. In the fifth step, SVM was used to classify the brain signals. Based on the results, the classification accuracy in the proposed algorithm (SFSU) was 98.75%. In future work, deep learning integrated with modern observers will be recommended for brain signal identification. Acknowledgements. This work was supported in part by the National Research Foundation of Korea through the Korean Government Ministry of Science and ICT (MSIT) under Grant NRF2021R1A2B5B01001721, and in part by the Regional Innovation Strategy (RIS) through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (MOE) under Grant 2021RIS-003.

References 1. Hasan, M.J., Shon, D., Im, K., Choi, H.K., Yoo, D.S., Kim, J.M.: Sleep state classification using power spectral density and residual neural network with multichannel EEG signals. Appl. Sci. 10(21), 7639 (2020) 2. Parvez, M.Z., Paul, M.: Features extraction and classification for Ictal and Interictal EEG signals using EMD and DCT. In: 2012 15th International Conference on Computer and Information Technology (ICCIT), pp. 132–137. IEEE (2012) 3. Gao, Z., Cecati, C., Ding, S.X.: A survey of fault diagnosis and fault-tolerant techniques—part I: fault diagnosis with model-based and signal-based approaches. IEEE Trans. Ind. Electron. 4(62), 3757–3767 (2015) 4. Cecati, C.: A survey of fault diagnosis and fault-tolerant techniques—part II: fault diagnosis with knowledge-based and hybrid/active approaches. IEEE Trans. Ind. Electron. 2(62), 3768– 3774 (2015) 5. TayebiHaghighi, S., Koo, I.: SVM-based bearing anomaly identification with self-tuning network-fuzzy robust proportional multi-integral and smart autoregressive model. Appl. Sci. 11(6), 2784 (2021) 6. Najeh, T., Lundberg, J.: Degradation state prediction of rolling bearings using ARX-Laguerre model and genetic algorithms. Int. J. Adv. Manuf. Technol. 112(3–4), 1077–1088 (2020). https://doi.org/10.1007/s00170-020-06416-1 7. Piltan, F., et al.: Strict-feedback backstepping digital twin and machine learning solution in AE signals for bearing crack identification. Sensors 22(2), 539 (2022) 8. Meng, X., Yu, H., Zhang, J., Xu, T., Wu, H., Yan, K.: Disturbance observer-based feedback linearization control for a quadruple-tank liquid level system. ISA Trans. 122, 146–162 (2021) 9. Piltan, F., Duong, B.P., Kim, J.M.: Deep learning-based adaptive neural-fuzzy structure scheme for bearing fault pattern recognition and crack size identification. Sensors 21(6), 2102 (2021)

Estimating Return Rate of Blockchain Financial Product by ANFIS-PSO Method Sule ¸ Öztürk Birim1(B)

, Filiz Erata¸s Sönmez1

, and Ya˘gmur Sa˘glam Liman2

1 Celal Bayar University, 45300 Salihli-Manisa, Turkey

[email protected] 2 Sinop University, 57200 Boyabat-Sinop, Turkey

Abstract. Today, blockchain technology is developing rapidly and the volume of blockchain financial product trading is increasing rapidly as well. The aim of this study is to predict the return rates of cryptocurrencies with the help of artificial learning applications, considering the complex and unstable structure of the financial system. The rate of return is one of the important criteria used for investment decisions. Therefore, an efficient method for return rate prediction will help investors in preparing their portfolios. Ethereum, one of the top three most traded cryptocurrencies in the world, was chosen for empirical analysis. The adaptive neuro-fuzzy inference system approach (ANFIS) has emerged as a method that has been frequently used in recent years. ANFIS uses optimization algorithms to obtain the best prediction performance based on neural network modeling. The ANFIS approach has a multilayered structure consisting of many nodes inside and connections between the layers. ANFIS retains the properties of a fuzzy system while applying the principles of a neural network. Computations in the layers are conducted to learn and reproduce the information of the system. In this study, the particle swarm optimization (PSO) algorithm is used to train the ANFIS network. PSO aims to find the best-performing model in predicting the prices of three major cryptocurrencies that are Bitcoin, Ethereum, and Tether. The prediction accuracy of the proposed models was checked on the test set with performance indicators of root mean squared error (RMSE) and mean absolute percentage error (MAPE). The ANFIS-PSO approach gives strong results in cryptocurrency rate of return estimation. Keywords: ANFIS · PSO · ANFIS-PSO · Cryptocurrencies · Bitcoin · Ethereum · Tether

1 Introduction and Literature Review Blockchain is a technology based on computational logarithm that stores and transmits everything on a network but mostly misunderstood or unknown because it goes beyond cryptocurrency system and has impacts on governance (legal and policy), society, economy, financial system, and technology. Also, Blockchain technology is based on transparency, trust-free, democracy and decentralization principles and provides solutions for countries at all levels of development [1]. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 802–809, 2022. https://doi.org/10.1007/978-3-031-09173-5_92

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The relationship between traditional currencies and the cryptocurrencies makes it very important for the financial and monetary systems (especially during the economic and financial crises while current policy tools are running out of solution). Because it proposes a new economic tool and a new behavior from the academic perspective. Cryptocurrencies have immense speed on transactions and compared to national currencies do not a have protocol. For policymakers and investors, it replaces conventional currencies and a hedging strategy (against negative shocks) during turmoil periods (eg. Pandemic Covid-19). Especially for risk-seeking investors it offers high rate of returns [2]. Many determinants have been considering exploring the price of assets and mostly risk factors (risk return trade-off), blockchain transaction volume and fees, trade volume, volatility, market capitalization, determinants of market and market phases has been selected. But the pricing mechanism is not linked to country specific. Therefore, empirical studies should be based on global benchmarks [3]. According to Yermack [4], Bitcoin is much more volatile than the other crypto currencies and uncorrelated with others. Bianchi [3] proposes that Bitcoin has illegal uses and possible to manipulate with mining. Ethereum and Bitcoin has the highest average volume in daily basis. Dhyrberg [5] indicates Bitcoin shows similar behaviors like gold [5]. Crypto currencies are new (global) assets with specific risk factors and an important subject to analyze with further econometric techniques. Adaptive neuro-fuzzy inference system (ANFIS) is a complex modelling combines fuzzy logic and neural network computing. As a hybrid system neuro-fuzzy both includes conventional fuzzy logic and neural network learning-trainability-high decision-making power. Both neural network and fuzzy logic can deal with uncertainties and encode the information thanks to model free estimators. Therefrom makes it possible to combine fuzzy logic and neural network. General Particle Swarm Optimization Algorithm (PSO) is a population-based algorithm of social behavior but the modified one removes worst particle in selected population and replaces with a new one [6]. Therefore, it is selected to train the system in order to find most suitable model for Bitcoin, Ethereum, and Tether return rates (prices) of cryptocurrencies. Bitcoin, Ethereum and Tether use their own blockchain technology but also differs in returns, liquidity, and price stability [7]. Therefore, PSO helps to minimize errors to ensure the accuracy and the precision of statistical indicators [8]. The most studied applications in crypto economy are Bitcoin (first created coin with a digital character and the most dominant one with the highest capitalization rate and accepted as a commodity) and the other most traded crypto-currencies. Also there are many studies investigating the issue of return rates of currencies in economic literature. Previous studies are mostly focusing on the modelling return rates with linear models. However the existing literature does not consider the complexity and non-linear (volatile) pattern of cryptocurrencies with traditional methodology. In this context reducing the complexity of return rates related parameters by the use of advance approaches such as artificial network systems. This study intends to estimate the return rates of cryptocurrencies with ANFIS-PSO approach and fill the gap in the literature. Our main contribution is therefore estimating prices of cryptocurrencies with a further methodology to provide evidence that risk factors are crucial to pricing cryptocurrencies.

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The remainder of the paper explains the methodology first. Then the results of the study are given in section three. Finally, the conclusion summarizes the results and the implications of our study.

2 Methodology This paper aims to design a return rate prediction model for the blockchain financial products. In this study an ANFIS model with PSO is developed for the predictive analysis of return rates of Bitcoin (BTC), Ethereum (ETH) and Tether (USDT). Blockchain is a data structure that records transactions and stores the information related to the transactions. In the storage data there are source and destination of the transactions [9]. Research objective is to predict return rate of BTC, ETH and USDT based on the historical return rates of each cryptocurrency. To follow this objective, daily price data is collected and prepared for data analysis. 2.1 Data Collection Price data for the selected currencies are collected between November 9th 2017 and March 22nd 2022, for the total of 1593 days. For each cryptocurrency daily return rates were calculated and added to the datasets. Then to make the datasets proper to be analyzed with ANFIS, input and target variables should be identified. While target variable is daily return, the input variables were the 3-day historical daily returns for each variables. Therefore there were three inputs and one target for each cryptocurrency dataset. To verify the proposed models datasets are divided into training and test sets. The first 80% of daily return for each currency is used as the training set, while the remaining 20% was used as the test set. ANFIS-PSO model were run on the training sets while the predictions to measure the performance were calculated using the test sets. In this study return rate is demonstrated in the form of ratio which is between -1 and 1. 2.2 Adaptive Neuro-Fuzzy Inference System (ANFIS) Neural networks are effective tools to model and solve real world problems. However when the data has high ambiguity and uncertainties a new application of neural networks can provide an alternative tool [10]. ANFIS can be a successful alternative to classical neural networks since it is a hybrid application of neural networks and fuzzy systems. With the ability to utilize fuzzy inference systems, ANFIS can provide effective solutions to the problems by handling uncertainty and ambiguity. ANFIS has five layers which are shown in Fig. 1. In Layer 1, inputs are converted outputs for the next layer with a fuzzy membership function. In this study generalize Bell function is used as the membership function. In Layer 2, multiplications of the memberships calculated in layer 1 is conducted to identify fuzzy rules and their corresponding strengths. In Layer 3, values computed in Layer 2 is normalized. In Layer 4, output of each rule is calculated utilizing the gradient descent optimization. In the final layer aggregate output for the network is computed [11].

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Fig. 1. Architecture of ANFIS, Source: Jang, 1993 [11]

In the ANFIS architecture, Layer 1 and Layer 4 have non-linear and linear parameters to be optimized and optimization of these parameters are necessary to obtain better prediction performance [12]. In this study PSO method is used to optimize parameters in ANFIS. 2.3 Particle Swarm Optimization (PSO) PSO was first introduced by Eberhart and Kennedy [13] based on the behaviors of a group of birds or fish randomly searching food in a specific area. Group of Birds or fish are regarded as particle in this example. PSO is an algorithm to search for the best solution among the possible ones. Every potential solution is regarded as a particle in the method and particles try to find the best solution by modifying their places until optimal state of the method is reached by achieving the computational targets [12]. Position of the particle and particle speed are two important criteria in PSO model. Fitness function measures how a particle is close to the solution or the best position. Positions and velocity of the particles are renewed at each iteration until the best position is reached. The location and velocity of each Particle are calculated according to the following equations [8]. j

j

j

Xi [t + 1] = Xi [t] + Vi [t + 1]     j j j j j j Vi [t + 1] = WVi [t] + C1 r1 Xp,best [t] − Xi [t] + C2 r2 Xg,best [t] − Xi [t]

(1) (2)

In above equations, X represents position while V represents velocity. During the search for solution current best state is called “pbest’, while the best postion closest to the solution among the entire swarm is called “gbest” [12]. r1 and r2 are uniformly distributed random vectors while c1 and c2 are the particle and collective learning coefficients respectively whose values change between 0 and 2 [8].

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2.4 Performance Indicators Prediction performance of the ANFIS-PSO method for the three cryptocurrencies are evaluated with Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE), which both calculate the average deviations from the real values. Metrics are calculated based these equations:  n    t=1 yt − y t (3) MAE = n  n 2 t=1 (yt − y t ) (4) RMSE = n 





where yt is the actual value on time t, and yt is the prediction of ANFIS-PSO on time t.

3 Results All the analysis and implementation of the models are handled with Python 3.8 programming language. Cyptocurrency price data is downloaded Yahoo Finance API with using Python. Descriptive statistics for the price data between November 9th 2017 and March 22nd 2022 for BTC, ETH and USDT can be seen in Table 1. Table 1. Descriptive statistics BTC

ETH

USDT

Count

1594

1593

1593

Mean

19277.58

1021.28

1.0012

Standard deviation

17761.80

1228.21

0.0061

Minimum

3236.76

84.31

0.9666

Maximum

67566.83

4812.09

1.0779

In this study PSO is used to optimize parameters in ANFIS method. As membership function Generalized Bell Membership (GbellMF) function is used. GbellMF calculated with the Eq. (4). An seen in Eq. (4), Gbellmf has three parameters to be optimized which are a, b and c. f (x; a, b, c) =

1  x−c 2b  1+

(5)

a

PSO parameters should also be determined carefully to develop and run the ANFISPSO model. Some of the parameters used in PSO model, their explanations and corresponding values used in the models are given in Table 2. In this study ANFIS-PSO implementation of Egilardi for a regression problem is adapted to be used for return rate prediction of cryptocurrencies. Implementation of Egilardi [14] base model can be found on https://github.com/gabrielegilardi/ANFIS.

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Table 2. Explanations and values for the selected PSO parameters [14] Parameter

Explanation

Value

K

Size of informants for each particle

3

phi

Coefficient to compute the self-confidence coefficient

2.05

vel_fact

Value to calculate the maximum and the minimum velocities

0.5

conf_type

Confinement type for the velocities

‘Random Back’

Three ANFIS-PSO models are run to predict return rates of BTC, ETH and USDT. Performance scores of each model on the test sets can be observed in Table 3. As Table 3 shows, ANFIS-PSO performs best for the USDT dataset with the lowest MAE and RMSE values that are 0.006240 and 0.00864 respectively. For BTC and ETH, RMSE and MAE vales are above 0.10. Performance differences between USDT and the remaining two datasets can come from the pattern of the original price data. when the descriptive statistics in Table 1 is examined, it is seen that USDT dah the lowest mean and standard deviation. Both BTC and ETH has large amounts of mean and standard deviation when compared with USDT. This means USDT prices has lower variation than BTC and ETH during the specified time period. This low variation resulted in superior performance in ANFIS-PSO. It can be said that when there is lower variation in data, ANFIS-PSO produces better prediction results. To evaluate prediction performance on the test set, graphs of predicted and actual values are also observed. Figures 1, 2 and 3 shows the demonstrations of actual vs predicted values for BTC, ETH and USDT respectively. As the figures show, for the three currencies predicted values follows the similar pattern with the actual values. Figures 1 and 2 shows that for BTC and ETH ANFIS-PSO produced close predictions with the actual values and can be accepted as an effective method to predict cryptocurrency return rate (Fig. 4). Table 3. Prediction scores on the test set Crpytocurrency

MAE

RMSE

BTC

0.12018

0.16157

ETH

0.16608

0.28356

USDT

0.006240

0.00864

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Fig. 2. Actual vs Predicted return rates of BTC in the test set

Fig. 3. Actual vs Predicted return rates of ETH in the test set

Fig. 4. Actual vs Predicted return rates of BTC in the test set

4 Conclusion In this study, return rate of Bitcoin, Ethereum and Tether was predicted using ANFIS with PSO. ANFIS-PSO was found to be more successful in return rate prediction of Tether. For all the cryptocurrencies, predicted rates were found to follow similar pattern with the actual values and there were small differences between predicted and actual outcomes. The possible reason for ANFIS-PSO providing better results with Tether lies in the less volatile nature of Tether close price data. This research showed that ANFISPSO is a valuable tool to predict return rate of cryptocurrencies and can further be used to predict return rates of other digital currencies. In the future ANFIS can be combined

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with other heuristics such as Genetic Algorithm or Simulated annealing. Additionally in future studies ANFIS with heuristics models can be compared with the traditional ANFIS and other machine learning algorithms.

References 1. Ben Dhaou, S.I., Rohman, I.K., Claims, A.I.: Everything and its opposite: socio-economic implications of blockchain technology: case of monetary policy. In: ICEGOV’18: Proceedings of the 11th International Conference on Theory and Practice of Electronic Governance, pp. 631–639 (2018). https://doi.org/10.1145/3209415.3209502 2. Mokni, K., Ajmi, A.N.: Cryptocurrencies vs. US dollar: evidence from causality in quantiles analysis. Econ. Anal. Policy 69, 238–252 (2021). https://doi.org/10.1016/j.eap.2020.12.011 3. Bianchi, D.: Cryptocurrencies as an asset class? An empirical assessment. J. Altern. Invest. 23, 162–179 (2020). https://doi.org/10.3905/JAI.2020.1.105 4. Yermack, D.: Is Bitcoin a real currency? SSRN Electron. J. (2013). https://doi.org/10.2139/ ssrn.2361599 5. Dyhrberg, A.H.: Bitcoin, gold and the dollar - a GARCH volatility analysis. Financ. Res. Lett. 16, 85–92 (2016). https://doi.org/10.1016/j.frl.2015.10.008 6. Seydi Ghomsheh, V., Aliyari Shoorehdeli, M., Teshnehlab, M.: Training ANFIS structure with modified PSO algorithm. In: 2007 Mediterranean Conference on Control and Automation, MED (2007). https://doi.org/10.1109/MED.2007.4433927 7. Nadler, P., Guo, Y.: The fair value of a token: how do markets price cryptocurrencies? Res. Int. Bus. Financ. 52, 101108 (2020). https://doi.org/10.1016/j.ribaf.2019.101108 8. Robati, F.N., Iranmanesh, S.: Inflation rate modeling: adaptive neuro-fuzzy inference system approach and particle swarm optimization algorithm (ANFIS-PSO). MethodsX 7, 101062 (2020). https://doi.org/10.1016/j.mex.2020.101062 9. Metawa, N., Alghamdi, M.I., El-Hasnony, I.M., Elhoseny, M.: Return rate prediction in blockchain financial products using deep learning. Sustainability (Switzerland). 13, 1–16 (2021). https://doi.org/10.3390/su132111901 10. Samanataray, S., Sahoo, A.: A comparative study on prediction of monthly streamflow using hybrid ANFIS-PSO approaches. KSCE J. Civ. Eng. 25(10), 4032–4043 (2021). https://doi. org/10.1007/s12205-021-2223-y 11. Jang, J.R.: ANFIS: adaptive network-based fuzzy inference system. IEEE Trans. Syst. Man Cybern. 23, 665–685 (1993) 12. Guleryuz, D.: Determination of industrial energy demand in Turkey using MLR, ANFIS and PSO-ANFIS. J. Artif. Intell. Syst. 3, 16–34 (2021). https://doi.org/10.33969/ais.2021.31002 13. Eberhart, R., Sixth, J.K.: A new optimizer using particle swarm theory. In: Proceedings of the IEEE Symposium on Micro Machine and Human Science, Nagoys, Japan, pp. 39–43 (1995) 14. Egilardi, G.: Multivariate Regression and Classification Using an Adaptive Neuro-Fuzzy Inference System (Takagi-Sugeno) and Particle Swarm Optimization (2021)

Intelligence

Intelligent Fuzzy Clinical Decision Support System to Predict the Coimbra Breast Cancer Dataset Y. F. Hernández-Julio1(B) , H. Muñoz-Hernández1 , L. A. Díaz-Pertuz1 , M. Prieto-Guevara2 , N. S. Arrieta-Hernández1 , N. A. Figueroa-Mendoza1 , M. Aviles-Román1 , and W. Nieto-Bernal3 1 Universidad del Sinú Elías Bechara Zainúm, Montería 230002, Colombia

[email protected]

2 Universidad de Córdoba, Montería 230002, Colombia 3 Universidad del Norte, Puerto Colombia 080001, Colombia

Abstract. The objective of this study was to design, implement, and validate different intelligent fuzzy clinical decision support systems based on a fuzzy set theory using clusters and pivot tables. The results were compared with other related works (Literature) to validate the proposed fuzzy systems for classifying the Coimbra breast cancer dataset. The validation methods used were cross-validation and random sampling for each comparison. The fuzzy Inference Systems had different input variables according to the ones mentioned in the literature. The originality of this work lies in the way of generating the membership functions and the rule base for the intelligent fuzzy clinical decision support systems. The results show that the Kappa Statistics and accuracy in some cases were higher than the obtained results from the literature for the output variable for the different Fuzzy Inference Systems – FIS, showing better accuracy. In a significant conclusion, these outcomes offer favorable evidence that models combining features such as age, BMI, and metabolic parameters can be an effective tool for a low-cosvaluableuseful biomarker for the Coimbra breast cancer dataset. Keywords: Fuzzy system · Breast Cancer · Clusters · Pivot tables

1 Introduction Cancer is a group of diseases that cause cells in the body to change and spread out of control [1]. Breast cancer is the second most common cancer among women in the United States. In 2018, the latest year for which incidence data are available, in the United States, 254,744 new cases of Female Breast Cancer were reported among women, and 42,465 women died of this cancer [2]. According to [3], among the signs and symptoms of breast cancer can find A lump or swell in the breast, upper chest, or armpit; changes in the size or shape of the breast; a change in skin texture and color; rash, crusting or modifications to the nipple. For the reasons above, it is crucial to develop models that help decisionmaking for initial detection, appropriate therapy, and therapy [4] to obtain an accurate © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 813–821, 2022. https://doi.org/10.1007/978-3-031-09173-5_93

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diagnosis. Fuzzy logic has been used to classify fibromyalgia syndrome [5] and breast cancer classification [5, 6]. For the mentioned reasons, the main objective of this work was to design, implement and validate different fuzzy inference systems using clusters and pivot tables for classification problems. The fuzzy inference systems were created to classify the Coimbra Breast Cancer dataset and compared with other models obtained from the literature to validate the proposed models. The originality of this work lies in generating the membership functions. Some authors use different approaches for the generation of these. We can find 2N + 1 regions, FCM, neural networks, GAs, etc. In our case, we proposed using clustering methods for this step. The main difference at this stage is that no fixed or random membership functions were generated, such as those caused by those works that used classical methods or were based on evolutionary algorithms, neural networks, or swarm intelligence techniques. Another difference between this study and the related works using neural networks, evolutionary or swarm algorithms is that we didn’t use random numbers, any chromosome, or particle scheme. Regarding the generation of the rule base for the system, some authors also used the same previously mentioned methods. The main difference with our work is that our approach uses pivot tables instead of other techniques. Other authors initialize with random weights and bias for each hidden neuron (neural networks), adjusting them through optimization functions like gradient descendent and non-linear activation functions. Other methods use random schemes for generating the fuzzy rules, using the objectives function to adjust membership functions and the rule base, i.e., MSE. Our study didn’t propose to use any objective function as a minimization problem. In addition, our study didn’t offer to employ or calculate any distances, attractiveness, or another parameter for generating the fuzzy rule base. The only component used for this task was pivot tables. Pivot tables didn’t use any calculation method or random or manually parameters (only sort options). The main job of this technique is to eliminate redundant information. The remaining of this paper is as follows: Sect. 2 indicates the material and methods used in the study. The results and discussion are presented in Sect. 3. Section 4 shows the conclusion of the work. 1.1 Literature Review of the Topic Fuzzy set theory is the basis of all fuzzy logic methods [7]. Fuzzy set theory was proposed by Zadeh [8] as an extension of the classical set theory to model sets whose elements have degrees of membership [9]. According to [8], a fuzzy set is a class of objects with a continuum of grades of membership. The fuzzy set theory provides the tools to effectively represent linguistic concepts, variables, and rules, becoming a natural model to represent human expert knowledge [10]. According to [9], a linguistic value refers to a label describing the experience that has meaning determined by its degree of the membership function. One of the most fruitful developments of fuzzy set theory is Fuzzy Rule-Base Systems – FRBs [9].

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2 Material, Methods A case study was developed to validate the framework proposed by [11]. Each of the phases presented in the framework for developing decision support systems through clusters and dynamic tables will be explained. 2.1 Identifying the Dataset The dataset for this case study was acquired from the UCI Machine Learning repository for evaluating the effectiveness of the proposed classification model using the Coimbra Breast Cancer Dataset (CBCD) [11]. The CBCD was compiled from females recently diagnosed with breast cancer in the Gynecology department of the University Hospital Center of Coimbra between 2009 and 2013 [11]. It contains 116 records with nine input variables. The primary goal is to forecast the existence of breast cancer in women. The descriptive statistics of the clinical variables are given in Table 1. Table 1. Variables in the Coimbra breast cancer dataset. Feature

Attribute

Patients

Controls

p-value

1 2

Age

53.0 (23.0)

65 (33.2)

0.479

BMI

27 (4.6)

28.3 (5.4)

0.202

3

Glucose

105.6 (26.6)

88.2 (10.2)

0.001

4

Insulin

12.5 (12.3)

6.9 (4.9)

0.027

5

HOMA

3.6 (4.6)

1.6 (1.2)

0.003

6

Leptin

26.6 (19.2)

26.6 (19.3)

0.949

7

Adiponectin

10.1 (6.2)

10.3 (7.6)

0.767

8

Resistin

17.3 (12.6)

11.6 (11.4)

0.002

9

MCP-1

563 (384)

499.7 (292.2)

0.504

Source: [11]

2.2 Data Preparation (Crisp Inputs) For the dataset, all input features were chosen for estimating the best performance among the interactions between those input features. In this phase, the pre-processed technique used was clustering. This technique will be explained in Sect. 2.7 [12]. 2.3 Reviewing Existing Models the primary goal is to see related studies of the problems to consider our results and compare them with the research found in the literature. In this phase, an academic and scientific quest of the different works related to the problem was taken. Indexed catalogs such as Scopus, Science Direct, Web of Science, Scielo, Google Scholar, ACM, etc., were utilized. The result of this phase is mentioned in the discussion section.

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2.4 Evaluating the Optimal Number of Clusters In this phase, dynamic tables were used for each classification problem for knowing the number of rows for every input and output variable. Table 2 illustrates the optimal number of clusters for each input and output for the Coimbra breast cancer dataset. Table 2. The optimal number of clusters for the Coimbra breast cancer dataset.

Rows Number Rounded Square root

Age

BMI

Glucose

51

110

50

7

10

7

Coimbra Breast Cancer InHO Leptin sulin MA 113 116 116 11

11

11

Adiponectin 115 11

Resistin

MCP-1

116

113

2

11

11

-

CT = Clump Thickness. UCSi = Uniformity of Cell Size. UCSh = Uniformity of Cell Shape. MA = Marginal Adhesion. SECS = Single Epithelial Cell Size. BN = Bare Nuclei. BC = Bland Chromatin. NN = Normal Nucleoli. MI = Mitoses. BMI = Body Mass Index. HOMA = HOMAhomeostasis model assessment for insulin resistance. MCP-1 = Monocyte Chemoattractant Protein-1. * Indicates that there are missing values and were replaced by zero

2.5 Setting Several Clusters According to the Previous Evaluation For the case study, the minimum number of clusters was 2. The user can select this parameter. The maximum number of groups for the classification problem was the optimal number of sets. 2.6 Random Permutations The observed inputs and outputs values were randomized and permuted when applied to the proposed algorithms for the dataset. 2.7 Cluster Analysis In this stage, three of the existing clusters types (kmeans, Ward, Fuzzy C-Means) were performed and analyzed with the range of solutions established in the previous step. The selection criteria for the clustering algorithm must be according to the implicitly or explicitly knowledge about the topic. 2.8 Sampling Datasets Two kinds of random data sampling were used for the experiments. The first one was random sampling, and the other one was the cross-validation method. 2.9 Pivot Tables The unique tables command was used to develop the following sub-phases for the case study.

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2.9.1 Combining Different Input Variable Clusters Datasets This stage involves making compositions between input features and the sets of output variables using dynamic tables. 2.9.2 Establishing the Fuzzy Rules This phase is based on the previous one. Table 3 reveals an example of some values obtained from the last step. The columns represent the groups’ numbers created by the inputs and output variable clusters. The rows correspond to the rules’ numbers found in the clusters’ datasets. Table 3. Instances of several values obtained from a unique table for the Coimbra breast cancer dataset. Inp_Fea 1

Inp_Fea 2

Inp_Fea 3

Inp_Fea 4

Inp_Fea 5

Out_Fea

1

1

2

1

2

1

2

2

1

2

1

1

3

4

3

1

2

2

6

3

2

2

2

2

Inp_Fea = Input feature. Out_Fea = Output feature.

2.10 Elaborating the Inference Engine for the Decision Support System Centered on Fuzzy Set Theory The fuzzy inference system implementation was carried out in the MATLAB® 2017 software for the case study. 2.11 Evaluating the Fuzzy System Performance For the case study, the Classification accuracy (ACC), sensitivity, specificity, Function Measure, Area under the curve, and Kappa statistics were used to measure the system’s performance. Additionally, we performed a statistical significance test called McNemar’s test.

3 Results and Discussion The following were the obtained results for the mentioned dataset using the crossvalidation data partition method: Table 4 shows the confusion matrix for the best results for six of nine features (1, 2, 3, 4, 5, 6), obtained by the k-means clustering method with a random sampling data partition. Patrício et al. [11] used logistic regression, random forests, and support vector machines as predictors of different numbers of variables. The resulting models were

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DDFDSS

Malign

Benign

48

4

Malign

0

64

Data-driven Fuzzy Decision Support System. Bold values denote accurate predictions.

Table 5. Classification accuracies were obtained with our proposed methodology (k-means method, cross-validation) and other classifiers from literature for CBCD. Main aspects Num of Variables Num of Rules or Hidden neurons /technique Accuracy (%): Sensitivity: Specificity: Performance

F-Measure: Area under curve: Kappa statistics:

[11] V1V2

V1V3

V1 -V4

V1V6

V1V9

SVM 0.81 0.86 0.7 0.76 0.76 0.81 -

0.87 -0.92 0.78 -0.83 0.82 - 0.86 -

0.8 2 -0.88 0.8 4 - 0.9 0.8 7 - 0.91 -

DDFDSS - this work (k-means). Cross-validation method.

[13] V1V5

0.8 4 - 0.9 0.8 1 - 0.87 0.8 6 - 0.9 -

0.8 1 - 0.86 0.8 - 0.86 0.8 3 - 0.88 -

0.7 5 - 0.81 0.7 8 - 0.84 0.8 1 - 0.85

V1-V8

V1V2

V1V3

V1V4

V1V5

V1V6

V1V7

V1V8

V1V9

AdaBoostM1 and MAD

64

94

99

103

104

104

104

104

80. 6% 0.9 3 0.7 2 0.8 0 0.8 2 61. 9% 0.7 0 0.9 3

91. 6% 0.9 3 0.9 0 0.9 2 0.9 2 83. 0% 0.9 2 0.9 3

94. 1% 0.9 3 0.9 6 0.9 5 0.9 4 88. 1% 0.9 7 0.9 3

95. 5% 0.9 2 1.0 0 0.9 6 0.9 5 90. 9% 1.0 0 0.9 2

95. 5% 0.9 2 1.0 0 0.9 6 0.9 5 90. 9% 1.0 0 0.9 2

95. 5% 0.9 2 1.0 0 0.9 6 0.9 5 90. 9% 1.0 0 0.9 2

95. 5% 0.9 2 1.0 0 0.9 6 0.9 5 90. 9% 1.0 0 0.9 2

95. 5% 0.9 2 1.0 0 0.9 6 0.9 5 90. 9% 1.0 0 0.9 2

91.37% 0.914 0.914 0.938

-

82.76%

Precision:

-

-

-

-

-

-

0.919

Recall:

-

-

-

-

-

-

0.914

V: Variable. SVM: Support Vector Machine. DDFDSS: Data-driven Fuzzy Decision Support Systems. - Didn’t mention it in the literature.

approximate 0.95 confidence intervals for the sensitivity, specificity, and Area Under Curve of the models. Accoding to the Table 5, we can see that the results of the DDFCDSS supported with the k-means cluster method and a cross-validation data partition have a good performance from the first two variables compared with the cited author [11]. Also, we can see that the performance metrics improve when more variables are added. From 1 to 5 variables, the results are stabilized regardless of whether the number of variables is increased. This fact serves to determine that it does not matter if 5 or 9 variables are chosen; the result will be the same. From variables 1 to 3, all the metrics obtained in the literature with the same data set are exceeded. In this case, if the oncologist wishes to choose a smaller number of biomarkers (features) to classify people with breast cancer correctly, he could and thus accelerate the decision-making process to take the necessary actions for possible treatments. In that case, the professional would determine which variables to work with. The results obtained with the Ward clustering method and a cross-validation data partition showed an improvement in the performance metrics and presented the stabilization pattern since the first two features or biomarkers. The performance with this clustering method is relatively better than the k-means because it converges quickly to the optimal number of rules for the best results for the specific clinical decision support. As mentioned above, the oncologist can choose which variables want to select for diagnosing.

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The Fuzzy c-means clustering (FCM) method didn’t have the excellent performance obtained for the two previous clustering methods. The percentage of classification accuracy for this clustering method was lower than the other results. However, by increasing the number of variables within fuzzy inference models, the pivot tables find the optimal pattern of rules to reach their maximum classification capacity. The followings are the results using the random data sampling data partition method: For the case of the k-means clustering method using the mentioned method, the best performance was obtained using six and seven variables. The classification accuracy was 0.966; the specificity value was 1.0, indicating an excellent performance in classifying true negatives cases of breast cancer. As mentioned before, the oncologist can select the number of biomarkers that they want in their Clinical fuzzy decision support system. The main idea is the professional chooses the best model with the best performance. The performance metrics were exceeded since the 1 to 3 variables, indicating that we can use those variables. For the case of the Ward clustering method using random sampling, the best fuzzy inference model could obtain the stabilization of the results with 80 rules approximately. In the random sampling method, the Ward clustering method found a rule pattern not as optimal as that found using the cross-validation method. Its percentage of correct classification was lower (0.931) using the same number of variables. This behavior may be due to the characteristics of the random sampling method, where 0.70 is chosen for training and the remaining 0.30 for the validation of the models. However, the cited authors did not use this type of data partition. Therefore, it is not necessary to compare them. This exercise was performed to take the best results from each of the three clusters and evaluate whether there is a significant difference between the models obtained through the clustering methods. For the case of the FCM clustering method, the obtained results using random sampling were better than those obtained using cross-validation. The performance metrics obtained for this data partition were higher than the first two variables. The pattern for the optimal rule base was detected for the first four variables; however, the classification accuracy percentages were lower than the other cluing method. Regarding the statistical differences between the three methods, McNemar’s test results indicate that none of the best models for each clustering method have a significant difference at 95% of the confidence interval. The test’s values were k-means vs. Ward method: X12 = 0.750; k-means vs. FCM: X12 = 1.7778; Ward vs. FCM: X12 = 0.

4 Conclusions The main aim of this study was to develop, design, implement, and validate different decision support systems to predict the Coimbra breast cancer dataset based on a fuzzy set theory using clusters and pivot tables and compare them with other related works obtained from the literature. For the mentioned dataset, the performance of our fuzzy inferences systems was higher than the studies obtained from the literature. All metric values were closer to 1, and the Kappa statistic was higher than 0.80, indicating a solid agreement between the classification predictions and the observed dataset. The selected features for random sampling were all variables such as for cross-validation, which were Age, Body

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Mass Index—BMI (kg/m2 ), Glucose (mg/dL), Insulin (µU/mL), Homeostasis Model Assessment—HOMA, Leptin (ng/mL), Adiponectin (µg/mL), Resistin (ng/mL), and Monocyte Chemoattractant Protein 1 MCP.1. Patrício et al. [11] concluded that, with four features (Age, BMI, glucose, and Resistin), they could forecast the existence or absence of breast cancer in female patients with sensitivity values ranging between 0.82 and 0.88 and specificity ranging between 0.85 and 0.9. As can be found, our results using all variables and applying random sampling and cross-validation were higher than those proposed by the mentioned authors. Involving the feature extraction, the results with the random sampling process were more elevated than obtained for the cross-validation. The six variables with the best performance were: Age (years), Body Mass Index—BMI (kg/m2), Glucose (mg/dL), Insulin (µU/mL), Homeostasis Model Assessment—HOMA, and Leptin (ng/mL). These outcomes offer favorable evidence that models combining features such as age, BMI, and metabolic parameters can be an effective tool for a low-cost and valuable biomarker for the Coimbra breast cancer dataset [11]. Regarding future works, the framework will be applied to large datasets using Parkinson’s disease data.

References 1. American Cancer Society: Cancer Facts & Figures 2018, p. 76. American Cancer Society Inc., NW, Atlanta (2018) 2. U.S. Cancer Statistics Working Group. Breast Cancer Statistics - U.S. Cancer Statistics Data Visualizations Tool. In: Control DoCPa (ed.) Centers for Disease Control and Prevention, Washington, D.C. (2021) 3. Breast Cancer Now: What are the signs and symptoms of breast cancer? (2021). https://bre astcancernow.org/about-us/media/facts-statistics#signs-and-symptoms. Accessed Feb 2021 4. Cardon, T.A.: An introduction. In: Cardon, T.A. (ed.) Technology and the Treatment of Children with Autism Spectrum Disorder. ACPS, pp. 1–2. Springer, Cham (2016). https://doi.org/ 10.1007/978-3-319-20872-5_1 5. Nilashi, M., Ibrahim, O., Ahmadi, H., Shahmoradi, L.: A knowledge-based system for breast cancer classification using fuzzy logic method. Telemat. Inform. 34(4), 133–144 (2017). https://doi.org/10.1016/j.tele.2017.01.007 6. Gayathri, B.M., Sumathi, C.P.: Mamdani fuzzy inference system for breast cancer risk detection. In: IEEE International Conference on Computational Intelligence and Computing Research (ICCIC), p. 1–6. IEEE (2015) 7. Ahmadi, H., Gholamzadeh, M., Shahmoradi, L., Nilashi, M., Rashvand, P.: Diseases diagnosis using fuzzy logic methods: a systematic and meta-analysis review. Comp. Methods Programs Biomed. 161, 145–172 (2018). https://doi.org/10.1016/j.cmpb.2018.04.013 8. Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965). https://doi.org/10.1016/S00199958(65)90241-X 9. Riza, L.S., Bergmeir, C.N., Herrera, F., Benítez Sánchez, J.M.: FRBS: Fuzzy rule-based systems for classification and regression in R. American Statistical Association (2015) 10. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning—I. Inf. Sci. 8(3), 199–249 (1975) 11. Patrício, M., Pereira, J., Crisóstomo, J., Matafome, P., Gomes, M., Seiça, R., et al.: Using Resistin, glucose, age and BMI to predict the presence of breast cancer. BMC Cancer 18(1), 29 (2018)

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12. Aghabozorgi, S., The, Y.W.: Stock market co-movement assessment using a three-phase clustering method. Expert Syst. Appl. 41(4, Part 1), 1301–14 (2014). http://dx.doi.org/https:// doi.org/10.1016/j.eswa.2013.08.028

Evaluation of Artificial Intelligence Applications in Aviation Maintenance, Repair and Overhaul Industry via MCDM Methods Metin Emin Aslan1(B) and A. Cagri Tolga2 1 Graduate School of Science and Engineering, Galatasaray University, Ortakoy,

34349 Istanbul, Turkey [email protected] 2 Industrial Engineering Department, Galatasaray University, Ortakoy, 34349 Istanbul, Turkey [email protected]

Abstract. Airline operators are looking for ways to improve flight performance and flight safety, and to minimize maintenance-repair costs and the number of unplanned breakdowns over time. It is exceedingly difficult to achieve optimal results in such a large system with hundreds of variable factors. However, technological developments facilitate the exchange of data between interrelated operational activities and make it meaningful by processing the big data that emerges from the operations performed. In this sense, artificial intelligence (AI) concept has started to be a big supporter of maintenance-repair-overhaul (MRO) companies. In this research, it will be carried out to determine the most appropriate area in which AI technology can be used in aviation MRO activities, and to detect the most suitable AI tool for this determined area via multi-criteria decision-making (MCDM) method. VIKOR method is used to determine which of these potential processes is more suitable for this technology, and the most appropriate AI tool for this specified process is determined by the TODIM method. As a result of the study, it has been determined that the “predictive and preventive maintenance” is the most suitable area and “Alternative-6” out of 11 alternative AI tools was found to be the most suitable alternative for this area. Keywords: Artificial intelligence · Machine learning · Aviation · MRO · Maintenance-repair-overhaul · MCDM · VIKOR · TODIM

1 Introduction According to the International Air Transport Association (IATA), it was reported that commercial airlines had carried out their business operations with a total of 27.343 aircrafts in 2019, and they had spent $82 billion on MRO activities for those aircrafts, which amounts to be about 10% of all operational costs [1]. In such a large-scale industry, a small improvement in operational processes provides companies with substantial financial benefits. On the other hand, it is a serious operation for the operators to organize © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 822–830, 2022. https://doi.org/10.1007/978-3-031-09173-5_94

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these activities determined by international authorities and original equipment manufacturers (OEMs) and to arrange maintenance schedules with allocating adequate resources. At this point, digitalization, and innovative technologies (such as artificial intelligence, internet of things, blockchain, etc.) offer great contributions and opportunities to reduce costs and increase profitability for companies. In this paper, a series of research are conducted on the use of AI in aviation MRO processes, and it is aimed to help decision maker to decide on both the most suitable AI usage area, and the most suitable tool for this determined area by using MCDM techniques, VIKOR1 and TODIM2 respectively. Contrary to the studies in the literature, which reveal potential usage areas and application methodologies in aviation, a comprehensive view of these areas and determination of the most appropriate process and tool using MCDM is carried out in this paper. The structure of the paper is as follows: First, the researches in the literature, which deal with aviation, MRO and AI topics are included in Sect. 2. Then, alternative usage opportunities regarding which areas AI can be used are revealed and prioritized with the VIKOR method in Sect. 3. Thereafter, in Sect. 4, the potential AI tools are identified for the highest priority process and the most suitable AI tool for the determined process is determined by using the TODIM method. Finally, the results of this study are discussed under Sect. 5 and recommendations for future work are offered in this section.

2 Literature Review The concept of AI, which dates back to the mid-20th century and emerged with the concept of “computing machines and thinking machines” by Alan Turing, is defined as the ability to read and correctly interpret the data flowing from the environment, to learn from this data and to use these learnings in order to achieve specific missions and objectives through flexible adaptation [2]. Today, AI technology, which is used in many fields and sectors together with machine learning and deep learning sub-concepts, is gaining importance in the aviation industry day by day and considerable steps are being taken towards its use [3]. In the literature, researches on the use of AI in the aviation industry are limited, and there are a couple of studies based on aviation MRO. These studies are mostly ones aimed at revealing potential usage areas, application methodologies and roadmaps. Kulida and Lebedev [4] discuss AI trends that are used in solving problems in civil and military aviation and that can be used in the future, and their advantages and disadvantages. Johnson [5] says that AI technology can be used as an intelligent tutoring system in aircraft maintenance training. Garcia et al. [6] mention that AI and ML technology can be used to overcome the problems in aviation cyber security, and they emphasize possible challenges by drawing up the usage methods and roadmap. Zeldam [7] studies on an AIbased model for the automated detection of anomalies and diagnosing failures in aviation maintenance activities. In the study of Apostolidis et al. [8], there are opinions on the 1 Stands for “VIekriterijumsko KOmpromisno Rangiranje”, and is an acronym in Serbian of a

“multi-criteria optimization and compromise solution”. 2 Stands for “TOmada de Decisao Interativa Multicriterio”, and is an acronym in Portuguese of

“interactive and multiple attribute decision making”.

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importance of AI-ML3 -based Data Analytics in MRO operations and how developments in this field will contribute positively to aviation MRO processes in terms of optimization and forecasting. Vincent et al. [9] details the opportunities and benefits that AI can offer to the industry by giving examples of today’s usages and impacts for aviation and space industry. Cheng et al. [10] establish an artificial neural network algorithm model, present a study on how this model can be applied in aviation, and analyze the prospects and difficulties of the application. Kaparthi and Bumblauskas [11] conduct a study on an algorithm with the ML approach to predetermine possible failures related with maintenance of an aircraft and to plan maintenance time in a more optimized way.

3 Deciding on the Most Appropriate MRO Process for AI Technology AI technology has started to take an active role in various sectors at different areas. There are also several potential areas where this technology can be used in aviation MRO. In this research, application area prioritization will be made for a company that has not yet integrated AI technology into any of its processes. In this sense, research has been conducted on the areas where AI technology can be used in the aviation MRO sector, and it has been determined that this technology can be integrated into eight different processes, most of which are mentioned in the literature review section: Document Management (A1)4 , Augmented Reality (A2), Anomaly Detection (A3), Recruitment (A4), Supply Chain Optimization (A5), Predictive and Preventive Maintenance (A6), Maintenance Scheduling (A7), and Automated Quality Control (A8). After an MRO company decides to integrate AI technology into its processes, it should consider some important criteria when deciding in which area it should primarily use this technology. These criteria also have different rating. Some processes have a direct impact positively on some of the following main criteria, which are important for maintenance operations, while the impact on others is less. While integrating innovation to the MRO processes, the positive correlation of the new technology with the following criteria should be considered: Airworthiness (C1)5 , Flight Safety (C2), Customer Satisfaction (C3), Employee Acceptance (C4), Maintenance Cost (C5), Revenue Growth (C6), Maintenance Time (C7), Occupational Health and Safety (C8), Business Quality (C9), Reputation (C10), and Applicability (C11). The alternative processes and the criteria to be considered when decision making on processes have been revealed heretofore. After this point, criteria weighting will be determined by the Analytical Hierarchy Process (AHP) method, and then prioritizing the processes will be made with the VIKOR method. It is also note that whole evaluations are made by sector experts as decision makers in this research. Determining the Criteria Weights via AHP Method. The first step of the AHP method is to create the binary comparison matrix, in which the superiority of the criteria to each other is calculate. In evaluation phase, decision makers were asked to score the 3 Acronyms of Machine Learning. 4 Indicates Alternative-1. 5 Indicates Criteria-1.

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criterion comparison from 1 to 5, with 1 being the lowest and 5 the highest value of importance. After the binary comparison matrix is created, the next step is the normalization of the matrix. The related weight is calculated with normalized values by the Eq. (1) [12]: Wi =

aij 1 n n j=1 n j=1 aij

(1)

After calculating the related values, the consistency rate needs to be calculated to investigate whether the decision makers’ assessments are consistent or not via the following equation: CR =

CI RI

(2)

where CI and RI are consistency index and random consistency index (for n = 11, it is equal to 1,51), respectively. The consistency rate value must be less than 0.10 for a consistent data set. To calculate CI, the first step is to calculate the eigenvalues of each criterion via the following equation: λmax =

1 n (AW )i i=1 Wi n

(3)

Then, the consistency index is then calculated via the Eq. (4); CI =

λmax − n n−1

(4)

where n is the total number of criteria, i.e., 11. After all necessary calculations were made, it was revealed that the consistency ratio was 0.9 and less than 0.10. As a result of the evaluations whose data set is confirmed to be consistent, it is revealed that the weighting of the criteria to be considered for the most appropriate process selection is as follows (Table 1).

Table 1. Criteria weights of process selection

Weights

C1

C2

C3

C4

C5

C6

C7

C8

C9

C10

C11

0,23

0,23

0,10

0,08

0,06

0,07

0,05

0,07

0,03

0,05

0,03

Deciding the Best Alternative via VIKOR Method. VIKOR method is one of the most effective MCDM methods suitable for decision-making processes where benefit and cost criteria are together [13]. The decision makers who decide to integrate AI technology into aviation MRO processes evaluate the alternative processes one-by-one based on the criteria set (Table 2) when deciding which alternative to be applied first. For benefit criteria, a value of 1 indicates the minimum impact, a value of 5 indicates

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M. E. Aslan and A. C. Tolga Table 2. Decision matrix of process selection C1

C2

C3

C4

C5

C6

C7

C8

C9

C10

C11

Weight

0,23

0,23

0,10

0,08

0,06

0,07

0,05

0,07

0,03

0,05

0,03

A1

5

2

2

5

4

1

4

1

3

2

5

A2

2

3

1

5

4

1

3

4

3

4

1

A3

2

5

3

2

5

2

5

3

5

4

2

A4

1

1

1

4

4

2

4

1

5

2

1

A5

3

1

4

4

1

4

2

1

2

3

4

A6

4

5

5

1

4

3

4

1

1

5

2

A7

4

3

4

4

1

5

1

3

4

3

4

A8

3

4

3

3

4

2

4

2

4

2

2

BV

5

5

5

5

1

5

1

4

5

5

5

WV

1

1

1

1

5

1

5

1

1

2

1

the highest impact, and vice versa for cost criteria in this research. While cost (C5) and maintenance time (C7) are cost criteria, the others are benefit ones. Once the alternatives have been evaluated by criteria, and the best value (BV) and the worst value (WV) have been determined, the data set normalization is carried out by the Eq. (5) [14]: Rij =

xi∗ − xij

(5)

xi∗ − x− i

where xi∗ is the best value and xi− is the worst value in each criterion. After normalization, the utility and regret measure, i.e., S and R respectively, are computed through following equations: n wi ∗ Rij (6) Sj = 

i=1

Rj = max wi ∗



xi∗ − xij



xi− − xij   S ∗ = min Sj , S − = max Sj , j = 1, 2, . . . , n   R∗ = min Rj , R− = max Rj , j = 1, 2, . . . , n

(7) (8) (9)

Then, to determine the best alternative, the VIKOR index Qj is calculated for each alternative by considering ν, which is weight of strategy that provides maximum group benefit, and 1 − ν, which is the weight of the strategy that provides the regret of the opposing views (see Eq. (10)). 

Rj − R∗ Sj − S ∗ − − ν) ∗ ( ) (10) Qj = ν ∗ (1 S− − S∗ R− − R∗

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After all Qj s are calculated for each alternative, then the Qj values are ranked ascendingly. For different v values, the best alternative must satisfy these two conditions: 1. The alternative with the best Qj value must have the best score at least one of the S and R values. Q2∗ − Q1∗ ≥ DQ

(11)

where Q1∗ , Q∗2 are the best and the second-best values, respectively, and DQ = 1/(j − 1)

(12)

After all calculations and controls are done, it is revealed that “Predictive and Preventive Maintenance (PdPvM)6 ” is the best option for primarily integrating AI technology to the aviation MRO sector.

4 Deciding on the Most Appropriate AI Tool for Predictive and Preventive Maintenance Many companies, large and small, produce software solutions in the field of PdPvM for the aviation MRO sector. The OEM and the MRO companies, especially leading the industry, spend a lot of time on this issue. In addition, several start-up and technology companies are also closely interested in the subject. Although big data and analyticsbased studies are not new in the aviation MRO industry, products for PdPvM have been available for approximately the last 5 years [15]. As a result of MCDM study carried out in Sect. 3, it is revealed that the first priority process for the use of AI in the aviation MRO sector is PdPvM. Accordingly, 11 different software tools7 that can be used in this field for the aviation MRO sector was determined by conducting market research. A different MCDM study is conducted in order to decide the most appropriate one for the process among these 11 tools that differ from each other in many aspects such as the technology used, features/capabilities, project cost, scope, after-sales services, and process requirements, etc. The weights of the cost-benefit criteria were designated via the AHP method, and the TODIM method is used as the MCDM method in this study. Based on the MCDM studies in the literature related to software selection [16, 17], and the evaluations of experts in IT sector, the alternatives were evaluated according to the following criteria while determining the most suitable AI tool for the PdPvM process: Data Security (C1), Compatibility with Existing IT Systems (C2), Project Cost (C3), Commissioning Time (C4), Degree of risk (C5), User-friendliness (C6), Service and Support (C7), Flexibility (C8), Functions/features (C9), Reliability (C10), Vendor Reputation (C11), Product Viability (C12), and Technology Preferences (C13). The alternative PdPvM tools and the criteria to be considered when decision making on processes have been revealed heretofore. Criteria weighting was determined by the AHP method again. By referring to the assessments of sector experts, the result in Table 3 is achieved after applying the AHP steps one by one as specified in Sect. 3. 6 After this point, “Predictive & Preventive Maintenance” can be referred to as such. 7 Because of information security, the company and the software names are kept confidential

throughout the study.

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M. E. Aslan and A. C. Tolga Table 3. Criteria weights of AI tool selection C1

C2

C3

C4

C5

C6

C7

C8

C9

C10 C11 C12 C13

Weights 0,26 0,19 0,10 0,03 0,13 0,10 0,06 0,06 0,07 0,10 0,07 0,12 0,07

Deciding the Best Alternative via TODIM Method. TODIM method is based on the “Prospect Theory”, which was proposed by Kahneman and Tverski in the 1970s and was awarded the Nobel Prize [16]. In other MCDM techniques, the decision maker always searches for the solution that corresponds to the highest value among alternatives, while in the TODIM method, a measurement value that can be calculated by applying the “Prospect Theory” paradigm is used, and according to Gomes (2009), TODIM steps are as shown below [18]: Step 1: Normalization. After the alternatives are evaluated by the decision makers according to the criteria, with 1 point being the lowest and 5 point the highest, then the criteria are normalized and a value between 0 and 1 is ensured. A criterion is normalized by dividing it by the total value it receives from all the alternatives. In the normalized Pnm matrix, n shows the number of alternatives and m, the number of criteria. Step 2: Relative Weights. The relative weights of the criteria (wrc ) are calculated using the Eq. (13). wrc =

wc (c = 1, 2, 3, . . . , m) wr

(13)

where wcr indicates the relative weights, wc is the criteria weight and wr = max{wc |c = 1, 2, . . . , m}. Step 3: Dominance Alternative. The sum of the dominance degrees of the Ai alternative over the Aj alternative, calculated for all Cm criteria, is made with Eqs. (14) and (15).  m  δ Ai , Aj = c Ai , Aj for ∀(i, j). (14) c=1

when ⎧ ⎪ wrc (P ic −P jc ) ⎪ m ⎪ ⎨ w

 P ic − P jc > 0, c=1 rc   c Ai , Aj = 0 if P ic − P jc = 0, ⎪   ⎪  ⎪ ⎩ −1 ( mc=1 wrc )(Pjc −Pic ) if P ic − P jc < 0. θ wrc if

(15)

where θ indicates the attenuation factor and it is taken as 2,25 in this study. Step 4: Global Measures. Normalization equation (see Eq. (16)) is used for the global value of the alternative:   n n j=1 δ Ai , Aj − min j=1 δ Ai , Aj   ξi = (16)   max nj=1 δ Ai , Aj − min nj=1 δ Ai , Aj

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Step 5. Ranking. After the normalized global values of the alternatives are calculated via Eq. (16), a ranking is performed according to these values and the best alternative result is achieved. After the alternatives were evaluated according to the criteria and the necessary calculations were made, the normalized global values of and the ranking of the alternatives were revealed. As shown in Table 4, as a result of the TODIM method implementation, it was understood that the “sixth alternative” is the best software tool among 11 alternatives for PdPvM. Table 4. Normalized global measure and rankings of the alternatives A1 A2 Global values Ranking

0 11

A3

A4

A5

A6 A7

A8

A9

A10

A11

0,025 0,513 0,665 0,527 1

0,985 0,443 0,41 0,074 0,731

10

2

6

4

5

1

7

8

9

3

5 Results In this research, a decision-making study was carried out to determine the most appropriate area where AI technology can be used for aviation MRO activities and to identify the most appropriate software tool available for this area, VIKOR and TODIM methods were used as decision making methods, respectively. Both studies refer to the AHP method for weighting the criteria. In the decision-making process, eight alternative application areas are specified and evaluated with 11 criteria. As a result of this study, it has been understood that “predictive and preventive maintenance” is the top priority area. Afterwards, there were 11 alternative software tools that could be used in this area, and these software tools were evaluated based on 13 criteria. As a result of this study, the most suitable software tool for use in predictive maintenance applications is “Alternative-6”. In future research, the study can be revised with different MCDM methods, and the results obtained can be compared and analyzed by making a sensitivity analysis, the financial statement of the project can be revealed by making a feasibility analysis, or it can be added to the study by performing a risk and impact analysis of the best alternatives.

References 1. IATA. Airline Maintenance Cost Commentary FY2019 Data. (2020). https://www.iata.org/ contentassets/bf8ca67c8bcd4358b3d004b0d6d0916f/fy2019-mctg-re-port_public.pdf 2. Haenlein, M., Kaplan, A.: A brief history of artificial intelligence: on the past, present, and future of artificial intelligence. Calif. Manage. Rev. 61(4), 5–14 (2019) 3. Roadmap, A.I.: A human-centric approach to AI in aviation. Eur. Aviat. Saf. Agency 1 (2020) 4. Kulida, E., Lebedev, V.: About the use of artificial intelligence methods in aviation. In: 2020 13th International Conference Management of Large-Scale System Development MLSD), pp. 1–5. IEEE (2020)

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5. Johnson, W.B.: Advanced technology for aviation maintenance training: an industry status report and development plan. In: Proceedings of the Human Factors Society Annual Meeting, vol. 34, no. 16, pp. 1171–1175. SAGE Publications, Sage CA, Los Angeles (1990) 6. Li, W., Zhong, R., Chen, Y., Pi, Q.: An overview. In: Orogenic-Type Polymetallic Mineralization Associated with Multistage Orogenesis in Northern North China Plate, pp. 1–13. Springer, Singapore (2021). https://doi.org/10.1007/978-981-16-1346-3_1 7. Zeldam, S.G.: Automated failure diagnosis in aviation maintenance using explainable artificial intelligence (XAI). Master’s thesis, University of Twente (2018) 8. Apostolidis, A., Pelt, M., Stamoulis, K.P.:. Aviation data analytics in MRO operations: prospects and pitfalls. In: 2020 Annual Reliability and Maintainability Symposium (RAMS), pp. 1–7. IEEE (2020) 9. Vincent, N.C., Bhakar, R.R., Nadarajan, S.R., Syamala, A., Varghese, J.: Impact of artificial intelligence in the aviation and space sector. In: Artificial Intelligence, pp. 209–229. CRC Press (2021) 10. Cheng, T., Wen, P., Li, Y.: Research status of artificial neural network and its application assumption in aviation. In: 2016 12th International Conference on Computational Intelligence and Security (CIS), pp. 407–410. IEEE (2016) 11. Kaparthi, S., Bumblauskas, D.: Designing predictive maintenance systems using decision tree-based machine learning techniques. Int. J. Qual. Reliab. Manag. (2020) 12. Vargas, R.V., IPMA-B, P.M.P.: Using the analytic hierarchy process (AHP) to select and prioritize projects in a portfolio. In: PMI Global Congress, vol. 32, no. 3, pp. 1–22 (2010) 13. Ploskas, N., Papathanasiou, J.: A decision support system for multiple criteria alternative ranking using TOPSIS and VIKOR in fuzzy and nonfuzzy environments. Fuzzy Sets Syst. 377, 1–30 (2019) 14. Tong, L.I., Chen, C.C., Wang, C.H.: Optimization of multi-response processes using the VIKOR method. Int. J. Adv. Manuf. Technol. 31(11), 1049–1057 (2007) 15. Klisauskaite, V.: Predictive aircraft maintenance: established practice or future focus? Aerotime Hub (2021). https://www.aerotime.aero/articles/28331-predictive-aircraft-mainte nance-MRO 16. Kazancoglu, Y., Burmaoglu, S.: ERP software selection with MCDM: application of TODIM method. Int. J. Bus. Inf. Syst. 13(4), 435–452 (2013) 17. Gürbüz, T., Alptekin, S.E., Alptekin, G.I.: A hybrid MCDM methodology for ERP selection problem with interacting criteria. Decis. Supp. Syst. 54(1), 206–214 (2012) 18. Gomes, L.F.A.M.: An application of the TODIM method to the multicriteria rental evaluation of residential properties. Eur. J. Oper. Res. 193(1), 204–211 (2009)

Rethinking Customer Analytics: The Impact of Artificial Intelligence Ali Pi¸sirgen(B)

, Abdulkadir Hızıro˘glu , and Onur Do˘gan

University of Bakırçay, ˙Izmir 35665, Turkey [email protected]

Abstract. With the triggering effect of Covid-19 pandemic, the role of digitalization has become a strategic target and expedited the digital transformation process. World’s direction to the digital future has therefore shaped the use of newage technologies, such as internet of things, artificial intelligence (AI), machine learning and blockchain. In response to this evolvement of new-age technologies, a noticeable shift from data-driven analysis to technology-oriented applications has occurred, particularly addressing the significance of analytics and AI. These rapid advancements of AI applications influence the use of customer analytics whilst enhancing the importance both for the general understanding and individual behavior of customers, within the scope of customer analytics. Considering the embeddedness of these technologies on practical applications, this study acknowledges the high-impact role and power of AI. In this regard, the study concentrates AI applications from the perspectives of customer analytics. Furthermore, the task of AI, the level of intelligence of AI applications and how the information from customer analytics is obtained and exploited by these applications are discussed. Focusing on the practical case applications, the study suggests a taxonomical structure of AI and customer analytics. Keywords: New-age technologies · Artificial intelligence · Customer analytics · Real-life cases

1 Introduction Nowadays, companies are at the center of disruptive change, powered by digitalization, machine learning, robotics, and artificial intelligence [1]. The increasing complexity of customer needs and practice in the digital era is being altered by increased information availability, higher reach and interactions with data, and faster transaction rates which can be considered as digital transformation process [2]. In addition, the rise of online marketing there is also a paradigm shift in customer analytics, where understanding the needs and demands of each individual customer is becoming significantly important, Therefore, firms are forced to respond by increasing the deployment of technology and redesigning processes and business models to change the way they do business [3]. In this regard, companies have just begun to investigate the integrated application of new-age technologies to their consumer-oriented processes. There has been a clear © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 831–838, 2022. https://doi.org/10.1007/978-3-031-09173-5_95

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movement toward data-driven business and customer analytics, with companies leveraging the power of new-age technologies to boost their customer relationship management applications, particularly via consumer analytics [4]. Four “new-age technologies” – the Internet of Things (IoT), Artificial Intelligence (AI), Machine Learning (ML), and blockchain – are particularly significant in the light of technology’s increasing relevance. At the center of these new-age technologies, AI plays a key role as the ability of a system to accurately understand data, learn from it, and apply what it has learned to accomplish specific goals and tasks through flexible adaptation [5]. The objective of this article is to examine how AI may enhance the role of consumer analytics. We concentrate on how AI increased the capabilities may lead to a variety of customer analytics applications and their ramifications. Thus, we aim to enhance customer analytics AI applications literature by providing a taxonomical framework that leads to better understanding of customer analytics and AI embedded intelligence capabilities. The organization of the study is as follows. The next section expresses the evolution of analytics and its relationship with AI. While Sect. 3 presents the real-life case studies from the perspective of AI embedded customer intelligence capabilities, this study revisits the cases to demonstrate the level of intelligence of AI applications. Before scrutinizing these topics, next section reviews the literature on AI and customer analytics.

2 Analytics and the Relationship with AI The field of business and management analytics is rapidly transforming. AI, in conjunction with other new-age technologies, is the core of this transformation [6]. The best and simplest approach for most firms to effectively begin on AI is to position AI as a natural evolutionary expansion of analytics, thereby benefiting from developed analytics capabilities [7].

Fig. 1. Evolution of analytics (Source: Adapted from [7])

To start with this developed analytics capabilities, Fig. 1 illustrates the four phases of analytics and their critical characteristics. Analytics 1.0 is the primitive era, including internal decision support systems with high labor and low speed using structured data

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whereas Analytics 2.0 is the era of producing customer-focused solutions by big data analytics tools, using unstructured data. Analytics 3.0 is the era of data economy analytics which companies transform their business models by applying various analytics techniques. Finally, in the last phase of this evaluation Analytics 4.0 is the subsequent step in analytical culture for companies, and it is the era of artificial intelligence or cognitive technologies. It focuses on AI methods and more effective autonomy in executing the techniques, mainly automated machine learning.

Fig. 2. Dimensions of analytics (Source: Adapted from [8])

Furthermore, previous studies indicate that analytics can be evaluated with several dimensions. This study considers three dimensions, i) domain, ii) orientation, and iii) techniques (Fig. 2). The domain dimension shows the application field of analytics. This study covers customer domain given in Fig. 1. Some domains (like marketing) can include sub-domains (like retail analytics). The orientation dimension indicates a direction of thought, analytics effort, or benefits. All indications referred here have some specific topics which present users a way of structuring the investigation, exploration, and execution of analytics considering the domain’s interest. The technique dimension demonstrates how an analytics task is achieved from multiple perspectives in which this study is interested in types of data.

3 AI-Embedded Customer Intelligence Capabilities: Evidence from Real Life Cases Customer analytics presents various AI applications and often examples of misnomer. To overcome this confusion, we intend to demonstrate a taxonomical framework of AI applications within the scope of customer analytics supported by real-life cases (Fig. 3). Customer analytics from the perspective of customer (relationship) management, is associated with four interrelated customer strategies that each could be considered as a step or phase of a life cycle. Customer identification is a process of profiling and segmenting customers on the basis of their similarities and differences. Companies relying on pre-defined data units benefit from these descriptive analytics and thus shape customer specific services. Customer retention refers to a set of operations to improve the number of repetitive customers and their profitability. Customer attraction is a strategy that helps you attract customers who are already interested in buying. Customer development is

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Fig. 3. Taxonomical framework of AI-embedded customer intelligence capabilities

a technique to understand the customer needs. To perform this, open-end questions are asked to the potential consumers about services or products. To examine the AI-embedded customer intelligence capabilities, this study presents four real life cases. These cases are chosen based on marketing strategies in line with customer analytics. Verizon is an American multinational telecommunications conglomerate that benefits customer analytics for segmentation. BNP Paribas S.A. is a French international banking group. It is the world’s 7th largest bank by total assets and the largest bank in Europe and uses customer analytics for complaint management so that it reiterates its customers. Moreover, Ratesdotco is a Canadian financial service provider which benefits from analytics for customer attraction. Stitch Fix is the personal style service for men and women that evolves with your tastes, needs and lifestyle which empowers customer development. 3.1 AI and Big Customer Data A big data revolution is underway, and consumer analytics is at the core of it. In real time, technology allows for the collection of rich and copious data about costumer phenomena. As a result, companies have access to unprecedented volumes, velocity, and diversity of primary data, pertaining to the customers, referred to as Big Data [9]. Customers communicate their needs, wants, attitudes, and beliefs in a variety of ways through a variety of channels [10]. Big data analytics is a technology that involves organizing large amounts of data, processing and uncovering information, patterns, and intelligence from that data, as well as presenting and reporting that knowledge to support decision-making [11].

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3.2 AI and Customer Analytics The main role of big data is to enable users to conduct analysis that leads to knowledge creation [11]. This is provided by analytics that are descriptive, diagnostic, predictive and prescriptive (Fig. 4).

Fig. 4. AI and customer analytics with regards to cases

To scrutinize the analytical perspective of our cases, starting with Verizon, interested in generating bundles based on customers usage, descriptive analytics is considered since the aim is to create internal reporting to encourage data-oriented decision. Furthermore, with regards to diagnostic analytics referred as deep-dive analysis of big data to understand the reasoning, Amelia benefits from unstructured data, particularly textual and voice recorded, of customers’ complaints that lead to present complaint management solutions. As an example of predictive analytics, which makes prediction via AI applications. Ratesdotco uses the data from pre-defined questionnaires as well as traffic records to understand customers’ preferences. It also supports for comparison of options to be able to provide best rates for car insurance. In this case, big data consists of both traffic records and answers of questionnaires that supports predictive analytics. Lastly, prescriptive analytics examines data to acknowledge the potential actions, likely to happen in the future while using some techniques such as simulation, neural networks, recommendation engines etc. Stitch fix here presents virtual reality-based fashion recommendations based on unstructured big data from social media. 3.3 Risk and Value Understanding the consequences and risks of rising AI use is a challenge not only for security of the data, but also for the use of this data as the input for customer analytics. The latter is recognized as AI has the potential to create value while also providing benefits to customers in the form of better service and context-aware offerings. Firms while acknowledging the increasing risks, also recognizes AI as the core component of customer analytics to create business value.

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4 Revisiting the Framework: Cases from a Taxonomical Angle In this study, a taxonomical framework was proposed to address the AI-embedded customer analytics. To link this framework with risk and value, it is important to address how AI is constructed and its dimensions with regards to the taxonomical framework provided. This study continues with a two-dimensional analysis of cases; level of intelligence and data type, that supports risk and value creation (Fig. 5).

Fig. 5. Revisiting the framework: cases from taxonomical angle

Level of intelligence of an AI application is defined based on its capabilities to perform automated or context-aware tasks. Both are compared as the former entails AI applications that are standardized, in the sense that they require consistency and rationality while context-awareness is a type of intelligence that enables systems to perform a function of how to learn and even improve beyond human programming [12]. AI performs effectively for the role of task automation in scenarios in which there are set boundaries and predictable outcomes. On the contrary, by using holistic thinking and context-specific reactions, context-aware AI applications can tackle complicated jobs. Data type is referred as whether data are preprocessed in line with the level of intelligence of the task. In this regard, data can be benefitted from AI operations as structured and unstructured. Data that have been allocated to certain fields and can thus be processed directly by computing equipments are referred to as structured data. Structured data is collected through certain criteria that eases to process predefined task, can be named automated tasks [13]. On the other hand, unstructured data, specific to context, require specific learning process for each individual AI operation. Based on the mentioned framework the cases that are within the scope of this study can be categorized and grouped into four quadrants of this framework. Box 1: Automated Tasks Based on Unstructured Data In Box 1, the importance of including unstructured data enables the AI applications to perform in-depth analysis which then empower to conduct the complaint management. As a complaint management process, AI analyzes the complaint data of each customer to perform them a better service while aiming to understand what the complaints are about.

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AI applications here have the capability of analyzing unstructured data such as voice and text. Amelia used by BNP Paribas, a case study for customer retention, processes words spoken to agents and interpret what customers complaint about while BNP Paribas monitor strategical performance and gain advantage on value creation. Box 2: Context-Aware Intelligent Robots Supported with Unstructured Data Context-aware intelligent robots supported with unstructured data is a case of customer development which enhances the customer experience management. AI applications as intelligent robots demonstrates the capability of analyzing customers’ unstructured data. Stitch Fix in this case presents unique business model that provides personalized products for each customer which relies on an AI application supported with the unstructured data from customers’ Facebook and Pinterest profiles while overcoming the limitations of expressing the styling needs. Customers are then presented with suitable fashion. Taken into account that Stitch Fix does not run any stores and only available online, this contextintelligent robot provides a strategical innovation based on customer analytics as a value creation tool. Box 3: Automated Tasks Based on Structured Data The third box demonstrates the automated tasks performed by AI. Verizon is an exemplary case study that AI applications are used to present optimized data bundles based on the customers usage. The logic behind this AI practice is to present the customer segments which will then enable Verizon to develop generic bundles. The data used here is structured customer data. In this regard, AI embedded customer analytics is used for ad hoc basis to highlight the customer segments. With regards to value creation, customer analytics to achieve segmentation is a holistic approach to customer strategy. Box 4: Context-Aware Intelligent Robots Supported with Structured Data This box is considerably similar to Box 3 while AI applications in this box supports a context-aware intelligent robot that provide customer-based solutions. At Ratesdotca, AI-based intelligent robot benefits from considerable amount of numeric data that enable it to show optimal rates. This is referred as direct marketing which identifies potential customers, what type of car insurance they are likely to purchase and what they are not interested in. Ratesdotca benefits from customer analytics as a strategic resource since the individual customer strategy to predict the best rate for car insurance is the adopted approach for value creation.

5 Conclusion AI embedded customer analytics plays significant role within the scope of customer analytics. Cases studies showed that customer analytics are the starting point of value creation within the organizations’ business processes and AI improves this value for better efficiency via both predefined tasks and context-aware intelligent robots. In fact, many organizations are launching AI initiatives too soon or taking on projects for which they lack the necessary resources. An ambitious plan can result in quick AI competency growth, but any AI strategy must be considered in the context of the organization’s present capabilities.

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For future studies on AI-based customer analytics, four additional contemporary topics should be considered to expend the numbers of the cases via taking into account of various functionalities of customer management. These are the analytics pertaining to the following domains: text, web, mobile and network. Text analytics is related to dynamic and real-time sentiment analysis. Web analytics offers personalized solutions to increase customer satisfaction by modeling their behaviors. Mobile analytics serves as a tool for increasing customer engagement. Network analytics produces network-based solutions, such as blockchain technology for more reliable customer transactions, which uses the network architecture.

References 1. Syam, N., Sharma, A.: Waiting for a sales renaissance in the fourth industrial revolution: Machine learning and artificial intelligence in sales research and practice. Ind. Mark. Manag. 69, 135–146 (2018). https://doi.org/10.1016/j.indmarman.2017.12.019 2. Kumar, V., Dixit, A., Raj, R., Javalgi, G., Dass, M.: Research framework, strategies, and applications of intelligent agent technologies (IATs) in marketing. J. Acad. Mark. Sci. 44(1), 24–45 (2015). https://doi.org/10.1007/s11747-015-0426-9 3. Kumar, V., Ramachandran, D., Kumar, B.: Influence of new-age technologies on marketing: a research agenda. J. Bus. Res. 125, 864–877 (2021). https://doi.org/10.1016/j.jbusres.2020. 01.007 4. Libai, B., et al.: Brave new world? On AI and the management of customer relationships. J. Interact. Mark. 51, 44–56 (2020). https://doi.org/10.1016/j.intmar.2020.04.002 5. Kaplan, A., Haenlein, M.: Siri, Siri, in my hand: who’s the fairest in the land? On the interpretations, illustrations, and implications of artificial intelligence. Bus. Horiz. 62(1), 15–25 (2019). https://doi.org/10.1016/j.bushor.2018.08.004 6. Haenlein, M., Kaplan, A., Tan, C.-W., Zhang, P.: Artificial intelligence (AI) and management analytics. J. Manag. Anal. 6(4), 341–343 (2019). https://doi.org/10.1080/23270012.2019.169 9876 7. Davenport, T.H.: From analytics to artificial intelligence. J. Bus. Anal. 1(2), 73–80 (2018). https://doi.org/10.1080/2573234X.2018.1543535 8. Holsapple, C., Lee-Post, A., Pakath, R.: A unified foundation for business analytics. Decis. Supp. Syst. 64, 130–141 (2014). https://doi.org/10.1016/j.dss.2014.05.013 9. Erevelles, S., Fukawa, N., Swayne, L.: Big Data consumer analytics and the transformation of marketing. J. Bus. Res. 69(2), 897–904 (2016). https://doi.org/10.1016/j.jbusres.2015.07.001 10. Kietzmann, J., Paschen, J., Treen, E.: Artificial intelligence in advertising. J. Advert. Res. 58(3), 263–267 (2018). https://doi.org/10.2501/JAR-2018-035 11. Sun, Z., Huo, Y.: The spectrum of big data analytics. J. Comput. Inf. Syst. 61(2), 154–162 (2021). https://doi.org/10.1080/08874417.2019.1571456 12. Huang, M.-H., Rust, R.T.: Artificial intelligence in service. J. Serv. Res. 21(2), 155–172 (2018). https://doi.org/10.1177/1094670517752459 13. Baars, H., Kemper, H.-G.: Management support with structured and unstructured data—an integrated business intelligence framework. Inf. Syst. Manag. 25(2), 132–148 (2008). https:// doi.org/10.1080/10580530801941058

Mixing Population-Based Metaheuristics: An Approach Based on a Distributed-Queue for the Optimal Design of Fuzzy Controllers Alejandra Mancilla , Oscar Castillo(B) , and Mario Garc´ıa Valdez Tijuana Institute of Technology, Tijuana, Mexico {alejandra.mancilla,mario}@tectijuana.edu.mx, [email protected]

Abstract. In this work, we present a distributed platform to execute multi-population metaheuristics. As proof of concept, we present an implementation using two metaheuristics: Genetic Algorithms, and Particle Swarm Optimization. We execute these multi-population algorithms asynchronously using a queue-based architecture. We optimize the parameters defining the membership functions of a rear-wheel fuzzy controller. We compare the results with a non-distributed sequential alternative and show the benefits of mixing the algorithms’ populations and integrating a migration process between them.

Keywords: Asynchronous algorithms Population-based metaheuristics

1

· Fuzzy control ·

Introduction

Since their inception, a natural application of fuzzy inference systems (FIS) [1] has been implementing solutions to control problems [2,3]. The success of fuzzy controllers is well-documented in both research and commercial systems [4]. Moreover, using fuzzy systems in real-world problems requires the use of some optimization technique to tune the parameters of the fuzzy system, for instance, the parameters of the membership functions (MFs) used to define linguistic variables, the structure of fuzzy rules, or even the type of defuzzification employed [5,6]. An algorithmic solution is justified because of the ample search space and the difficulty of establishing the performance of a fuzzy controller. Traditionally, designers must run time-consuming simulations to validate the performance of a single fuzzy system configuration, causing manual tuning to be impractical [7,8]. Designers often apply population-based metaheuristics when adjusting FISs. In previous works, we established that tuning MFs demands the extensive use of computational resources when using simulations, taking a few seconds of wall-time in most cases [9,10]. In order to parallelize the execution of the optimization algorithm and reduce the time it takes to run, this work c The Author(s), under exclusive license to Springer Nature Switzerland AG 2022  C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 839–846, 2022. https://doi.org/10.1007/978-3-031-09173-5_96

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proposes a distributed optimization method for tuning a fuzzy controller for a mobile robot [11]. The architecture has the additional advantage of being capable of executing several bio-inspired algorithms simultaneously. We organized this paper as follows. Next, in Sect. 2 we present a brief literature review of the state of the art; afterwards, in Sect. 3 we describe the implementation of our proposal in detail. In Sect. 4, we test our implementation by optimizing a fuzzy rear-wheel controller using different configurations using a benchmark control problem and the results. Finally, we present our conclusions and future work in Sect. 5.

2

Literature Review

A common approach to the challenge of time-consuming fitness evaluations in population-based metaheuristics has been to take advantage of the parallel nature of evolution. The fitness evaluation of each individual is independent of others in the same population, and there is also the opportunity to have several small populations evolving in parallel. Moreover, current techniques take advantage of parallel or distributed designs by using cloud services [12]. An early work, the FlexGP system by Garc´ıa Arenas et al. [13], proposes a deployment of an island model executed on multiple virtual machines on Amazon EC2 instances. More recent approaches follow a cloud-native paradigm using containers as a lightweight alternative to virtual machines [14], enabling the replicable deployment of the distributed system locally or on a cloud service. Examples of these works are those of Salza and Ferrucci [15] proposing the speed-up of evolutionary algorithms using containers in a cloud infrastructure. Also, several strategies follow an event-driven design, using distributed queues to communicate the work between containers. The EvoSwarm model [16,17] uses containers and message queues to communicate populations between containers following an event-driven architecture. In this work, we follow this approach by applying the design to develop a distributed fuzzy-controller optimization solution.

3

Proposed Method

As we mentioned before, running simulations is very computationally expensive, so we propose a distributed population-based algorithm to execute the search in parallel. We present a design based on EvoSwarm [18], an asynchronous and event-based architecture for population-based bio-inspired algorithms. We propose an event-based architecture that exchanges data between processes we call workers using message queues (see Fig. 1) for asynchronous communication. Workers take messages asynchronously (3) to then process the data (populations). In this implementation, each worker runs inside a Docker container. Containers are lightweight, isolated software packages that share operating system resources, using fewer resources than traditional virtual machines. Each worker inside a container continuously checks for messages in the Population Queue and, after receiving a population, executes a metaheuristic on this population

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for several iterations. Each message contains a configuration object with the algorithm’s parameters and a small population of candidate solutions that could be new or the result of an earlier execution shows that we need two queues, one called Population Queue (2) from where workers take populations to evolve, and another we call the Evolved Population Queue (4), receiving the resulting (evolved) populations. To initialize the algorithm, first, a one-time task (1) pushes n population configurations to the Population Queue. The main idea is that each worker runs a population-based metaheuristic for a small number of iterations on a population received as a message and then pushes the resulting population to the output queue. An essential component of the architecture is the Combinator process, responsible for taking the resulting populations from the Evolved Population Queue, and after reading the message, stop the algorithm if the number of function evaluations has been reached or if a suitable solution was found. However, the primary responsibility of this component is to migrate or combine populations that are arriving from the queues. This operation is similar to migration between islands in the island genetic algorithm model, where one or several candidate solutions are exchanged between populations. The combination method we propose in this work is as follows. We take the top two best candidate solutions from each population received and insert them in a buffer that always keeps the top-k solutions. Finally, we replace the two worst solutions o the received solution and replace them with the current first and second-best solutions in the buffer.

Fig. 1. Proposed architecture for event-based distributed population-based algorithms.

Before starting an algorithm execution, we must first write a file with the configuration for that particular optimization. The configuration file has the number of populations, their size, type of algorithm to execute, the number of iterations to run each time a worker receives the population, and the algorithm’s

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parameters. To run an experiment, a user only needs to have the docker-compose tool and execute the experiment, sending the number of workers to start as a parameter. Currently, we implemented workers capable of executing Genetic and Particle Swarm Optimization algorithms. The proposed method to tune the parameters of membership functions (MFs) of a Fuzzy controller is as follows: A list of MFs defines all fuzzy variables and each MF has certain number of parameters. Each candidate solution is a list of real-type values for each parameter of the MF. As a strategy to reduce the search space, we simplify and reduce the number of parameters needed to define a MF. The simplifications we propose for this type of fuzzy systems are: – Symmetrical Functions. Tracking errors can be positive or negative, depending on the robot’s position with respect to the path. Values are naturally symmetrical so that we can specify symmetrical MFs. – Minimum Error is Zero. In this system, the highest membership value for the lowest error will always be at zero, so we can leave these parameters fixed at zero. – Extremes Values. When using trapezoidal MFs to define extreme values error or motion, we are only interested in one side of the MF, leaving the parameters fixed at some extreme values out of the domain of the fuzzy variable. 3.1

Control Problem

The benchmark control problem we use to validate our proposal is the rear-wheel controller described by Paden [11], in which the error e is measured as the distance between the rear wheel and the nearest point to the trajectory. If the wheel is to the left, the error is considered positive. If the wheel is to the right, then it is negative. The second variable θe is the angle between the tangent at the nearest point in the trajectory and the bearing vector. The controller’s output is the angular velocity ω needed to calculate the steering angle of the front wheel. We take the design of the controller from a previous work [10] in which we have the same fuzzy variables as above, and five membership functions for each HighN egative, M ediumN egative, Low, M ediumP ositive, and HighP ositive. We have two signs because the error and the heading can be to the left or the right. Using the simplifications mentioned above, we have are tuning the MFs of both input variables, using ten parameters in total, the fixed and variable parameters are shown in Table 1. With these variables, we proposed a controller with twenty five fuzzy rules. 3.2

Implementation

To run the algorithms, we created a docker-compose script, with the configurations needed to create and start each experiment. Each container is described and stored as a Docker image, containing all the dependencies, libraries, code, and software needed to create the infrastructure automatically. Container images are instantiated into one or many containers that run in a Docker Engine. This engine runs as a native application in Linux systems and virtually in macOS and Windows.

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Table 1. Fuzzy rules for the rear-wheel controller

4

Variable Linguistic value

MF

Parameters

θe θe θe θe θe

High negative Medium negative Low Medium positive High positive

μtrap μtria μtria μtria μtrap

[−50, −5, −b, −b + c] [−d − e, −d, −d + e] [−a, 0, a] [d − e, d, d + e] [b − c, b, 5, 50]

error error error error error

High negative Medium negative Low Medium positive High positive

μtrap μtria μtria μtria μtrap

[−50, −5, −g, −g + h] [−i − j, −i, −i + j] [−f, 0, f ] [i − j, i, i + j] [g − h, g, 5, 50]

ω ω ω ω ω

High negative Medium negative Low Medium positive High positive

μtrap μtria μtria μtria μtrap

[−50, −5, −1, −0.5] [−1, −0.5, 0] [−0.5, 0, 0.5] [0, 0.5, 1] [0.5, 1, 5, 50]

Experiments and Results

As a benchmark for the distributed system, we implemented a simulation in Python adapting the Python Robotics library by Sakai [19]. We ran the experiments on a Desktop PC with AMD Ryzen 9 3900x 12-core processor with 24 threads and 48 GB RAM with Fedora Linux 35 Kernel Version: 5.16, Docker Client v0.9.1 and Server Version: 20.10.13, running Python 3.7.5 code. Code can be found in GitHub: https://github.com/mariosky/fuzzy-control. We compared the algorithms using the mean, median, and standard deviation of the RMSE of 30 runs. In this work, we are interested in comparing a distributed execution versus a sequential execution of the algorithm, keeping the same number of evaluations. We tested with three configurations, the first and second consisted of all GA and PSO populations, and the third was a mix of four PSO populations and three GA. All the algorithms used the same parameters in a homogeneously distributed execution. 4.1

Setup

The parameters of the sequential and distributed algorithms are shown in Table 2 we can see that the number of function evaluations is almost the same. In the distributed case, we configured the algorithm with seven populations with nine candidate solutions each, each worker receiving the population will execute just four iterations (generations) of the algorithm before returning the population

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to the output queue. All populations will complete four cycles; this means that they will pass through the combinator four times. Table 2. Parameter values for the algorithms compared Algorithm

Parameter

Value

GA

Selection Mutation Mutation probability Crossover

Tournament selection (k = 3) Gaussian (μ = 0.0 and σ = 0.2) 0.3 One point (probability = 0.7)

PSO

Topology Fully connected Speed limit Min = −0.25, Max = 0.25 Cognitive and social constants C1 = 2, C2 = 2

Multi-population Pop size Number of Number of Number of Number of Sequential

4.2

populations iterations cycles func. evaluations

9 7 4 4 1008

Pop size Number of iterations Number of func. evaluations

50 20 1000

Results

Tables 3 and 4 show the results of the experiments. Distributed results are compared against sequential versions found in our previous work [10]. We can see that the results show comparable results between the distributed and sequential executions. We can note that the distributed GA implementation yields better results than the sequential version on average. At the same time, the sequential PSO version gave the best results. In this case, combining the PSO and GA algorithms did not improve the results. Table 3. Results of running the algorithms 30 times, here we show the best RMSE obtained by the best fuzzy controller found in each run. GA Seq. GA Dist. PSO Seq. PSO Dist. PSO-GA Dist. AVERAGE 0.0156

0.01091

0.00546

0.00645

0.00656

STDDEV

0.0316

0.00600

0.00202

0.00148

0.00185

MEDIAN

0.0091

0.00955

0.00536

0.00643

0.00625

MIN

0.0057

0.00384

0.00158

0.00360

0.00336

MAX

0.1820

0.03455

0.01026

0.01000

0.0116

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When comparing the time needed to complete each run of the algorithms, there is a substantial difference between sequential and distributed versions. As expected, the distributed version is several times faster. This result is obtained even with the communication overhead of inter-process communication via the Redis queue. Table 4. Results of running the algorithms 30 times, here we show the time in seconds needed to complete each run. GA Seq.

GA Dist. PSO Seq. PSO Dist. PSO-GA Dist.

AVERAGE 2664.1652 2802.506 421.672

5

343.550

28.540

415.649 23.4744

431.525

STDDEV

5066.8643

22.6012

MEDIAN

1727.9649 2762.295 417.845

412.685

432.366

MIN

1574.9495 2029.470 364.654

365.816

394.616

MAX

29488.776 3822.015 526.768

467.471

478.807

Conclusions and Future Work

We presented a design and implementation of a distributed multi-population, multi-algorithm method to optimize the parameters of the MFs for a fuzzy controller. Preliminary results show that a distributed execution gives similar results as those of a sequential implementation in a fraction of the time. As future work, we need to run the experiments in a computer with more cores or on the cloud. As a next step, we will experiment with other combination methods and heterogeneous configurations of the algorithms; each population will have different parameters chosen, for instance, at random. Finally, we could implement other optimization algorithms. Acknowledgment. This research was funded by project TecNM-15340.22-P.

References 1. Driankov, D., Hellendoorn, H., Reinfrank, M.: An introduction to fuzzy control. Springer Science & Business Media (2013) 2. Mamdani, E.H.: Application of fuzzy algorithms for control of simple dynamic plant. In: Proceedings of the Institution of Electrical Engineers, vol. 121, pp. 1585– 1588. IET (1974) 3. King, P.J., Mamdani, E.H.: The application of fuzzy control systems to industrial processes. Automatica 13(3), 235–242 (1977) 4. Driankov, D., Saffiotti, A.: Fuzzy Logic Techniques for Autonomous Vehicle Navigation, vol. 61. Physica (2013) 5. Xia, J., Zhang, J., Feng, J., Wang, Z., Zhuang, G.: Command filter-based adaptive fuzzy control for nonlinear systems with unknown control directions. IEEE Trans. Syst. Man Cybern. Syst. 51, 1945–1953 (2019)

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6. Isaka, S., Sebald, A., Karimi, A., Smith, N., Quinn, M.: On the design and performance evaluation of adaptive fuzzy controllers. In: Proceedings of the 27th IEEE Conference on Decision and Control, pp. 1068–1069. IEEE (1988) 7. Martinez-Soto, R., Castillo, O., Aguilar, L.T., Baruch, I.S.: Bio-inspired optimization of fuzzy logic controllers for autonomous mobile robots. In: 2012 Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS), pp. 1–6. IEEE (2012) 8. Salem, M., Mora, A.M., Merelo, J.J., Garc´ıa-S´ anchez, P.: Evolving a TORCS modular fuzzy driver using genetic algorithms. In: Sim, K., Kaufmann, P. (eds.) EvoApplications 2018. LNCS, vol. 10784, pp. 342–357. Springer, Cham (2018). https:// doi.org/10.1007/978-3-319-77538-8 24 9. Mancilla, A., Castillo, O., Valdez, M.G.: Evolutionary approach to the optimal design of fuzzy controllers for trajectory tracking. In: Kahraman, C., Cebi, S., Cevik Onar, S., Oztaysi, B., Tolga, A.C., Sari, I.U. (eds.) INFUS 2021. LNNS, vol. 307, pp. 461–468. Springer, Cham (2022). https://doi.org/10.1007/978-3-03085626-7 54 10. Mancilla, A., Garc´ıa-Valdez, M., Castillo, O., Merelo-Guerv´ os, J.J.: Optimal fuzzy controller design for autonomous robot path tracking using population-based metaheuristics. Symmetry 14(2) (2022). https://www.mdpi.com/2073-8994/14/2/202 ˇ M., Yong, S.Z., Yershov, D., Frazzoli, E.: A survey of motion plan11. Paden, B., Cp, ning and control techniques for self-driving urban vehicles. IEEE Trans. Intell. Veh. 1(1), 33–55 (2016) 12. Jankee, C., Verel, S., Derbel, B., Fonlupt, C.: A fitness cloud model for adaptive metaheuristic selection methods. In: Handl, J., Hart, E., Lewis, P.R., L´ opezIb´ an ˜ez, M., Ochoa, G., Paechter, B. (eds.) PPSN 2016. LNCS, vol. 9921, pp. 80–90. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-45823-6 8 13. Arenas, M.G., Guerv´ os, J.J.M., Castillo, P.A., Laredo, J.L.J., Romero, G., Mora, A.M.: Using free cloud storage services for distributed evolutionary algorithms. In: Krasnogor, N., Lanzi, P.L. (eds.) Proceedings of the 13th Annual Genetic and Evolutionary Computation Conference, GECCO 2011, Dublin, Ireland, 12–16 July 2011, pp. 1603–1610. ACM (2011). https://doi.org/10.1145/2001576.2001792 14. Dziurzanski, P., Zhao, S., Przewozniczek, M., Komarnicki, M., Indrusiak, L.S.: Scalable distributed evolutionary algorithm orchestration using docker containers. J. Computat. Sci. 40, 101069 (2020) 15. Salza, P., Ferrucci, F.: Speed up genetic algorithms in the cloud using software containers. Fut. Gener. Comput. Syst. 92, 276–289 (2019). https://doi.org/10.1016/j. future.2018.09.066 16. Merelo Guerv´ os, J.J., Garc´ıa-Valdez, J.M.: Introducing an event-based architecture for concurrent and distributed evolutionary algorithms. In: Auger, A., Fonseca, C.M., Louren¸co, N., Machado, P., Paquete, L., Whitley, D. (eds.) PPSN 2018. LNCS, vol. 11101, pp. 399–410. Springer, Cham (2018). https://doi.org/10.1007/ 978-3-319-99253-2 32 17. Valdez, M.G., Guerv´ os, J.J.M.: A container-based cloud-native architecture for the reproducible execution of multi-population optimization algorithms. Fut. Gener. Comput. Syst. 116, 234–252 (2021) 18. Garc´ıa-Valdez, J.M., Merelo-Guerv´ os, J.J.: A modern, event-based architecture for distributed evolutionary algorithms. In: Proceedings of the Genetic and Evolutionary Computation Conference Companion, pp. 233–234 (2018) 19. Sakai, A., Ingram, D., Dinius, J., Chawla, K., Raffin, A., Paques, A.: PythonRobotics: a Python code collection of robotics algorithms. CoRR abs/1808.10703 (2018). http://arxiv.org/abs/1808.10703. eprint: 1808.10703

Fuzzy Subsets Theory-Based Imprecision Modeling Using Ontology and Applied to Risk Estimation in Project Intelligent Management Larbi Abdelmadjid1(B) and Malki Mimoun2 1 ENERGARID Laboratory, SimulIA Team, Tahri Mohamed University, Bechar, Algeria

[email protected]

2 Ecole Supérieure Informatique, Sidi Bel Abbes, Algeria

[email protected]

Abstract. The increasing complexity and dynamism of construction projects has imposed substantial uncertainties and subjectivities into the risk analysis process. Effective risk management involves a process that includes risk identification, risk assessment, risk response and risk monitoring. Risk assessment is already solved using fuzzy expert systems, entropic weighting or fuzzy linguistic multiple attribute decision making. Given the methods or algorithms absence for project risk management, we opt to solve this kind of problem through a fuzzy ontology where we were able to welcome the expertise of a few executives and projects managers in the project management domain. So, the objective of this paper is to develop a fuzzy ontology-based risk assessment model in intelligent project management compared to our expert systembased previous work which have used a translation scheme and contrary to the previous works in this domain and which focus on either fuzzy language-based works or fuzzy expert-based solution. To my knowledge, there has been no intelligent project management risk estimation study using both a fuzzy ontology and a syntax-driven translation scheme. For simplification reasons, we present in this paper only predicate fuzziness case of a simple fuzzy query. The first results are encouraging although the work is still in its early stages. To illustrate this solution, we use again the Cox work, based on the Metus System group managers’ directives to determine the project risks. Keywords: Fuzzy databases · Fuzzy SQL · Fuzzy queries · Fuzzy logic · Ontology · Meta knowledge · Project intelligent management · Risk estimate

1 Introduction 1.1 Project Intelligent Management and Risk Assessment Project risk can be defined as an “unacceptable event” that puts the project in a critical situation. The risks of a project are characterized either by their nature or by their origin. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 847–855, 2022. https://doi.org/10.1007/978-3-031-09173-5_97

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Risks Nature. Technical, financial, human, organizational, regulatory, legal or commercial or managerial (related to decisions processes, hierarchical relations, specifications inconsistency and resources unavailability) [1]. Risks Origin. Is multiple (customers, suppliers, etc.). Once this identification has been made, it is then necessary to analyze, in a more or less detailed way, their causes and their potential impacts, and to characterize them, because we cannot act effectively on what we know at least partially. Indeed, risks are rarely independent of each other [2]. Risk Assessment. This is an extremely complex problem. The process launched must analyze, both, the importance of vulnerabilities in the disaster scenarios taken into account also to know and control the external factors [3]. The two fundamental risk parameters: Risk Impact (RI) and Risk Probability (RP). The risk impact parameter studies the potential effect of risk on a project objective such as schedule, cost, quality, or performance. The risk likelihood metric looks at the probability of each specific risk occurring [1] Project total risk is also presented with linguistic values (Tables 1 and 2). Table 1. Description of RI and RP [1] Description

General interpretation

Fuzzy number

Critical (C)

Very highly impact

(0.8,0.9,1,1)

Serious (S)

Highly impact

(0.6,0.75,0.75,0.9)

Modern (M)

Moderate impact

(0.3,0.5,0.5,0.7)

Miner (Mi)

Only small impact

(0.1,0.25,0.25,0.4)

Negligible (N)

No substantive impact

(0,0,0.1,0.2)

High (H)

Very likely to occur

(0.7,0.9,1,1)

Medium (M)

Likely to occur

(0.2,0.5,0.5,0.8)

Low (L)

Occurrence is unlikely

(0,0,0.1,0.2)

Table 2. Range of linguistic variables [4] Linguistic value

Numerical range

Linguistic variable: probability Very unlikely

[0,0.25]

Unlikely

[0.05,0.5]

Even

[0.25,0.75]

Likely

[0.5,0.95]

Very likely

[0.75, 1] (continued)

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Table 2. (continued) Linguistic value

Numerical range

Linguistic variable: severity Very little

[0,2.5]

Little

[0.5,5]

Medium

[2.5,7.5]

High

[5,9.5]

Catastrophic

[7.5,10]

Linguistic variable: risk Low

[0,0.33]

Medium

[0.05,0.66]

Significant

[0.33,0.95]

High

[0.66,1]

1.2 State of Art Existing methods in this area are generally based on the analysis of the risk matrix H, in which the relevant risk factors [5]. These initial scores are then arithmetically aggregated into an overall risk score. They’ve developed a fuzzy expert system, called the Research Prototype Early Assessment System, to support the independent assessment of projects in the very early phases of the software life cycle. Our previous work in this area [6] aims at implementing an interface based on the derivation of fuzzy queries into Boolean queries using a Syntax Oriented Translator Scheme (SDTS) that allows a better interpretation of a fuzzy query. We have applied it to the project management case (see Fig. 1). The solution proposed by the authors in [4] presents a fuzzy expert system-based solution for equipment selection of artificial aggregate systems through risky decision making. Although the difficulties encountered by the authors lie in the risk and the reliability initial estimation. The authors in [7] proposed a fuzzy expert system-based solution for software project risk assessment. This system receives the failure probability and the impact severity as numerical values and, after a two-level fuzzy inference, returns the risk of each factor as well as the project total risk, which allows decision makers to compare different projects through the obtained results. The authors in [8] present a fuzzy linguistic decision making-based solution with multiple attributes for the software projects risk assessment purpose. This solution allows to classify the risk elements and to determine the causes of these risks. These methods allow project managers to respond to risks. Therefore, the authors of [9] propose a solution based on fuzzy statistics for decision support in order to minimize the risks of competitive investment projects. The risk assessment solution proposed by [10] is based on Fuzzy Cognitive Maps (FCM) to calculate risks and test on an e-health system.

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The authors in [11] present a hybrid ontology-based solution for risk assessment, which harmonizes the concepts of reliability, safety and security based on industrial standards. This solution is applied to cyber security risk analysis.

Fig. 1. Syntax-Directed Translation Schemes (SDTS) [6]

2 Choice of the Risk Management Ontology Faced with the lack of risk management methods and algorithms, it was decided by many researchers to solve this problem by means of an expert system capable of accommodating the expertise of certain executives and field project management. The expert rules as well as the priority of the rules can explain the correlation between the metrics. The fuzzy expert system deals with the phenomenon that is uncertain in nature, and its fuzziness accounts for all the uncertainties encountered by an early risk assessment. These systems use fuzzy logic which favors linguistic imprecision. Therefore, they are interesting for independent assessments [9]. In the last years, researchers in this field have tried solutions based on ontologies and fuzzy cognitive maps. This led us to think about improving our previous solution based on an SDTS and a fuzzy expert system by introducing a fuzzy ontology in its concept definition and fuzzy relations part and in its reasoning part. We also chose to keep the use of the syntax-driven translation scheme in order to generalize later the proposed solution. 2.1 Project Management and Intelligent Risk Estimate This interactive modeling associated business risk assessment of a project, capital budgeting, and strategic decision support, in a system using its own managing relational databases. Figure 2 shows the general layout of the components of the project management model inspired by Cox’s work [2]. This model consists of three main modules: • Risk estimation, which is an ontology-linked software solution containing a consistent independent expert judgment on project management risk, based on a number of characteristics.

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• Fuzzy SQL + SDTS allowing to identify the part of the fuzziness in the request before translating it in order to prepare it for the evaluation. • Enterprise database and Project database.

Fig. 2. Project management system and risk estimation

2.2 Our Solution Description Following our previous works which were based on an SDTS (Syntax-Directed Translation Scheme) and an expert system, our new solution like the majority of previous works in this field focuses on the software project but the novelty consists in the fuzzy domain ontology use and implementing expert risk management rules. Except that for purely simplification reasons, we assume in this paper that fuzziness only exists in the query predicate. The basic rules: it brings together the knowledge and expertise of the experts Mary Williams, Bill Smith, who work in Metus System Group inc. It does not evolve during a work session. The rules are of the form [2]: R1: If the project budget is high or the duration of the project is long then the risk is acceptable; R2: if (the project is long enough or the project budget is high) or (the project is long or the size of the budget is comfortable) then the risk is important; R3: if the project is long enough or the project budget is high or the project is long and the actual budget is comfortable then the risk is high.

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2.3 Company Database Description We present in this section a company database description so that it can support the flexible queries concept. We added new fuzzy objects especially linguistic labels, etc. This description is as follows: * A department has a name, a unique number and a director whose entry date is stored. * A department has a local. It can manage several projects but a project is controlled by a single department. * Each project is characterized by a name, a number, a budget, a time to complete an actual project, a number of phases. * An employee is described by a name, a single Number, address, salary, sex and date of birth. * An employee has a single supervisor. It also has a level of education and performance. * An employee is assigned to one department but may work on several projects not necessarily related to his department. The number of hours per week spent by an employee on each project is stored. * A position is described by a unique code name (profession) and requires a level of education and experience. * Each employee has persons who are supported (children, etc.) Or dependent. These are described by: name, sex, date of birth and Family relationship with the employee. * Each project risks, the risk level of a project is often a factor taken into account, the risk depends on: - The project leader experience, - The actual project, - The actual budget complexity and duration, - Performance of employees Attributes described above (in bold) can be interrogated by flexible queries, that have the following estimated characteristics: Salary: has the linguistic labels defined on trapezoidal possibility distributions as follows: Low (50, 80, 120, 180), Medium (150, 300, 400, 550), High (400, 600, 800, 1000). These values are in Dollars. Hours_Number: has the linguistic labels: Small (0, 2, 7, 8), Medium (5, 10, 15, 20) High (15, 20, 25, 30). These values represent the number of hours. Budget: has the linguistic labels: Small (1000, 5000, 10000, 18000), Middle (15000, 50000, 100000, 150000), Big (120000, 200000, 500000, 100000). These values are in Dollars. Workforce_budg: has the linguistic labels: Small (1000, 5000, 10000, 18000), Medium (15000, 50000, 100000, 150000), Comfortable (120000, 200000, 500000, 1000000). These values are in Dollars. B_Duration: has the linguistic labels: Small (0, 10, 50, 100), Enough_Long (80, 120, 180, 220), Long (210, 270, 310, 380). These values are in days.

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Workforce_proj: has the linguistic labels defined on trapezoidal possibility distributions as follows: Poor (1, 6, 10, 16), Medium (14, 18, 22, 28), Cosy (25, 30, 36, 43). These values are team number. Complexity: the number of phases of the project, it has the linguistic labels defined on trapezoidal possibility distributions as follows: Down (1, 2, 4, 6), means (5, 8, 10, 12), High (11, 13, 15, 17). These values express the number of phases. Age: This attribute was added in place of Date_Birth to facilitate the representation and not to repeat the calculation Date_System - Date_Birth whenever we need the person age. It has the linguistic labels defined on trapezoidal possibility distributions as follows: Young (18, 22, 30, 35), Adult (25, 32, 45, 50), Old (50, 55, 62, 70). Experience: has the linguistic labels: Small (2, 3, 5, 6) Good (5, 7, 10, 12), Sufficient (7, 8, 15, 20), Large (12, 15, 50, 50). These values depend on the number of years worked by an employee. Level of risk: has the linguistic labels: Low (0.5, 10, 15, 20) Acceptable (15, 20, 25, 40) High (35, 40, 75, 100). These values describe the level of risk (percentage). Consequently, we can represent these criteria according to the relational model as follows: Department (num_d name, matricule_director, start_date, local) Position_work (cod_pw, occupation, education, experience) Employee (num, num_d, code_pos, name, sex, adr, Birth_date, salary, education, performance, experience, soc_supervisor) Project (p_num, num_d name, budget, duration_realization, staff_project, budget_staff, phases_number) Dependant (number, name, sex, Date_Birth, relationship) Works_in (number, num_pw, many hours)

Fig. 3. Risk estimation

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The software that we present provides a simple interactive fuzzy SQL interface, which allows editing of SQL queries and fuzzy SQL and which permits a risk evaluation in an intelligent project (Fig. 3).

3 Conclusion and Perspectives In the decision support context on risk estimation for intelligent project management, we continue to develop a new solution composed of two elements: * A query language so that the decision maker has answers to his queries even in the presence of flexible queries using an SDTS. * A fuzzy ontology to allow him to judge the fate of the project by estimating the risk of the latter, using some rules given by experts. Moreover and as a perspective of this work, we plan to develop a model solution to solve the risk estimation problem for any type of intelligent project management. Similarly, we plan to consider any type of flexible query using a syntax-driven translation scheme to simplify and translate the complex fuzzy query.

References 1. Zhang, R., Li, D. et al.: Development of risk assessment model in construction project using fuzzy expert system. In: 2nd IEEE International Conference on Emergency Management and Management Sciences, pp. 866–869. IEEE (2011) 2. Cox, E.D.: Fuzzy Logic for Business and Industry. [éd.] Bk & Disk edition (1995) 3. M˘az˘areanu, V.P.: Risk management and analysis: risk assessment (qualitative and quantitative). In: Analele Stiintifice ale Universitatii “Alexandru Ioan Cuza” din Iasi - Stiinte Economice, vol. 54, pp. 42–46 (2007) 4. Qin, H., Meng, S., Du, X., Ma, X.: Study on fuzzy expert system for artificial aggregate system equipment selection by risky decision making. In: International Workshop on Intelligent Systems and Applications, pp. 1–4 (2009) 5. Xu, Z., Khoshgoftaar, T.M., Allen, E.B.: Early operational risk assessment of software using fuzzy expert systems. In: Proceedings of the 5th Biannual World Automation Congress, pp. 435–442 (2002) 6. Larbi, A., Malki, M.: Modeling the imprecision of flexible queries using a fuzzy SQL language. In: ICSENT Conference. s.n. Tunis (2013) 7. Iranmanesh, S.H., Khodadadi, S.B., Tahere, S.: Risk Assessment of Software Projects sing Fuzzy Inference System (2009) 8. Li, N., Li, Y.: Software project risk assessment based on fuzzy linguistic multiple attribute decision making. In: IEEE International Conference on Grey Systems and Intelligent Services, pp. 1163–1166 (2009) 9. Sirbiladze, G., Khutsishvili, I., Dvalishvili, P.: Decision precising fuzzy technology to evaluate the credit risks of investment projects. In: 10th International Conference on Intelligent Systems Design and Applications, pp. 103–108 (2009)

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10. Szwed, P., Skrzy´nski, P.: A new lightweight method for security risk assessment based on fuzzy cognitive maps. Int. J. Appl. Math. Comput. Sci. 24(1), 213–225 (2014) 11. Alanen, J., et al.: Hybrid ontology for safety, security, and dependability risk assessments and Security Threat Analysis (STA) method for industrial control systems. Reliab. Eng. Syst. Saf. 220, 108270 (2022)

Personalized Literature Selection System Based on the Nearest Neighbor Algorithm Hubert Zarzycki(B) and Oskar Skubisz General Tadeusz Kosciuszko Military Academy of Land Forces, Wroclaw, Poland [email protected], [email protected]

Abstract. Greedy algorithms are a commonly used paradigm of combinatorial algorithms. Combinatorial problems cover a group of problems for which possible solutions are subsets of a finite set. In this work, the research procedure was performed on the nearest neighbor algorithm, classified as one of the greedy algorithms. The conducted research resulted in the development of a functional system for obtaining recommendations from literature, textbooks and other books on the basis of data obtained as a result of previous choices made by the system user. The program in question, using the nearest neighbor algorithm, made it possible to create a recommendation system for individual users, libraries and other institutions dealing with the distribution of books. Keywords: Nearest neighbour algorithm · Greedt algorithm · Swarm inteligence · Combinatorial problems

1 Introduction The human decision-making process for selecting books, music, movies or other media is complex. Selection is often made from a wide variety of objects, and is often based on unverbalised premises. We are not able to fully explain why we like a piece of music, a movie or a book due to its objective features. The purpose of building recommendation systems is to suggest subsequent, correct decisions to a person. When analyzing the history of user behavior, the recommendation system has information about the choice and usually also about the product evaluation. Both ratings, regardless of the scale, can be issued explicitly, in the evaluation process, or implicitly, as a result of an objective analysis of the user’s activity. Another important data is attendance analysis, which concerns the selection of a given product by a large group of users. It should be noted that the systems collecting implicit information provide more reliable recommendations, because in the systems of open (explicit) evaluation, dissatisfied people have a greater tendency to vote - so such data are sometimes burdened with a systematic error. The authors of this study have considerable knowledge and experience with various optimization methods, swarm intelligence [1, 4], fuzzy numbers [7, 8], and information systems. The article is a continuation of work in these areas by the team of Zarzycki [9], Skubisz [10], Czerniak, Ewald and Dobrosielski. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 856–863, 2022. https://doi.org/10.1007/978-3-031-09173-5_98

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1.1 Recommendation Systems Content recommending systems are used in many areas, ranging from streaming platforms offering access to audio-visual content through online stores to advertising. One of the most effective content recommendation systems has been developed by video streaming companies. It is also one of the most complex systems that uses many data tracking elements to create highly accurate recommendations. These systems track items such as: • The time the user selected the title. In this case, the obtained data can be used to determine whether the selection of a given item was influenced by p. holiday period or the choice was made as a result of direct interest in a given title. (the popularity of some titles grows during the holidays). • Personal data, in particular age, gender, geographic location and content indicated when creating a usage profile in order to better match the recommendations. This type of data has an impact on the operation of the algorithm, which, for example, may recommend content more often to a younger audience, and feature films to an older audience. • User behavior of fast forwarding the movie. The algorithm using this information may classify a given title as boring for the user and may recommend subsequent parts of a given title or a similar title with less frequency in the future. • Watching the series - The algorithm checks how a given title attracted the user. If the series finished faster compared to other titles, it means that the series was well suited for it. • Typed in the content platform search engine. The system checks what titles are searched by the user on the platform and tries to recommend similar titles. The recommendation systems of streaming platforms check many other parameters that may affect the recommendations of movies or series, which makes these algorithms one of the most effective and generate as much as 80% of user activity [12]. 1.2 Nearest Neighbour Algorithm If we introduce two points in space, we can connect these points with vectors to the origin of the coordinate system. Knowing the lengths of the vectors and the connection length of these two points, we can calculate the cosine of the angle between the vectors. The cosine of this angle can be interpreted as the similarity between two points. Below is the equation to calculate these values.     (1) a · b = ab cos θ cos θ =

a · b     ab

(2)

Below are pictorial drawings showing the placement of two points (objects) in space, vectors and angle between vectors (Fig. 1).

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(a)

(b)

(c)

Fig. 1. Cosine similarity of two points in space: a) obtuse angle close to 180°, b) 90°, c) a couple of degrees

If the angle is obtuse and close to 180° then the cosine value tends to −1. Also, the correlation between the points is negative. If the angle is close to 90° then the relation value is close to 0 (neutral). On the other hand, when the vectors are close to each other and the angle is a dozen or so degrees, then the similarity (the cosine) is close to the value of 1. It is a value that determines the precision of recommending a given book, the closer to 1 the book corresponds to the user’s preferences. This property can be used to find the similarity of points in two-dimensional or multi-dimensional spaces. In the created system, points adjacent to the examined book will be arranged in terms of the cosine value (similarity) for the given parameters.

2 Approach to the Problem The authors undertook to create a system recommending the selection of literature using the nearest neighbor algorithm. This algorithm is a greedy algorithm (an algorithm that is currently looking for the best solution) and was originally created to solve the traveling salesman problem. The traveling salesman problem is finding the shortest path that goes through all the points only once (Fig. 2). The system in question was written in the python programming language, for which the following solutions were selected: PyCharm programming environment, Microsoft SQL Server database, Tkinter library, Pyodbc Library, Pandas Library, SciPy Library. The figure below shows an example of a solution to the traveling salesman problem [2] using the nearest neighbor algorithm (Fig. 3). The method of operation of the nearest neighbor algorithm: The calculation starts from the user-selected starting point (base) and marks it as a visited point. In the case of a created system, it is a literature item for which the user intends to obtain a recommendation. Beginning with marking the selected point, the algorithm searches for the next point with the lowest weight, i.e. the point closest to the base point. In the created system it is the book which, based on the calculations, has the shortest distance to the previously selected base book. The algorithm then repeats the cycle until it has used all the points considered.

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Fig. 2. An example of a solution to the traveling salesman problem.

Fig. 3. An example of the operation of the nearest neighbor algorithm

In this way, the algorithm searches through the literature entries, compiling a list of books that most closely match the book originally selected by the user. In order for the algorithm to find such books, the constructed system must prepare the necessary data. The algorithm calculates the similarity based on the vector distances, which are computed using an array with ratings, year of publication, genre, author and book titles. The created system recommending literature is operated on computers without the need for a network connection, which allows the application to be used from anywhere. The application was developed on Windows 7 and works correctly on any Windows and Linux system, provided that the version of your system supports the database used. The constructed system was created with individual users, libraries and other institutions dealing with the distribution of literature in mind. The user receives recommendations for further items regarding the book of his choice. The nearest neighbor algorithm that was used in the constructed system uses only information about the books available in the database.

3 Creation of the System In order to build the system [5, 11], the following functional assumptions were adopted: 1. The application should allow for the evaluation of books in order to increase the number of recommendable books (Assuming that the algorithm only considers books that meet the required number of grades).

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2. The user can view the list of books in the database and the list of recommended books. 3. The user can add a book that is not yet in the database. 4. The application should recommend books based on the book selected by the user. 5. The application should have a login system. 3.1 Data Processing The application uses a Microsoft SQL Server database [3]. The database stores data that is used by the nearest neighbor algorithm to properly match the book to the user, and data such as the book and user list. The database consists of three linked tables. The first table “Books” contains the International Standard Book Number “ISBN”, the title of the book “Book_Title”, the author of the book “Book_Author”, the year of publication “Year_Of_Publication” and the publisher “Publisher”. The table has a unique “ISBN” primary key. The second table, “NBookRatings”, with book ratings, stores data such as: User ID “User_ID”, International Standard Book Number “ISBN” and book rating “Book_Rating”. The table has two foreign keys from the “Users” and “Books” tables. The third table “Users” lists the users with their id “User_ID”, city they live in “Location”, and age “Age”. The table has a master key “User_ID”, thanks to which each user has his own original number. There is a many-to-one relationship between the tables designed to enforce integrity to avoid invalid references. The “NBookRatings” table has the “ISBN” foreign key from the “Books” table and the “User_ID” foreign key from the “Users” table. Most of the columns of the tables are of the nvarchar type, which allows to enter both numbers and characters. The “User_ID”, “Book_rating” columns from the “NBookRatings” table and the “Year_Of_Publication” column from the “Books” table contain the int data type that allows to enter integers in the range −2,147,483,648 to 2,147,483,647. Linked database comes with the application using the Pyodbc library (Fig. 4).

Fig. 4. Database diagram

The program that uses the nearest neighbor algorithm to recommend books consists of layers that are assigned specific functions. The first is the data layer where the database resides. It stores data used in the business layer. The business layer is the layer responsible for connecting the data layer with the presentation layer. Thanks to this solution, the

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presentation layer receives the data that is displayed in it. It also allows the delivery of user input in the presentation layer to the data layer. This layer is also responsible for using the nearest neighbor algorithm to obtain book recommendations and the correct operation of the entire program. The last layer is the presentation layer. This layer allows one to handle all possible functionalities of the application, such as: Browsing the list with books. The user obtains a recommendation for a given book. Viewing the list of books for which a recommendation is possible. Adding books to the database. Login. Adding the rating of the item to the database.

4 Analysis of the Results One base item was selected for each test and the application was launched to find 15 recommended items. Where fifteen is the first integer fulfilling the condition k ≤ sqrt(n). Runs of tests for a variety of data showed no anomalies. Spatial points have been scaled to correspond to the ranking value and the year of release. The similarity also takes into account the genre of the book and the author. 4.1 Exemplary Results The parameters of the tested case were set as follows. Number of items in the database 250. The database contains a variety of items, including many modern popular science books. Each book can have a rating between 0 and 10. We look for the k Nearest Neighbors of the analyzed object in the algorithm. The value of k cannot be too large because the results will include objects that are not actually neighbors of the analyzed object. We calculate the value of k with the formula: k ≤ sqrt(n) where n is the number of books (records) used for the study. For a clear presentation of the results, only the first author of the book is included in the table. The year of publication shows the year of the last issue/reprint of the book. The following list shows an example of a list of recommended books with their selected parameters. In the example below, books similar to the base “The Hidden Life of Trees” are searched for. The table contains recommended items. As can be seen in the table below with the obtained results, there are a dozen or so books with a similar rank, year of publication and genre. Thanks to the k-Nearest Neighbor algorithm, it was possible to identify fifteen items that were close to the base book (The Hidden Life of Trees) in terms of parameters (Table 1). The 2011 book is the most distant in terms of the year of publication, which gives a 5-year difference. The newer book is 2020, it is 4 years older. The largest number of books is from 2017, and the year of publication differs only by one year from the base book. Book no. 15 with a value of 7.9 is the furthest in terms of rating from the base position, the difference is 0.9. Book No. 12 is ranked 0.5 higher. All items in the list are in the genre of science books. There is no base book author’s second entry in the database, nor a book with a similar title that could affect the results. The table above shows that the system correctly found the items with parameters similar to the base book.

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H. Zarzycki and O. Skubisz Table 1. Results data number 1.

No

Title

Author

Rating

Year of publication

Base

The Hidden Life of Trees

Peter Wohlleben

8,8

2016

1

Human Universe

Brian Cox

8,8

2016

2

Pandora’s Lab

Paul A. Offit

8,8

2017

3

Sapiens. A Brief History of Yuval Noah Harari Humankind

8.9

2017

4

The Revolutionary Genius of Plants

Stefano Mancuso

8,7

2018

5

Rewilding: The Radical new Science of Ecological Recovery

Cain Blythe

8,8

2020

6

Astrophysics for People in a Neil de Grasse Tyson Hurry

8,5

2017

7

Forces of Nature

Brian Cox

9,1

2017

8

The Gene: An Intimate History

Siddhartha Mukherjee

8,3

2016

9

Orgin Story

David Christian

8,4

2018

10

The Sixth Extinction

Elizabeth Kolbert

8,6

2014

11

The Emperor of All Maladies

Stephen Hoye

8,7

2011

12

Why we Sleep

Matthew Walker

9,3

2017

13

Life on Earth

David Attenborough

9,2

2018

14

The Knowledge Illusion

Philip Fernbach

8,0

2017

15

The Green Witch

Arin Murphy

7,9

2018

5 Conclusions As part of the solution verification, the authors generated multiple sets of results. One of these sets of results was presented in the article. The obtained results indicate that the system created on the basis of the proposed algorithm works correctly. No anomalies in the operation of the application were found [6]. The article proposes a book recommendation system that uses the approach of searching for distances and interpreting the value of cosines between the points representing the base book and the recommended book. The system finds and recommends books that can be accepted by the user. The system estimates a book’s similarity based on factors such as ratings of books and information about the books such as their year of publication, genre, author, and title. The analysis shows that the system presents interesting results by returns related books. In subsequent versions of the system, it will be possible to include a recommendation based also on further parameters such as keywords, titles selected in the system by users

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with similar tastes and preferences, or interactions with the recommendation system, such as browsing history. Significant improvement may also be brought by fine-tuning and better weight matching for particular parameters of similarity.

References 1. Engelbrecht, A.P.: Fundamentals of Computational Swarm Intelligence. Wiley (2005) 2. Laporte, G., Nobert, Y.: Exact algorithms for the vehicle routing problem. Ann. Discr. Math. 31, 147–184 (1987) 3. Lebiediewa, S., Zarzycki, H., Dobrosielski, W.T.: A new approach to the equivalence of relational and object-oriented databases. In: Atanassov, K.T., et al. (eds.) Novel Developments in Uncertainty Representation and Processing. AISC, vol. 401, pp. 85–93. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-26211-6_8 4. Merkle, D.: Swarm Intelligence: Introduction and Application. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-74089-6 5. Shakhovska, N. (ed.): Advances in Intelligent Systems and Computing. AISC, vol. 512. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-45991-2 6. Zarzycki, H., Apiecionek, Ł., Czerniak, J.M., Ewald, D.: The proposal of fuzzy observation and detection of massive data DDOS attack threat. In: Advances in Intelligent Systems and Computing, Springer, Cham (2021). https://doi.org/10.1007/978-3-030-47024-1_34 7. Zarzycki, H., Czerniak, J.M., Dobrosielski, W.T.: Detecting Nasdaq composite index trends ´ ezak, D. with OFNs. In: Prokopowicz, P., Czerniak, J., Mikołajewski, D., Apiecionek, Ł, Sl¸ (eds.) Theory and Applications of Ordered Fuzzy Numbers. SFSC, vol. 356, pp. 195–205. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59614-3_11 8. Zarzycki, H., Dobrosielski, W.T.: Use of ordered fuzzy numbers to observe quotations on financial markets. In: Advances in Intelligent Systems and Computing. Springer, Cham (2021) 9. Zarzycki, H., Dobrosielski, W.T., Vince, T., Apiecionek, Ł.: Center of circles intersection, a new defuzzification method on fuzzy numbers. Bull. Polish Acad. Sci. Tech. Sci. (2020) 10. Zarzycki, H., Ewald, D., Skubisz, O., Kardasz, P.: A comparative study of two nature-inspired algorithms for routing optimization. In: Advances in Intelligent Systems and Computing, Springer, Cham (2021). https://doi.org/10.1007/978-3-030-95929-6_17 11. Zarzycki, H., Czerniak, J.M., Lakomski, D., Kardasz, P.: Performance comparison of CRM ´ systems dedicated to reporting failures to IT department. In: Madeyski, L., Smiałek, M., Hnatkowska, B., Huzar, Z. (eds.) Software Engineering: Challenges and Solutions. AISC, vol. 504, pp. 133–146. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-436067_10 12. https://www.lighthouselabs.ca/en/blog/how-netflix-uses-data-to-optimize-their-product. Accessed 20 Mar 2022

A Meta-heuristic Approach to the Single Machine Scheduling Problem with Periodic Maintenance Kadir Büyüközkan1

, Mehmet Emin Baysal2 and Ahmet Sarucan2

, Cahit Yalçın2(B)

,

1 Karadeniz Technical University, Trabzon, Turkey 2 Konya Technical University, Konya, Turkey

[email protected]

Abstract. A major challenge facing manufacturing companies is working together on scheduling and maintenance activities. The machine shuts down for various reasons, which causes disturbances in production schedules. These problems are often overlooked in research. This study deals with the problem of the periodical maintenance of a single machine, which is subject to the constraints of the periodic availability of the machine. A new solution method is suggested for the problem with an ABC (Artificial Bee Colony) algorithm. As far as we know, this is the first study to address the issue of periodic maintenance of a single machine using the ABC algorithm. An operation-based sequence of sequential integers is adopted to solve it using the ABC algorithm. To update the array, the solution with the highest ordinal value is replaced by a non-dominant solution in each particular cycle. The efficiency of the ABC has been demonstrated by the use of sample sets. Altogether, 500 problems have been solved. For comparison purposes, the relative percentage difference for each sample was computed. The results of these calculations indicate that the proposed method is very satisfying. Keywords: Artificial Bee Colony algorithm · Periodic maintenance · Single machine scheduling

1 Introduction All sorts of repairs, renewals, inspections, etc., performed to ensure that production activities can continue uninterrupted in any system are referred to as maintenance. Activities that will ensure that production plant machines and technologies operate without failure are defined as maintenance planning. Maintenance activities fall into three categories: corrective maintenance, periodic maintenance, and predictive maintenance [1]. This study deals with periodical maintenance. Periodic maintenance consists of precautionary activities such as adjusting the machine and replacing parts at certain times before a malfunction occurs. The problem of identifying tasks going into the system in a single process and in what order is a single machine scheduling problem. Establishing a © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 864–869, 2022. https://doi.org/10.1007/978-3-031-09173-5_99

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production schedule independent of the maintenance schedule, creates a significant difference between the planned schedule and the actual one, and causes the works not to be completed at the specified times. With the effective inclusion of maintenance in the scheduling, the production process will not be interrupted, and customer demands will be responded to timely [2]. This study contributes to the literature by recommending a solution procedure with the ABC algorithm for the first time to the single machine periodic maintenance problem, which is the periodic machine availability constraint. There’s also an example of an intelligent practice. This paper is organized as follows. Section 3 describes an artificial bee colony algorithm. Computational results are given in Sect. 4. In Sect. 5, the results and future research are discussed.

2 Literature Review The literature review of the single-machine scheduling problem with periodic maintenance is given as follows. Liao and Chen [3] studied a single-machine scheduling problem with periodic maintenance and proposed a solution. Ji et al. [4] In their research, they considered several maintenance periods, in which each maintenance activity was scheduled after a periodic time interval. Sadfi et al. [5] examined the single-machine scheduling problem with the maintenance period and total completion time. Chen [6] studied a single-machine scheduling problem with limited machine availability. The result was a schedule that minimized the total flow time subject to periodic maintenance and unsustainable work. Chen [7] studied a single-machine scheduling problem with periodic maintenance, in which the machine is periodically stopped for maintenance for a fixed time w during the scheduling period. Low et al. [8] investigated a single-machine scheduling problem with usability constraints. Low et al. [9] presented a particle swarm optimization (PSO) algorithm to solve the single-machine programming problem with periodic maintenance activities. Yu et al. [10] discussed a single-machine scheduling problem with periodic maintenance and uninterrupted jobs. Their goal was to minimize the completion time. Wei-Wei Cui and Lu [11] addressed the problem of scheduling production on a single-machine with flexible periodic preventive maintenance that also considers release dates. Nesello et al. [12] minimized makespan by scheduling the single-machine scheduling problem, periodic maintenance and installations on a singlemachine, with periodic maintenance and sequential setup times. Gonzalez and Framinan [13] addressed the problem of scheduling jobs on a single-machine with periodic machine availability periods. Krim et al. [14] studied the single-machine scheduling problem with periodic preventive maintenance to minimize the sum of weighted completion times. Qamhan et al. [15] discussed a time window of a periodic maintenance strategy with different time windows and job scheduling activities in a single-machine environment. Prata et al. [16] provided heuristics for a single-machine scheduling environment with periodic resource constraints. In this study, the problem of scheduling jobs on a single-machine is handled with periodic maintenance. The scheduling horizon consists of periods in which the machine is used and other periods in which no operations are made. This problem is defined as the

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scheduling of periodic maintenance. This is because it is generally assumed that these availability times are used to perform maintenance activities.

3 Artificial Bee Colony (ABC) Algorithm An artificial bee colony algorithm has been developed, based on the behaviour of honeybees in search of food [17]. In this algorithm, bees, it is divided in three such as worker bees, onlooker bees and scout bees. Worker bees try to find a food source and keep the food source in their minds. Onlooker bees tend to find better food supplies than worker bees. A few of the workers are turning into Scout bees, looking for new sources of food. The loop continues until the stopping criterion is fulfilled. Similar to other population-based algorithms, the ABC algorithm is an iterative process.

4 Illustrated Example A sequential operation-based integer array is adopted to solve the problem with ABC algorithm. Swap methodology has been used to provide viable solutions to this problem. Domination based on greed and, tournament principles have been adopted. To refresh the array, the solution with the highest ordinal value in each specific loop has been replaced by a non-dominant solution. The algorithm steps are Step 1: Randomly generate as many advanced food sources as the number of bees used. Step 2: Create an adjacent food source for each worker bee as well as the number of onlooker bees using the swap method. Step 3: Calculate the Cmax of each onlooker bee and compare it to the Cmax of the worker bee. If this value is smaller, select this onlooker with the new worker bee; else compare it to other onlookers. Step 4: Compare the newly selected worker bees among themselves and memorise the worker with the smallest Cmax. Step 5: Repeat the above procedure for the number of iterations. The Swap operation: Every worker bee creates N number of adjacent food sources. These neighbors are created by swapping mutations of randomly selected elements from the sequence of the leading sources. Sample Sets: Sample sets of n ∈ {10, 20, 30, 40, 50, 60, 70, 80, 90, 100} 10 used by Gonzalez and Framinan [1] are used to prove and compare the efficiency of the ABC algorithm adapted to the problem. Since there are 50 problems with each sample set, 500 problems were solved. For each sample, operation times were randomly generated between 1 and 50 min in accordance with uniform distribution, and the time between blocks was randomly between 150 and 200 min in accordance with uniform distribution.

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For comparison, the RPD (Relative Percent Deviation) value of each compared sample was considered. RPD =

Cmax (METH ) − MIN 100 MIN

(1)

Given in Eq. (1), MIN is the optimal or best bound makespan obtained for the methods compared; METH is the resulting makespan for each method. ARPD corresponds to average RPD. Calculating the lower bound: Because optimal solutions are difficult to achieve for a NP-hard scheduling problem, the lower limits used to measure the performance of heuristic algorithms are commonly found in the literature. For this problem, Hsu et al. [18] used a lower bound to assess the performance of heuristics algorithms. The lower bound is presented as in Eq. 2 and estimated as follows:   n n j=1 Pj −1 ·t (2) Pj + LBLow = j=1 T The first term in Eq. (2) is the total processing time, and the second term is the minimum total maintenance time. As maintenance time is not taken into consideration, the lower limit is the total processing time.

5 Computational Results The results of ABC algorithm are compared with the results of NEW, NEW_BF, NEW_FF, BFR, BFD, BFI, BFHILO, BFLOHI, BFV, BFA, FFR, FFD/MFFD, FFI, FFHILO, FFLOHI, FFV, FFA methods whose solutions are given in the literature. Algorithm parameters: Number of pioneer bees (workers): 10. Number of follower bees (onlooker): 30. Iteration: 100. The algorithm is encoded in C# and runs on a computer with an Intel Core i5 2.40 GHz 6 GB of RAM. The Cmax, Waste Time, Best Time and RPD values for each set of 10 jobs were calculated based on the job order and solved for 50 sample problems. Table 1 presents the calculated values of these problems as well as the results of the methods used in the literature. Based on these results, the ABC algorithm performed better for certain sample sets from BFR, BFD, BFI, BFHILO, BFLOHI, BFV, BFA, FFR, FFD/MFFD, FFI, FFHILO, FFLOHI, FFV, FFA and NEW methods. However, NEW_BF has not performed well compared to NEW_FF. This is explained either by the fact that the number of pioneer bees, onlooker bees and iterations is small in the given parameters, or there’s some need to improve the algorithm.

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K. Büyüközkan et al. Table 1. The ARPD values for the methods used in the problem.

Method

10

20

30

40

50

60

70

80

90

100

NEW

0.695 1.258 1.124

1.472

1.219

0.712

0.791

1.254

1.422

1.294

NEW_BF

0.000 0.035 0.087

0.049

0.085

0.062

0.029

0.037

0.038

0.020

NEW_FF

0.000 0.035 0.088

0.056

0.096

0.083

0.048

0.061

0.053

0.035

BFR

4.240 3.232 2.871

1.981

2.255

1.472

1.709

1.538

1.409

1.299

BFD

0.651 0.738 0.415

0.265

0.024

0.161

0.107

0.093

0.072

0.057

BFI

8.996 9.805 9.577 10.655 10.316 10.067 10.273 10.700 10.363 11.278

BFHILO

3.238 3.451 4.367

3.975

4.043

3.528

3.703

3.628

3.818

3.618

BFLOHI

3.858 3.539 4.066

4.130

4.558

3.955

3.815

4.187

3.971

3.694

BFV

5.929 5.168 5.094

5.752

5.578

4.885

5.109

5.233

5.282

5.562

BFA

1.639 1.450 1.035

0.781

0.621

0.458

0.281

0.305

0.336

0.217

FFR

4.240 3.274 3.006

2.041

2.289

1.589

1.775

1.620

1.465

1.409

FFD/MFFD 0.565 0.698 0.415

0.278

0.239

0.176

0.113

0.098

0.075

0.060

FFI

8.996 9.805 9.577 10.655 10.316 10.067 10.273 10.700 10.363 11.278

FFHILO

3.238 3.451 4.297

4.064

4.043

3.528

3.754

3.651

3.843

3.626

FFLOHI

3.858 3.689 4.066

4.130

4.637

4.014

3.815

4.282

4.035

3.680

FFV

5.929 5.168 5.094

5.884

5.578

4.885

5.109

5.233

5.282

5.562

FFA

1.639 1.446 1.038

0.803

0.618

0.472

0.308

0.314

0.343

0.231

ABC

0.397 0.148 0.565

1.363

2.907

2.053

0.126

0.201

0.093

0.422

6 Conclusion and Future Research In this study, 10 sets of samples for the machine maintenance problem and 50 sample problems for each set of samples were solved under the constraint of periodical availability of the single machine. A total of 500 sample problems were solved using the ABC algorithm and compared to methods developed in the literature over the past few years. Near optimal results were obtained for the majority of the problems tested. As an alternative to the methods discussed in this study, the ABC method with a powerful algorithm is proposed. The initial results of the algorithm’s performance were assessed using data sets from the literature. The findings show that the ABC algorithm can make further improvements to NEW_BF and NEW_FF. Better results can be achieved by optimizing parameters on different parameters with the ABC algorithm used in the suggested method. In the meantime, different hybrid methods can be developed by combining them with different metaheuristic methods. For future research, periodic maintenance and time window problems can be considered together and analyses can be made on parallel machines.

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References 1. Köksal, M.: Maintenance Planning. Seçkin, Ankara (2007). (in Turkish) 2. Dündar, D.R., Sarıçiçek, ˙I, Yazıcı, A.: Machine scheduling with maintenance activities: literature review. Uluda˘g Univ. J. Fac. Eng. 26(2), 737–756 (2021). (in Turkish) 3. Liao, C.J., Chen, W.J.: Single-machine scheduling with periodic maintenance and nonresumable jobs. Comput. Oper. Res. 30(9), 1335–1347 (2003) 4. Ji, M., He, Y., Cheng, T.C.E.: Single-machine scheduling with periodic maintenance to minimize makespan. Comput. Oper. Res. 34(6), 1764–1770 (2007) 5. Sadfi, C., Penz, B., Rapine, C., Blazewicz, J., Formanowicz, P.: An improved approximation algorithm for the single machine total completion time scheduling problem with availability constraints. Eur. J. Oper. Res. 161(1), 3–10 (2005) 6. Chen, J.S.: Optimization models for the machine scheduling problem with a single flexible maintenance activity. Eng. Optim. 38(1), 55–71 (2006) 7. Chen, J.S.: Scheduling of nonresumable jobs and flexible maintenance activities on a single machine to minimize makespan. Eur. J. Oper. Res. 190(1), 90–102 (2008) 8. Low, C., Ji, M., Hsu, C.J., Su, C.T.: Minimizing the makespan in a single machine scheduling problems with flexible and periodic maintenance. Appl. Math. Model. 24(2), 334–342 (2010) 9. Low, C., Hsu, C.J., Su, C.T.: A modified particle swarm optimization algorithm for a singlemachine scheduling problem with periodic maintenance. Exp. Syst. Appl. 37(9), 6429–6434 (2010) 10. Yu, X., Zhang, Y., Xu, D., Yin, Y.: Single machine scheduling problem with two synergetic agents and piece-rate maintenance. Appl. Math. Model. 37(3), 1390–1399 (2013) 11. Cui, W.W., Lu, Z.: Minimizing the makespan on a single machine with flexible maintenances and jobs’ release dates. Comput. Oper. Res. 80, 11–22 (2017) 12. Nesello, V., Subramanian, A., Battarra, M., Laporte, G.: Exact solution of the single-machine scheduling problem with periodic maintenances and sequence-dependent setup times. Eur. J. Oper. Res. 266(2), 498–507 (2018) 13. Gonzalez, P.P., Framian, J.M.: Single machine scheduling with periodic machine availability. Comput. Ind. Eng. 123, 180–188 (2018) 14. Krim, H., Benmansour, R., Duvivier, D., Artiba, A.: A variable neighborhood search algorithm for solving the single machine scheduling problem with periodic maintenance. RAIRO Oper. Res. 53, 289–302 (2019) 15. Qamhan, A.A., Ahmed, A., Al-Harkan, I.M., Badwelan, A., Al-Samhan, A.M., Hidri, L.: An exact method and ant colony optimization for single machine scheduling problem with time window periodic maintenance. IEEE 8, 44836–44845 (2020) 16. Prata, B., de Abreu, L.R., Lima, J.Y.F.: Heuristic methods for the single-machine scheduling problem with periodical resource constraints. TOP 29(2), 524–546 (2020). https://doi.org/10. 1007/s11750-020-00574-x 17. Karaboga, D.: An idea based on honey bee swarm for numerical optimization. Technical report, Computer Engineering Department, Erciyes University, Turkey (2005) 18. Hsu, C.-J., Low, C., Su, C.-T.: A single-machine scheduling problem with maintenance activities to minimize makespan. Appl. Math. Comput. 215(11), 3929–3935 (2010)

The Intelligent System for Interactive Analysis and Forecasting of Graph Data Vadim Moshkin(B)

, Nadezhda Yarushkina , and Irina Moshkina

Ulyanovsk State Technical University, Severny Venets str., 32, Ulyanovsk 432027, Russian Federation {v.moshkin,jng,i.timina}@ulstu.ru

Abstract. The article describes a mobile software system that recognizes function graphs using computer vision and machine learning methods, their analysis and prediction using several intelligent algorithms. The software system recognizes the graph in the photograph, determines the numerical values of the graph points, predicts the resulting time series and draws the continuation of the graph. Hough Transform is used to recognize graphs, and several models were used to predict time series: linear regression, ARIMA, S-model and a neural network of our own architecture using keras. Three function graphs were recognized to select an efficient forecasting approach. The RMSE was used to assess the effectiveness of forecasting. Experiments have shown that for different types of charts, different methods are needed; different forecasting methods are effective. In this regard, it is necessary to implement a method for selecting a forecasting model for a specific type of recognizable graph. Keywords: Machine vision · Forecasting · Time series · Neural network

1 Introduction The goal of the project is to improve the convenience of mobile and interactive forecasting of statistical graph data by developing a mobile system designed to predict time series from a graph photograph. This software receives a digital representation of images, simultaneously analyzes the data and predicts the received data for a specific date (Fig. 1). This work can become the basis for creating similar software products and can be used in industries where work with graphics is required. For example, the use of a software product of this type would be appropriate for: • • • •

economists; scientists; engineers; and other professions that require work with graphs. It is necessary to solve several problems for the development of this application:

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 870–878, 2022. https://doi.org/10.1007/978-3-031-09173-5_100

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Fig. 1. Predicting function graph data

1. Find an effective library or develop a module for recognizing graphic information (graphics) with a high level of detail. 2. To translate the data obtained as a result of recognition into time series. 3. Develop or select an effective algorithm (model) for forecasting time series. 4. Display the forecast result on the original chart. The second chapter describes the most effective and popular approaches and libraries for machine vision, as well as libraries for intelligent image analysis. Section 3 presents a brief description of some methods of time series forecasting. Section 4 describes the architecture of the developed software. Section 5 presents the results of experiments on forecasting the time series of points recognized on the chart.

2 Libraries for Machine Vision OpenCV. OpenCV is an open source library of computer vision, image processing and numerical algorithms [1]. OpenCV is implemented in C/C++ and is also being developed for Python [2], Java, Ruby, Matlab, Lua and other languages. OpenCV is free to use for academic and commercial purposes and is distributed under the BSD license. SimpleCV. SimpleCV [3] is a Python framework of several powerful open source computer vision libraries in one package. Software using SimpleCV can access high-level algorithms for feature detection, filtering and recognition in a single framework. Accord.Net framework. The Accord.NET Framework [4] is a .NET computer learning platform combined with audio and image processing libraries written entirely in C#. It is a complete framework for building production-grade computer vision, computer listening, signal processing and statistics applications even for commercial use.

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Libdwt. Libdwt is a software library for computing discrete wavelet transform [5], which is mainly implemented in C/C++, as well as in other languages intended for target platforms (assembly languages). Libdwt implements a fast wavelet transform algorithm using a lifting scheme. We used biorthogonal spline bursts, also known as Cohen-Daubechies-Feovo wavelets of order 4 (with four vanishing moments). FastCV computerVision. FastCV [6] allows you to add new user experiences to camera-based applications: gesture recognition, tracking and real-world recognition. All of these libraries have good documentation and support, and also contain many examples. But it especially stands out from the list of libraries OpenCV, since this software is free, has many implementations on various software platforms (for example, android). Numpy [7]. NumPy is an open source library for the Python programming language. The main features of NumPy are: • support for multidimensional arrays (including matrices); • support for high-level mathematical functions designed to work with multidimensional arrays. Sklearn. Sklearn [8] is a machine learning library for the Python programming language that provides many capabilities such as multistage analysis, regression, and clustering algorithms. In addition, Sklearn interacts well with the NumPy and SciPy libraries. Keras [9]. Keras is an open source neural network library written in Python. Keras is built on top of the Deeplearning4j, TensorFlow and Theano frameworks. Keras is designed to work quickly with deep learning networks. Keras is compact, modular and extensible. Pandas [10]. Pandas is a Python programming library for data processing and analysis. Pandas’ data manipulation is built on top of the NumPy library, which is a lower-level tool. Pandas provides special data structures and operations for manipulating numeric tables and time series. ML Kit for Firebase [11]. Firebase ML Kit is a library that makes it easy to use a variety of highly accurate, pre-trained deep models in Android apps with minimal code. Most of the models on offer are available both locally and on Google Cloud. FbProphet is a data analysis library from Facebook [12]. FbProphet allows you to analyze charts, however, it showed not very effective performance following the implementation of previous projects.

3 Forecasting Algorithms Currently, more than 100 different methods for forecasting time series have been developed. The main groups of algorithms are:

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Linear regression; Fuzzy S-model; Regression and autoregressive models; Neural network models; Markov chain models; Genetic algorithm; Support Vector Machine; Transfer function method, etc.

Let’s take a closer look at the Fuzzy S-model. Modeling fuzzy time series in accordance with the fuzzy model proposed by Song, 1993, consists in implementing the following steps: 1. Definition of fuzzy variables is a division of a range of time series data into a set of intervals (carriers of fuzzy sets), definition for each range of linguistic values of fuzzy sets and their membership functions. 2. Creating logical relationships according to the model: Yt → Yt−1 : Yt = Yt−1 ◦ R(t, t − 1) 3. The dependence in fuzzy values can be in the form of the dependence of the current value on the previous one and on the order of the fuzzy model (dependence on the p-th previous value): Yt = (Yt−1 × Yt−2 × · · · × Yt−p ◦ R(t, t − p) 4. Fuzzification of input data is the determination of the degree of membership of input data by input fuzzy variables. 5. The result of applying the fuzzy rule for each implication is calculated according to the following model Rij (t, t − 1) 6. The resulting ratio R as a union is calculated according to the following model:  Ri,j (t, t − 1) i,j

7. Application of the obtained model to the input data and obtaining the output fuzzy results. 8. Defuzzification of fuzzy results, for example by calculating the center of gravity.

4 Development of a Mobile Graph Analysis System The information system consists of two components: a client (mobile device) and a server. The following functions are defined in the information system:

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• Recognition function; • Function of analysis (forecasting) of the graph; • The function of creating a complement to the image. The recognition function is implemented on a device running Android OS. Analyzing and generating an image with the results are server tasks. The mobile device recognizes the graph lines in the smartphone photo. Determination of lines is carried out using the OpenCV library, the Hough transformation is used for recognition [13]. The recognized data is processed and prepared for training using the pandas [10] and Numpy [7] libraries. Depending on the chosen training method, the neural network is trained. The following time series forecasting approaches have been implemented as alternatives: • Linear regression - to determine the trend, • Fuzzy S-model, • ARIMA [14],

Fig. 2. The algorithm of the application

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• Neural network LSTM architecture (using the keras library) [9]. • • • • • • • •

Dense [15] (64 neurons), BatchNormalization () [16] - normalization of the received data, LeakyReLU () [17], Dense (16 neurons), BatchNormalization () - normalization of the received data, LeakyReLU (), Dense (1 neuron), Activation (‘linear’) [18, 19],

The algorithm of the application is shown in Fig. 2.

5 Experimental Results For the experiment, 3 photographs of the graph were selected, on which the analysis efficiency was measured in turn. The effectiveness of the forecasting method is determined by the value of the RMSE error [14]. Figure 1 shows 3 stages of the system operation: obtaining a photograph of a graph, recognizing a graph, analyzing and forecasting data.

Fig. 3. Recognized graph №1, Linear regression, ARIMA

Figure 3 shows the result of analyzing and predicting the resulting graph of the function by two algorithms - Linear regression and ARIMA.

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Fig. 4. Recognized graph №2, Linear regression, ARIMA

Figure 4 shows the result of analyzing and predicting the resulting graph of the function by two algorithms - Linear regression and ARIMA.

Fig. 5. Recognized graph №3, settings dialog, ARIMA

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Figure 5 shows an image of a graph obtained from a photograph and a dialog for choosing a prediction algorithm and setting up recognition. The result of predicting the function graph by the ARIMA algorithm is also presented. Table 1 shows the results of the experiments carried out on the analysis and prediction of the graphs of 3 functions. Table 1. Experimental results Model/graph Linear regression

Image 1 9.19

Image 2 167

Image 3 43.37

ARIMA

24.41

53.56

54.77

S-Model

148.73

83.78

175.97

Neural network on keras

564.77

291.8

629.63

Based on the results of the experiments, the leaders in the analysis were identified: the ARIMA and linear regression models proved to be the most effective.

6 Conclusions Thus, the subject area of the system being developed was analyzed, and the selection of tools was made, the initial implementation of the software system was made, and the effectiveness of the data analysis models was analyzed. For the analysis function, a set of libraries was chosen, a tandem of which will provide maximum flexibility and ease of customizing the neural network: Pandas, Keras, numpy. Libraries allow you to carry out resource-intensive calculations in a fairly short time. In addition, these libraries work in conjunction with Python, which will provide convenient and low-cost development. The ARIMA and S-model were also analyzed additionally. Based on the results of the experiments, the ARIMA and linear regression models proved to be the most effective. The problems of filtering noise in recognition, analysis of anomalies of the process presented in the form of a time series and improving the speed of data processing remained unsolved. Experiments have shown that for different types of charts, different methods are needed; different forecasting methods are effective. In this regard, it is necessary to implement a method for selecting a forecasting model for a specific type of recognizable graph.

References 1. Deep learning in OpenCV. https://habr.com/ru/company/intel/blog/333612/. Accessed 20 Mar 2022 2. Rosebrock, A.: Deep Learning for Computer Vision with Python, p. 330 (2017) 3. SimpleCV. http://simplecv.org/. Accessed 20 Mar 2022

878 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

15. 16. 17. 18. 19.

V. Moshkin et al. Accord-framework. http://accord-framework.net. Accessed 20 Mar 2022 Libdwt. https://github.com/xbarin02/libdwtv. Accessed 20 Mar 2022 OpenCV analogues and alternatives. http://lostapp.ru/soft/opencv. Accessed 20 Mar 2022 Numpy. https://numpy.org. Accessed 20 Mar 2022 Scikit-learn.org: machine learning in python. https://scikit-learn.org/stable. Accessed 20 Mar 2022 Keras. https://keras.io. Accessed 20 Mar 2022 Pandas. http://pandas.pydata.org/pandas-docs/stable. Accessed 20 Mar 2022 ML kit firebase. https://firebase.google.com/docs/ml-kit. Accessed 20 Mar 2022 FbProphet. https://facebook.github.io/prophet. Accessed 20 Mar 2022 Hough transform. https://planetmath.org/houghtransform. Accessed 20 Mar 2022 Yarushkina, N.G., Filippov, A.A., Romanov, A.A., Moshkin, V.S., Egov, E.N.: Developing a system for time series data mining on the basis of F-transform and the domain-specific ontology. In: 2017 Joint 17th World Congress of International Fuzzy Systems Association and 9th International Conference on Soft Computing and Intelligent Systems (IFSA-SCIS), pp.1–6. IEEE (2017) Dense Layer. https://keras.io/api/layers/core_layers/dense. Accessed 20 Mar 2022 BatchNormalization Layer. https://keras.io/api/layers/normalization_layers/batch_normaliza tion. Accessed 20 Mar 2022 LeakyReLU Layer. https://keras.io/api/layers/activation_layers/leaky_relu. Accessed 20 Mar 2022 Layer Activation function. https://keras.io/api/layers/activations. Accessed 20 Mar 2022 Yashin, D., Moshkina, I., Moshkin, V.: An approach to the selection of a time series analysis method using a neural network. In: Gervasi, O., et al. (eds.) ICCSA 2020. LNCS, vol. 12249, pp. 692–703. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-58799-4_50

Classification of Concrete Surface Damage Using Artificial Intelligence Technology Ching-Lung Fan(B) Department of Civil Engineering, The Republic of China Military Academy, No. 1, Weiwu Rd., Fengshan, Kaohsiung 830, Taiwan [email protected]

Abstract. Using conventional manual methods for inspection of building images is a time-consuming, costly process, and the results often contain inconsistent standards of examination. Because it is crucial to understand building surface conditions and make maintenance decisions at an appropriate time, the construction industry has been developing an automated defect and damage classification method. The objective of this study is to obtain low-cost and high-quality images from digital cameras for building damage detection experiments. The researchers conducted sample training and testing through artificial intelligence technologies and later analyzed the testing results to evaluate the performance of supervised machine learning methods for concrete efflorescence detection. The support vector machine (SVM) enables clearly distinguishing differences between normal concrete and concrete with efflorescence and the results classification indicated the most satisfactory assessment performance. Analysis indicated that the efflorescence scalar was 56.7% and the efflorescence vector was 53.1% in the study. The quantity of digitized surface damage could indicate the extent of building degradation and provide an initial reference for estimating damage scope and severity. Keywords: Machine learning · Efflorescence · Digital images · Concrete · Classification

1 Introduction A humid environment with frequent precipitation can easily result in faults in buildings, such as efflorescence on wall surfaces, scaling on concrete, corrosion of reinforcing materials, and cracks. Such visible defects on buildings are both unsightly and detrimental to the living quality of residents and structural safety. Degradation of building surfaces is common; therefore, routine detection and quantification of surface defects are essential because these operations enable engineering personnel to conduct timely maintenance. Reinforced concrete (RC) can be caused by multiple factors, the most common of which is corrosion caused by chloride invasion or concrete carbonization [1]. Common types of damage to RC include efflorescence, crack, spalling, and rebar exposure. Efflorescence is caused by salt and carbon dioxide from water interacting with © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 879–886, 2022. https://doi.org/10.1007/978-3-031-09173-5_101

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other atmospheric gases after the water moves inside concrete and later evaporates from its surface. It frequently occurs in buildings with concrete or cement mortar. The American Society for Testing and Materials (ASTM) defines efflorescence as a type of crystalline deposit, usually white, of water-soluble compounds on the surface of masonry. It is directly related to the quantity of water-soluble compounds within, or exposed to, the wall; and to the quantity of water exposed to these compounds [2]. Efflorescence is often accompanied by other defects, such as cracking or spalling [3]. Crack can be defined as the result of accidental interruption and local material faults in structural materials; small cracks result in insufficient serviceability, and large cracks result in structural failure [4]. Crack is a critical indicator in the evaluation of the conditions of current buildings and infrastructure facilities [5]. Spalling refers to the concrete surface peeling without exposing the rebars [6]. Despite the importance of recognizing deterioration early, no authoritative test standards currently exist for evaluating efflorescence in concrete masonry units or mortar [2]. As a result, engineers sometimes use the ASTM C67 [7] method for efflorescence sampling and testing. This method involves observing the efflorescence potential of concrete masonry units through visual inspection, but, since the result is not quantitative, the manual presents no information about the precision or bias of the efflorescence test method. Therefore, this method cannot effectively quantify the efflorescence present. Bianchini et al. [8] noted that technical personnel’s subjectivity is inevitably dependent on experience level, and this affects evaluation results, even when using carefully drafted, reliable manuals for evaluation. Therefore, development of sensor-based automated classification is imperative; these tools could lower dependence on manual measurement, reduce inspection time, and enhance inspection accuracy. Automated digital image recognition is more efficient, consistent, accurate, and objective than human visual inspection. Some factors must be considered in image recognition and classification—such as the objects’ material, texture, number, range, shape, size, and color—to accurately analyze the spectrum reflection and image features. Color and texture have always been used as classification indicators because they describe the surfaces of objects properly [9]. In particular, feature extraction is the process of determining the unique features of images, and it is a crucial part of using image processing for object recognition [10]. However, the colors and textures of some building surfaces are similar to those of damage features. For example, the color of concrete is light grey, and efflorescence is mostly milky. The two are easily confused, resulting in a high probability of errors in recognition and classification. How to improve recognition accuracy is one of the problems that should be solved first in classification techniques. The organization of the paper is structured as follows: Sect. 2, literature review is presented and machine learning applications. Section 3 adopts the methodology (AI) and briefly introduces image processing. Section 4 discusses the results and analyses. Section 5, conclusion discovers the findings and proposes the research directions to be addressed in the future.

2 Literature Review Machine learning methods are advanced tools that use the extraction of image features to operate certain tasks such as classification, regression, and clustering [11]. Among

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them, classification is a machine learning task, and its purpose is to deduce the relations between “objects” and “labels” using training sets. A training set is a set of the type of objects of a known label. Later, such generalization can be used for the classification of objects with unknown labels [12]. Machine learning is a technique that allows computers to learn about certain tasks and performance measures from a massive amount of data, and this technique can be gradually improved through experience. Unsupervised machine learning refers to the automated classification or grouping of input data without training examples that are labeled in advance. Supervised machine learning refers to learning or establishing a model from training data with labels or directions that are defined in advance, and new examples are inferred through this model. Machine learning has developed algorithms with various functions. For example, unsupervised machine learning has clustering, and supervised learning has the SVM, maximum likelihood, decision tree, and random forest (RF). Machine learning using SVM or artificial neural network (ANN) provides a promising avenue for automating visual inspection. ANNs are divided into supervised ANNs (e.g., back-propagation neural network (BPNN) and probabilistic neural network (PNN)) and unsupervised ANNs (e.g., Kohonen neural network). Cluster analysis is an unsupervised machine learning method suitable for when computation resources are limited. With increasing numbers of extremely high-resolution images, a highly automatized, simple, and effective image classification technique is increasingly needed. Therefore, unsupervised classification concepts must be used. Unsupervised classification methods can classify images purely from statistical methods. Therefore, unsupervised classification methods can quickly specify the number of clusters that must be classified. For example, Kashani and Graettinger [13] tested a clustering-based method. When scanning damaged buildings, this method can automatically detect roof coverage damage caused by windstorms. Leichtle et al. [14] used K-means clusters to distinguish changed and unchanged buildings. SVMs exhibit superior classification and recognition ability for complex structures and multiclass classifications compared to other types of classifiers. For example, Kim et al. [15] analyzed three machine learning methods (SVMs, Gaussian mixture model, and ANNs), and their results indicated that SVMs possess advantages for detecting the constitution of concrete structures in colored images. Rashidi et al. [16] compared the efficiency of three machine learning algorithms—SVMs, multilayer perceptrons, and the radial basis function—in detecting construction materials. The results indicated that SVMs performed more favorably than did the other techniques in predicting the material texture in images. RFs are applied as classifiers [17] and are used extensively in various facility damage detection [18–20], and building image classification [21–23].

3 Method 3.1 Support Vector Machine SVM is originally for binary classification problems. A hyperplane is found in a highdimensional space as the division of two types, such that the two types have the longest distances to the hyperplane. The longer the distances, the smaller the classification errors. The principle is the linear Eq. (1) that divides the hyperplane in a sample space, where

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the training sample set D = {x i , yi }; yi = {−1, +1}. Moreover, w = (w1 , w2 , …, wn ) is the normal vector that determines the direction of the hyperplane. The deviation value b can determine the distance between the hyperplane and the origin. The distance of any point x in the sample space to the hyperplane is r. The range within the two hyperplanes is called the “margin” with a distance of 2/w. To make the distance between them as long as possible, the w must be minimized. The hyperplane in the middle of the largest margin is the optimal hyperplane. Additionally, to make all the sample data points outside the margin of the hyperplanes, the conditions in Eq. (1) must be satisfied for all the training samples. To find the optimal hyperplane, the parameters w and b in Eq. (2) must be satisfied, and the value of 2/w must be maximized.



wT x + b = 0

(1)

wT xi + b ≥ +1, yi = +1 wT xi + b ≥ −1, yi = −1

(2)

3.2 Random Forest Supervised machine learning is when a model learns through training datasets to achieve optimal performance on testing datasets (new samples). Overfitting and underfitting may occur if the training model is too simple and too complicated, respectively; both problems must be avoided in a supervised machine learning technique. An RF classifier, however, can avoid overfitting by applying the entirety of classifier-collected knowledge, resulting in better generalization capabilities. The RF algorithm is based on the CART concept. In the CART training process, a subset with k attributes is randomly selected from the attribute sets of the tree nodes, and an optimal attribute in this subset is then selected to partition. By contrast, a conventional decision tree selects the partitioning attribute from the current node’s attribute set. For such an attribute set with d attributes in a k = d conventional decision tree where k = 1 is randomly selected as the attribute for partition, the general recommendation is for k to be such that k = log2 d. 3.3 Image Processing The supervised machine learning procedures in this study were divided into two parts: testing set and training set. For the training set, supervised machine learning methods were supplied RGB color values as the baseline, and the training pixels came from manually digitizing the efflorescence features in the image [see Fig. 1(a)]. The distribution of the training area is illustrated in Fig. 1(b). For the testing set, because different features in the research area exhibit spectral properties containing different colors, predictor variables (features) were calculated from the image. The actual efflorescence of the sample was digitized to constitute the standard. Testing involved first training the two machine learning methods using the subset of the training pixels and then applying the model to the test image (Fig. 1(c) and (d)). Finally, the performance for detecting efflorescence of the two machine learning methods (SVM and RF) was compared.

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(b)

(c)

(d)

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Fig. 1. Image information of efflorescence in the study area.

4 Results In this study, the researchers detected concrete efflorescence by using two supervised machine learning methods: SVM and RF. Two classification categories were used in the current study: efflorescence areas (black) and normal areas (light gray). The SVM and RF classification results, as displayed in Fig. 2(a) and (b), were then compared to the original efflorescence image in Fig. 1(a). The two classifiers produced nearly identical results for concrete efflorescence classification.

Fig. 2. Concrete efflorescence classification results of machine learning methods.

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(a)

Scalar

(b)

vector

Fig. 3. Scalar and vector of the spectrum of SVM-based efflorescence classification.

The digital images of building surfaces contained valuable information, including surface damage which could indicate the extent of degradation. In the SVM efflorescence classification results, the scalar size of the spectrum of the digital image (Fig. 3(a)) and vector of the spectrum (Fig. 3(b)) were calculated. Analysis indicated that the efflorescence scalar was 170, approximately 56.7% of the known scalar quantity of 300. The efflorescence vector captured was 102 (compared to a known quantity of 192), constituting 53.1% of total vector quantity. If consistent, the efflorescence ratio data could serve as a reference for facility managers to determine the scope of maintenance operations.

5 Conclusion The study constructed a recognition model for concrete efflorescence using digital images and supervised machine learning methods, creating an automated, rapid machine learning detection method to calculate concrete efflorescence within images and subsequently use these features as the basis of classification. Overall, the supervised machine learning methods produced satisfactory classification results. They could clearly distinguish differences between concrete efflorescence and normal concrete surfaces. Through analyzing the different spectral compositions of concrete efflorescence and normal concrete features, the supervised machine learning methods could produce correct judgment results from RGB colors and texture. The results indicated the consistent classification performance of supervised machine learning methods. With the gradual enhancement of digital camera remote sensing image quality and the operability of remote sensing digital cameras, images can be captured from different angles by using noncontact operations. Remote sensing image capturing is advantageous because it is simple, mobile, and rapid. It can be used to conduct wide-scope, high-efficiency, and high-quality digital image capturing operations. When used with supervised machine learning methods, it enables instant classification and rapid evaluation results. This is useful for detecting and recognizing different building materials in images and beneficial for investigating, monitoring, and diagnostically operating buildings. In the future, the researchers aim to combine the advantages of different machine learning approaches by developing image analysis and a process system for integrated

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calculation of remote sensing images’ spectral characteristics, defect recognition, and surface texture.

References 1. Neville, A.M.: Properties of Concrete. Longman, London (2011) 2. American Society for Testing and Materials: Standard guide for reduction of efflorescence potential in new masonry walls. ASTM C1400-11 (2017) 3. Hüthwohl, P., Brilakis, I., Borrmann, A., Sacks, R.: Integrating RC bridge defect information into BIM models. J. Comput. Civ. Eng. 32(3), 04018013 (2018) 4. Yao, Y., Tung, S.E., Glisic, B.: Crack detection and characterization techniques – an overview. Struct. Control. Health Monit. 21(12), 1387–1413 (2014) 5. Yang, X.: Automatic pixel-level crack detection and measurement using fully convolutional network. Comput.-Aided Civil Infrastruct. Eng. 33(12), 1090–1109 (2018) 6. Zhang, C., Chang, C., Jamshidi, M.: Concrete bridge surface damage detection using a singlestage detector. Comput.-Aided Civil Infrastruct. Eng. 35(4), 389–409 (2020) 7. American Society for Testing Methods: Standard test methods for sampling and testing brick and structural clay tile. ASTM C67-02c (2002) 8. Bianchini, A., Bandini, P., Smith, D.W.: Interrater reliability of manual pavement distress evaluations. J. Transp. Eng. 136(2), 165–172 (2010) 9. Zhu, Z., Brilakis, I.: Parameter optimization for automated concrete detection in image data. Autom. Constr. 19(7), 944–953 (2010) 10. Kim, H., Ahn, E., Shin, M., Sim, S.H.: Crack and noncrack classification from concrete surface images using machine learning. Struct. Health Monit. 18(3), 725–738 (2019) 11. Zhang, C., Chang, C., Jamshidi, M.: Concrete bridge surface damage detection using a singlestage detector. Comput.-Aided Civil Infrastruct. Eng. 35(4), 389–409 (2019) 12. Meijer, D., Scholten, L., Clemens, F., Knobbe, A.: A defect classification methodology for sewer image sets with convolutional neural networks. Autom. Constr. 104, 281–298 (2019) 13. Kashani, A.G., Graettinger, A.J.: Cluster-based roof covering damage detection in groundbased lidar data. Autom. Constr. 58, 19–27 (2015) 14. Leichtle, T., Geiß, C., Lakes, T., Taubenböck, H.: Class imbalance in unsupervised change detection – a diagnostic analysis from urban remote sensing. Int. J. Appl. Earth Obs. Geoinf. 60, 83–98 (2017) 15. Kim, C., Son, H., Kim, C.: Automated color model-based concrete detection in constructionsite images by using machine learning algorithms. J. Comput. Civ. Eng. 26(3), 421–433 (2012) 16. Rashidi, A., Sigari, M.H., Maghiar, M., Citrin, D.: An analogy between various machinelearning techniques for detecting construction materials in digital images. KSCE J. Civ. Eng. 20(4), 1178–1188 (2016). https://doi.org/10.1007/s12205-015-0726-0 17. Guo, L., Chehata, N., Mallet, C., Boukir, S.: Relevance of airborne lidar and multispectral image data for urban scene classification using Random Forests. ISPRS J. Photogramm. Remote. Sens. 66(1), 56–66 (2011) 18. Li, J., Hao, H., Wang, R., Li, L.: Development and application of random forest technique for element level structural damage quantification. Struct. Control. Health Monit. 28(3), e2678 (2021) 19. Guo, X., Hao, P.: Using a random forest model to predict the location of potential damage on asphalt pavement. Appl. Sci. 11(21), 10396 (2021) 20. Yang, X., Zhang, Y., Lv, W., Wang, D.: Image recognition of wind turbine blade damage based on a deep learning model with transfer learning and an ensemble learning classifier. Renew. Energy 163, 386–397 (2021)

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21. Alipour, M., Harris, D.K., Barnes, L.E., Ozbulut, O.E., Carroll, J.: Load-capacity rating of bridge populations through machine learning: application of decision trees and random forests. J. Bridg. Eng. 22(10), 04017076 (2017) 22. Assouline, D., Mohajeri, N., Scartezzini, J.L.: Building rooftop classification using random forests for large-scale PV deployment. In: The Earth Resources and Environmental Remote Sensing/GIS Applications VIII Warsaw, Poland (2017) 23. Harvey, R.R., McBean, E.A.: Predicting the structural condition of individual sanitary sewer pipes with random forests. Can. J. Civ. Eng. 41(4), 294–303 (2014)

Extraction of Delay Parameters of Fluid Flows by Genetic Algorithm Cihan Bayindir1,2(B) 1

¨ uner1 and Onur Ust¨

˙ Istanbul Technical University, Istanbul, Turkey {cbayindir,ustunero}@itu.edu.tr 2 ˙ Bo˘ gazi¸ci University, Istanbul, Turkey

Abstract. In this paper, we study delayed fluid flows. More specifically, we examine the extraction of delay parameters of fluid flows by the genetic algorithm. With this motivation, we first derive the analytical solutions of some reduced forms of the Navier-Stokes equation with time delay. In these problems, the governing equations simply become delayed diffusion equations. These reduced problems can be named as Stokes second problem (Stokes boundary layer) with delay and Poiseuille flow with delay. We derive the analytical solutions of these problems under the effect of the constant delay. Then, using the velocity profiles of the delayed flows, we show that the delay time can be extracted using the genetic algorithm (GA). We discuss the possible usage, applications, and limitations of our findings. Keywords: Delayed Navier-Stokes equations

1

· Time delay · GA

Introduction

Ordinary and partial differential equations (ODEs and PDEs) are generally used as mathematical models for describing physical phenomena [1]. However, in some problems, the delay in the motion or in the forcing can affect the physical processes significantly, thus extensions of these equations to include the effects of such delays are performed. These types of equations can be generally named as delay differential equations (DDEs), and depending on the number of parameters involved can be named as delay ordinary differential equations (DODEs) or delay partial differential equations (DPDEs). The literature on this subject is vast [1]. These type of DDEs are studied in the field of dynamics, vibrations and motion [1], circuit design and electronics [2], and heat conduction [3], just to name a few fields. Also, there are some studies about the effect of delayed processes on fluid flows [4]. Such studies generally examine the full form of the Navier-Stokes equations, however, to our best knowledge, studies on the reduced forms of these equations with delays and their engineering uses are very limited. In this study, we examine the analytical solutions of the delayed fluid flows and their delay parameter extraction using a genetic algorithm (GA). With this motivation time-delayed Navier-Stokes is reduced to a time-delayed diffusion c The Author(s), under exclusive license to Springer Nature Switzerland AG 2022  C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 887–894, 2022. https://doi.org/10.1007/978-3-031-09173-5_102

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equation for which proper boundary and initial conditions are considered to formulate the Stokes flow with delay and Poiseuille flow with delay. Using the separation of variables technique, it is shown that the ODE obtained in the temporal domain admits solutions in terms of Lambert omega function. The properties of these delayed flows and their possible engineering applications are discussed. Also, the extraction of delay parameters using the flow velocity profile is performed by defining an optimization problem and solving it via GA.

2 2.1

Methodology Stokes Second Problem with Constant Time Delay

Starting from the Navier-Stokes equation it is possible to obtain the secondorder diffusion equation to analyze the Stokes second problem [6]. The time delay imposed on the advective acceleration term yields the differential equation ∂ 2 u(y, t) ∂u(y, t − τ ) =ν ∂t ∂y 2

(1)

where u is the horizontal flow velocity, τ is the time delay term, t is the time parameter, y is the spatial parameter directed away from the wall and ν is the kinematic viscosity term. For the Stokes second problem, the boundary conditions can be given as u(y = 0, t) = Re[U e−iωt ] = U cos(ωt) to formulate the oscillatory motion of the wall with a velocity magnitude of U and u(y → ∞, t) = 0 to formulate the decaying effect of the motion away from the wall [5]. To seek a solution in the form of eiωt f (y), we use the ansatz u = U Re[eiωt f (y)]

(2)

Plugging this expression into Eq. 1, one can obtain U iωeiω(t−τ ) f (y) = U νeiωt f  (y)

(3)

After cancellation, one can get f  (y) −

iω −iωτ e f (y) = 0 ν

This second order equation can be easily solved to obtain √ iω −iωτ √ iω −iωτ y y f (y) = Ae ν e + Be− ν e

(4)

(5)

where A and B are some arbitrary constants. Applications of the aforementioned boundary conditions yield A = 0 and B = 1. Thus, the complete solution can be written as    u = U Re eiωt e−

iωe−iωτ ν

y

(6)

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which can be simplified as u = U e−

√ω ν

ωτ cos( π 4 − 2 )y

   π ωτ   ω sin − y cos ωt − ν 4 2

(7)

The associated flow parameters such as flowrate and laminar shear stress can also be easily computed using Eq. 7. In Fig. 1, the exact solution of the Stokes second problem is depicted at time t = 7 s for the cases of no delay and with a dimensionless time delay of ωτ = π/3. t= 7 s

1

With dimensionless time delay of Without time delay

0.9

= /3

0.8 0.7

y (m)

0.6 0.5 0.4 0.3 0.2 0.1 0 -0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

U (m/s)

Fig. 1. Comparison of the free and delayed velocity profiles of the Stokes second problem.

As this figure confirms, time delay introduces a substantial change in the velocity profile, such as reduced backflow regions and faster decay in the velocity magnitude as y grows. Such findings can lead to many important engineering challenges and advantages such as reducing backflow, sieving sediments and nanoparticles, reducing and delaying velocity, flowrate and shear stress parameters. It is also possible to impose the time delay on the diffusion process in Eq. 1, which can be easily solved using the process above and would yield the exponential term with τ parameter to have an opposite signed argument. Also, it is possible to extend our findings to the multi-frequency wall motion using Fourier analysis by taking the advantage of the linearity of the governing equation. Unsteady Poiseuille Flow with Constant Time Delay. One of the forms of the Poiseuille flow occurs when the flow between stationary parallel plates is initiated by the sudden application of a constant pressure gradient [5]. The governing equation for this type of Poiseuille flow is 1 dp(x, t) ∂ 2 u(y, t) ∂u(y, t − τ ) =− +ν ∂t ρ dx ∂y 2

(8)

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where ρ is the fluid density, dp/dx is the pressure gradient and the other parameters are as before [5]. The two boundary conditions for this type of Poiseuille flow can be formulated as i) u(±b, t) = 0 for all t, and ii) u(y, 0) = 0 for −b ≤ y ≤ b. Here, b is the half-length between parallel plates [5]. Considering the parabolic profile is attained in the steady-state of the motion we seek a solution in the form of y2 u = 1 − 2 − f (y, t) (9) 2 (−1/2μ)(dp/dx)b b where μ = νρ is the dynamic viscosity [5]. This substitution yields ∂f (t − τ, y) ∂ 2 f (t, y) =ν ∂t ∂y 2

(10)

Seeking a solution in terms of separation of variables f (y, t) = Y (y)T (t) can obtain Y (y)T  (t − τ ) = νY  (y)T (t) (11) which gives two ODEs in the form of Y  (y) + λ2 Y (y) = 0

(12)

T  (t − τ ) + λ2 νT (t) = 0

(13)

Here, λ is a constant indicating the wavenumber. It is known that the first ODE given in Eq. 12 admits solution in the form of cosine series [5], thus for the sake of brevity is not repeated here. The solution of the second DODE given by Eq. 13 is discussed here. Seeking a solution in the form of an exponential function given as T (t) = eβt yields (14) βeβ(t−τ ) + λ2 νeβt = 0 After cancellation, this expression reduces to βe−βτ = −λ2 ν

(15)

multiplying both sides of Eq. 15 with −τ give − βτ e−βτ = λ2 ντ

(16)

which can be solved in terms of Lambert omega function to obtain β as β=

−Wk (λ2 ντ ) τ

(17)

The solution is defined if λ2 ντ ≥ −1/e. When real numbers are considered only, the two branches of the Wk emerges, W0 for λ2 ντ > 0 and W−1 for −1/e ≤ λ2 ντ < 0. A plot of Wk as a function of its argument x is depicted in Fig. 2. Thus the solution of the DODE given by Eq. 10 becomes T (t) = e

−Wk (λ2 ντ ) t τ

(18)

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Lambert W function, two main branches

2

1

Wk(x)

0

-1

-2

-3 W 0 (x) W -1 (x)

-4 -0.5

0

0.5

1

1.5

x

2

2.5

3

3.5

4

Fig. 2. Two branches of the Lambert omega function Wk (x).

The solution for f (y, t) in Eq. 10 can be written as f (y, t) = Y (y)T (t) =

32 (−1)n −Wk (λ2n ντ ) t τ e cos(λn y) π 3 n=0 (2n + 1)3

(19)

where the discrete wavenumber parameter is given by λn = (2n + 1)π/2b [5]. To sum, the solution of the delayed Poiseuille flow is given as  u y2 32 (−1)n −Wk (λ2n ντ ) t πy  τ =1− 2 − 3 e cos (2n + 1) 3 2 (−1/2μ)(dp/dx)b b π n=0 (2n + 1) 2b (20) which is one of the contributions of this paper. It is also useful to mention that in the zero delay limit τ → 0, the Lambert omega function approaches Wk (λ2n ντ ) t → λ2n νt which can be derived by using the L’Hospital’s rule and the τ derivative relations of the Lambert omega function.  u y2 32 (−1)n −λ2n νt πy  (21) = 1 − − e cos (2n + 1) (−1/2μ)(dp/dx)b2 b2 π 3 n=0 (2n + 1)3 2b which is the solution of the Poiseuille problem with no delay given in [5]. In Fig. 3, the exact solution of the Poiseuille flows with and without time delays is depicted at dimensionless times of νt/b2 = 0.1 and νt/b2 = 0.4. For both cases a constant time delay of τ = 0.75 s is considered. The number of Fourier modes is selected to be N = 10. As depicted in Fig. 3, the delay parameter introduces a substantial change in the flow profile. For the values used, this change is a reduction in the parabolic-shaped flow velocity profile. However, in our simulations for different values delay and other parameters involved, opposite effects are also observed. These types of changes in the velocity profiles are of major significance to the engineering challenges mentioned in the previous subsection.

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Without time delay for t/b2=0.1 With time delay for t/b2=0.1 and

0.4

With time delay for t/b2=0.4 and

= 0.75 s

Without time delay for t/b2=0.4

0.2

y/b

= 0.75 s

0 -0.2 -0.4 -0.6 -0.8 -1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

u/[-1/(2 )dp/dxb2]

Fig. 3. Poiseuille flow velocity profile comparisons: profiles with no delay versus constant time delay of τ = 0.75 s.

3

Results and Discussion

In this section, we analyze the extraction of the delay parameters of the aforementioned problems via the genetic algorithm (GA). A genetic algorithm (GA) is a population-based search and optimization algorithm. For optimization and problem-solving purposes, GA mimics the evolution processes such as genetic cross-over and mutation [7]. To find the optimal solutions of a given optimization problem, exploiting the best solutions obtained and exploring the problem domain are simultaneously performed in GA. GA computes the solutions of these types of problems in an optimal setting while combining the exploration and exploitation phases [7]. The literature on this subject is vast [8]. In this paper, we simply use MATLAB’s GA toolbox for the optimization and extraction of time delay parameters of delayed Stokes and delayed Poiseuille flows. For a more comprehensive discussion of GA, the reader is referred to [8]. 3.1

Extraction of Delay Parameters of Stokes Second Problem by Genetic Algorithm

For the extraction of time delay parameter of the Stokes flow, we first define the square error E 2 as the square of the difference between velocities of u for variable dimensionless delay ωτ and u defined for constant dimensionless delay of ωτ = π/3 ≈ 1.0472. Summation is performed over the y parameter. The resulting curve to be minimized by GA is depicted in Fig. 4. As shown in Fig. 4, for various values of dimensionless delay parameter ωτ , the error is obtained. The range of parameters is selected as ωτ = [0 − π] with a step size of π/100. For the minimization of the error, the GA algorithm is utilized with a function tolerance of 10−6 and a cross-over fraction of 0.8. As depicted in Fig. 4, GA finds the dimensionless delay parameter as 1.0478, with an accuracy on the order of 10−4 .

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Fig. 4. Extraction of the dimensionless delay parameter of the Stokes flow by GA.

3.2

Extraction of Delay Parameters of Unsteady Poiseuille Flow by Genetic Algorithm

As before, for the extraction of the delay parameter of the Poiseuille flow, the square error is defined similarly to the Stokes flow and the difference between velocities of u for variable dimensional delay τ and u defined for a constant delay time of τ = 0.65 is used. A plot of E 2 calculated this way is plotted in Fig. 5 as a function of τ . 0.31335 Square error as a function GA solution

0.3133

E2 (m2/s2)

0.31325

0.3132

Time Delay=0.65s

0.31315

GA Solution=0.6592s

0.3131

0.31305

0.313

0

1

2

3

4

5

6

7

8

9

10

Fig. 5. Extraction of the delay parameter of the Poiseuille flow by GA.

As illustrated in Fig. 5, a delay time interval of τ = [0 − 10]s is used with a step size of 10−2 s. As before, for the minimization of the error, the GA algorithm is utilized with a function tolerance of 10−6 and a cross-over fraction

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of 0.8. As depicted in Fig. 5, GA determines the dimensionless delay parameter as τ = 0.6592, with an accuracy on the order of 10−3 . Thus it is possible to state that GA can be used for the extraction of the delay parameters with high accuracy. In our simulation, we also observe that the solutions are sensitive to delay parameters, which may change the behavior of the Lambert omega function. Our findings can be used for fluid engineering purposes with applications including but not limited to controlling flow fields and parameters like velocity profiles, shear stresses and flowrates using delays and delayed feedbacks. As a future work we aim to extend our findings to other forms of fluid problems discussed in [5]. We also aim to investigate the effect of parameter resolution of the performance of GA in capturing delay parameters and properties. We also plan to extend our results to account for variable delays, other types of flows where some other reduced forms of Navier-Stokes equations are used. Another research direction to follow is to extend our findings to some types of nonlinear equations such as the nonlinear Schr¨ odinger [9] and the Kundu-Eckhaus [10].

References 1. Erneux, T.: Applied Delay Differential Equations. In: Surveys and Tutorials in the Applied Mathematical Sciences. Springer, New York (2009). https://doi.org/10. 1007/978-0-387-74372-1 2. Bellen, A., Guglielmi, N., Ruehli, A.: Methods for linear systems of circuit delay differential equations of neutral type. IEEE Trans. Circ. Syst. I 46(1), 212–215 (1999) 3. Castro, M.A., Rodr´ıguez, F., Cabrera, J., Mart´ın, J.A.: Difference schemes for time dependent heat conduction models with delay. Int. J. Comput. Math. 91(1), 53–61 (2014) 4. Caraballo, R., Real, J.: Navier-Stokes equations with delays. Proc. Math. Phys. Eng. Sci. 457, 2441–2453 (2014) 5. Erdogan, M.E.: On the unsteady unidirectional flows generated by impulsive motion of a boundary or sudden application of a pressure gradient. Int. J. Nonlinear Mech. 37(6), 1091–1106 (2002) 6. Munson, B.R., Okiishi, T.H., Huebsch, W.W., Rothmeier, A.P.: Fundamentals of Fluid Mechanics. Wiley, New York (2012) 7. Holland, J.: Adaptation in Natural and Artificial Systems. MIT Press, Massachusetts (1975) 8. Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, New York (1989) 9. Bayindir, C.: Compressive split-step Fourier method. TWMS J. Appl. Eng. Math. 52, 298–306 (2015) 10. Bayindir, C.: Self-localized solutions of the Kundu-Eckhaus equation in nonlinear waveguides. Results Phys. 14, 102362 (2019)

Optimal Control and Dynamic Stability of Power Injection Based on Fuzzy Intelligent Controller Yousif I. Al Mashhadany1(B)

, Gozde Ulutagay2

, and Baraa Jalil Abdulelah3

1 University of Anbar, Anbar, Iraq [email protected] 2 Department of Industrial Engineering, Gedik University, Istanbul, Turkey [email protected] 3 Ministry of Electricity, Anbar, Iraq

Abstract. Many countries are witnessing nice developments in construction, urban planning, technological development moreover as grid management the increasing demand for energy of every kind and totally different generation strategies as well because the want for low and medium voltage distribution altogether areas. The assembly of this energy varies per user needs, initial requirements, capacity, supposed use, waste generation, and economic potency. The improvement of those different energies depends on the number of synchronization achieved within the injection of power into the mains together with force control, tool stability, voltage quality, efficiency - and redundant power return. During this paper, a proposal is given for associate intelligent management unit supported the modeling and stabilization of the alarm force system. So as to satisfy the challenges of the planned overvoltage of the presented system, it’s doable to feed the plentiful power from the surplus power of the private households into the grid. Use and profit economically from star collectors through good grid smart control systems. So as to review and analyze the practicableness of the proposed grid coordination and energy storage privately PV networks based on solar energy, a mathematical model was created consisting of 4 main parts: simulation, correlation, stability, and evaluation. An Adaptive Neuro-Fuzzy Inference System (ANFIS) to assess the impact of those basic limitations in sensible application. The simulation of the planned system is dispensed with the most powerful system with a capability of 600 V which will be operated with this power. The proposed system was evaluated from Matlab simulation bars and graphs for every part of the system, and therefore the overall system simulation results were taken into account. Keywords: Analysis modeling · Optimal control · Dynamic stability · Power injection · Intelligent controller

1 Introduction There is an extraordinary difference between the characteristic of the dynamic dissemination system, which implies a two-way dispersion network, and the detached dissemination system, which implies single direction conveyance organization, and we need © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 895–904, 2022. https://doi.org/10.1007/978-3-031-09173-5_103

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to realize how to pick the proper size of a little organization for our framework and its impact on our framework [1]. The possible voltage control of transports that we have little organizations on the grounds that these transports experience voltage violence because of transmission line interference [2]. Firstly, we need to change the responsive force and the dynamic force estimation of the little network to know its impact on the voltage, as we realize that the Moro transport has a voltage in the voltage and the transmission voltage is not exactly the necessary worth, so we need to infuse the receptive force and the dynamic force of the framework to build the voltage and return it to the necessary worth And put it to the ideal incentive in its common area, which is shown by the network administrator. Moreover, this chance to control the voltage of the Moro vector, we need to change the size of the receptive force just and watch the impact of the changing responsive force on the voltage of the voltage and how the voltage gets back to the necessary level [3]. As we probably are aware by expanding the responsive force in the force network, the network voltage will increment and make the network steadier. Additionally, the Lynn transport will encounter voltage violence because of line disengagement from the network and cause this transport to experience the ill effects of voltage brutality and make the framework shaky, and accordingly, we need to lessen the responsive force from the network to take the voltage back to its necessary spot [4]. Changing the receptive force an incentive in the framework will influence the voltage in the network as opposed to diminishing the network voltage where we need to ingest the responsive energy from the network and make up for the Lynn transport voltage which is more prominent than the necessary worth, so we need to ingest more responsive energy from the network to 29 to return this voltage to Required worth. To start with, we change the estimation of responsive force and dynamic force of the subsequent fine organization to control the voltage of this vector, and afterward we just change the estimation of receptive force as it were [5]. Additionally, few systems will change the force of the transmission line, which is sent between transports. By changing the dynamic force of the little organizations, the energy sent by the transmission lines between the transports will change because of the commitment of the little systems. Right off the bat, we change the dynamic force of the fine matrix in the Moro transport and see the difference in the energy communicated from the Moro transport to the Moro transport which implies that the energy sent by every transmission line likewise changes because of the commitment of the single little system [6]. Moreover, by changing the dynamic force of the grid, which is available in the Lynn transport, the force sent to and from the Lynn transport will change, which implies that the force communicated by every transmission line is changed because of the commitments of the little system [7].

2 Modeling of Power Injection with an Intelligent Controller The construction of the insightful voltage control network that will be investigated in this exploration is portrayed in Fig. 1, where the smart control gadget comprises an

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advanced unit dependent on the affectability network and the information base including an assortment of data identified with the force network, position and information control [8, 9].

Fig. 1. Structure for intelligent voltage control system [9]

Knowledge Base Information in a specific trouble spot is characterized by reality and rule and afterward, it is put away in the data set and the standard base, respectively. Information base and base data set are in the following [10]: Database • • • • •

The upper and lower cutoff points of every vector voltage. The upper and lower breakage point of voltage guideline. The upper and lower breakage point of the number of pay gadgets. Need remuneration gadgets. Generator terminal quantization level.

Rule Base • Whether the voltage surpasses the upper and lower cutoff points of every vector voltage, the network turns on the control unit. • In case of a strange voltage, the regulator first structures an affectability tree. • The regulator chooses the remuneration gadget with the best affectability. • If the limit of the predefined responsive force remuneration gadget is short, the regulator chooses the second-most compensation device.

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• The regulator works the set need of remuneration gadgets. • In case of an unusual voltage in a few kinds of transport, the control unit will work based on the biggest strange transport voltage. • If the transmitter voltage isn’t set inside the voltage guideline utilizing a first-request pay gadget, at that point the following request remuneration gadget is submitted. • The measure of receptive force pay decides the Linear Prediction strategy [11]. Accepting the N transport power network together with M control activities, the connection between transport voltages and control measures can be addressed as demonstrated in Fig. 2. It is demonstrated that adjustments of each control methodology effects affect the voltage in several transports. For a specific voltage infringement, it is feasible to ascertain the control activity important to dispense with this voltage infringement by affectability innovation. It ought to be noticed that the control measure ought not to surpass as far as possible and not reason new voltage infringement for other transports. The affectability network is a essential boundary in the canny voltage control network [12]. By characterizing the association of variations in the conductor voltage as indicated by the pay changes in the voltage of the terminal of the generator, the maneuver capacitor/reactor, and the converter tap, it characterizes the estimates of control when a voltage infringement happens and measures the compensation requirement [13].

Bus voltage

SN,M

S1,1 Controller

Fig. 2. Control and bus voltage actions description

The sensitivity matrix is recreated by the relation between the voltages and the reactive power in the Jacobean matrix generated from the load flow Eq. [14]. ⎡ ∂P ∂P ⎤    ∂δ · · · ∂V  P ⎢ .. . . .. ⎥ δ =⎣ . (1) . . ⎦ V Q ∂Q ∂Q ∂δ · · · ∂V Expecting that the voltage point is immaterial regarding the responsive force, the connection between voltage and receptive force is epitomized in (2).   

 ∂Q

(2) V Q = ∂V

Optimal Control and Dynamic Stability of Power Injection







∂Q V = ∂V

−1



Q



899

(3)

[∂Q/∂V] is the Jacobian matrix to process the heap motion in (3.2). This implies that

−1 Q/V is the inverse matrix [∂Q/∂V] and it is known as the affectability matrix that assesses the transport voltage changes against the receptive force changes as demonstrated in (3). The sensitivity matrix is given by control gauges as demonstrated in (4). V i = SVg .U Vg V i = Ssh .U sh

(4)

V i = Stap .U tap The circuit of PV comprises two sub-schemes, a convertor of power and PV. The cell of photoelectric is the fundamental component of the photovoltaic board that is transmitted into energy. A photocell is for the most part on the request for 1 or 2 watts. A variety of photovoltaics addresses the PV module. An arrangement equal cluster of numerous photovoltaic modules structures a PV board. For energy system examines, the single paired model that appeared in Fig. 3 is adequately precise [15].

Fig. 3. Equivalent circuit of PV module [15]

In a PV matrix, the open circuit voltage and short circuit current are presented by the quantity of series and parallel cells [16]. V OC = N s .V oc

(5)

I SC = N p .I sc

(6)

The PV I-V and P-V features of the PV are take out as follows. I ph = SN .I sc + I t (T c − T r )

(7)

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 q(V L + I L RS −1 I d = I o exp AkT  

qEg 1 Tc 1 .exp I o = I or − Tr Bk T r Tc I L = I ph − I d −

V L + I L RS Rsh

(8) (9) (10)

Equation (3) is substantial for a particular radiation level SN and for a particular cell temperature T c accompanying conditions. The DC yield of the PV board I(V) is determined and it is an element of the voltage V with the PV module as follows, I(V) = I ph (G, T) − I d (V) − I p (V)

(11)

Iph (G,T) in (3.11) addresses the current produced by the PV, as a component of temperature and the radiation G. Id (V) addresses the current moving through the equal counter diode and the misfortune current is Ip (V). Subbing the definite articulation for diode flow (Shockley’s equation) and misfortune flow,  β(V+Rs I)  (V + Rs ) − 1 ]−[ ] I(V) = [I ph (G, T)]−[{I o (T)}. e a Rp

(12)

In (12), I o (T) addresses the diode’s opposite immersion current which relies upon the temperature T, Rs is the arrangement obstruction, Rp is the equal opposition, and an is the diode admiration factor. The converse warm potential β in (12) relies upon the temperature and the charge of the electron q. β(T) =

q N S kT

(13)

At (14) k is Boltzmann’s consistent and N is the number of arrangement associated PV cells. Short-term outsource current ward on radiation Gstc, temperature Tstc, cut off Isc, and stc in STC is determined as follows,

 G I ph (G, T) = I sc,stc + K I (T − T stc ) Gstc 

I sc,stc + K I (T − T stc ) I o (T) = β e α [V oc,stc +K V (T−T stc )] − 1

(14) (15)

Figure 4 shows the total outline of the single-stage electrical network associated with the PV network concentrated in this search. The body comprises a PV exhibit, trailed by a DC-DC help converter and a solitary stage full-connect inverter for network association. The test set to be executed depends on the advanced sign processor, where all calculations, for example, stage shut circle (PLL) and MPPT, and regulators are incorporated, notwithstanding the current regulator, inverter, MPPT support converter, and inverter DC transmission regulator.

Optimal Control and Dynamic Stability of Power Injection

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Fig. 4. PV grid-connected system [6]

3 Simulation Results The keen voltage control network controls the voltage utilizing profoundly delicate parts. For example, PV array, ANFIS logic controller with rule-viewer, DC-DC Boost converter voltage, equal/impedance capacitor, and tap transformer. It can set the voltage reach and target voltage run and can utilize the info fundamental force framework information, for example. When all is said in done, the effective astute strategy is the main factor to improve the presentation of the network on the grounds that the way toward getting an answer in an insightful framework needs to look through the state space with target surmising. This network proposed the utilization of the current weighted assessment work and the least-cost examination technique. The error is the distinction between the ideal yield of the item or cycle leveled out or setpoint and the real yield. This is a critical element of customary input control. Further, by relationship with an ordinary control center, we have: e(t) = ysp − y(t) e (t) = e(t)− e(t −1) and u (t) = u(t)− u(t −1); In the articulations, ysp represents the ideal interaction output or setpoint, and y is the process output variable (the control variable). The relationship of u with e and e is addressed in Fig. 5. This figure shows the guidelines for the ANFIS intelligent controller and the upsides of e and e were 10 in the control center simulation. The simulation of the proposed system will be discussed in this section. The block diagram of the developed system is displayed in Fig. 6. The input light for the system is converted to electrical power inside this system. This power can be used to feed the main electricity grid with 600 V of power. In addition to the capability of using the power immediately to any load can be added to system. Figure 7, shows the parameters and curves of the system within 10 s time period. The curves of the output power and irradiance are showed a high stability and perfect output. Also, the scopes gave a statistics of power, since the max power of MPPT was 2.7 ∗ 104 .When the min power was 7.4 ∗ 101 and the median was 7.6 ∗ 103 . The injected active power (P) and reactive power (Q) to the grid is shown in Fig. 7. The output of DC-AC simulation is shown in this figure. The measured time period is 10 s in the figure we can see stability in the output action power near of 1 × 10ˆ5W at action power. In another hand, the reaction power is continuing to be near of zero.

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Fig. 5. The rules of ANFIS controller

Fig. 6. The structure of overall control system

Fig. 7. Simulation results for overall injection power system based on intelligent voltage control

Optimal Control and Dynamic Stability of Power Injection

903

4 Conclusion The main task of the proposed network is to study in detail the difficulty of controlling constant voltage through special lighting on the regulator, taking into account the photovoltaic corridor. Typical voltage regulators (such as ANFAS and MPPT) work on many power distribution sources, and the dynamic feed of power generated by the voltage regulator affects the operation of these systems. One of the difficulties is to increase the injection volume to eliminate intermittent voltage spikes due to the generation of voltage drivers. 3 Another problem is the voltage regulator. The impedance of the photovoltaic power source and the excitation point of the substation, the voltage regulator control setting, the voltage regulator capacitance, and the reactive power control setting of the voltage control inverter is important parameters that determine the possibility of voltage loss. The voltage regulator is analyzed in detail in various scenarios of the operation of the distribution branch in the system. The branch voltage that is too low or too high is caused by a voltage regulator running at maximum power. Control is driven by the need to prevent leakage in order to seamlessly integrate photovoltaic energy into the distribution source. The traditional written method of coordinating reaction forces focuses on keeping the power supply voltage within set limits. The photoelectric field results, ANFAS and MPPT. The plan to significantly upgrade the operating system to meet these challenges is another compromise in the proposal. This strategy defines the range from the pump power to the maximum pressure value VR of the main network. This methodology organizes various voltage regulators and response power support methods for photovoltaic power generation. An important finding of this review is that it is important to help the photoelectric lifetime intensity response. Photovoltaic systems must provide ideal energy support to cope with power feeding and various difficulties. Various nonfunctional sources, including the generation of photovoltaic energy, are supported by private household energy from renewable energy sources.

References 1. Yu, W., Lee, H.: Application of intelligent voltage control system to Korean power systems. Int. J. Appl. Eng. Res. 12(19), 8529–8533 (2017) 2. Hemanand, T., Subramaniam, N.P., Venkateshkumar, M.: Comparative analysis of intelligent controller based microgrid integration of hybrid PV/wind power system. J. Ambient. Intell. Humaniz. Comput. 1–20 (2018). https://doi.org/10.1007/s12652-018-0961-6 3. Abdulelah Jalil, B., Al Mashhadany, Y., Algburi, S., Ulutagay, G.: Modeling and analysis: power injection model approach for high performance of electrical distribution networks. Bull. Electr. Eng. Inform. 10(6), 2943–2952 (2021) 4. Kassarwani, N., Ohri, J., Singh, A.: Performance analysis of dynamic voltage restorer using improved PSO technique. Int. J. Electron. 106(2), 212–236 (2019) 5. Hu, B., Yang, J., Li, J., Li, S., Bai, H.: Intelligent control strategy for transient response of a variable geometry turbocharger system based on deep reinforcement learning. Processes 7(9), 601 (2019)

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6. Al-Mashhadany, Y.I., Attia, H.A.: Novel design and implementation of portable charger through low-power PV energy system. In: Advanced Materials Research, vol. 925, pp. 495– 499. Trans Tech Publications Ltd. (2014) 7. Zhao, J.: Study of simulating human intelligent control. J. Phys. Conf. Ser. vol. 1544(1), p. 012152. IOP Publishing, May 2020 8. Adnan, A.Y., Abdul, H.M., Iwan, M.K.: Intelligent control for ship manoeuvering. J. Adv. Res. Appl. Mech. 67, 1–9 (2020) 9. Sayad Haghighi, M., Farivar, F., Jolfaei, A., Tadayon, M.H.: Intelligent robust control for cyber-physical systems of rotary gantry type under denial of service attack. J. Supercomput. 76(4), 3063–3085 (2019). https://doi.org/10.1007/s11227-019-03075-2 10. Donadel, C.B., Fardin, J.F., Encarnação, L.F.: An improved methodology to operate electrical distribution networks with distributed generation units in a pre-smart grid environment. In: 2018 13th IEEE International Conference on Industry Applications (INDUSCON), pp. 756– 762. IEEE, November 2018 11. Mancini, E., Longo, M., Yaici, W., Zaninelli, D.: Assessment of the impact of electric vehicles on the design and effectiveness of electric distribution grid with distributed generation. Appl. Sci. 10(15), 5125 (2020) 12. Al Mashhadany, Y.I.: Design and analysis of 7-DOF human-link manipulator based on hybrid intelligent controller. Infopmatika i avtomatizaci 19(4), 774–802 (2020) 13. Quarton, C.J., Samsatli, S.: Should we inject hydrogen into gas grids? Practicalities and whole-system value chain optimisation. Appl. Energy 275, 115172 (2020) 14. Ahmed, Y.A., Al-Mashhadany, Y.I., Nayyef, M.A.: High performance of excitation system for synchronous generator based on modeling analysis. Bull. Electr. Eng. Inform. 9(6), 2235–2243 (2020) 15. Lavaei, J., Tse, D., Zhang, B.: Geometry of power flows and optimization in distribution networks. IEEE Trans. Power Syst. 29(2), 572–583 (2014) 16. Attia, H.A., Ping, H.W., Al-Mashhadany, Y.: Design and analysis for high performance synchronized inverter with PWM power control. In: 2013 IEEE Conference on Clean Energy and Technology (CEAT), pp. 265–270. IEEE, November 2013 17. Kayal, P., Chanda, C.K.: A multi-objective approach to integrate solar and wind energy sources with electrical distribution network. Sol. Energy 112, 397–410 (2015)

Optimization of Moving Averages as Trend Indicators of a Stock Market Asset with Particle Swarm Optimization Algorithm Francisco Solano L´ opez Rodr´ıguez(B) and Jos´e Manuel Zurita L´ opez E.T.S. de Ingenier´ıas Inform´ atica y de Telecomunicaci´ on, C/Periodista Daniel Saucedo Aranda S/N, 18071 Granada, Granada, Spain [email protected]

Abstract. Predicting price movements in the stock market has been a relevant topic, which has attracted the attention of many investors for years. One of the ways to predict future price trends is by making use of technical indicators, among which we can highlight moving averages as one of the most widely used indicators. One of the most important aspects when elaborating a strategy based on moving averages is the choice of the number of periods to consider in the calculation of the average, it would be interesting to have some method that would be able to find the best values in order to optimize the strategy. In this paper we are going to propose a method to optimize a strategy based on moving averages, specifically we are going to use an algorithm known as Particle Swarm Optimization, to try to find the best combination of periods of the moving averages, with the aim of maximizing the profits obtained. The performance of the strategy based on optimized moving averages will be evaluated on some stocks of companies belonging to the NASDAQ-100.

Keywords: Particle Swarm Optimization market

1

· Moving averages · Stock

Introduction

Moving averages have been widely used to develop strategies based on signals generated by the crossing of moving averages. A crucial aspect when developing such strategies is the choice of the values to be used in the period of the moving averages, so it would be interesting to have an objective method to choose the optimal values for the strategy to achieve the maximum possible benefit. Our paper aims to contribute to the study of moving averages as trend indicators, with the goal of developing a buying and selling strategy based on moving averages optimized by means of the Particle Swarm Optimization algorithm. One of the novelties we propose is to generate a single buy and sell signal resulting c The Author(s), under exclusive license to Springer Nature Switzerland AG 2022  C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 905–913, 2022. https://doi.org/10.1007/978-3-031-09173-5_104

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F. S. L. Rodr´ıguez and J. M. Z. L´ opez

from combining several signals generated by crossing moving averages with different periods. Another contribution of this paper is the use of dynamic parameters that are adjusted during the use of the strategy to adapt to the new market situation. The rest of the paper is organized as follows. Section 2 review some of the most relevant research related to the topic of this study. Section 3 describes the theoretical concepts on which this research is based. Section 4 describes the proposed strategy, as well as the parameters selected in the experiments carried out. Section 5 presents the experiments performed, as well as the metrics used and an analysis of the results. Section 6 summarizes the conclusions and proposes future work.

2

Literature Review

The use of moving averages is very popular in trading and in the literature we can find many studies that analyze its use, [1,2,7]. Typically, moving average studies use fixed periods or only make use of simple or exponential moving averages, rather than both [4,6]. An important decision when developing strategies with moving averages is the choice of the values to be used in the moving average period, the profit of the strategy can vary greatly depending on the chosen parameters. Therefore, a relevant topic of study is the optimization of strategies based on moving averages, where again we can find different papers that make use of various optimization methods. For example, we have papers that make use of genetic algorithms for the optimization of moving averages [10]. We also find other papers using population-based algorithms, where we can highlight the use of the Particle Swarm Optimization algorithm [8,9].

3 3.1

Background Moving Averages

A moving average is defined as a trend indicator whose purpose is to identify or signal the beginning or end of a trend or its upcoming change. They help us take advantage of seasonality and eliminate distortions by smoothing out fluctuations and making it easier to see a trend. These are usually used on the closing price, although certain strategies also use the opening price, high or low of the selected period. The simple moving average is the simplest to calculate and it is also the best known and most widely used. Its mathematical expression is as follows: M M St (n) =

n−1 1 Pt−i n i=0

(1)

The simple moving average considers all sessions in the same way, which delays the signals that warn of possible trend changes. Instead of weighting every day with the same value, as in the case of the simple moving average,

Optimization of Moving Averages with PSO Algorithm

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the exponential moving average uses an exponential type of weighting that gives greater importance to the most recent quotations, while the older ones progressively lose importance. Its mathematical expression can be seen in the following equation: M M Et (n) = α · Pt + (1 − α) · M M Et−1 (n)

(2)

where α is the weighting factor bounded between 0 and 1 and M M Et−1 is the value of the exponential moving average of the previous period. Strategies Based on Moving Averages. Once the moving average has been calculated, it can be used to generate a buy or sell signal. Such signals are usually obtained by crossing the moving average with the price or crossing with another moving average. In buy and sell strategies with signals produced by the crossing of two moving averages, a short-term and a long-term moving average are used. The crossing of these suggests the beginning of a trend, either bullish or bearish. The strategy consists of entering the market when the short term moving average exceeds the long term moving average and exiting when it is below it. 3.2

Particle Swarm Optimization

The Particle Swarm Optimization (PSO) algorithm is a population-based search algorithm, where individuals, called particles (candidates solution), move through the search space affected by the cognitive desire to search individually and the collective action of the group or its neighbors. The first implementation of the PSO algorithm is attributed to the paper by [3]. It consists in the iterative search of optimal solutions in the search space, for that in each iteration the position of each particle is updated following an equation. Let xi (t) denote the position of the particle i in the search space and let t be the time instant (t will be understood as a discrete time step). The current position will be modified by adding a velocity vector vi (t). This process is reflected in the equation below, where xi (0) is initialized with a random distribution. xi (t + 1) = xi (t) + vi (t + 1)

(3)

We are going to use a variant of PSO known as Local Best PSO, where each particle communicates with only a subset of the swarm and it is attracted to the best position in its neighbourhood. The mathematical expression for the velocity calculation would be: vij (t + 1) = wvij (t) + c1 r1j (t)[yij (t) − xij (t)] + c2 r2j (t)[ˆ yij (t) − xij (t)]

(4)

With i ∈ {1, . . . , ns }, where ns the number of particles in the swarm and j ∈ {1, . . . , nx }, with nx the dimension of the search space. – xij (t) and vij (t) correspond to the j-th position of the position and velocity vectors respectively of particle i at time t.

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– c1 and c2 are the cognitive and social parameters respectively, with which the particle’s behavior is controlled to track its personal best and the global best position of the swarm. – The parameter w corresponds to the inertial weight. – r1j , r2j ∼ U (0, 1), two random numbers in the range [0, 1] that follow a uniform distribution. – yi refers to the personal best position of particle i. – yˆi refers to the best position in the neighbourhood of the i particle. The best personal position, yi , associated with the particle i, at each instant t will correspond to the best position found so far, so the calculation of the best position at instant t + 1 , assuming that it is a minimization problem, will be calculated as:  yi (t), si f (xi (t + 1)) ≥ f (yi (t)) yi (t + 1) = (5) xi (t + 1), si f (xi (t + 1)) < f (yi (t)) where f : Rnx → R is the objective function to be optimized. The best local position of the particle in the neighbourhood Ni , is defined as follows: yˆi (t) = yk (t), such that f (yk (t)) = min{f (x)}, ∀x ∈ Ni

(6)

where Ni is the neighbourhood of the i particle which has been previously defined by the index of each particle. The pseudocode of the Local Best PSO algorithm is shown below. Algorithm 1: Local Best PSO Initialize particle swarm while stopping criterion == False do for each particle i = 1, . . . , n do if f (xi ) < f (yi ) then yi = xi end yi ) then if f (yi ) < f (ˆ yˆi = yi end end for each particle i = 1, . . . , n do update velocity using the Eq. 4 update the position using the Eq. 3 end end

Optimization of Moving Averages with PSO Algorithm

4

909

Proposed Approach

Combination of Buying and Selling Rules. It is proposed to generate a signal as a result of the combination of buy and sell rules based on moving average crossover. Each of the rules will have two defined values, one for the short term average and one for the long term average. We will generate a buy signal when the short term average is above the long term average and a sell signal otherwise. The final signal will be obtained as the weighted sum of each of the signals generated by each of the defined rules. We are going to see mathematically how the combined signal is obtained. Let ri be the rule i with i = 1, . . . , n, where n is the total number of rules and wi is the weight assigned to that rule. Each of the rules will generate a signal si,t in period t, this signal will take the values −1 or +1, depending on whether it is a sell or buy signal respectively. The combined signal will be calculated as follows: st =

n 

wi si,t

(7)

i=1

 where we have that wi = 1 and wi ∈ [0, 1], thus guaranteeing that the value of st must be between −1 and +1. Thus, when the value of st is close to −1 it will be due to the predominance of sell signals in the defined rules and when it is close to +1 the predominance of buy signals. To determine when to send a buy or sell order, two thresholds θ1 and θ2 will be defined. In this way a buy signal will be generated when st > θ1 and a sell signal will be generated when st < θ2 . In the event that θ2 < st < θ1 no action will be taken. To ensure that when we make modifications to the vector of weights w with the PSO  algorithm, the resulting vector will continue to comply with the restrictions wi = 1 and wi ∈ [0, 1], we are going to introduce a new vector denoted by α that we will use to be optimized by the PSO algorithm. This vector will have a dimension of n + 2, where the first n values will be associated to the vector w, while the last 2 values will be associated to the parameters θ1 and θ2 . The vector w will be calculated from the vector α as follows: eαi wi = n k=1

eαk

, i = 1, . . . , n

(8)

Thus by modifying the vector α we can ensure that the vector w will continue to satisfy the constraints. Objective Function. We will use an objective function based on the profit to optimize the combined signal. Let us assume that we have an initial equity EI , transaction with cost c and the first buy signal received is obtained on day b (buy) and that the closing price on that day is pb . For the strategy considered we will buy as many shares as the available capital allows us, so on day b when we make our first purchase, we are buying k shares:

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k=

EI pb (1 + c)

(9)

The capital obtained after executing the sale order on day s where closing price is ps is obtained as follows: Es = ps k(1 − c) = EI ·

ps (1 − c) pb (1 + c)

(10)

Following the above process we can calculate the final capital of the strategy simulation using the following formula. EF = EI

m  psi (1 − c) p (1 + c) i=1 bi

(11)

where m indicates the number of operations that have been carried out, bi and si correspond to the purchase and sale made in operation i. EF refers to the final equity after the trading period. Obtaining the Rules of Purchase and Sale. As already mentioned, the buying and selling rules we will use will be based on the crossover of moving averages. The obtaining of each of the rules will be achieved from a list of defined periods. The list of periods is as follows: 5, 7, 9, 10, 12, 14, 15, 18, 20, 21, 24, 27 and 30. The rules will be obtained by all possible combinations of the list, taking into account that the short term period must be less than the long term period. The total number of rules obtained is 78. Therefore we will have 78 rules with simple moving average crossovers and 78 rules with exponential moving average crossovers. Signal Combined Optimization with PSO. In order to be able to use the signal generated by the combination of rules, it is necessary to have previously defined a value for the weights and thresholds used. The objective is to find values for these parameters in order to maximize the profitability of the strategy. To achieve this we will use the Local Best PSO algorithm with the following parameters: – – – – – –

Number of particles in the swarm: 50. Cognitive parameter (c1): 0.5. Social parameter (c2): 0.3. Inertial weight (w): 0.9. Number of neighbors of each particle: 10.   Norm used in the neighborhood calculation: L2 (x2 = ( x2i )).

The number of iterations of the algorithm has been set to 100 to establish the initial parameters. Additionally, after obtaining the parameters, during the simulations performed to validate the model, the algorithm is run again to retrain

Optimization of Moving Averages with PSO Algorithm

911

the model. The retraining is performed every 30 periods taking as training set the 90 periods prior to the current period by subtracting the number of periods from the objective function, from which it is.

5

Study Cases and Experimental Results Table 1. Nasdaq-100 strategy results Strategy: moving average crossover Stock

Profit (%) Max DD (%) Total oper Oper.+ Oper.− A. Oper A. Oper. + A. Oper. − +/−

AAPL

32.43%

−27.85

10

5

5

0.04

0.12

−0.05

ADBE

73.56%

−9.69

1

0

1

−0.01

0

−0.01

−0.0

ADSK

−3.187%

−39.4

7

1

6

−0.04

0.11

−0.07

1.57

AKAM −13.16%

2.4

−26.31

4

2

2

−0.03

0.03

−0.1

0.3

17.08%

−25.23

6

4

2

0.02

0.05

−0.03

1.67

AMAT 18.25%

−18.07

8

3

5

0.03

0.16

−0.05

3.2

AMGN 26.95%

−11.94

13

4

9

0.02

0.11

−0.02

5.5

AMZN 42.11%

−19.02

9

4

5

0.01

0.06

−0.04

1.5

Total

–

58

23

35

ALXN

24.25%

Strategy: PSO combined signal Stock

Profit (%) Max DD (%) Total oper Oper.+ Oper.− A. Oper A. Oper. + A. Oper. − +/−

AAPL

62.15%

−22.15

5

3

2

0.09

0.18

−0.06

ADBE

56.74%

−14.66

7

4

3

0.08

0.16

−0.03

5.33

ADSK

−2.708%

−41.4

8

2

6

−0.04

0.08

−0.08

1.0

AKAM −20.11%

3.0

−38.91

8

2

6

−0.02

0.08

−0.06

1.33

32.97%

−27.29

7

3

4

0.04

0.15

−0.04

3.75

AMAT 20.22%

−24.66

7

4

3

0.03

0.1

−0.06

1.67

AMGN 34.74%

−13.01

8

6

2

0.04

0.06

−0.02

3.0

AMZN 24.10%

−24.49

9

4

5

−0.01

0.05

−0.05

1.0

Total

–

59

28

31

ALXN

26.01%

Strategy: fuzzy candlesticks

[5]

Stock

Profit (%) Max DD (%) Total oper Oper.+ Oper.− A. Oper A. Oper. + A. Oper. − +/−

AAPL

−1.012%

−8.29

30

16

14

0.00

0.17

−0.20

0.83

ADBE

−3.309%

−7.93

22

9

13

−0.13

1.69

−1.38

1.22

ADSK

9.776%

−3.50

23

14

9

0.74

2.41

−1.79

1.35

−2.85

24

16

8

1.73

3.49

−1.36

2.57

AKAM −28.98%

−8.23

22

13

9

0.08

1.00

−1.24

0.81

AMAT −0.054%

−7.86

23

13

10

−0.09

3.88

−5.25

0.74

ALXN

3.927%

AMGN 18.05%

−6.60

26

16

10

0.42

1.12

−0.71

1.58

AMZN 12.55%

−3.89

28

16

12

0.10

0.32

−0.20

1.58

Total

−1.56

226

126

100

5.1

8.264%

Metrics Used

The metrics that we are going to use to measure the performance of the proposed strategy are the following: the percentage of profit obtained (Profit (%)), the number of total operations carried out (Total oper.), the number of positive operations (Oper.+), the number of negative operations (Oper.−) (by operation we mean the purchase of a security and the subsequent sale of it), the average

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profit of each operation (A. Oper.), the average of the negative operations (A. Oper.−), the average of the positive operations (A. Oper.+), the result of dividing the average of the positive ones by the average of the negative ones (+/−) and the maximum DrawDown (Max DD (%)). 5.2

Experiments Performed

In this paper we will perform the same experiments as those carried out in the research Fuzzy modeling of stock trading with fuzzy candlesticks [5], so that we can compare our results with those of another research focused on stock trading. As in the aforementioned paper, the training periods of the model will comprise the time interval from 22-Dec-2009 to 21-Dec-2011 and the validation period the 2 subsequent years. The data on which the validations will be carried out correspond to quotation values belonging to the Nasdaq-100. The initial investment portfolio will be 6 thousand dollars and the cost of each operation performed will be 1%. It should be noted that during the strategy validation period, the PSO algorithm continues to be used so that the combined signal adapts to the new market situation. The 8 stocks considered for the Nasdaq-100 are: Apple (AAPL), Adobe (ADBE), Autodesk (ADSK), Akamai Technologies (AKAM), Alexion Pharmaceuticals (ALXN), Applied Materials (AMAT), Amgen (AMGN) and Amazon (AMZN). 5.3

Analysis of the Results

We are going to analyze the results shown in the Table 1. Looking at the number of operation we can see that moving average crossover and combined signals strategy have made a similar number, and both have a higher number of negative operation than positive operation, although the combined signals strategy has a higher proportion of positive operation compared to the MA crossover strategy, which may explain its higher percentage of profit. The fact that both strategies had a positive profit despite having a higher number of negative trades compared to positive trades is due to the fact that the average profit per positive trade is higher than the average loss per negative trade. On the other hand, the paper [5] has a fairly high number of trades compared to the previous ones, and despite having a higher number of positive trades compared to negative ones, it has obtained a lower profit, which may be due to the cost of the commissions that may be involved in making so many trades.

6

Conclusions and Future Work

In this paper we have seen a method to optimize a strategy based on moving averages by using the Local Best PSO algorithm, in order to obtain a buy and sell signal by combining several trading rules obtained from the crossing of moving averages with different periods. For this we have used a function that calculates the profit obtained by the strategy with the aim of maximizing said function

Optimization of Moving Averages with PSO Algorithm

913

with PSO. We have been able to see how results exceed the classic strategy of moving average crossover for a set of tests performed on Nasdaq-100 markets. For future work, other variants of PSO could be used to optimize the parameters of the combined signal or for example other optimization algorithms such as genetic algorithms. Another future work would be to combine the proposed strategy with other classic strategies, which could improve their performance. New rules could even be defined to add to the combined signal, by using other technical indicators such as the relative strength index or stochastic oscillator.

References 1. Ellis, C.A., Parbery, S.A.: Is smarter better? A comparison of adaptive, and simple moving average trading strategies. Res. Int. Bus. Financ. 19(3), 399–411 (2005). https://doi.org/10.1016/j.ribaf.2004.12.009 2. Huang, J.Z., Huang, Z.J.: Testing moving average trading strategies on ETFs. J. Empir. Financ. 57, 16–32 (2020). https://doi.org/10.1016/j.jempfin.2019.10.002 3. Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of ICNN 1995 - International Conference on Neural Network, vol. 4, pp. 1942–1948 (1995) 4. Milionis, A.E., Papanagiotou, E.: Decomposing the predictive performance of the moving average trading rule of technical analysis: the contribution of linear and non-linear dependencies in stock returns. J. Appl. Stat. 40(11), 2480–2494 (2013). https://doi.org/10.1080/02664763.2013.818624 5. Naranjo, R., Arroyo, J., Santos, M.: Fuzzy modeling of stock trading with fuzzy candlesticks. Exp. Syst. Appl. 93, 15–27 (2018). https://doi. org/10.1016/j.eswa.2017.10.002. https://www.sciencedirect.com/science/article/ pii/S0957417417306784) 6. Pavlov, V., Hurn, S.: Testing the profitability of moving-average rules as a portfolio selection strategy. Pac. Basin Financ. J. 20(5), 825–842 (2012). https://doi.org/ 10.1016/j.pacfin.2012.04.003 7. Sobreiro, V.A., et al.: The profitability of moving average trading rules in brics and emerging stock markets. North Am. J. Econ. Financ. 38, 86–101 (2016). https:// doi.org/10.1016/j.najef.2016.08.003 8. Wang, F., Yu, P.L., Cheung, D.W.: Combining technical trading rules using particle swarm optimization. Exp. Syst. Appl. 41(6), 3016–3026 (2014). https://doi.org/ 10.1016/j.eswa.2013.10.032 9. Wang, L., An, H., Liu, X.: A PSO approach to search for adaptive trading rules in the eua futures market. Energy Procedia 75, 2504–2509 (2015). https://doi.org/ 10.1016/j.egypro.2015.07.246. Clean, Efficient and Affordable Energy for a Sustainable Future: The 7th International Conference on Applied Energy (ICAE2015) 10. Wang, L., An, H., Liu, X., Huang, X.: Selecting dynamic moving average trading rules in the crude oil futures market using a genetic approach. Appl. Energy 162, 1608–1618 (2016). https://doi.org/10.1016/j.apenergy.2015.08.132

Intelligent Valid Inequalities for No-Wait Permutation Flowshop Scheduling Problems Damla Yüksel1(B)

, Levent Kandiller1

, and Mehmet Fatih Ta¸sgetiren2

1 Department of Industrial Engineering, Yasar University, Bornova, 35100 Izmir, Turkey

[email protected] 2 Department of Industrial and Systems Engineering, Auburn University, Auburn, USA

Abstract. The no-wait permutation flowshop scheduling problem is a wellrecognized scheduling problem. Examples can be encountered in several industries such as hot metal rolling, painting, chemical, steel industries, etc. In this flowshop setting, the jobs are not allowed to wait between consecutive machines. Owing to the NP-hardness identity of the problem, the developed mathematical models to solve this problem cannot reach optimal solutions for large instances in polynomial time. However, the quality of the objective functions and the gap values obtained by the mathematical models in a specific time window can be improved by valid inequalities. This study generates intelligent valid inequalities to improve a mathematical model’s performance in optimizing the no-wait permutation flow shop scheduling problems. Valid inequalities’ performance is tested for three significant objective functions: (i) makespan, (ii) total flow time, and (iii) total tardiness. According to the computational experiments, the new valid inequalities improve the outcomes of the mathematical models mostly in the way of the gap values for makespan, total flow time, and total tardiness objective criteria. Keywords: Valid inequalities · No-wait permutation flowshop scheduling problem · Mathematical models

1 Introduction and Problem Definition The no-wait permutation flowshop scheduling problem (NWPFSP) is a well-recognized scheduling problem [1]. No queue for jobs is allowed between consecutive machines in NWPFSP; it is also considered a continuous flowshop scheduling problem [2]. The processing of jobs on machines must be maintained without any disruption. Owing to the NP-hardness identity of the problem [3], the developed mathematical models to solve this problem cannot reach optimal solutions for large instances in polynomial time. However, the quality of the objective functions and the gap values obtained by the mathematical models in a specific time window can be improved by valid inequalities. The aim of generating valid inequalities over the mathematical models is to enhance the outcomes of mathematical models, i.e., the objective function and the gap values. In the literature, the valid inequalities are widely utilized on the mathematical models for various combinatorial optimization problems such as discrete lot-sizing and scheduling [4, 5], production scheduling (chemical) [6], railway traffic management [7], project © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 914–922, 2022. https://doi.org/10.1007/978-3-031-09173-5_105

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scheduling [8]. In the field of flowshop scheduling problems, the mathematical models aiming to optimize unrelated parallel machine scheduling [9, 10], two-machine permutation flowshop scheduling [11], single machine scheduling [12, 13] with sequence and time-dependent variants [14], continuous energy-constraint scheduling [15] problems are enhanced by some sort of valid inequalities. Among these studies, [4, 8], and [14] have implemented their valid inequalities into their branch and cut algorithms. Regarding NWPFSPs, a set of valid inequalities as lower and upper bounds are generated for makespan minimization by [16]. Additionally, a certain number of valid inequalities are produced to strengthen the developed mathematical models for two-machine NWPFSP [17] and two-stage hybrid NWPFSP [18] problems. In this study, new valid inequalities are proposed to improve a mathematical model’s performance, optimizing the NWPFSP. The performance of valid inequalities is tested for three significant objective functions: (i) makespan, (ii) total flow time, and (iii) total tardiness, and then the computational outcomes are reported.

2 Mathematical Model The mathematical model to optimize the NWPFSPs is provided below. Pir is the processing time of ith job (i ∈ I ) on r th machine (r ∈ R) and DDi is the due date of ith job (i ∈ I ). The model aims to find the values of the following decision variables. Cir is the finishing time of ith job (i ∈ I ) on r th machine (r ∈ R), Cmax is the makespan, Dij equals to 1 if job i is positioned any time earlier than job j, 0 otherwise (i < j), and Ti is the tardiness of ith job (i ∈ I ). Objective   CiR or Ti (1) Minimize Cmax or i∈I

i∈I

Constraints Ci1 ≥ Pi1 Cir − Ci,r−1 ≥ Pir Cir − Cjr + QDij ≥ Pir Cir − Cjr + QDij ≤ Q − Pjr Cir − Ci,r−1 ≤ Pir Cmax ≥ CiR Ti ≥ CiR − DDi Ti ≥ 0

∀i ∈ I ∀i ∈ I , ∀r ∈ R : r ≥ 2 ∀i, j ∈ I : j > i, ∀r ∈ R ∀i, j ∈ I : j > i, ∀r ∈ R ∀i ∈ I , ∀r ∈ R : r ≥ 2 ∀i ∈ I ∀i ∈ I ∀i ∈ I

(2) (3) (4) (5) (6) (7) (8) (9)

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Cir ≥ 0 Dij ∈ {0, 1}

∀i ∈ I , ∀r ∈ R ∀i, j ∈ I : j > i

(10) (11)

This mathematical model is constituted for NWPFSP by [16] as it is adapted from Manne’s good-old PFSP formulation [19]. The computational results for makespan, total flow time, and tardiness minimization were reported in [16] separately. Since the computational results are good enough, this mathematical model is also studied for energy-efficient scheduling of NWPFSPs in [20–22]. The objective function (1) minimizes either makespan or total flow time or total tardiness. Constraint (2), (3), (4), (5) is the good-old PFSPs formulation of Manne [19]. Constraint (6) is the no-wait restriction supported by Constraint (3). They provide that the starting time of a job in a machine equals the completion time of that job on the previous machine. Then, calculation of the makespan is implemented by constraint (7). Constraints (8) and (9) ensure the tardiness of each job. Constraints (9), (10), and (11) are the sign and variable restrictions. With the help of this formulation, constraints (2), (3), (4), (5), (6), (7), (10), and (11) shape the model for makespan minimization if it is the objective function. The same constraints still shape the total flow time minimization model if it is the objective function. However, for total tardiness minimization, we have to include (8) and (9) in the model and consider the total tardiness as the objective.

3 Valid Inequalities In this study, new intelligent valid inequalities are proposed for the aforementioned mathematical model of NWPFSPs. Chvatal-Gomory (C-G) valid inequalities are applied to Eq. (3) of the mathematical model of NWPFSPs explained above, and the following C-G valid inequalities are acquired.    α ∗ Pir  ∀i ∈ I (12) CiR − Ci1 ≥ (1/α) ∗ r∈{2,..,R}    α ∗ Pit  Cir − Ci1 ≥ (1/α) ∗ ∀i ∈ I , ∀r ∈ {3, . . . , R} (13) t∈{2,..,r}    α ∗ Pit  CiR − Cil ≥ (1/α) ∗ ∀i ∈ I , ∀l ∈ {1, . . . , R − 2} (14) t∈{l+1,..,R}    α ∗ Pit  Cir − Cil ≥ (1/α) ∗ t∈{l+1,..,r}

∀i ∈ I , ∀r ∈ {3, . . . , R} ∀l ∈ {1, . . . , R − 2}|l < r − 1

(15)

Equation (12) constructs a relationship between a job’s finishing time on the first and the last machine. Equation (13) is one step extended version of Eq. (12) in which it considers the relationship between a job’s finishing time on the first machine and all machines from 3 to |R|. Similarly, Eq. (14) is another point of view to Eq. (12) in which it considers the relationship between a job’s completion time on the last machine and all machines from 1 to |R − 2|. Finally, Eq. (15) is the complete version of all combinations. It considers the relationship between a job’s completion time on the two different machines r and l such that l is always less than r − 1.

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4 Computational Experiment The valid inequalities are added on the MILP model as new set of constraints. To decide the value of α in the formulation, an experiment is conducted considering all combinations of α values, which can be obtained from the finite prime numbers set, that is {2,3,5,7,11,13,17,19}. The experiment is conducted over the truncated small instances of Taillard proposed to the literature by [21]. There are 30 small instances consisting of 10 instances in each set of 5 jobs and 5, 10 and 20 machines. According to the experiment results, the best α values yielding to solve the small instances fastest are 13/19, 7/11, and 2/17 for makespan, total flow time, and total tardiness objective functions, respectively. Therefore, these α values are carried out to measure the valid inequalities’ performances in large instances. The mathematical model is executed by valid inequalities and corresponding α values on the Taillard dataset [23]. The detailed computation results are provided on the website https://data.mendeley.com/datasets/ck35y8gfxk/1. Each instance is run for 3600 s. The objective values and the gap values of the model without valid inequalities, the objective values, and the gap values of the model with valid inequalities, the improvement on objective value, and on gap percentage are reported in Tables 1, 2, 3, 4, 5 and 6. Tables 1 and 2 represent the results for makespan with valid inequalities (1) and (4), respectively. Tables 3 and 4 depict the results for total flow time with valid inequalities (1) and (4), respectively. Table 5 and 6 list the results for total tardiness with valid inequalities (1) and (4), respectively. Table 1. Comparison of results with valid inequality (1) for makespan Instance

Objective value

Gap %

Objective value with valid inequality (1)

Gap % with valid inequality (1)

Improvement on objective value

Improvement on gap %

20 × 5_Avg

1508.3

43.47%

1500.0

39.66%

0.55%

8.76%

20 × 10_Avg

2019.4

38.07%

2004.4

35.51%

0.74%

6.73%

20 × 20_Avg

2996.0

33.55%

2989.7

30.68%

0.21%

8.56%

50 × 5_Avg

3814.3

82.46%

3773.2

82.30%

1.08%

0.19%

50 × 10_Avg

5037.2

79.96%

4982.7

79.76%

1.08%

0.25%

50 × 20_Avg

6980.1

75.32%

6889.1

75.26%

1.30%

0.08%

100 × 5_Avg

8024.9

92.36%

7894.6

91.68%

1.62%

0.73%

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Instance

Objective value

Gap %

Objective value with valid inequality (4)

Gap % with valid inequality (4)

Improvement on objective value

Improvement on gap %

20 × 5_Avg

1508.3

43.47%

1500.6

37.99%

0.51%

12.60%

20 × 10_Avg

2019.4

38.07%

2007.1

34.21%

0.61%

10.14%

20 × 20_Avg

2996.0

33.55%

3000.7

30.08%

−0.16%

10.34%

50 × 5_Avg

3814.3

82.46%

3763.3

81.60%

1.34%

1.04%

50 × 10_Avg

5037.2

79.96%

4933.0

78.90%

2.07%

1.33%

50 × 20_Avg

6980.1

75.32%

6839.9

75.29%

2.01%

0.04%

100 × 5_Avg

8024.9

92.36%

7879.2

91.57%

1.82%

0.86%

Table 3. Comparison of results with valid inequality (1) for total flow time Instance

Objective value

Gap %

Objective value with valid inequality (1)

Gap % with valid inequality (1)

Improvement on objective value

20 × 5_Avg

16169.6

48.26%

20 × 10_Avg

23873.8

20 × 20_Avg

Improvement on gap %

16230.8

45.42%

−0.38%

5.88%

41.40%

23688.4

37.67%

0.78%

8.99%

38717.5

34.38%

38752.7

31.58%

−0.09%

8.15%

50 × 5_Avg

91507.5

81.86%

87902.8

81.39%

3.94%

0.58%

50 × 10_Avg

126194.9

75.33%

122682.1

74.92%

2.78%

0.55%

50 × 20_Avg

183150.1

68.61%

180125.1

68.34%

1.65%

0.39%

100 × 5_Avg

369081.0

90.38%

363814.8

90.40%

1.43%

−0.03%

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Table 4. Comparison of results with valid inequality (4) for total flow time Instance

Objective value

Gap %

Objective value with valid inequality (4)

Gap % with valid inequality (4)

Improvement on objective value

20 × 5_Avg

16169.6

48.26%

20 × 10_Avg

23873.8

20 × 20_Avg

Improvement on gap %

16247.5

45.60%

−0.48%

5.51%

41.40%

23712.6

38.32%

0.68%

7.43%

38717.5

34.38%

38652.4

31.37%

0.17%

8.75%

50 × 5_Avg

91507.5

81.86%

87608.6

81.26%

4.26%

0.73%

50 × 10_Avg

126194.9

75.33%

123469.1

75.33%

2.16%

0.01%

50 × 20_Avg

183150.1

68.61%

180784.6

68.54%

1.29%

0.10%

100 × 5_Avg

369081.0

90.38%

369219.8

91.53%

−0.04%

−1.28%

According to Tables 1 and 2, 8.76%, 6.73%, and 8.56% improvement on gap percentage is achieved on the first three sets of instances by valid inequality (1), whereas 12.60%, 10.14%, and 10.34% improvement on gap percentage is achieved on the same set of instances by valid inequality (4). This result illustrates that the performance of the valid inequality (1) is immensely improved by valid inequality (4) in makespan minimization. According to Tables 3 and 4, 5.88%, 8.99%, and 8.15% improvement on gap percentage is achieved on the first three sets of instances by valid inequality (1), whereas 5.51%, 7.43%, and 8.75% improvement on gap percentage is achieved on the same set of instances by valid inequality (4). According to Tables 5 and 6, 5.35% and 22.91% improvement on gap percentage is achieved on the first two sets of instances by valid inequality (1), whereas 5.71% and 31.02% improvement on gap percentage is achieved on the same set of instances by valid inequality (4). This outcome illustrates that the valid inequality (1) performance improves significantly by valid inequality (4) in the 20 × 10 set of instances in total tardiness minimization. In the 20 × 20 set of instances, all the instances are solved optimally. Thus, it seems like there is no improvement. However, it is essential to mention that there is also a time improvement. In the 20 × 20 set of instances, the average run time is 76.8 s, whereas it reduces to 12.1 and 11.2 s, including valid inequalities (1) and (4), respectively. Similarly, In the 20 × 10 set of instances, the average run time is 3348.7 s, whereas it reduces to 3119.2 and 2820.6 s by adding the valid inequality (1) and (4), respectively. The fact is that the number of optimal solutions found in this set

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of instances increases from 2 to 3 and to 4 with the inclusion of valid inequality (1) and (4), respectively. Table 5. Comparison of results with valid inequality (1) for total tardiness Instance

Objective value

Gap %

Objective value with valid inequality (1)

Gap % with valid inequality (1)

Improvement on objective value

Improvement on gap %

20 × 5_Avg

4512.5

80.49%

4484.9

76.19%

0.61%

5.35%

20 × 10_Avg

1805.1

48.92%

1787.8

37.71%

0.96%

22.91%

20 × 20_Avg

0.00%

815.7

0.00%

0.00%

0.00%

50 × 5_Avg

59010.9

815.70

99.11%

58983.8

98.96%

0.05%

0.16%

50 × 10_Avg

66065.2

99.24%

64352.6

99.09%

2.59%

0.16%

50 × 20_Avg

69870.4

99.17%

68033.8

98.94%

2.63%

0.23%

100 × 5_Avg

300853.7

99.67%

295578.4

99.74%

1.75%

-0.07%

Table 6. Comparison of results with valid inequality (4) for total tardiness Instance

Objective value

20 × 55_Avg

4512.5

80.49%

20 × 510_Avg

1805.1

20 × 520_Avg

815.70

Gap %

Objective value with valid inequality (4)

Gap % with valid inequality (4)

Improvement on objective value

Improvement on gap %

4461.6

75.89%

1.13%

5.71%

48.92%

1772.1

33.74%

1.83%

31.02%

0.00%

815.7

0.00%

0.00%

0.00%

50 × 55_Avg

59010.9

99.11%

56492.6

98.92%

4.27%

0.20%

50 × 510_Avg

66065.2

99.24%

62879.4

99.07%

4.82%

0.18%

50 × 520_Avg

69870.4

99.17%

68508.1

99.03%

1.95%

0.15%

100 × 55_Avg

300853.7

99.67%

295574.3

99.75%

1.75%

-0.08%

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5 Conclusion In conclusion, new Chvatal-Gomory valid inequalities are proposed to improve a mathematical model’s performance of NWPFSP. The performance of valid inequalities is tested for three significant objective functions: (i) makespan, (ii) total flow time, and (iii) total tardiness, and then computational results are reported. According to the results, the valid inequalities are pretty beneficial in the first three sets of instances, with a good amount of improvement on the gap percentage value. As future research directions, the valid inequality generation procedures can be applied to other mathematical models for NWPFSPs. They will eventually enhance the performance of the other models in the way of the run time or percent deviations from the best integer solutions found. The lower and upper bounds can be integrated into the mathematical models and the generated valid inequalities. In that way, the performance of the valid inequalities may improve much higher. Furthermore, the small set of instances is easily solvable in seconds. Hence, to compare the performance of the valid inequalities more sensitive in terms of the run time, a larger size small set of instances can be studied, such as ten jobs.

References 1. Aldowaisan, T., Allahverdi, A.: New heuristics for m-machine no-wait flowshop to minimize total completion time. Omega 32(5), 345–352 (2004) 2. Fink, A., Voß, S.: Solving the continuous flow-shop scheduling problem by metaheuristics. Eur. J. Oper. Res. 151(2), 400–414 (2003) 3. Röck, H.: The three-machine no-wait flow shop is NP-complete. J. ACM 31(2), 336–345 (1984) 4. Gicquel, C., Minoux, M.: Multi-product valid inequalities for the discrete lot-sizing and scheduling problem. Comput. Oper. Res. 54, 12–20 (2015) 5. Kaczmarczyk, W.: Valid inequalities for proportional lot-sizing and scheduling problem with fictitious microperiods. Int. J. Prod. Econ. 219, 236–247 (2020) 6. Merchan, A.F., Maravelias, C.T.: Preprocessing and tightening methods for time-indexed MIP chemical production scheduling models. Comput. Chem. Eng. 84, 516–535 (2016) 7. Pellegrini, P., Pesenti, R., Rodriguez, J.: Efficient train re-routing and rescheduling: valid inequalities and reformulation of RECIFE-MILP. Transp. Res. Part B Methodol. 120, 33–48 (2019) 8. Kis, T.: A branch-and-cut algorithm for scheduling of projects with variable-intensity activities. Math. Program. 103(3), 515–539 (2005) 9. Hassan, M.A., Kacem, I., Martin, S., Osman, I.M.: Valid inequalities for unrelated parallel machines scheduling with precedence constraints. In: International Conference on Control, Decision Information Technologies, CoDIT 2016, pp. 677–682, October 2016 10. Saberi-Aliabad, H., Reisi-Nafchi, M., Moslehi, G.: Energy-efficient scheduling in an unrelated parallel-machine environment under time-of-use electricity tariffs. J. Clean. Prod. 249, 119393 (2020) 11. Hamdi, I., Toumi, S.: MILP models and valid inequalities for the two-machine permutation flowshop scheduling problem with minimal time lags. J. Industr. Eng. Int. 15(1), 223–229 (2019). https://doi.org/10.1007/s40092-019-00331-1 12. Dauzere-Peres, S.: Efficient formulation for minimizing the number of late jobs in singlemachine scheduling. In: IEEE Symposium Emerging Technologies Factory Automation. ETFA, pp. 442–445 (1997)

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An Intelligent Smartphone-Based ADAS Manolo Dulva Hina1,2(B) , Assia Soukane1,2 , and Amar Ramdane-Cherif1,2 1 ECE Ecole d’Ingénieurs (ECE Engineering School), Paris, France

[email protected] 2 LISV Laboratory, Université de Versailles Paris-Saclay, Velizy, France

Abstract. There is a need for an alternative ADAS (advanced driving assistance system) given that current ones are expensive and closed to proprietary constraints. CASA (CAr Safety App) is a low-cost, alternative ADAS which is deployable in a driver’s smartphone or tablet. Its cognition of driving context is based upon the fusion of various parameters representing the context of the environment, the driver, and the vehicle. The decisional system of CASA determines if there are situations (notification, alert, or danger) that must be mitigated. If so, the driving assistance takes effect, and the assistance message/signal is sent to the driver, the vehicle or both. This ADAS also contains a fuzzy logic system infers the driver’s profile based on the behavior of the person on the wheels and sends assistance messages suitable for such driver. Overall, this intelligent smartphonebased alternative ADAS is a tool that minimizes accident and keeps road navigation safe. Keywords: ADAS · Intelligent transportation · Fuzzy logic · Inference engine

1 Introduction Navigation tools are intended to assist people in finding path in moving from position A to destination B. The traditional GPS (global positioning system) satisfies this, but it is incapable of informing the driver of his traffic rules and regulations’ infractions (i.e., over speeding, etc.). Moreover, it does not assist the driver in mitigating complex driving situations (e.g., driving in a foggy area, poor visibility). The advanced driving assistance system (ADAS) [1, 2] fills this gap by informing, notifying and assisting drivers in mitigating various driving situations. Typical ADAS are typical expensive and closed to proprietary constraints, which means that ADAS X works well only for vehicle X, but not for others. CASA [3, 4] is an alternative ADAS that works for all types of vehicles because its proposed solution is generic in nature. It is an app deployable on a smartphone or a tablet, in contrast to traditional ADAS which are made by car manufacturers and deployed in-vehicle. This paper presents the cognition of driving situation and driver’s profile, and accordingly provides its driving assistance mechanisms. The contributions of this work are as follows: • A detailed representation of the driving context which is derived from the fusion of various parameters related to the contexts of the environment, driver, and the vehicle. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 923–931, 2022. https://doi.org/10.1007/978-3-031-09173-5_106

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This fusion also occurs in different levels of abstraction. Each parameter is received as a value obtained from a sensor, analyzed, and sent as a high-level event into the fusion system. • Knowledge representation of concepts and events is done using ontology. Rules governing cognition of driving context and driving assistance action are represented using SWRL notation. This formalism presents suitable reasoning on what suitable assistance action is to be invoked.

2 Approach and Methodology In relation to proposing an alternative ADAS, the aim of this work is threefold. First, we wish to correctly perceive the driving environment. This is done through the collection and fusion of various parameters representing the context of the vehicle, the driver, and the environment, obtained from various sources, such as sensors and connected objects. These parameters and their values are collectively called the pre-condition of the driving context. Second, selected driving context that needs assistance are stored in the knowledge database. For each driving context/situation, we determine what action needs to be done; these results (i.e., actions) make up the post-condition of the driving context. The fission process defines the smaller actions (sub-actions) which when taken as a whole implement the desired action. Third, this ADAS should be able to detect the profile of the person on the wheel and adopt the driving assistance message for such driver. Finally, all these processes must be validated through a use case scenario. Altogether, the use case is a representative sample of an ADAS implementation. The architecture of CASA is shown in Fig. 1 and the components of the system are described below:

Actuators (Display, Audio, Sensation) Web service resetful API with JSON file

Action for the vehicle

Message for the driver

API for Service Providers (CEA)

Fusion-Fission Component

Web service resetful API with JSON file Sensor 1 information CAN Bus

Sensor 2 information

...

Bluetooth

Sensor n information LiFi

ENVIRONMENT (Vehicle, Smartphone, Road Infos, Infrastructure, Etc.)

Fig. 1. Architecture of an intelligent vehicle implementing CASA driving assistance system

• The environment contains various sensors and connected objects whose values may be used to figure out the state of such environment. These data are then transmitted to their destinations using different means of communications, such as CAN (controller area network) bus, Bluetooth, WiFi, 4G, 5G or LiFi.

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• The real-time data needed by the intelligent vehicle are saved into the repository. In CASA’s case, the data obtained from the vehicle and the environment are forwarded to the CEA (Car Easy Apps) [5, 6], which is an API for service providers component developed by PSA1 (a partner in this project) hence it is deployed in the vehicle manufactured by PSA, such as Peugeot and Citroën. For other brands of vehicle (e.g., Toyota), then CEA is deployed in the cloud. The communication protocol used is a unique bus using web service restful API with JSON file. • The interpretation-decision component of an intelligent vehicle is implemented in the Fusion-Fission component. It receives driving context data/signals, combines them to identify the current driving context. If such driving context merits an assistance, this component uses fission that yields the appropriate action for such situation. The resulting assistance action and signals intended for the driver and the vehicle are sent back to CEA. • The CEA then sends signals to the appropriate actuators. The actuators implement the action for the vehicle and/or broadcast message for the driver. Different actuators are involved (display, audio, sensation, etc.). A smartphone, to which CASA software is deployed, is used for both audio and message display.

3 Detection of Driving Context Multimodal fusion [13] is the process of combining two or more data obtained from different sources, the result of which provides more meaningful information than if the data is interpreted individually [7]. In this work, direct fusion is used. The data (or signals) are themselves generated by sensors, sent to, and recovered from the repository (CEA). They are provided as input service, represented in higher-level of abstraction. The signals are fused, producing a result that is a type of driving situation which is again interpreted in the higher-level of abstraction. The result of the fusion process [8] is looked up in the knowledge base containing rules. If a corresponding rule is found, it means that such situation has a special meaning to the ADAS system and therefore merits an action (a driving assistance). To demonstrate the fusion process, and associate it to a driving rule, let there be some individuals or instances of various objects or classes in the ontology of objects and concepts. We will use SWRL (Sematic Web Rule Language) [9, 10] notation wherein the symbol ‘?’ represents an instance/individual of a class: • • • • • • •

Let A be a car object == Car(?A) Let R be a road object == Road(?R) Let car A be on road R == isOnTheRoad(?A, ?R) Consider L to be lane and let L be on road Y == hasLane(?L, ?R) Let our car A be on lane L == isOnLane(?A, ?L) Assume that W is an object on lane L == hasObject(?W, ?L) Assume that W’s distance from A be near == hasDistanceFromVehicle(?W, nearDistance)

1 PSA vehicle (Peugeot or Citroën): https://www.groupe-psa.com/en/.

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If we perform the fusion of these parameters (the premise or pre-condition), we will arrive at a conclusion/post-condition that W is an obstacle to vehicle A. That is:

Multimodal fission [11, 12] refers to a set of smaller steps that when implemented in order and collectively would form the action (driving assistance) to be implemented by the machine. This process makes use of different actuators, each of which executes an action. For example, for obstacle W in lane Z of road Y ahead of vehicle X, the fission process determines which of the following options is most apt for the driver: (1) Change lane or overtake – if a lane to overtake is available; (2) Remain in the same lane – no lane to overtake is available; and (3) Brake for obstacle and remain in the same lane – if the obstacle speed is slow compared to the driver’s speed.

4 Fission and Actions for Driving Situations The fission process yields a result called “Action”. In our ontology, every driving situation that merits an assistance is represented by an abstract class called “Action”. Similar to the concept of object-oriented programming, this abstract action is extended by one or more concrete actions. See Fig. 2. As shown, the class “Action” can have the following representative concrete sub-classes: • ChangeLane: this concrete action is invoked if an obstacle to the ego vehicle is in the same lane and their distance is near and a lane for overtaking is available. • RemainInTheSameLane: this concrete action is suggested when an obstacle ahead is detected and but no lane for overtaking is available. • Brake: is invoked to avoid hitting an obstacle. It has four sub-types: (1) BrakeForPedestrian – here, the obstacle detected is a pedestrian. The ego vehicle must stop to allow the pedestrian to cross the street; (2) BrakeForObstacle – this is invoked when any other obstacle (mobile or static) is detected. If braking is not carried out, a collision will occur. (3) BrakeForRedLight – this action is invoked upon detecting that a ‘TrafficLight’ object is present in the driving scenario, and its colour is ‘Red’. If the colour is ‘Yellow’ and the distance of the ego vehicle to the TrafficLight is near, then this action is also invoked; (4) BrakeForStop: a mandatory stop is executed when a “Stop” sign is detected and the ego vehicle’s distance from the sign is near. • SlowDown: this concrete action is carried out if the ego vehicle is over speeding or is going downhill or if it to turn in a curve. • HaveABreak: the action is suggested if the ADAS detected that the driver is tired, stressed or is having a malaise. • BadWeather: an action suggested when the intelligent vehicle has sensed poor visibility due to rain, snow, or fog.

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Fig. 2. The ontological representation of the actions to some driving events

5 Fuzzy Logic-Based Driving Assistance System Different drivers have different driving styles, even in identical condition [13]. For this reason, it is necessary to classify the type of driver based on his/her the behavior and other relevant data. The idea is to provide the right kind of driving assistance system based on the profile of person driving the vehicle. This profile is obtained in real-time, hence the assistance system is relevant in real time. For example, the way a danger notification assistance sent to a reckless driver and to a prudent driver should be delivered differently. In this work, the profile of a driver is based on various parameters as given below:

The detail of quantification or value designation of each parameter is given below: • Age: Based on the age of the person driving the vehicle: – Young = 16 to 20 years old | Matured = 21 to 30 years old | Middle Age = 31 to 50 years old | Old = 51 to 64 years old | Very Old = 65 years old and above • Driving Experience: The number of years of driving experience: – Novice or VL (0 to 2 years) | Advanced Beginner or L (3 to 5 years) | Competent or M (6 to 10 years) | Proficient or H (11 to 19 years) | Expert or VH (20 years and above) • Over Speeding: The number of times the driver over speed throughout the duration of the trip: – Prudent or VL (0 to 2%) | Cautious or L (3% to 5%) | Risky or M (6% to 10%) | Very Risky or H (11% to 20%) | Reckless or VH (21% and above)

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• Acceleration: The number of times the driver accelerated throughout the duration of the trip: – Prudent or VL (0 to 5%) | Cautious or L (6% to 10%) | Risky or M (11% to 20%) | Very Risky or H (21% to 30%) | Reckless or VH (31% and above) • Braking: The number of times the driver braked throughout the duration of the trip: – Prudent or VL (51% and above) | Cautious or L (41% to 50%) | Risky or M (31% to 40%) | Very Risky or H (21% to 30%) | Reckless or VH (20% and less) • Direction Indicator Missed: The number of times the driver failed to indicate his direction when turning left or right in all intersections throughout the duration of the trip: – Prudent or VL (0 to 2%) | Cautious or L (3% to 5%) | Risky or M (6% to 15%) | Very Risky (16% to 25%) | Reckless (26% and above) where VL = very low, L = low, M = medium, H = high and VH = very high. The calculation of percentage of over speeding, acceleration, braking and missing the activation of direction indicator begins when the engine of the vehicle is activated (i.e., CASA activation) and ends when the engine is turned off. There is a separate counter for over speeding, accelerating, braking, and missing direction indicator. The count happens in every road segment. A straight road is one road segment. When a vehicle turns to the left or to the right or continues straight ahead after an intersection, the driver goes to another road segment. In the case of a long highway, a segment is one area of the highway with a specific speed limit. If the driver exits the highway, he is in another road segment. If the speed limit in a highway changes, then the area with a new speed limit is considered a new road segment. Over time, we can calculate the percentage of over speeding, accelerating, braking, and missing direction indicator of the driver. Together with the driver’s age and driving experience, we can now determine the profile of the driver. Given below are sample rules that detect whether the profile of the person driving the vehicle (designated as ?X) is reckless or prudent:

The distinction whether the driver is reckless is prudent or reckless is important. The notification message for a prudent driver is gentle whereas the one for a reckless driver

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is course or rough. For example, for an over speeding infraction, the audio message sent to a prudent driver is something like: “Please slow down. The speed limit is 70 km/h”, delivered in a gentle voice. The one sent to a reckless driver is something like “Slow down, you might get into a fatal collision. The speed limit is 70 km/h” delivered in a forceful voice.

6 Use Case Simulation and Validation Figure 3 shows the use case by which our intelligent smartphone-based ADAS would be able to assist our ego vehicle. As shown, in road segment 1, there is a road limit sign board. By comparing the vehicle’s speed vs. road speed limit, we should be able to detect if the driver is over speeding or not. There is also a Stop sign, and we can detect if the vehicle brakes near the Stop sign or not. There is also an intersection wherein the driver could turn to left or to the right. In this case, we should be able to determine if the driver missed turning the direction indicator or not.

Road Segment 2

Road Segment 2

A

B

LeŌ direcƟon

Right direcƟon

fog

fog

Road Segment 3

car obstacle (not moving)

Road Segment 1 Road Segment 3

car obstacle (not moving)

Road Segment 4

Road Segment 4

Fig. 3. The case scenario for the cognition of driving context and driving assistance.

In road segment 2 on the right (direction B), there is a fog, and the visibility is poor. We should be able to figure out if the driver slows down or not. If he does not, over speeding infraction is noted. In road segment 2 on the left (direction A), there is a speed limit and a pedestrian crossing. Here, we can figure out if the driver brakes or over speeds. In road segment 3 on the right, speed limit, vehicle obstacle and pedestrian crossing are all present. Here, we should be able to figure out if over speeding or braking infractions are committed. In road segment 3 on the left, speed limit, fog and vehicle obstacle are all present. Similarly, we can determine if the driver commits over speeding or not braking near the obstacle. In road segment 4, there is not much obstacle except for the speed limit. Here, we should be able to see if the driver accelerates unnecessarily apart from determining if over speeding infraction is committed.

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Without CASA, the driver is left on his own to do as he pleases, including committing traffic infractions without consequences. With CASA, every infraction is merited with driver notification. Moreover, the driver is notified about incoming Stop sign, and danger such as poor visibility. As our intelligent ADAS determines the driver’s profile, the delivery of the notification messages will vary. As stated earlier, reckless driver must be forcefully notified of his infractions so as to avoid possible fatal collision. A moderate notification is sent to risky or very risky driver while a gentle notification is sent to prudent and cautious drivers.

7 Conclusion An intelligent ADAS is part of an intelligent vehicle. Here, an inexpensive driver assistance system (CASA) that promotes safe driving is presented. It determines driving context by fusing various parameters related to the context of the driver, the vehicle, and the environment. It contains rules that deduces the driving situation and its associated driving assistance. The assistance is implemented by sending signals to the actuators and/or the driver. For autonomous vehicle, all signals are executed by the concerned actuators. Notification or Alert messages are sent to the driver to inform of relevant driving information or to alert the driver that a dangerous situation exists, or an infraction has been made. In this paper, we presented a fuzzy logic-based mechanism to determine the profile of the driver. The driver’s profile determines how should these notification or alert messages are to be delivered.

References 1. Thalen, J.P.: ADAS for the Car of the Future, in Engineering Technology. University of Twente (2006) 2. Li, L., Wen, D., et al.: Cognitive cars: a new frontier for ADAS research. IEEE Trans. Intell. Transp. Syst. 13(1), 395–407 (2012) 3. Hina, M.D., Guan, H., et al.: CASA: an alternative smartphone-based ADAS. Int. J. Inf. Technol. Decis. Making 21(01), 273–313 (2022) 4. Hina, M.D., Guan, H., et al.: CASA: safe and green driving assistance system for real-time driving events. In: SAI Intelligent Systems Conference, IntelliSys 2016, London, UK (2016) 5. Groupe, P.: Car Easy Apps: PSA Peugeot Citroën’s Application programming interface (2014). https://www.youtube.com/watch?v=3cTsNeKZDTU 6. Groupe, P.: Car Easy Apps: Co-designing the connected car of the future (2016). https://www. groupe-psa.com/en/newsroom/automotive-innovation/car-easy-apps/ 7. Elmenreich, W.: Sensor Fusion in Time-Triggered Systems, p. 173. Vienna University of Technology, Vienna, Austria (2002) 8. Blasch, E., Kadar, I., et al.: Issues and challenges in situation assessment (level 2 fusion). J. Adv. Inf. Fus. 1(2), 122–139 (2006) 9. Julien, S., Maret, P.: Semantic agent model for SWRL rule-based agents. In: International Conference on Agents and Artificial Intelligence, ICAART 2010, Valencia, Spain. INSTICC Press (2010) 10. W3C. SWRL: A Semantic Web Rule Language Combining OWL and RuleML. https://www. w3.org/Submission/SWRL/

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11. Landragin, F.: Physical, semantic and pragmatic levels for multimodal fusion and fission. In: 7th International Workshop on Computational Semantics, pp. 346–350. Tilburg, The Netherlands (2007) 12. Costa, D., Duarte, C.: Adapting multimodal fission to user’s abilities. In: Stephanidis, C. (ed.) UAHCI 2011. LNCS, vol. 6765, pp. 347–356. Springer, Heidelberg (2011). https://doi.org/ 10.1007/978-3-642-21672-5_38 13. Hattori, H., Nakajima, Y., Ishida, T.: Learning from humans: agent modeling with individual human behaviors. IEEE Trans. Syst. Man Cybern. Part A Syst. Hum. 41(1), 1–9 (2011)

Selectivity: The Essence of Natural and Artificial Intelligence Yinsheng Zhang(B) Institute of Scientific and Technical Information of China, Beijing 100038, China [email protected]

Abstract. The paper summarizes definitions of (artificial) intelligence in three kinds of disciplines, which are (1) anthropology as well as relevant fields of biology, psychology and cognitive science on intelligence, (2) philosophy, and (3) artificial intelligence theories. It tries to generalize the definitions of intelligence in the three disciplines, giving universally formal models of (artificial) intelligence to represent adaptability upon environment proposed in (1), and rational mind proposed in (2), and Turing machines embodying general recursion functions proposed in (3). The core function of (artificial) intelligence is specified as selectivity which covers the essential functions over the three kinds of representations of (artificial) intelligence, and coheres the biological, logical and mechanical natures. In summary, it formally proposes that (artificial) intelligence is just the selectivity, which represents and implements (artificial) intentionality based on environmental knowledge. Keywords: Universal intelligence · General intelligence · Selectivity · Intentionality · Turing machine · AI models · Features of intelligence

1 Introduction Existing definitions of “artificial intelligence” prominently take two paradigms: first, regarding AI as emulating natural intelligence (NI), or second, as one beyond NI to some extents. Certainly, the two paradigms all need an exact definition of NI to lay the foundation for elaborating them. Although definitions of intelligence appear multifarious, according to the present study, they essentially have a certain consensus. The original study fields, anthropology, biology, psychology and cognitive science (hereafter “anthropological views on intelligence”, AVoI) have concluded a common understanding—with some variants, that intelligence is the abilities adapting environments. Even though, the early artificial intelligence theories on intelligence (hereafter, “AIToI”) seem not widely to accept this conclusion, for that key aspects of definitions in AIToI represent algorithms based on Turing machines, while AVoI mostly exhibit empirical descriptions of mind, which seem to be far from that abstract Turing machines. Later, with the evolution of AI, some “advanced” strands, like Strong AI, Hyper AI, Artificial Generalized Intelligence (AGI), AI Next, have been emerging. However, the emerging ones prefer describing upcoming © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 932–940, 2022. https://doi.org/10.1007/978-3-031-09173-5_107

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functions like human minds to specifying definitions of intelligence in terms of representations infused in both AIToI and AVoI styles. The case demonstrates a predicament in defining intelligence and AI. It requires confirming the essence of intelligence, extracting the characteristics of intelligence and AI, to compare them to obtain an integrated expression of intelligence as well as AI. AVoI propose that intelligence owns both biological and logical natures [1, p. 3]. The present study attempts to converge the three natures—besides the two, the mechanical nature should be added, so that interpretations of any two kinds of nature be commensurable. Namely, any one aspect among biological, logical and mechanical natures should be representing, and represented by, the other two, or be interpretations and grounds of the other two, as shown in Fig. 1. Correspondingly, the three disciplines are intended to play the roles commonly representing intelligence in a novel definition as shown in Fig. 2.

Biological nature

Logical nature

Anthropological “intelligence”

Selec-

Selectivity

tivity

Mechanical nature

Philosophical “intelligence”

AI Theoretical “intelligence”

Fig. 1. The goal of the present study: making the Fig. 2. The goal of the present study: three natures of intelligence commensurable. making intelligence commensurable in the three disciplines.

In the schemes driven from Fig. 1 and Fig. 2, there will be an intrinsic characteristics in intelligence, that is selectivity serving as the key function to be expounded and modeled. In detail, AVoI are explained in Sect. 2, which are followed by an analysis on the discrepancies between AVoI and AIoI in Sect. 3, between AVoI and PIoI in Sect. 4, and by a convergence of the three–AVoI, PIoI and AIoI in Sect. 5, finally, the conclusion will come in Sect. 6.

2 Anthropological Viewpoints on Intelligence Prominently owing to the research on human, further on all biological intelligence, there are some near agreements on what is intelligence, even though with divergent opinions. Piaget summaries all the possible 6 interpretations on intelligence in view of the points focusing on the relationship between the subjective and the environment. The classification is divided by the two original theories of development of biology: I. Darwin’s evolutionism and II. Lamarck’s mutationism, with subdivide by explaining adaptive variations of 1) external, 2) internal, and 3) interactive factors, respectively to the level I and II. Nevertheless, Piaget still claims there should be a commonly recognized definition of intelligence:

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[…] intelligence constitutes the state of equilibrium towards which tend all the successive adaptions of a sensori-motor and cognitive nature, as well as all assimilatory interactions between the organism and the environment [1, p. 11]. A similar viewpoint is taken as [2, 3]. What is intelligence? Every person has her or his own definition, and psychologists, too, disagree about in this question (e.g., Glazer 1993; Stermberg 1985). Most would include in their definitions of intelligence the ability to think abstractly and to learn readily from experience, but beyond these basics, there is little consensus [2]. Encyclopedia Wikipedia, as commonsense media, chooses an influential definition of intelligence which regards intelligence as interaction between the subject and the environment [3]. From “Mainstream Science on Intelligence” (1994), an opened statement in the Wall Street Journal signed by fifty-two researchers (out of 131 total invited to sign): A very general mental capability that, among other things, involves the ability to reason, plan, solve problems, think abstractly, comprehend complex ideas, learn quickly and learn from experience. It is not merely book learning, a narrow academic skill, or test-taking smarts. Rather, it reflects a broader and deeper capability for comprehending our surroundings—“catching on”, “making sense” of things, or “figuring out” what to do. [4], [5, pp. 37–90], [6], [7, p. 17], [8] and [9, pp. 352–353] parallel to [2, 3], and all of them roughly belong to Piaget’s definition of intelligence in [1].

3 The Gap Between AI Theories and Anthropological Views on Intelligence AIToI have been for nearly one century if taking Turing’s definition of intelligence into account. Fortunately, some summarize the development of various definitions. [10, pp. 4–5] lists definitions showing that many activities of a mind are collected as the essences such as decision making, thinking perceive reasoning etc. Where, there is not a consensus like [1] extracting adaption to environment as the essence of intelligence. In comparison to the definitions cited by Russell, some definitions in AVoI highlight adaptability upon environment. “Universal Intelligence” reconsiders intelligence as agents against environment, in the cases, machine intelligence was defined as Turing computations at minimum cost deciding a strategy on a space of acting environment [11]. The proponents of defining intelligence based on Turing models in the line of AVoI also can be taken, typically, as [12]. Therefore, AIToI needs formalizing an interface depicting Turing models in adaption referred as by AVoI.

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4 The Gap Between AI Theories and Philosophical Views on Intelligence In contrast to characterizing AI by symbolism, PVoI treat AI with huge disagreements. It is well known that an important disputation has emerged since Searle put forward the Chinese Room Argument (CRA) that computers could not really understand “Chinese”—a metaphor of natural languages and other human intelligent things, for that computers only processing syntax without semantics. [13]. The point is that the brain’s causal capability to produce intentionality cannot consist in its instantiating a computer program, since for any program you like it is possible for something to instantiate that program and still not have a mental state. Whatever it is that the brain does to produce intentionality, it cannot consist in instantiating a program since no program by itself is sufficient for intentionality [13]. Some [14] gave criticism, declaring that AI is capable of capturing semantics to understand real intelligent things. Similar citation also sees [15]. Against symbolism, the non-reasonable factors in the mind like some factors in intention, perception, emotion, etc. are predicated by the theories of “artificial general intelligence” as cited in [16]. By advanced artificial general intelligence, I mean AI systems that rival or surpass the human brain in complexity and speed, that can acquire, manipulate and reason with general knowledge, and that are usable in essentially any phase of industrial or military operations where a human intelligence would otherwise be needed. Such systems may be modeled on the human brain, but they do not necessarily have to be, and they do not have to be “conscious” or possess any other competence that is not strictly relevant to their application. What matters is that such systems can be used to replace human brains in tasks ranging from organizing and running a mine or a factory to piloting an airplane, analyzing intelligence data or planning a battle [16]. Against the things like intention, perception, emotion, etc., the non-reasonable factors in the mind were predicated by the theories of Artificial General Intelligence [17] (HLAGI) which is becoming more influential. It aims to achieve the goal of “humanlevel general intelligence” with the cognitive architecture that absorbs Piaget’s theory of personal cognitive development and Vygotsky’s social-cultural engagement. Moreover, qualia, a term declaring a kind of artificial sense by AI chips and other physical parts like sensors was created [18], which can feel pain, happy, etc. Similarly, self-consciousness was declared to be made with various minds functions by robot-makers in terms of Husserl’s phenomenology [19]. These AI trends go far beyond early AI in symbols processing, even depart from connectionism without symbols processing, to simulate physically continuous quantities. As the variant AI involves the complex mind as referred as by Searle in CRA, AIToI’s definitions on intelligence seem to more separate to PVoI.

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5 Convergence on Extraction and Formalization of Intelligence 5.1 AI Should not Wholly Emulate Human Minds In fact, not only AGI and HLAGI, but also PVoI such as Searle [13] and his opponent Boden [14, pp. 253–266], take simulating human minds as AI’s goal. This trend neglects a fact that in AVoI intelligence is a narrow field on minds. It is a common classification that there are different factors separating from the cognitive functions which traditional AI deems to be able to realize. These different factors in question contain the non-intelligence system, mainly referred as by psychologists, like instinctive factors such as emotions, feelings opposed and associated to the intelligent facilities [1, p. 6]. In this case, not all the efforts simulating human minds should be concluded in AI. Then, AGI, HLAGI and so on may develop their visions, but it might not be proper to nominate these efforts of emulating non-intelligence factors inner homeostasis like creating “pain” or “happy” under the term “AI”; maybe, the term “artificial mind” is more suitable. If we narrow AI on simulating or realizing specific fields of human minds, focusing on the parts of rationality such as logic functions, rather than non-intelligence factors, the definition of AI would be more feasible. 5.2 AI Can Essentially and Functionally Realize Anthropomorphic and Philosophical “Intelligence” to Help Unifying the Triplet Suppose we avoid the non-intelligence factors in the human mind, the residence left, in the name of “intelligence”, should cover adaptability as proposed by AVoI. Further we suppose the scheme of adaptability can entirely be represented by logic, then adaptability specified in AVoI should also be represented as rationality, which appeals to logic, in PVoI, further as AI if AI can be interpreted by program made of by logic expressions. However, there are still mind phenomena put forward by PVoI, which should be considered as adaptability, but not be recognized by PVoI and AI. In CRA, intentionality is just this kind of mind phenomena. Searle insists on that AI cannot obtain intentionality, which is the boundary between NI and AI although AI can do logic operations that human conducts. So, solving the unsolved problem of if intention is computable (so belonging to AI) is the last bulwark at present to confirm that the rationality represented by logic is realized by AI in principle. Completing the solution, there would be common expressions of AVoI, PVoI and AIToI with adaptability-advocating in logic representations. As analyzed by Dennett, intention is classified into three kinds: beliefs, desires and behaviour [20, pp. 298–320]. The first two ones—beliefs and desires—characterized by biology, seem to reject AI simulating it. However, from the view of functionalism, the distinctions between biological and electronic quality are not essential if they function equivalently. Note that the definitions of intelligence for AVoI and AIoI all are of functionalism, so is PVoI if it takes that the continuous experience like feelings, emotions etc. critically relying on biological features is non-intelligence. Another architecture of intention was analyzed by Anscombe in PVoI. Anscombe [21] believes that both people and animals, but not machines, own intentions. In

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Anscombe’s view, intention certainly belongs to the spiritual world which can be confirmed by its representation and related actions “intentional action” represented by the actor’s answer when asking “Why do you do so?” although sometimes the answer might represent “involuntary”; but, if the “involuntary” answer represents the thinking for the factors “known without observation”, then it is still viewed as an intentional representation for it is in a structure of knowledge. A kind of mental causes—forward-looking motivates is classified into pre-intentional factors such as admirement, curiosity, hostility, friendship, love for truth, despair and so on, which seems to be more instinct than intention. Some motivates are classified into motivate-in-general. The architecture of the intention in views of Anscombe is illustrated as in Fig. 3.

The known without observa on TThe he mental mental cause The involuntary Backwardlooking mo ves Mo ve-in-general Inten on Fig. 3. Intention in view of Anscombe.

Thus, Anscombe confirms that all the intention even more instinct factors (“nonintelligence”) in the mind are infused in a cognitive process, which must be represented in a process of cognition. Figure 3 illustrates that intention wholly can be regarded as nested in a knowledge system, which represents knowledge using limited symbols, to depict the knowledge owner relating to the environment. The system will be obtained by the process (i), (ii) and (iii). (i) Abstracting (describing) a historical or environmental event to be a reason R. (ii) Applying the existing knowledge to genera a knowledge R→G, where G denotes the goal, “→”, approaching. (iii) Choosing a reason pattern R from the facing world for input, matching R and R in similarity. If yes, substitutes R for R , and applies the intention knowledge in (ii), achieving an adaptive evolution or mutation from (R , R → G ) to G, i.e. (R , R → G ) → G, where, G is the goal reflecting the real world similar with G, as an output (virtual realization) of the intention on the facing world. In the process, (i) and (ii) constitute intention; (iii) applies and updates the intention.

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Thus, intention can be defined as a 3-tuple as formulated in (1). Intention = (R, G, K)

(1)

R: Reason abstracted as pattern, from E. G: Goal as virtual transformation from R. K: Knowledge of making R to G; K: R → G. Obviously, (i), (ii) and (iii) constructs an information system, which runs relying on some necessary conditions such as information memory, computation etc., to carry out (2) recognition, (3) knowledge representation and acquisition, (4-1) knowledge application and (4-2) knowledge updating. M (E) = R

(2)

K :R→G

(3)

R = M (I ) ≈ M (E)

(4-1)

    R , R → G → G

(4-2)

where, M denotes Model; I: Input; E: Event in history or in environment. The process (2) to (4-2) can be regarded as “selection” which certainly meets the semantics of this word in natural languages, namely, electing R among E, electing G upon R, and electing R’ in the similar objects, interpreting the root of “intelligence” (elli-, meaning “election”, i.e. “selection”) to obtain the argument from linguistics. In the history, AVoI such as Piaget and PVoI such as Anscombe [21, p. 24] consider intelligence as selectivity. [22] treats selection as higher-level of learning or adaption to environment. (2) to (4-2) satisfying the schemes of selection evolution (evolution) in learning proposed in [22]. Therefore, (i) to (iii) with (1) have realized representing adaptability described in AVoI and representing rationality in PVoI. Next, we shall see that they also represent computability in AIoI. To complete the steps (2) to (4.2), the conditions (a) to (e) should be met. (a) Having an information system (especially, (a1) there is a virtual system diverting the physically real objects to be information objects by representation, i.e. creating correspondence between objects in the virtual system and objects in objective world; (a2) the information system enables the itself saving all the arguments and intermediate data, and (a3) with Input and Output). (b) Freedom to pick out an object as a scheme (in the information system even in the real world), which enable (2) to (4-2) possible. (c) Recognition and Representation (namely abstraction, converting data into information), like (2) and (4-1). (d) Mapping (namely, making the correspondence which, e.g., associates a symbol to a pattern as depicted in (2), or links a representation to a real object in the outer as

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(4-1); Or creating a conditional to imply a reaction against a specific environment in the system even acting on the real world) as in (3) and (4-2). (e) Recursion (including primitive recursion like (2) and (3), and (general) recursion like (4-1 and 4-2) that carries out an operational result as an intermedia data into a variable of operand in a new or a restarted operation in the system even acting on the real world). It is easy to be seen that the conditions (a) to (e) constitute Turing computations. Among which, (a) to (c) are the preparing terms, and (d) can be considered as the transition function in a Turing machine. (e) is the mathematical representation of that Turing machine, according to the proof by Minsky etc. [23, pp. 169–198] that recursion is the mathematical facet of Turing machines, where, recursion was standardized by Gödel [24, pp. 144–195]. In other words, (e) guarantees that all the selections based on logic operations, are Turing-computable, and mathematically represented by recursion functions. As (a) to (e) are AI models, the solution of the most troubling problem up to present for acknowledging AI matching the human mind, namely for formalizing PVoI and AVoI expressions corresponding to AIToI, has been regarded as solved.

6 Conclusion As AVoI can be formalized as stated in (2), (3), (4-1) and (4-2) which are Turingcomputable, which displays the interface between AVoI and AIToI. Meanwhile, (2), (3), (4-1) and (4-2) show a landscape of (1): intention, the linkage of PVoI and AIToI, confirming AVoI, PVoI and AIToI are commensurable. This to say, intelligence is adaptability on environment, essentially the rationality in the logical mind, also Turing computability; there is not essential difference between AI and NI. The core function for all the three natures can be refined as selectivity. The research in the future should focus modeling AVoI and PVoI in view of AIVoI, in addition, interpreting and realizing AIVoI by AVoI and PVoI. Acknowledgement. Some results in the paper are cited from the author’s doctoral thesis.The author is full of gratitude to the tuition of Prof. LIU, Dachun.

References 1. Piaget, J.: The Psychology of Intelligence, 5th edn. Routledge & Kegan Paul Ltd., London (1967) 2. Baron, R. A.: Psychology, p. 417, 3rd edn. Allyn & Bacon, Needham Heights (1989) 3. Gottfredson, L. S.: Mainstream science on intelligence: an editorial with 52 signatories, history, and bibliography. The Wall Street J., 13 December 1997 4. “Intelligence” from Wikipedia, the free encyclopedia. https://en.wikipedia.org/wiki/Intell igence. Accessed 31 Dec 2018 5. Binet, A.: New methods for the diagnosis of the intellectual level of subnormals, Translation by Binet-Simon Scale. In: Kite, E.S. (eds.) The Development of Intelligence in Children, 1st edn. Williams & Wilkins, Baltimore (1916)

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6. Wechsler, D.: The Measurement of Adult Intelligence, 3rd edn. Williams & Wilkins, Baltimore (1944) 7. Fagan, B.M.: People of the Earth: An Introduction to World Prehistory, 14th edn. Pearson Prentice Hall, NJ (2004) 8. Sternberg, R.J.: Toward a triarchic theory of human intelligence. Behav. Brain Sci. 7(2), 269–287 (1984) 9. Nairne, J.S.: Psychology: The Adaptive Mind, 1st edn. Brooks/Coke Publishing Company, Pacific Grove (1996) 10. Russell, S.: Norvig, P: Artificial Intelligence–A modern Approach, 2nd edn. Pearson Education & People’s Post & Telecommunications Press, Beijing (2002) 11. Legg, S., Hutter, M.: Universal intelligence: a definition of machine intelligence. Mind. Mach. 17, 391–444 (2007) 12. Proudfoot, D.: Anthropomorphism and AI: Turing’s much misunderstood imitation game. Artif. Intell. 175, 950–957 (2011) 13. Searle, J.R.: Mind, Brain and Program. Behav. Brain Sci. 3(3), 417–424 (1980) 14. Boden, M.A.: Escaping from the Chinese room, 1st edn. In: Heil, J. (ed.) Philosophy of Mind. Oxford University Press, Oxford (2004) 15. Wakefield, J.C.: The Chinese room argument: reconsidered: essentialism. Indeterminacy String AI Mind Mach. 13, 285–319 (2003) 16. Gubrud, M.: Nanotechnology and international security. In: 5th Foresight Conference on Molecular Nanotechnology (1997). https://foresight.org/Conferences/MNT05/Papers/Gub rud/ 17. Adams, S.A., et al.: Mapping the landscape of human-level artificial general intelligence. AI Mag. 33(1), 25–42 (2012) 18. Haikonen, P.O.: Consciousness and Robot Sentience, 1st edn. World Scientific Publishing Co. Pte. Ltd., New Jersey (2012) 19. Takeno, J.: Creation of a Conscious Robot. Mirror Image Cognition and Self-Awareness, 1st edn. Pan Stanford Publishing, Danvers (2013) 20. Dennett, D.: Three kinds of intentional psychology, 1st edn. In: Heil, J. (eds.) Philosophy of Mind. Oxford University Press, Oxford (2004) 21. Anscombe, G.E.M.: Intention, 1st edn. Harvard University Press, Cambridge (2000) 22. Arnold, S., Suzuki, R., Arita, T.: Selection for representation in higher-order adaptation. Mind. Mach. 25(1), 73–95 (2015) 23. Minsky, M.L.: Computation/Finite and Infinite Machines, 1st edn. Prentice Hall. Inc., Englewood Cliffs (1967) 24. Gödel, K.: Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. In: Feferman, S. (ed.) Kurt Gödel: Collected Works, vol. 1. Oxford University Press, Oxford (1986)

An Intelligent Understanding of the Post-COVID-19 Uncertainty: Provided Guidelines and Strategies for Resilient Supply Chain Networks Fariba Farid1

and Yaser Donyatalab2(B)

1 Department of Management, University of Nabi Akram, Tabriz, Iran 2 Industrial Engineering Department, University of Moghadas Ardabili, Ardabil, Iran

[email protected]

Abstract. COVID-19 outbreak has damaged the global supply chains, it has affected both goods and service provider supply chains unprecedentedly. Post COVID-19 era is full of uncertainty based on many changes that have happened. Some new parameters are introduced because of the outbreak and bring out new circumstances. These new challenges consequently will increase the ambiguity around the supply chain networks. This study is designed to investigate and evaluate the ambiguity of supply chain networks in the post-COVID-19 era, to strengthen and increase the resilience of SCN systems. The challenges are clustered into different patterns and for each pattern, many strategy approaches are introduced in the literature part. But not only those are not useful without understanding challenges specifically for each SCN but also, it is not possible to apply all of those strategy solutions. This study aims to first understand the challenges and effects of each disruption pattern specifically for each SCN and then select in a more detailed way the most appropriate strategy. To catch the goal of evaluating the resilience of supply chain networks, some significant challenges are identified based on the literature part. An algorithm consists of three stages, first define the uncertainty, second pattern recognition of disruption patterns, and third strategy selection to increase SCN resilience is proposed based IVq-ROFSs Hamacher Aggregation operators and Dice similarity measures. An illustrative example of the SCN resilience problem is evaluated by the proposed algorithm under the Interval Valued q-Rung Ortho Pair Fuzzy structure to show the applicability and reliability of the proposed method. Finally, this paper provides guidelines and strategies for increasing the resilience of supply chain networks in the post-COVID-19 outbreak. Keywords: Supply Chain Network (SCN) · Resilient in supply chain · Post-COVID-19 era · IVq-ROFSs hamacher aggregation · Dice similarity measure

1 Introduction and Literature Background The unprecedented crisis of SARS-CoV2 during the last couple of years is severely engulfed business activities all over the world [1], therefore it has seriously affected © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 941–956, 2022. https://doi.org/10.1007/978-3-031-09173-5_108

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supply chain management (SCM) [2]. The COVID-19 pandemic spread all over the world in a short time after the initial case detection [3], so it is highly challenging for supply chains and there remained the least chance for strengthening those. Many researchers all over the world studied different supply chain problems under the effect of coronavirus [4–6]. The COVID-19 outbreak affected different aspects of the SCM including the demand, transportation, supply, and storage also have diverse impacts on different sectors [7]. For example in some sectors, it caused a decrease in demand, and in some other parts, there was the steepest incline in requests, or in transportation, some aspects of logistic process faced hardship and caused unacceptable delays while in others it eased the delivery process. So, the conclusive point is the uncertainty that the COVID19 pandemic brings out and caused many out-of-control impacts on the Supply Chain Networks (SCN). Based on the United Nations Sustainable Development Goals (SDGs), the COVID19 pandemic seriously delayed achieving some of the defined goals [8]. However, the virus makes it difficult to conduct the necessities to catch the goals, but at the same time, it highlighted the significance of progress and being more resilient for us, the lesson behind the COVID-19 pandemic. So, we learned that there should be a big difference between pre-COVID and post-COVID viewpoints over the SCN. The main goal of this manuscript is to evaluate conditions before and during the epidemic to have a comprehensive analysis of the circumstance and then be capable of suggesting some guidelines and appropriate strategies for having a more resilient SCN in the post-COVID era. The SCN by itself carries many vague parameters to measure, but the incidence of COVID-19 disturbed many in stable conditions and therefore caused an immense increase in uncertainty of the problem. Uncertainty of the SCN problem under the COVID-19 epidemic makes it essential to first determine the challenges [9]. So, it is required to study the facing challenges of SCN due to the outbreak era and many researchers investigated it [10], and interestingly noticed low levels of resilience in our SCN in front of the challenges [11, 12]. Different authors investigated the barriers that SCN faced during the COVID-19 and categorized them [13], the identified challenges in four main categories are enlisted in Table 2. In this paper, we categorized the challenges based on their similarities in four main classes. Four main categories are clusters of sub-level challenges and rising strategies to mitigate such challenges definitely will cause more resilience of SCN [9]. The four main levels are related to the Upstream Network (UN), Downstream Network (DN), Management Network (MN), and Transportation Network (TN). The Upstream Network (UN) is including all factors related to supply flows of SCN, and the Downstream Network (DN) is clarifying the factors related to the demand side of SCN. Management Network (MN) is directly pointed to challenges in the areas of planning, and managerial decisions, and Transportation Network (TN) considers the issues on the delivery, and transportation side. The nature of the problem is carrying different possibilities from upstream and downstream sides. The vagueness of the problems is not limited to the supply and demand sides and many uncertainties have come from other managerial and transportation issues.

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Zadeh, in 1965 [14], introduced fuzzy logic to handle the uncertainty of realworld cases. Many different generations of fuzzy sets are introduced by different researchers. The Intuitionistic Fuzzy Sets (IFSs) [15], The Hesitant Fuzzy Sets (HFSs) [16], Pythagorean Fuzzy Sets (PyFSs) [17], Picture Fuzzy Sets (PFSs) [18] are next developed generations of fuzzy sets, which are also characterized based on membership, non-membership and hesitant values between 0 and 1. Then in 2017, the concept of ortho pair logic and the novel q-Rung Ortho Pair Fuzzy Sets (q-ROFS) are introduced in [19]. To increase the capability of q-ROFSs for demonstrating the uncertainties the possibility degrees are defined by the interval [0,1] and it is called Interval Valued q-Rung Otho Pair Fuzzy Sets (IVq-ROFSs) in [20]. IVq-ROFSs have an outstanding ability and applied in many research fields and attracted many researchers, some similarity measures are introduced in the q-ROFSs environment in [21, 22] and in [23] proposed Hamacher aggregation operators for IVq-ROFSs together with their applications in the decision-making process is illustrated. In traditional definitions for measuring SCN, the most important factors pointed as cost, quality, delivery, and manufacturing parameters control [24]. In recent studies, because of the impact of COVID-19, the resilient factor is considered the most significant measurement of an SCN. The resilience could bring a quick recovery ability to an SCN in facing disastrous events [25]. In this paper, we aim to evaluate the SCN based on the clusters of challenges to find out the patterns of disruption in each case. Then disruption patterns of each SCN will be compared with different strategies from the strategy pool. Afterward, we will be able to reach the most effective strategy or set of strategies that will bring rightfully the needed resilience for our SCN system. For this goal, we defined the SCN challenges and designed a q-ROFSs framework for being able to consider such a huge amount of uncertainties, and then we used some Hamacher aggregation operators for combining part of the problem to determine the patterns based on the four categories. Then compare each patern with the appropriate bounch of strategies and for that we evaluate the similarity measures to reach the most effective strategy or set of strategies for increasing the resilience of our SCN. This paper aims to deliver a clear introduction to the SCN, challenges, and patterns of SCN disruptions, strategies proposed for the post-COVID environment, and the approach together with a detailed literature review. In this manuscript, we tried to define a robust relationship between the derived points from the literature part and the proposed method in this study. Motivated by the above discussion, we first define the problem in the IVqROFSs environment and then proposed an algorithm based on Hamacher Aggregation and IVq-ROFSs and Dice similarity measures to evaluate the problem. The rest of the chapter is designed as follows. In Sect. 2, some concepts of IVq-ROFSs are defined mathematically then the algorithm is introduced and discussed step by step. Section 3 refers to the evaluation, results, and discussion around the defined SCN problem is shown in detail finally, in Sect. 4 all material is summarized and the paper is concluded.

2 Methodology Interval-Valued q-Rong Ortho Pair Fuzzy Sets (IVq-ROFSs):

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Definition 1. Let X be a nonempty fixed set, then Interval Valued q-Rung Orthopair Fuzzy Sets (IVq-RDHFS) A˜ on X is defined as:       L U A˜ = x, μLA (x), μU A (x) , ϑA (x), ϑA (x) |x ∈ X   L U where μLA (x), μU A (x) and ϑA (x), ϑA (x) denote the membership degree and nonmembership degree of x ∈ X satisfies the following condition: for respectively,  L which  U (x) ∈ [0, 1] and μU (x)q +ϑ U (x)q ≤ (x) ∈ [0, 1], ϑ (x), ϑ every x ∈ X : μLA (x), μU A A A A A 1, (q ≥ 1), and,   πAL (x), π U (x) =

 q  U q

 q  q (x) − ϑA (x) , q 1 − μLA (x) − ϑAL (x) ] (1) [ q 1 − μU A Denotes the hesitancy degree  of x ∈ X .  L For convenience, we call μLA (x), μU (x) , ϑA (x), ϑAU (x) an IVq-ROFN, which is

 L U  L U  A denoted by a˜ = μa , μa , ϑa , ϑa .

    L U 

 Definition 2. Let A˜ = μL , μU , ϑ L , ϑ U , A˜ 1 = μL1 , μU and A˜ 2 = 1 , ϑ1 , ϑ1

 L U  L U  μ2 , μ2 , ϑ2 , ϑ2 be three IVq-ROFNs, and λ be a positive real number, then the operational laws are defined as follows [20]:   q  q  q  q  q1 μL1 + μL2 − μL1 A˜ 1 ⊕ A˜ 2 = μL2 , 

μU 1

q

+



μU 2

 q  q  q  q1   U U μ2 − μ1 , ϑ1L ϑ2L , ϑ1U ϑ2U

(2)

   q  q  q  q  q1  L L U U ϑ1L + ϑ2L − ϑ1L A˜ 1 ⊗ A˜ 2 = μ1 μ2 , μ1 μ2 , ϑ2L ,  q  q  q  q  q1 ϑ2L ϑ1L + ϑ2L − ϑ1L A˜ =



 (3)

 q λ  q1     q λ  q1  λ  λ  L U ,λ > 0 1− 1−μ , 1− 1− μ , ϑL , ϑU

(4)   1 1         q λ  q    q λ  q λ λ A˜ λ = μL , μU , 1 − 1 − ϑL , 1 − 1 − ϑU ,λ > 0 (5) Furthermore, the score and accuracy function of a q-ROFNs are defined as follows:

An Intelligent Understanding of the Post-COVID-19 Uncertainty

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 Definition 3. Let A˜ = μL , μU , ϑ L , ϑ U be an IVq-ROFN, then the score function ˜ and the accuracy function H (A) ˜ of A˜ are defined as follows [20]: S(A)  q  q  q  q  1 ˜ ∈ [0, 1] 1 + μLA − ϑAL + 1 + μU , S(A) − ϑAU A 4  q  q  q  q  ˜ = 1 μL + μU + ϑ L + ϑ U ˜ ∈ [0, 1] H (A) , H (A) A A A A 2

˜ = S(A)

(6) (7)

Then based on the score and the accuracy functions could compare IVq-ROFNs as follows:     If S A˜ 1 > S A˜ 2 then A˜ 1 > A˜ 2 ;         If S A˜ 1 = S A˜ 2 and H A˜ 1 > H A˜ 2 , then A˜ 1 > A˜ 2 ;         If S A˜ 1 = S A˜ 2 and H A˜ 1 = H A˜ 2 , then A˜ 1 = A˜ 2 . IVq-ROFSs Hamacher Aggregation Operators: In the following part, we will first introduce the novel concept of Hamacher Aggregation operators for IV-qROFSs which are introduced in [23] and discussed in detail.     ; ∀i = 1, 2, . . . n Definition 4. Let A˜ q (xi ) = μL˜ (xi ), μU˜ (xi ) , ϑ L˜ (xi ), ϑ U (x ) i A Aq A A˜ q q  q  and B˜ q (xi ) = μL˜ (xi ), μU˜ (xi ) , ϑ L˜ (xi ), ϑ U ˜ (xi ) ; ∀i = 1, 2, . . . n be two Interval Bq

Bq

Bq

Bq

Valued q-Rung Ortho Pair Fuzzy Numbers (IVq-ROFNs) which are defined on universe discourse X and  xi ∈ X , which convenience will be rep for  more computation  resented as A˜ q (xi ) = aA˜ (xi ), bA˜ (xi ) , cA˜ (xi ), dA˜ (xi ) q ; ∀i = 1, 2, . . . n and B˜ q (xi ) =

   aB˜ (xi ), bB˜ (xi ) , cB˜ (xi ), dB˜ (xi ) q ; ∀i = 1, 2, . . . n and q ≥ 1, then Hamacher addition, multiplication, scalar multiplication, and scalar power operations will be as follows: A˜ q (xi ) ⊕Hλ B˜ q (xi ) = ⎡ 1 ⎤ q q q q q q a ˜ (xi )+a ˜ (xi )−a ˜ (xi )a ˜ (xi )−(1−λ)a ˜ (xi )a ˜ (xi ) q B B B A A A ,⎥ ⎢ q q 1−(1−λ)a ˜ (xi )a ˜ (xi ) ⎥ ⎢ B A ⎢ q 1 ⎥,  q q q q q ⎦ ⎣ b ˜ (xi )+b ˜ (xi )−b ˜ (xi )b ˜ (xi )−(1−λ)b ˜ (xi )b ˜ (xi ) A

B

⎡⎛

A

B q A

q B

1−(1−λ)b ˜ (xi )b ˜ (xi )

A

q

B

⎞1 ⎤

q q q c ˜ (xi )c ˜ (xi ) ⎢ ⎥ B A ⎢⎝   ⎠ ,⎥ ⎢ ⎥ q q q q ⎢ λ + (1 − λ) cA˜ (xi ) + cB˜ (xi ) − cA˜ (xi )cB˜ (xi ) ⎥ ⎢⎛ ⎞1 ⎥ ⎢ ⎥ q⎥ q q ⎢ d ˜ (xi )d ˜ (xi ) ⎢⎝ ⎥ B A  ⎠ ⎦ ⎣ q q q q λ + (1 − λ) d ˜ (xi ) + d ˜ (xi ) − d ˜ (xi )d ˜ (xi ) B B A A

A˜ q (xi ) ⊗Hλ B˜ q (xi ) =

(8)

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$1 ⎤ q   ,⎥ q q q q ⎥ λ+(1−λ) a ˜ (xi )+a ˜ (xi )−a ˜ (xi )a ˜ (xi ) ⎥ B B A A , 1 $ ⎥ # q ⎥ q q b ˜ (xi )b ˜ (xi ) ⎦ B A  

⎡# ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡#

q A

q B

a ˜ (xi )a ˜ (xi )

q A

q B

q A

q B

λ+(1−λ) b ˜ (xi )+b ˜ (xi )−b ˜ (xi )b ˜ (xi )

q A

q B

q A

q B

q A

q B

c ˜ (xi ) + c ˜ (xi ) − c ˜ (xi )c ˜ (xi ) − (1 − λ)c ˜ (xi )c ˜ (xi )

$ q1 ⎤

(9)

⎢ ,⎥ q q ⎢ ⎥ 1 − (1 − λ)c ˜ (xi )c ˜ (xi ) ⎢ ⎥ B A ⎢# q 1⎥ ⎢ d (x ) + d q (x ) − d q (x )d q (x ) − (1 − λ)d q (x )d q (x ) $ q ⎥ i B˜ i i B˜ i ⎣ A˜ i ⎦ B˜ i A˜ A˜ q q 1 − (1 − λ)d ˜ (xi )d ˜ (xi ) B

A

α ⊗Hλ A˜ q (xi ) = ⎡⎛ ⎞1 ⎤  α  α q q q 1 − (1 − λ)a ˜ (xi ) − 1 − a ˜ (xi ) ⎢⎜ ⎥ ⎟ A A ⎢ ⎝  α α ⎠ ,⎥ ⎢ ⎥ q q ⎢ ⎥ 1 − (1 − λ)a ˜ (xi ) − (1 − λ) 1 − a ˜ (xi ) ⎢ ⎥ A A , ⎢⎛ 1 ⎞ ⎥  α  α ⎢ q ⎥ q q ⎢ ⎥ 1 − (1 − λ)b ˜ (xi ) − 1 − b ˜ (xi ) ⎢⎜ ⎟ ⎥ A A ⎣ ⎝  α α ⎠ ⎦ q q 1 − (1 − λ)b ˜ (xi ) − (1 − λ) 1 − b ˜ (xi ) A A  ⎡⎛ ⎞1 ⎤  α q q λ c ˜ (xi ) ⎢⎜ ⎥ ⎟ A ⎢ ⎝  α α ⎠ ,⎥ ⎢ ⎥ q q ⎢ ⎥ 1 − (1 − λ)c ˜ (xi ) − (1 − λ) c ˜ (xi ) ⎢ ⎥ A A ⎢⎛ 1 ⎞ ⎥  α ⎢ q ⎥ q ⎢ ⎥ λ d ˜ (xi ) ⎢⎜ ⎟ ⎥ A ⎣ ⎝ α α ⎠ ⎦  q q 1 − (1 − λ)d ˜ (xi ) − (1 − λ) d ˜ (xi ) A A   A˜ q (xi ) ∧Hλ α = ⎡# $1 ⎤   q

λ a (x )

α

(10)

q

i A˜ ⎢  ⎥ ⎢ 1−(1−λ)aq (xi )α −(1−λ)aq (xi )α , ⎥ ⎢ ⎥ A˜ A˜ , ⎢# $1 ⎥  α ⎢ q q ⎥ λ b ˜ (xi ) ⎣ ⎦ A

 α α  q q 1−(1−λ)b ˜ (xi ) −(1−λ) b ˜ (xi ) A A $1 ⎤  α  α q q q 1−(1−λ)c ˜ (xi ) − 1−c ˜ (xi ) A A ⎢  ⎥   ⎢ 1−(1−λ)cq (xi ) α −(1−λ) 1−cq (xi ) α , ⎥ ⎢ ⎥ A˜ A˜ ⎢#  $1 ⎥ α  α ⎢ q q q ⎥ 1−(1−λ)d ˜ (xi ) − 1−d ˜ (xi ) ⎣ ⎦ A  A α  α q q 1−(1−λ)d ˜ (xi ) −(1−λ) 1−d ˜ (xi )

⎡#

A

where λ ∈ (0, ∞) and α > 0 are crisp numbers.

A

(11)

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The studied aggregation operators in this article are Interval Valued q-Rung  Orthopair Fuzzy Sets Hamacher Weighted Arithmetic Mean IVq − HWAMHγ and Interval Valued q-Rung Orthopair Fuzzy Sets Hamacher Weighted Geometric Mean  IVq − HWGMHγ .

   Definition 5. Assume A˜ qi = aA˜ (xi ), bA˜ (xi ) , cA˜ (xi ), dA˜ (xi ) q ; ∀i = 1, 2, . . . n be a collection of IVq-ROFNs with corresponding aggregation weight vector wi = ' (w1 , w2 , . . . , wn ) where wi ∈ [0, 1] and ni=1 wi = 1 with the power of q > 0 Hamacherity coefficient λ ∈ (0, ∞), then IVq − HWAM Hλ and IVq − HWGMHλ are a mapping function IVq − HWAMHλ : [0, 1]n , [0, 1]n → [[0, 1], [0, 1]] and defined in Eqs. 12 and 13, respectively.   IVq − HWAMHλ A˜ q (xi ) =   , μLIVq−HWAMH , μU IVq−HWAMHU λ  λ = L U ϑIVq−HWAM , ϑIVq−HWAM λ Hλ ⎡⎛ ⎞1 ⎤  wi (  wi (n q q q n − i=1 1 − a ˜ (xi ) ⎢⎜ ⎥ i=1 1 − (1 − λ)aA˜ (xi ) ⎟ A ⎢⎝ wi wi ⎠ ,⎥ ⎢ (n  ⎥ (n  q q ⎢ ⎥ − (1 − λ) i=1 1 − a ˜ (xi ) i=1 1 − (1 − λ)aA˜ (xi ) ⎢ ⎥ A ⎢⎛ ⎥, 1 ⎞ wi (  wi ⎢ (n  q ⎥ q q n ⎢ ⎥ − i=1 1 − b ˜ (xi ) i=1 1 − (1 − λ)bA˜ (xi ) ⎢⎜ ⎟ ⎥ A ⎣ ⎝(  ⎦ wi   ⎠ wi (n q q n 1 − (1 − λ)b 1 − b − (1 − λ) (x ) (x ) i i i=1 i=1 A˜ A˜ ⎡⎛ (12) ⎞1 ⎤ wi (n  q q λ i=1 c ˜ (xi ) ⎢⎜ ⎟ ⎥ A ⎢⎝  wi wi ⎠ ,⎥ ⎢ (n ⎥ (n  q q ⎢ ⎥ − (1 − λ) i=1 c ˜ (xi ) i=1 1 − (1 − λ)cA˜ (xi ) ⎢ ⎥ A ⎢⎛ ⎥ 1 ⎞ wi ⎢ (n  q q ⎥ ⎢ ⎥ λ i=1 d ˜ (xi ) ⎢⎜ ⎟ ⎥ A ⎣ ⎝(  ⎦  wi  ⎠ wi (n q q n 1 − (1 − λ)d d − (1 − λ) (x ) (x ) i i i=1 i=1 A˜ A˜   IVq − HWGMHλ A˜ q (xi ) =   L U μIVq−HWGMH , μIVq−HWGM U , λ H = λ  L U ϑIVq−HWGMH , ϑIVq−HWGMλ λ

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⎡⎛

⎞1 ⎤  wi q q λ i=1 a ˜ (xi ) ⎢⎜ ⎥ ⎟ A ⎢⎝  wi wi ⎠ ,⎥ ⎢ (n  ⎥ (n  q q ⎢ ⎥ − (1 − λ) i=1 a ˜ (xi ) i=1 1 − (1 − λ) 1 − aA˜ (xi ) ⎢ ⎥ A , ⎢⎛ 1 ⎞ ⎥ wi ⎢ (n  q q ⎥ ⎢ ⎥ λ i=1 a ˜ (xi ) ⎢⎜ ⎟ ⎥ A ⎣ ⎝(   wi wi ⎠ ⎦ (n  q q n − (1 − λ) i=1 b ˜ (xi ) i=1 1 − (1 − λ) 1 − bA˜ (xi ) A ⎡⎛ ⎤    wi ⎞ q1 w (n ( i q q n − i=1 1 − c ˜ (xi ) ⎢⎜ ⎥ i=1 1 − (1 − λ)cA˜ (xi ) ⎟ A ⎢⎝ ⎥   wi ⎠ , w ⎢ (n ⎥ (n  q i q ⎢ ⎥ − (1 − λ) i=1 c ˜ (xi ) i=1 1 − (1 − λ)cA˜ (xi ) ⎢ ⎥ A ⎢⎛ 1 ⎞ ⎥ wi (  wi ⎢ (n  q⎥ q q n ⎢ ⎥ − i=1 1 − d ˜ (xi ) i=1 1 − (1 − λ)dA˜ (xi ) ⎢⎜ ⎟ ⎥ A ⎣ ⎝(  ⎦  wi  ⎠ wi (n q q n 1 − (1 − λ)d 1 − d − (1 − λ) (x ) (x ) i i i=1 i=1 ˜ ˜ (n

A

(13)

A

Weighted Dice (Sorensen) Similarity Measure for IVq-Rung Orthopair Fuzzy Sets:













Definition 6. Let A˜ qi = aA˜ (xi ), bA˜ (xi ) , cA˜ (xi ), dA˜ (xi ) q and B˜ qi a(xi ), bB˜ (xi ) , cB˜ (xi ), dB˜ (xi ) q ; ∀i = 1, 2, . . . n be two groups of IVq-ROFNs which are defined on universe discourse X , and τi = ' (τ1 , τ2 , . . . , τn ) be the weight vector, which τi ∈ [0, 1] and ni=1 τi = 1. The weighted Dice similarity measure between IVq-ROFSs A˜ qi and B˜ qi is proposed as follows:   )n WDSq A˜ qi , B˜ qi = τ i=1 i       q q q q q q q q aA (xi ) + bA (xi ) aB (xi ) + bB (xi ) + cA (xi ) + dA (xi ) cB (xi ) + dB (xi )         2q 2q 2q 2q 2q 2q 2q 2q aA (xi ) + bA (xi ) + cA (xi ) + dA (xi ) + aB (xi ) + bB (xi ) + cB (xi ) + dB (xi )

(14)

The weighted Dice similarity measure between q-ROFSs A˜ q and B˜ q also satisfies the following properties:   (1) 0 ≤ WDSq A˜ qi , B˜ qi ≤ 1     (2) WDSq A˜ qi , B˜ qi = WDSq B˜ q , A˜ q    (3) WDSq A˜ qi , B˜ qi = 1 if A˜ qi = B˜ qi → aA˜ (xi ), bA˜ (xi ) =    aB˜ (xi ), bB˜ (xi ) and cA˜ (xi ), dA˜ (xi ) = cB˜ (xi ), dB˜ (xi ) .  Remark 1. If the weight vector are equal amount like that τi = 1n , 1n , . . . , 1n , the     weighted Dice similarity measure WDSq A˜ qi , B˜ qi will reduce to DSq A˜ qi , B˜ qi . Proposed Disruption Pattern Recognition and Resilient Strategy Suggestion Algorithm for SCN:

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In the following section, we will introduce the steps of disruption pattern recognition and resilient strategy suggestion algorithm in the SCN under the IVq-ROFSs environment. The algorithm includes 3 different stages. The first stage, defining the challenges and categorizing those into the right clusters of challenges which will construct the patterns of disruptions in our SCN. In this stage, we also gather and transform the data into the IVq-ROFSs environment. In stage 2, by applying the Hamacher Aggregation operators the pattern of challenges and disruption of the SCN will be determined. Then in stage 3, we will apply Dice Similarity measures to compare the strategies in the strategy pool with calculated patterns to be able to suggest the most appropriate strategy or set of strategies to provide the resilience of the SCN system. So, we will have the following stages and steps for the proposed algorithm: Stage I. Define Challenge, Disruption Patterns, and Strategy Pool:

Step 1. Collect the decision matrices of judgments. Consider a group of d decisionmakers, D = {D1 , D2 , . . . , Dd } with corresponding weight vector τj = {τ1 , τ2 , . . . , τd } ' where dj=1 τj = 1, τj ≥ 0, which participated in a group decision-making problem, where a finite set of alternatives, A = {A1 , A2 , . . . , AM } are evaluated based on a finite set of criteria, C = {C1 ,' C2 , . . . , CN }, with corresponding weight vecN tor wi = {w1 , w2 , . . . , wN } where i=1 wi = 1, wi ≥ 0. Each class of criteria could be constructed of some sub-level criteria. So, we could have the set of criteria C = {Ci |i = 1, * 2, . . . , N } which +are patterns of SCN disruptions, and a set of sub-criteria Ci = Cip |p : 1, 2, . . . , P that represents the challenges in different patterns. Comments of decision-makers are stated by using linguistic terms introduced in Table 1. Each decision-maker d expresses his opinion about the performance of d , so the notation will be like this: alternative Am regard to challenge Cip using Qm(ip)           d d d d d ˜ Qm(ip) = aQ˜ xm(ip) , bQ˜ xm(ip) , cQ˜ xm(ip) , dQ˜ xm(ip) . q

Step 2. Construct the strategy pool matrix based on the literature review part. In the pool, we will have at least one appropriate strategy for each pattern of disruption and then collect the judgment of each expert to construct the strategy pool matrix for each expert. The matrix will be the set of strategies S = {Sis |i = 1, . . . , N ∧ s = 1, . . . , S} which are stated based on linguistic terms in Table 1. Table 1. IVq-ROFSs linguistic scales   IVq-ROFSs Linguistic Scales L˜ s

SFNs (μ, ϑ, h)

Very high Possible (VHP)

High Possible (HP)

Equally Possible (EP)

Low Possible (LP)

Very Low Possible (VLP)

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Step 3. Transform all individual decision matrices of challenges and strategy pool into IVq-ROFNs by using values defined in Table 1. Stage II. Disruption Pattern Recognition: Step 4. Aggregate the individual decision matrices of different experts by using Hamacher aggregation operators to get the GDM matrix. Step 5. Aggregate the GDM matrix based on each cluster of challenges to get the aggregated pattern GDM matrix. Step 6. Compute the score matrix by utilizing the IVq-ROFSs score function. Step 7. Establish the correspondence matrix  = [λmi ]M ×N which are showing which pattern is significantly describing the resilient disruption of the SCN alternatives. This step will rank the patterns for each alternative based on the score matrix. Stage III. Strategy Selection to Increase SCN Resilience: Step 8. Aggregate the strategy pool matrices of experts by using Hamacher aggregation operators to get the aggregated strategy pool matrix. Step 9. Construct the concordance matrix C for each disruption pattern between the strategies related to the pattern and the SCN alternatives. Elements of the concordance matrix are calculated IVq-ROFSs Dice Similarity measures. So each element will describe the similarity between strategies in the strategy pool of each alternative in the GDM matrix in comparison. Step 10. Rank the strategies for alternatives in concordance matrices and select appropriate strategies for each alternative based on the concordance matrix C and correspondence matrix  for each disruption pattern.

3 Evaluation, Results, and Discussion In the evaluation part, we consider the SCN problem with 3 different experts D = {D1 , D2 , D3 } and weight vector of {0.35, 0.25, 0.4}, 5 SCN alternatives. We discussed the 4 clusters of challenges and sub-level criteria (challenges) are introduced in Table 2, and the weights of all challenges are considered equal. For this problem assumed q = 3 and λ = 1. The comments of experts for different alternatives based on challenges are gathered into individual decision matrices are constructed by using linguistic terms in Table 1. Also, strategy pool matrices are established based on experts’ ideas and for transforming data into the IVq-ROFSs environment Table 1 is applied. Then, based on steps 4, 5 the Hamacher Aggregation operator is applied to combine the ideas, and then score values of the aggregated GDM matrix are evaluated based on Eq. 6–7. Based on step 7, correspondence matrix  is established among disruption patterns and SCN alternatives shown in Fig. 1a. The strategies in Table 3 which construct the strategy pool matrices are combined based on comments of different 3 experts in step 8 by using Hamacher aggregators, then based on step 9, we construct the concordance matrices C between strategies for each alternative by considering different patterns. In this step, the concordance matrices are constructed by using Dice similarity relations. The pattern-strategy relationship for the SCN alternatives based on Dice concordance similarity measures is shown in Fig. 1b and Table 4.

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 Table 2. SCN challenges Cip and patterns of disruption (Ci ) 1. C1 : Upstream Network (UN) a.C11 : Scarcity of Material (SoM) b. C12 : Scarcity of Labor (SL) c. C13 : Suboptimal Substitute Adoption (SSA) d. C14 : Inconsistency in Supply (IS) 2. C2 : Downstream Network (DN) a. C21 : Uncertainty in Demand Behavior (UDB) b. C22 : Uncertainty in Demand Quantity (UDQ)

3. C3 : Management Network (MN) a. C31 : Constraint in Capacity (CC) b. C32 : Delay of Delivery Management (DDM) C33 : Suboptimal Manufacturing/Service (SM/S) 4. C4 : Transportation Network (TN) a. C41 : Transportation Unavailability and Delays (TUD) b. C42 : Last-Mile Delivery (LMD) C43 : Transportation Costs (TC)

Table 3. Strategies pool (Sis ) – – – – – –

S11 : Provide alternative material/labor S12 : Plan to use contractual labor S13 : Forming Umbrella Agreements S14 : Labor welfare & insurance strategies S15 : Business continuity plans S16 : Additive and automated manufacturing – S17 : Network insight development – S18 : Supplier risk management

– – – – –

S31 : Develop local (onshore) vendors S32 : Use AI and data analytics S33 : Product mix optimization S34 : Scenario planning techniques S35 : Tracking and transparency of the delivery process – S36 : Omni-channel business model – S37 : Scenario planning techniques

– S21 : Excellent customer response & delight – S22 : Creating direct and safe channels for feed backward and data collecting from DN – S23 : Real-time visibility and tracking to customers – S24 : Real-time visibility and tracking of customers – S25 : Differential pricing to customers

– S41 : Use of mobility solutions – IoT, Autonomous Vehicles & Drones – S42 : Partnering with third party logistic and warehousing providers – S43 : Supply chain control tower technology for real-time tracking and monitoring of transportation – S44 : Logistic fleet maintenance

Results are demonstrating the most significant approach to facing specific patterns and the priority of those strategies that should take into consideration. In this paper we based on priority we select three different strategies for each pattern and those selected significant strategies are our suggestions to the SCN for the post-COVID era. These strategies are the top approaches that could directly and effectively improve the negative effects of the pandemic on the SCN to bring out the resilience of any SCN system for post-epidemic conditions.

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4

3

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2

2

2

2

1

1

1

1

RANK C1 RANK C2 RANK C3 RANK C4 A1

A2

A4

A5

A3

(a)

(b)

Fig. 1. (a) Correspondence matrix . (b) Pattern-strategy relationship for SCN alternatives and suggest strategies based on dice concordance similarly Table 4. Pattern-Strategy relationship to suggest appropriate strategies based on Dice concordance similarity for each SCN alternatives SCN alternatives

Pattern-strategy

Strategies (dice concordance)

A1

C2-S21

0.86539294

A1

C2-S25

0.61978198

A1

C2-S23

0.61439706

A1

C1-S15

0.8094844

A1

C1-S13

0.35715294

A1

C1-S17

0.35715294

A1

C3-S37

0.85696956

A1

C3-S32

0.85110783

A1

C3-S33

0.54587443

A2

C1-S15

0.80906979

A2

C1-S13

0.35353534

A2

C1-S17

0.35353534

A2

C2-S21

0.81482502

A2

C2-S25

0.53347441

A2

C2-S23

0.5320189

A2

C3-S37

0.79564914

A2

C3-S32

0.79141855

A2

C3-S33

0.46780278

A3

C3-S37

0.82891839 (continued)

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Table 4. (continued) SCN alternatives

Pattern-strategy

Strategies (dice concordance)

A3

C3-S32

0.8234076

A3

C3-S33

0.51172825

A3

C4-S43

0.18857113

A3

C4-S42

0.12922671

A3

C4-S41

0.11956313

A3

C1-S15

0.73462987

A3

C1-S13

0.27749902

A3

C1-S17

0.27749902

A4

C1-S15

0.84363536

A4

C1-S13

0.40869647

A4

C1-S17

0.40869647

A4

C3-S37

0.88076629

A4

C3-S32

0.8720737

A4

C3-S33

0.61466625

A4

C4-S43

0.29071125

A4

C4-S42

0.23095653

A4

C4-S41

0.22113068

A5

C4-S43

0.22318131

A5

C4-S42

0.160192

A5

C4-S41

0.15042895

A5

C1-S15

0.76527888

A5

C1-S13

0.31142607

A5

C1-S17

0.31142607

A5

C3-S37

0.75446959

A5

C3-S32

0.75064952

A5

C3-S33

0.43002632

4 Conclusion This paper aims to discuss the challenges around the SCN problem under the impact of the COVID-19 pandemic and introduce an algorithm to handle the uncertainty of this complex problem based on the IVq-ROFSs environment. The SCN system learns from the challenges and this is the understanding of SCN challenges to learn and then suggest the guidelines for the post-COVID-19 era. The algorithms include 3 different stages, defining the problem, challenges, patterns of disruptions, and strategies also collecting and transforming information into IVq-ROFSs is in this stage. Then in the

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second stage, the expert’s comments are combined by using Hamacher aggregation operators to reach a consensus aggregated decision matrix, and then it will be possible to determine which pattern of disruption works for which SCN alternative. In the final stage after understanding the challenges and type of disruptions specifically for each SCN, it would be reasonable to check among the solution to find the most appropriate ones. In this stage, the Dice similarity measures will be calculated between strategies and patterns for each alternative to constructing the concordance matrix. So we could suggest the appropriate guidelines of strategies for establishing a more resilient SCN system for the post-COVID-19 environment. Our discussed problem includes different 3 experts, 5 SCN alternatives, and 10 challenges of 4 different patterns. The criteria (challenges) and strategy approaches are selected from the literature part. The algorithm is applying the Hamacher aggregation operator and Dice similarity measure for IVqROFSs, evaluates challenges, and determines the pattern of disruption for each SCN alternative. Thereafter, the proposed algorithm calculates the Dice similarity measures of different strategies in the pool with patterns of disruption. In this stage, we compare the approaches with issues and suggest the set of most appropriate strategies for each alternative which will bring more resilience SCN system. For future studies, we propose various applications in different fields of study like different aspects of SCN problems and also real case study applications like real SCN in the fields of financial, banking, health care, and manufacturing systems.

References 1. Donthu, N., Gustafsson, A.: Effects of COVID-19 on business and research. J. Bus. Res. 117, 284–289 (2020) 2. Verma, S., Gustafsson, A.: Investigating the emerging COVID-19 research trends in the field of business and management: a bibliometric analysis approach. J. Bus. Res. (2020). https:// doi.org/10.1016/j.jbusres.2020.06.057 3. Ivanov, D., Dolgui, A.: Viability of intertwined supply networks: extending the supply chain resilience angles towards survivability. A position paper motivated by COVID-19 outbreak. Int. J. Prod. Res. (2020). https://doi.org/10.1080/00207543.2020.1750727 4. Govindan, K., Mina, H., Alavi, B.: A decision support system for demand management in healthcare supply chains considering the epidemic outbreaks: A case study of coronavirus disease 2019 (COVID-19). Transp. Res. Part E Logist. Transp. Rev. (2020). https://doi.org/ 10.1016/j.tre.2020.101967 5. Farid, F., Donyatalab, Y.: Novel spherical fuzzy eco-holonic concept in sustainable supply chain of aviation fuel. In: Kahraman, C., Aydın, S. (eds.) Intelligent and Fuzzy Techniques in Aviation 4.0. SSDC, vol. 372, pp. 201–235. Springer, Cham (2022). https://doi.org/10.1007/ 978-3-030-75067-1_9 6. Lopes de Sousa Jabbour, A.B., Chiappetta Jabbour, C.J., Hingley, M., Vilalta-Perdomo, E.L., Ramsden, G., Twigg, D.: Sustainability of supply chains in the wake of the coronavirus (COVID-19/SARS-CoV-2) pandemic: lessons and trends. Mod. Supply Chain Res. Appl. 2(3), 117–122 (2020). https://doi.org/10.1108/mscra-05-2020-0011 7. Ivanov, D.: Predicting the impacts of epidemic outbreaks on global supply chains: a simulation-based analysis on the coronavirus outbreak (COVID-19/SARS-CoV-2) case. Transp. Res. Part E Logist. Transp. Rev. 136, 101922 (2020). https://doi.org/10.1016/j.tre. 2020.101922

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8. Filho, W.L., Brandli, L.L., Salvia, A.L., Rayman-Bacchus, L., Platje, J.: COVID-19 and the UN sustainable development goals: threat to solidarity or an opportunity? Sustain. (2020). https://doi.org/10.3390/su12135343 9. Raj, A., Mukherjee, A.A., de Sousa Jabbour, A.B.L., Srivastava, S.K.: Supply chain management during and post-COVID-19 pandemic: mitigation strategies and practical lessons learned. J. Bus. Res. 142, 1125–1139 (2022). https://doi.org/10.1016/J.JBUSRES.2022. 01.037 10. Queiroz, M.M., Ivanov, D., Dolgui, A., Fosso Wamba, S.: Impacts of epidemic outbreaks on supply chains: mapping a research agenda amid the COVID-19 pandemic through a structured literature review. Ann. Oper. Res. (2020). https://doi.org/10.1007/s10479-020-03685-7 11. van Remko, H.: Research opportunities for a more resilient post-COVID-19 supply chain – closing the gap between research findings and industry practice. Int. J. Oper. Prod. Manag. (2020). https://doi.org/10.1108/IJOPM-03-2020-0165 12. Golan, M.S., Jernegan, L.H., Linkov, I.: Trends and applications of resilience analytics in supply chain modeling: systematic literature review in the context of the COVID-19 pandemic. Environ. Syst. Decis. 40(2), 222–243 (2020) 13. Raj, A., Dwivedi, G., Sharma, A., Lopes de Sousa Jabbour, A.B., Rajak, S.: Barriers to the adoption of industry 4.0 technologies in the manufacturing sector: an inter-country comparative perspective. Int. J. Prod. Econ. (2020). https://doi.org/10.1016/j.ijpe.2019. 107546 14. Zadeh, L.A.: Fuzzy sets. Inf. Control. (1965). https://doi.org/10.1016/S0019-9958(65)902 41-X 15. Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. (1986). https://doi.org/10.1016/ S0165-0114(86)80034-3 16. Torra, V.: Hesitant fuzzy sets. Int. J. Intell. Syst. (2010). https://doi.org/10.1002/int.20418 17. Yager, R.R.: Pythagorean fuzzy subsets. 2013 Jt. IFSA World Congr. NAFIPS Annu. Meet. 2, 57–61 (2013). https://doi.org/10.1109/IFSA-NAFIPS.2013.6608375 18. Cuong, B.C., Kreinovich, V.: Picture fuzzy sets - a new concept for computational intelligence problems. In: 2013 3rd World Congress on Information and Communication Technologies, WICT 2013 (2014) 19. Yager, R.R.: Generalized orthopair fuzzy sets. IEEE Trans. Fuzzy Syst. 25, 1222–1230 (2017) 20. Joshi, B.P., Singh, A., Bhatt, P.K., Vaisla, K.S.: Interval valued q-rung orthopair fuzzy sets and their properties. J. Intell. Fuzzy Syst. 35, 5225–5230 (2018). https://doi.org/10.3233/ JIFS-169806 21. Donyatalab, Y., Farrokhizadeh, E., Seyfi Shishavan, S.A.: Similarity measures of q-Rung orthopair fuzzy sets based on square root cosine similarity function. In: Kahraman, C., Cevik Onar, S., Oztaysi, B., Sari, I.U., Cebi, S., Tolga, A.C. (eds.) INFUS 2020. AISC, vol. 1197, pp. 475–483. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-51156-2_55 22. Farrokhizadeh, E., Shishavan, S.A.S., Donyatalab, Y., Abdollahzadeh, S.: The dice (Sorensen) similarity measures for optimal selection with q-Rung orthopair fuzzy information. In: Kahraman, C., Cevik Onar, S., Oztaysi, B., Sari, I.U., Cebi, S., Tolga, A.C. (eds.) INFUS 2020. AISC, vol. 1197, pp. 484–493. Springer, Cham (2021). https://doi.org/10.1007/978-3-03051156-2_56 23. Donyatalab, Y., Farrokhizadeh, E., Shishavan, S.A.S., Seifi, S.H.: Hamacher aggregation operators based on interval-valued q-Rung orthopair fuzzy sets and their applications to decision making problems. In: Kahraman, C., Cevik Onar, S., Oztaysi, B., Sari, I.U., Cebi, S., Tolga, A.C. (eds.) INFUS 2020. AISC, vol. 1197, pp. 466–474. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-51156-2_54

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Intelligent Supply Chains Through Implementation of Digital Twins Oray Kulaç1(B)

, Banu Y. Ekren2,3

, and A. Özgür Toy2

1 Yasar University Graduate School, Izmir, Turkey

[email protected]

2 Industrial Engineering Department, Yasar University, Izmir, Turkey 3 Cranfield University, Cranfield, UK

Abstract. Data-driven decision-making process can be defined to be the sequential activities of real-time data collection, data analytics, optimization and decision making. Developments in Industry 4.0 technologies have made it possible to realize that new quality decision-making process. When that decision-making process is performed under the simulation model of a system developed on real-time databased and end-to-end connection manner, to prevent the disruption risks and to improve resilience in a system, then it constitutes a digital twin (DT). A DT is a virtual representation of an object or system that can help organizations monitor operations, perform predictive analytics, and improve processes. For instance, a DT could provide a digital replica of the operations of a factory, communications network, or the flow of goods through a supply chain system. In this work, we focus on DT implementations in supply chain networks. We present state of the art implementation of DTs in supply chains and their prospective utilizations towards creating intelligent supply chains. Keywords: Digital twin · Supply Chain Management · Data-driven decision making

1 Introduction Data-driven decision-making process is the sequential activities of data collection, data analysis, data interpretation and decision making. Customarily, this process is run over the models detached from the actual system. Likewise, simulation is one of the modelling approaches that is used to understand and predict the behavior of the system under interest. Developments in information, computation, and communication technologies as well as Industry 4.0 technologies like IoT, real-time data collecting, and embedded sensors in physical systems etc. have created opportunities for restructuring and reengineering the simulation modelling paradigm emerging with the Digital Twin (DT). DT is a virtual replica of an object or system to help organizations monitor operations, perform predictive analytics, and improve processes. While it could be a digital replica of operations in a factory, communications network, or the flow of goods through a supply chain system, it could also be a replica of a physical object such as an airplane, a space craft, or a wind turbine, etc. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 957–964, 2022. https://doi.org/10.1007/978-3-031-09173-5_109

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A DT consists of three main components. These are: an actual system, a detailed simulation model of that system (virtual system) and a data link in between [1]. High quality data is the backbone of a DT. Specifically, a data link flow exists between the actual system and its digital replica where continuous correspondence and inference information flow take place in both directions. Different debates on definition of DTs exist in literature. In this work, we carry out a survey study to identify those definitions by also presenting how the technological developments affect those definitions in time. To contribute to the dissemination of DT applications, the intelligibility of the concept, as well as the implementation of DTs specifically on supply chain (SC) problems, we conduct an extensive literature survey work. Here, we focus on SC problems. Recent COVID-19 pandemic has shown the clear shortcomings of traditional manufacturing’s over-reliance on complex and often very extended supply chains, and the growing necessity for sustainable, resilient, and innovative designs in product supplies. By the help of DT implementations, it might be possible to alter disruption risks by predictive analytics and improve resilience in SCs. The main research question of the work can be given as: RQ: How does SCs benefit from DT for resilience and efficiency? The rest of this work is organized as follows. In Sect. 2 we outline the evolution of DT along with its enabling technologies. We discuss implementation areas of DTs in Sect. 3. We focus on implementation of DTs in SCs in Sect. 4. Finally, we conclude in Sect. 5.

2 Evolution of DT DT has been first applied by the NASA Apollo program, where simulators and physical models of space crafts are developed to mimic the effects of space conditions on the actual vehicle. Apollo-13 rescue mission may be considered a successful implementation of a basic DT concept. In that case, the data from the crippled space vehicle is utilized to modify the simulators on ground, and then their outputs are used to produce new policies to rescue the crew [2]. The DT concept emerges in academia with the studies of Grieves. He explores the opportunity of utilization of DT in product life-cycle management [3]. Later on, Grieves and Vickers propose following definition for DT “A set of virtual information constructs that fully describes a potential or actual physical manufactured product from the micro atomic level to the macro geometrical level. At its optimum, any information that could be obtained from inspecting a physical manufactured product can be obtained from its Digital Twin” [4]. By the technological developments, the definition of DT has changed by involving the utilization of advantages of those technologies. For instance, a definition involving Internet of Things (IoT) is given by Lee and Kim [5] as follows: “A near real-time digital image of a physical object or process that helps optimize business performance. Two concepts of IoT (Internet of things) and IoS (Internet of Service) are combined to realize the smart factory based on a digital twin”. Another definition is given by Asimov et al. [6] including the Artificial Intelligence (AI) concept as: “a virtual replica of real physical installation, which can check the

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consistency for monitoring data, perform data mining to detect existing and forecast upcoming problems, and which uses an AI knowledge engine to support effective business decisions”. In their systematic literature review, Semeraro et al. [7] summarize different definitions as: “A set of adaptive models that emulate the behavior of a physical system in a virtual system getting real-time data to update itself along its lifecycle. The digital twin replicates the physical system to predict failures and opportunities for changing, to prescribe real-time actions for optimizing and/or mitigating unexpected events observing and evaluating the operating profile system”. While the definition of DT evolves over time, meanwhile several characteristics of DT have also been identified. From findings of Moshood et al. [8] and Gerlach et al. [9] following list of characteristics is formed: • Physical and virtual: As discussed earlier a DT is composed of both a physical system and a detailed simulation model of that system (the virtual system). • Bidirectional data: There is a data link between physical and virtual systems. On this link data exchange is bidirectional. Data flow from physical system to virtual system allows managers and decision makers to receive early warnings, to conduct risk analysis and identify bottlenecks for various physical and operational conditions. Data flow from virtual system carries inferences and advised policies to the physical system. • Timely updates: Bidirectional data exchange is conducted on regular intervals. A continuous data flow is preferred when possible. • Maintain state: A DT holds the last state of the physical system in memory in the case of disconnection of data link. Keeping the different states of different case scenarios is also a desirable characteristic. • Modelling and analytics: A DT provides modelling and analytics capabilities. By using these capabilities, various scenarios on different states of physical system can be experimented, for the purpose of optimization or prediction. Moreover, integration of machine learning (ML) methodology may increase the power of analytical capabilities. • Reporting: A DT generates reports and visualizations of analyses results for the user (human or machine) in certain formats. In the following section, we give information on the enabling technologies of DTs. 2.1 Enabling Technologies The latest developments in hardware, software, and communication technologies have paved the way of improved capabilities of simulation modelling. In addition to those, Industry 4.0 technologies, and the ML applications are embodied in DT. In this section, we investigate the enabling technologies of DT. • Machine Learning: ML is a part of Artificial Intelligence (AI) field which relies on the fact that machines can process larger data and information compared to human.

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In this process, machines can recognize the patterns and complex relationships which can be used as basis for policy analysis and decision making in DTs [7]. Internet of Things: IoT describes the objects connected via an internet network. These objects can collect, process and exchange data with each other or with other devices connected to this internet network. As discussed above, Lee and Kim describe implementation of IoT in DT [10, 11]. 5G: 5G is the new technology standard for mobile networks. 5G transmits data at faster speeds than its predecessors with lower latency rates. This technology enhances data collection and communication capacity in a DT structure through establishing a broadband link between virtual and real system [11]. Cloud Computing: Cloud computing delivers easy access to computing services from a network. There are three different services offered by cloud computing. These are infrastructure as a service (IaaS), platform as a service (PaaS) and software as a service (SaaS). The advantage of using a cloud platform is that there is no investment cost for hardware, computing space or software. This technology helps DT to become more accessible by any user at a lower cost [10, 11]. Augmented and Virtual Reality: Virtual reality is a technology that emulates the real world by simulating different senses to create a virtual world. Augmented reality embeds virtual world to real world. For DT, both augmented and virtual reality may become useful tools for visualization and monitoring purposes [10]. Application Programming Interface (API) and Open Standards: APIs are the interface programs between softwares/computers. APIs and open standards enable sharing of data among different software and computers. Moreover, reusability of software pieces has been improved by the help of APIs and Open Standards. These interfaces and standards enhance DTs capability of sharing and exchanging data easier and more reliable than ever [10]. Cyber Security: Cyber security is the combination of all efforts to protect digital systems, software, and data from malicious cyber-attacks. Due to their nature, DTs are attractive targets for cyber criminals. Since any distrust in security of DT may diminish the desire for such a system, cyber security becomes an important enabler technology for DTs [10].

Next, we discuss implementation areas of DTs based on aforementioned technological developments.

3 Implementation Areas of DT DTs tend to be implemented by several different sectors. To investigate the implementation areas, a literature search is conducted in the peer reviewed journals and conference proceedings indexed in Scopus and WOS by using the keywords of “Digital Twin” and the business areas listed in Table 1. Number of publications for each business area in between 1994–2022 depicted in Table 1. Our findings in Table 1 verify findings of [1, 12] where DT is mostly implemented in the “manufacturing and production” area. “Maintenance” and “service industry” follow the manufacturing sector in order. DT is implemented on “SC management” relatively

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Table 1. The number of publications about DT based on business areas. Business areas

Number of publications

Manufacturing/Production

3,248

Maintenance

851

Service systems

265

Supply chain/Supply Chain Management

262

Marketing

73

Retail

6

Management/Leadership

6

less than the “manufacturing and maintenance” areas. Scarcity of DT research on the SC area has motivated us to focus on this field. When we repeat the literature search with the sectoral keywords, we obtain Table 2. Table 2. The number of publications published in DT based-on sectors. Sectors

Number of publications

Energy/Energy management

1776

City/City management

730

Aerospace

576

Education

380

Automotive

254

Healthcare

192

Construction industry

150

Maritime/Shipbuilding

87

From Table 2 it is observed that “Energy/Energy Management” area is the widely applied sector in DT implementations. City/City management, aerospace, education, and automotive follow that sector in order.

4 DT in Supply Chain Management Supply Chain Management (SCM) is the management of the flow of goods and services including all processes to transform raw materials into final products. It is a complex management issue that involves all stages in the chain to complete an efficient operation. Recent COVID-19 pandemic has shown the clear shortcomings of traditional manufacturing’s over-reliance on complex and often very large supply chains. The experience

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during the pandemics made it well understood that there is a growing necessity for sustainability and innovation by renewal of manufacturing and product design which is also shown in Barclays’ survey where 25% of professional participants declare that they had to change their supply chains in response to the pandemic [13]. DT may provide advantage for SCM by creating value in the following dimensions: • Descriptive Value: End-to-end visibility of a SC is a significant issue in intelligent SC designs. DT may provide immediate and real-time visualization of those systems. By the embedded sensors and information technologies like ERP, real time data can be tracked and processed in SCs. Thus, real-time state of any asset in SC system can be traced, and necessary precautions can be taken. DT can provide SCM transparency by providing visibility in all stages such as, warehouses, transportations (cargo and fleet), and production [8, 11]. • Analytical and Predictive Value: By the help of DT of a system, it would be possible to conduct an enhanced what-if analysis on the simulation model, which might not be reasonable to apply directly on the real system. This capability can be utilized efficiently in complex problem solving and optimization purposes. By the help of end-to-end visibility, high quality data gathered from the real system can be utilized in real-time decision making in SCM. For instance, predictive analytics, and necessary precautions can be proposed in advance [8]. • Diagnostic Value: DT can provide huge amount of data about assets of a SCM system. By using big data analytics and machine learning algorithms embedded in DT, hidden patterns, complex relationships, and abnormalities can be identified. This knowledge helps us to understand the causes of the assets’ behaviors, and again necessary precautions can be taken in advance [8]. A SC may be investigated in four levels: Asset Level, Site Level, Network Level 1–2. DT has the potential of implementation and contribution at all levels [8, 9] (Fig. 1).

Network Level 2

Network Level 1

Site Level

Asset Level

Fig. 1. DT levels for SCM.

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Followings are some other examples of DT implementations in different levels of SC systems [10]: Packaging and container DTs, DTs for shipments, DTs of warehouses and distribution centers, DTs of logistics infrastructure, DTs of global/local logistics networks. DTs increase visibility, resilience and flexibility in SCs as well as reduction in lead times and reaction times and increase efficiency in processes. DTs may provide basis for construction of enhanced SCs such as agile SC, adaptive SC, etc. Besides those benefits, there are challenges in successful implementation of DTs in SCs. Detailed modelling requirement and investment on technologies may come with high cost. Moreover, data and communication infrastructure in DTs may bring up high cost Cyber security precautions. Another challenge would be the collection of precise and timely data collection from SC systems. DT set up for SC yields excessive data and information which need to be analyzed and processed for any decision making. Due to the closed structure of legacy systems interoperability issues, that may create challenges in implementation of DTs in SCM [10].

5 Conclusion In this study we survey the Digital Twin technology implementations in industry focusing on supply chain systems. We provide a statistical summary of publications on DT which display a growing interest in all business areas and sectors. Our aim is to shed a light on how SCs can benefit from DT applications. DT has the capability to cope with the recent resiliency and sustainability design requirements of SCs which emerged by the recent COVID-19 pandemic. By the recent technological and IT developments, it is possible to realize the digital replica of such complex systems to make intelligent decisions towards their efficient management. The literature indicates that 80% of executives expect increase in spending on digital business initiatives in the near future. Hence, although there might be several challenges in their implementations, SCs may benefit from DTs in variety of ways. We foresee that along with the digitalization efforts DT employment will be widespread for decision making in SCs as well as in other fields.

References 1. Jones, D., Snider, C., Nassehi, A., Yon, J., Hicks, B.: Characterizing the Digital Twin: a systematic literature review. CIRP J. Manuf. Sci. Technol. 29, 36–52 (2020) 2. Siemens Blog Home Page: Apollo 13: The First Digital Twin. https://blogs.sw.siemens.com/ simcenter/apollo-13-the-first-digital-twin/. Accessed 24 Mar 2022 3. Grieves, M.: Digital Twin: Manufacturing Excellence through Virtual Factory Replication. Whitepaper (2014) 4. Grieves, M., Vickers, J.: Digital twin: mitigating unpredictable, undesirable emergent behavior in complex systems. In: Kahlen, F.-J., Flumerfelt, S., Alves, A. (eds.) Transdisciplinary Perspectives on Complex Systems, pp. 85–113. Springer, Cham (2017). https://doi.org/10. 1007/978-3-319-38756-7_4 5. Lee, H., Kim, T.: Smart factory use case model based on digital twin. ICIC Express Lett. Part B Appl. 9(9), 931–936 (2018)

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6. Asimov, R.M., Chernoshey, S.V., Kruse, I., Osipovich, V.S.: Digital twin in the analysis of a big data. In: Big Data and Advanced Analytics (2018) 7. Semeraro, C., Lezoche, M., Panetto, H., Dassisti, M.: Digital twin paradigm: a systematic literature review. Comput. Ind. 130, 103469 (2021) 8. Moshood, T.D., Nawanir, G., Sorooshian, S., Okfalisa, O.: Digital twin driven supply chain visibility within logistics: a new paradigm for future logistics. Appl. Syst. Innov. 4(2), 30 (2021) 9. Gerlach, B., Zarnitz, S., Nitsche, B., Straube, F.: Digital supply chain twins, conceptual clarification, use cases and benefits. Logistics 5(4), 86 (2021) 10. DHL Insights & Innovation Home Page: Digital Twins on the Logistics Industry. https:// www.dhl.com/content/dam/dhl/global/core/documents/pdf/glo-core-digital-twins-in-logist ics.pdf. Accessed 24 Mar 2022 11. Busse, A., Gerlach, B., Lengeling, J.C., Poschmann, P., Werner, J., Zarnitz, S.: Towards digital twins of multimodal supply chains. Logistics 5(2), 25 (2021) 12. Errandonea, I., Beltrán, S., Arrizabalaga, S.: Digital twin for maintenance: a literature review. Comput. Ind. 123, 103316 (2020) 13. Barclay Insights Homepage: Additive Manufacturing: Advancing the 4th Industrial Revolution. https://www.cib.barclays/our-insights/3-point-perspective/additive-manufacturing-adv ancing-the-fourth-industrial-revolution.html. Accessed 24 Mar 2022

Evaluation of Control and Management System Performance for the Complex Objects Under Uncertainty Olesiya Kosenko , Stanislav Belyakov , Alexander Bozhenyuk(B) and Margarita Knyazeva

,

Southern Federal University, Nekrasovsky str. 44, 347922 Taganrog, Russia [email protected]

Abstract. This article considers the problem of optimizing the control and management system performance for a complex object. An industrial network with various resource flows is considered as a complex system. The production process model is represented by a fuzzy temporal graph. The fuzzy temporal graph makes it possible to consider the change in parameters over time, which affects the efficiency of the system under uncertainty. The possibility of applying the theory of fuzzy sets to describe the production process in the form of variations of route maps is analyzed. To evaluate the efficiency of the system, the production problem was formalized in a fuzzy form. The calculation of the duration of the route charts of the technological process was carried out, the maximum conjunctive strength and the degree of internal stability were estimated. Keywords: Complex system · Resource allocation · Optimization · Uncertainty · Fuzzy temporal graph · Conjunctival strength · Internal stability of the path

1 Introduction One of the criteria for the effective functioning of a complex production system is the operational control and management of the technological process. To predict the possible states of a complex system, it is necessary to consider many of its parameters. In this case, it is necessary to predict the change in the states of production parameters over time [1–3]. Changes in controlled values, such as production volumes, amount of resources and other parameters entail a change in the route map of the technological process. The route technological map defines many parameters. One of them is to determine the features of the technological process with different input data. Among the features of planning the production process can be noted [4]: – the name of the necessary equipment; – the product configuration, since it can be represented by a combination of several components; – data on the resources that are available at the enterprise; © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 965–973, 2022. https://doi.org/10.1007/978-3-031-09173-5_110

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– data on specific processing modes, etc. The flow chart of the technological process is a complex and necessary element of the production system. But for the correct consideration of all input parameters during planning, it is sometimes impossible to indicate the exact values of the initial parameters. The use of fuzzy set theory for decision-making problems in complex systems has found justification as an adequate tool for reflecting uncertainty [5]. To solve the problem of analyzing the effectiveness of the functioning of the control and management system, it is proposed to use the fuzzy sets theory, which allows to represent the uncertainty and to evaluate the main criterion for production efficiency the duration of the technological process [6]. Network planning makes it possible to take into consideration all the variety of connections between activities and allows evaluating the impact of deviations from the plan on the further course of project performance [7]. Graph theory has been successfully used to solve network problems of various types. The use of temporal graphs [8] makes it possible to reflect temporal changes between the elements of the system. Graph temporal models are widely used: establishing topological relationships between objects on the map, financial and political forecasts, biological and sociological problems [9, 10]. At the same time, it should be taken into account that predicting the behavior of complex multi-parameter systems is characterized by partial or complete uncertainty of the parameters [11, 12]. This paper proposes the use of temporal fuzzy graphs when choosing a route map of a technological process. The use of temporal fuzzy graphs makes it possible to adequately assess the efficiency of the production process in fuzzy conditions. The paper is organized as follows. In the second section a complex system is considered using the example of a production complex with many resource flows of various types. It should be noted that the static variables situation is far from the real production process. The concept of production system efficiency is defined. In the third section the production process is considered in the form of a temporal graph, which corresponds to the description of a dynamic system. The conditions necessary for assessing the effective functioning of the production system are considered. The fourth section considers the assessment of the efficiency of a dynamic system under conditions of uncertainty, namely: the parameters were calculated to assess the feasibility of adjusting the values of the technological process; the maximum conjunctive strength and the degree of internal stability of the path (route map of the technological process) were calculated. In conclusion, it was shown that the application of fuzzy temporal graphs for the formalization of technological processes makes it possible to take into account the relationship and mutual influence of various production flows that may change over time. The validity and advantage of applying the apparatus of fuzzy logic to solving problems of decision making in complex systems are discussed. Directions for future research are also defined.

2 Control System Analysis The production system can be considered as a set of some material (resources) and informational (temporary) objects. The total resource flow of each subsystem of the production complex can be determined as follows (Fig. 1) [13]:

Evaluation of Control and Management System Performance

u1 x11 x21 x30

u2

w1

1

y11 y21

x12 x32

u3

w2

2

y12x13

3

x33

967

w3 y13 y33

Fig. 1. The flow diagram of the production complex

Let’s consider the function that determines the flows of the production system as follows: Y k = F k (X k , U k , W k ), where Y k - is a set  determines the output flows of the k-th subsystem of the production  that k k complex, Y = yj , j = 1 . . . mk ; X k - set of input streams of the k-th subsystem, X k =    k xi , i = 1 . . . nk ; U k - set that determines the control action, U k = upk , p = 1 . . . lk ; W k - is a set that determines the disturbances that affect the process in this subsystem, W k = wtk , t = 1 . . . rk . N - the number of subsystems in the production complex, nk , mk - the number of input and output flows, lk - the number of control parameters, rk - the number of disturbing factors. The selection of objects or flows in the system is not unambiguous and depends both on the formulation of the problem and on the goals of the study. Objects change their states during the operation of the system. State change moments can be associated with one of the following events: – off-system events, which are determined by the arrival of information moments from external sources; – intra-system events associated with changes in the states of system objects; – deterministic events that depend on the regulation of the system operation. To reflect the relationship between the elements of complex systems, it is convenient to use graph theory [14]. Moreover, these relationships between elements are constant and do not change over time. Such graphs were called “static” [8]. Consider the production system on the example of a graph [12]. Figure 2 shows a certain production process, consisting of a sequence of works or activities to be performed. When drawing up network diagrams, the entire complex of work of the technological process is divided into R components, their relationship and sequence are established. Let’s consider that any work connects two events. At the same time, the event is considered not as a process of any labor, but its result. An event, unlike work, has no duration. An event denotes the completion of one or more previous activities, or so-called precedence relations between them. The event is denoted by a circle in the network diagram. For analyzing and planning the production process, let’s consider the critical path of the route map. The critical path is a sequence of operations that determines the set of operations performed and is characterized by the maximum duration of all possible

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R4

1

4

R7

5

7

3 3

R3

0 6 R2

3

4 R6

R5

2

5

R8

4

6

6

2

Fig. 2. Example of a production process

paths [15]. For the production process shown in Fig. 2, the critical path is defined by the following types of work and events: 0-2-5-6, tcr = 16 [12]. It should be noted that the static situation is far from the real production process. The technological production process should be considered as a time-varying dynamic system [16]. The process of functioning of a dynamic system can be represented as a successive change in time of its states. Modeling of such a process presupposes constructing a certain system of functions and calculating performance indicators by their values. In the general case, efficiency is understood as the degree of adaptability of certain means and methods of their use to solve the set tasks [17].

3 Application of Fuzzy Temporal Graphs for Solving Production Problems The quality of the network schedule and the effectiveness of the operation of the management and control system of the production process largely depend on the reliability of time estimates. Estimates of the duration of individual work can be deterministic, probabilistic and fuzzy. Deterministic estimates mean unambiguous estimates of work. They are used in cases where the estimated duration of work can be estimated accurately or with a relatively small error. If there are no objective and reasonable norms of time for the work, then time estimates must be established under conditions of uncertainty. In such cases, either probabilistic methods or methods based on fuzzy sets are used to estimate the duration of each job. These methods make it possible to take into account the degree of uncertainty of works that depend on many parameters [18]. The introduction of fuzzy time estimates is a valid planning approach. Uncertainty in time becomes an objectively recognized factor, the effect of which must be considered. The methods for solving the problems of production planning and process control can be based on the following principles: displaying the state of permanent objects in the process of modeling and displaying the state of temporary objects of the system [19]. If we consider classical methods for solving network problems, then their application under conditions of partial uncertainty is difficult and the results obtained in a

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clear statement will give distorted solutions that do not correspond to real values [20]. Temporal fuzzy graphs will allow you to display the relationship between the state of permanent objects and the state of temporary objects of the production system [14]. Let’s consider a production facility consisting of n pieces of equipment (for example, machines). To control the technological process, information is needed on the progress of production on each of the equipment, determination of deviations in the actual production progress from planned indicators. The operation process can be described as follows. On each machine, some products are processed, provided for by the route map. The performance of the equipment for each type of product is assumed to be given. At random times, equipment stops for various reasons. Let’s denote them as: t1 = t0 + k1 Tp , where T p is the control step, k 1 is the number of the control step, t 0 is the initial moment, which determines the actual number of parts manufactured on each machine. Comparison of manufactured parts with the planned quantity is carried out at time t 0 to determine deviations. If the deviations exceed some set values, then a control decision is formed to eliminate deviations from the plan (introduction of additional equipment, redistribution of parts between machines, changing the size of batches of parts, etc.). The decisions made are entered into the system to correct the plan and change the route map. A new work schedule is drawn up and issued for production at time points t 2 = t 0 + k 2 T p . The task of the study is to calculate a certain performance indicator and determine the values of the system parameters that optimize this criterion. Such parameters can be the duration of the planning period, the control step, the values of the limits of production parameters, etc. When presenting objects on a route map at different points in time, there may be a change in their relationships. Let machines (O, A, B, C, D, E, F) be selected as permanent model objects, and ({1}, {2}, {3}, {4}, {5}) are the moments of changing the production regime and the moments of control and planning. Then the state of the system under consideration can be characterized by the values {t i }, corresponding to the moments of change in the state of the machines and the moments of receipt of control and planning signals (Fig. 3):

A

D

B

O

E

C

Fig. 3. Temporal graph of the system

F

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To solve the problems of production planning under the conditions of changing fuzzy or uncertain parameters over time, the use of fuzzy temporal graph models is proposed [8, 14]. ˜  the technological route can be represented as a fuzzy temporal graph G =  Thus, 2 X , U˜ t , in which X is a set of vertices, U˜ t = {µt (xi , xj )|(xi , xj ) ∈ X } is fuzzy set of oriented edges (works), µt is a membership function mapping X 2 → [0, 1] at times t = −

1, T . ˜ In this case, the route map of the production process is the path L(xi, xk) in the fuzzy temporal graph:  L(xi, xk) = (µt1 (xi , x1 )|(xi , x1 )), (µt2 (x1 , x2 )|(x1 , x2 )), . . . , (µtk (xk−1 , xk )|(xk−1 , xk )), for which µt1 (xi , x1 ) > 0, µt2 (x1 , x2 ) > 0, …, µtk (xk−1 , xk ) > 0, and t1 ≤ t2 ≤ … ≤ tk . The conjunctive strength of a graph path is determined by the maximum value of the membership function of the edges included in the path under consideration. At the same time, the conjunctive strength of the path will make it possible to determine the stability of the route map to various production situations.

4 Numerical Example Let the temporal graph presented in Fig. 3 be given the following variations of route maps (Fig. 4):

t1 O(t1)

t2

B(t1)

t4

t5

O(t2) A(t2)

C(t1)

t3

B(t2) C(t2)

A(t3) B(t3) C(t3) D(t3)

D(t4)

E(t3)

E(t4)

E(t5)

F(t4)

F(t5)

Fig. 4. Temporal graph of manufacturing process variations

Table 1 shows the values of the membership functions of the arcs between the vertices xi , xk at times t 1 –t 5 . ˜ i , xk ) of the presented technological process Let us define all possible route maps L(x from vertex O to vertex F:  L2 (xO , xF ) = xO xA xD xE xF ;  L3 (xO , xF ) = xO xB xE xF ; L1 (xO , xF ) = xO xA xD xF ; 

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Table 1. Values of edge membership functions in route maps. O

A

B

C

D

E

F

O

0





0

0

0

A

0

0

0

0

0

0

B

0

0

0

0

0

0

C

0

0

0

0

0

D

0

0

0

0

0



E

0

0

0

0

0

0

F

0

0

0

0

0

0

0

 L5 (xO , xF ) = xO xC xB xE xF . L4 (xO , xF ) = xO xC xE xF ;  The conjunctive strength of the path (route map of the technological process) is defined as: µL˜ 1 µL˜ 2 µL˜ 3 µL˜ 4 µL˜ 5

= µ(xO , xA )&µ(xA , xD )&µ(xD , xF ) = 0.5&0.2&0.7 = 0.2; = µ(xO , xA )&µ(xA , xD )&µ(xD , xE )&µ(xE , xF ) = 0.5&0.2&0.1&0.4 = 0.1; = µ(xO , xB )&µ(xB , xE )&µ(xE , xF ) = 0.3&0.2&0.4 = 0.2; = µ(xO , xC )&µ(xC , xE )&µ(xE , xF ) = 0.6&0.6&0.4 = 0.4; = µ(xO , xC )&µ(xC , xB )&µ(xB , xE )&µ(xE , xF ) = 0.6&0.1&0.2&0.4 = 0.1.

Hence, the maximum conjunctive strength of the path (route map of the technological process) is 0.4. Thus, the conjunctive strength of the path allows determining the stability of the route map to various production situations and uncertainty.

5 Conclusion The process of determining and studying the optimal structures of complex systems is one of the topical problems of forecasting. The complexity of solving this problem is associated with the difficulty of obtaining a mathematical description of the systems under study in an analytical form, due to the variety of system components and characteristics. The difficulty of the description is also associated with varying degrees of complexity of the interaction of these components. The description of the degree of interaction of various components using the theory of fuzzy sets makes it possible to consider various information and material flows of the production system. Fuzzy temporal graphs provide an opportunity to describe the technological process considering temporary changes and evaluate the stability of route maps. The stability assessment affects the degree of efficiency of the system under consideration and makes it possible to analyze the possible adjustment of the problem parameters. In the future, it is planned to study the evaluation of route maps on real technological processes with various variations of fuzzy input data.

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Acknowledgments. The reported study was funded by the Russian Foundation for Basic Research according to the research project N20-01-00197.

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18. Cao, B.-Y. (ed.): IWDS 2016. AISC, vol. 646. Springer, Cham (2018). https://doi.org/10. 1007/978-3-319-66514-6 19. Mönch, L., Fowler, J.W., Mason, S.J.: Production Planning and Control for Semiconductor Wafer Fabrication Facilities: Modeling, Analysis, and Systems. Springer, New York (2013). https://doi.org/10.1007/978-1-4614-4472-5 20. Bozhenyuk, A., Kosenko, O., Kosenko, E., Knyazeva, M.: Analysis of using the fuzzy intervals apparatus for applied tasks. In: Singh, P.K., Veselov, G., Vyatkin, V., Pljonkin, A., Dodero, J.M., Kumar, Y. (eds.) FTNCT 2020: CCIS, vol. 1395, pp. 368–378. Springer, Singapore (2021). https://doi.org/10.1007/978-981-16-1480-4_33

A Price Sensitivity Based Intelligent Pricing System for Global E-commerce Pelin Yurdadön1 , Ba¸sar Öztay¸si2(B) , and Egemen Berki Çimen1 1 Modanisa Head Office, Altunizade, Ku¸sbakı¸sı Cd. No: 27/1, 34662 Istanbul, Turkey

[email protected]

2 Industrial Engineering Department, ˙Istanbul Technical University, 34367 ˙Istanbul, Turkey

[email protected]

Abstract. Modanisa is a global E-commerce company which provide modest fashion products. Since each country has different currency and different economic conditions, purchasing capacity of the residents change. As a result, the price that the market is willing to pay vary among the countries. Price sensitivity is the degree to which demand changes when the cost of a product or service changes. Price sensitivity is commonly measured using the price elasticity of demand, which states that some consumers won’t pay more if a lower-priced option is available. In this study, a decision support system is proposed based on price sensitivity of products. To this end, first previous data is processed to obtain the price sensitivity. At the second step, a mathematical model, which aims to maximize the profit, is proposed. In order to show the efficiency of the approach a mathematical model is also provided. Keywords: Price sensitivity · E-commerce · Pricing system

1 Introduction Retailing is a broad concept that encompasses more than just store selling. Shopping centre-oriented retailing service is also a kind of retailing service. With this, retailing concept, from banking service to online shopping experience and hairdresser. It covers a wide range of areas from telemarketing to telemarketing. According to this broad area of the retailing concept, retailing, retailing and retailer definitions should be made in detail. Basic definition of retail is to sell products and services to users [1]. The concept of retailing can be defined as intermediary services between producers and final consumers [2]. A detailed definition of retailing is all the actions necessary to meet the individual and formal needs of customers [3]. The retail industry is the ultimate platform for the transfer of goods and services between manufacturers and consumers. A relatively novel channel for retailing is E-commerce. buying, selling, transferring, or exchanging products, services, and/or information via computer networks is defined as E-Commerce [4]. A Classification of E-commerce can be done based on the nature of the transactions or the relationship among the participants. Business-to-business; businessto-consumers, consumers-to-business are among the most common E-commerce types. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 974–981, 2022. https://doi.org/10.1007/978-3-031-09173-5_111

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E-commerce has also improved by adopting mobile technologies and social media so that new retailing type such as social commerce and mobile commerce have emerged. The term price is a monetary value that defines the benefit from a product or service [5]. Price is a system of producers, consumers and resource owners. Price works as a rational invisible hand in the resource distribution system [6]. There are different approaches to the definition of price in the literature. The most common feature of the price definition is its focus on money in the modern market. However, pricing can be seen as more than just a monetary value. Price is a concept that includes the time and effort that may be required for the production and distribution of products and services. E-commerce has greatly affected the competition between companies. Since it is possible for customers to give orders independent from location in e-commerce, the number of potential customers of companies engaged in e-commerce increases on the one hand, and on the other hand, why non-existent global competitors emerge. At this point, the importance of price in competition has also changed. Modanisa.com is one of the leading ecommerce companies, located in Turkey which focus on selling textile products to more than 150 countries worldwide. The company sells 70.000 products of 650 different brands. In this context, determining the correct price for the correct market is vital for the success of the company. To this end, a price sensitivity based pricing model is proposed in this paper. The model is composed of two steps. In the first step, using historical data price sensitivity of the market is determined. In the second step, a mathematical model which represent the objectives and constraints of the company is built. As a result of this mathematical model, the optimum price for a product is determined.

2 A Brief Literature on Pricing There are several factors that affect the pricing decision. These factors are effective in the pricing decisions of businesses. In the literature, cost is important and market share and production capacity are effective in price decision [7]. Competitive degree of products, value of competition, quality between consumer and producer, availability of substitute products, marketing objectives of the firm and official regulations are the most important factors in pricing decision [8]. Vital elements in pricing decision can be listed as follows: Costs, Distribution channels, Consumers, Competition, Government regulations. • Cost: Costs are important in pricing strategy, and production of goods and properties of goods are vital in cost decision [9]. Firms should pay attention to cost and changing production factors resulting from different conditions. Cost is not the only factor in the price decision. For example, a cold drink may be sold as One Turkish Lira in a market and the same beverage may be marketed as Three Turkish Liras in a restaurant or cafe [9].

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• Consumers: The power and demands of consumers are vital in the pricing decision. Upper and lower price decisions are adjusted according to consumer demands and needs. In the pricing decision, consumers can choose different products from various alternatives. Due to the existence of various alternatives, companies and marketing professionals who demand high prices for their products should reassure consumers. They are required to provide consumers with sufficient information about the quality of the goods and the satisfaction of the products. Even if a firm produces a product that is not a substitute in the world, it must mobilize the consumer for an effective sale [10]. • Competition: Competitors and pricing policies are effective in pricing decisions. If the company does not have a monopoly in the market in which it operates, the reactions of the competitors are effective in the price decision. The firm should pay attention to transactions related to competitors [11]. Competitors’ price may be higher due to competitors, which may result in a decrease in sales size. However, if the company benefits its differentiation strategies; can prevent sales decline due to competition. The formation of markets gains importance in the competitive structure. If the market is a perfectly competitive area of expertise and the number of firms in the market is too high; a firm cannot reach many consumers with price reductions. If the number of companies in the market is less (for example, if there is an oligopoly market structure); a discount made by the firm can be effective in attracting consumers [12]. • Distribution Channels: Distribution Channels are effective in pricing decision. A company can produce high quality products at affordable prices. The same company can provide its marketing strategy with promotional activities. However, without an effective distribution channel, final consumers cannot reach the product. Therefore, elimination of wholesalers may be an alternative to reduce the price. For the service industry, as a barber shop, eliminating middlemen can be an effective way. However, intermediaries for goods and services need to be used in many distribution channels [13]. • Government Regulations: The price is regulated by the government and government agencies in the market. For example, steel and cement prices are decided by the government to liberalize the economy. The government can limit the production and price of certain goods and services in the market. Pricing steps in the literature are listed as follows [13]. • Setting the pricing target: The pricing objective should be linked to company targets. It should be defined that the company aims to increase its market share or maximize revenue. • Purchasing ability and price assessment of the target market: Consumers may be more sensitive to different services and goods. For example, the price of food is more striking than the price of alcohol. In addition, the income of the consumer is also effective in the purchase decision. • Analysis of the relationship of demand, cost and revenue: A company must establish production costs appropriate to the market due to the revenue it needs.

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• Evaluation of competitors’ price and price strategies: At this stage, market prices should be researched and the possibility of entry of new competitors should be analyzed. If the price is higher than the price of the competitors, a more qualified and special perception should be created about the product. • Developing the pricing method: The firm must choose a method for pricing. This method is about the factor taken seriously by the company. • Setting the price: The price is easily identifiable if the necessary steps are done properly

3 Application In this study, it is aimed to determine the price elasticity of customers by using historical data and to establish a decision support system for pricing. In this section we summarize the studies in two parts. First the studies about price elasticity is given and in the second part mathematical model is explained. 3.1 Modelling Price Elasticity In the first step of the application, the relationship between price and sales is examined. However, the stated relationship could not be determined at a certain level of significance. It has been concluded that the main reason for this is the spread of the purchasing decision over time and therefore the price changes during the decision stage prevent the establishment of a successful model. When the purchasing behavior in e-commerce is examined, it can be observed that displaying the product page and adding the product to the basket are critical events, and it is aimed to determine the price elasticity indirectly through these events. To test the validity of this approach, the correlation between pageviews, add-to-cart, and sales is examined. As can be seen in Fig. 1, there is a high degree of correlation between page views and cart, page views and sales, and basket and sales. This finding shows that the indirect price elasticity model is meaningful.

Fig. 1. Correlation matrix

In the continuation of the study, the collection and processing of the necessary data for the sample product groups was carried out. Figure 2 shows an example of the data used for analysis. When the data is analyzed in a descriptive manner, the sales price ranges and the sales price standard deviations have emerged as indicated in Fig. 3.

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Later, the Polynomial Regression model was established to determine the price elasticity. As a result of the studies carried out in the Python environment, two different models were created to determine the relationship between product price and cart, and between product price and page view. Table 1 shows the adjusted R2 values of the models between product page display and price under different degrees of polynomial (N). The validity of the established polynomial models was made according to the p score of the F value of the model. Models with a p-score less than 0.1 were considered valid.

Fig. 2. A sample data view

Fig. 3. Sales price analysis

Table 1. Results of the polinomial regression.

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When the data in Table 1 is examined, it is observed that the best result is obtained for N = 5. In other words, the best model is formed as follows. y = β0 + β1 x + β2 x2 + β3 x3 + β4 x4 + β5 x5

(1)

where βi refers to regression coefficient, x refers to price, and y refers to page views.

Fig. 4. Estimated and Actual values for a sample product

Figure 4 shows the estimated values and actual values of the page view and cart models developed for a sample product. In the figure, the blue line in the graph shows the actual values, and the yellow line shows the estimated values. It has been observed that both models make very successful predictions for the selected product. 3.2 Establishment of Mathematical Model In the second stage of the study, an optimization model was established based on price elasticity and the constraints used by the firm in determining the price. The aim of the optimization was determined as maximizing profit. Profit, by definition, is calculated by subtracting costs from revenue. Revenue is calculated by multiplying the selling price and the number of sales. Cost includes several sub-items. Two of the most basic of these are shipping costs and taxes. The shipping cost is charged to the entire order and is allocated based on the number of items in the order. Therefore, in the optimization model, the shipping cost is calculated proportionally to the number of sales. Another important cost item is taxes. The tax is proportional to the sales revenue. The amount of tax varies according to the money earned from the sale. Accordingly, the objective function is proposed as in the following. Profit = Revenue − Cost,

(2)

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where revenue and cost are defined as in Eqs. (3) and (4), respectively. Revenue = Sales Quantity ∗ Price,

(3)

Cost = (Sales Quantity ∗ Product Purchase Cost) + (Sales Quantity ∗ Tax Multiplier ∗ Price) + (Sales Quantity ∗ Shipment Cost Multiplier)

(4)

The first model we propose uses sales quantity in the model. However, since we do not have a significant model to forecast sales quantity directly, we need to modify this first model by using pageview instead of sales quantity. Since there is a correlation between the number of pageviews and the number of sales, and the conversion rates of the views to sales (CR: Conversion Rate) are known; sales quantity can be estimated by using pageviews. Accordingly, the number of sales can be found by multiplying the number of views by CR. Another important part of the mathematical model is the constraints. As a result of the studies carried out, it was seen that there should be 3 constraints in the mathematical model. Firstly, the product that is out of stock cannot be sold, so a constraint related to the stock constraint is defined. Secondly, it is requested that the profit rate obtained from a product should not exceed a certain limit, as required by the firm’s decision. Finally, the number of page views greater than zero is defined as the constraint. Accordingly, the optimization model can be written as: Model notation: P = Price. PW = Pageview. COGS = Cost of goods sold, product purchase cost. μ = Tax multiplier. η = Shipment cost multiplier. CR = Conversion rate of page views to sales I = On-hand inventory CM_max = Allowed maximum limit of contribution margin i = Power of polynomial regression (0,1,2,3,4,5) β i = Regression coefficient corresponding to the term with ith power Max. Z = CR ∗ PW ∗ (P − (COGS + μ ∗ P + η))

(5)

subject to PW ∗ CR ≤ I

(6)

(P - COGS - μ−η) / COGS ≤ CM_max

(7)

PW ≥ 0, P > 0

(8)

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where page view (PW) is a polynomial function of price (P) as shown in Eq. (9). PW = β0 + β1 ∗ P + β2 ∗ P + β3 ∗ P + β4 ∗ P + β5 ∗ P

(9)

The established model was tested with sample data and evaluated by field experts, and the results were found to be appropriate.

4 Conclusion In this study, we aim to determine the price by establishing an automatic decision support system. In this direction, it is aimed to make pricing according to price elasticity, considering the economic conditions in different markets. Although price elasticity is a definition based on the relationship between price and number of sales, a statistically significant model was not found within the study, instead a model based on page views is established. Finally, with the established mathematical model, a model that takes into account the company’s constraints and maximizes profits has been created. As a result of this study, it has been determined that factors such as being on the homepage and being displayed at the top the category page are significant factors that affect sales. In future studies, it is suggested to develop a prediction model that takes into account the effects of these factors on sales. Acknowledgements. This work is supported by TUBITAK (The Scientific and Technological Research Council of Turkey) under project number 3190848.

References 1. Kunz, G.: Merchandising: Theory, Principles, and Practice. Fairchild Books, New York (2005) 2. Tek, Ö.B., Özgül, E.: Modern Pazarlama ˙Ilkeleri, Birle¸sik Matbaacılık, ˙Izmir (2005) 3. Berman, B., Evans, J.: Retail Management: A Strategic Approach. Prentice Hall College Div, Upper Saddle River (2004) 4. Turban, E., King, D., Liang, P.L., Turban, D.: Electronic Commerce 2012: Managerial and Social Networks Perspectives. Prentice Hall, Upper Saddle River (2012) 5. Akça, H.: Regülasyon Ekonomisi. Nobel Kitabevi (2007) 6. Gwartney, R.L., Stroup, J.D.: Temel ekonomi, Liberte Yayınları (2008) 7. Forman, H., Hunt, J.M.: Managing the influence of internal and external determinants on international industrial pricing strategies. Industr. Mark. Manag. 34(2), 133–146 (1996). Forman, H., Hunt, J.M. (2005) 8. Kotler, P., Armstrong, G.: Principles of Marketing. Prentice-Hall, Upper Saddle River (2006) 9. Nagle, T.T., Holden, R.K.: The Strategy and Tactics of Pricing. New Jersey Pearson, Upper Saddle River (2002) 10. Stiving, M.: Impact Pricing: Your Blueprint for Driving Profits. Irvine Entrepreneur Press, Irvine (2011) 11. Sherlekar, S., Prasad, K.N., Victor, S.S.: Principles of Marketing. IND Himalaya Publishing House, Mumbai (2010) 12. Chung, K.Y.: Hotel room rate pricing strategy for market share in oligopolistic competitioneight-year longitudinal study of super deluxe hotels in Seoul. Tourism Management, Seoul (2000) 13. Blythe, J.: Essentials of Marketing. Pearson Education Limited, Gosport (2005)

Intelligent Approach Based on Group Method of Data Handling to Predict Economic Growth Through Entrepreneurship and Innovativeness with Time Series 1(B) and Melis Zeren2 Özlem Senvar ¸ 1 Department of Industrial Engineering, Marmara University, Istanbul, Turkey

[email protected], [email protected] 2 Institute of Pure and Applied Sciences, Marmara University, Istanbul, Turkey

Abstract. Entrepreneurship and innovativeness are the key factors for determination of economic viability along with preservation of sustainability. Entrepreneurship with innovation is a crucial part of economic improvement and growth and substantial for the steady dynamism of the modern economy. Since entrepreneurship and innovation generate value for the economy through creative destruction, their impacts on GDP growth (annual %) can be examined through anticipatory capacities. Brexit is expected to have serious consequences of generating international entrepreneurship and business opportunities for companies worldwide. This study aims to anticipate economic growth through entrepreneurial activities and innovativeness before and after the Brexit decision. In this study, New Business Density and R&D Expenditure (% of GDP) are handled to make anticipations regarding annual GDP Growth (%) via time series forecasting algorithm. We consider Iceland, Ireland and the UK before and after Brexit decision. Iceland and Ireland are taken into account due to their close relationships with the UK. Keywords: Entrepreneurship · Innovativeness · Economic growth · Anticipation · Group Method of Data Handling (GMDH)

1 Introduction The global economy is characterized by pervasive, profound technological differentiation and accompanying social changes. For example, the recent event, Brexit, is anticipated to have profound economic consequences both for the UK and the rest of the world. Anticipations about the local impact of Brexit are suggested via two different consequences: the bad scenario and the good scenario. Brexit was officially initiated when the UK government notified its exit from the European Union on 29 March 2017, after the 23 June 2016 plebiscite.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 982–989, 2022. https://doi.org/10.1007/978-3-031-09173-5_112

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Some researchers suggest that the consequences of economic nationalism will be negative, both socially and economically. Other scientists suggest that the results of independence will be positive for the UK economy. For example, Dhingra et al. (2017) predict the average effects of Brexit on the UK to be negative due to the spatial and sectoral specialization of economic areas. The UK’s overall GDP is anticipated to decline while some sectors are expected to be better off (Felbermayr et al. 2017). Research on the effects of Brexit is generally made on financial indicators such as FDI, inflation, market integration, tariff barriers etc. Nevertheless, not many studies show regard to entrepreneurship and innovation. We propose that besides the negative effects of Brexit, there might be positive impacts on the UK economy via fostered economic activities. Accelerated economic activities also mean new businesses registered and new innovative endeavors with new ideas and inventions. The economy might compensate for the negative impacts through proliferating new businesses and innovations. The impact of Brexit might not be as negative as the pessimistic view foresees. This study handles new business density and R&D Expenditure (% of GDP) are handled to make anticipations regarding annual GDP Growth (%) via time series forecasting algorithm. New Business Density, measured by new registrations per 1,000 people between ages 15 and 64, is fundamentally the prevalence rate of individuals in the working-age population who are actively involved in starting a business as new entrepreneurs or owner-managers of new firms. And following the World Bank and OECD, we employ Research and Development Expenditure (% Of GDP) as the indicator for innovativeness. R&D spending as a percentage of Gross Domestic Product is referred to as the current and capital expenditure on R&D carried out by all resident research institutes, companies, government laboratories and universities, etc., in a country. It involves R&D funded by foreign investments but excludes domestic funds made outside of the domestic country (OECD 2019). The organization of this research paper is given as follows: In section two, we consider related literature. The next section introduces the Group Method of Data Handling, displaying also the relevant algorithm. The fourth section reveals the results of the research demonstrating the output tables and prediction graph. And finally, the fifth section discusses the conclusions of this research, including suggestions for future research.

2 Literature Review Traditional literature states that entrepreneurship fosters innovation and innovations promote economic growth. Furthermore, economic growth stimulates further innovation and also encourages entrepreneurial activity. Beugelsdijk (2007) subsequently relates entrepreneurial culture to innovativeness and economic growth in 54 European regions. Tang and Koveos (2004) employ Global Entrepreneurship Monitor (GEM) data to reveal the impact of entrepreneurship, as defined by new business generation, in confluence with innovation, on economic growth at the macro level. Galindo and Méndez-Picazo (2013) analyze the relationship between innovation and economic growth following the Schumpeter approach with the consideration of entrepreneurship activity. Wong et al.

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(2005) utilize overall Total early-stage Entrepreneurial Activity (TEA), necessity TEA, high growth potential TEA and opportunity TEA as separate determinants by employing an augmented Cobb–Douglas production function to explore economic growth. It is desirable to predict economic growth, understand the current and past economic performance of countries, and make plans for the future (Stimson et al. 2006). There are numerous ways to prognosticate the future, and simple protrusions of recent trends, for illustration, tell us both veritably little about the present and not important about the future. On the other hand, analytical forecasting modeling that attempts to sort out the main influences that are likely to shape the future can deepen our understanding of the mechanisms driving economic growth. Although the forecasts involve errors, a good model allows analysts to review a forecast’s strengths and limitations and to identify specific shortcomings that contributed to the gap between predictions and ultimate outcomes. Technology forecasting is handled as foresight, which is equivalent to a bundle of systematic efforts to look ahead and to choose more effectively. Foresight considers that there is not a single future. That is to say, depending on action or non-action at present, many futures are possible, but only one of them will happen. In particular, technology and innovation policies select a desirable future and facilitate realizations. Foresight is the process involved in systematically attempting to look into the longer-term future of economic growth, innovation, and entrepreneurship with the aim of identifying the areas of strategic research and the emerging policies as well as technologies likely to yield the greatest economic and social benefits (Howland and Voss 2003). Adams et al. (2009) emphasize anticipation with its epistemic value of a virtue emerging through actuarial saturation as the sciences of the actual are displaced by speculative forecasts.

3 Group Method of Data Handling (GMDH) The Group Method of Data Handling (GMDH) was introduced by Ivakhnenko (1968). GMDH can be applied to perform time-series prognosticating problems. For (giving level) considerably noisy data, GMDH algorithms based on external criteria are better than statistical methods and neural networks Lepoutre et al. (2013). Therefore, GMDH is a good method to solve the problem of noisy time series prediction (Howland and Voss 2003; Yang et al. 2009). GMDH can be considered as an alternative to the conventional statistical approach. It determines the model of the optimal complexity from the given class of models based on experimental data. GMDH employs two or more subsets from an existing dataset for model creation, selection, and validation. It takes into account in-definiteness concerning features of source data automatically (Fig. 1).

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Multivariate Time Series Data Potential input variables for GMDH R1 Feature Selection

Residual Extraction with Traditional TS Forecasting Methods

Useful input variables for GMDH R2 Data Preparation for GMDH Inducing best model

Residual extraction

GMDH modeling Fitted model forecast results

Visualization and applications

Accuracy evaluation

Performance errors

Benchmarking

Fig. 1. The Operational Flow of the Residual-Feedback GMDH Method (Fong et al. 2012).

4 Applications and Results This study shows evidence that entrepreneurship has a positive and significant effect (alpha = 0.10) and innovation has a negative and significant effect on GDP Growth (Annual %) after Brexit in the UK. In Ireland, the same goes for the time interval before Brexit. In Iceland, entrepreneurship and innovation don’t seem to have a statistically significant impact on annual GDP growth. Additionally, GDP Growth (Annual %) shows a negative correlation with entrepreneurship activities and a positive correlation with innovation. However, entrepreneurship and innovation exhibit a small negative correlation with each other in the UK. The same goes for Ireland, but Iceland shows opposite correlative results. Table 1, 2, 3, 4, 5, and 6 exhibit the results of time series and correlation analyses. Figure 2 shows the results of annual GDP Growth (%) forecasts made via the GMDH time series algorithm. Evidence shows that the GDP growth of the UK tends to have a negative slope until 2029 and a steep increase right after that year. These results might be related to the negative effects of Brexit on economic growth through entrepreneurship and innovation.

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Iceland-time series before Brexit

R-squared: 0.0061

Dependent variable: GDP growth (annual %) Variable

Coefficient

New business density

0.0178

R&D expenditures (% of GDP) const

p-value 0.974

−0.737

0.894

4.628

0.769

Iceland-time series after Brexit New business density

R-squared: 0.7609 0.892

0.350

R&D expenditures (% of GDP)

−0.864

0.419

onst

−5.229

0.602

Table 2. Correlation analysis for Iceland Iceland-correlation analysis GDP growth (annual New business density R&D expenditures %) (% of GDP) GDP growth (annual %)

1.0000

New business density

0.3534

1.0000

R&D expenditures (% −0.6000 of GDP)

0.3849

1.0000

Table 3. Time series analysis of Ireland before and after Brexit Ireland-time series before Brexit

R-squared: 0.3925

Dependent variable: GDP growth (annual %) Variable New business density R&D expenditures (% of GDP) const

Coefficient

p-value

0.8772

0.087*

−16.6660

0.066*

22.7994

0.067*

Ireland-time series after Brexit New business density R&D expenditures (% of GDP) const

R-squared: 0.5969 −4.2747

0.806

−29.0794

0.612

−219.8975

0.613

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Table 4. Correlation analysis for Ireland Ireland-correlation analysis GDP growth (annual New business density R&D expenditures %) (% of GDP) GDP growth (annual %) New business density

1.0000 −0.7464

1.0000

0.6329

−0.9394

R&D expenditures (% of GDP)

1.0000

Table 5. Time series analysis of UK before and after Brexit UK-time series before Brexit

R-squared: 0.3172

Dependent variable: GDP growth (annual %) Variable

Coefficient

p-value

New business density

−0.2131

0.283

R&D expenditures (% of GDP)

−8.7565

0.575

const

17.0201

0.483

0.2019

0.071*

−0.5161

0.063*

9.2409

0.054*

Ireland-time series after Brexit New business density R&D expenditures (% of GDP) const

R-squared: 0.9946

Table 6. Correlation analysis for UK UK-correlation analysis GDP growth (annual New business density R&D expenditures %) (% of GDP) GDP growth (annual %) New business density R&D expenditures (% of GDP)

1.0000 −0.7499

1.0000

0.6709

−0.0181

1.0000

Table 7 reveals accuracy levels of the GMDH predictions with an R-square of 0.9809 and a correlation of 0.9912.

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Fig. 2. UK-GDP growth (annual %) forecasts of UK via GMDH ALGORITHM

Table 7. Accuracy of GMDH predictions

5 Conclusion From theoretical and empirical points of view, the relationship between innovations, entrepreneurship and economic growth has been analyzed frequently in the literature. As a matter of fact, greater entrepreneurship and innovation enhance economic activity. The risk management function affects both innovation and entrepreneurship. Predicting economic growth by taking into account innovation and entrepreneurship is vital for proactive policymaking on economic growth. In this regard, anticipating pitfalls in terms of innovative entrepreneurship must be considered by decision-makers for robust strategic planning for economic growth. This study analyzes the UK’s economic growth before Brexit and economic growth potential after Brexit for a period of 12 years. It implements time series and correlation analysis and employs the GMDH algorithm to make anticipations about the future economic performance of the UK. Evidence shows that the UK’s economic growth should carry a steep downslope after Brexit and this result might be related to the decaying of innovative activities. The decay of innovation might well be connected to the newly imposed barriers to international trade and immigration. Consequently, consistent with the literature, Brexit is anticipated

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to have negative impacts on the economic growth of the United Kingdom. Future research might regard different state-of-the-art machine learning algorithms employing varying innovation metrics along with a broader country set.

References Adams, V., Murphy, M., Clarke, A.E.: Anticipation: technoscience, life, affect, temporality. Subjectivity 28(1), 246–265 (2009) Beugelsdijk, S.: Entrepreneurial culture, regional innovativeness and economic growth. J. Evol. Econ. 17(2), 187–210 (2007) Dhingra, S., Machin, S., Overman, H.: Local economic effects of Brexit. Natl. Inst. Econ. Rev. 242(1), R24–R36 (2017) Felbermayr, G., Fuest, C., Gröschl, J.K., Stöhlker, D.: Economic effects of brexit on the European economy (No. 4). ifo Institute-Leibniz Institute for Economic Research at the University of Munich (2017) Fong, S., Nannan, Z., Wong, R.K., Yang, X.S.: Rare events forecasting using a residualfeedback GMDH neural network. In: 2012 IEEE 12th International Conference on Data Mining Workshops, pp. 464–473. IEEE, December 2012 Galindo, M.Á., Méndez-Picazo, M.T.: Innovation, entrepreneurship and economic growth. Manag. Decis. 51(3), 501–514 (2013) Howland, J.C., Voss, M.S.: Natural gas prediction using the group method of data handling. In: 7th International Conference on Artificial Intelligence and Soft Computing, Banff, Alberta, July 2003 Ivakhnenko, A.G.: the group method of data of handling-a rival of the method of stochastic approximation. Soviet Autom. Control 1(3), 43–55 (1968) Lepoutre, J., Justo, R., Terjesen, S., Bosma, N.: Designing a global standardized methodology for measuring social entrepreneurship activity: the Global Entrepreneurship Monitor social entrepreneurship study. Small Bus. Econ. 40(3), 693–714 (2013) OECD Homepage: Gross domestic spending on R&D (indicator) (2019). https://doi.org/10.1787/ d8b068b4-en. Accessed 14 Aug 2019 Stimson, R.J., Stough, R.R., Roberts, B.H.: Regional Economic Development: Analysis and Planning Strategy. Springer, Cham (2006). https://doi.org/10.1007/3-540-34829-8 Tang, L., Koveos, P.E.: Venture entrepreneurship, innovation entrepreneurship, and economic growth. J. Dev. Entrep. 9(2), 161 (2004) Wong, P.K., Ho, Y.P., Autio, E.: Entrepreneurship, innovation and economic growth: evidence from GEM data. Small Bus. Econ. 24(3), 335–350 (2005) World Bank (2019). https://datatopics.worldbank.org/world-development-indicators/themes/eco nomy.html. Accessed 15 Feb 2022 Yang, C.H., et al.: Constructing financial distress prediction model using group method of data handling technique. In: 2009 International Conference on Machine Learning and Cybernetics, vol. 5, pp. 2897–2902. IEEE, July 2009

Intelligent Word Embedding Methods to Support Project Proposal Grouping for Project Selection Meltem Yontar Aksoy1(B) , Mehmet Fatih Amasyali2 , and Seda Yanık1 1 Istanbul Technical University, Maçka, Istanbul, Turkey

[email protected] 2 Yildiz Technical University, Be¸sikta¸s, Istanbul, Turkey

Abstract. Project proposal selection for allocating the fund is a critical decisionmaking process in government/private funding agencies, universities, and research institutes. Project proposal grouping according to their similarities is an essential procedure in the project selection process and is done to simplify the work that follows, such as reviewer assignment and evaluation of projects. Current approaches to grouping proposals are primarily based on manual matching of similar topics, discipline areas, and keywords declared by project applicants. When the number of proposals increases, this task becomes complex and takes too much time. Furthermore, because of their subjective viewpoints and potential misinterpretations, applicants frequently fail to select the correct research field or keywords for their proposals. Due to time constraints, a lack of understanding of the proposal’s content, divergent perspectives, and incomplete information, proposals are misclassified, resulting in decreased evaluation quality. This article discusses how to effectively use rich information in the abstract and title of Turkish proposals by utilizing word embedding models. In the proposed method, texts are vectorized using the FastText, BERT and TF-IDF algorithms. The presented method is validated based on the proposals submitted to the Istanbul Development Agency. Experiments indicate that generated word embeddings can effectively represent proposal texts as vectors and be used as input for clustering or classification algorithms. In this way, proposal grouping can be conducted more efficiently, accurately, and without any loss of meaning. Keywords: Project proposal grouping · Word embedding · FastText · BERT · TF-IDF

1 Introduction Project proposal selection for allocating the fund is a critical decision-making process in government/private funding agencies, universities, and research institutes. Countless efforts are made to guarantee proposal selection efficiency and accuracy because of limited resources. Therefore, organizations have to deal with various strategic, tactical, and operational issues for project selection. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 990–998, 2022. https://doi.org/10.1007/978-3-031-09173-5_113

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Different funding organizations receive project proposals from individuals or institutions for grant allocation within the scope of various financing programs. Project proposals go through the selection and evaluation process. This process evaluates project proposals against the evaluation criteria specified in the financial support program and determines which projects are eligible for grants. Figure 1 illustrates the general project selection process proposed by Rathore et al. [1]. While this workflow is specific to research projects, it is a general methodology for how various funding organizations select projects for grant allocation. The project selection process begins with a call for proposals from any funding organization. Following that, these organizations receive proposals from a variety of individuals and institutions. Additionally, received project proposals are categorized according to the techniques or problems they address. Following categorization, proposals are assigned to numerous experts in the relevant field for evaluation. Experts review and evaluate proposals in accordance with the financing organization’s rules and criteria. The review results are collected and sorted according to various methods [2]. In support of these evaluation results, the panel discusses the proposal’s significance and then makes the final decision. The final decision may include whether proposals are eligible for funding or not, as well as the fund’s maximum size.

Call for proposals

Receive proposals

Categorize proposal

Assign to reviewer for evaluation

Receive evaluation result

Panel discussion & evaluation

Final panel decision

Allocating fund to finalized project proposals

Fig. 1. General research project selection process [1].

Grouping project proposals based on their similarities is a critical step in the project selection process. This is done to streamline the process of assigning reviewers and evaluating projects. Currently, grouping proposals is accomplished primarily through manual comparison of similar topics, discipline areas, and keywords declared by project applicants. As the number of proposals increases, this task becomes more complicated and time-consuming. Additionally, applicants frequently have difficulty selecting the precise research field or keywords for their proposals due to their subjective viewpoints and potential misinterpretations. Because of time constraints, a lack of understanding of the proposal’s content, differing perspectives, and incomplete information, proposals are misclassified, resulting in decreased evaluation quality. This study examines the grouping of project proposals, which is a critical step in the project selection process and is typically performed manually. Proposals should be automatically classified and/or clustered to effectively use the rich information of the project proposals and increase the efficiency and effectiveness of the project selection process. Since machine learning algorithms work with numbers, inputs can be created with numerical representation of words. Thus, vectorizing project proposal texts is the

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initial but critical step in the process of project categorization. Textual properties must be represented numerically in order to perform learning-based Natural Language Processing (NLP) tasks. The term “word representation” or “word embedding” is used in the literature to refer to this process. This approach, in which words, sentences, or documents are converted to number vectors, is critical for modeling natural language and feature engineering in natural language processing studies. The quality of such representations significantly impacts the success rates of documents in classification, clustering, machine translation tasks, etc. This study aims to demonstrate how to effectively use rich information in the abstract and title of Turkish proposals by utilizing word embedding models. The proposed method has been tested and validated based on the proposals submitted to the Istanbul Development Agency (IDA). In contrast to previous research, this study employs highly effective textual feature extraction techniques such as BERT, FastText and TF-IDF. This paper is organized as follows: The following section discusses related research on project proposal groping. The third section presents the research methodology. The fourth section summarizes the dataset, the empirical analysis, and the findings. The fifth section contains the conclusion and discussion of the findings.

2 Related Works The grouping of project proposals is critical during the project selection process. Therefore, some approaches have been proposed to solve the various problems in the proposal grouping procedure. Fan et al. [3] created a hybrid method that combines knowledge rules and genetic algorithms. The study’s objective was to classify the proposals based on the applicant’s characteristics, such as gender and academic title, and to ensure that the number of groups was as close to one as possible while maintaining diversity. The technology called ontology-based text mining has often been used to automatically cluster project proposals. Ontology is the systematic identification of concepts and relationships within a field, as well as the representation of data that can be used to facilitate communication between actors from disparate fields. Ma et al. [4] described how they combined ontology-based text mining with statistical methods and optimization models to cluster project proposals submitted to the Chinese National Natural Science Foundation. Xu et al. [5] proposed an ontology-based frequent set method (OFIM) for grouping project proposals that combines an ontology-based text mining method (OTMM) and a frequent set of elements. Preethi and Lakshmi [6] proposed a novel approach to clustering Chinese research project proposals based on ontology-based text mining. To classify projects into related disciplines, the fuzzy c-means clustering method was used. Rathore et al. [1] classified research projects on the basis of their ontology. The k-Nearest Neighbor (kNN) algorithm was used to cluster each research proposal class in this study. Patil and Uddin [7] also classified project proposals by research field using ontology keywords. The k-means algorithm is used to cluster the projects in each class. Another study classified proposals according to their discipline areas using an ontologybased text mining approach and a variety of classification algorithms, including Kernel Support Vector Machine (KSVM), Self-Organizing Map (SOM), kNN, and Naive Bayes [8]. Rajkamal [9] clustered proposals and reviewers using an ontology-based text mining approach.

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As seen in studies, classifying or clustering the proposals was generally made according to the keywords and discipline areas. However, keywords and discipline areas may not fully reflect the project proposals. For this reason, benefiting from the rich information in the texts of the project proposals will provide much more accurate results. Three studies were identified during the literature review that attempted to classify projects by identifying project characteristics using the full text or a portion of the text of the project with the help of NLP methods. Some studies obtain features from the proposal’s abstract using the TF-IDF [10]. The other studies used the Latent Dirichlet Allocation (LDA) to discover the information in project proposals’ documents and determine the terms representing each document [11, 12]. This study aims to demonstrate how various word embedding methods can be used to represent the abstract and title of proposals in Turkish. In contrast to previous research, this study employs the most widely used textual feature extraction techniques, including BERT and FastText. Along with recently developed neural network-based methods, the text is represented using the TF-IDF model, a classic frequency-based word representation method. The results of three distinct embedding methods are compared using data visualization.

3 Methodology Word embedding is a technique for constructing a real-valued vector representation of words by embedding their semantic and syntactic meanings from a sizeable unlabeled corpus. It is a powerful tool that is widely used in modern natural language processing tasks such as document classification or clustering, question answering, information retrieval, and machine translation. The quality of word vectors highly affects the success rates on these tasks. Word embedding methods are classified into three groups which are frequency-based word embedding, static word embedding, and contextualized word embedding, respectively. Frequency-based word embedding methods, also known as traditional methods, are based on determining the frequencies of words in documents. With the deep learning-based word embeddings methods developed in recent years, the disadvantages of frequency-based methods have been tried to be eliminated. These techniques, referred to as static or prediction-based embedding, can be used to encode the syntax and semantic properties of words. They can also encode the morphologies of terms because they take sub-word elements into account (character n-grams). Static word embedding techniques are based on simple neural networks and do not consider the possibility of a word having multiple meanings in context. Regardless of how a term is used, it always has the same representation. As a result, static representations cannot resolve the polysemy problem. Contextualized word embedding methods that use extremely deep architectures compared to static word embedding algorithms can generate unique representations of words within the corpus in which they occur. In general, static word representation methods use a fixed dense vector to represent the word, whereas contextual word representation methods use contextual information. The purpose of this study is to examine the effect of three different word embedding methods on the representation of Turkish texts: TF-IDF, FastText, and BERT. The following title summarizes the techniques used in this study.

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3.1 TF-IDF (Term Frequency Inverse Document Frequency) The TF-IDF algorithm calculates the relative frequency of words in a document based on their inverse ratio across the entire data set. This calculation, intuitively, determines the relevance of a particular term to a particular document. Terms that are unique to a single or small group of documents have a higher TF-IDF value than generic terms. 3.2 FastText FastText is a word representation method developed at Facebook’s AI Research-FAIR lab in 2016 to extend the Word2vec [13]. Instead of using words in the corpus, FastText uses n-grams. FastText uses the subword information explicitly; therefore, the embedding of rare or unknown words can still be represented well. FastText outperforms popular word embedding models with its large vocabulary, low sensitivity to incorrect terms, and multilingual support. FastText provides pre-trained word representation data for 294 different languages, including Turkish. 3.3 BERT (Bidirectional Encoder Representation from Transformers) Along with traditional dense word vector representations, this article employs BERT to construct word embeddings. BERT was introduced as a pre-trained transformer encoder model by the Google AI research group in 2018 [14]. BERT is a ground-breaking algorithm in deep learning due to its bidirectional architecture and structure that combines Masked Language Model and Next Sentence Prediction approaches. It outperforms older contextualized methods significantly. The BERT algorithm is capable of processing a large amount of text and is also easier to use than pre-trained models. BERT-Base and BERT-Large were presented in the original BERT article as two fundamental models with distinct hyperparameters. Due to the open-source nature of the BERT model, it can be configured for languages other than English, which is the native tongue. Stefan Schweter created the BERTurk model specifically for the Turkish language, based on the Turkish OSCAR and OPUS corpora, Turkish Wikipedia, and Turkish news documents shared by Kemal Oflazer.

4 Empirical Analysis The empirical analysis was conducted to validate the effectiveness of the proposed method using real data from IDA. IDA invites qualified applicants to submit proposals for projects that align with previously-identified themes and requirements as part of a specific support program. The dataset of this study contains 2434 project proposals submitted to IDA between 2012 and 2021. These project proposals were submitted in four themes: innovation, entrepreneurship, creative industries, and children and youth. Only the abstract and titles were used from the project proposal’s full text. The use of full text was deemed unnecessary due to the length of the project proposal texts. Table 1 summarizes the dataset’s statistical characteristics.

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Table 1. Statistical information of dataset. Number of documents

2434

Maximum document length

817

Average document length

277,728

Total number of words

675990

Number of individual words

54369

Average word length

7,460404

Before constructing word embeddings, the following preprocessing steps are applied to the dataset to increase representation quality: (i) spelling errors are corrected, (ii) unnecessary gaps have been cleared, (iii) uppercase letters are converted to lowercase letters, (iv) e-mail addresses, URLs, etc. are removed from the text, (v) all punctuation has been cleared, (vi) Turkish stop words such as “ve”, “çünkü”, “belki” that do not affect the sense of the sentence are removed from the text. Python NLTK library is used to extract stop words. In addition, Turkish Stemmer, developed as a stemming library in the Python programming language, was used to perform the stemming process for only TF-IDF. The cloud-based Google Colab is used for the analysis, and the coding part of the research is developed entirely in Python software. 4.1 Empirical Results The preprocessed texts are separately vectorized with BERT and FastText pre-trained models. FastText pre-trained model for Turkish has a 300-dimensional attribute matrix. The architecture of the BERT-base-turkish-cased contains 12 layers, each of which contains 768 layers of information about the word. Additionally, TF-IDF is used as a more traditional method for obtaining the dataset’s vector representation. Recently proposed word embedding approaches are able to provide meaningful, measurable word representations of textual data that can be used in various text mining tasks. Since this type of data is frequently multi-dimensional, it isn’t easy to intuitively comprehend the effectiveness of the word embedding methods with graphs. t-distributed stochastic neighbor embedding (t-SNE) algorithm, introduced by van der Maaten and Hinton [15], can be used to create an interpretable chart. t-SNE is an unsupervised, nonlinear technique used mainly for visualizing high-dimensional data. This study uses t-SNE to visualize high-dimensional BERT, FastText, and TF-IDF matrices in 2D space. The visualization can aid in comprehending how words are represented and in interpreting relationships between extracted vectors from texts prior to their use in machine learning algorithms.

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The results are presented in Fig. 2, 3, and 4. Each point in the figures represents a project proposal. The four colors depicted in the Figures illustrate the IDA-determined themes. The project proposals are submitted in line with previously-designated themes. Accordingly, the color red denotes projects related to the creative industries, the color green represents projects related to innovation, the color blue denotes projects related to children and youth, and the color purple indicates projects related to entrepreneurship. When Fig. 2, 3, and 4 are examined according to four determined clusters, it can be said that the BERT, FastText, and TF-IDF algorithms can represent text consisting of project abstracts and titles vectorially well. The BERT and FastText word embedding methods generate multi-dimensional vectors with 768 and 300 dimensions, respectively. These multi-dimensional vectors attempt to depict the relationship between two words. TF-IDF vectorizer creates a sparse and large matrix where each word maps to just a single value captures no meaning. In this study, the vector size of the TF-IDF model is of length 21191. As pre-trained models, BERT and FastText techniques can be compared in terms of computing time for the fine-tuning process. Due to the complex fine-tuning process, BERT encodes documents at 14 min 35 s. FastText performs better, having a much faster computing time of 2 min 1 s. Considering the large vector size of the traditional TF-IDF method and the high computing time of BERT, it is understood that the Fasttext method can be implemented much more practically and fast.

Fig. 2. Visualization of BERT word embeddings in 2D space.

Fig. 3. Visualization of FastText word embeddings in 2D space.

Fig. 4. Visualization of TF-IDF word embeddings in 2D space.

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5 Discussion and Conclusions This article discusses how to effectively use rich information in the summary and title of proposals written in Turkish using word embedding models. Experiments demonstrate that word embeddings generated with FastText, BERT, and TF-IDF can accurately represent proposal texts. FastText, on the other hand, encodes documents much more practically, with a shorter computation time and a smaller vector size. In future research, the obtained vectors can be used as input for clustering and classification algorithms to group project proposals automatically and efficiently. The proposals can be easily classified using classification algorithms into predefined clusters. This way, proposal grouping can be accomplished more efficiently, accurately, and without distorting the text’s meaning. Additionally, the proposed word embedding approach could be extended to other funding agencies that face the same problem of proposal grouping in IDA.

References 1. Rathore, D.S., Jain, R.C., Ujjainiya, B.: A text mining method for research project selection using kNN. In: International Conference on Green Computing, Communication and Conservation of Energy, pp. 900–904. IEEE, Chennai, India (2013) 2. Cook, W.D., Golany, B., Kress, M., Penn, M., Raviv, T.: Optimal allocation of proposals to reviewers to facilitate effective ranking. Manage. Sci. 51(4), 655–661 (2005) 3. Fan, Z.P., Chen, Y., Ma, J., Zhu, Y.: Decision support for proposal grouping: a hybrid approach using knowledge rule and genetic algorithm. Expert Syst. Appl. 36(2), 1004–1013 (2009) 4. Ma, J., Xu, W., Sun, Y.H., Turban, E., Wang, S., Liu, O.: An ontology-based text-mining method to cluster proposals for research project selection. IEEE Trans. Syst. Man Cybern. Part A Syst. Hum. 42(3), 784–790 (2012) 5. Xu, W., Xu, Y., Ma, J.: An ontology-based frequent itemset method to support research proposal grouping for research project selection. In: Annual Hawaii International Conference on System Sciences, pp. 1174–1182. IEEE, Wailea, HI, USA (2013) 6. Preethi, T., Lakshmi, R.: An implementation of clustering project proposals on ontologybased text mining approach. In: International Conference on Information Communication and Embedded Systems, pp. 547–550. IEEE, Chennai, India (2013) 7. Patil, S.S., Uddin, S.A.: Research paper selection based on an ontology and text mining technique using clustering. J. Comput. Eng. 17(1), 65–71 (2015) 8. Saravanan, R.A., Rajesh Babu, M.: Enhanced text mining approach based on ontology for clustering research project selection. J. Ambient. Intell. Humaniz. Comput. 1–11 (2017). https://doi.org/10.1007/s12652-017-0637-7 9. Rajkamal, S.: Selecting reviewers for research by clustering proposals using expectation maximization clustering algorithm.In:International Conference on Technical Advancements in Computers and Communication, pp. 56–60. IEEE, Melmaurvathur, India (2017) 10. Wang, Y., Xu, W., Jiang, H.: Using text mining and clustering to group research proposals for research project selection. In: Annual Hawaii International Conference on System Sciences, pp. 1256–1263. IEEE, Kauai, HI, USA (2015) 11. Safi’ie, M.A., Utami, E., Fatta, H.A.: Latent Dirichlet Allocation (LDA) model and kNN algorithm to classify research project selection. In: IOP Conference Series: Materials Science and Engineering, vol. 333. IOP Publishing (2018)

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12. Xu, Y., Zuo, X.: A LDA model-based text-mining method to recommend reviewer for proposal of research project selection. In: 13th International Conference on Service Systems and Service Management, pp. 1–5. IEEE, Kunming, China (2016) 13. Bojanowski, P., Grave, E., Joulin, A., Mikolov, T.: Enriching word vectors with subword information. Trans. Assoc. Comput. Linguist. 5, 135–146 (2017) 14. Devlin, J., Chang, M.W., Lee, K., Toutanova, K.: BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding. arXiv Preprint, pp. 1–16 (2019) 15. van der Maaten, L., Hinton, G.: Visualizing data using t-SNE. J. Mach. Learn. Res. 9, 2579– 2605 (2008)

Comparative Study of the Firefly Algorithm and the Whale Algorithm Hubert Zarzycki(B) General Tadeusz Kosciuszko Military Academy of Land Forces in Wroclaw, Wroclaw, Poland [email protected]

Abstract. The firefly algorithm is one of the relatively new algorithms based on swarm intelligence. This algorithm has various applications, it is especially good at solving combinatorial optimization problems. Contemporary research on optimization algorithms assumes the introduction of frequent modifications in order to increase the efficiency of algorithms and adjust their operation to the complexity of a given research problem. In this work, the firefly algorithm and the whale algorithm were subjected to the research procedure in order to solve an optimization problem. The achieved results enabled the comparison of both methods. Keywords: Firefly algorithm · Whale algorithm · Optimization · Swarm intelligence · Wireless sensor network

1 Introduction For centuries, mankind has been observing nature and trying to understand how it works. Along with the progress of science, it manages to explain and describe phenomena occurring in nature in a more and more detailed way. Thanks to evolution, nature created certain mechanisms on the basis of which the world as we know it functions. Over hundreds of millions of years, animals and plants have unknowingly developed more and more optimal approaches to solving complex problems. The world of nature that surrounds us is full of natural solutions, empirical data and even algorithms, the transfer of which into practice brings measurable benefits. In modern times, with the development of computerization and the increasing access to information, it has become possible to use data, mechanisms and algorithms inspired by phenomena occurring in nature. As a result, many complex problems can be solved in a more optimal way. Among them there are also such issues that so far have not had a solution or for which the computation time was beyond the acceptable range. Biologyinspired algorithms are heuristic or meta-heureistic algorithms. This means that they have a certain element of randomness in them, which means that the result may be different for subsequent runs of the algorithm. Thus, they differ from the deterministic algorithms used for decades in computer science, which always return the same result for given data. In the case of (meta) heuristic algorithms, the randomness of the results is desirable, thus it is possible to generate results even for problems that do not have a © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 999–1006, 2022. https://doi.org/10.1007/978-3-031-09173-5_114

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known solution or it is very difficult to find a solution. Such an issue is, for example, the N-complete traveling salesman problem. This article presents and compares two modern algorithms inspired by nature. 1.1 Swarm Intelligence Swarm intelligence (SI) is part of solutions inspired by nature. Swarm intelligence uses the phenomenon of cooperation between many natural agents (e.g. an ant colony) in order to increase the chance of survival. Characteristic is the lack of a commanding body or a predefined manner of agents’ conduct. Nevertheless, the cooperation of many agents who effectively perform simple functions leads to the solution of complex problems. Swarm intelligence algorithms include the ant (ACO) and bee (ABC) algorithms, the bat algorithm (BA) and particle swarm optimization (PSO). Currently, some of the newest include the firefly, whale, cuckoo algorithms presented in the article. The author of this article has extensive experience with optimization methods [5], fuzzy numbers [6–9], control systems [11], nature-inspired algorithms [10], and in particular with swarm intelligence algorithms. An original comparative study of the firefly (FA) and the whale (WOT) algorithm will be carried out in this paper.

2 Firefly Algorithm The firefly algorithm belongs to the group of meta-heuristic algorithms [3]. It was first developed in 2008 by Xin-She Yang. The principle of operation of the algorithm reflects the method of communication of these insects, the so-called bioluminescence. Bioluminescence is a unique feature that allows living organisms to produce light. In the natural environment, this method is used to communicate, warn against dangers and to attract each other to mating. These insects transmit information to each other in the form of light signals, flashing in appropriate sequences. In addition to the blink sequence and the light intensity, the distance between the fireflies is also important, because the brightness of the light decreases with the distance. This means that fireflies are typically only attracted to those that are only a certain distance away, most often closest to the sender of the signal. The method of operation of the firefly algorithm assumes that each firefly can be attracted by all other fireflies, and the strength of this interaction is directly proportional to the light intensity and inversely proportional to the distance between the insects. In practice, this means that the firefly will always look for the brightest firefly and ignore the others. The most intensely luminous insect will move randomly and attract all other individuals to itself until the condition terminating the algorithm’s operation is reached, which is a defined number of iterations. The schematic diagram of the algorithm is presented below: The most important steps of the algorithm: 1. The fireflies are placed in space and the intensity of their illumination is determined. 2. Fireflies search the area around them for a brighter light source.

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3. If the brightest light source is identified, the fireflie moves towards that light. If not, it moves randomly. 4. The luminous intensity of fireflies is being updated. 5. If the terminating condition (last iteration) is not reached, the algorithm repeats the operation (Fig. 1).

START Initiation of the firefly population Computing the optimum of each firefly and finding a global optimum If opt (j)> opt (i) then move Firefly i towards Firefly j Calculating the attractiveness of fireflies and updating the luminous intensity

Last iteration?

END Fig. 1. Schematic diagram of the firefly algorithm (based on [3]).

3 Whale Algorithm (WOA) The Whale Optimization Algorithm (WOA) is a relatively new optimization algorithm. The authors of the algorithm are Seyedali Mirjalili and Andrew Lewis, who developed it in 2016. One of the largest representatives of whales are humpback whales, which, despite their large size, feed mainly on krill and small fish. They developed a hunting method that inspired Mirjalili and Lewis [4] to develop the WOA algorithm. In the wild, whales prefer to hunt close to the surface. In 2011, it was noticed that humpback whales

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shepherd their prey near the surface of the water, creating a spiral formation of air emitted from the nostril. The organisms that humpback whales hunt are so small that a network of air bubbles surrounds them and pushes them upwards, where they then become easy prey for whales. This unusual behavior has not been observed in whale species other than humpback whales [4] (Fig. 2).

Fig. 2. The method of whale hunting by creating a spiral network of air bubbles [4]

The method on the basis of which the algorithm was developed consists of three phases. The first step is surrounding the victim (pray). In this step, all agents (humpback whales) move towards the leader, i.e. the agent who found the best solution in this iteration. In the next step, the agent has a choice of two behaviors - tightening the loops around the victim or creating a spiral. Both these behaviors occur simultaneously in nature. For the purposes of efficient operation of the algorithm, one of them is drawn with a probability of 50%. The last phase is to continue searching for a potentially better solution at random by free agents. When the most optimal solution is found or a certain number of iterations is reached, the operation of the algorithm is interrupted and the result obtained is communicated. Below the mathematical formulas concerning the specific phases. Phase I At the beginning, the position of the prey in space is unknown. Humbag whales search for the leader (agent who found the best solution). D = |CX ∗ (t) − X (t)|

A = 2ar − a

X (t + 1) = X ∗ (t) − AD

C = 2r

(1) (2)

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where t - iterative number, X* - best position whale vector, X - whale current vector, r random number [0,1], a - convergence factor (a = 2−2t/tmax ). Phase II At this phase logarithmic spiral position is updated. Narrowing the circular area delimiting the prey. The probability of choosing one of the below methods is 50%.   (3) D = X ∗ (t) − X (t) 

X (t + 1) = D ebl cos(2π l) + X ∗ (t)  X (t + 1) =

X ∗ (t) − AD if p < 0.5 D ebl cos(2π l) + X ∗ (t) if p ≥ 0.5 

(4) (5)

where D - distance between whale and the pray, l - random number [−1, 1], b - a constant defining the shape of a spiral, p - random number [0, 1]. Phase III Phase III depended on the value of parameter A. At this stage, the algorithm does not update the prey-based position. Prey is searched randomly based on the position of individual whales. The goal is to conduct a global search and prevent a fall to a local minimum. D = |CXrand (t) − X (t)|

(6)

X (t + 1) = Xrand (t) − AD

(7)

where Xrand - random positional vector (random whale).

4 Optimizing the Operation of the Wireless Sensor Network Wireless sensor networks are, as the name suggests, networks composed of many interconnected sensors that perform a specific function. They can monitor temperature, movement, humidity and many other phenomena. The problem of a wireless network is quite high power consumption. All hardware sensors must be activated whether or not they receive a signal at the moment. The proposed solution uses the whale algorithm to turn off and on the appropriate nodes in order to minimize energy consumption while maintaining maximum coverage of the monitored space. Each node is the equivalent of a whale and, based on their position and the received signal, the nodes that should be activated at a given moment were calculated. The proposed solution was tested in the form of a simulation in the Java-based Atarraya tool. The nodes imitated the operation of simple sensors with a defined, default energy consumption. The obtained results were compared with the Firefly algorithm.

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5 Analysis of the Obtained Results Regardless of the number of nodes in the network, both the number of active sensors and the energy consumption were lower for the whale algorithm solution. The whale algorithm has already been indicated as one of the best in solving the problem of wireless sensors [1]. The comparison in the application with the firefly algorithm confirms the effectiveness of the WOT algorithm. The results for the whale algorithm are 10 to over 30% better than the FA (Table 1). Table 1. Results data number 1. Network size

Number of active nodes

Energy consumption

WOT

FA

WOT

FA

100

29

41

11326

15801

200

38

53

17643

25319

300

37

52

17371

22596

400

39

54

18283

23833

500

40

56

19274

28553

600

38

52

18967

22617

700

37

51

18298

25696

800

37

52

16926

24778

900

37

56

20556

28687

1000

39

54

17634

24856

In both algorithms, when the network size increases to 100 and 200, there is a visible increase in the number of necessary constraints. Then the number of constraints remains at a similar level, and even drops for network sizes of 700, 800, 900. The whale algorithm can find a more optimal solution for each of the cases (Fig. 3). Here, too, the initial increases in grid size result in a significant increase in energy demand. Then the whale algorithm is able to maintain the energy consumption at a similar level for virtually any size of network except 900. The firefly algorithm optimizes energy expenditure to a lesser extent (Fig. 4). Characteristic for FA is also the fact that for various network sizes there are significant increases (200, 500, 900) and decreases (300, 600, 1000) of energy consumption. In either case, the FA algorithm has worse results than the WOT. The study shows that it is worth looking for different algorithms to solve modern optimization problems related to networks. New algorithms of swarm intelligence, such as TDF, can bring a new quality and perhaps represent the future in the area of sensor networks.

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1005

Number of Active Nodes

60 50 40 30

WOT FA

20 10 0 100 200 300 400 500 600 700 800 900 1000 Network Size

Fig. 3. The number of active nodes for the Firefly algorithm (FA) and the whale optimization algorithm (WOT) [1]

Energy Consumption

35000 30000 25000 20000 15000

WOT

10000

FA

5000 0 Network Size

Fig. 4. The energy consumption for the Firefly algorithm (FA) and the whale optimization algorithm (WOT) [1].

6 Conclusions Biology has found many methods to solve all kinds of natural problems, and people observing it for centuries have noticed that they can use these solutions for their own purposes. Many of these methods have been written in the form of algorithms, and algorithms known for many years, such as the ant or bee colony, are still being improved and updated, while new solutions are constantly discovered, such as the fairly recently developed whale and firefly algorithm. Nature-inspired algorithms are often the only and very good way to solve the most complex optimization tasks. The analytical part of the article presents an example of an unusual application of algorithms. Namely, FA

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and WOT were used to optimize energy consumption and the number of active nodes in wireless sensor networks. The results of the algorithm operation presented in the paper clearly indicate the advantage of the whale algorithm in the tested application. Both in terms of active nodes and the amount of energy used, the WOT algorithm provides solutions better than the FA algorithm by 10 to 30%. Further work may include the comparison of further new swarm intelligence algorithms in the area of wireless sensor network and other optimization problems. It is also worth bearing in mind that swarm intelligence algorithms compare favorably with deterministic algorithms or the brute force method. Therefore, nature-inspired algorithms and especially swarm intelligence algorithms are rapidly gaining popularity in practical applications. With their help, it is possible to obtain optimal solutions to the problem in realistic time and with a reduced amount of resources. In addition, the presented swarm intelligence algorithms are flexible - one can influence their operation in many ways, modifying the appropriate parameters according to the assumptions.

References 1. Ahmed, M.M., Houssein, E.H., Hassanien, A.E., Taha, A., Hassanien, E.: Maximizing lifetime of wireless sensor networks based on whale optimization algorithm. In: Hassanien, A.E., Shaalan, K., Gaber, T., Tolba, M.F. (eds.) AISI 2017. AISC, vol. 639, pp. 724–733. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-64861-3_68 2. Engelbrecht, A.P.: Fundamentals of Computational Swarm Intelligence. Wiley (2005) 3. Khan, W.A: A Review and Comparative Study of Firefly Algorithm and Its Modified Versions, Optimization Algorithms - Methods and Applications, by Ozgur Baskan (2016) 4. Mirjalili, S., Lewis, A.: The whale optimization algorithm. Adv. Eng. Software 95, 51–67 (2016) ´ 5. Smigielski, G., Dygdała, R., Zarzycki, H., Lewandowski, D.: Real-time system of delivering water-capsule for firefighting. In: Kobayashi, S., Piegat, A., Peja´s, J., El Fray, I., Kacprzyk, J. (eds.) Hard and Soft Computing for Artificial Intelligence, Multimedia and Security. ACS 2016. AISC, vol. 534. Springer, Cham (2017) 6. Zarzycki, H., Apiecionek, Ł., Czerniak, J.M., Ewald, D.: The proposal of fuzzy observation and detection of massive data DDOS attack threat, Advances in Intelligent Systems and Computing. Springer, Cham (2021) 7. Zarzycki, H., Czerniak, J.M., Dobrosielski, W.T.: Detecting nasdaq composite index trends ´ ezak, D. with OFNs. In: Prokopowicz, P., Czerniak, J., Mikołajewski, D., Apiecionek, Ł, Sl¸ (eds.) Theory and Applications of Ordered Fuzzy Numbers. SFSC, vol. 356, pp. 195–205. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59614-3_11 8. Zarzycki, H., Dobrosielski, W.T.: Use of Ordered Fuzzy Numbers to observe quotations on financial markets, Advances in Intelligent Systems and Computing. Springer, Cham (2021) 9. Zarzycki, H., Dobrosielski, W.T., Vince, T., Apiecionek, Ł.: Center of Circles Intersection, a new defuzzification method on fuzzy numbers, Bulletin of the Polish Academy of Sciences. Technical Sciences (2020) 10. Zarzycki, H., Ewald, D., Skubisz, O., Kardasz, P.: A comparative study of two natureinspired algorithms for routing optimization, Advances in Intelligent Systems and Computing. Springer (2021) 11. Zarzycki, H., Czerniak, J.M., Lakomski, D., Kardasz, P.: Performance comparison of CRM ´ systems dedicated to reporting failures to IT department. In: Madeyski, L., Smiałek, Michał, Hnatkowska, B., Huzar, Z. (eds.) Software Engineering: Challenges and Solutions. AISC, vol. 504, pp. 133–146. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-43606-7_10

A Novel Multiswarm Firefly Algorithm: An Application for Plant Classification Nebojsa Bacanin1(B) , Miodrag Zivkovic1 , Marko Sarac1 , Aleksandar Petrovic1 , Ivana Strumberger1 , Milos Antonijevic1 , Andrija Petrovic1 , and K. Venkatachalam2 1

Singidunum University, Danijelova 32, 11000 Belgrade, Serbia {nbacanin,mzivkovic,msarac,aleksandar.petrovic,istrumberger, mantonijevic,apetrovic}@singidunum.ac.rs 2 University of Hradec Kralove, Hradec Kralove, Czech Republic [email protected]

Abstract. Areas of swarm intelligence and machine learning are constantly evolving, recently attracting even more researchers world-wide. This stems from the no free lunch which states that universal approach that could render satisfying results for all practical challenges does not exist. Therefore, in this research a novel multi-swarm firefly algorithm, that tries to address flaws of original firefly metaheuristics, is proposed. Devised algorithm is applied to interesting and important practical challenge of plants classification, as part of the hybrid framework between machine learning and optimization metaheuristics. For this purpose, a set of 1,000 random images of healthy leaves, from one public repository, is retrieved for the following plants: apple, cherry, pepper and tomato. Hybrid framework includes pre-processing, constructing bag of features and classification steps. After pre-processing, a bag of features is constructed by utilizing well-known scale-invariant feature transform algorithm, K-means-based vocabulary generation and histogram. Such images are then categorized with support vector machine classifier. However, to obtain satisfying results for a particular dataset, the support vector machines hyper-parameters’ need to be tuned and in the proposed research multi-swarm firefly algorithm is employed to determine optimal (sub-optimal) hyper-parameters’ values for this practical challenge. Comparative analysis with the basic firefly metaheuristics and other well-known swarm intelligence algorithms was conducted to assess the performance of the proposed method in terms of precision, recall, Fscore for this multi-class classification challenge. Obtained results show significant performance improvements of devised method over the original firefly algorithm and also better metrics than other state-of-the-art techniques in the majority of cases. Keywords: Multi-swarm firefly algorithm · Optimization · Plan classification · Swarm intelligence · Support vector machine

c The Author(s), under exclusive license to Springer Nature Switzerland AG 2022  C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 1007–1016, 2022. https://doi.org/10.1007/978-3-031-09173-5_115

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Introduction

The domain of metaheuristics is constantly evolving and new applications emerge every day. It is well-known that this group of artificial intelligence methods is able to render satisfying solutions for various NP-hard challenges withing a short period of time [9,21,32,34]. However, the general algorithm that can achieve promising results for all tasks does not exist and according to the no free lunch (NFL) theorem there is always space for improvements. Also, by examining most recent references, it can be undoubtedly concluded that the field which combines different artificial intelligence methods in hybrid approaches follows exponential growth. Large majority of such hybrid methodologies refers to employing metaheuristics for solving machine learning challenges. Some of the most commonly machine learning problems addressed by optimization metaheuristics include hyper-parameters’ optimization [5,7,15], feature selection [8,14,19,33] and training [3,4,6,12]. Guided by the NFL assumption, in this research a novel firefly algorithm, that guides the search by employing sub-populations, and aims to address flaws of original firefly metaheuristics [29], is proposed. Devised method is validated, as part of the hybrid framework, for support vector machine (SVM) hyperparameters’ tuning and assessed against practical challenge of plant classification based on leaves. Efficient and reliable plants categorization would enable farmers world-wide to better perform plant management. Plants can be differentiated by fruit, leaf, and flower, while all these components can be used as criteria for grouping. However, no matter what criterion is taken, plan classification is not an easy challenge, e.g. the physical characteristics of a leaf for each particular plan can also be similar to those of another plant hence creating confusion between the choice. Therefore, by using its visual capabilities human beings are not able to accomplish this task successfully and it is necessary to employ artificial intelligence methods, especially machine learning. By surveying modern literature, two facts can be derived: first, there are not so many applications from this domain and secondly, most machine learning applications for plant classification use plants’ leaves images as dataset [17,25]. By taking all of the above into account, the basic goals and main contributions of the research shown in this manuscript are to develop more robust upgraded FA metaheuristics and to further improve important plants classification by using a devised swarm intelligence approach. The remaining of the manuscript is structured in the following way. After Introduction, in Sect. 2, devised FA method is described along with the hybrid machine learning framework utilized in simulations, simulation details, comparative analysis, and discussion is provided in Sect. 3, while final remarks with limitations of the proposed study are given in Sect. 4.

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Proposed Methodology

In this section, basic working details of the original FA algorithm are provided, followed by some observed flaws and proposed improved method. At the end, specifications of the hybrid framework utilized in simulations are given. 2.1

Devised Firefly Approach

Recently after emergence in 2009., the FA metaheuristics [29] proved as one of the most robust optimizer. However at the same time some of its flaws were identified and many improved/hybrid versions came into the play [10,11,13,27,31]. The FA’s mathematical model, that approximates real-world environment, is based on the principle that brighter firefly (better solution) attracts less brighter one (worse individual). The brightness denotes a fitness or objective function, depending on the specific implementation. The FA conducts search process by updating every component k of each individual i (xi,k ) in every iteration t with the following basic expression [29]: 2

= xti + β0 · e−γri,j (xtj − xti ) + αt (κ − 0.5) xt+1 i

(1)

where the attractiveness at r = 0, randomization and light absorption parameters are denoted as β0 , α and γ, respectively, pseudo-random number drawn from the Gaussian or uniform distribution as κ, while the distance between two individuals i and j is ri,j . The solution xi is moved towards the position of xj if and only if the xj exhibits better fitness. The distance between two individuals is calculated by using the notion of simple Cartesian distance. The values that have proven to bear results with the large number of cases are 1 and between 0 and 1, for β0 and α, respectively [29]. More details regarding the basic FA approach can be captured from [29]. According to one of the previous studies [31], basic FA metaheuristics suffers from inefficient exploration that leads to inadequate exploitation-exploration balance and worse mean results. Specifically, it happens that in some runs the search process is unable to converge towards promising domain due to its stochastic nature and considering strong exploitation abilities of the FA, the whole population may converge to improper parts of the search region. One strategy for avoiding this is to divide initial population into that consists of N S solution into M sub-populations that all execute the search process independently, where M is an even integer. In this way, there will be a greater chance that at least one sub-population will manage to identify the right part of the search space. However, due to the smaller sub-population size, search ability of larger initial population would evaporate. To overcome this, some kind of information sharing between sub-populations needs to be established. Therefore, in the proposed approach, after ψ iterations, pairs of sub-populations are randomly selected and within each pair, the worst solution from first population (xworst ) is discarded and replaced with the best solution from the second

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population (xbest ), and vice-versa. The ψ is additional control parameter that controls when the swap will take place. The swap should take place after each sub-population is provided with enough iterations to find an optimum part of the search domain. Conversely, if the swap would execute throughout the whole run, then all sub-populations may converge into dis factory domain of the search space, as it is the case with original FA. Proposed method is named multi-swarm FA (MSFA) and its working details are summarized in Algorithm 1. Algorithm 1 Proposed MSFA metaheuristics Generate the initial population of fireflies xi , (i = 1, 2, 3, ...N S) Intensity of light Ii at position xi is defined by f (x) Define the coefficient of light absorption γ and the number of iterations M axIter Divide population into M sub-populations while t < M axIter do for each sub-population do for j = 1 to N S do for i = 1 to j do if Ii < Ij then Move the firefly i in the direction of the firefly j in D dimension Attractiveness changes with distance r as exp[−γr] Evaluate the new solution, replace the worst solution with better one and update intensity of light end if end for end for end for Sort all sub-populations based on fitness if t >= ψ then Randomly choose M/2 pairs of sub-populations Replace xworst with xbest solutions between each pair end if All fireflies are ranked in order to find the current best solution end while

2.2

Image Classification Framework

In this study, similar framework as proposed in [2] is used. First, all input images are transformed from RGB (red,green,blue) to gray-scale. Afterwards, a bag of features (BOF) is constructed by utilizing well-known scale-invariant feature transform algorithm (SIFT) [20], K-means-based vocabulary generation and histogram. Such features are then categorized with SVM classifier. Performance of SVM depends at large extent on hyper-parameters’ values that should be tuned for each practical test. Recent studies suggest that two of the most important ones include regularization parameter C that establishes balance (trade-off) between the model’s complexity and the training cost and parameter γ, that performs non-linear mapping between input and feature space. In this study, proposed metaheuristics was used to tune C and γ parameters. However, the kernel was not considered to be optimized. According to extensive empirical tests, it was concluded that for the plant classification challenge, SVM with radial basis kernel (RBF) function obtains the best results and this kernel

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was used in experiments. Therefore, each solution from the population is encoded as two-dimensional continuous array.

3

Research Findings, Comparative Analysis and Discussion

To validate proposed method, dataset that consists of healthy plant leaves images are used. All images are retrieved from the repository that consists of 61,486 images of healthy and plant leaves with 39 different classes of diseases [18]. Such large number of images is generated by performing six different augmentation techniques against original images from the PlantVillage repository. However, for the purpose of this study four groups of 1,000 random images of healthy leaves from the following plants were captured: apple, cherry, pepper, tomato. By following the 80%-20% train-test split rule, 800 labeled random images of each class are included in the train set, while 200 images are used for testing purposes. Comparative analysis was performed against the same methods which were tested in [1]: differential evolution (DE) [26], bat algorithm (BA) [30], salp swarm algorithm (SSA) [23], sine-cosine algorithm (SCA) [22], whale optimization algorithm (WOA) [24] and state-of-the-art modified WOA (MWOA) [1]. Moreover, to measure performance of proposed MSFA over the baseline methods, original FA was also implemented and validated. Due to the abundance of data science libraries in Python, all implementations are done in this programming language. As it was already pointed out in Subsect. 2.2, each metaheuristics was used to optimize the SVM C and γ hyper-parameters. Based on the findings of extensive empirical research for this study, as well as according to previous findings [16,28], lower and upper bounds for C and γ parameters are set as tuple (2−75 , 275 ). Further, the same experimental conditions as in [1] are established: all algorithms were tested in 100 iterations (maxIter = 100) over 30 independent runs with population consisting of 100 individuals (N S = 100). Since the utilized dataset is balanced, overall accuracy is employed as the fitness function. However, to establish real comparative analysis, overall accuracy is not enough, therefore the following metrics were also captured from simulations for each class: no. of true positives, precision, recall, F-score and accuracy. All metaheuristics are tested with default control parameters’ values as suggested in the original papers, while for the proposed MSFA M is set to 4, while φ = 60. These values were determined empirically by conducting simulations on standard unconstrained benchmarks. Comparative analysis findings are summarized in Table 1. Reported results represent the best individual from 30 runs and they are rounded to two decimal places. Obtained simulation results prove the potential of MSFA for tackling feature selection challenges. It is observed that two best methods are proposed MSFA and MWOA, where the MSFA achieves better overall accuracy for 4%, which is substantial in the computer vision domain. Moreover, almost all performance metrics for all classes are in favor to MSFA. For example, the MSFA establishes

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N. Bacanin et al. Table 1. Comparative analysis between MSFA and other metaheuristics Algorithm Accuracy Plant leaf class n Truth Precision Recall F-measure Acc. per. class DE

BA

SSA

SCA

WOA

MWOA

FA

MSFA

65.13%

69.58%

71.64%

76.41%

75.01%

79.03%

74.32%

83.10%

Apple

98

0.61

0.49

0.54

0.80

Cherry

136

0.74

0.68

0.70

0.86

Pepper

132

0.52

0.66

0.58

0.76

Tomato

155

0.78

0.78

0.78

0.89

Apple

125

0.70

0.63

0.66

0.84

Cherry

134

0.73

0.67

0.70

0.86

Pepper

156

0.62

0.78

0.69

0.83

Tomato

142

0.76

0.71

0.73

0.87

Apple

134

0.72

0.67

0.69

0.85

Cherry

122

0.75

0.61

0.67

0.85

Pepper

163

0.67

0.82

0.73

0.85

Tomato

154

0.74

0.77

0.76

0.87

Apple

144

0.76

0.72

0.74

0.88

Cherry

137

0.83

0.69

0.75

0.89

Pepper

169

0.73

0.85

0.78

0.88

Tomato

161

0.77

0.81

0.79

0.89

Apple

148

0.73

0.74

0.73

0.87

Cherry

151

0.78

0.76

0.79

0.88

Pepper

158

0.74

0.79

0.76

0.87

Tomato

143

0.76

0.72

0.74

0.87

Apple

162

0.73

0.81

0.77

0.88

Cherry

151

0.87

0.76

0.80

0.91

Pepper

170

0.73

0.85

0.79

0.89

Tomato

145

0.84

0.73

0.78

0.90

Apple

151

0.72

0.76

0.74

0.86

Cherry

144

0.78

0.72

0.75

0.88

Pepper

154

0.73

0.77

0.75

0.87

Tomato

145

0.75

0.73

0.73

0.87

Apple

176

0.81

0.88

0.84

0.92

Cherry

162

0.89

0.81

0.85

0.93

Pepper

161

0.78

0.81

0.79

0.89

Tomato

166

0.86

0.83

0.84

0.92

better recall for all classes except the pepper, and that implies that the MSFA managed to identify more positive cases, which is very important. When compared with the original FA, it can be observed that the MSFA substantially outperforms baseline method for all indicators, verifying improvements in exploration and diversification-intensification trade-off. By conducting further analysis, it can be stated that among original metaheuristics, FA, WOA and SCA perform similarly establishing average results, while SSA, BA and DE show worse results. To provide more insights into simulation findings, generated confusion matrices without normalization for all algorithms included in this study are shown in Fig. 1.

A Novel Multiswarm Firefly Algorithm

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Fig. 1. Confusion matrices for plant leaves classification

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Conclusion

In the presented study, guided by assumptions of NFL, MSFA is proposed and validated against the practical challenge of plants leaves classification. The devised approach was incorporated into the hybrid framework for image classification and used to optimize C and γ parameters of the SVM, which was used as the classifier. For the experimental purpose, the dataset of 1,000 random images of healthy leaves, from one public repository, is retrieved for the following plants: apple, cherry, pepper, and tomato. All images are pre-processed and BOF is constructed using SIFT, K-means-based vocabulary generation, and histogram. Comparative analysis was conducted between proposed MFSA and basic FA, 5 other wellknown metaheuristics, as well as with 1 improved swarm intelligence approach. According to experimental findings, proposed MSFA facilitates exploration ability of the basic implementation and manages to obtain better accuracy, precision, recall, and F-measure than all approaches included in comparison for the majority of tests. Due to its potential, the MSFA will be adopted in future research for tackling other NP-hard practical challenges. Acknowledgment. The paper is supported by the Ministry of Education, Science and Technological Development of Republic of Serbia, Grant No. III-44006.

References 1. Altameem, A., Kumar, S., Poonia, R., Saudagar, A.: Plant identification using fitness-based position update in whale optimization algorithm. Comput. Mater. Continua 71, 4719–4736 (2022). https://doi.org/10.32604/cmc.2022.022177 2. Azhar, R., Tuwohingide, D., Kamudi, D., Suciati, N., et al.: Batik image classification using sift feature extraction, bag of features and support vector machine. Procedia Comput. Sci. 72, 24–30 (2015) 3. Bacanin, N., Alhazmi, K., Zivkovic, M., Venkatachalam, K., Bezdan, T., Nebhen, J.: Training multi-layer perceptron with enhanced brain storm optimization metaheuristics. Comput. Mater. Continua 70(2), 4199–4215 (2022) 4. Bacanin, N., Alhazmi, K., Zivkovic, M., Venkatachalam, K., Bezdan, T., Nebhen, J.: Training multi-layer perceptron with enhanced brain storm optimization metaheuristics. Comput. Mater. Continua 70(2), 4199–4215 (2022). https://doi.org/10. 32604/cmc.2022.020449,http://www.techscience.com/cmc/v70n2/44706 5. Bacanin, N., Bezdan, T., Venkatachalam, K., Al-Turjman, F.: Optimized convolutional neural network by firefly algorithm for magnetic resonance image classification of glioma brain tumor grade. J. Real-Time Image Proc. 18(4), 1085–1098 (2021). https://doi.org/10.1007/s11554-021-01106-x 6. Bacanin, N., et al.: Artificial neural networks hidden unit and weight connection optimization by quasi-refection-based learning artificial bee colony algorithm. IEEE Access (2021) 7. Bacanin, N., Bezdan, T., Zivkovic, M., Chhabra, A.: Weight optimization in artificial neural network training by improved monarch butterfly algorithm. In: Shakya, S., Bestak, R., Palanisamy, R., Kamel, K.A. (eds.) Mobile Computing and Sustainable Informatics. LNDECT, vol. 68, pp. 397–409. Springer, Singapore (2022). https://doi.org/10.1007/978-981-16-1866-6 29

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Author Index

A Abdelmadjid, Larbi, 847 Abdulelah, Baraa Jalil, 895 Ahmad, Muhammad Zaini, 90 Ajay, D., 641 Akdemir, Halid, 237, 271, 761 Akın, Erhan, 769 Akta¸s, Ahmet, 649 Al Mashhadany, Yousif I., 895 Alam, Nik Muhammad Farhan Hakim Nik Badrul, 556 Aldring, J., 641 Alekperov, Ramiz, 435 Aliyev, Elchin, 378 Alkan, Nur¸sah, 702 Al-Shanableh, Filiz, 168 AlZahrani, M. Y., 208 Amasyali, Mehmet Fatih, 990 Amézquita, Lucio, 53 Andonov, Velin, 616, 624 Antonijevic, Milos, 1007 Arrieta-Hernández, N. S., 813 Arslan, Ozcan, 352 Aslan, Metin Emin, 822 Atanassov, Krassimir, 529 Atanassov, Krassimir T., 519 Atasoy, Batuhan, 744 Aviles-Román, M., 813 Avramova-Todorova, Gergana, 573 Ayaz, Halil ˙Ibrahim, 73 Aydın, Ilhan, 769 Aydın, Serhat, 649

B Bacanin, Nebojsa, 1007 Bal, Mustafa, 489 Barakath, A. Jamal, 328 Barroso, María, 219 Ba¸sar, Ramazan, 279 Bayhan, Nevra, 735 Bayindir, Cihan, 237, 271, 761, 887 Baysal, Mehmet Emin, 425, 864 Beldek, Tu˘gçe, 723 Bella, Kaoutar, 106 Belyakov, Stanislav, 192, 965 Benjamin, Josephine Bernadette, 142 Birim, Sule ¸ Öztürk, 802 Biswas, George, 405 Boltürk, Eda, 508 Boulmakoul, Azedine, 19, 82, 106 Bozhenyuk, Alexander, 192, 566, 965 Bozov, Hristo, 665 Bozukyan, Kami, 387 Bulut, Önder, 177 Bureva, Veselina, 673 Büyüközkan, Kadir, 279, 864 C Çakır, Esra, 589 Castillo, Oscar, 53, 785, 839 Cebi, Selcuk, 252, 261 Cevik Onar, Sezi, 498 Challenger, Moharram, 98 Cherradi, Ghyzlane, 19 Çimen, Egemen Berki, 974 Çini, Gülce, 177

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 C. Kahraman et al. (Eds.): INFUS 2022, LNNS 504, pp. 1017–1020, 2022. https://doi.org/10.1007/978-3-031-09173-5

1018

Author Index

Çoban, Veysel, 295 Cortes-Antonio, Prometeo, 53

Hung, Nguyen Nhut, 537 Husin, Nurain Zulaikha, 90

D Dare, V. R., 606 Demir, Ezgi, 744 Díaz-Pertuz, L. A., 813 Dogan, Nuri Ozgur, 598 Do˘gan, Onur, 831 Dolu, Aslı, 303 Dönmez, ˙Ilknur, 160 Donyatalab, Yaser, 941 Durmus, Mahmut, 744

I ˙Ilhan, Melike, 693 Irvanizam, Irvanizam, 360

E Ekici, Cengiz Vefa, 352 Ekincek, Sema, 151 Ekren, Banu Y., 957 El Bouziri, Adil, 19 El Kaissi, Souhail, 82 Elfayani, Elfayani, 360 Engin, Orhan, 279 Erdem, Gamze, 311, 339 Erkal Sönmez, Özlen, 184 Ervural, Bilal, 73 F Fan, Ching-Lung, 879 Farid, Fariba, 941 Figueroa-Mendoza, N. A., 813 G Garai, Totan, 405 García-Zamora, Diego, 396 Garg, Harish, 714 Gładysz, Barbara, 460 Gökçe, Mahmut Ali, 413 Gómez, Daniel, 219 Gucluer, Fatih, 744 Güçlükol, Simge, 339, 413 Gul, Zunaira, 714 Gündo˘gdu, Fatma Kutlu, 693 Gutiérrez, Inmaculada, 219 H Haktanır, Elif, 64, 471 Hernández-Julio, Y. F., 813 Hina, Manolo Dulva, 923 Hissamudin, Aisya Irdina, 228 Hızıro˘glu, Abdulkadir, 831 Hristozov, Iasen, 529

J Jaganath, T. S., 641 Jansirani, N., 606 K Kabak, Mehmet, 649 Kacprzyk, Janusz, 3 Kahraman, Cengiz, 64, 200, 498, 566, 656, 702 Kandiller, Levent, 914 Karaduman, Burak, 98 Karamustafa, Merve, 261 Kara¸san, Ali, 693 Karim, Lamia, 19 Kichu, Limainla, 208 Kim, Jong-Myon, 244 Kizielewicz, Bartłomiej, 27 Klaus-Rosi´nska, Agata, 319 Knyazeva, Margarita, 192, 566, 965 Konyalıo˘glu, Aziz Kemal, 369, 723 Koo, Insoo, 794 Köse, Rana Ezgi, 723 Kosenko, Olesiya, 965 Kuchta, Dorota, 319, 460 Küçükdeniz, Tarık, 119, 184 Kulaç, Oray, 957 Kuvvetli, Ümit, 303 L Labella, Álvaro, 396 Lbath, Ahmed, 19, 82, 106 Lee, Young-Doo, 794 Liman, Ya˘gmur Sa˘glam, 802 López, José Manuel Zurita, 905 M Mahmood, Tahir, 714 Mancilla, Alejandra, 839 Martínez, Luis, 396 Marzuki, Marzuki, 360 Mavrov, Deyan, 681 Mazarbhuiya, Fokrul A., 208 Md Akhir, Mohd Kamalrulzaman, 90 Melin, Patricia, 785 Mimoun, Malki, 847 Mohamad, Daud, 228 Moshkin, Vadim, 870

Author Index Moshkina, Irina, 870 Muñoz-Hernández, H., 813 N Nasir, V. Kamal, 328 Nieto-Bernal, W., 813 Novák, Vilém, 44 O Onar, Sezi Çevik, 112, 200, 295, 656 Öner, Adalet, 311 Osman, Abdullah, 119 Oturakçı, Murat, 369 Özgür Toy, A., 957 Özok, Ahmet Fahri, 16 Öztay¸si, Ba¸sar, 112, 200, 498, 656, 974 Ozturk, Ulku, 352 P Pakirdasi, Osman, 36 Paldrak, Mert, 339, 413 Paradowski, Bartosz, 27 Parveen, Shazia, 142 Pesek, Arda, 387 Petrov, Petar, 673 Petrova, Yaroslava, 665 Petrovic, Aleksandar, 1007 Petrovic, Andrija, 1007 Phu, Nguyen Dinh, 537 Piltan, Farzin, 244 Pi¸sirgen, Ali, 831 Poleshchuk, Olga, 445, 452 Popov, Stanislav, 673 Poryazov, Stoyan, 616, 624 Prieto-Guevara, M., 813 Pulido, Martha, 785 Q Quynh, Le Thi Ngoc, 537 R Radaev, Alexander, 64 Rahmatika, Azalya, 360 Ramdane-Cherif, Amar, 923 Ramiz, Alekperov, 128, 135 Ramli, Nazirah, 556 Razzouqi, Maroua, 19 Rençber, Neriman, 723 Ribagin, Simeon, 529 Rodríguez, Francisco Solano López, 905 Rodríguez, Rosa M., 396 S Sałabun, Wojciech, 27 Salmanov, Fuad, 378

1019 Santra, Uttaran, 405 Sarac, Marko, 1007 Saranova, Emiliya, 616, 624 Sari, Irem Ucal, 387 Sarucan, Ahmet, 425, 864 Senvar, ¸ Özlem, 982 Sheikhmemari, Saeid, 752 Simsek Yagli, Burcu, 598 Singh, Yashpal, 777 Skubisz, Oskar, 856 Sofyan, Hizir, 360 Sönmez, Filiz Erata¸s, 802 Sotirov, Sotir, 529, 573, 665 Sotirova, Evdokia, 529, 665 Soukane, Assia, 923 Staiou, Efthimia, 339 Strumberger, Ivana, 1007 Susan, Seba, 777 T Tabakh, Rahma, 735 Tan Taco˘glu, Melis, 339, 413 Ta¸s, Mehmet Ali, 589 Tasdemir, Kadim, 744 Ta¸sdemir, Sakir, 287 Ta¸sgetiren, Mehmet Fatih, 914 TayebiHaghighi, Shahnaz, 794 Tezel, Baris Tekin, 98 Tirmikcioglu, Nihan, 481 Tiryaki, Hasan, 735 Todorov, Milen, 573 Tolga, A. Cagri, 36, 822 Torra, Vicenç, 7 Tosun, Emre, 744 Toy, Ayhan Özgür, 177, 311 Tranev, Stoyan, 581, 632, 681 Traneva, Velichka, 581, 632, 681 Tunç, Ali, 287 U Ucal Sari, Irem, 489 Ullah, Kifayat, 714 Ulutagay, Gozde, 895 Üstüner, Onur, 887 V Valdez, Mario García, 839 Venkatachalam, K., 1007 Vijayaraghavan, N., 606 Vuqar, Salahli, 135 W Wi˛eckowski, Jakub, 27

1020 Y Yagli, Ibrahim, 598 Yalçın, Cahit, 864 Yalcinkaya, Irem, 252 Yang, Miin-Shen, 142 Yanık, Seda, 990 Yarushkina, Nadezhda, 870 Ya¸slı, Fatma, 151 Yatsalo, Boris, 64 Yel, ˙Ibrahim, 425

Author Index Yi˘git, Fatih, 160 Yontar Aksoy, Meltem, 990 Yüksel, Damla, 914 Yurdadön, Pelin, 112, 974 Z Zarzycki, Hubert, 856, 999 Zeren, Melis, 982 Zhang, Yinsheng, 932 Zivkovic, Miodrag, 1007