15th International Conference on Applications of Fuzzy Systems, Soft Computing and Artificial Intelligence Tools – ICAFS-2022 3031252519, 9783031252518
The general scope of the book covers diverse areas of fuzzy systems, soft computing, AI tools such as uncertain computat
397 20 38MB
English Pages 776 [777] Year 2023
Preface
Organization
Keynote Speeches
Summarization of Bimodal Information from Large Data Sets
A System of Systems Framework for Intelligence in Autonomy, Big Data Analytic and Applications
Granular Knowledge Transfer and Knowledge Distillation: At the Junctions of Machine Learning and Granular Computing
Quo Vadis AI?
Contents
On Some De Novo Type Approaches to Fuzzy Decision Making, Optimization and Control: An Application to Sustainable Regional Development
The Ideas of L. Zadeh and R. Aliev in the 3rd Generation of Artificial Intelligence
Multiattribute Decision Making in Material Selection Under Z-Valued Information
1 Introduction
2 Preliminaries
3 Statement of the Problem
4 Solution Method
5 Conclusion
References
Maximum Dynamic Evacuation Modelling in Networks in Fuzzy Conditions with Partial Lane Reversal
1 Introduction
2 Preliminaries and Problem Statement
3 Definition of Maximum Dynamic Evacuation Flow with Lane Reversal
4 Example
5 Conclusion and Future Scope
References
Z-Number-Based Similarity Reasoning in Control Systems
1 Introduction
2 Preliminaries
3 Statement of the Problem
4 Application of Numerical Example
5 Conclusion
References
Design of Quasi-Resonant Flyback Converter Integrated by Fuzzy Controller
1 Introduction
2 Controllers Design
2.1 Design QRFBC Using Fuzzy Logic Controller
2.2 Methodology of Investigation of QRFBC Controlled by FLC
2.3 Testing the QRFBC Controlled by PI Controller
3 Results and Discussions
4 Conclusion
References
Experimental Selecting Appropriate Fuzzy Implication in Traffic IF-Then Rules
1 Introduction
2 Preliminaries
3 Statement of the Problem
4 Conclusion
References
Prediction of Cold Filter Plugging Point of Different Types of Biodiesels Using Various Empirical Models
1 Introduction
2 Material and Methods
2.1 Data
2.2 Machine Learning Models (MLMs)
2.3 QM and MLR models
3 Results and Discussion
3.1 Estimating the CFPP Using MLPNN and RBFNN
3.2 Estimating the CFPP Using QM and MLR
3.3 Performance Evaluation of Proposed Models
4 Conclusions
References
Comparison of Fuzzy Solution Approaches for a Bilevel Linear Programming Problem
1 Introduction
2 A BLP Problem for an Industrial Symbiosis Network
3 Fuzzy Solution Approaches for the BLP Problem
3.1 Fuzzy Programming Approach – FPA
3.2 Fuzzy Goal Programming – FGP
4 Computational Results
5 Conclusion
References
Decision Making on Students’ Performance Estimation
1 Introduction
2 Preliminaries
3 Statement of the Problem
4 Application
5 Conclusion
References
A Comparative Analysis of the Different CNN Models Using Fuzzy PROMETHEE for Classification of Kidney Stone
1 Introduction
2 Materials and Methods
2.1 Dataset
2.2 Deep Learning Models
2.3 Evaluation Methods
3 Fuzzy-Based MCDM Models
4 Results
5 Conclusion
References
Developing Efficient Frontier for Investment Portfolio: A Fuzzy Model Approach
1 Introduction
2 Preliminaries
3 Problem Definition and Solution Method
4 Conclusion
References
Impact of Online Education Classes on Students’ Satisfaction: The Case of Near East University
1 Introduction
2 Research Method
2.1 Participants
2.2 Data Collection Tools
2.3 Data Analysis
2.4 Results
2.5 Discussion
3 Conclusion and Recommendation
References
Decision Making on Selection of Ferritic Stainless Steel
1 Introduction
2 Preliminaries
3 Statement of the Problem
4 Application
5 Discussion and Conclusion
References
Multicriteria Group Decision Making on Information System Project Selection Using Type-2 Fuzzy Set
1 Introduction
2 Preliminaries
3 Statement of the Problem
4 Solution of the Problem
5 Conclusion
References
Forecasting Demand in the Commodity Market of Food Products Using Neural Networks
1 Introduction
2 Basic Definitions
3 Choosing a Neural Network Architecture for Predicting the Coefficient of Demand Elasticity
4 Conclusion
References
Introducing Uncertainty-Based Dynamics in MADM Environments
1 Introduction
2 TOPSIS
3 An Illustrative Numerical Exercise
4 Perception-Based Evaluation Intervals
4.1 Value Functions
5 Analysis
6 Conclusions
References
Analyzing the Digital Marketing Strategies Role in Post Pandemic Recovery Period
1 Introduction
2 Preliminaries
3 Statement of the Problem
4 Solution of the Problem
5 Conclusion
References
Artificial Intelligence and Digital Economy: Development Prospects
1 Introduction
2 Artificial Intelligence: Historical Aspect
3 Contribution of AI Technologies to Economic Activity
4 Projected Gap Between Countries, Companies and Workers
5 Conclusion
References
Evaluation of Logistics Services of Airlines in the Azerbaijan Passenger Transportation Market
1 Introduction
2 Statement of the Problem
3 Estimation of Airlines Using a Fuzzy Inference System
4 Identification of Weights of Evaluation Criteria
5 Estimating Airlines Using the Fuzzy Maximin Convolution Method
6 Evaluation of Airlines by Pareto Rules and Bord Method
7 Conclusion
References
Customer Characteristics in Digital Marketing Model
1 Introduction
2 Preliminaries
3 Statement of the Problem
4 Solution of the Problem
5 Conclusion
References
Estimation of Countries’ Economic Development by Using Z-Number Theory
1 Introduction
2 Preliminaries
3 Statement of the Problem
4 Solution of the Problem
5 Conclusion
References
Fuzzy Approach to Explainable Artificial Intelligence
1 Introduction
2 Review of Fuzzy Rules Extraction Algorithms
3 Rule Extraction Algorithm Based on Decision Trees
3.1 Rule Extraction Algorithm
3.2 Rules Extraction from ANN Based on the Decision Trees
4 Discussion
References
Z-Numbers Based Evaluation of Expert Opinions on Agricultural Structure
1 Introduction
2 Statement of the Problem
3 The Algorithm and Solution of the Problem
4 Conclusions
References
Pareto-Optimality-Based Investigation of Quality of Fuzzy IF-THEN Rules
1 Introduction
2 Preliminaries
3 Statement of the Problem
4 Solution of the Problem by Using Numerical Example
5 Conclusion
References
Predicting Solar Power Generated by Grid-Connected Two-Axis PV Systems Using Various Empirical Models
1 Introduction
2 Material and Methods
2.1 Study Area and Data
2.2 Adaptive-Neuro Fuzzy Inference System (ANFIS)
2.3 Response Surface Methodology
3 Results and Discussion
3.1 Modeling with ANFIS
3.2 Modeling with RSM
3.3 Performance Evaluation of ANFIS and RSM
4 Conclusions
References
Z-Preferences in Consumer Buying Behavior
1 Introduction
2 Preliminaries
3 Statement of the Problem
4 Solution of the Problem
5 Conclusion
References
Prediction of the Power Output of a 4.5 kW Photovoltaic System Using Three Empirical Models: A Case Study in Nahr El-Bared, Lebanon
1 Introduction
2 Material and Methods
2.1 Study Area and Data
2.2 Machine Learning Models (MLMs)
2.3 Response Surface Methodology
3 Results and Discussion
3.1 Estimating the PV-Power Using MFFNN and CFNN
3.2 Estimating the PV Power Using RSM
3.3 Performance Evaluation of MFFNN, CFNN, and RSM
4 Conclusions
References
Z-Decision Making for the Selection of IT Engineers
1 Introduction
2 Preliminaries
3 Statement of the Problem
4 Solution of the Problem
5 Conclusion
References
Optimal Implicatıon Based Fuzzy Control System for a Steam Generator
1 Introduction
2 Statement of the Problem
3 Solution of the Problem
4 Conclusion
References
Prediction of Runoff Using Artificial Neural Networks, MLR Regression, and ARIMA Model (A Case Study: Bared River, Lebanon)
1 Introduction
2 Material and Methods
2.1 Data
2.2 Machine Learning Models (MLMs)
2.3 ARIMA Model
2.4 MLR Model
3 Results and Discussion
3.1 Estimating the Runoff Using MLPNN and RBFNN
3.2 Estimating the Runoff Using ARIMA and MLR
3.3 Performance Evaluation of Proposed Models
4 Conclusions
References
Devices with Fuzzy Logic Control of Artificial Lung Ventilation
1 Methods and Models
2 Statement of the Problem and Its Solution
3 Conclusions
References
Structural Analysis of Piston Machines by Using Computer Software
1 Introduction
2 The Mechanical and Thermodynamically Analysis of the Piston Machines
3 Dynamical Parameters for the Piston Machine
4 Modeling and Meshing of the Connecting Rod
5 Conclusions
References
Using of Conventional Neural Network to Diagnose Scabies by Dermoscopy
1 Introduction
2 Materials and Method
2.1 Datasets
2.2 Data Preparation
2.3 Data Augmentation
2.4 CNN
2.5 Activation Function
2.6 Fully-Connected Layer
2.7 Optimizer Adam
2.8 Transfer Learning
3 Experiments
3.1 Experimental Results and Analysis
4 Conclusion
References
Determination of the Dynamic and Interactive Event in Exascale Computing Systems via Request Clustering
1 Introduction
2 Dynamic and Interactive Event
3 Grouping of the Requests Using Their Requirements
4 Argument
5 Conclusion
References
Evaluation of Techniques Used in Phenol Removal from Wastewater Using Fuzzy PROMETHEE Method
1 Introduction
1.1 Techniques Applied in Phenol Removal in Wastewater
2 Materials and Methodology
2.1 PROMETHEE (Preference Ranking Organization Method for Enrichment Evaluations)
3 Results and Discussion
4 Conclusion
References
Research of the Manufacturing Quality of Plastic Details with Complex Forms of Connection
1 Introduction
2 Optimal Control of Technological Regimes
3 Establishing the Mathematical Dependence Between the Quality Indicators (Shrinkage and Strength) of Details on the Pressing Temperature
4 Discussion and Conclusions
References
Tableaux Deduction System for Fuzzy Logic with Estimates of Fuzziness Values
1 Introduction. Main Definitions
2 Equivalences in the Logic of Estimates LE
3 System Σ
4 Completeness of the System Σ for Logic of Estimates LE
5 Deduction in the Logic of Estimates LE
References
Research of Bitumen-Based Asphalt Compositions Using Neural Network
1 Introduction
2 Materials Used in Practice
3 Methodology of Sample Preparation
4 Results and Discussion
5 Conclusion
References
Logical-Linguistic Model for Reactor Cleaning from Impurities
1 Introduction
2 Statement of the Problem
3 Fuzzy Control Algorithm
4 Conclusion
References
Quantitative Assessment of the Risk of Failure and Vulnerability of Oil and Gas Pipelines at Underwater Crossings
1 Introduction
2 Modeling of the Process of General Erosion
3 Application of the Model
4 Conclusions
References
Prediction of Energy Consumption in Residential Buildings Using Type-2 Fuzzy Wavelet Neural Network
1 Introduction
2 T2-FWNN Model for Energy Consumption
3 Simulations
4 Conclusions
References
Modeling the Interaction of Components of a Distributed Information and Communication Environment
1 Introduction
2 Conceptual Representation of a Behavioral Model of a Distributed Information Space
3 Conclusion
References
Fuzzy Approach to Analysis of the Temporal Variability of the Vegetation in a Specific Area
1 Introduction
2 Problem Definition
3 FTS: Initial Steps for Building a Predictive Model
4 Modeling the NDVI FTS
5 Conclusion
References
Application of Fuzzy TOPSIS in Server Selection Problem
1 Introduction
2 Fuzzy TOPSIS Method
3 Server Selection Problem Solving
4 Conclusion
References
Fuzzy Inference Based Quadcopter Flight Regulation Under Overland Monitoring
1 Introduction
2 Problem Formulation
3 Fuzzy Inference System for Quadcopter Autopilot Regulation
4 Conclusion
References
Fuzzy Logic Analysis of Parameters Affecting Students’ Satisfaction with Their Life at University
1 Introduction
2 Research Problem
3 Data Collection and Data Analysis
4 The Analysis Process of Satisfaction Values Using Fuzzy Logic
5 Conclusion
References
Investigation of Submarine Pipeline Failure Accidents in Deepwater Based on the Fuzzy Analytical Hierarchy Process
1 Introduction
2 Materials and Methods
3 Solution of the Problem
4 Conclusion
References
Healthy Weight Estimation by Using Fuzzy Concept
1 Introduction
2 Methodology
3 Statement of the Problem
4 Solution of the Problem
5 Conclusion
References
Using Residual Learning in the Food Processing Sector: The Case of Banana Sorting
1 Introduction
1.1 Dataset
2 Transfer Learning of ResNet-50
3 Results and Discussion
4 Conclusion
References
Electre Method for Supermarket Selection Under Imperfect Information
1 Introduction
2 Methodolody
3 Numerical Example
4 Conclusion
References
Study of Gas Dynamic Processes of Drainage Zone of Oil Wells
1 Introduction
2 Conclusions
References
Appling Fuzzy Inference Logic System to Dynamic Model of Gross Domestic Product (in Case of Azerbaijan)
1 Introduction
2 The Dynamic Model of GDP with Two Controls
3 Conclusion
References
Analysis of Knee Osteoarthritis Grading Using Deep Learning
1 Introduction
2 Materials and Methods
3 Results
4 Discussion
References
Navigation of a Mobile Robot Based on Fuzzy Images in an Uncertain Environment
1 Introduction
2 Visual Image Processing
2.1 Fuzzy Image Processing
3 Simulation of the System
4 Conclusion
References
Comparison of Oil Quality of Various Fields Based on Fuzzy Cluster Analysis
1 Introduction
2 Brief Analysis of Existing Works
3 Application of Fuzzy Clustering to Modeling Relationship Between Oil Properties and Difficulty of Oil Extraction
4 Conclusion
References
Interdisciplinary Nature of Borderline Disciplines: A Transition from Binary Logic to Fuzzy Logic
1 Introduction
2 Preliminaries
2.1 Membership Characteristic Function
2.2 Intersection of Fuzzy Sets
2.3 Fuzzy Logic Dialogical “Both-And” Approach
3 Borderline Disciplines as an Interdisciplinary Field of Research
4 Criticism of “Either/Or” Approach to Borderline Disciplines
5 Logic of Interdisciplinarity – Fuzzy Logic
6 Borderline Disciplines in the Light of Fuzzy Logic
7 Conclusion
References
Decision Making in Hepatitis B Diagnosis by Using Fuzzy Expert System: Case of Near East Hospital
1 Introduction
2 The Fuzzy Expert SYSTem’s Working Principle
3 Methodology
4 Computer Simulation
5 Conclusion
References
Application of Leointief’s Input-Output Model of Azerbaijan Economy Under Fuzzy Information
1 Introduction
2 Leontief’s Model Described by Fuzzy Linear Equations
3 Technology Matrix A"0365 A with Fuzzy Entries
4 Leontief Model of the Azerbaijani Economy Described by Fuzzy Linear Equations
5 Conclusion
References
Simulation of Fractal Kinetics of Thermooxidation of Polymer Melts Based on Fractional Differential Equations
1 Introduction
2 Analysis of Existing Works
3 Results of Experimental Studies
4 Conclusion
References
Fuzzy Models for Calculation of Oil and Gas Reserves
1 Introduction
2 Problem Statement
3 Calculation of Oil Reserves Based on the Theory of Fuzzy Sets
4 Conclusion
References
Vendor Selection by Using Ideal Solution Methodology with Fuzzy Numbers
1 Introduction
2 Preliminaries
3 Statement and Solution of the Problem
4 Conclusion
References
Selection Core Banking System by Using Fuzzy AHP and Fuzzy TOPSIS Hybrid Method
1 Introduction
2 Preliminaries
3 Statement of the Problem
4 Conclusion
References
Performance Analysis of Machine Learning Algorithms for Medical Datasets
1 Introduction
2 Materials and Methods
2.1 Datasets
2.2 Machine Learning Models
2.3 Design of Experiments and Evaluation
3 Results
3.1 Results of Binary Classification Experiments
3.2 Results of Multi-class Experiments
4 Discussions
5 Conclusion
References
Difference Between Digital Marketing and Traditional Marketing Models
1 Introduction
2 Preliminaries
3 Difference Between Digital Marketing and Traditional Marketing Concepts
3.1 Traditional Marketing Model
3.2 Digital Marketing Model
4 Statement of the Problem
5 Solution of the Problem
6 Conclusion
References
Determination of Green Field Plants Most Suitable for Geographical Features of Places with Fuzzy Logic Methods
1 Introduction
2 Purpose of the Research
3 The Research Method
3.1 Classification by Decision Tree Method
3.2 Fuzzy Application
4 Conclusion
References
Z-Information Based MCDM Model for Assessing Green Energy Resources: A Case of Resort and Tourism Areas
1 Introduction
2 Definitions and Operations with Z-numbers
2.1 Z-Number-Based ORESTE Method
3 Results
3.1 Application of Z-numbers Based ORESTE
3.2 Application of the Z-TOPSIS
4 Discussions and Conclusion
References
Assessing the Impact of Innovations on the Volume of Production of the Final Product in a Fuzzy Information Environment
1 Introduction
2 Calculation of the Final Product of the Region Using a Production Function that Takes into Account the Innovation Factor
3 Estimation Results of Output (Y) Using the Fuzzy Cobb-douglas (Innovation) Model
4 Conclusion
References
Application of WASPAS Method to Data Platform Selection Under Z-Valued Information
1 Introduction
2 Preliminaries
3 Statement of the Problem and a Solution Method
4 Conclusion
References
Using Deep Learning Algorithm for Prediction and Detection of Covid-19
1 Introduction
2 Machine Learning Algorithm
3 Methodology of the Process
4 Result of Prediction and Detection
5 Conclusion
References
Fuzzy Logic-Based Planning of the Behavior of Autonomous Vehicles
1 Introduction
2 Models and Methods
3 Statement of the Problem and Simulation of the System
4 Conclusion
References
Digitization of Centrifugal Compressor Asset as One of Key Elements of Overall Digitized Industrial Plant
1 Introduction
2 Description of Scientific-Technical Solution
3 Conclusion
References
Investment Decision Making by Using Natural Language Processing
1 Introduction
2 Preliminaries
3 Statement of the Problem
4 Solution of the Problem
5 Conclusion
References
Multi-attribute Decision Making Under Z-Set Valued Uncertainty
1 Introduction
2 Preliminaries
3 Statement of the Problem and a Solution Method
3.1 Hurwicz Approach
3.2 Fair Price Approach [1]
4 Numeric Example
5 Conclusion
References
Fuzzy Processing of Hydrodynamic Studies of Gas Wells Under Uncertainty
1 Introduction
2 Statement of the Problem
3 Method
4 Results
5 Discussion
6 Conclusion
References
Fuzzy Modeling for Marketing Plan Development
1 Introduction
2 Fuzzy c-means Method
3 Statement of the Problem and Solution
4 Discussion and Conclusion
References
Solving Employee Selection Problem Under Fuzzy-Valued Information
1 Introduction
2 Preliminaries
3 Statement of the Problem
4 Solution of the Problem
5 Conclusion
References
The Use of Fuzzy Numbers for the Rational Choice of the Structure of the Distribution Channel of Goods
1 Introduction
2 Basic Definitions
3 Method for the Rational Choice of the Structure of the Distribution Channel of Goods
4 An Example for the Rational Choice of the Structure of the Distribution Channel for the Company’s Product with Certain Characteristics
5 Conclusion
References
“Dede Korkud” Epos in Light of Fuzzy Logic
1 About Fuzzy Logic Facets [1, 2]
2 Evaluating Fuzzy Uncertainties in “Dede-korkud” Text
3 Conclusion
References
Toward Z-Number-Based Classification of Dataset
1 Introduction
2 Statement of Problem
3 Solution Approach
4 An Application
References
Application of Enterprise Solution Software for a Hotel Chain
1 Introduction
2 Materials and Methods
3 Research Findings and Results
4 Conclusion
5 Conflicts of Interest
References
Fuzzy Logic Modelling of the Relationship Between Attitudes Towards Military Services and Soldiers’ Self-esteem
1 Introduction
2 Set of Problem
3 Methodology
3.1 Design the Attitude Scale
4 Fuzzy Logic Modelling the Impact of ATMS on the Self-esteem of Soldiers
5 Conclusion
References
Applying Type-2 Fuzzy TOPSIS Method to Selection of Facility Location
1 Introduction
2 Preliminaries
3 Statement of Problem and Solution Procedures
4 Conclusion
References
Applying a Fuzzy-Set Approach to Assessing Capital Flight Management: Empirical Research from Azerbaijan
1 Introduction
2 Methodology
3 Validity of the Use of the Fuzzy Set Approach
4 Practical Calculation of a Multicriteria Problem
5 Conclusion
References
Decision Making with Z-Bounded Interval Preference
1 Introduction
2 Preliminaries
3 Statement of the Problem and Solution Methods
4 Example
5 Conclusion
References
Teacher Assessment Model with Basic Uncertain Information
1 Introduction
2 Preliminiaries
3 Statement of the Problem
4 Solution of the Problem
5 Conclusion
References
Design of Receiver in Fuzzy-Chaotic Communication Systems
1 Introduction
2 Preliminaries
3 Problem Statement and Solution
4 Experimental Investigation
5 Conclusion
References
Smart Traffic Monitoring and Control System
1 Introduction
2 Literature Analysis and Problem Statement
3 Problem Solving and Basic Material
4 Conclusion
References
Extension of Delphi Method to Z-Environment
1 Introduction
2 Z-Number Related Some Preliminary Information
3 Z-Valued Delphi Steps
4 Numerical Example
5 Conclusion
References
Analysis of Intelligent Interfaces Based on Fuzzy Logic in Human-Computer Interaction
1 Introduction
2 Interface Assessment Methods
2.1 Expert Appraisals and Heuristics
3 Fuzzy Logic and Expert Systems
4 Conclusion
References
Determination of the Uncertainty of the Parameters of Oxidative-Reduction Reactions of Titanomagnetites
1 Introduction
2 Thermodynamics of Oxidative Reduction Reactions of Titanomagnetites
2.1 Determination of Reaction Conditions by Using MGA
3 Results and Discussion
4 Conclusions
References
Solving Problem of Unit Commitment by Exchange Market Algorithm and Dynamic Planning Method
1 Introduction
2 Methods
2.1 Forward Dynamic Programming Approach
2.2 Formation of the Priority Table
2.3 Exchange Market Algorithm
3 Problem Formulation
4 Applying the Proposed Method to the Unit Commitment Problem
5 Simulation and Results
6 Conclusion
References
Regular Identification Algorithms for a Special Class of Neuro-Fuzzy Models ANFIS
1 Introduction
2 Problem Definition
3 Solution
4 Conclusion
References
Author Index
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Lecture Notes in Networks and Systems 610
R. A. Aliev · J. Kacprzyk · W. Pedrycz · Mo. Jamshidi · M. B. Babanli · F. Sadikoglu Editors
15th International Conference on Applications of Fuzzy Systems, Soft Computing and Artificial Intelligence Tools – ICAFS-2022
Lecture Notes in Networks and Systems
610
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]).
R. A. Aliev · J. Kacprzyk · W. Pedrycz · Mo. Jamshidi · M. B. Babanli · F. Sadikoglu Editors
15th International Conference on Applications of Fuzzy Systems, Soft Computing and Artificial Intelligence Tools – ICAFS-2022
Editors R. A. Aliev Azerbaijan State Oil and Industry University Baku, Azerbaijan W. Pedrycz Department of Electrical and Computer Engineering University of Alberta Edmonton, AB, Canada M. B. Babanli Azerbaijan State Oil and Industry University Baku, Azerbaijan
J. Kacprzyk System Research Institute Polish Academy of Sciences Warsaw, Poland Mo. Jamshidi Department of Electrical and Computer Engineering The University of Texas at San Antonio San Antonio, TX, USA F. Sadikoglu Department of Mechatronics Near East University Nicosia, Turkey
ISSN 2367-3370 ISSN 2367-3389 (electronic) Lecture Notes in Networks and Systems ISBN 978-3-031-25251-8 ISBN 978-3-031-25252-5 (eBook) https://doi.org/10.1007/978-3-031-25252-5 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 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
The Fifteenth International Conference on Application of Fuzzy Systems, Soft Computing and Artificial Intelligence Tools (ICAFS-2022) is the premier international conference organized by Azerbaijan Association of “Zadeh’s Legacy and Artificial Intelligence” (Azerbaijan), Azerbaijan State Oil and Industry University (Azerbaijan), University of Siegen (Siegen, Germany), BISC—Berkeley Initiative in Soft Computing (Berkeley, USA), University of Texas, San Antonio (USA), Georgia State University (Atlanta, USA), University of Alberta (Alberta, Canada), University of Toronto (Toronto, Ontario, Canada), Polish Academy of Sciences, System Research Institute (Poland) and Near East University (North Cyprus). This volume presents an edited selection of the presentations from ICAFS-2022 which was held in Budva, Montenegro, August 26–27, 2022. ICAFS-2022 is held as a meeting for the communication of research on application of fuzzy logic, uncertain computation, Z-information processing, neuro-fuzzy approaches and different constituent methodologies of soft computing applied in economics, business, industry, education, medicine, earth sciences and other fields. The conference provided an opportunity to present and discuss state-of-the-art research in this expanding domain. This volume will be a useful guide for academics, practitioners and graduates in fuzzy logic and soft computing. It will allow for increasing of interest in development and applying of soft computing and artificial intelligence methods in various real-life fields. August 2022
R. A. Aliev Chairman of ICAFS-2022
Organization
Chairman R.A. Aliev, Azerbaijan
Co-chairmen and Guest Editors J. Kacprzyk, Poland M. Jamshidi, USA W. Pedrycz, Canada M. B. Babanli, Azerbaijan F. S. Sadikoglu, North Cyprus
International Program Committee A. Averkin, Russia A. Piegat, Poland B. Fazlollahi, USA B. Kang, China B. Turksen, Canada, Turkey C. Kahraman, Turkey D. Dubois, France D. Enke, USA D. Kumar Jana, India E. Babaei, Iran F. Aminzadeh, USA G. Imanov, Azerbaijan H. Berenji, USA H. Hamdan, France, UK H. Prade, France H. Roth, Germany I. Batyrshin, Mexico I. G. Akperov, Russia I. Perfilieva, Czech Republic K. Atanassov, Bulgaria
K. Bonfig, Germany K. Takahashi, Japan L. Gardashova, Azerbaijan M. Nikravesh, USA N. Yusupbekov, Uzbekistan O. Huseynov, Azerbaijan O. Kaynak, Turkey R. R. Aliev, North Cyprus R. Abiev, North Cyprus R. O. Kabaoglu, Turkey R. Yager, USA S. Ulyanov, Russia T. Allahviranloo, Turkey T. Fukuda, Japan T. Takagi, Japan V. Kreinovich, USA V. Loia, Italy V. Niskanen, Finland V. Nourani, Iran V. Novak, Czech Republic
viii
Organization
Organizing Committee Chairman U. Eberhardt, Germany Co-chairmen L. Gardashova, Azerbaijan T. Abdullayev, Azerbaijan Members N. Adilova, Azerbaijan A. Alizadeh, Azerbaijan V. Nourani, Iran J. Lorkowski, USA K. Rizvanova, Russia H. Hamdan, France, UK H. Igamberdiev, Uzbekistan M. Karazhanova, Kazakhstan N. Mehdiyev, Germany M. Knyazeva, Russia M. M. M. Elamin, Sudan M. A. Salahli, Turkey V. Ogunbode, Nigeria Sahin Akdag, North Cyprus
Conference Organizing Secretariat Azadlig Ave. 20, AZ 1010 Baku, Azerbaijan Phone: +99 412 493 45 38, Fax: +99 412 598 45 09 E-mail: [email protected], [email protected]
Keynote Speeches
Summarization of Bimodal Information from Large Data Sets
R. A. Aliev 1
2
Georgia State University, USA Azerbaijan State Oil and Industry University, Azerbaijan, 20 Azadlig Ave., AZ1010 Baku, Azerbaijan [email protected]
Abstract. Clustering is a technique used to find groups within a data set. Complexity of data sets is characterized by large volume, imprecision and partial reliability of data. This may involve fusion of fuzzy and probabilistic information, referred to as bimodal information. Sometimes, it may be possible to describe such data by using some kind of “If-Then” rules with fuzzy probabilistic components. In this work, an approach to clustering of data sets for extraction rules that contain bimodal information is proposed. The approach is based on the fuzzy C-means objective function and an evolutionary technique to produce type-2 fuzzy clusters. Further, Z-number-based cluster descriptions are formed by using the relationship between type-2 fuzzy set and Z-number. A real-world application is considered to demonstrate the usefulness of the proposed approach.
A System of Systems Framework for Intelligence in Autonomy, Big Data Analytic and Applications
Mo Jamshidi The University of Texas, San Antonio, TX, USA [email protected] Abstract. Large data has been accumulating in all aspects of our lives for quite some time. Advances in sensor technology, the Internet, wireless communication and inexpensive memory have all contributed to an explosion of “Big Data”. System of Systems (SoS) is integration of independent operatable and non-homogeneous legacy systems to achieve a higher goal than the sum of the parts. Today’s SoS is also contributing to the existence of unmanageable “Big Data”. Recent efforts have developed promising approach, called “Data Analytics”, which uses machine learning tools from statistical and soft computing (SC) such as principal component analysis (PCA), clustering, fuzzy logic, neuro-computing, evolutionary computation, Bayesian networks, deep architectures and deep learning to reduce the size of “Big Data” to a manageable size and apply these tools to a) extract information, b) build a knowledge base using the derived data and c) eventually develop a nonparametric model for the “Big Data”. This keynote attempts to construct a bridge between SoS and Data Analytics to develop reliable models for such systems. A photovoltaic energy-forecasting problem of a microgrid SoS, traffic jams forecasting, brain disease prediction and a system of autonomous vehicles will be offered for case studies. These tools will be used to extract a nonlinear model for a SoS-generated Big Data. Videos for autonomous vehicles will be shown.
Granular Knowledge Transfer and Knowledge Distillation: At the Junctions of Machine Learning and Granular Computing
Witold Pedrycz Department of Electrical and Computer Engineering, University of Alberta, Edmonton AB T6R 2V4, Canada [email protected] Abstract. Machine Learning methods are inherently faced with masses of data leading to time-consuming learning procedures and huge black box-style architectures of classifiers and predictors (e.g., such as deep neural networks). We advocate that Granular Computing (GrC) delivers a conceptually and algorithmically sound alternative and a viable augmentation to conveniently address the challenges identified above. In particular, it is demonstrated that the notion of information granularity becomes beneficial in the formalization and knowledge-sharing essential in a slew of problems of transfer learning. Transfer learning is concerned with extraction of knowledge (expressed by some model) acquired for the previous (source) environment and its successive usage to a new (target) environment. Information granularity helps realize knowledge transfer from the source to the target domain. What becomes even more important, through GrC one can quantify the relevance of the knowledge in the new environment by constructing granular generalizations of the model existing in the source environment with the level of information granularity (viz., specificity of information granules) reflecting upon the proximity between the source and target domains. Knowledge distillation (referred to as model compression) becomes an interesting learning paradigm supporting a design of compact models (student) guided by transfer knowledge from the reference model (teacher). In this setting, the roles of granular augmentation of the learning environment of knowledge distillation are discussed. A supplementary illustrative material is focused on the design and analysis of transfer learning and knowledge distillation applied to rulebased architectures.
Quo Vadis AI?
Okyay Kaynak Bogazici University, Turkey [email protected] Abstract. During the last two decades, profound technological changes have occurred around us, supported by disruptive advances both on the software and on the hardware sides. Additionally, we have witnessed a cross-fertilization of concepts and an amalgamation of information, communication and control technology-driven approaches. This has led to what is termed as digital transformation, i.e., the integration of digital technology into all areas of business, fundamentally changing how companies operate and deliver value to customers. The most recent development is integrating artificial intelligence (AI) in digital transformation as the primary enabler and the facilitator. It is expected that the applications of AI will truly transform our world and impact all facets of society, economy, living, working, health care and technology. The study of artificial intelligence (AI) has been a continuous endeavor of scientists and engineers for over 65 years. The simple contention is that human-created machines can do more than just laborintensive work; they can develop human-like intelligence. AI has been very appealing as it aligns with the nature of human beings in terms of their never-satisfied demands for higher productivity on the one hand and, on the other hand, the curiosity of how we understand and try to change the world. Having gone through several historical stages with several winters, AI has become a leading technology today and plays novel roles like never. Therefore, it is time to discuss the past, the present and the future of both the AI tools and the AI “beings” at this juncture. In this presentation, in addition to the technical aspects of AI technology in short to mid-term, thoughts and insights are also presented regarding the symbiotic relationship of AI and humans in the long run.
Contents
On Some De Novo Type Approaches to Fuzzy Decision Making, Optimization and Control: An Application to Sustainable Regional Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Janusz Kacprzyk
1
The Ideas of L. Zadeh and R. Aliev in the 3rd Generation of Artificial Intelligence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Alexey Averkin
4
Multiattribute Decision Making in Material Selection Under Z-Valued Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. B. Babanli
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Maximum Dynamic Evacuation Modelling in Networks in Fuzzy Conditions with Partial Lane Reversal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Janusz Kacprzyk, Alexander Bozhenyuk, and Evgeniya Gerasimenko
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Z-Number-Based Similarity Reasoning in Control Systems . . . . . . . . . . . . . . . . . . Nigar E. Adilova and Aziz Nuriyev
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Design of Quasi-Resonant Flyback Converter Integrated by Fuzzy Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fahreddin Sadikoglu, Samsam Bakhtiari, and Ebrahim Babaei
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Experimental Selecting Appropriate Fuzzy Implication in Traffic IF-Then Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shamil A. Ahmadov
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Prediction of Cold Filter Plugging Point of Different Types of Biodiesels Using Various Empirical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Youssef Kassem, Hüseyin Çamur, Ahmed Hamid Mohamed Abdalla Zakwan, and Nkanga Amanam Nkanga Comparison of Fuzzy Solution Approaches for a Bilevel Linear Programming Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bü¸sra Altınkaynak, Tolunay Göçken, Murat Ye¸silkaya, Burak Birgören, and Gülesin Sena Da¸s Decision Making on Students’ Performance Estimation . . . . . . . . . . . . . . . . . . . . . J. M. Babanli
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A Comparative Analysis of the Different CNN Models Using Fuzzy PROMETHEE for Classification of Kidney Stone . . . . . . . . . . . . . . . . . . . . . . . . . . Fahreddin Sadıko˘glu, Özlem Sabuncu, and Bülent Bilgehan
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Developing Efficient Frontier for Investment Portfolio: A Fuzzy Model Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Leyla R. Hasanova
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Impact of Online Education Classes on Students’ Satisfaction: The Case of Near East University . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Saide Sadıko˘glu, S¸ ahin Akda˘g, and Murat Tezer
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Decision Making on Selection of Ferritic Stainless Steel . . . . . . . . . . . . . . . . . . . . 101 Mustafa Babanli, Latafat Gardashova, and Tural Gojayev Multicriteria Group Decision Making on Information System Project Selection Using Type-2 Fuzzy Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Aygul Dadasheva Forecasting Demand in the Commodity Market of Food Products Using Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 Mikayilova Rena Nuru Introducing Uncertainty-Based Dynamics in MADM Environments . . . . . . . . . . 130 Debora Di Caprio and Francisco J. Santos Arteaga Analyzing the Digital Marketing Strategies Role in Post Pandemic Recovery Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Khatira J. Dovlatova Artificial Intelligence and Digital Economy: Development Prospects . . . . . . . . . . 147 Ali Abbasov and Ramin Rzayev Evaluation of Logistics Services of Airlines in the Azerbaijan Passenger Transportation Market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 Sevil Imanova Customer Characteristics in Digital Marketing Model . . . . . . . . . . . . . . . . . . . . . . . 164 Gunay E. Imanova and Gunel Imanova Estimation of Countries’ Economic Development by Using Z-Number Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 Rafig R. Aliyev
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Fuzzy Approach to Explainable Artificial Intelligence . . . . . . . . . . . . . . . . . . . . . . 180 Alexey Averkin and Sergey Yarushev Z-Numbers Based Evaluation of Expert Opinions on Agricultural Structure . . . . 188 G. Imanov, A. Aliyev, and R. Mikayilova Pareto-Optimality-Based Investigation of Quality of Fuzzy IF-THEN Rules . . . . 196 Nigar E. Adilova Predicting Solar Power Generated by Grid-Connected Two-Axis PV Systems Using Various Empirical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 Youssef Kassem, Hüseyin Gökçeku¸s, Marilyn Hannah Godwin, James Mulbah Saley, and Momoh Ndorbor Mason Z-Preferences in Consumer Buying Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 Khatira J. Dovlatova Prediction of the Power Output of a 4.5 kW Photovoltaic System Using Three Empirical Models: A Case Study in Nahr El-Bared, Lebanon . . . . . . . . . . . 218 Hüseyin Çamur, Youssef Kassem, Mustapha Tanimu Adamu, and Takudzwa Chikowero Z-Decision Making for the Selection of IT Engineers . . . . . . . . . . . . . . . . . . . . . . . 226 Gunay A. Huseynzada Optimal Implicatıon Based Fuzzy Control System for a Steam Generator . . . . . . 234 L. A. Gardashova and K. A. Mammadova Prediction of Runoff Using Artificial Neural Networks, MLR Regression, and ARIMA Model (A Case Study: Bared River, Lebanon) . . . . . . . . . . . . . . . . . . 247 Youssef Kassem, Hüseyin Gökçeku¸s, Francis Surfia Dioh, Marcus Paye Quoigoah, and Marilyn Hannah Godwin Devices with Fuzzy Logic Control of Artificial Lung Ventilation . . . . . . . . . . . . . 256 Aynur J. Jabiyeva Structural Analysis of Piston Machines by Using Computer Software . . . . . . . . . 265 Valeh Bakhshali, Nail Mardanov, Ismayil Ismayil, and Aygun Bekirova Using of Conventional Neural Network to Diagnose Scabies by Dermoscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274 Husam Zendah and Kamil Dimililer
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Determination of the Dynamic and Interactive Event in Exascale Computing Systems via Request Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 Nigar Ismayilova Evaluation of Techniques Used in Phenol Removal from Wastewater Using Fuzzy PROMETHEE Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 Basil Bartholomew Duwa, Ay¸seGünay Kibarer, Berna Uzun, S¸ erife Kaba, and Dilber Uzun Ozsahin Research of the Manufacturing Quality of Plastic Details with Complex Forms of Connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 Naila A. Gasanova, Agali A. Quliyev, Aynur V. Sharifova, Tamilla U. Khankishiyeva, and Rafiga S. Shahmarova Tableaux Deduction System for Fuzzy Logic with Estimates of Fuzziness Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 Gerald S. Plesniewicz and Alexey N. Aparnev Research of Bitumen-Based Asphalt Compositions Using Neural Network . . . . . 313 D. S. Mamed Hasan-zade, A. I. Babayev, and G. S. Hasanov Logical-Linguistic Model for Reactor Cleaning from Impurities . . . . . . . . . . . . . . 321 E. A. Melikov, T. M. Magerramova, and A. A. Safarova Quantitative Assessment of the Risk of Failure and Vulnerability of Oil and Gas Pipelines at Underwater Crossings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330 I. A. Habibov and S. M. Abasova Prediction of Energy Consumption in Residential Buildings Using Type-2 Fuzzy Wavelet Neural Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 Rahib Abiyev and Sanan Abizada Modeling the Interaction of Components of a Distributed Information and Communication Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346 Nodirbek Yusupbekov, Nargiza Usmanova, and Shukhrat Gulyamov Fuzzy Approach to Analysis of the Temporal Variability of the Vegetation in a Specific Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354 Elchin Aliyev and Fuad Salmanov Application of Fuzzy TOPSIS in Server Selection Problem . . . . . . . . . . . . . . . . . . 364 V. H. Salimov
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Fuzzy Inference Based Quadcopter Flight Regulation Under Overland Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 Tunjay Habibbayli and Murad Aliyev Fuzzy Logic Analysis of Parameters Affecting Students’ Satisfaction with Their Life at University . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382 M. A. Salahli, T. Gasimzade, V. Salahli, F. Alasgarova, and A. Guliyev Investigation of Submarine Pipeline Failure Accidents in Deepwater Based on the Fuzzy Analytical Hierarchy Process . . . . . . . . . . . . . . . . . . . . . . . . . . 391 Hajar Ismayilova, Mansur Shahlarli, and Fidan Ismayilova Healthy Weight Estimation by Using Fuzzy Concept . . . . . . . . . . . . . . . . . . . . . . . 399 Farida Huseynova Using Residual Learning in the Food Processing Sector: The Case of Banana Sorting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406 Khaled Almezhghwi, Wadei Algazewe, and Rabei Shwehdi Electre Method for Supermarket Selection Under Imperfect Information . . . . . . . 413 Hasan Temizkan Study of Gas Dynamic Processes of Drainage Zone of Oil Wells . . . . . . . . . . . . . 421 T. H. Ibrahimli and R. S. Gurbanov Appling Fuzzy Inference Logic System to Dynamic Model of Gross Domestic Product (in Case of Azerbaijan) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427 Yadulla Hasanli, Shafizade Elnure, and Guliev Fariz Analysis of Knee Osteoarthritis Grading Using Deep Learning . . . . . . . . . . . . . . . 435 Serag Mohamed Akila, Elbrus Imanov, and Khaled Almezhghwi Navigation of a Mobile Robot Based on Fuzzy Images in an Uncertain Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444 A. B. Sultanova Comparison of Oil Quality of Various Fields Based on Fuzzy Cluster Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452 G. Efendiyev, S. Abbasova, G. Moldabayeva, and O. Kirisenko Interdisciplinary Nature of Borderline Disciplines: A Transition from Binary Logic to Fuzzy Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459 Mehman A. Damirli
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Decision Making in Hepatitis B Diagnosis by Using Fuzzy Expert System: Case of Near East Hospital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469 Gunel Imanova and Arzu Gul Seyfi Application of Leointief’s Input-Output Model of Azerbaijan Economy Under Fuzzy Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476 V. J. Axundov Simulation of Fractal Kinetics of Thermooxidation of Polymer Melts Based on Fractional Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485 Habibov Ibrahim Abulfas, Abasova Sevinc Malik, and Agamammadova Sevda Alipasha Fuzzy Models for Calculation of Oil and Gas Reserves . . . . . . . . . . . . . . . . . . . . . . 493 I. Y. Bayramov, A. N. Gurbanov, I. Z. Sardarova, G. G. Mammadova, and S. V. Abbasova Vendor Selection by Using Ideal Solution Methodology with Fuzzy Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502 K. R. Aliyeva Selection Core Banking System by Using Fuzzy AHP and Fuzzy TOPSIS Hybrid Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507 Nihad Mehdiyev Performance Analysis of Machine Learning Algorithms for Medical Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514 Fahreddin Sadikoglu, Boran Sekeroglu, and Deborah Amaka Ewuru Difference Between Digital Marketing and Traditional Marketing Models Gunay E. Imanova
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Determination of Green Field Plants Most Suitable for Geographical Features of Places with Fuzzy Logic Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 530 Rü¸stü Ilgar, Vugar Salahli, Yagub Sardarov, Zarifa Imanova, and Zhala Jamalova Z-Information Based MCDM Model for Assessing Green Energy Resources: A Case of Resort and Tourism Areas . . . . . . . . . . . . . . . . . . . . . . . . . . . 539 Mahammad Nuriyev, Aziz Nuriyev, and A. N. Mahamad Assessing the Impact of Innovations on the Volume of Production of the Final Product in a Fuzzy Information Environment . . . . . . . . . . . . . . . . . . . . 549 ˙ S. Rustamov V. J. Akhundov and I.
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Application of WASPAS Method to Data Platform Selection Under Z-Valued Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557 K. I. Jabbarova Using Deep Learning Algorithm for Prediction and Detection of Covid-19 . . . . . 564 Elbrus Imanov and Vidura Lakshitha Liyanagamage Fuzzy Logic-Based Planning of the Behavior of Autonomous Vehicles . . . . . . . . 572 A. B. Sultanova Digitization of Centrifugal Compressor Asset as One of Key Elements of Overall Digitized Industrial Plant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579 Nodirbek Yusupbekov, Farukh Adilov, and I. Arsen Investment Decision Making by Using Natural Language Processing . . . . . . . . . . 588 Nigar F. Huseynova Multi-attribute Decision Making Under Z-Set Valued Uncertainty . . . . . . . . . . . . 595 Rafig R. Aliyev and Akif V. Alizadeh Fuzzy Processing of Hydrodynamic Studies of Gas Wells Under Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 608 Salahaddin I. Yusifov, Imran Y. Bayramov, Azar G. Mammadov, Rza S. Safarov, Rashad G. Abaszadeh, and Elmira A. Xanmammadova Fuzzy Modeling for Marketing Plan Development . . . . . . . . . . . . . . . . . . . . . . . . . . 616 Seving R. Mustafayeva Solving Employee Selection Problem Under Fuzzy-Valued Information . . . . . . . 620 Aynur I. Jabbarova and K. I. Jabbarova The Use of Fuzzy Numbers for the Rational Choice of the Structure of the Distribution Channel of Goods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 626 Alekperov Ramiz Balashirin “Dede Korkud” Epos in Light of Fuzzy Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634 Kamal Abdulla and Rafik A. Aliev Toward Z-Number-Based Classification of Dataset . . . . . . . . . . . . . . . . . . . . . . . . . 637 R. R. Aliyev, O. H. Huseynov, and Babek Guirimov Application of Enterprise Solution Software for a Hotel Chain . . . . . . . . . . . . . . . 645 Serdar Oktay
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Fuzzy Logic Modelling of the Relationship Between Attitudes Towards Military Services and Soldiers’ Self-esteem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653 Konul Memmedova and Banu Ertuna Applying Type-2 Fuzzy TOPSIS Method to Selection of Facility Location . . . . . 662 K. R. Aliyeva Applying a Fuzzy-Set Approach to Assessing Capital Flight Management: Empirical Research from Azerbaijan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 669 Ulviyya Rzayeva and Rena Mikayilova Decision Making with Z-Bounded Interval Preference . . . . . . . . . . . . . . . . . . . . . . 677 Akif V. Alizadeh and Rafig R. Aliyev Teacher Assessment Model with Basic Uncertain Information . . . . . . . . . . . . . . . . 686 Farida Huseynova and Nigar F. Huseynova Design of Receiver in Fuzzy-Chaotic Communication Systems . . . . . . . . . . . . . . . 696 K. M. Babanli Smart Traffic Monitoring and Control System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 703 L. R. Bakirova and A. R. Bayramov Extension of Delphi Method to Z-Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 712 Rafig R. Aliyev, O. H. Huseynov, and E. R. Zeynalov Analysis of Intelligent Interfaces Based on Fuzzy Logic in Human-Computer Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 720 Rahib Imamguluyev and Aysel Aliyeva Determination of the Uncertainty of the Parameters of Oxidative-Reduction Reactions of Titanomagnetites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 727 U. N. Sharifova, A. N. Mammadov, D. B. Tagiev, and M. B. Babanly Solving Problem of Unit Commitment by Exchange Market Algorithm and Dynamic Planning Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 734 Ebrahim Babaei and Sadig Mammadli Regular Identification Algorithms for a Special Class of Neuro-Fuzzy Models ANFIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 747 H. Z. Igamberdiev, A. N. Yusupbekov, U. F. Mamirov, and Sh. D. Tulyaganov Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 755
On Some De Novo Type Approaches to Fuzzy Decision Making, Optimization and Control: An Application to Sustainable Regional Development Janusz Kacprzyk(B) Finnish Society of Sciences and Letters Systems Research Institute, Warsaw, Poland [email protected]
Abstract. The paper is basically concerned with optimization, static and dynamic, under imprecise (fuzzy) information. Usually, the optimization problem is formulated as the maximization (or minimization) of some utility function, for instance, some financial result of an activity, subject to some constraints on, for instance, available resources, values of decision variables, etc. This general setting, which is the essence of virtually all traditional optimization problems considered, presupposes that parameter of the problem, for instance, constraints on resources devoted to particular types of activities, are given in advance.
These optimization problems have been found very useful, and over the decades many problem classes, solution methods, algorithms, software packages, etc. have been developed and have shown great usefulness for solving a multitude of practical problems. One can however readily see that all the above-mentioned optimization type problems boil down to an optimal allocation of fixed or limited resources in each problem or system considered, for instance, a transportation problem. In very many, if not all, real-world practical problems the essence is not only to find an optimal allocation of fixed, specified in advance resources in a given and specified system but rather to the (optimally) design of the particular system. For example, in the case of a large-scale transportation system, we can be interested in a proactive extension of the transportation problem, like assigning some resources for increasing total quantities at sources and destinations by building some additional facilities. Or, in the case of a regional agriculture modeling problem in which, briefly speaking, there are constraints related to the use of, for example. Fertilizers and watering (irrigation). In the traditional optimization type approach, we just have as the right-hand sides of the two respective constraints the limits (possibly financial) of the number of available fertilizers and water, which are considered separately. However, in practice it can often happen that we have some available funds for fertilizers, water, etc. which implies those limits on them because we can, for instance, purchase more (or less) fertilizering and spend more (or less) funds for the watering system. Then additionally, we should in the J. Kacprzyk---Polish Academy of Sciences Member, Academia Europaea Member, European Academy of Sciences and Arts Foreign Member, Bulgarian Academy of Sciences Foreign Member, Spanish Royal Academy of Economic and Financial Sciences (RACEF) Foreign member © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 1–3, 2023. https://doi.org/10.1007/978-3-031-25252-5_1
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course of optimization, distribute these funds into parts devoted to the purchasing of fertilizers and water. This can clearly be done with respect to involving multiple objectives, too. The above philosophy of an optimal system design, termed de novo programming has been introduced by Zeleny in 1981, first for single objective problems and then extended for multi-objective problems. This approach has attracted much attention in optimization, operations research, systems analysis, etc. communities, and has been applied to solve many practical problems. In a rich literature on de novo programming, one can cite, for instance, the following developments: new general de novo programming problems with the maximization and minimization type objectives (GDNPP), cf. Li and Lee (1990a, 1990b), Chen and Hsieh (2006), Umarusman (2013), and Chakraborty& Bhattacharya (2012, 2013), to just mention a few. What concerns the applications, Miao et al. (2014) have proposed an interval-fuzzy de novo programming method for planning water resource systems under uncertainty, and Saeedi et al. (2015) have shown an application to determine the capacity in a closedloop supply chain network with a queueing system, Sarjono et al. (2015) have shown an application for production planning optimization at an Indonesian ceramics company, Chen (2014) has proposed an application in integrated circuit (IC) design, Sharah & Khalili-Damghani (2019) have proposed an application in the gas supply chain, Zhang, Huang and Zhang (2009) have proposed an application for water resources systems planning, etc. There is a long tradition of using fuzzy logic and fuzzy optimization in de novo programming. Just to mention a few, one can cite here: Chen and Hsieh (2006) who introduced a new approach to the solution of multi-stage GDNPP using fuzzy dynamic programming (cf. Kacprzyk, 1997), Chakraborty and Bhattacharya (2012, 2013) who have proposed a new method for the solution of GDNPP in one step under fuzzy environment using the Zimmermann’s (fuzzy linear programming approach, Ghorbani et al. (2014) proposed the use of a fuzzy goal programming approach, Chakraborty et al. (2014) introduced the concept of duality, Sen (2016) showed how the concept of a penalty function can be employed, Sharahi and Khalili-Damghani (2019) showed the use of type 2 fuzzy sets, etc. A good source of information is the recent paper by Banik and Bhattacharya (2020). 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. The best-known paper is presumably here by Chen and Hsieh (2006) who introduced a new de novo type model using fuzzy dynamic programming in the sense of Bellman and Zadeh (1970) and Kacprzyk (1983, 1997). We will basically follow the line of reasoning of Chen and Hsieh (2006) but will add another important dimension related to the temporal distribution of funds over 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 indirectly, in terms of some value to various stakeholders, for
On Some De Novo Type Approaches
3
instance, the inhabitants whose preference is possibly fast attainment of some socioeconomic objectives, and it is obvious that more funds at earlier stages can have a positive effect on the attainment of these objectives. Moreover, we add to the traditional de novo fuzzy dynamic programming model the condition of the so-called stability which boils down to a 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 optimization, related to discounting and stability, maybe a powerful tool for solving a multitude of problems. In the paper, an application for sustainable regional agriculture planning is shown.
The Ideas of L. Zadeh and R. Aliev in the 3rd Generation of Artificial Intelligence Alexey Averkin1,2(B) 1 Federal Research Centre of Informatics and Computer Science of RAS, Vavilova Street, 42,
Moscow, Russia [email protected] 2 Russia Educational and Scientific Laboratory of Artificial Intelligence, Neuro-Technologies and Business Analytics, Plekhanov Russian University of Economics, Stremyanny Lane, 36, Moscow, Russia
Abstract. Every decade technology makes revolutionary shifts that become the new platforms on which application technology is built. Artificial intelligence (AI) is no different. AI has moved from 1st Generation shallow learning and handcrafted features to 2nd Generation deep learning, which has been effective at learning patterns. We have now entered the 3rd Generation of AI which is machine reasoning-driven – where the machine can interpret decision making algorithm, even if it has the black-box nature. Explainable artificial intelligence and augmented intelligence are the main part of the 3rd Generation of AI. The role of Professor Lotfi Zadeh and Professor Rafik Aliev in these AI generations are tremendous. Professor L. Zadeh was the founder of the theory of fuzzy sets and linguistic variables, the “father” of fuzzy logic and approximate reasoning, the author of the theory of possibility and general theory of uncertainty, the creator of Z-numbers theory and generalized restrictions, the ancestor of granular and soft computing. His ideas and theories not only opened a new epoch in the development of scientific thought, free from the limitations of narrow scientific directions and contributing to their synergy. They made a significant contribution to the development of new information and cognitive technologies, led to the creation of effective industrial technologies, such as fuzzy computers and processors, fuzzy regulators, fuzzy clustering and recognition systems, and many others. Professor L. Zadeh has been deservedly included in the IEEE Computer Society’s gallery of fame scientists who have made pioneering contributions to the field of artificial intelligence and intelligent systems. The role of L. Zadeh in AI is also hard to overestimate especially in the l focus on the concept of soft computing, originally combining hybrid models based on fuzzy sets, neural networks, and soft computing. The emergent properties of these models were one of the foundations of the current hype in artificial intelligence and machine learning. For many years L. Zadeh fruitfully cooperated with Professor Rafik Aliev. The result of their research was fundamental scientific achievements published in several joint monographs. The generalized theory of stability created by L. Zadeh and R. Aliev jointly has been recognized as a major contribution to the development of mathematics, management theory, dynamic economics and a number of other © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 4–5, 2023. https://doi.org/10.1007/978-3-031-25252-5_3
The Ideas of L. Zadeh and R. Aliev in the 3rd Generation of Artificial Intelligence sciences. The main scientific directions of Professor Rafik Aliev’s research are the theory of decision-making in terms of high uncertainty, the theory of coordination in complex social, economic, and technical systems, fuzzy logic, and neurocomputing. Applied fields of his scientific results are economics, conflictology, space objects and technical systems. These areas of modern artificial intelligence are referred to augmented intelligence (intelligence decision-making). Augmented intelligence is a design pattern for a human-centered partnership model where humans and artificial intelligence work together to improve cognitive functions, including learning, decision-making, and new experiences. The business value forecast for augmented intelligence in 2025 will be 44 percent of all AI business applications. Explainable artificial intelligence now represents a key area of research in artificial intelligence and an unusually promising one in which many fuzzy logics could become crucial. Research in the of area of explainable artificial intelligence can be divided into three stages, which correlates with the 3 generation of AI: in the first stage (starting from 1970) expert systems were developed; in the second stage (mid-1980s), the transition was made from expert systems to knowledgebased systems; and in the third phase (since 2010), deep architectures of artificial neural networks, which required new global research on the construction of explainable systems, have been studied. On each stage the ideas of L. Zadeh and R. Aliev played the important roles. They were the first ones in explainable artificial intelligence field with neuro-fuzzy systems – a synergistic combination of fuzzy logic and neural networks, providing the first interpretable AI system based on neural network learning. Since 2011 L. Zadeh had been involved in Z Advanced Computing, Inc. (ZAC), the pioneer Cognitive Explainable Artificial Intelligence (Cognitive XAI). The Cognitive Explainable-AI approach also use the results of Prof. Rafik Aliev, Prof. Ronald Yager, Prof. Mo Jamshidi. Nowadays, explainable and augmented intelligence are prominent and fruitful research fields where many of Zadeh’s and R. Aliev’s contributions can become crucial if they are carefully considered and thoroughly developed. It is worth noting that about 30% of publications in Scopus related to XAI, dated back to 2017 or earlier, came from authors well recognized in the fuzzy logic field. This is mainly due to the commitment of the fuzzy community to produce interpretable intelligent systems since interpretability is deeply rooted in the fundamentals of fuzzy logic.
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Multiattribute Decision Making in Material Selection Under Z-Valued Information M. B. Babanli(B) Azerbaijan State Oil and Industry University, 20 Azadlig Avenue, AZ1010 Baku, Azerbaijan [email protected]
Abstract. Material selection is a complex problem that involves analysis of a series of factors. One of the issues is imperfect decision relevant-information stemming from incomplete theoretical knowledge and experimental data. Often, fuzzy logic and soft-computing-based approaches are used to deal with this complexity. However, works devoted to account for both fuzziness and partial reliability of information in material selection are scarce. To account for such kind of information, Zadeh introduced the concept of a Z-number. In view of this, a problem of an optimal alloy selection for pressure vessel under Z-number-valued information is considered in this paper. Degrees of relative importance of attributes and values of attributes for alternatives are described by Z-numbers. Differential evolution optimization technique is used to reduce inconsistency of degrees of relative importance provided by an expert. An ideal solution idea is used to determine an optimal alternative (alloy). The applied solution procedures are characterized by relatively low computational complexity. Keywords: Alloy selection · Decision making · Z-number · Pairwise comparison matrix · Differential evolution
1 Introduction Material selection is a complex task that requires analysis of four groups of factors [1]: material properties, material processing requirements, availability of materials, cost of materials [2]. Decision making in material selection includes three stages: initial screening, development and comparison of alternatives, and determination of best solution [3]. Thus, theoretical knowledge and experimental data are sources for decisionrelevant information in material selection. Often, multiattribute decision making methods (MADM) are used to solve problems of decision making in material selection. Let us shortly overview existing works on this topic. A series of works is devoted to the use of AHP method in selection of Al/SiC composite materials [4], semiconductor switching devices [5], minimization of environmental impact while choosing of aluminum alloy in screw manufacturing [6]. In [7] it is proposed not to deal with material selection decision matrices but to determine the most important criterion for whole selection process. In the article, five material selection problems are examined from different point of views. VIKOR, TOPSIS and PROMETHEE methods are used. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 6–15, 2023. https://doi.org/10.1007/978-3-031-25252-5_7
Multiattribute Decision Making
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Systematic analysis of the field may be found in [3, 7–10]. [8] is devoted to selection problems in the mechanic field. Classical optimization techniques-based approaches and several case studies are considered. Both analytical and computer-aided approaches are considered in [9]. In [10], authors analyze existing methods of material screening and selection based on their advantages, drawbacks and potential applications. A wide overview of existing works on material selection is also given in [11]. To deal with imperfect decision relevant information and other complexities in material selection problems, they considered the use of soft-computing-based approaches [8, 12]. The related works includes application of MADM methods under fuzzy information, genetic algorithms, fuzzy expert systems and other approaches. For the first time, MADM problem of material selection under Z-number valued information is considered in [13]. Selection of titanium alloys based on their properties is considered. Z-numbers were used to describe attributes values (describe alloy properties) and attributes weights. The solution approach is based on simple additive weighting of Z-numbers. Further, a series of problems of material selection under fuzzy and Z-number-valued information was considered in book [14]. For solving the problems, VIKOR and AHP methods, If-Then rules and other approaches are used. The existing works on material selection under fuzzy and Z-valued information are characterized by problems of consistency and information aggregation. Often, simplified assumptions are used. For example, it is assumed that importance weights of decision attributes are initially given in form of fuzzy or Z-numbers. Usually, some information about comparative importance of attributes can be provided. In this case, a problem of consistency of pairwise comparisons arises, whereas initially consistent information is assumed to be given. From the other side, aggregation of attribute values leads to loss of information (especially in case of dependence of attributes). This paper is devoted to material selection under Z-valued information for pressure vessel. Information about relative importance of attributes is described in form of userderived Z-number-valued pairwise comparison matrix (PCM). Based on consistency requirements, a consistent Z-number-valued PCM is obtained by solving optimization problem. Next, Z-number-valued attributes importance weights are found by computing the 1st eigenpair of this matrix. Finally, the optimal alternative is determined as one closest to the ideal alternative (to reduce loss of information that arise due to aggregation of attribute values).
2 Preliminaries Definition 1. A continuous Z-number [15]. A continuous Z-number is an ordered pair Z(A, B). A is a continuous fuzzy number playing a role of a fuzzy restriction on a value that a random variable X may take: Value of X is A.
(1)
In other words, A is used to describe imprecise information about a value of X. A degree of reliability of A is described as a value of probability measure P(A) =
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M. B. Babanli
μA (x)p(x)dx, where p is probability distribution of X and μA (x) is membership func-
R
tion of A. If p is precisely known, then P(A) is a crisp number. However, in real-world problems an actual p may not be precisely known, and one considers a set of distributions. This requires dealing with fuzzy restriction on a value of P(A). Thus, a fuzzy number B with a membership function μB : [0, 1] → [0, 1] [0, 1] is used as a fuzzy restriction: The value of P(A) is B
(2)
This implies that fuzzy uncertainty related to p induces fuzziness of a value of P(A). Thus, a value of a random variable X can be described as a Z-number Z(A, B): A is a fuzzy estimation of a value, and B is a fuzzy reliability of this estimation. Definition 2. A Z-number-valued pairwise comparison matrix [16]. A Z-numbervalued pairwise comparison matrix (PCM) (Zij ) is a square matrix of Z-numbers: ⎛
⎞ Z11 = (A11 , B11 ) ... Z1n = (A1n , B1n ) ⎠. (Zij = (Aij , Bij )) = ⎝ . ... . Zn1 = (An1 , Bn1 ) ... Znn = (Ann , Bnn )
(3)
A Z-number Zij = (Aij , Bij ), i, j = 1, ..., n describes partially reliable information on degree of preference for i-th criterion against j-th one. Definition 3. A Distance between Z-numbers [17]. A Z-number Z = (A, B) is characterized by fuzzy number A, fuzzy number B and an underlying set of probability distributions G. We propose to define distance between Z-numbers D(Z1 , Z2 ) as follows. Distance between A1 and A2 is computed as D(A1 , A2 ) = supα∈(0,1] D(Aα1 , Aα2 ), D(Aα1 , Aα2 )
(4)
α A11 + Aα12 Aα21 + Aα22 − = . 2 2
Aα1 and Aα2 denote α-cuts of A1 and A2 respectively, Aα11 , Aα12 denote lower and upper bounds of Aα1 (Aα21 , Aα22 are those of Aα2 ). Distance between B1 and B2 is computed analogously. A distance between sets G1 and G2 of probability distributions p1 and p2 can be expressed as
1 1 2 D(G1 , G2 ) = inf p1 ∈G1 ,p2 ∈G2 (1 − (p1 p2 ) 2 dx) , R
where the expression in figure brackets is the Hellinger distance between two probability distributions p1 and p2 . The use of inf operator implies that among all the possible pairs of distributions, the pair of the closest p1 ∈ G1 and p2 ∈ G2 is found to define distance D(G1 , G2 ).
Multiattribute Decision Making
9
Given D(A1 , A2 ), D(B1 , B2 ) and D(G1 , G2 ), the distance for Z-numbers is defined as D(Z1 , Z2 ) = βD(A1 , A2 ) + (1 − β)Dtotal (B1 , B2 )
(5)
Here Dtotal (B1 , B2 ) is a distance for reliability restrictions which is computed as: Dtotal (B1 , B2 ) = wD(B1 , B2 ) + (1 − w)D(G1 , G2 ),
(6)
β, w ∈ [0, 1] are DM’s assigned importance degrees. Definition 4. An inconsistency index for Z-number-valued PCM [17]. An inconsistency index K for Z-number-valued PCM (Zij ) is defined as follows:
Zij Zjk Zik D Z(1), , (7) K Zij = max min D Z(1), i 0˜ is satisfied, the residual arc capacity of the opposite arc is equal to u˜ μr (j, i, v, t) = ξ˜ μ (i, j, t, v). μ
2.2. Implement the breadth-first search that seeks for the shortest trails p˜ e from the source s to the sink r . μ 2.2.1. Transition to the Step 2.3 if p˜ e is detected. 2.2.2. The value of fuzzy maximum flow and corresponding flow partition is detected ˜ eμr , transition to the Step 3. if there isn’t any augmenting path in the network G ∼μ 2.3. Transmit the given flow according to residual capacity σ e = min[˜uμr xi , xj , t, v ]. 2.4. Update the flow using the rule: ∼μ μr 1) decrease ξ˜ μ xi , xj , t, v by value σ e for arcs between vertex (xj , v) and vertex μr (xi , t). Go to 2.1. ∼μ μr μr 2) increase ξ˜ μ xi , xj , t, v by σ e for arcs between vertex (xi , t) and vertex (xj , v). Go to 2.1. Step 3. Arc reversal
∼μ
3.1. For ∀t ∈ T reverse the arc between (j, v) and (i, t) up to ξ (i, j, t, v)−u˜ (i, j, t, v), ∼μ if ξ (i, j, t, v) > u˜ (i, j, t, v) with replacing u˜ (i, j, t, v) by 0˜ if the arc (i, t) (j, v) ∈ / A. 3.2. For ∀t ∈ T and the arc joining (i, t) with (j, v) if the arc connecting (i, t) with (j, v) should be reversed, and the value of saved arc capacity s˜(i, j, t, v) = ˜ s˜ (i, j, t, v) = u˜ (i, j, t, v) − ξ˜ (i, j, t, v) if u˜ μr (i, j, t, v) − ξ˜ (j, i, v, t) and s˜ (j, i, v, t) = 0. both arcs connecting (i, t) with (j, v) alongside (j, v) with (i, t) are not reversed. 3.3. Remove super vertices and artificial arcs connecting them. A path in the timeexpanded network connecting vertices (s, t) and (r, γ = t + τst (t)) with ξ˜ (s, r, t, γ ) corresponds to ξ˜sr (t). Thus, the time-spaced network transits to the original dynamic one.
4 Example We consider the evacuation scenario to convey the evacuees from endangered node s to the destination d in the evacuation network with fuzzy arguments and the partial lane reversal within T = 5 considering dynamic nature of evacuation. Network for modelling is represented by fuzzy dynamic graph (Fig. 1). Transit arc capacities are given in Tables 1 and 2. Transition to the modified network with the new values of the arc capacities is implemented by the step 1, as shown in Fig. 2. The figure represents modified arc capacities in Table 2. The modified version of the graph is represented in Fig. 3.
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Fig. 1. Example of fuzzy dynamic network with the arguments in Tables 1 and 2.
Table 1. Transit arc capacities u˜ ij (t) at time periods t. Arcs (s, 1) (1, s) (s, 2) (2, s) (1, 2) (2, 1) (1, 3) (3, 1) (2, 3) (3, 2) (2, r) (r, 2) (3, 4) (4, 3) (4, r) (r, 4)
Periods 0
1
2
3
4
5
20 18
22 18
23 20
19 17
19 17
23 20
18 15
23 17
17 16
10 17
18 15
15 18
22 18
22 18
30 20
30 20
20 20
20 20
22 18
22 23
18 22
22 23
22 23
18 22
11 9˜
11 9˜
12 11
6˜ 9˜
6˜ 9˜
12 11
15 11
15 11
15 11
20 15
22 16
22 16
19 21
19 21
24 22
24 22
22 18
21 15
20 18
20 18
13 17
18 14
18 14
20 18
The maximum flow finding algorithm is implemented by finding augmenting paths and conveying the flow among them in order to define the evacuation flow of the maximum value in the fuzzy network in Fig. 3. Fuzzy maximum dynamic flow distribution after partial lane reversal is presented in Table 3. We can conclude that modified outbound arc capacities by the lane reversal procedure units. Let us evaluate the saved allow us to increase the total fuzzy flow value up to 131 dynamic arc capacities by the step 3 of the algorithm. The final network is shown in Fig. 4.
Maximum Dynamic Evacuation Modelling in Networks μ
Table 2. Modified transit arc capacities u˜ ij (t) at time periods t. Arcs (s, 1) (s, 2) (1, 2) (1, 3) (2, 3) (2, 5) (3, 4) (4, 5)
Periods 0
1
2
3
4
5
1 38, 2 33,
2 40, 2 40,
2 43, 2 33,
1 36, 1 27,
1 36, 1 33,
1 43, 2 33,
1 40, 2 40,
2 40, 45, 2
2 50, 2 40,
3 50, 3 45,
3 40, 45, 3
3 40, 3 40,
2 20, 26, 2
1 20, 26, 3
1 23, 3 26,
1 15, 2 35,
1 15, 1 38,
2 23, 1 38,
2 40, 2 38,
2 40, 1 38,
1 46, 1 30,
1 46, 1 32,
1 40, 1 32,
2 36, 1 38,
Fig. 2. Modified network in fuzzy terms
Fig. 3. The time-expanded version of the modified fuzzy network
21
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J. Kacprzyk et al. Table 3. Fuzzy maximum dynamic flow distribution after partial lane reversal.
The path
Departure time (T)
Arrival time (T)
Flow value
s0 → 22 → r5
0
5
s0 → 22 → 33 → 44 → r5 s0 → 11 → 33 → 44 → r5 s0 → 11 → 23 → r5
0
5
26 7˜
0
5
0
5
s1 → 23 → r5 s1 → 13 → 24 → r5
1
5
1
5
25 13 22 38 1 31
Total flow
Fig. 4. The time-expanded network with the saved arc capacities.
5 Conclusion and Future Scope This work presents the method for macroscopic evacuation of the maximum possible amount of aggrieved as a model with the partial lane reversal in fuzzy conditions. Implementing the pattern of the partial lane reversal enables us to redirect the traffic by increasing the outbound modified capacities and optimizing the routes of the vehicles in such a way that revers the movement direction along the roads with low traffic, thereby enhancing the traffic along the overloaded road sections. A lack of the initial information on the values of the arc capacities of the road segments, traversal times, the number of aggrieved etc. leads to the fuzzy evacuation modelling. The novelty of the method is in fuzzy nature of evacuation due to the concept of partial lane reversal
Maximum Dynamic Evacuation Modelling in Networks
23
in the network with time-varying arc capacities and traversal times. A case study was carried out to illustrate the proposed algorithm. Generalized evacuation models in fuzzy modified networks allowing partial lane reversal will be examined as a series for future studies. Acknowledgments. The research was funded by the Russian Science Foundation (project No. 22-71-10121, implemented by the Southern Federal University).
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17. Pyakurel, U., Nath, H.N., Dempe, S., Dhamala, T.N.: Efficient dynamic flow algorithms for evacuation planning problems with partial lane reversal. Mathematics 7(10), 993 (2019). https://doi.org/10.3390/MATH7100993 18. Bozhenyuk, A., Gerasimenko, E., Kacprzyk, J., Rozenberg, I.: Flows in Networks Under Fuzzy Conditions. Studies in Fuzziness and Soft Computing, vol. 346, Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-319-41618-2 19. Bozhenyuk, A., Gerasimenko, E., Rozenberg, I.: Method of maximum two-commodity flow search in a fuzzy temporal graph. In: Kacprzyk, J., Szmidt, E., Zadro˙zny, S., Atanassov, K.T., Krawczak, M. (eds.) IWIFSGN/EUSFLAT - 2017. AISC, vol. 641, pp. 249–260. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-66830-7_23
Z-Number-Based Similarity Reasoning in Control Systems Nigar E. Adilova(B)
and Aziz Nuriyev
Azerbaijan State Oil and Industry University, 34 Azadlyg Ave., Baku AZ1010, Azerbaijan [email protected], [email protected]
Abstract. The application of Z-based If-Then rules is a contemporary direction in the research of uncertain decision-making environment. Stemming from necessity, the ranking fuzzy and Z-numbers has become a prerequisite procedure for decision-making problems. Numerous techniques including similarity-based methods have been proposed to deal with fuzzy ranking problems. However practically there is no analysis of similarity reasoning in a Z-based control system. This paper provides to investigate Z-based similarity reasoning in the control system. The suggested approach is illustrated with a numerical example. Keywords: Z-number · Z-based control system · Reasoning · Similarity measure · IF-THEN rules
1 Introduction Similarity measure can be used to detect and group fuzzy numbers. In more general terms, similarity can also be applied to comparing alternatives. Up to now, many authors have suggested different types of fuzzy ranking methods, and some of them are related to similarity measure which was first presented by [1] considering compatibility between fuzzy numbers. In [2] ranking fuzzy numbers using distance method was discussed and presented based on 3 numerical examples. Various similarity measure techniques have been developed in time. Afterward, Jaccard similarity measure has been suggested and applied in ranking fuzzy numbers. Despite the popularity of standard Jaccard index, it has successfully been replaced by FUJI (Fuzzy Jaccard Index). The extension of Jaccard index in different types of fuzzy numbers has been introduced in [3]. Apart from that, the authors investigated a functional approach based on a fuzzy Jaccard index with a degree of optimism [4]. Broadly developed theories in the field of Jaccard similarity measures are also available in the literature [5–10]. In [11] fuzzy Jaccard index has been demonstrated by showing the limitations of other similarity measures, and the authors compared FUJI with different proposed scores. Although the author in [12] offered investigations on the consistency of fuzzy If-Then rules regarding similarity for rule premise (antecedent) and rule consequent, unfortunately, research on similarity reasoning of Z-based rules is still scarce. In this paper, we address Z-number-based similarity reasoning in control systems. The motivation of the study is on the analysis of the Jaccard similarity measure for rule © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 25–30, 2023. https://doi.org/10.1007/978-3-031-25252-5_9
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premise in a Z-based control system. For a comprehensive review of the matter, the proposed work is characterized as follows: Section 2 interprets the basic concept of Jaccard similarity measure, we also briefly review the definitions of Z-numbers and Jaccard similarity index. Section 3 demonstrates the problem description and its solutional approach. In Sect. 4, a practical example is illustrated as an application of the method. Eventually, Sect. 5 is related to the concluding marks.
2 Preliminaries For convenience, a Z-number can be characterized as below: Definition 1: Z-numbers [13–15]. A discrete Z-number is an ordered pair Z = (A, B) of discrete fuzzy numbers (A,B). Here A has the same meaning as it has in a continuous Z-number. B is a discrete fuzzy number with a membership function µB : {b1 , ..., bn } → [0, 1], {b1 , ..., bn } ⊂ [0, 1] [0, 1]. Definition 2. Z-based If-Then rules [16, 17]: Z-based IF-THEN rules comprehensively identify conditional statements as fuzzy If-Then rules. In contrast to the fuzzy If-Then rules, Z-based If-Then rules are defined as below: IF X is Z1 = (A1 , B1 ) THEN Y is Zy1 = (Ay1 , By1 ) ... IF X is Zn = (An , Bn ) THEN Y is Zyn = (Ayn , Byn ) Definition 3. Jaccard similarity measure [6, 18–20]. The Jaccard similarity measure between two Z-numbers Z1 and Z2 , in which parts A and B are expressed with triangular fuzzy numbers, is calculated by the given formula: 3 1 i=1 aA1i aA2i J = 3 3 3 2 2 − 2 i=1 aA1 + i=1 aA2 i=1 aA1i aA2i i i 3 1 i=1 bB1i bB2i + 3 2 i=1 b2B1 + 3i=1 b2B2 − 3i=1 bB1i bB2i i
(1)
i
where aA1 , aA2 bB1 , bB2 and are the components of the first and second Z-numbers respectively.
3 Statement of the Problem Consider that Z-based control system [21] consists of n of rules given below: IF X is Zx1 = (A1 , B1 ), THEN Y is Zy1 = (Ay1 , By1 ) IF X is Zx2 = (A2 , B2 ), THEN Y is Zy2 = (Ay2 , By2 ) . . . .. IF X is Zxn = (An , Bn ), THEN Y is Zyn = (Ayn , Byn )
(2)
Z-Number-Based Similarity Reasoning in Control Systems
27
Each of the components in the control system is characterized by Z-numbers. The problem is to analyze similarity reasoning in a Z-based control system. In the first step, the solution of the problem will be realized by defining Jaccard’s similarity measure between the new antecedent and current inputs of the control system. After the calculation of similarity indexes, some of the antecedents of the rules must be selected regarding to the threshold. In the end, the new consequent has to be formalized based on Z-number similarity reasoning. A numerical example illustrates the application of the described methodology.
4 Application of Numerical Example For overcoming the above-mentioned problem, let us take a look at the Z-based control system. Parts A and B of Z-numbers are expressed by triangular fuzzy numbers. 1. IF X is Z1A = [(−10, −10, −7), sure] THEN Y is Z1B = [(−1, −0.9, −0.7), sure] 2. IF X is Z2A = (−10, −7, −3), very sure THEN Y is Z2B = [(−0.7, −0.6, −0.4), sure] 3. IF X is Z3A = (−7, −4, −1), very sure THEN Y is Z3B = (−0.4, −0.25, −0.1), very sure 4. IF X is Z4A = [(−3, 0, 3), less sure]THEN Y is Z4B = [(0, 0.1, 0.3), less sure] 5. IF X is Z5A = [(0, 3.5, 7), sure]THEN Y is
(3)
Z5B = [(0.25, 0.4, 0.55), less sure] 6. IF X is Z6A = (3, 5, 8), very sure THEN Y is Z6B = [(0.6, 0.8, 0.85), sure] 7. IF X is Z7A = [(7, 10, 10), less sure]THEN Y is Z7B = [(0.85, 0.9, 1), less sure] where less sure, sure, very sure are B part of Z-number which defines the degree of belief. The values for B components are as follows: less sure = [0.4; 0.5; 0.6], sure = [0.7; 0.8; 0.9], very sure = [0.8; 0.9; 1] Regarding to the control system in (2) the graphical representation of Z-numbers is shown in Figs. 1, 2 and 3. For solving the problem, assume that the antecedent of the new rule is in the form of Z-number Znew = [(−8, 2, 6), (0.1, 0.8, 0.9)]. We suggest applying formula (1) to separately calculate the similarity between new and current promises of Z-based rules. For this purpose, firstly, membership functions must be evaluated for the given 7 rules. By using the values of membership functions Jaccard similarity measure will be defined as below:
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Z1
Z2
1Z4 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
Z5
Z3
1
2
3
Z6
4
5
Z7
6
7
8
9 10
Fig. 1. A part of promises of Z-based rules
Z1
Z2
Z3
1
Z4
Z5
Z6 Z7
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -1 -0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Fig. 2. A part of consequents of Z-based rules 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0.3
0.4
0.5
0.6
0.7
Fig. 3. B part of Z-based rules
0.8
0.9
1
Z-Number-Based Similarity Reasoning in Control Systems
29
Table 1. Jaccard similarity measure Matches
Similarity index
J(R1 - R-new)
0.431
J(R2 - R-new)
0.497
J(R3 - R-new)
0.549
J(R4 - R-new)
0.655
J(R5 - R-new)
0.615
J(R6 - R-new)
0.486
J(R7 - R-new)
0.428
Then we define the threshold as the value of 0.5 (as a sample). Corresponding to the threshold we will take only the promises which are greater than the determined value. As seen in Table 1 fourth and fifth rules must be chosen in the next process of similarity reasoning. After that weights for the antecedent parts of the selected rules will compute using the following formula: J1 J2 J3 , w2 = , w3 = J1 + J2 + J3 J1 + J2 + J3 J1 + J2 + J3 After calculations we have w1 = 0.3, w2 = 0.36, w3 = 0.34. The result of similarity reasoning will be found by considering the following expression on the consequent parts of the selected rules (Rule-3, Rule-4, and Rule-5). w1 =
Z3B ∗ w1 + Z4B ∗ w2 + Z5B ∗ w3 Thus, new consequent will be formalized as Z3B ∗ w1 + Z4B ∗ w2 + Z5B ∗ w3 = (−0.035, 0.097, 0.265) (0.128, 0.225, 0.36) As a result, we get a new rule IF X is Zxnew = (−8, 2, 6)(0.1, 0.8, 0.9) THEN Y is Zynew = (−0.035, 0.097, 0.265)(0.128, 0.225, 0.36).
5 Conclusion In this study the applicability of jaccard similarity measure for Z-based reasoning in the control system was analyzed. The developed apparatus and the axiomatics of Z-numbers potentiate the determining of similarity measures and usage of them for decision-making. The suggested approach to determination of similarity measures makes it possible to select appropriate rules during the Z-based reasoning. In this research the Z-numberbased similarity reasoning has been solved in the example of a control system. We showcased the validity of suggested approach on the experimental analysis. The experimental analysis has revealed new consequent for the control system on the new premise (antecedent).
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References 1. Setnes, M., Cross, V.: Compatibility-based ranking of fuzzy numbers. Proc. Fuzzy Information Processing Society, NAFIPS-97, 305–310 (1997) 2. Cheng, C.-H.: A new approach for ranking fuzzy numbers by distance method. Fuzzy sets syst. 95, 307–317 (1998) 3. Ramli, N., Mohamad, D.: On the Jaccard index similarity measure in ranking fuzzy numbers. Matematika 25(2), 157–165 (2009) 4. Ramli, N., Mohamad, D.: Fuzzy Jaccard with degree of optimism ranking index based on function principle approach. J. Electr. Eng. 4(4), 9–15 (2010). https://doi.org/10.1234/mjee. v4i4.305 5. Niwattanakul, S., Singthongchai, J., Naenudorn, E., Wanapu, S.: Using of Jaccard coefficient for keywords similarity. In: Proceedings of the International Multi Conference of Engineers and Computer Scientists, vol. 1, p. 5 (2013) 6. Aliyev, R.R.: Similarity-based multi-attribute decision making under Z-information. bQuadrat Verlag, Germany, 33–38 (2015) 7. Hwang, Ch.-M., Yang, M.-Sh., Hung, W.-L.: New similarity measures of intuitionistic fuzzy sets based on the Jaccard index with its application to clustering. Int. J. Intell. Syst. 1–17 (2018). https://doi.org/10.1002/int.21990 8. Mahmood, T., Rehman, U.U., Ali, Z., Chinram R.: Jaccard and dice similarity measures based on novel complex dual hesitant fuzzy sets and their applications. Comput. Intell. Complex Decision Making, p. 25(2020). https://doi.org/10.1155/2020/5920432 9. Aliyev, R.R.: Fuzzy logic’s Z-extension-based decision tools and their applications. Dissertation work for the degree of Doctor of Philosophy, p. 104. Baku, Azerbaijan (2021) 10. Poruthukaren, K.: An attempt to estimate the noises in homeopathic pathogenetic trials by employing the jaccard similarity index and noise index. Homeopathy 111(3), 176–183 (2021). https://doi.org/10.1055/s-0041-1735983 11. Petkovic, M., Skrlj, B., Kocev, D., Simidjievski, N.: Fuzzy Jaccard index: A robust comparison of ordered lists. Appl. Soft Comput. 113 (2021). https://doi.org/10.1016/j.asoc.2021.107849 12. Adilova, N.E.: Consistency of Fuzzy IF-THEN rules for control system. Adv. Intell. Syst., Springer 1095, 137–143 (2019) 13. Aliev, R.A., Alizadeh, A.V., Huseynov, O.H.: The arithmetic of discrete Z-numbers. Inform. Sci. 290, 134–155 (2015) 14. Aliev, R.A., Huseynov, O.H., Aliyev, R.R., Alizadeh, A.V.: The Arithmetic of Z-Numbers: Theory and Applications. World Scientific, Singapore (2015) 15. Aliev, R.A.: Uncertain computation-based decision theory, p. 521. World Scientific, Singapore (2017) 16. Aliev, R.A., Pedrycz, W., Huseynov, O.H., Eyupoglu, S.: Approximate reasoning on a basis of Z-Number-valued if-then rules. IEEE T. Fuzzy Syst. 25(6), 1589–1600 (2017) 17. Aliev, R.A., Huseynov, O.H., Zulfugarova, R.Kh.: Z-Distance based if-then rules. Sci. World J. 2016, 9 (2016). https://doi.org/10.1155/2016/1673537 18. Zhang, L., Xu, X., Tao, L.: Some similarity measures for triangular fuzzy number and their applications in multiple criteria group decision-making. J. Appl. Math. 2013(3), 7 (2013). https://doi.org/10.1155/2013/538261 19. Ye, J., Jiang, W.: Multicriteria decision-making method based on a cosine similarity measure between trapezoidal fuzzy numbers, IEEE Int. Conf. Intell. Syst. Knowl. Eng. 3(1), 95–97 (2011). https://doi.org/10.1109/ISKE.2010.5680802 20. Ye, J.: Vector similarity measures of simplified neutrosophic sets and their application in multicriteria decision making. Int. J. Fuzzy Syst. 16(2), 204–211 (2014) 21. Aliev, R.A., Gardashova, L.A.: Z-set based approach to control system design. In: ICAFS2020, Adv. Intell. Syst. Comput. 1306, 10-21 (2021). https://doi.org/10.1007/978-3-030-640 58-3_2
Design of Quasi-Resonant Flyback Converter Integrated by Fuzzy Controller Fahreddin Sadikoglu1,2
, Samsam Bakhtiari1(B)
, and Ebrahim Babaei3
1 Engineering Faculty, Near East University, Mersin 10, 99138 Nicosia, North Cyprus, Turkey
{fahreddin.sadikoglu,samsam.bakhtiari}@neu.edu.tr
2 Odlar Yurdu University, Koroglu Rahimov Street, 13, 1072 Baku, Azerbaijan
[email protected]
3 Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran
[email protected]
Abstract. One of the disadvantages of on-off switching of the Flyback Converter (FBC) at a fixed frequency is the power switching losses that negatively affect the efficiency of the switching process. This problem can be met in switching modes: Discontinuous Conduction Mode (DCM) and Continuous Conduction Mode (CCM). Development of the Quasi Resonant Flyback Converter (QRFBC) operating with variable frequency decreases the loss of switching and improves its efficiency. This study considers the development of QRFBC converter using MATLAB Simulink controlled by fuzzy logic controllers (FLC). The performance analysis of the FLC is compared with traditional PI-controller using the different values of the input, reference voltages and loads. The results show that FLC provides efficiency control to the output voltage of QRFBC, the efficient switching of zero voltage, reducing switching losses, and increasing switching speed and precision. Keywords: Flyback converter · Fuzzy logic controller · PI controller · Quasi-resonant
1 Introduction The Quasi Resonance Flyback Converter (QRFBC) are used in mobile systems, laptops, notebooks, Liquid-Crystal Display (LCD), etc. These converters are used in switchedmode power supply (SMPS) applications. The QRFBC is simpler than other topologies in SMPS applications, so this converter is popular in industries. The power efficiency of QRFBC is enhanced using different methods such as soft-switching and synchronous rectification [1–5]. They achieved cost-effective power conversion with less power losses. In [6], the authors proposed a divided resonant capacitor to enhance the voltage spikes and the power conversion efficiency of QRFBC The both negative and positive sides of using high switching frequency in resonant mode are discussed in [7]. A resonant mode based flyback converter is introduced with the aim of soft switching, decreased loss and reduced electromagnetic interference using a high switching frequency. The results © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 31–39, 2023. https://doi.org/10.1007/978-3-031-25252-5_10
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of their experimental reveal that quasi-peak and harmonics are decreased compared to conventional discontinuous-conduction mode based converters. This converter can be used in low-power isolated – limited voltage converters. In [8], a single switched QRFBC with a high switching frequency is applied by using a resonant inductor and capacitor in primary and secondary, respectively. The proposed converter improves leakage energy along with zero current and valley switching. A result, switching losses and noises decreased remarkably. A zero voltage multi-output QRFBC is applied in [9]. The two most significant achievements of the model are proper voltage regulation for load changing and supply disturbance with minimum settling time. In [10], an adaptive frequency reduction model is proposed for QRFBC. The control system skips some valleys switching to decrease the frequency for lighter load and power loss. A resistor measures the primary current and sets the sensor output, which is shifted and compared with the feedback voltage value. In [11], the dynamic behaviour of QRFBC is analyzed, and the efficiency is enhanced by using a digital control method. The continuous conduction modulation mode controls the input power for the voltages less than a certain value. If the voltage is more than the specific value, a proportional iterative of switching period is applied to detect the stable control parameters of the changed load. The control parameters are applied by setting the output voltage to the reference value. A Quasi-resonant and fixed time control-based method for a flyback converter is proposed in [12]. The control system can select 2 statues in operation as changing input voltage and load amount and optimized the efficiency and losses simultaneously. Fixed off time control acts in low input voltage and high load, while QR acts at high voltage and low load. Also, the valley skipping ability is discussed as one of the advantages of the proposed method. In [13], self-calibrated valley switching and voltage regulation in QRFBC using a simple analogue method and perturbs and observes method is presented. The model is simulated in SPICE and applied to 5–40 high-voltage CMOS process. The results show the efficiency of the control model to regulate the output voltage to 0.8 percent by 10% to full and 127 to 375 V changes in load and input voltage, respectively. A PID controller is applied in [14] to control the performance of a flyback converter. In the respond model, different operation modes, including on and off statues of switching, overshoot, settling and rise time parameters, are improved by optimizing the controlling parameters. Also, a minimum overshoot is achieved using a PI controller. In [15], the authors applied a feed-forward Artificial Neural Network (ANN) to control a multi-output flyback zero voltage of a quasi-resonant converter. The results show the method’s efficiency in controlling changes in the set point and load values. A single output fuzzy logic model is used in [16] to control a zero voltage switching QRFBC. The main idea of using fuzzy model is to overcome the nonlinearity and complexity of the control process. The paper’s objective is to regulate the output voltage of the variable load. ISE value, rise time, settling time and offset are performance measurement parameters compared with a single input fuzzy logic controller. The results show that single fuzzy logic performs better in the case of ISE and offset values.
Design of Quasi-Resonant Flyback Converter
33
2 Controllers Design 2.1 Design QRFBC Using Fuzzy Logic Controller Figure 1 shows the QRFB converter associated with the fuzzy logic controller (FLC). The system consists of a QRFBC, a comparator that defines the differences U = Uo − Ur between the output voltage Uo of QRFBC and the reference voltage Ur , FLC and voltage-controlled oscillator (VCO). The FLC is based on Mamdani inference model. Ui
Uo +
QRFBC
-
Ur
ΔU VCO
FLC
Fig. 1. Quasi-resonant flyback converter controlled by fuzzy logic
Input and output of FLC is represented by nine linguistic variables (membership functions): TL = Too Low, NL = Negative Large, NM = Negative Medium, NS = Negative Small Z = Zero, PS = Positive Small, PM = Positive Medium, PL = Positive Large, TH = Too High. The rule base consists of the following nine rules (Table 1): Table 1. IF-Then rules Rules
1
2
3
4
5
6
7
8
9
IF Input
TL
NL
MM
NS
Z
PS
PM
PL
TH
Then Output
PS
Z
Z
NM
Z
TL
PS
PS
PM
Example rule 1: If Input is TL then Output is PS The output frequency of VCO varies according to the output of FLC. Output of VCO is applied to the Metal Oxide Semiconductor Field Effect Transistor (MOSFET) to switch the QRFBC. Figure 2 presents QRFBC circuit with FLC and VCO. Circuit was developed using MATLAB Simulink.
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2.2 Methodology of Investigation of QRFBC Controlled by FLC The three different tests are performed for the study: 1. For the input of QRFBC was used two different voltages: Ui = 190 V and Ui = 280 V; reference voltage Ur and output load R are fixed (Ur = 28.5 V; R = 15.7 ) 2. For the reference voltages are used two different values, Ur = 25 V and Ur = 37 V; input voltage and output load R are fixed (Ui = 240 V; R = 15.7 ) 3. The two different loads are used (R = 12 and R = 17 ); the input and reference voltages are fixed (Ui = 240 V, Ur = 28.5 V). The simulation results are presented in Fig. 3, 4, 5, and 6. In each case overshoot, the values of peaks, rise, and settling times are recorded (see Table 2).
Fig. 2. QRFBC circuit with FLC and VCO generated MATLAB Simulink
Fig. 3. Output scope of circuit in Ui = 190 V (a) and in Ui = 280 V (b)
Design of Quasi-Resonant Flyback Converter
35
Fig. 4. Voltage and current of MOSFET Ui = 190 V (a) and in Ui = 280 V (b)
Fig. 5. Voltage and current of MOSFET Ur = 25 V (a) and Ur = 37 V (b)
By looking the Fig. 3, it can understand that the output voltage is controlled very well around the reference voltage. Also, by looking at Fig. 4–Fig. 5 it can easily find out that the MOSFET switched to zero voltage. By comparing figures, it can be concluded that MOSFET current and voltage are increased by increasing the reference voltage. Also, by increasing the load value (Fig. 6) the current of MOSFET is decreased.
Fig. 6. Voltage and Current of MOSFET in R = 12 (a) and R = 17 (b)
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2.3 Testing the QRFBC Controlled by PI Controller In this case, FLC is replaced by the PI-controller, and VCO is needed like the previous circuit. As with FLC, the three tests are performed with PI-controller. The results are represented in Fig. 7, 8 and 9.
Fig. 7. Voltage and current of MOSFET in 190 V(a) and 280 V (b)
By simple glance to the Fig. 7, 8 and 9, it can understand that the behaviour of the PI-controller is the same as the fuzzy logic controller, but the values of the specifications are different (see Table 2). Like FLC, in PI-controller output voltage are controlled very well around the reference voltage, and MOSFET is switched at zero voltage, so in this way, the efficiency increased. Also, by comparing figures in each experiment, it is clear that by increasing the input voltage and load MOSFET current decreased.
Fig. 8. Voltage and current of MOSFET Ur = 25 V (a) and Ur = 37 V(b)
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Fig. 9. Voltage and current of MOSFET in R = 12 (a) and R = 17 (b)
3 Results and Discussions With a simple glance at Table 2, it is evident in fuzzy logic and PI controller by increasing the input voltage and value of the load, the amount of overshoot is increased (especially when the input voltage is increased), but the rise time of both controllers are decreased by changing input voltage, and does not change by changing load. Table 2. QRFBC circuit specification by using FLC and PI Controller Parameters Overshoot Peak value Peak time Rise time Settling time Fuzzy controller Vi = 190 Vi = 280
PI-controller
134.8809
67.2628
0.0013
0.00038
0.0204
245.3225
99.1892
0.0019
0.00026
0.0173
Vref = 25
246.3747
87.0530
0.0014
0.00026
0.0175
Vref = 37
129.2971
84.8951
0.0019
0.00039
0.0166
Load = 12 195.1413
84.7773
0.0013
0.00030
0.0186
Load = 17 196.1259
85.2974
0.0019
0.00030
0.0167
Vi = 190
25.9138
35.8726
0.0103
0.0020
0.0729
Vi = 280
57.8641
45.2444
0.0055
0.00078
0.0574
Vref = 25
57.0299
39.5799
0.0061
0.00078
0.0607
Vref = 37
22.1385
45.5439
0.0095
0.0021
0.0428
Load = 12
36.7397
39.3773
0.0073
0.0011
0.0508
Load = 17
45.2919
41.5382
0.0070
0.0011
0.0615
By increasing the reference voltage in both controller’s overshoot is decreased and rise time is increased. The value of peak voltage increases with increasing the input voltage, reference voltage, and load, when the PI controller controls the circuit. The
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peak voltage has a lower value by changing reference voltage, and by changing the load value almost does not change when the circuit is controlled with FLC. In all conditions, by using FLC we faced increasing the value of peak time, but by using the PI controller, peak time decreased (except when the reference voltage is changed). Finally, it is obvious that using FLC, settling time in all conditions is decreased,also this is valid for PI controller (except when the load value is increased).
4 Conclusion Results of the study show that both controllers could control the output voltage of the QRFBC efficiently. Both controllers provide zero voltage switching and the reduction of power switching losses. Comparing these two controllers shows that both had good efficiency in controlling the output parameters of QRFBC, but the fuzzy controller had a quick response. The rise time for FLC is approximately 3–5, setting time 2.6–3.7 and peak time 3–8 times is less than PI controller. However, the amount of overshoot and peak voltage in the PIcontroller is less than by comparison with the fuzzy controller. Generally, the overshoot in the fuzzy logic controller is greater than the PI controller (4.2–5.8 times), and this range is around 1.9–2.2 times for the peak value.
References 1. Watson, R., Lee, F.C., Hua, G.C.: Utilization of an active-clamp circuit to achieve soft switching in flyback converters. IEEE Trans. Power Electron. 11(1), 162–169 (1996). https://doi. org/10.1109/63.484429 2. Dong, H., Xie, X., Zhang, L.: A new primary PWM control strategy for CCM synchronous rectification flyback converter. IEEE Trans. Power Electron. 35(5), 4457–4461 (2020). https:// doi.org/10.1109/TPEL.2019.2944492 3. Dong, H., Xie, X., Zhang, L.: A new CCM/DCM hybrid-mode synchronous rectification flyback converter. IEEE Trans. Ind. Electron. 67(5), 3629–3639 (2020). https://doi.org/10. 1109/TIE.2019.2920474 4. Wang, J., Lin, C., Huang, K., Wong, J.: The novel quasi-resonant flyback converter with the auto regulated structure for parallel/serial input. IEEE Trans. Ind. Electron. 67(2), 992–1004 (2020). https://doi.org/10.1109/TIE.2019.2902827 5. Li, M., Ouyang, Z., Andersen, M.A.E.: Analysis and optimal design of high frequency and high efficiency asymmetrical half-bridge flyback converters. IEEE Trans. Ind. Electron. 67(10), 8312–8321 (2020). https://doi.org/10.1109/TIE.2019.2950845 6. Park, H.P., Jung, J.H.: Design methodology of quasi-resonant flyback converter with a divided resonant capacitor. IEEE Trans. Ind. Electron. 68(11), 10796–10805 (2021). https://doi.org/ 10.1109/TIE.2020.3029481 7. Li, J., van Horck, F.B.M., Daniel, B.J., Bergveld, H.J.: A high-switching-frequency flyback converter in resonant mode. IEEE Trans. Power Electr. 32(11), 8582–8592 (2017). https:// doi.org/10.1109/TPEL.2016.2642044 8. Xu, S., Wang, C., Qian, Q., Zhu, J., Sun, W., Li, H.: A single-switched high-switchingfrequency quasi-resonant flyback converter with zero-current-switching and valley-switching. In: 2019 IEEE Applied Power Electronics Conference and Exposition (APEC), pp. 2123– 2127. Anaheim, CA, USA (2019). https://doi.org/10.1109/APEC.2019.8721815
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9. Arulselvi, S., Deepa, K., Uma, G.: Design, analysis and control of a new multi-output flyback CF-ZVS-QRC. In: 2005 IEEE International Conference on Industrial Technology, pp. 413– 418. Hong Kong, China (2005). https://doi.org/10.1109/ICIT.2005.1600673 10. Park, J., et al.: Quasi-resonant (QR) controller with adaptive switching frequency reduction scheme for flyback converter. IEEE T. Ind. Electr. 63(6), 3571–3581 (2016). https://doi.org/ 10.1109/TIE.2016.2523931 11. Wang, C., et al.: New digital control method for improving dynamic performance of a quasi-resonant flyback converter. In: Applied Power Electronics Conference and Exposition (APEC), pp. 1788–1793. IEEE Press, Anaheim (2019). https://doi.org/10.1109/APEC. 2019.8721873 12. Stracquadaini, R.D.: Mixed mode control (fixed off time & quasi resonant) for flyback converter. In: 36th Annual Conference IEEE Industrial Electronic Society, pp. 556–561. IEEE Press, Glendale (2010). https://doi.org/10.1109/IECON.2010.5675222 13. Hsieh, P.C., Chang, C.H., Chen, C.L.: A primary-side-control quasi-resonant flyback converter with tight output voltage regulation and self-calibrated valley switching. In: IEEE Energy Conversion Congress and Exposition, pp. 3406–3412. IEEE Press Denver (2013). https://doi. org/10.1109/ECCE.2013.6647148 14. Modak, S., Panda, G.K., Saha, P.K., Das, S.: Design of novel fly-back converter using PID controller. Int. J. Adv. Res. Electr., Electron. Instrum. Eng. 04(01), 289–297 (2015). https:// doi.org/10.15662/ijareeie.2015.0401046 15. Arulselvi, S., Uma, G., Kalaranjini, B.: Design and Simulation of Model-Based Controllers for Quasi-Resonant Converters using Neural Networks. In: Proceedings of India International Conference Power Electronics, pp. 197–202. IEEE Press, Chennai (2006). https://doi.org/10. 1109/IICPE.2006.4685367 16. Anitha, T., Arulselvi, S.: Design of single-input fuzzy logic control of flyback multi-output quasi-resonant converter. Int. J. Develop. Res. 4(3), 672–677 (2014)
Experimental Selecting Appropriate Fuzzy Implication in Traffic IF-Then Rules Shamil A. Ahmadov1,2(B) 1 Azerbaijan State Oil and Industry University, 34 Azadliq Avenue, Az 1010, Baku, Azerbaijan
[email protected]
2 French-Azerbaijani University, 183 Nizami Street, Baku, Azerbaijan
[email protected]
Abstract. Nowadays, implications are widely used in Fuzzy Logic and decision making. Implication is the basic operation of fuzzy reasoning. Choosing the right fuzzy implication for each specific application is a complex task. In the scientific literature, there are methods that take into account the compatibility of fuzzy implication with theoretical recommendations. The theoretical results of these methods, which include generalized inference rules, are not always correct for every situation. In spite of that, existing methods are based on theoretical idea of fuzzy statement. In reality the expert’s opinion regarding the suitability of the resulting appropriate implications for interpreting the application data is not taken into account by these approaches. This paper include the method for selecting the best fuzzy implication. Used if-then rules for selecting appropriate fuzzy implication covers linguistic model of traffic problem. Experimenting several fuzzy implications can be used for number of problems, however traffic congestion problem is one of the global problem for most of the countries and for this reason named problem is selected. Keywords: Fuzzy implication · Fuzzy aggregation · Fuzzy set · Traffic problem · Efficiency index · Fuzzy logic
1 Introduction Fuzzy logic is the leading tool for describing subjective information and fuzzy sets are a universal approximator in modelling unknown objects. Implications in Fuzzy logic are one of the main logical operations. In scientific literature a number of works are devoted to application of fuzzy implications. Professor Zadeh is denoted the following in study [1]: “The problem is that the term ‘fuzzy logic’ has two different meanings. More specifically, in a narrow sense, fuzzy logic, FLn, is a logical system which may be viewed as an extension and generalization of classical multivalued logics. But in a wider sense, fuzzy logic, FLw, is almost synonymous with the theory of Fuzzy Sets. In this context, what is important to recognize is that: a) FLw is much broader than FLn and subsumes FLn as one of its branches; © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 40–49, 2023. https://doi.org/10.1007/978-3-031-25252-5_11
Experimental Selecting Appropriate Fuzzy Implication
41
b) the agenda of FLn is very different from the agendas of classical multivalued logics; and c) at this juncture, the term fuzzy logic is usually used in its wide rather than the narrow sense, effectively equating Fuzzy Logic with FLw.” It has been proven in the scientific literature that fuzzy implication is an extension crisp implication to the [0, 1] interval. Authors of book [2] have analyzed algebraical, analytical and experimental aspects of fuzzy implications. Selection method of fuzzy implication based on the distance is described in [3]. Authors of study [4] discussed selection method of fuzzy implication based on Statistical Data. Obtained theoretical and practical results of selection metod for fuzzy implication are not supported for each situation. Fuzzy implications play an important role in fuzzy reasoning and information about them is given in[5]. In study [6], authors examine the statistical characteristics of the fuzzy implication. They have determined that truth values of an fuzzy implication depend on truth values of the input(antecedent) and the output(consequent). Aggregating fuzzy implications is discussed in [7]. In [8] author described a framework for simultaneously learning first order fuzzy rules and the corresponding implication operator. It has been determined that the use of finite dimensional representations of implication is a good compromise between expressivity and prediction ability. In paper [9] is given an approach for selecting implication based on truth value of the rule consequent. A method of inference based on fuzzy implication is described in [10]. It is based on the theorem of decomposition fuzzy implication and depend on a truth value. Discussed method is possible to implement for modeling large-dimensional MISO-structure systems. Also, authors have analyzed set of implications sush as: Goguen, Godel, Rescher, Ali-1, Ali-2, Ali-3, Yager, Kleene-Dienes, Reichenbach, Fodor, etc. implications. Also in this paper properties of Lukasiewicz, Ali-3, Yager and Reichenbach implications are graphically demonstrated. Experimental selection of fuzzy implication and analysis set of implications are discussed in [11]. Basic characteristics of fuzzy implication are discussed in [12] and shown that fuzzy implications can give the evidence for belief or disbelief in the result. There are serious works of researches based on application of fuzzy implication, such as Aliev, Weber, Dubois and Prade, Baldwin, Willmot, etc. Application of Fuzzy Logic to Control Traffic Signals is discussed in [14]. It is reality that implication based reasoning approaches has a number of shortcomings, since the index of efficiency is often not considered. It is clear that, the index of efficiency [11] gives possibility to select the best implication. The aim of the paper is experimental selecting appropriate fuzzy implication. The structure of the paper is as follows. The preliminaries is given in Sect. 2. Statement of the problem and its solution is discussed in next Section. Last part of the paper concludes the work.
42
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2 Preliminaries Definition 1 [2] . A binary operation I on [0; 1] is called a fuzzy implication if (i) I is decreasing in the first variable, (ii) I is increasing in the second variable, (iii) I(0; 0) = I(1; 1) = 1 and I(1; 0) = 0. The set of all fuzzy implications is defined on [0; 1]. Definition 2 [11–13] . Fuzzy implications and connectives: Lukasiewicz implication: I (x,⎧y) = min(1, 1 − x + y), ⎧ T = max(x + y−1, 0). ⎨ 1 − x, if x < y ⎨ x, if x + y < 1 AL˙I-1 implication: I (x, y) = 1, if x = y , T = 0, if x + y = 1 ⎩ ⎩ b, if x > y y, if x + y > 1 1, if x ≤ y 0, if x + y ≤ 1 T= Ali-2 implication: I (x, y) = (1 − x)ˆy, if x > y max(a,b), if x + y > 1 1, if x ≤ y Ali-3 implication: I (a, b) = , T = y/ x + (1 − y) , otherwise 0, if x + y ≤ 1 1 − [(1 − x)/(x + y)], if x + y > 1 Mamdani implication: I (x, y) = min(x, y), T = min(x,y). Klir and Yuan 1 implication: I (x, y) = 1 − x + x2 y), T = xy. Definition 3. Selection of appropriate implication algorithm consists of the following steps: 1. Creation relation matrix using fuzzy implication on the rules(for instance, Ali-3 implication [11]). 2. Creation the composed fuzzy relation matrix R = ∪RS , s = 1, ..., n using logical connectives. Every implication has own logical connectives (Definition 2) [11]. 3. Determination new outputs usin maxmin aggregation [12] according to antecedents of the given rules. 4. Calculation of the adequacy of fuzzy model. The index of efficiency is computed as: ρ=
n
[μY˜ i (x) − (μYˆ i (x)]2 ,
i=1
where i - number of the point of membership functions on input and calculated fuzzy fuzzy data, μY˜ (x) is used in the construction of the fuzzy relation R, μYˆ (x) is obtained membership function using implication based reasoning. 5. Selection the best fuzzy implication. J = min(ρj ), j = 1, m m-number of implication. j
Experimental Selecting Appropriate Fuzzy Implication
43
3 Statement of the Problem Selection of appropriate implication is main objective of this study using traffic problem described IF-THEN rules. Let’s describe linguistic model using the following data. Traffic problem represented by 7 rules which values of antecedent and concequent as follows (Table 1) [14]: Fuzzy rules are represented by its 3 inputs (X1 , X2 , X3 ) and an output (Y ). The membership functions of the three inputs (X1 , X2 , X3 ) are: for (X1 ) Less = (0; 6; 10), Medium = (7; 11; 25), High = (20; 27; 50). for (X2 )Less = (0; 7; 10), Medium = (7; 19; 25), High = (20; 26; 50). for (X3 )Less = (1000; 1200, 1500), Medium = (400; 900; 1200), High = (50; 400; 500). Values of concequent of the rule are: (Y ) Short = (0; 7; 10), Medium = (8; 24; 30), Long = (25; 30; 60) Membership functions [15, 16] for given 7 rules and their three properties (Arrival car, Queuing car, Humidity or Fog) were evaluated (Table 1). Table 1. Fuzzy IF-THEN rule base [14] Rules no
Antecedents
Consequent
X1
X2
X3
Y
1
High
Less
Less
Short
2
High
Less
Medium
Medium
3
High
Less
High
Long
4
High
Medium
Less
Medium
5
High
Medium
Medium
Medium
6
Medium
Less
Less
Short
7
Medium
Medium
Less
Medium
Selection of appropriate implication and performing fuzzy inference is main objective of the considered problem. Used initial data as follows: (X1 ) - Number of cars passing during green light (AC Arrival Car), (X2 ) - Number of cars waiting during the red light (QC-Queuing Car), (X3 ) - Weather variation (FHumidity or Fog). (Y ) - The green light duration (GD). It describe the extension time required for green light on the arrival side. Using above given rule are formulated fuzzy relations (Tables 2, 3, 4, 5, 6, 7 and 8). Intersection of relations are performed using ALI-3 conjunction connective [15]: 0, μRs,k (x, y) + μRs+i,k (x, y) ≤ 1 μs (x, y) = max(μRs,k (x, y), μRs+i,k (x, y)), μRs,k (x, y) + μRs+i,k (x, y) > 1 where s-number of relation and k-number of points on relation, i = 1,…6.
44
S. A. Ahmadov Table 2. Fuzzy relation matrix for the first rule
Input
Output 0
0.328571429
0.657142857
1
0.666666667
0.333333333
0
0
1
1
1
1
1
1
1
0.285714286
0
1
1
1
1
1
0
0.571428571
0
0.264367816
1
1
1
0.269230769
0
1
0
0.196581197
0.489361702
1
0.5
0.2
0
0.666666667
0
0.245551601
0.650943396
1
1
0.25
0
0.333333333
0
0.327014218
1
1
1
1
0
0
1
1
1
1
1
1
1
Table 3. Fuzzy relation matrix for the second rule Input
Output 0
0.3125
0.625
1
0.666666667
0.333333333
0
0
1
1
1
1
1
1
1
0.285714286
0
1
1
1
1
1
0
0.571428571
0
0.24822695
1
1
1
0.269230769
0
1
0
0.185185185
0.454545455
1
0.5
0.2
0
0.666666667
0
0.230769231
0.6
1
1
0.25
0
0.333333333
0
0.306122449
1
1
1
1
0
0
1
1
1
1
1
1
1
0.333333333
0
Table 4. Fuzzy relation matrix for the third rule Input
Output 0
0.32
0.64
1
0.666666667
0
1
1
1
1
1
1
1
0.285714286
0
1
1
1
1
1
0
0.571428571
0
0.255707763
1
1
1
0.269230769
0
1
0
0.19047619
0.470588235
1
0.5
0.2
0
0.666666667
0
0.237623762
0.623376623
1
1
0.25
0
0.333333333
0
0.315789474
1
1
1
1
0
0
1
1
1
1
1
1
1
Experimental Selecting Appropriate Fuzzy Implication
45
Table 5. Fuzzy relation matrix for the fourth rule Input
Output 0
0.3125
0.625
1
0.66667
0.3333333
0
0
0.3125
1
1
1
1
1
1
0.285714286
0.625
1
1
1
1
1
0
0.571428571
1
0.24822695
1
1
1
0.269231769
0
1
0.666666667
0.185185185
0.454545
1
0.5
0.2
0
0.666666667
0.333333333
0.230769231
0.6
1
1
0.25
0
0.333333333
0
0.306122449
1
1
1
1
0
0
1
1
1
1
1
1
1
Table 6. Fuzzy relation matrix for the fifth rule Input
Output 0
0.3125
0.625
1
0.666667
0.3333333
0
0
0.3125
1
1
1
1
1
1
0.2857143
0.625
1
1
1
1
1
0
0.5714286
1
0.24822695
1
1
1
0.2692308
0
1
0.666666667
0.185185185
0.45454545
1
0.5
0.2
0
0.6666667
0.333333333
0.230769231
0.6
1
1
0.25
0
0.3333333
0
0.306122449
1
1
1
1
0
0
1
1
1
1
1
1
1
Table 7. Fuzzy relation matrix for the sixth rule Input
Output 0
0.328571429
0.657142857
1
0.666666667
0.333333333
0
0
1
1
1
1
1
1
1
0.328571429
0
1
1
1
1
1
0
0.657142857
0
0.247311828
1
1
1
0.251798561
0
1
0
0.196581197
0.489361702
1
0.5
0.2
0
0.666666667
0
0.245551601
0.650943396
1
1
0.25
0
0.333333333
0
0.327014218
1
1
1
1
0
0
1
1
1
1
1
1
1
46
S. A. Ahmadov Table 8. Fuzzy relation matrix for the seventh rule
Input
Output 0
0.3125
0.625
1
0.666666667
0.333333333
0
0
1
1
1
1
1
1
1
0.325
0
0.308641975
1
1
1
1
0
0.65
0
0.23364486
0.609756098
1
1
0.253164557
0
1
0
0.185185185
0.454545455
1
0.5
0.2
0
0.666666667
0
0.230769231
0.6
1
1
0.25
0
0.333333333
0
0.306122449
1
1
1
1
0
0
1
1
1
1
1
1
1
Result of conjuction connective is as follow between first and second relation (Table 9): Table 9. Result of conjuction connective (R1 and R2) R1 and R2 1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0.720965
1
1
0
0
0
0
1
1
1
1
0
1
1
1
1
1
1
1
Now we define a composed fuzzy relation matrix R, R =
7
Ri (Table 10) with the
i=1
membership function as result of conjuction connective of ALI-3 implication: Table 10. Composed fuzzy relation matrix Rcomposed 1
1
1
1
1
1
1
0
1
1
1
1
1
0 (continued)
Experimental Selecting Appropriate Fuzzy Implication
47
Table 10. (continued) Rcomposed 0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0.956732
1
1
0
0
0
0
1
1
1
1
0
1
1
1
1
1
1
1
Table 11. New obtained individual output (Y1) Input 0
0
0
0
0
0
0
0
0.285714
0
0.285714
0.285714
0.285714
0.285714
0.285714
0
0.571429
0
0
0.571429
0.571429
0.571429
0
0
1
0
0
0
1
0
0
0
0.666667
0
0
0.666667
0.666667
0.666667
0
0
0.333333
0
0
0.333333
0.333333
0.333333
0.333333
0
0
0
0
0
0
0
0
0
Y1
0
0.285714
0.666667
1
0.666667
0.333333
0
The next step we calculate individual outputs (Table 11) of the rule using maxmin composition. The index of efficiency is determined on first rule using primary value of the output and obtained value on the the first rule output as follow: ρ1 =
7
[μY˜ i (x) − (μYˆ i (x)]2 = 0.001927438
i=1
Obtained values of the index efficiency for 2–7 rules are determined as follow: ρ2 = 0.002453586; ρ3 = 0.001886621; ρ4 = 0.002453586; ρ5 = 0.002453586; ρ6 = 9.07029E − 05; ρ7 = 0.001892361. Then we get estimated value on ALI-3 implication ρAli−3 = 0.001879697. For Ali-1 implication obtained values of the index efficiency for 1–7 rules are determined as follow: ρ1 = 0.001033; ρ2 = 0.140883; ρ3 = 0.000298; ρ4 = 0.000258; ρ5 = 0.000258; ρ6 = 0.001033; ρ7 = 0.000258 Then we get estimated value on ALI-1 implication ρAli−1 = 0.020575.
48
S. A. Ahmadov
For Ali-2 implication obtained values of the index efficiency for 1–7 rules are determined as follow: ρ1 = 0.009183673; ρ2 = 0.003587372; ρ3 = 0.005877551; ρ4 = 0.003587372; ρ5 = 0.003587372; ρ6 = 0; ρ7 = 0.00078125 Then we get estimated value on ALI-1 implication ρAli−2 = 0.003800656.For Mamdani implication obtained values of the index efficience for 1–7 rules are determined as follow: ρ1 = 0.444444; ρ2 = 1.445736; ρ3 = 0.444812; ρ4 = 0.445736; ρ5 = 0.445736; ρ6 = 0.444444; ρ7 = 0.444812 Then we get estimated value on Mamdani implication ρMamd = 0.58796. For Klir and Yuan 1 implication obtained values of the index efficience for 1–7 rules are determined as follow: ρ1 = 2.548841; ρ2 = 3.513017; ρ3 = 2.529413; ρ4 = 2.513017; ρ5 = 2.513017; ρ6 = 2.548841; ρ7 = 2.513017 Then we get estimated value on Klir and Yuan 1 implication ρKlirandYuan = 2.668451818. For Lukasiewicz’s implication obtained values of the index efficience for 1–7 rules are determined as follow: ρ1 = 0.006513; ρ2 = 1.00217; ρ3 = 0.930644; ρ4 = 0.00857; ρ5 = 0.00857; ρ6 = 0.006513; ρ7 = 0.00857 Then we get estimated value on Lukasiewicz’s implication ρLukasiewicz = 0.281650251. Ranking of efficient indices of implications is defined appropriate fuzzy implication is Ali-3: ρAli−3 = 0.001879697 < ρAli−2 = 0.003800656 ρAli−1 = 0.020575 ρLukasiewicz = 0.28165025 < ρMamd = 0.58796 < ρKlirandYuan = 2.66845181. So, obtained value J=0.00187969.
4 Conclusion Proposed approach for selecting the appropriate implication is detailed by example. Efficiency index is calculated and the best alternative has been defined where index value is small. Terms are represented by discrete fuzzy numbers in a model. By using these terms it is created fuzzy relation on the rules and is fulfilled fuzzy inference algorithm. In addition, using wide range of dataset and comparing several methods such as Lukasiewicz, Ali-3, Ali-2, Ali-1, Zadeh, Klin and Yuan1, Mamdani appropriate implication which is close to the expert’s opinion is found theoretically. In this work Ali-3 and Ali-2 implications are defined as best options for interpretation of information.Selection of appropriate
Experimental Selecting Appropriate Fuzzy Implication
49
implication is the kernel of suitable demonstration of information. The given approach is possible to use in fuzzy control, artificial intelligence and uncertainty based reasoning. Moreover, ideal implication can be applied for analyzing several problems and selecting appropriate implication facilities.
References 1. Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic. Theory and Applications. Prentice Hall, Upper Saddle River (1995). ISBN 0-13-101171-5 2. Michał, B., Balasubramaniam, J.: Fuzzy Implications. Studies in Fuzziness and Soft Computing. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-69082-5 3. Papadopoulos, B.K., Trasanides, G., Hatzimichailidis, A.G.: Optimization method for the selection of the appropriate fuzzy implication. J. Optim. Theory Appl. 134, 135–141 (2007). https://doi.org/10.1007/s10957-007-9246-5 4. Pagouropoulos, P., Tzimopoulos, C.D., Papadopoulos, B.K.: Selecting the most appropriate fuzzy implication based on statistical data. Int. J. Fuzzy Syst. Adv. Appl. 3, 32–42 (2016). ISSN 2313-0512 5. Wei, J.: Fuzzy implications in lattice effect algebras. Fuzzy Sets Syst. 405, 40–46 (2021). https://doi.org/10.1016/j.fss.2020.04.021 6. Aliev, R., Tserkovny, A.: Systemic approach to fuzzy logic formalization for approximate reasoning. Inf. Sci. 181, 1045–1059 (2011) 7. Reiser, R.H.S., Bedregal, B., Baczy´nski, M.: Aggregating fuzzy implications. Inf. Sci. 253, 126–146 (2013). https://doi.org/10.1016/j.ins.2013.08.026 8. Mathieu, S., Didier, D., Henri, P., Thomas, S.: Learning fuzzy rules with their implication operators. Data Knowl. Eng. 60, 71–89 (2007). https://doi.org/10.1016/j.datak.2006.01.007 9. Suraj, Z., Lasek, A., Lasek, P.: Inverted fuzzy implications in approximate reasoning. Fund. Inform. 143(2), 151–171 (2016). https://doi.org/10.3233/FI-2016-1309 10. Sinuk, V.G., Panchenko, M.V.: Method of fuzzy inference for one class of MISO-structure systems with non-singleton inputs. IOP Conf. Ser. Mater. Sci. Eng. 327 (2018). https://doi. org/10.1088/1757-899X/327/4/042074 11. Aliev, R.A., Aliev, R.R.: Soft Computing and its Application. World Scientific, London, Singapore, Hong Kong (2001) 12. Aliev, R., Aliev, F., Babaev, M.: Fuzzy process control and knowledge engineering in Petrochemical and robotic manufacturing, Verlag TUV Rheinland (1991) 13. http://www.scholarpedia.org/article/Triangular_norms_and_conorms 14. Mohanaselvi, S., Shanpriya, B.: Application of fuzzy logic to control traffic signals. In: AIP Conference Proceedings, vol. 2112, no. 1 (2019). https://doi.org/10.1063/1.5112230 15. Adilova, N.E.: Quality criteria of fuzzy IF-THEN rules and their calculations. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, Mo., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS-2020. AISC, vol. 1306, pp. 55–62. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-640 58-3_7 16. Aliev, R.A., Gardashova, L.A.: Z-set based approach to control system design. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, Mo., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS-2020. AISC, vol. 1306, pp. 10–21. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-640 58-3_2
Prediction of Cold Filter Plugging Point of Different Types of Biodiesels Using Various Empirical Models Youssef Kassem1,2,3,4(B) , Hüseyin Çamur1 , Ahmed Hamid Mohamed Abdalla Zakwan1 , and Nkanga Amanam Nkanga1 1 Faculty of Engineering, Mechanical Engineering Department, Near East University,
99138 Nicosia, North Cyprus, Turkey {yousseuf.kassem,huseyin.camur}@neu.edu.tr, {20213770, 20206631}@std.neu.edu.tr 2 Faculty of Civil and Environmental Engineering, Near East University, 99138 Nicosia, North Cyprus, Turkey 3 Energy, Environment, and Water Research Center, Near East University, 99138 Nicosia, North Cyprus, Turkey 4 Engineering Faculty, Kyrenia University, 99138 Kyrenia, North Cyprus, Turkey
Abstract. In this paper, multi-layer perceptron neural network (MLPNN) and Radial basis function neural network (RBFNN) have been used to predict the cold filter plugging point (CFPP) of different types of biodiesel. Moreover, the accuracy of the proposed models is compared with the Quadratic model (QM), and Multiple Linear Regression (MLR). For this aim, estimating monounsaturated (MUFAMEs), polyunsaturated (PUFAMEs), and saturated (SFAMEs), the degree of unsaturation (DU), and long-chain saturated factor (LCSF) were collected and used as input parameters for the proposed models. Among the developed models, the MLPNN and QM models presented significantly better prediction performance based on the value R2 and RMSE. Keywords: CFPP · Biodiesel · MLPNN · RBFNN · QM · MLR
1 Introduction Biodiesel is domestically obtained from refined and waste vegetable oils, animal fats, or other lipids [1]. It has many advantages such as renewable fuel, higher viscosity, density, cold flow properties, and emissions reduction [2]. Because of these advantages, it is gained the scientific community’s attention considerably over the past decade. The characteristics of biodiesel depend on feedstock’s chemical and physical properties; thus, biodiesel’s physicochemical properties depend on the fatty acid profile and its characteristics [3]. Accordingly, the combustion and emissions characteristics are dependent on the type of biodiesel used. Generally, cold flow properties are considered crucial properties that influence the characteristics of the engine [4]. They depend on the fatty acid profile of the source © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 50–57, 2023. https://doi.org/10.1007/978-3-031-25252-5_12
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utilized for biodiesel production [3, 4]. The characteristics of biodiesel’s cold flow are the reason that limits its widespread use. One of the important low-temperature properties of biodiesel is the cold filter plugging point (CFPP). Fuel shouldn’t gel early in the cold, and clog the fuel filter [5]. The cold flow properties, mainly, CFPP, of biodiesel must meet the specifications of fuel to utilize the biodiesel directly in the diesel engine or as a blend component in petro-diesel. Therefore, it is necessary to provide a predictive model that can estimate the CFPP of biodiesel with different fatty acid compositions. In this regard, four empirical models, namely, MLPNN, RBFNN, QM, and MLR are developed to estimate the CFPP of biodiesel. In this study, MUFAMEs, PUFAMEs, SFAMEs, DU, and LCSF are used as input variables for the proposed models. The overall flowchart of the current study is illustrated in Fig. 1.
2 Material and Methods 2.1 Data In this work, CFPP value and the fatty acid compositions (Lauric acid, Myristic acid, Palmitic acid, Palmitoleic acid, Stearic acid, Oleic acid, Linoleic acid, Linolenic acid, Arachidic acid, and Paullinic acid) of various types of biodiesel are collected from the previous studies [6–14]. For determining the estimated monounsaturated (MUFAMEs), polyunsaturated (PUFAMEs), saturated (SFAMEs), the degree of unsaturation (DU), and long-chain saturated factor (LCSF) based on the fatty acid compositions, Eqs. (1)–(5) are used. Table 1 lists the statistical parameters of the used variables. MUFAMs = wt%Cxx : 1 (1)
PUFAMs =
wt%Cxx : 2 +
SFAMs =
wt%Cxx : 3
wt%Cxx : 00
DU = [monounsatuarted Cn : 1] + 2 polyunsaturated Cn : 2, 3
(2) (3) (4)
LCSF = 0.1 × [C16 : 0] + 0.5 × [C18 : 0] + [C20 : 0] + 1.5 × [C22 : 0] + 2 × [C24 : 00]
(5)
2.2 Machine Learning Models (MLMs) MLMs are utilized as a tool to describe a complex system [15, 16]. Wide ranges of ML models are utilized to solve complex problems in a variety of fields [15, 16]. In this study, MLPNN and RBFNN are developed to determine the CFPP of Biodiesel. MLPNN and RBFNN are the most popular artificial neural network approaches for modeling nonlinear and complex processes in the real world [17]. The description of the MLPNN and RBFNN models was given in Ref. [17]. The training (70%) and testing data (30%) were used to develop and validate the models, respectively. The results of the proposed models are compared with observed data.
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Fig. 1. Flowchart of the current study
Table 1. Statistical parameters of mean hourly data during 2020. Variable
Unit
Mean
Standard deviation
Coefficient of variation
Minimum
Maximum
MUFAMEs
wt%
39.68
23.06
58.11
1.92
91.90
PUFAMEs
wt%
35.88
26.02
72.52
0.70
85.30
SFAMEs
wt%
21.56
18.54
85.96
2.00
79.50
DU
wt%
111.43
40.51
36.36
9.90
177.20
LCSF
wt%
4.21
3.19
75.63
0.64
15.95
CFPP
°C
−0.83
8.05
−965.23
−13.00
17.00
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2.3 QM and MLR models The QM is a mathematical and statistical method polynomial model as expressed below [15]. Y = β0 +
n i=1
βi xi +
n i=1
βii xi2 +
n n−1 i
βij xi xj
(6)
i=i+1
where Y is the predicted response, β0 , βi , are related to the main effects and βii and βij to interaction, xi and xj are the independent variables. Moreover, MLR is used to predict the DV of biodiesel. MLR is expressed as Y = β0 + β1 x1 + . . . + βi xi i = 1, 2 . . . n
(7)
where Y , β0 , βi , and xi are defined above. In general, these models aim to show the relationship between the variables as shown in eq. (8). CFPP = f MUFAMs, PUFAMs, SFAMs, DU .LCSF (8)
3 Results and Discussion 3.1 Estimating the CFPP Using MLPNN and RBFNN Aforementioned,two machine learning models were utilized to estimate the CFPP of biodiesel. Thus, MUFAMs, PUFAMs, SFAMs, DU, and LCSF are used as input parameters. The best network configuration was found by the trial and error method and selected based on the lowest value of mean squared error (MSE). The best function is selected through several trials in the training phase. The developed MLPNN and RBFNN model architectures for predicting the CFPP of biodiesel are shown in Figs. 2 and 3, respectively. Based on the analysis, it is found that the sum squared error of MLPNN and RPFNN was estimated to be 13.527 and 10.331, respectively based on the training data. For testing data, it is observed that sum squared error was found to be equal to 2.034 and 6.168 for MLPNN and RPFNN, respectively. Fig. 4 shows the scatter plot between the estimated data and actual data of CFPP.
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Fig. 2. The structure of MLPNN for predicting the CFPP of biodiesel.
Fig. 3. The structure of RBFNN for predicting the CFPP of biodiesel.
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EsƟmated value [ ]
15 10 5 0 -5
R-squared (MLPNN) = 0.753 R-squared (RBFNN) = 0.668
-10 -15 -15
-10
-5
0
5
10
15
Actual data [ ] MLPNN
RBFNN
Fig. 4. Comparison of the estimated data with the observed data using MLPNN and RBFNN
3.2 Estimating the CFPP Using QM and MLR The mathematical equation that was developed using RSM (3) for predicting the CFPP is expressed as shown below. Fig. 5 shows the scatter plot between the estimated data and actual data of CFPP. CFPP = 24.5 − 4.0 · MUFAMs + 41.1 · PUFAMs + 76.3 · SFAMs− 2 2 2 PUFAMs + 81.1 · SFAMs − 24 · LCSF − 17.6 · MUFAMs + 29.3 · 24.8 · DU 2 − 10.19 · LCSF 2 + 44.8 · MUFAMs · SFAMs − 51.5 · MUFAMs· LCSF + 80.3 · PUFAMs · SFAMs − 44.7 · PUFAMs · LCSF − 50.4 · SFAMs· LCSF
(9) CFPP = −10.38 − 0.366 ·
MUFAMs + 5.015 · LCSF + 0.00407 ·
MUFAMs
2
−0.2026LCSF 2
(10)
3.3 Performance Evaluation of Proposed Models The performance of MLPNN and RBFNN is compared with the QM and MLR to evaluate the performance of the proposed models. The values of R-squared and root mean squared error (RMSE) are listed in Table 2. It is noticed that the maximum R-squared value and minimum RMSE were obtained from the MLPNN model.
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RBFNN
QM
R-squared
0.753
0.668
0.728
0.010
RMSE
3.002
3.316
3.080
14.251
EsƟmated value [ ]
Statistical indicator
20 10 0 -10 -20 -30 -40 -50
MLR
R-squared (QM) = 0.728 R-squared (MLR) = 0.01 -15
-10
-5
0
5
10
15
Actual data [ ] QM
MLR
Fig. 5. Comparison of the estimated data with the observed data using MLR and QM.
4 Conclusions CFPP is one of the most important properties of biodiesel. Therefore, four empirical models (MLPNN, RBFNN, QM, and MLR) were developed to determine the CFPP of various types of biodiesel. The results demonstrated that MLPNN and QM models were suitable for predicting the CFPP of biodiesel based on the value R2 and RMSE. In future work, various models with various combinations of parameters including oxidation stability, flash point, viscosity, and density should propose to categorize the most influencing input parameters for predicting the CFPP of the biodiesel.
References 1. Rashid, U., Hazmi, B.: Advances in production of biodiesel from vegetable oils and animal fats. In: Rokhum, S.L., Halder, G., Assabumrungrat, S., Ngaosuwan, K. (eds.) Biodiesel Production: Feedstocks, Catalysts, and Technologies, pp. 1–31. Wiley (2022). https://doi.org/ 10.1002/9781119771364.ch1 2. Dey, S., Reang, N.M., Das, P.K., Deb, M.: A comprehensive study on prospects of economy, environment, and efficiency of palm oil biodiesel as a renewable fuel. J. Clean. Prod. 286, 124981 (2021). https://doi.org/10.1016/j.jclepro.2020.124981 3. Kassem, Y., Çamur, H., Alassi, E.: Biodiesel production from four residential waste frying oils: proposing blends for improving the physicochemical properties of methyl biodiesel. Energies 13(16), 4111 (2020). https://doi.org/10.3390/en13164111
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4. Saeed, R.H.S., Kassem, Y., Çamur, H.: Effect of biodiesel mixture derived from waste frying-corn, Frying-Canola-Corn and Canola-corn cooking oils with various Ages on physicochemical properties. Energies 12(19), 3729 (2019). https://doi.org/10.3390/en1219 3729 5. Sajjadi, B., Raman, A.A.A., Arandiyan, H.: A comprehensive review on properties of edible and non-edible vegetable oil-based biodiesel: composition, specifications and prediction models. Renew. Sustain. Energy Rev. 63, 62–92 (2016). https://doi.org/10.1016/j.rser.2016. 05.035 6. Ramos, M.J., Fernández, C.M., Casas, A., Rodríguez, L., Pérez, Á.: Influence of fatty acid composition of raw materials on biodiesel properties. Bioresour. Technol. 100(1), 261–268 (2009). https://doi.org/10.1016/j.biortech.2008.06.039 7. De Lima Da Silva, N., Benedito Batistella, C., Maciel Filho, R., Maciel, M.R.W.: Biodiesel production from castor oil: optimization of alkaline ethanolysis. Energy Fuels 23(11), 5636– 5642 (2009). https://doi.org/10.1021/ef900403j 8. Sanford, S.D., White, J.M., Shah, P.S., Wee, C., Valverde, M.A., Meier, G.R.: Feedstock and biodiesel characteristics report. Renew. Energy Group 416, 1–136 (2009). https://doi.org/10. 2172/1360190 9. Giakoumis, E.G.: A statistical investigation of biodiesel physical and chemical properties, and their correlation with the degree of unsaturation. Renew. Energy 50, 858–878 (2013). https://doi.org/10.1016/j.renene.2012.07.040 10. Hoekman, S.K., Broch, A., Robbins, C., Ceniceros, E., Natarajan, M.: Review of biodiesel composition, properties, and specifications. Renew. Sustain Energy Rev. 16(1), 143–169 (2012). https://doi.org/10.1016/j.rser.2011.07.143 11. Dunn, R.O.: Cold flow properties of biodiesel by automatic and manual analysis methods. J. ASTM Int. 7(4), 1–16 (2010). https://doi.org/10.1520/jai102618 12. Tang, H., Salley, S.O., Ng, K.S.: Fuel properties and precipitate formation at low temperature in soy-, cottonseed-, and poultry fat-based biodiesel blends. Fuel 87(13–14), 3006–3017 (2008). https://doi.org/10.1016/j.fuel.2008.04.030 13. Moser, B.R.: Influence of blending canola, palm, soybean, and sunflower oil methyl esters on fuel properties of biodiesel. Energy Fuels 22(6), 4301–4306 (2008). https://doi.org/10.1021/ ef800588x 14. Usta, N., Aydo˘gan, B., Çon, A.H., U˘guzdo˘gan, E., Özkal, S.G.: Properties and quality verification of biodiesel produced from tobacco seed oil. Energy Convers. Manag. 52(5), 2031–2039 (2011). https://doi.org/10.1016/j.enconman.2010.12.021 15. Kassem, Y., Othman, A.A.: Selection of most relevant input parameters for predicting photovoltaic output power using machine learning and quadratic models. Model. Earth Syst. Environ. 8(4), 4661–4686 (2022). https://doi.org/10.1007/s40808-022-01413-7 16. Kassem, Y., Gökçeku¸s, Hüseyin., Janbein, W.: Predictive model and assessment of the potential for wind and solar power in Rayak region, Lebanon. Model. Earth Syst. Environ. 7(3), 1475–1502 (2020). https://doi.org/10.1007/s40808-020-00866-y 17. Kassem, Y., Gokcekus, H.: Do quadratic and poisson regression models help to predict monthly rainfall? Desalin. Water Treat. 215, 288–318 (2021). https://doi.org/10.5004/dwt. 2021.26397
Comparison of Fuzzy Solution Approaches for a Bilevel Linear Programming Problem Bü¸sra Altınkaynak1
, Tolunay Göçken1 , Murat Ye¸silkaya2 and Gülesin Sena Da¸s3(B)
, Burak Birgören3
,
1 Department of Industrial Engineering, Alparslan Türke¸s Science and Technology University,
Adana, Turkey [email protected] 2 Niksar Vocational School, Tokat Gaziosmanpa¸sa University, Tokat, Turkey [email protected] 3 Department of Industrial Engineering, Kırıkkale University, Kırıkkale, Turkey [email protected], [email protected], [email protected]
Abstract. In this study, we consider solution approaches used to solve the proposed bilevel linear programming model for an Industrial Symbiosis network. We first solve this model with the well-known Karush-Kuch-Tucker (KKT) approach. However, transforming a bilevel programming model with the KKT approach increases the number of variables and constraints. For this reason, we use the fuzzy programming approach and the fuzzy goal programming approaches as alternatives to the KKT approach. Next, we compare the results of the KKT approach with these methods and examine the suitability of these approaches to solve our bilevel problem. Unlike previous studies, which claimed that fuzzy approaches mostly outperform the KKT approach, in our case, the best solution is obtained with the KKT approach. This is most probably because these approaches ignore the hierarchical nature of the problem. We believe that more research on fuzzy approaches is needed to evaluate the suitability of these approaches for solving bilevel programming problems. Keywords: Industrial symbiosis · Bilevel programming · Fuzzy programming approach · Fuzzy goal programming
1 Introduction Bilevel programming (BLP) problems are hierarchical optimization problems of two or more players [1]. In these problems, optimal decision of the upper decision maker (leader) is constrained by the decision of the lower-level decision maker (the follower) [2]. That is the upper-level decision-makers choose their optimal positions whereas the lower-level decision-makers optimize their objectives given the dominant players’ positions determined at the first stage [3]. BLP is difficult to solve owing, fundamentally, to bad mathematical properties and huge size [4]. Therefore, several methods have been presented to solve BLP. Interested © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 58–66, 2023. https://doi.org/10.1007/978-3-031-25252-5_13
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readers can refer to [5]. Among these approaches, Karush-Kuch-Tucker (KKT) approach [6, 7], is probably the most popular one. In this approach, the lower-level problem is replaced with the KKT conditions of the problem which results in a single-level problem with nonlinear constraints. Although linearizing these constraints are possible, as the number of constraints and the number of decision variable increase the size of the resultant problem also in-crease. To avoid this, we use the fuzzy programming approach (FPA) and fuzzy goal programming (FGP) approaches to solve our bilevel problem. We prefer these fuzzy approaches since they are known to be successful in dealing bilevel problems without increasing the size of the problem greatly. The first approach we test to solve our problem, which is introduced in the next section, is the FPA proposed by Lai [8] and Shih et al. [9]. This approach offers a solution if there is a collaborative relationship between decision-makers. The second approach that we will use is the FGP method which is extended by [10–14] to solve BLP problems. We summarize the details of the FPA and FGP approaches in Sect. 3. In Sect. 4, we present a comparison of the considered fuzzy approaches with the KKT approach. Finally, we conclude in Sect. 5.
2 A BLP Problem for an Industrial Symbiosis Network In this study, we consider a theoretical Industrial Symbiosis (IS) network located in an eco-industrial park. This network consists of plants from the forest products industry, including a sawmill, a fiberboard plant, a particleboard plant, a pulp and paper producer and a pellet producer. Plants in the network produce final products by using raw materials (rm) and/or by-products (bp) to make a profit. As a result of this production, by-products that could be used by other plants emerge. The park authority wants companies to use these by-products to minimize the total use of raw materials in the park. We assume that each plant uses a single type of by-product and/or raw material to produce a single type of final product. More information about the case study can be found in [15, 16]. Notations used in the proposed model are; Sets I is the set of plants in EIP (i, j ∈ I ) K is the set of bp types (k ∈ K) M is the set of rm types (m ∈ M ) Decision variables rm Qim bp,in Qijk bp,out
Qik
bp,buy Qijk bp,use Qik
amount of rm type m purchased by plant i (tonne) amount of bp type k sold to plant j from plant i (tonne) amount of bp type sold out the park (tonne) amount of bp type k purchased by plant i of plant j (tonne) amount of bp type k used (tonne)
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Parameters Di Capi rm,bp wimk bp
wik rm wim rm,CO2 wm bp,CO2 wk wtrn,CO2 rm pm bp pk fp pi C CO2 Cmtrn,rm Ce Ciksto upp θilow , θi trn,bp Ck e,bp ak e,rm am dij di
fp demand of plant i (m 3 ) production capacity of plant i (m 3 ) conversion rate (cr) for obtaining bp type k by processing rm type m from plant i cr of obtaining fp by using bp type k in plant i cr of obtaining fp by using rm type m in plant i The amount of CO2 released while processing rm type m (tonne) The amount of CO2 released while processing bp type k (tonne) The amount of CO2 emitted during transporting per km (tonne) unit purchasing price of rm type m (/tonne) unit sales price of bp type k (/tonne) unit sales price of fp produced by plant i (/m3 ) tax paid for produced carbon dioxide (/tonne) unit transportation cost per km for rm type m (/tonne) unit cost of energy (/kWh) inventory holding cost of bp type k of plant i (/tonne) lower bound for ratio of bp to rm, upper bound for ratio of bp to rm unit transportation cost per km for bp type k (/tonne) the amount of energy required to process bp type k (kWh/tonne) the amount of energy required to process rm type m (kWh/tonne) distance between plant i and plant j (km) distance between the rm supplier and plant i (km)
The profit of each plant is calculated by considering the difference between the revenue and cost. Revenue of each plant is composed of revenues obtained from selling final products and by-products (1). The cost of each plant consists of (i) by-product and raw material purchasing costs (2a), (ii) transportation costs (2b), (iii) energy costs (2c), (iv) emission-related costs depending on the use of by-products, raw materials and transportation (2d,2e) (v) inventory holding costs (2e). We assume that a holding cost Invi occurs when a plant produces more than demand. bpsell bp,in bpsell bp,out fp fp fREV ,i = pi Qi + pik Qijk + pik Qik (1) fCOST ,i =
j∈I k∈K rm rm pm Qim +
m∈M
m∈M
k∈K
trn,bp
Ck
bp,buy
dij Qijk
+
(2b)
j∈I k∈K
e,rm rm C e am Qim +
m∈M
(2a)
j∈I k∈K rm Cmtrn,rm di Qim +
k∈K bpbuy bp,buy pjk Qijk +
e,bp
C e ak
k∈K bp,CO2
C CO2 wk
bp,use
Qik
+
bp,use
Qik
j∈I k∈K
+
(2c) bp,buy
C CO2 wktrn,CO2 dij Qijk
+
(2d)
Comparison of Fuzzy Solution Approaches
rm rm,CO2 trn,CO2 Qim (C CO2 wm + cCO2 wm di ) + Cisto Invi
61
(2e)
m∈M
In the proposed bilevel model the park authority is the upper-level decision maker who wants to minimize the total use of raw materials in the park to pro-mote the exchange of materials between companies in the network. On the other hand, plants in the network are the lower-level decision-makers who want to maximize their profits. The proposed linear bi-level model (LBP) is as follows; rm Qim (3) LBP:min i∈I m∈M
s.t. max
fREV ,i − fCOST ,i
(4)
i∈I
s.t.
bp,use
Qik
rm Qim ,i ∈ I
(5)
rm Qim , i∈I
(6)
m∈M
k∈K
≥ θilow
bp,use
Qik
upp
≤ θi
m∈M
k∈K
fREV ,i − fCOST ,i ≥ 0, i ∈ I
rm rm wim Qim
+
m∈M
rm wimk Qim =
m∈M k∈K bp,in
Qijk
m∈M
bp,buy
≤
− Di = Invi , i ∈ I bp,in
Qijk
j∈I k∈K
= Qjik
bp,use
Qik
bp bp,use wik Qik
k∈K rm,bp
(7)
rm rm wim Qim +
bp,out
Qik
, i∈I
(9)
k∈K
, i, j ∈ I , k ∈ K
(10)
bp,buy
, i ∈ I, k ∈ K
(11)
bp
(12)
Qijk
j∈I
+
(8)
bp,use
wik Qik
≤ Capi , i ∈ I
k∈K
bp,buy bp,in bp,out bp,use rm Qijk , Qijk , Qik , Qik , Qim , Invi
≥ 0, i, j ∈ I , k ∈ K, m ∈ M
(13)
Constraints (5–6) express a lower limit and an upper limit representing the ratio of the by-product used to the raw material used. Constraint (7) ensures that every plant is profitable as long as they are in the network. Constraint (8) ensures that the amount of the final product produced satisfies the demand. The excess amount of final products is stocked. Constraint (9) expresses that a certain amount of by-products can be produced
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with the use of raw materials. By-products produced can be sold to other plants in the network or to plants outside the park. Constraint (10) is a balance constraint and ensures that the amount of by-product sold to plant j is equal to the amount of byproduct purchased by plant j. Constraint (11), ensures that a plant cannot use more than the amount of by-product purchased. Finally, constraint (12) represents the production capacity of each plant.
3 Fuzzy Solution Approaches for the BLP Problem In this section, we shortly summarize utilized fuzzy solution approaches. 3.1 Fuzzy Programming Approach – FPA In FPA, the leader specifies goals for the control variable and the objective function. This information is modeled through membership functions and transmitted to the follower at the leader’s request. The follower tries to satisfy the leader’s objective, as well as his/her objective. Then, the follower presents the solution to the leader. If the leader accepts the proposed solution, this solution is called a satisfactory solution. If this solution is not suitable, then the leader updates the tolerance values of his/her membership function until a satisfactory solution is reached. This approach aims to maximize the minimum satisfaction level [17, 18]. Trapezoidal membership functions are used for the upper and lower-level objective functions. On the other hand, the triangular membership function is used for the leader’s control variable. When our bilevel model is rearranged according to the FPA, the following model is obtained. max λ s.t.
(14)
i∈I
m∈M
rm,U rm Qim + p1 − i∈I m∈M Qim
p1
L i∈I fREV ,i − fCOST ,i − TP ≥λ U L TP − TP rm Qrm,f − m∈M Qim ≥λ Qrm,f − Qrm,l
≥λ
(15) (16) (17)
Eq. (5) − (13)
(18)
λ ∈ [0, 1]
(19)
where Qrm,l and TQrm,f represent the lower and upper bounds for the leader’s objective function, TP L and TP U represent the lower and upper bounds for the follower’s objective function, p1 is the tolerance value, Qrm is the control variable of the leader, and Qrm,U − p1 , Qrm,U + p1 are the lower and upper bounds for the leader’s control variable. This model contains fewer constraints and decision variables compared to the model obtained with the KKT approach. However, this method does not always provide the desired solution, due to the inconsistency between the membership function of the leader’s decision variable and the membership function of the objective functions [10].
Comparison of Fuzzy Solution Approaches
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3.2 Fuzzy Goal Programming – FGP In the goal programming problem, targets to be reached for each goal are determined precisely by the decision makers. The aim is to minimize the sum of deviations from target values since it is not possible to satisfy all goals simultaneously. However, determining these target values precisely is often difficult for decision makers. In FGP, target values for each goal are represented as a membership function. The decision-maker provides an acceptable range for the target level instead of a single value. In the case of bilevel programming, we define membership functions for each goal and deviation variables by considering the objectives of the leader and the follower. To obtain an FGP model of our bilevel model we defined deviation variables. We assume that d1+ , d1− , d2+ , d2− represent the deviation from the membership functions defined for the leader’s control variable. d3+ , d3− denote deviations from the goal of the membership function defined for the follower’s objective function whereas d4+ , d4− represent deviations from the goal values of the membership function defined for the leader’s objective function. Finally, w1r , w2l , w3 , w4 represent weights for each fuzzy goal. The proposed FGP model is as follows;
(20) min w1r d1+ + d1− + w2l d2− + d2+ + w3 d3+ + w4 d4− s.t.
i∈I
m∈M
i∈I
m∈M
rm,U rm Qim + p1 − i∈I m∈M Qim
rm − Qim
p1 i∈I
m∈M
p1
rm,U Qim − p1
fREV ,i − fCOST ,i − TP L − d3+ + d3− = 1 TP U − TP L rm Qrm,f − m∈M Qim − d4+ + d4− = 1 Qrm,f − Qrm,l
i∈I
Eq. (5) − (13)
− d1+ + d1− = 1
(21)
− d2+ + d2− = 1
(22)
(23) (24) (25)
4 Computational Results The results of the considered approaches are summarized in Table 1. In the first and second columns, we present the solution obtained only by considering only the leader’s objective function and the follower’s objective function. Next, we supply the results obtained with the KKT approach, FPA and FGP approaches in columns 3, 4 and 5, respectively. The results obtained by using the FPA enabled us to reach a meaningful result both in terms of profit and raw material use. As expected, plants consumed less raw material
64
B. Altınkaynak et al. Table 1. Solution of the bilevel problem with various solution approaches. Leader’s model
Total raw material used (tonne)
Follower’s model
1665454.5
1759021.1
KKT
FPA
1665454.5
FGP
1709292.0
1759021.5
Sawmill P.
640000.0
640000.0
640000.0
640000.0
640000.0
Particleboard P.
276620.0
276620.0
276620.0
276620.0
337126.0
Fiberboard P.
674446.0
747016.0
674446.0
718283.0
707507.0
Pellet P. Pulp & Paper P. Total by-product used (tonne) Sawmill P.
226.5
7317.8
226.5
226.5
226.5
74162.0
88067.3
74162.0
74162.0
74162.0
492883.4
287882.0
492883.4
367392.0
312466.3
0
0
0
0
0
Particleboard P.
182569.0
182569.0
182569.0
182569.0
96795.0
Fiberboard P.
215213.0
7470.2
215213.0
89721.1
120570.0
Pellet P.
22422.7
11536.8
22422.7
22422.7
22422.7
Pulp & Paper P.
72678.7
86306.0
72678.7
72678.7
72678.7
Total 274833346.0 278550350.0 274832160.0 271393546.0 275947946.0 production cost ($) Sawmill P. Particleboard P. Fiberboard P. Pellet P. Pulp & Paper P. Total profit ($)
103315000.0 103315000.0 103315000.0 103315000.0 103315000.0 42009600.0
41659400.0
41659400.0
41659400.0
45760200.0
107593000.0 102196000.0 107593000.0 104333000.0 105134000.0 797446.0
1053550.0
1012760.0
797446.0
797446.0
21118300.0
30326400.0
21252000.0
21288700.0
20941300.0
122909032.0 131529904.0 122910123.0 127490932.0 122909132.0
Sawmill P.
18866800.0
18866800.0
18866800.0
18866800.0
18866800.0
Particleboard P.
22016300.0
22366500.0
22366500.0
22366500.0
18519500.0
Fiberboard P.
46877700.0
54165100.0
46877700.0
51279800.0
50197600.0
605532.0
360404.0
390223.0
605532.0
605532.0
34542700.0
35771100.0
34408900.0
34372300.0
34719700.0
Pellet P. Pulp & Paper P.
compared to the follower’s model, and more raw materials compared to the leader’s model. In this sense, we could say that reasonable results are obtained. However, the KKT approach provides a better result compared to FPA in terms of raw material use. Because the FPA approach generates a more profitable solution with more raw material use and less by-product use.
Comparison of Fuzzy Solution Approaches
65
The FGP approach provides a solution almost having an equal profit compared to the solution obtained by the KKT approach. However, FGP offers more raw material use compared to other approaches. In this sense, we can say that KKT performs better than the FGP approach. FGP approach almost underestimates the hierarchy of the objectives. It offers a solution having a total profit nearly equal to the one obtained in the leader’s model. On the other hand, FGP requires raw material use as much as the follower’s model.
5 Conclusion In this study, we investigate the suitability and efficiency of some fuzzy solution approaches such as FPA and FGP for a BLP problem. The approaches are selected as an alternative to the KKT approach. As we mentioned previously, the transformation of bilevel models to single objective models with the KKT approach increases the size of the problem. In spite, computational results show that KKT performs better. Although using FGP and FPA is better in terms of the size of the model, these approaches do not outperform KKT in our case. This is most probably due to the fact that these approaches underestimate the bilevel structure of the problem. In this sense, we believe that further studies are needed to develop fuzzy solution approaches that handle bilevel models better. Acknowledgments. This study is supported by the Scientific and Technological Research Council of Turkey (TUB˙ITAK) under 1001 Grants with Project Number: 122M223.
References 1. Dempe, S.: Bilevel Optimization: Theory, Algorithms and Applications. Springer (2018) 2. Caramia, M., Dell’Olmo, P.: Multi-objective optimization. In: Multi-Objective Management in Freight Logistics. Increasing Capacity, Service Level, Sustainability, and Safety with Optimization Algorithms, pp. 21–51. Springer, Cham (2020). https://doi.org/10.1007/978-3-03050812-8_2 3. Zhang, D., Lin, GH.: Bilevel direct search method for leader–follower problems and application in health insurance. Comput. Oper. Res. 41, 359–373 (2014). https://doi.org/10.1016/ j.cor.2012.12.005 4. Angulo, E., Castillo, E., García-Ródenas, R., Sánchez-Vizcaíno, J.: A continuous bi-level model for the expansion of highway networks. Comput. Oper. Res. 41, 262–276 (2014). https://doi.org/10.1016/j.cor.2013.02.022 5. Lachhwani, K., Dwivedi, A.: Bi-level and multi-level programming problems: taxonomy of literature review and research issues. Arch. Comput. Method E. 25(4), 847–877 (2018). https://doi.org/10.1007/s118311-017-9216-5 6. Bard, J.F.: Practical Bilevel Optimization: Algorithms and Applications, vol. 30. SSBM (2013) 7. Bialas, W.F., Karwan, M.H.: Multilevel linear programming. Technical report no. 78-1, May 1978 8. Lai, Y.J.: Hierarchical optimization: a satisfactory solution. Fuzzy Set Syst. 77(3), 321–335 (1996)
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9. Shih, H.S., Lai, Y.J., Lee, E.S.: Fuzzy approach for multi-level programming problems. Comput. Oper. Res. 23(1), 73–91 (1996). https://doi.org/10.1016/0165-0114(95)000860 10. Mohamed, R.H.: The relationship between goal programming and fuzzy programming. Fuzzy Set Syst. 89(2), 215–222 (1997). https://doi.org/10.1016/S0165-0114(96)00100-5 11. Baky, I.A.: Solving multi-level multi-objective linear programming problems through fuzzy goal programming approach. Appl. Math. Model 34(9), 2377–2387 (2010). https://doi.org/ 10.1016/j.apm.2009.11.004 12. Pramanik, S., Roy, T.K.: Fuzzy goal programming approach to multilevel programming problems. Eur. J. Oper. Res. 176(2), 1151–1166 (2007). https://doi.org/10.1016/j.ejor.2005. 08.024 13. Moitra, B.N., Pal, B.B.: A fuzzy goal programming approach for solving bilevel programming problems. In: Pal, N.R., Sugeno, M. (eds.) Advances in Soft Computing — AFSS 2002. LNCS (LNAI), vol. 2275, pp. 91–98. Springer, Heidelberg (2002). https://doi.org/10.1007/3-54045631-7_13 14. Haeri, A., Hosseini-Motlagh, S.M., Samani, M.R.G., Rezaei, M.: A bi-level programming approach for improving relief logistics operations: a real case in Kermanshah earthquake. Comput. Ind. Eng. 145, 106532 ( 2020). https://doi.org/10.1016/j.cie.2020.106532 15. Ye¸silkaya, M., Da¸s, G.S., Türker, A.K.: A multi-objective multi-period mathematical model for an industrial symbiosis network based on the forest products industry. Comput. Ind. Eng. 150, 106883 (2020). https://doi.org/10.1016/j.cie.2020.106883 16. Da¸s, G.S., Ye¸silkaya, M., Altinkaynak, B., Birgoren, B.: Modeling an industrial symbiosis network using bilevel programming. In: 62nd International Scientific Conference on Information Technology and Management Science of Riga Technical University, pp. 1–6. IEEE Press, New York (2021). https://doi.org/10.1109/ITMS52826.2021.9615312 17. Zimmermann, H.J.: Fuzzy programming and linear programming with several objective functions. Fuzzy Set Syst. 1(1), 45–55 (1978). https://doi.org/10.1016/0165-0114(78)900 31-3 18. Zimmermann, H.J.: Fuzzy mathematical programming. Comput. Oper. Res. 10(4), 291–298 (1983). https://doi.org/10.1016/0305-0548(83)90004-7
Decision Making on Students’ Performance Estimation J. M. Babanli(B) Azerbaijan State Oil and Industry University, Azadlig Avenue, 20, Baku AZ1010, Azerbaijan [email protected]
Abstract. A frequent problem in the awarding of scholarships is the identification and proper selection of students who are eligible for scholarships due to the limited quota. In the process of determining scholarship, we use the criteria which evaluated subjectively and some students who have the ability or value that is not so different. In this case, the application of fuzzy logic theory is an effective tool. Thus, fuzzy logic allows to describe the knowledge of experts. This paper devoted to the usage of fuzzy logic on scholarship evaluation. For this purpose, student evaluations of 4 experts on 5 criteria are used and the fuzzy approach is applied proposed by author. The basic of represented method is Zadeh’s fuzzy set theory for aggregation of properties. The objective of this study is to detect the chances of students to get a scholarship and to rank the students according to the evaluation of 5 criteria. Keywords: Fuzzy number · Scholarship · Fuzzy logic · Aggregation · Zadeh’s concept
1 Introduction Scholarships are a supporting factor for students. A scholarship is a form of financial aid given to students. Each educational institution, especially universities, offers many scholarships to students. These scholarships are provided by the government or the private sector in partnership with the university. Evaluation of students eligible for scholarships is based on predetermined criteria. These criteria may be different for each university. In recent years, there are several works related to this problem in the latest literature. Consider such scientific research. [1] is offered by DSS to determine the scholarship. Applying fuzzy logic [2] to this decision support system can determine who gets the scholarship. This system uses the Tsukamoto Fuzzy Logic method with pre-defined criteria, namely: overall grade point average (GPA), distance from the student’s home to campus, and the economic status of the student’s family. Paper [3] is devoted to An Evaluative Study of an Education Scholarship Program BM (BidikMisi) for Students in Indonesia. The method applied in this work is based on the Discrepancy Evaluation Model (DEM). Evaluation of data subjectivity in this study is based on university internal rules. The outcome of the BM is an impetus to increase the efficiency and competitiveness of Indonesian human resources. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 67–76, 2023. https://doi.org/10.1007/978-3-031-25252-5_14
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The Relationship between Scholarships and Student Success is discussed in [4]. Race, Parental marital status, In-state status, father education level, Mother education level, Log of total institutional aid, Log of total need-based aid, HS GPA, Entrance score, CC GPA criteria and crisp data are used for determining scholarship. The research work [5] is devoted to design an expert system based on fuzzy logic for anticipating students’ academic results for ASUM. Reasoning method based on Fuzzy Inference System and Gaussian membership function is discussed here. All calculations performed by using MATLAB package. Disadvantage of this system is dependence of results performed by membership function, type of aggregation and defuzzification methods. Combination of FCM method and SAW in Scholarship of Decision Support Systems is discussed in [6]. Advantage of offered approach is using Fuzzy logic properties. Brilliant but Needy Students Selection Using Fuzzy Logic is represented in [7]. Given work describes Fuzzy Logic Approach (FLA) for developing an evaluation model for finding intelligent students for scholarships. Grade, Interview Marks, School Type, Financial Status is used by author of paper as the input variable. Implementation of fuzzy logic using Sugeno Method of scholarship determination is discussed in [8]. The method used by the author in this study is a quantitative method because in this study the author relies on numerical calculations that use numbers. The author used observation, interview, and literature in data collection. The aim of the work [9] is to describe a neuro-fuzzy approach to classify students into different groups. SVM, neural network, Naive Bayes, and decision tree approaches methods were used in this study. Above mentioned proves that neuro-fuzzy approach is effective compared to the implemented methods, but there are also shortcomings here. These include the choice of membership function, inference algorithm, and training algorithm, which directly affect the results. Designing Decision Support System for Scholarship Prediction Using Adaptive Neuro Fuzzy Inference System Algorithm is detailed in [10]. The researchers created a DSS for predicting scholarship recipients and implemented an artificial neural network method using the Backpropagation method. Based on the results of the research, the design of the decision support system was successfully implemented. However, there are problems waiting to be solved here as mentioned above. In [11–18] is proved that under such conditions, approximate reasoning methodbased approach is effective tool. In this study we analyze the problem a decision making on students’ performance estimation. The rest of the work contains 5 parts. Section 2 gives information about preliminaries. The statement of problem is described in Sect. 3. The basic steps of used approach is represented on the next Section. Last part of the paper demonstrates examples of usage of methods for scholarship issue.
2 Preliminaries Group Decision Making Method suggested by J.Babanli [12]. This method contains given steps:
Decision Making on Students’ Performance Estimation
1. 2. 3. 4. 5. 6.
69
Creating team of the experts which evaluate criteria on alternatives. Evaluation of the alternatives by experts on criteria vector F = (f1 , . . . , fn ), Aggregation of alternative vectors. Calculation the arithmetic mean ϕl (ai ), l ∈ {1, . . . , L} for every importance group Calculation weighted average of values ϕl (ai ). 2 +agg3 − Ranking of the alternatives using distance d (Agg, Q) = agg1 +4∗agg 6 q1 +4∗q2 +q3 , d- distance between two fuzzy numbers- Q and Agg(ai ). Here Q the 6 highest linguistic term of the scale of estimation.
Definition 1. Aggregation of fuzzy numbers [12]. Let C1 , . . . , Cm be fuzzy numbers. An arithmetic mean-based aggregation of fuzzy numbers, C is defined as follows: m Ci C = i=1 , m Definition 2. Distance between triangular fuzzy numbers [12] Let C1 = (c11 , c12 , c13 ), C2 = (c21 , c22 , c23 ) be two triangular fuzzy numbers. A distance between C1 and C2 is defined as d (C1 , C2 ) = |P(C1 ) − P(C2 )|, where P(C1 ) =
c11 + 4c12 + c13 c21 + 4c22 + c23 , P(C2 ) = . 6 6
3 Statement of the Problem Aim of this study is to solve scholarship problem by using Fuzzy logic-based approach. This multi attribute decision making problem consist of n alternatives A = {a1 , . . . , am } and n criteria F = (f1 , . . . , fn ). Decision making matrix is given in Table 1. Outcomes on the table according to criteria is determining by expert team. Table 1. Preference values of alternatives f1
…
fj
…
fn
…
k f1n
…
f1jk fijk
…
ai
k f11 f1ik
…
fink
…
…
…
…
…
…
am
k fm1
…
k fmj
…
k fmn
a1
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Here, fijk - is the evaluation of k-th expert for i-th alternative and j-th criterion. Criteria are sorted by importance degree and for defining best alternative ranking evaluation is used. So, a* is the best or optimal alternative is found as follow Agg a∗ = max Agg(a), a∈A
Here Agg(a∗ ) is an aggregated index of the alternatives.
4 Application Numerical example for the discussed problem has 5 alternative-a1, a2, a3, a4, a5 and 5 criteria-f1 - Knowledge Level, f2 -Scientific-experience Knowledge, f3 -Mental World view, f4 -Lesson attendance, f5 -Attitude and Behaviour. Described issue was solved by using the method which is already discussed above. There are 4 experts in a group which evaluates all alternatives one by one. Experts’ evaluations are shown in Tables 2, 3, 4, 5, and 6. Table 2. Values on A1 alternative N
Criteria
Expret 1
Expert 2
Experts 3
Expert 4
1
Knowledge level
G
VG
G
G
2
Scientific- experience knowledge
G
G
M
G
3
Metal world view
VG
M
M
G
4
Lesson Attendance
G
G
G
G
5
Attitude and behavior
VG
G
M
VG
Table 3. Values on A2 alternative N
Criteria
Expret 1
Expert 2
Experts 3
Expert 4
1
Knowledge level
VG
G
G
M
2
Scientific- experience knowledge
G
G
M
G
3
Metal world view
VG
M
M
G
4
Lesson Attendance
VG
G
G
G
5
Attitude and behavior
VG
G
M
VG
Decision Making on Students’ Performance Estimation
71
Table 4. Values on A3 alternative N
Criteria
Expret 1
Expert 2
Experts 3
Expert 4
1
Knowledge level
VG
VG
G
VG
2
Scientific- experience knowledge
G
VG
G
M
3
Metal world view
VG
M
M
G
4
Lesson Attendance
VG
G
G
G
5
Attitude and behavior
VG
VG
M
VG
Table 5. Values on A4 alternative N
Criteria
Expret 1
Expert 2
Experts 3
Expert 4
1
Knowledge level
G
G
G
G
2
Scientific- experience knowledge
G
G
M
G
3
Metal world view
VG
M
G
G
4
Lesson Attendance
M
G
G
G
5
Attitude and behavior
VG
G
M
VG
Table 6. Values on A5 alternative N
Criteria
Expret 1
Expert 2
Experts 3
Expert 4
1
Knowledge level
VG
G
M
M
2
Scientific- experience knowledge
G
G
M
M
3
Metal world view
VG
M
M
M
4
Lesson Attendance
VG
G
G
G
5
Attitude and behavior
VG
G
M
VG
Criteria vector f i of expert group for each ai alternative are calculated using. K
fi k
f i = K Here f i -ai is found on the basis of overall opinion of the expert group. The estimation of the criteria are represented by fuzzy numbers according to the codebook shown in Fig. 1. k=1
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μf
i
Very low (VL)
1
0
Medium (M)
Low (L)
0.2
0.5
Good (G)
0.75
Very Good (VG)
1
fi
Fig. 1. Representation of the linguistic terms K
fi k
k
Using math expression f i = K , f i k = 1, . . . , K the vector f i is determined. For instance, the determined values for a1 are: k=1
G + VG + G + G VG + G + M + G = (0.65; 0.85; 1), f2 = = (0.6; 0.8; 0.95) 4 4 VG + VG + G + M G+G+G+G f3 = = (0.65; 0.85; 0.95), f4 = = (0.6; 0.8; 1) 4 4 VG + G + M + M f5 = = (0.55; 0.75; 0.9) 4
f1 =
Obtained values from Table 3: G+G+M +G G+G+M +M = (0.55; 0.75; 0.95), f2 = = (0.5; 0.7; 0.9) 4 4 G + VG + G + M G+G+M +G = (0.6; 0.8; 0.95), f4 = = (0.55; 0.75; 0.95) f3 = 4 4 M +M +G+G = (0.5; 0.7; 0.9) f5 = 4 f1 =
Obtained values from Table 4: VG + M + M + G VG + M + M + G = (0.55; 0.75; 0.9), f2 = = (0.55; 0.75; 0.9) 4 4 VG + M + M + G VG + M + M + G = (0.55; 0.75; 0.9), f4 = = (0.55; 0.75; 0.9) f3 = 4 4 M + M + M + VG = (0.5; 0.7; 0.85) f5 = 4 f1 =
Decision Making on Students’ Performance Estimation
73
Obtained values from Table 5: G+G+G+G VG + G + G + G = (0.6; 0.8; 1), f2 = = (0.65; 0.85; 1) 4 4 VG + G + G + G M +G+G+G f3 = = (0.65; 0.85; 1), f4 = = (0.55; 0.75; 0.95) 4 4 VG + G + G + G f5 = = (0.65; 0.85; 1) 4 f1 =
Obtained values from Table 6: VG + G + M + VG VG + G + M + VG = (0.65; 0.85; 0.95), f2 = = (0.65; 0.85; 0.95) 4 4 VG + G + M + VG VG + G + M + VG = (0.65; 0.85; 0.95), f4 = = (0.65; 0.85; 0.95) f3 = 4 4 VG + G + M + VG = (0.65; 0.85; 0.95) f5 = 4 f1 =
For alternatives the arithmetic mean for every importance group ϕ1 (ai ), ϕ2 (ai ), ϕ3 (ai ) values are calculated. Importance criteria subgroups are represented in Table 7. Table 7. Importance Criteria Subgroups Importance rates
Criteria
IR1 (High) (0.5 0.55 0.75)
f1 f2
IR2 (Medium) (0.2 0.35 0.45)
F3
IR3 (Low) (0 0.1 0 .25)
F4 f5
So, φ1 (ai ) =
f 1 + f2 f 4 + f5 , φ2 (ai ) = f3 , φ3 (ai ) = . 2 2
Values for a1 as follows: ϕ1 (a1 ) = (0.6; 0.8; 0.975), ϕ2 (a1 ) = (0.55; 0.75; 0.9), ϕ3 (a1 ) = (0.625; 0.825; 0.975) Obtained values for a2: ϕ1 (a2 ) = (0.55; 0.75; 0.925), ϕ2 (a2 ) = (0.55; 0.75; 0.9), ϕ3 (a2 ) = (0.65; 0.85; 0.975)
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J. M. Babanli
Obtained values for a3: ϕ1 (a3 ) = (0.625; 0.825; 0.95), ϕ2 (a3 ) = (0.55; 0.75; 0.9), ϕ3 (a3 ) = (0.65; 0.85; 0.975) Obtained values for a4: ϕ1 (a4 ) = (0.575; 0.775; 0.975), ϕ2 (a4 ) = (0.55; 0.75; 0.9), ϕ3 (a4 ) = (0.6; 0.8; 0.95) Obtained values for a5: ϕ1 (a5 ) = (0.525; 0.725; 0.9), ϕ2 (a5 ) = (0.5; 0.7; 0.85), ϕ3 (a5 ) = (0.65; 0.85; 0.975) The final aggregate grades for first alternative is calculated using Agg(ai ) = IG1 ϕ1 (ai ) + . . . . + IGl ϕl (ai ) + . . . + IGL ϕL (ai ). IGl , i = 1, . . . L for a1: Agg(a1 ) = (0.5; 0.6; 0.7)(0.6; 0.8; 0.975) + (0.2; 0.3; 0.4)(0.55; 0.75; 0.9)+ (0; 0.1; 0.2)(0.625; 0.825; 0.975) = (0.41; 0.7875; 1.2325) Obtained result for a2 as follows: The values for a2 are shown: Agg(a2 ) = (0.5; 0.6; 0.7)(0.55; 0.75; 0.9) + (0.2; 0.3; 0.4)(0.55; 0.75; 0.9)+ (0; 0.1; 0.2)(0.65; 0.85; 0.975) = (0.385; 0.76; 1.2025) The values for a3 are shown: Agg(a3 ) = (0.5; 0.6; 0.7)(0.625; 0.75; 0.9) + (0.2; 0.3; 0.4)(0.55; 0.75; 0.9)+ (0; 0.1; 0.2)(0.65; 0.85; 0.975) = (0.4225; 0.805; 1.22) The values for a4 are shown: Agg(a4 ) = (0.5; 0.6; 0.7)(0.575; 0.775; 0.975) + (0.2; 0.3; 0.4)(0.55; 0.75; 0.9)+ (0; 0.1; 0.2)(0.6; 0.8; 0.95) = (0.3975; 0.77; 1.2325) The values for a5 are shown: Agg(a5 ) = (0.5; 0.6; 0.7)(0.525; 0.725; 0.9) + (0.2; 0.3; 0.4)(0.5; 0.7; 0.85)+ (0; 0.1; 0.2)(0.65; 0.85; 0.975) = (0.3625; 0.73; 1.165) Distance between aggregation value of the alternatives and very good (VG) are determined as follows according to Definition 2: d (Agg(a1 ), VG) = |0.7600 − 0.9583| = 0.1983, d (Agg(a2 ), VG) = |0.7375 − 0.9583| = 0.2208 d (Agg(a3 ), VG) = |0.8104 − 0.9583| = 0.1479, d (Agg(a4 ), VG) = |0.785 − 0.9583| = 0.1733 d (Agg(a5 ), VG) = |0.7413 − 0.9583| = 0.2170
Decision Making on Students’ Performance Estimation
75
The results obtained are given in Table 8: Table 8. The rank of alternatives Alternative
Distance
(a1 )
0.1983
(a2 )
0.2208
(a3 )
0.1479
(a4 )
0.1733
(a5 )
0.2170
Using distance alternatives are ranked as: a3 a4 a1 a5 a2 . In our case 3rd alternative is the best, because the smallest distance is in this alternative.
5 Conclusion To sum up, it is defined that which student can get scholarship by using fuzzy informationbased method. Used method based on Zadeh’s idea. Determining the chances of students to get a scholarship issue contains 5 criteria, that given criteria and obtained results assists to show the relevance of this method. Obtained result describes effectiveness of the used methodology.
References 1. Sukenda, S., Puspitarani, Y., Wibowo, A.P.W., Yustim, B., Sunjana, S.: Fuzzy logic implementation using the Tsukamoto method as a decision support system in scholarship acceptance. Turkish J. Comput. Math. Edu. 12(11), 1411–1417 (2021). https://doi.org/10.48047/rigeo.11. 1.34(3) 2. Aliev, R.A., Aliev, R.R.: Soft Computing and its Application. World Scientific, New Jersey, London, Singapore, Hong Kong (2001). https://doi.org/10.1142/4766 3. Aliyyah, R. R., Rosyidi U., Yazid, R.: An Evaluative Study of an Education Scholarship Program (BidikMisi) for Students in Indonesia. 1st International Conference on Advance and Scientific Innovation (ICASI) IOP Conf. Series: J. Physics: Conf. Series 1175 (2019). https:// doi.org/10.1088/1742-6596/1175/1/012171 4. Ganem, N. M., Michelle M.: The Relationship between Scholarships and Student Success: An Art and Design Case Study. Edu. Research Int., 2011, 8 p. (2011). https://doi.org/10.1155/ 2011/743120 5. Goni, I., Gumpy, J.M., Zira, P.B.: Designing a fuzzy rule based system to predict students academic performance in adamawa State University Mubi. Arch. Appl. Sci. Res. 10(2), 28–35 (2018) 6. Trisudarmo, R., Sediyono, E., Suseno, J.E.: Combination of Fuzzy C-Means clustering methods and simple additive weighting in scholarship of decision support systems. Adv. Social Sci., Edu. Humanities Res. 547, 161–169 (2021). https://doi.org/10.2991/assehr.k.210430.025
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7. Aazagreyir, P., Damnyag, J.B.K., Kuuboore, M.: Brilliant but needy students selection using fuzzy logic. Int. J. Comput. Eng. Inform. Tech. 11(8), 178–185 (2019) 8. Sitanggang, B. A., Gunawan, I., Irawan, Parlina, I., Siregar, Z. A., Implementation of fuzzy logic using sugeno method of scholarship determination. J. Artificial Intell. Eng. Appl., 1(2), 135–141 (2022) 9. Do, Q. H., Chen, J.-F..: A Neuro-Fuzzy Approach in the Classification of Students’ Academic Performance. Computational Intell. Neuroscience. 2013, 7 pages. https://doi.org/10.1155/ 2013/179097 10. Pujianto, A., Kusrini, Sunyoto, A.: Designing decision support system for scholarship prediction using adaptive neuro fuzzy inference system algorithm. Conf. Series: J. Physics: Conf. Series 1140 (2018). https://doi.org/10.1088/1742-6596/1140/1/012049 11. Gardashova, L.A.: Z-number based TOPSIS method in multi-criteria decision making. In: Aliev R., Kacprzyk J., Pedrycz W., Jamshidi M., Sadikoglu F. (eds) ICAFS-2018. Adv. Intel. Syst. Comput., vol. 896, pp. 42–50. Springer, Cham (2018). https://doi.org/10.1007/978-3030-04164-9_10 12. Babanli, J.M.: Fuzzy approach for evaluation of student’s performance. In: 14th International Conference on Theory and Application of Fuzzy Systems and Soft Computing, ICAFS-2020. Adv. Intel. Syst. Comput., vol. 1306, pp. 140–147 (2020). https://doi.org/10.1007/978-3= 030-64058-3_18 13. Zadeh, L.A.: A Very Simple Formula for Aggregation and Multicriteria Optimization. Int. J. Uncertainty, Fuzziness Knowl.-Based Syst., 24(6), 961–962 (2016). https://doi.org/10.1142/ S0218488516500446 14. Aliev, R.A., Gardashova, L.A.: Z-set based approach to control system design. In: ICAFS2020, Adv. Intel. Syst. Comput., 1306, 10-21 (2021). 15. Aliev, R.A., Tserkovny, A.: Systemic approach to fuzzy logic formalization for approximate reasoning. Inform. Sci. 181, 1045–1059 (2011) 16. Mirzakhanov, V.E., Gardashova L.A.: Modification of the Wu-Mendel approach for linguistic summarization using IF-THEN rules. J. Exp. Theoretical Artif. Intell., 77–97 (2019). https:// doi.org/10.1080/0952813X.2018.1518998 17. Adilova, N.E.: Construction of fuzzy control system rule-base with predefined specificity. Adv. Intell. Syst. Comput, vol. 896, pp. 901–904 (2019). Doi:https://doi.org/10.1007/978-3030-04164-9_119 18. Gardashova, L.A., Salmanov, S.: Using Z-number based information in personnel selection problem. Lecture Notes in Networks and Systems, 362, 302–307(2021). https://doi.org/10. 1007/978-3-030-92127-9_42
A Comparative Analysis of the Different CNN Models Using Fuzzy PROMETHEE for Classification of Kidney Stone Fahreddin Sadıko˘glu1,2
, Özlem Sabuncu1(B)
, and Bülent Bilgehan1
1 Department of Electrical and Electronic Engineering, Near East University, Nicosia,
Mersin 10, Turkey {fahreddin.sadikoglu,ozlem.sabuncu,bulent.bilgehan}@neu.edu.tr 2 Odlar Yurdu University, Koroglu Rahimov Street, 13 AZ1072 Baku, Azerbaijan [email protected]
Abstract. A kidney stone is the crystallization of acid salts and minerals in the kidneys. It is a urinary system disease with a rapidly increasing prevalence. Computed tomography (CT) imaging is preferred for imaging kidney stone disease. This study aims to compare the accuracy capabilities of deep learning models in classifying abdominal CT images. In this paper, we examine the use of pre-trained deep learning models to distinguish between patients with and without kidney stones. A dataset of 681 previously not used before images was obtained from the public hospital in Cyprus and used to train and test five pre-trained models. This study also aims to evaluate and compare deep learning models in kidney stone classification using the multi-criteria decision-making technique. The performance of the various deep learning methods is evaluated using the Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE) test. The test uses a set of very important conditions for assessment with related weights associated with the kidney stone. The overall result reflects the value of each assessment as well as the overall performance of the model. The PROMETHEE test identified the most suitable deep learning method to be the Inception-V3 algorithm. Keywords: Kidney stone · Deep learning · CNN models · Fuzzy PROMETHEE · Medical image
1 Introduction Kidney stone disease is a common health problem worldwide. It is an increased urinary system disease of human health and affects approximately 12% of the world population [1]. It refers to the formation of stones in the collecting ducts of the kidneys or renal tubules. This disease affects kidney function and can obstruct the urinary system [2]. The first step in the detection and management of kidney stone disease is the imaging of the kidneys. Imaging the kidneys, diagnostic and therapeutic data can be obtained [3]. In patients with kidney stones, non-contrast CT is often used to scan the kidneys. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 77–84, 2023. https://doi.org/10.1007/978-3-031-25252-5_15
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Kidney stones have different compositions, absorb a lot of radiation, and can be easily visualized without the need for contrast [4]. Radiologists need to manually scan multiple CT sections to diagnose kidney stone disease. This process is time-consuming. Instead, automatic classifiers have been developed to relieve the work of radiologists. Deep learning (DL) methods have high accuracy potential in medical analysis compared to human experts for disease detection and assessment. DL algorithms are capable of achieving a reproducible result in less time than it takes a person to make an assessment. It also has the potential to evaluate numerous features, including those missed by radiologists [5]. Deep neural networks use tags to extract features from complex data. Convolutional neural networks (CNNs), one of the deep learning algorithms, have a deep architecture and therefore are successful in extracting distinctive features [6]. CNN’s are used in image recognition tasks. They are used for many tasks such as image classification, segmentation, and detection [7]. The paper [8] introduced a hybrid method of computer vision and deep learning algorithm to be effective to detect kidney stones. The task is to enable the automatic prediction of kidney stones. Several other research papers are using different types of deep learning algorithms such as ResNet-101 quoting the prediction success percentage [9]. The researchers moved further ahead to classify the type of kidney stone and also identify the type that can lead to predicting the cause of the kidney stone. It is for this reason that deep learning with higher accuracy should be applied to obtain the initial classification. Therefore, a precise evaluation of the available methods should be undertaken to identify the best-performing algorithm. In this study, five CNN models were used for kidney stone classification using CT images. In this study, CNN models used for the classification of kidney stones are discussed and analyzed. A multi-criteria decision-making method known as Fuzzy PROMETHEE is used for analysis and ranking. The article is organized as follows: Sect. 1 is an introduction to the article. Sect. 2 discusses the dataset, deep learning models, and training for this article, and Fuzzy PROMETHEE used for analysis and comparison of models. Sect. 3 shows the results of multi-criteria decision-making methods. Finally, Sect. 4 describes the conclusion.
2 Materials and Methods 2.1 Dataset Deep networks need a lot of data to provide high performance. In this study, after securing the ethics committee’s approval, a dataset was constructed consisting of 681 abdominal CT images. The abdominal CT images were collected from the Department of Radiology associated with Dr. Burhan Nalbanto˘glu State Hospital. The dataset includes images of two different classes: with a kidney stone and without a kidney stone. These images are labelled separately by the radiologist as images with and without kidney stones to train the network. In the CT scan images of 120 patients, 45 of the images belong to the normal group and 75 belong to the kidney stone patients. The data collected is comprised of 216 kidney stones and 465 non-kidney stone images. Figure 1 shows a sample of kidney stone and non-kidney stone images from the dataset.
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Fig. 1. Dataset description
2.2 Deep Learning Models Deep convolutional neural networks (CNN) are trained on datasets containing many images, such as ImageNet. They have high success in image classification. It is used for medical image classification purposes properly to its high success [10]. The transfer learning technique is used for a pre-trained network using ImageNet [11]. In this study, five different pre-trained CNN models use for kidney stone detection. These are; Inception-V3, NasNet-Mobile, InceptionResNet-V2, Xception, and DenseNet-201. Some parameters of these pre-trained networks are fine-tuned. These networks are trained with our raw CT images for the classification task. During the training, techniques such as rotation and enlargement apply to the images used to prevent the problem of overfitting. Figure 2 illustrates a training process for Xception. The performance of the CNN models was evaluated using the test images. The results are evaluated as true positive (TP), true negative (TN), false positive (FP) and false negative (FN). 2.3 Evaluation Methods The classification evaluation is based on many parameters. These parameters are derived from the training and test results. The true-positive (TP), true-negative (TN), falsepositive (FP), and false-negative (FN) values are subtracted from the test results. These are the parameters used to evaluate test accuracy, sensitivity, and specificity. (1) is used to calculate test accuracy. (2) is used to calculate the sensitivity. (3) shows the specificity calculation. Test Accuracy =
(TP + TN ) (TP + FN + FP + TN )
(1)
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Fig. 2. Training progress Xception
Sensitivity =
TP (TP + FN )
(2)
Specificity =
TN (TN + FP)
(3)
3 Fuzzy-Based MCDM Models The PROMETHEE technique, a multi-criteria decision-making technique, is based on comparing alternatives according to the selected criteria. It is an easier and more efficient method than other techniques. It can be used for real-life decision problems [12]. The paper [13] used the multi-criteria decision-making theory. This study aimed to evaluate and compare the best model for diagnosing a retinal disease. For this purpose, the decision theory they are interested in is Fuzzy PROMETHEE. Many factors affect the cancer treatment process. Therefore, various treatment procedures need to be evaluated. Fuzzy PROMETHEE decision-making theory was used to evaluate the best non-pharmacological treatment option in the paper [14]. These techniques were evaluated and compared according to certain criteria. The paper [15] aims to unravel the complexity of different diagnostic models for COVID19. For this, multi-criteria decision-making (MCDM) methods are used to compare Covid-19 diagnostic models and determine the most effective model. In this work, the fuzzy PROMETHEE method was applied to deep convolutional neural network models. After all the parameters needed for the classification by CNN models were collected, each criterion used a visual PROMETHEE decision lab program. Table 1 shows the parameters and weights of the criteria including the values of the parameters as used for the analysis. The Visual PROMETHEE Decision program was used in this study to rank alternative methods. The data in Table 1 was applied to the Visual PROMETHEE Decision program. The criteria required for the program are entered, and the weights of all criteria were determined. The criteria required for the program were entered based on the data obtained from the training and testing phase of five different CNN models. The weights of all criteria were determined. Preference functions and threshold values were entered for each criterion for analysis.
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Table 1. Fuzzy based visual PROMETHEE application for the classification of CNN models CNN models
SN
SP
Time
TP
FN
FP
TN
NL
Inception-V3
95,34
100,00
96 min 51 s
41
2
0
93
316
InceptionResNet-V2
79,06
88,17
286 min 21 s
34
9
11
82
825
NasNet-Mobile
86,04
95,69
379 min 33 s
37
6
4
89
914
Xception
65,11
68,81
59 min 13 s
28
15
29
64
171
DenseNet-201
67,44
73,11
151 min 52 s
29
14
25
68
709
TA: Test accuracy, SN: Sensitivity, SP: Specificity, TP: True-positive, FN: False-negative, FP: False-positive, TN: True-negative, NL: Number of layers.
4 Results The performance analysis of the different models is examined using the fuzzy PROMETHEE. Positive (Phi+) and negative (Phi−) flow values for PROMETHEE-I partial sequencing results and net (Phi) flow values for PROMETHEE-II were calculated with Visual PROMETHEE software. The Fuzzy-PROMETHEE comparison results of CNN models based on the specified criteria are shown in Table 2. Table 2. Complete Ranking of CNN models used to classify kidney stones. Rank
Phi
Phi+
Phi−
Inception-V3
0,6402
0,7847
0,1445
NasNet-Mobile
0,1711
0,5277
0,3567
InceptionResNet-V2
−0,0445
0,4405
0,4850
Xception
−0,3678
0,2454
0,6132
DenseNet-201
−0,3989
0,2257
0,6246
Table 2 lists the Phi, Phi+ and Phi− values and provides a ranking of the CNN models. The application of PROMETHEE indicates the most suitable model for this application. The positive outranking flow (Phi+) with the highest value shows the model that best fits the selected criteria. According to this, the Inception-V3 model is successful compared with other models. The comparison between the different models has been further evaluated using the action profile matrice generated using the Fuzzy PROMETHEE. The decision-makers relative importance (weights) and information priorities are applied for evaluation. Figures 3–7 shows each CNN model’s positive and negative side for selected nine criteria (accuracy, sensitivity, specificity, time, true positive, false negative, false positive and true negative and the number of layers). According to the action profile matrices, the model with the highest positive value shows the best fitting of the selected nine criteria.
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Fig. 3. Action profile for InceptionResNet-V2 model
Fig. 4. Action profile for Inception-V3 model
Fig. 5. Action profile for NasNet-Mobile model
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Fig. 6. Action profile for Xception model
Fig. 7. Action profile for DenseNet-201 model
Figures 3–7 indicates the performance of each model based on the selected weights. Inception-V3 (Fig. 4) is the most applicable model to identify kidney stones under all conditions.
5 Conclusion In this study, the Fuzzy PROMETHEE technique is used to compare the performance of different CNN models. Multi-criteria decision-making techniques offer sensitive and meaningful solutions to experts at the decision-making stage. The effectiveness of the alternatives was evaluated according to the selected criteria, and the experts determined the corresponding weights. The Visual PROMETHEE software ranking test results indicate the Iınception-V3 model to be the most successful compared with the other models regarding the highest positive flow value (Phi+ = 0,784) and action profile matrices showing the best fitting of selected criteria.
References 1. Alelign, T., Petros, B.: Kidney stone disease: an update on current concepts. Adv. Urol. 2018, 1–12 (2018). https://doi.org/10.1155/2018/3068365 2. Evan, A.P.: Physiopathology and etiology of stone formation in the kidney and the urinary tract. Pediatr. Nephrol. 25(5), 831–841 (2010). https://doi.org/10.1007/s00467-009-1116-y 3. Rao, P.N.: Imaging for kidney stones. World J. Urology 22(5), 323–327 (2004). https://doi. org/10.1007/s00345-004-0413-0 4. Brisbane, W., Bailey, M.R., Sorensen, M.D.: An overview of kidney stone imaging techniques. Nat. Rev. Urol. 13(11), 654 (2016). https://doi.org/10.1038/nrurol.2016.154
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5. Mazurowski, M.A., Buda, M., Saha, A., Bashir, M.R.: Deep learning in radiology: an overview of the concepts and a survey of state of the art with a focus on MRI. J. Magn. Reson. Imaging 49(4), 939–954 (2019). https://doi.org/10.1002/jmri.26534 6. Tajbakhsh, N., et al.: Convolutional neural networks for medical image analysis: full training or fine-tuning. IEEE Trans. Med. Imaging 35(5), 1299–1312 (2016). https://doi.org/10.1109/ TMI.2016.2535302 7. Ker, J., Wang, L., Rao, J., Lim, T.: Deep learning applications in medical image analysis. IEEE Access 6, 9375–9389 (2017). https://doi.org/10.1109/ACCESS.2017.2788044 8. Black, K.M., Law, H., Aldoukhi, A., Deng, J., Ghani, K.R.: Deep learning computer vision algorithm for detecting kidney stone composition. BJU Int. 125(6), 920–924 (2020). https:// doi.org/10.1111/bju.15035 9. Lopez, F., et al.: Assessing deep learning methods for the identification of kidney stones in endoscopic images. In: 43rd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, pp. 2778–2781 (2021). https://doi.org/10.1109/EMBC46164. 2021.9630211 10. Sabuncu, Ö., Bilgehan, B.: Performance evaluation for various deep learning (DL) methods applied to kidney stone diseases. In: 2021 Int. Conf. Forthcoming Networks Sustainability in AIoT Era (FoNeS-AIoT) IEEE, pp. 1–3 (2021). https://doi.org/10.1109/FoNeS-AIoT54873. 2021.00010 11. Dodge, S., Karam, L.: Human and DNN classification performance on images with quality distortions. ACM Trans. Appl. Percept. 16(2), 1–17 (2019). https://doi.org/10.1145/3306241 12. Brans, J.-P., De Smet, Y.: PROMETHEE methods. In: Greco, S., Ehrgott, M., Figueira, J.R. (eds.) Multiple Criteria Decision Analysis. ISORMS, vol. 233, pp. 187–219. Springer, New York (2016). https://doi.org/10.1007/978-1-4939-3094-4_6 13. Saleh, N., Salaheldin, A.M.: A benchmarking platform for selecting optimal retinal diseases diagnosis model based on a multi-criteria decision-making approach. J. Chin. Inst. Eng. 45(1), 27–34 (2022). https://doi.org/10.1080/02533839.2021.1983466 14. Batur Sir, G.D.: Evaluating treatment modalities in chronic pain treatment by the multi-criteria decision-making procedure. BMC Med. Inform. Decis. Mak. 19(1), 1–9 (2019). https://doi. org/10.1186/s12911-019-0925-6 15. Mohammed, M.A., et al.: Benchmarking methodology for selection of optimal COVID-19 diagnostic model based on entropy and TOPSIS methods. IEEE Access 8, 99115–99131 (2020). https://doi.org/10.1109/ACCESS.2020.2995597
Developing Efficient Frontier for Investment Portfolio: A Fuzzy Model Approach Leyla R. Hasanova(B) Azerbaijan State Oil and Industry University, 34 Azadlig Avenue, AZ1010 Baku, Azerbaijan [email protected]
Abstract. Investment in financial securities is a compound process involving decision concerning possible expected rates of return and risk. As a rule, decision maker often deals with insufficient data while selecting investment portfolio, due to uncertain business environment. Markowitz’s portfolio theory is a methodology in financial world that aims to maximize investment portfolio expected return for a given level of risk or minimize the risk of investment for a certain level of expected return. The classic mean-variance approach to portfolio selection is performed in this paper under the assumption that the returns and risk of financial securities are fuzzy values, which can successfully integrate the experts’ knowledge and the managers’ subjective opinion. The real financial world is very sensitive and influenced by changes in political-economic environment. Therefore, classical approach based only on historical data may lead to inaccurate results. The methodology performed in this paper considers fuzzy environment which contributes to actuality of this study. The aim of this paper is to develop fuzzy efficient frontier for portfolio consisting of eight assets. Modeling of sample investment portfolio is provided by using statistical data provided by Yahoo Finance web-platform and expert opinion. The software based on C# programming language is developed for determining efficient portfolios and constructing fuzzy efficient frontier. Obtained results of this study completely elucidate the efficiency of the proposed approach. Keywords: Mean-variance model · Fuzzy sets · Portfolio selection · Efficient frontier
1 Introduction The formation of an investment portfolio [1] is a process of making decision associated with the distribution of funds between several assets with the objective to obtain financial returns in condition of risk and uncertainty. The classic mean-variance approach to portfolio selection problem, introduced initially by Markowitz [2], has played a key role in the formation and development of modern portfolio theory. The goal of Markowitz theory is maximizing return of portfolio while simultaneously minimizing risk of investments. This method also explained the process of maximization the expected rate of return and minimization the risk of investment through proper diversification. Therefore, an optimal combination of the assets in © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 85–93, 2023. https://doi.org/10.1007/978-3-031-25252-5_16
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portfolio for maximizing the expected rate of return should be selected by investors. A key factor in this process is the correlation between the returns of securities as well as the weights of securities in the portfolio. Thus, at the same correlation coefficients between securities’ returns, alternative portfolios correspond to different values of risk (standard deviation), due to various weights of assets [3, 4]. The fundamental assumption of Markowitz’s mean-variance model says that the environment of financial markets in future can be accurately predicted based on asset’s historical data, namely, the mean and covariance of financial securities in future is resembling to the past one. [5]. It is hardly possible to assure this kind of assumption for contemporary ever-changing asset markets in real life. In addition, to statistical data, there are several factors which may have influence on future expected returns of stocks, such as economical and financial behaviors of the enterprises, their business development strategies, etc. This is ignored in classical approach. Using fuzzy models permits remove demerits and allows the incorporation of the expert knowledge. Several researchers have paid special attention to the formation of fuzzy portfolio. In paper [6] author suggested a fuzzy portfolio model for defining efficient portfolios in the context of behavioral analysis. Researcher developed a fuzzy portfolio model with the focus on various investor risk attitudes. Author demonstrated numerical example of a portfolio selection problem to address the issue presented by a diversity of investor risk attitudes. The study [7] perform the fuzzy portfolio optimization problem with the asset returns are performed in the shape of fuzzy numbers. A mean-absolute deviation risk function model and Zadeh’s extension principle are employed for solving portfolio optimization problem with fuzzy returns. Membership functions for return and risk were represented. In paper [8] authors use developed fuzzy portfolio model by applying Genetic Algorithm (GA) to define optimal values of risky assets. The effectiveness of proposed method is represented with numerical examples. As it was mentioned above, the aim of an investor is to compose a portfolio that provides maximum return with minimum acceptable risk. This process involves two important components: return and risk. Following portfolio theory, we use the term efficient frontier, which is a set of efficient portfolios, having the minimum risk measured with standard deviation for any given expected return. [9] Each point on the frontier represents a portfolio of investment assets. Usually, the portfolios that comprise the efficient frontier are the most diversified ones. Having given the risk attitude of the investor, the optimal portfolio is defined by selecting the mean and standard deviation on the frontier that together represent the most desirable utility and then pursue the weights of the assets in that portfolio. This paper studies the problem of constructing an efficient frontier by determining a set of efficient investment portfolios based on optimization model with the use of fuzzy numbers. For this purpose, software based on C# programming language has been developed. In this paper historical data for 8 stocks obtained on Yahoo Finance platform was used. The study framework involved several steps: a. Considering historical data for stock returns, financial reports of companies the expected quarterly returns are defined by experts in the shape of fuzzy numbers for each security;
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b. On the base of previous information, the average annual return and risk are calculated for each asset, covariance matrix is created. c. Two bounds of efficient frontier are determined: portfolio with the lowest risk and portfolio with the highest expected return based on optimization model d. Employed software allows to minimize the risk and maximize returns for these portfolios simultaneously. e. Additional efficient portfolios with the best risk-returns characteristics are defined and efficient frontier is developed.
2 Preliminaries Definition 1. Arithmetic Operations on Fuzzy Numbers [9–16] Arithmetic operations on fuzzy numbers such as addition (1), subtraction (2), multiplication (3) and division (4) are performed below: Suppose A and B are two fuzzy numbers and Aα and Bα their α-cuts Aα = a1α , a2α ; Bα = bα1 , bα2 (1) Then we can write Aα + Bα = [aα1 , aα2 ] + [bα1 , bα2 ] = [aα1 + bα1 , aα2 + bα2 ]
(1)
Aα = {x/μA (x) ≥ a}; Ba = {x/μB (x) ≥ a} (A − B)α = Aα − Bα = [aα1 − bα2 , aα2 − bα1 ], ∀α ∈ [0, 1]
(2)
(A · B)α = Aα · Bα = [aα1 , aα2 ] · [bα1 , bα2 ] ∀α ∈ [0, 1]
(3)
Aα : Bα = [aα1 , aα2 ] : [bα1 , bα2 ] ∀α ∈ [0, 1]
(4)
where
Definition 2. Fuzzy Minimum and Maximum of Fuzzy Numbers [10, 11]. The set R of real numbers has linear order. For ∀x, y ∈ R the pair (R, ≤) as mentioned above is a lattice. It worth noting, that fuzzy numbers are not structured in linear order; they may be ordered fractionally. It is essential to extend the lattice operation max and min to fuzzy minimum m˜in and fuzzy maximum m˜ax while ordering of fuzzy numbers. Take into consideration two fuzzy numbers A, B ⊂ R. Fuzzy minimum and fuzzy maximum we may define as: m˜in(A, B)(z) =
sup
min[A(x), B(y)]
(5)
min[A(x), B(y)]
(6)
z=min(x,y)
m˜ax(A, B)(z) =
sup z=max(x,y)
By using α-cuts we define ∀α ∈ [0, 1] m˜in(Aα , Bα ) = [min(aα1 , bα1 ), min(aα2 , bα2 )]
(7)
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m˜ax(Aα , Bα ) = [max(aα1 , bα1 ), max(aα2 , bα2 )]
(8)
Definition 3. Absolute Value of Fuzzy Number [9, 10] Absolute value of fuzzy number is identified as: max(A, −A), for R+ abs(A) = 0, for R− Definition 4. Mean –Variance Model. The Mean-variance model [3] evaluates the investment portfolio return and risk by defining mean and standard deviation of return distribution. Let n be the set of financial securities considering for investment and Rt = (r1t , r2t , r3t , …, rnt ) are their returns at the t th scenario, t = 1,…, T. An investment portfolio x = (w1 , …, wn ) ∈ X ⊆ Rn , relates to the vector of proportions of the incipient budget to be allocated in each security, suppose X is a number of reasonable portfolios, given by, X = {(w1 , …, wn ) | ni=1 wi = 1, wi ≥ 0, i = 1,…, n}. Here, ni=1 wi = 1 is a normalized budget constraint. To estimate the return of investment portfolio x, we use the following formula: n E(x) = r˜i wi (9) t=1
The variance of investment portfolio returns R(x) is defined such as: n n σ2 = σik wi wk i=1
k=1
(10)
where σik is the covariance between returns of ith and k th assets Definition 6. Efficient Frontier. The efficient frontier is referred as the set of efficient portfolios that provide the maximum expected return for a certain degree of risk or the minimum risk for a specified degree of expected return. Portfolios that located under the efficient frontier are inefficient as they do not offer sufficient return for the given level of risk. Investment portfolios which congregate to the right of the efficient frontier are inefficient because they have relatively high level of risk for the specified rate of return.
3 Problem Definition and Solution Method Assume that eight securities Si (i = 1, 2, . . . , 8) are viewed by an investor to select the superior portfolio that will give the optimal allocation of resources among these securities. The success of the proposed strategy of investor is measured by higher returns and lower risk. Securities issued by following companies have been randomly chosen: Apple Inc., Pfizer Inc., Netflix Inc., Coca Cola Company, Tesla Inc., Unilever Plc., Micron Technology Inc., Moderna Inc. In order to construct efficient frontier, two bounds have to be determined: 1) investment portfolio with the lowest risk and appropriate return. and 2) investment portfolio with the highest return and relevant risk. Variations within these bounds shape the efficient frontier of portfolios. To determine the abovementioned bounds for risk and return, an investor must settle the optimization problems below: n n σik wi wk (11) min DP = i=1
k=1
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subject to w ∈ W;
n i=1
wi = 1; wi ≥ 0; , i = 1, 2, . . . ., n
where, DP -is the variance of portfolio σik -is the covariance between securities i and k wi -is the weight of ith security wk -is the weight of k th security σp = DP
(12)
where, σp - is a standard deviation of portfolio max Rp =
n t=1
r˜i wi
(13)
subject to w ∈ W w ∈ W;
n i=1
wi = 1; wi ≥ 0; , i = 1, 2, . . . ., n
where Let (w1 , . . . , wn ) be an optimal value of risk obtained in Problem 11, 12 with opti ) be an optimal result of (13) with optimal value of return mal σp and (w1 . . . , wn1 return and risk of portfolios range in the intervals [ nt=1 r i xi ; nt=1 r i xi ] and R p . The [ ni=1 nk=1 σik xi xk ; ni=1 nk=1 σik xi xk ] respectively. At the next step we select 4 values of return within this interval and based on optimization model the minimum risk for chosen expected return values is defined. Obtained results allow us to construct efficient frontier on the graph with the Risk on horizontal axis and Expected return on vertical axis. The analysis conducted based on dataset of securities for the period February 1, 2021, to January 30, 2022 was taken from Yahoo finance website. The data consisting of the monthly closing prices of abovementioned eight securities have been used. The v −vit ∗ 100%, t = 1, 2, …, monthly return of the ith security is calculated by rit = i(t+1) vit th 12, where vi(t+1) and vit are the closing prices of i security in months t + 1 and t, respectively. The Table 1 performs the monthly returns of securities: Table 1. Monthly returns of stocks
M1 M2
0.009 0.076
0.082 0.067
-0.032 -0.016
0.076 0.033
-0.011 0.062
0.083 0.052
-0.036 -0.024
M12
-0.0075
-0.007
0.023
0.001
-0.015
0.079
-0.022
…………………………….
0.154 0.366 -0.055
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In order to facilitate further calculations quarterly returns will be considered for each security. Expert opinion based on comprehensive analysis of historical data and financial reports of the enterprises is used to define quarterly returns for each security in the shape of fuzzy numbers. The expected quarterly returns are evaluated as performed in Table 2: Table 2. Expected quarterly returns of securities Quarter 1 Quarter 2 Quarter 3 Quarter 4 (0.010,0.011,0.012) (0.066,0.069,0.072) (0.030,0.0318,0.033) (0.0078,0.008,0.009) (0.048,0.050,0.053) (0.063,0.067,0.070) (0.057,0.060,0.063) (0.0057,0.0059,0.006) …………… (0.078,0.082,0.086) (0.266,0.280,0.294) (-0.019,-0.020,-0.021) (-0.190,-0.199,-0.210)
Based on expected quarterly returns covariance matrix has been created (Table 3), expected average annual returns and variance have been defined (Table 4). Table 3. Covariance Matrix 0.001 0.000 0.001 0.000 ………………………… 0.003 0.004 0.006 -0.002
0.001
0.000
0.000
0.003
0.003
-0.001
-0.005
0.030
Table 4. Average annual returns and variance of securities Stock
Average annual return
Variance
S1
(0.0285, 0.03, 0.0315)
(0.00046, 0.00059, 0.000740)
S2
(0.0433, 0.0456, 0.0479)
(0.00042, 0.00056, 0.00074)
S3
(−0.0018, 0.0004, 0.0026)
(0.00172, 0.00210, 0.00252)
S4
(0.0017, 0.0021, 0.0025)
(0.00069, 0.00086, 0.00105)
S5
(0.0383, 0.0419, 0.0455)
(0.00583, 0.00700, 0.00829)
S6
(0.0005, 0.0018, 0.0031)
(0.00081, 0.00097, 0.00114)
S7
(0.0005, 0.0024, 0.0042)
(0.00122, 0.00149, 0.00179)
S8
(0.0283, 0.0356, 0.0429)
(0.02521, 0.03010, 0.03546)
Considering abovementioned data two bounds of efficient frontier (12,13) and then interim efficient portfolios are defined. Return and risk (Standard Deviation) for each case are represented in Table 5. The portion of investment in each security for relevant portfolio is demonstrated in Table 6. Based on data represented in Table 5 Fuzzy Efficient frontier has been constructed with the expected return on vertical axis and risk on horizontal axis. (see Fig. 1).
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Table 5. A set of efficient portfolios Efficient portfolios
Return
RISK (%)
I
(0.0151, 0.0166, 0.0182)
(0.000, 0.1324, 1.2862)
II
(0.0200, 0.0216, 0.0233)
(0.000, 0.1976, 1.3202)
III
(0.0260, 0.0278, 0.0296)
(0.000, 0.2133, 1.3712)
IV
(0.0325, 0.0345, 0.0365)
(0.000, 0.6760, 1.5357)
V
(0.0400,0.0422,0.0444)
(1.1762, 1.7022, 2.1701)
VI
(0.0433,0.0456,0.0479)
(2.0525, 2.3614, 2.7164)
Table 6. Portion of investment in each stock for a set of efficient portfolios Efficient portfolios
Weights of stocks in portfolio (%) S1
S2
S3
I
44.928
0.000
0.000
II
36.701
11.203
0.000
III
21.961
28.909
0.000
IV
0.400
57.685
V
0.000
84.948
VI
0.000
100
S4
S5
S6
S7
S8
9.947
0.000
26.144
18.981
0.000
21.492
0.000
13.849
16.754
0.000
33.780
0.000
0.470
14.880
0.000
0.000
34.782
0.000
0.000
7.133
0.000
0.000
15.052
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
Fig. 1. Fuzzy efficient frontier
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4 Conclusion The primary purpose of this research is to design fuzzy efficient frontier for investment portfolio. Originally, some important concepts and definitions were covered. The real statistical data and experts’ opinion were employed to illustrate methodology. Every point on the developed fuzzy efficient frontier performs an optimal combination of financial securities that provide the highest rate of return for any given level of risk. The proposed methodology allows investors to derive a set of efficient portfolio considering fuzzy environment and make a decision depending on their risk preferences. Further study of this issue can be extended to the developing the efficient frontier by using Z numbers theory.
References 1. Bakar, N.A., Rosbi, S.: Efficient frontier analysis for portfolio investment in Malaysia stock market. Sci. Int., Lahore 30(5), 723–729 (2018) 2. Markowitz, H.: Portfolio Selection: Efficient Diversification of Investments. John Wiley Sons, New York (1959). https://doi.org/10.2307/2975974 3. Hasanova, L.: Portfolio selection model using z-numbers theory. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 308–315. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-92127-9_43 4. Park, S., Lee, S.: Linear programing models for portfolio optimization using a benchmark. Eur. J. Finance 25(2), 1–23 (2018). https://doi.org/10.1080/1351847x.2018.1536070 5. Zhang, W.-G., Wang, Y.-L., Chen, Z.-P., Nie, Z.-K.: Possibilistic mean–variance models and efficient frontiers for portfolio selection problem. Inf. Sci. 177(13), 2787–2801 (2007). https:// doi.org/10.1016/j.ins.2007.01.030 6. Tsaur, R.-C.: Fuzzy portfolio model with different investor risk attitudes. Eur. J. Oper. Res. 227(2), 385–390 (2013). https://doi.org/10.1016/j.ejor.2012.10.036 7. Liu, S.-T.: A fuzzy modeling for fuzzy portfolio optimization. Expert Syst. Appl. 38, 13803– 13809 (2011) 8. Abiyev, R.H., Menekay, M.: Fuzzy portfolio selection using genetic algorithm. Soft Comput. 11, 1157–1163 (2007). https://doi.org/10.1007/s00500-007-0157-z 9. Aliev, R.A., Aliev, R.R.: Soft Computing and its Applications. World Scientific (2001). https:// doi.org/10.1142/4766 10. Zadeh, L.A., Aliev, R.A.: Fuzzy Logic Theory and Applications: Part I and Part II. World Scientific (2018). https://doi.org/10.1142/10936 11. Aliev, R.A., Pedrycz, W., Huseynov, O.H., Kreinovich, V.: The general theory of decisions. Inform. Sci. 327, 125–148 (2016). https://doi.org/10.1016/j.ins.2015.07.055 12. Aliev, R.A., Huseynov, O.H.: Decision Theory with Imperfect Information, p. 444. World Scientific, Singapoure (2014) https://www.worldscientific.com/worldscibooks/10.1142/9186 13. Gardashova, L.A.: Application of operational approaches to solving decision making problem using Z-numbers. J. Appl. Math. 5(9), 1323–1334 (2014). https://doi.org/10.4236/am.2014. 59125 14. Aliev, R.A., Pedrycz, W., Alizadeh, A.V., Huseynov, O.H.: Fuzzy optimality based decision making under imperfect information without utility. Fuzzy Optimization and Decision Making, Springer, Germany. 12(4), 357–372, (2013) https://link.springer.com/article/10.1007/s10 700-013-9160-2
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15. Alizadeh, A.V.: Application of the fuzzy optimality concept to decision making. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 542–549. Springer, Cham (2020). https://doi.org/10. 1007/978-3-030-35249-3_69 16. Aliyeva, K.R.: Demand forecasting for manufacturing under Z information. Procedia Comput. Sci. 120, 509–514 (2017). https://doi.org/10.1016/j.procs.2017.11.272
Impact of Online Education Classes on Students’ Satisfaction: The Case of Near East University Saide Sadıko˘glu , Sahin ¸ Akda˘g(B)
, and Murat Tezer
Near East University, Nicosia, Northern Cyprus {saide.sadikoglu,sahin.akdag,murat.tezer}@neu.edu.tr
Abstract. In this study, it is aimed to reveal student satisfaction regarding the use of distance education in classes of asynchronous joint courses at Near East University, and the opinions of the students, who are the end users, about these processes. The research method was determined as a mixed research method. In the research, both quantitative and qualitative methods were used together. The population of the research consists of 120 students of the Faculty of Tourism who take their common courses at the university through distance education. A questionnaire consisting of 20 items was used to collect the data. According to the results of the research, it was seen that the satisfaction of the students with the use of distance education in the courses was good. In general, the students stated that they did not encounter any problems in taking the courses online or face-to-face and that they did not experience any difference. Students have a positive attitude towards distance education. They also stated that they had the advantage of better learning by watching the missed lessons many times later. Apart from this advantage, students also stated that they do not have to pay for travel, accommodation, and other expenses for distance education. Keywords: Distance education · Asynchronous · Joint distance courses · Satisfaction · Attitude
1 Introduction With the rapid developments in technology have also been reflected in the education sector and have revealed the necessity of restructuring education systems. One of the education systems that emerged from this point of view is distance education. Distance education, which started by mail in 1728, has progressed with technology until today [1]. Distance learning is a discipline that teaches, learns, and tries to eliminate the limitations of learning resources and the problems created by these limitations while using existing technologies [2]. Distance Education is the realization of education when students and teachers are separated in terms of time and space When we look at the common features of the definitions, distance education; It is a system that takes advantage of the technology at the highest level and eliminates the elements of space and time between the educator and the trained, by following an effective way in reaching information sources and transporting students [3]. Dixon and Pelliccione [4] stated that it is possible to support © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 94–100, 2023. https://doi.org/10.1007/978-3-031-25252-5_17
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knowledge sharing and thus social communities through remote online communications between students from different countries. Distance education provides many benefits such as sustainability, flexibility in the learning process, time-saving, opportunity to continue working [5], equal opportunity, individualization of learning, global learning environments, receiving training on new subjects, benefiting from new technologies and methods [6]. In the epidemic process, not only primary, high school, and university students but also distance education is affected. As it is known, the Covid-19 epidemic, which affected the whole world, affected all the lives of people, and required certain changes. These changes have affected people’s entire lives, both personal and professional. Education The process of education has undoubtedly been affected by these changes and institutions have begun to give more importance to distance education methods and technologies. In this study, it is aimed to reveal student satisfaction regarding the use of distance education in classes of asynchronous joint courses at Near East University, and the opinions of the students, who are the end users, about these processes.
2 Research Method Mixed method research was preferred in the study. Mixed method research emerges as a research method in which practitioners gather and combine quantitative and qualitative data around the same subject to achieve better in subjects such as verification, logical testing, detail and research breadth, and interpretation [7]. While the survey method was used as a quantitative research method in the research, the interview was used as one of the qualitative research methods. At the same time, the mixed method is a method that increases the efficiency rate because it makes the result more valuable by evaluating multiple dimensions of perception together, making the findings more verifiable by examining from different perspectives, being more suitable for discussion and dialogue, and enabling to use qualitative and quantitative methods [7]. 2.1 Participants The participants of this research consist of 120 undergraduate students studying at the Near East University School of Tourism and Hotel Management in the spring semester of 2021–2022. The participants of the research consist of two parts. For the application of the questionnaire in the quantitative research department, 100 students who took their courses in the form of distance education within the high school were formed. In the qualitative research department, 20 students who were chosen on a voluntary basis among the students who took these courses and used the distance education system (UZEM) were determined to get user opinions. Moodle learning management system is used as the learning management system in the courses. When students click on https:// uzem.neu.edu.tr/, the login screen appears. They can log in by typing their username and password on the screen.
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2.2 Data Collection Tools In the collection of quantitative data, the questionnaire form “Satisfaction Questionnaire for Use of Distance Education in Common Courses” developed was used in [8]. The questionnaire was in a 5-point Likert type (From 1: Absolutely Disagree to 5: Absolutely Agree) and consisted of 20 items in total. Some sub-research topics were included in the survey questions; these are “1-Satisfaction with the course content”, “2. System and interface competence”, “3. Opinions about the instructors”, “4. Satisfaction and suitability of exams”, “5. Technical and institutional functioning”. Three field experts were consulted on the applicability of the questionnaire in universities in Northern Cyprus and face validity was ensured. For the reliability study of the questionnaire, the Cronbach alpha test was applied to the data obtained for 20 items in the SPSS 24 program. The Cronbach alpha coefficient was found to be 0.84 and the questionnaire was found to be reliable. In the qualitative part of the study, an unstructured interview form consisting of 2 open-ended questions for students and developed by taking the opinions of researchers and experts was used. Question 1. Do you think it is an advantage to take courses with distance education? Question 2. Do you plan to take the courses you will take in the future with distance education again? 2.3 Data Analysis Because of the Covid-19 Pandemic, the questionnaire and interview form were written in Google Forms. Students were asked to access this form and fill out the questionnaire form. In the analysis of quantitative data, descriptive statistics of the survey items were made using SPSS 24 software, and mean and standard deviation values were given. The content analysis method was used for the answers to open-ended questions. In addition, coding was done, and the expressions were explained as themes. 2.4 Results The data obtained through the questionnaire and interview forms were transformed into tables and presented in this section. As research finding, firstly, the average and standard deviation values of the questionnaire items are given in Table 1 as quantitative findings. In general, when Table 1 is examined, students have positive thoughts about “Satisfaction with the course contents”, “System and interface competence”, “Opinions about the instructors”, “Satisfaction with the exams and the appropriateness of the exams”, and “Technical and institutional functioning”. In addition, when the mean values were examined, they gave the answers of “I agree” and “I absolutely agree” to the questionnaire items. It can be said that students’ satisfaction with the use of distance education in courses is generally good. Content analysis was used to obtain the qualitative findings of the research, and the data obtained from the two open-ended questions were explained as themes in Table 2 and Table 3. With the emergence of new variants after the Covid-19 pandemic, universities continued to offer some, but not all, courses online in the form of distance education. When
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Table 1. Average and standard deviation values of the questionnaire items. No
Items
Average
Standard deviation
1
In terms of course content, PDF Text files are sufficient 4.10
0.899
2
In terms of course content, PPT text files are sufficient
4.23
0.987
3
In terms of course content, videos are enough
3.97
1.105
4
The language of the lecturers can be understood in the videos
3.85
1.102
5
The examples given in the lessons are enough
3.64
1.012
6
Course contents are up to date
3.88
1.123
Satisfaction with the course contents
System and interface competence 7
Instructional videos about the use of the system are enough
3.94
1.256
8
The functioning of the education system in which you receive distance education is sufficient
3.86
0.954
9
Announcements published in the system are sufficient
3.38
0.987
10
The system interface is user-friendly
3.65
0.895
11
Access to course materials is sufficient
3.42
0.999
Opinions about the instructors 12
Online communication between the instructor and the student is sufficient
3.98
1.111
13
The method used by the teaching staff in the lecture is sufficient
4.22
1.138
14
The teaching staff gives active feedback to the student during the learning process
4.25
1.125
Satisfaction and suitability of exams 15
It is convenient to conduct exams in a face-to-face classroom environment
1.96
1.001
16
The questions asked in the exams are in accordance with the course content
3.94
1.203
17
Exam questions are understandable
3.86
1.119
Technical and institutional functioning 18
Any time you encounter a problem, the necessary assistance is provided
3.85
0.886
19
Technical glitches in the system are fixed on time
4.16
0.982
20
The student is informed about the updated works
4.21
1.085
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Table 2 is examined, the students also stated that it is useful to have their courses in the form of distance education, and it is helpful and saving for them. In addition, the students mostly stated that they did not encounter any problems in taking the courses online or face-to-face and that they did not experience any difference. Students have a positive attitude towards distance education. They also stated that they had the advantage of better learning by watching the missed lessons many times later. Apart from this advantage, students also stated that they do not pay for travel, accommodation, and other expenses for distance education. Some students stated that it was difficult for them to take mathematics courses in the form of distance education. Table 2. Average and standard deviation values of the questionnaire items. Theme
N
When new variants came out, it was useful to take the courses with distance education
15
Helps and saves a lot
18
Has no problems taking courses both online and face to face
17
Have positive attitudes to distance education
16
Learn the courses better by watching videos many times
16
No need to travel, no money for accommodation, no other costs
19
Family support advantage
10
Difficulty in online math class
5
Students can take their courses professionally from online systems
12
Missed classes can be followed from the course page at the distance education system
16
When Table 3 is examined, all of the students gave the answer “Yes” to the situation of taking courses again with distance education in the near future. In general, the majority of students stated that they did not encounter any problems in distance education. However, very few students stated that they had problems due to the internet infrastructure in their homes. In addition, the students stated that they thought of taking the courses that they did not do well and were not successful in before, in the form of distance education. Table 3. Students’ views about taking courses again with distance education in the near future. Theme
N
To take courses with distance education at the near future
20
Do not have problems with distance education
15
To take courses that were not well-done before
6
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2.5 Discussion On the subject, according to the data obtained from the master’s thesis studied by Yadigar (2010) [9], students stated that they would like to choose distance education again in the future and that the technical infrastructure was properly prepared. This result is in parallel with the results of this study. However, in addition to these positive results, according to the other result obtained from the thesis, it was seen that the content of the program was insufficient, there was a need for improvement in participation and feedback, and there were also criticisms. After this thesis, after twelve years, no such result was found in this research. This result found in this study was seen as a reflection of the positive results achieved in distance education. Literature [10] conducted the research using a mixed method with 16 lecturers from three different universities. As a result of this research conducted in [10], it was found that the instructors’ knowledge about distance education is not clear, there is no common opinion because they make lecture-based explanations, they find themselves technically competent, they find distance education less useful than traditional education due to the lack of interaction for students. It has been found to be problematic in terms of infrastructure and usability. Unlike this study, students mostly stated that they did not encounter any problems in terms of both systematic and instructional aspects. In [8], in which the views of lecturers and students about the teaching of courses through distance education were examined, the average satisfaction with distance education in common courses was determined as 56.4%, and it was concluded that the students were partially satisfied. In this study, when the averages of the survey items are taken into account, it has been concluded that the satisfaction level of the students is at the level of “agree” and that the students are satisfied with the distance education courses.
3 Conclusion and Recommendation Considering the findings of the research, it was seen that the satisfaction of the students in the use of distance education in the courses was good. In general, the students stated that they did not encounter any problems in taking the courses online or face-to-face and that they did not experience any difference. Students have a positive attitude towards distance education. They also stated that they had the advantage of better learning by watching the missed lessons many times later. Apart from this advantage, students also stated that they do not have to pay for travel, accommodation, and other expenses for distance education. Universities will have to take the necessary precautions in this regard, considering that students may have difficulties in coming back to the university and starting their classes, as their accommodation, transportation, and other costs are reduced by distance education. Since the mathematics course is a difficult course in general, it is natural for students to have difficulties in distance education. However, in order to overcome these difficulties, it is necessary to take necessary precautions in distance education and conduct new research.
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References 1. Ak, A., Oral, B., Topuz, V.: Evaluation of distance learning process of Marmara University vocational school of technical sciences (in Turkish). SEAT J. 2(1), 71–80 (2018). Retrieved https://dergipark.org.tr/en/download/article-file/624965 2. Bozkurt, A.: The past, present and future of the distance education in Turkey (in Turkish). 3(2), 85–124 (2017). Retrieved https://dergipark.org.tr/en/download/article-file/403827 3. Erturgut, R.: Organizational, social, pedagogic components of the internet basic distance education (in Turkish). Bili¸sim Teknolojileri Dergisi 1(2), 79–85 (2008). Retrieved https:// dergipark.org.tr/en/download/article-file/75244 4. Dixon, K., Pelliccione, L.: Reactions to online learning from novice students in two distinct programs. In: Atkinson, R., McBeath, C., Jonas-Dwyer, D., Phillips, R. (eds.) Beyond the Comfort Zone: Proceedings of the 21st ASCILITE Conference, pp. 255–262 (2004). Retrieved http://www.ascilite.org.au/conferences/perth04/procs/dixon 5. Sadeghi, M.: A shift from classroom to distance learning: advantages and limitations. Int. J. Res. Engl. Educ. 4(1), 80–88 (2019). Retrieved http://ijreeonline.com/article-1-132-en.pdf 6. Gürer, M.D.E., Tekinarslan, M.D., Açık, G.: Fundamentals of open and distance learning (in Turkish). Pegem Akademi 1–28 (2021) 7. Creswell, J.W., Sözbilir, M.: Introduction to mixed methods research. Pegem Akademi (2017) 8. Erfidan, A.: Perspectives of Lecturers and Undergraduate Students on University Distance Education Courses: The Case of Balikesir University (in Turkish) (2019). Retrieved https:// dspace.balikesir.edu.tr/xmlui/handle/20.500.12462/5606 9. Yadigar, G.: Evaluation of the effectiveness of distance education program (in Turkish). Unpublished Master’s Thesis, Ankara (2010). Retrieved https://dspace.gazi.edu.tr/handle/20. 500.12602/188231 10. Yıldız, M.: The Relationships Among Distance Education Instructors’ Knowledge, Belief and Practices Towards Distance Education (in Turkish). Unpublished Master’s Thesis, Hacettepe Üniversitesi E˘gitim Bilimleri Enstitüsü, Ankara (2015). Retrieved http://www.openaccess. hacettepe.edu.tr:8080/xmlui/handle/11655/1741
Decision Making on Selection of Ferritic Stainless Steel Mustafa Babanli1
, Latafat Gardashova2(B)
, and Tural Gojayev1,2
1 Azerbaijan State Oil and Industry University, Azadlig Avenue 34, Nasimi, Baku, Azerbaijan 2 Azerbaijan University, Jeyhun Hajibeyli Street 71, Nasimi, Baku, Azerbaijan
[email protected]
Abstract. The selection of proper material based on fuzzy based MCDM methods for engineering purposes has gained importance in recent years. When selecting a material for a specific application based on properties, appropriate selection method must be applied to make sure that the suitable material has been selected and it will remain convenient for its intended application. Thus, scientists have developed different selection methods in accordance with all these reasons. This article aims to choose an optimal alloy alternative of the ferritic type of stainless steel, while using the Fuzzy logic-based method on the material properties of FY, FT, young’s modulus, density, CTE, and ThrmCond. For this purpose, Fuzzy logic is an effective tool and is well-established and applied in the scientific literature for the representation of reliable information. To describe a basic characteristic of ferritic stainless steel, fuzzy logic is useful because of inaccurate information. In this paper, material selection based on the criteria is used and a fuzzy-based approach is applied, which is proposed by Babanli. The essence of this particular technique is Zadeh’s fuzzy set concept for aggregation of features. Keywords: Fuzzy number · Fuzzy logic · Aggregation · Zadeh’s concept · Material selection · Stainless steel
1 Introduction In order to make a decision when selecting a material, engineers have to take into consideration the balance between cost, quality, resistance, performance and other related indicators. The essential object of material selection in the matter of product design is to reduce cost while reaching outcome performance objectives [1]. To attain such goals, engineers have to apply qualitative and quantitative methods [2]. The necessity of material selection in manufacturing has dramatically increased in latest years. In this article, the primary object is to choose an optimal alloy option of the ferritic type of stainless steel that will be used in production. The particular type of stainless steels called ferritic are cost-effective, price-stable, and resist against corrosion. By contrast with austenitic steel, ferritic steel has weak thermal enlargement, strong thermal conductivity. The ferritic steels are broadly employed
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 101–112, 2023. https://doi.org/10.1007/978-3-031-25252-5_18
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in producing automotive parts, industrial machinery and household device sectors. Constructive implementations of these materials in the construction sector are, however, limited, due to some barriers [3]. Li Y. et al. [4] discussed the modelling of the corrosion characteristics of FerriticMartensitic steels in water above a critical threshold. They forecasted 7 essential independent variables, including, oxygen concentration, flow-rate, heat, exposure duration, key chemical compound and outside state of steels by implementing a controlled artificial neural network (ANN). K.A. Cashell et al. [5] studied ferritic stainless steels in structural implementations. The empirical data was added by numerical analysis for the purpose of study a broad range of parameters. This study experimentally investigated the effect of heating temperature and holding duration on heating on the stress-strain behavior after a fire of three grades of ferritic stainless steel.. Honysz R. et al. [6] made an attempt to apply fuzzy logic to the study of artificial neural networks with radial basis functions (RBF), multilayer perceptron with 1 and 2 hidden layers (MLP) and universalized regression neural networks (GRNN) those were applied for modeling. Li-An Xie et al. [7] experimentally investigated the effect of heating temperature and holding duration on heating on the stress-strain behavior after a fire of three grades of ferritic stainless steel (e.g., EN 1.4003, 1.4016, 1.4509). The test outcomes demonstrated that the 3 grades treated very distinctly after exposure to upraised temperatures due to microstructure changes throughout heating and chilling down to room temperature. Zhige Wang et al. [8] investigated laser treatment of 430 ferritic stainless steel for enhanced mechanical specifications. These outcomes could be useful with the purpose of locally alter the behavior of moderate chrome ferritic stainless steel to reach industrial demands. But the selection problem of the ferritic steel depending on the characteristics should be solved. For solving this problem, we need a new approach. In this paper, we will discuss implementation of a new technique for selection of ferritic stainless steel. Ferrites have better durability, ductility and strength, and also an appealing appearance. They can be quite economical and effective. Although, it has lots of appealing specifications, ferritic stainless steels are underused at present in structural implementation because of the lack of credible information. Today, Fuzzy logic is an effective tool that has proved itself in scientific literature in representation of reliable information [9]. To describe basic characteristic of ferritic stainless steel, fuzzy logic is useful, because inaccurate information exists there [10]. The application of fuzzy based approach to the materials selection problem is a new addition to the broad range of methods convenient for the engineers. Throughout the publications on fuzzy based materials selections, there are a broad variety of techniques used to achieve the material selections. This is because of an innate quality achievable within the structure of fuzzy approach. The “fuzziness” of fuzzy logic enables human explication. Fuzzy logic based decision making has an important role if the information is under state of ambiguity [11, 12]. The aim of the paper is to present a neuro-fuzzy approach to select candidate Ferritic stainless steel based on the material specifications of FY (yield strength), FT (tensile strength), young’s modulus (a measure of elasticity), density, CTE (the coefficient of linear thermal expansion) and ThrmCond (thermal conductivity).
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The comparative analysis shows that the neuro-fuzzy approach is better than the other implemented methods, but there are also shortcomings here. These include the choice of membership function, inference algorithm, and training algorithm, which directly affect the results [10]. In this article, we discuss the decision-making problem on material selection. The paper consists of 5 sections. Basic formulas used in the research are described in Sect. 2. Section 3 ensures the problem statement. When it comes to Sect. 4, which is connected to the offered way of fuzzy based decision-making and the implementation of the procedure to the material selection problem. Section 5 provides the results and concludes the paper.
2 Preliminaries The considered problem is addressed by implementing the “Group Decision Making” Method. This particular method, introduced by J.Babanli [10, 13]. The steps of algorithm are as follow: 2.1. Identification of an expert team for criterion assessment. 2.2. Determination of criterions by the experts. 2.3. The result of the evaluation is summarized based on the following formula: K
fi =
k=1
fi k (1)
K
Here f i - ai is established on the basis of total review of the group of experts. Every element of f i = (fi1 , ..., fij , ..., fin )T . fij is defined as: K
f ij =
k=1
fijk
K
(2)
2.4. Calculation of the arithmetic mean [10]. 2.5. Determination of weighted mean of values ϕl (ai ) based on alternatives: Agg(ai ) = IG1 ϕ1 (ai ) + . . . . + IGl ϕl (ai ) + . . . + IGL ϕL (ai ).
(3)
Here, IGl , i = 1, . . . L is the coefficient representing the necessity of groups. 2.6. Alternatives ai are ranked based on their indexes, i = 1, ..., n. For that purpose Agg(ai ) is compared based on the distance distance to the fuzzy number Q, that denotes the utmost linguistic term of the scale of prediction. a1 a2 if d(Agg(a1 ), Q) < d(Agg(a2 ), Q). Here d - is the distance between fuzzy numbers. Therefore, an alternative that has a near distance to the fuzzy number Q is considered as higher-up. The distance d is determined by using the following formula: agg1 + 4 ∗ agg2 + agg3 q1 + 4 ∗ q2 + q3 (4) − d (Agg, Q) = 6 6
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3 Statement of the Problem Solution of material selection problem by applying fuzzy logic based approach is the primary object of the article. In this paper, A = {a1 , . . . , am }, are alternatives and F = (f1 , . . . , fn ) is a criterion vector. Value of alternatives are calculated by a single expert. It illustrates that expert assesses every alternative concerning the criterion given (Table 1). Table 1. Priority values of alternatives f1
…
fj
…
fn
…
k f1n
…
f1jk fijk
…
ai
k f11 f1ik
…
fink
…
…
…
…
…
…
am
k fm1
…
k fmj
…
k fmn
a1
Here, fijk - is the assessment of k-th expert for i-th alternative and j-th criterion. Criterions are grouped by significance degree. The considering problem of ranking leads to the search for an best alternative. So, a* is the best or optimal alternative is obtained as follow: Agg a* = max Agg(a), where Agg a* is an aggregated index of the alternatives. a∈A
(5)
Table 2. Material specifications of candidate Ferritic stainless steel UNS
Industry
FY (MPa)
FT (MPa)
Young’s modulus
Density (g/cm3 )
CTE (μm/m*°C)
ThrmCond. (W/m*k)
S43000
430
205
415
200
7.80
10.4
26.1
S44627
E-Brite
275
450
200
7.66
9.9
16.7
S44635
Monit
515
620
200
7.80
10
16
S44660
Sea-Cure
450
585
214
7.70
9.5
16.4
S44735
29–4C
415
550
200
7.67
9.2
15.2
S44800
29–4–2
415
550
200
7.70
9.2
15.1
4 Application In this section of the paper, selection of the ferritic stainless-steel problem is discussed. Assume that we have a MCDM problem, in which there are 6 alternatives (A1,…,6) and 6 criteria (f1 , …, f6 ). Alternatives are given below:
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A1-AS43000-430; A2-S44627-E-Brite; A3-S44635-Monit; A4-S44660-Sea-cure; A5-S44735-29-4C; A6-S44800-29-4-2. Criterions are shown below (properties): f1 -Fy(MPa); f2 - Ft(MPa); f3 -Young’s Modulus; f4 -Density(g/cm3); f5 - (CTE(μm/m•°C); f6 - Thrmcond (W/m•K)). Each option is evaluated in proportion to criteria (Table 2). Discussed problem was solved based on the methodology produced by J.Babanli [10]. A team consists of 1 expert. Each alternative is evaluated by one expert-specialist in materials. Initial evaluation by specialist in materials is illustrated in Table 3 and 4 below (Tables 5 and 6): Table 3. Initial data Fy
Ft
Ym
a
b
c
a
b
c
a
B
c
196.8
205
211.15
406.7
415
427.45
196
200
204
264
275
283.25
441
450
463.5
196
200
204
494.4
515
530.45
607.6
620
638.6
196
200
204
432
450
463.5
573.3
585
602.55
209.72
214
218.28
398.4
415
427.45
539
550
566.5
196
200
204
398.4
415
427.45
539
550
566.5
196
200
204
Table 4. Initial data (continue) D
CTE
ThrmCond
a
b
c
a
b
c
a
b
c
7.566
7.8
7.956
10.192
10.4
10.712
25.578
26.1
26.622
7.4302
7.66
7.8132
9.702
9.9
10.197
16.366
16.7
17.034
7.566
7.8
7.956
−9.8
−10
−10.3
−15.68
−16
−16.32
7.469
7.7
7.854
9.31
9.5
9.785
16.072
16.4
16.728
7.4399
7.67
7.8234
9.016
9.2
9.476
14.896
15.2
15.504
7.469
7.7
7.854
9.016
9.2
9.476
14.798
15.1
15.402
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Fy
Ft
YM
a
b
c
a
b
c
a
0.32541
0.3379 34404
0.3473 0.645 91 0.658 58 0.677 59 0.324 19 0.3303 24864
0.33641
0.428 02 0.44481 0.4574 0.698 28 0.712 03 0.732 64 0.324 19 0.3303 7688 14646
0.33641
0.779 82 0.8112 7466
0.8348 0.952 67 0.971 6 65327
0.33641
0.684 54 0.7120 25896
0.7326 0.900 29 0.918 16 0.944 96 0.345 14 0.35168 0.35821 39101
0.633 24 0.6585 84255
0.6775 0.847 92 0.864 72 0.889 91 0.324 19 0.3303 9421
0.33641
0.633 24 0.6585 84255
0.6775 0.847 92 0.864 72 0.889 91 0.324 19 0.3303 9421
0.33641
1
b
0.324 19 0.3303
c
Table 6. Normalized decision matrix (continue) D a
CTE b
c
a
ThrmCond b
0.03647 0.03683 0.03707 0.04048 0.040798876
c
a
b
c
0.04128 0.06397 0.06477 0.06557
0.03626 0.03662 0.03685 0.03973 0.0400354424 0.04049 0.04991 0.05042 0.05093 0.03647 0.03683 0.03707 0.00996 0.009650034
0.00919 0.00098 0.00049 0
0.03632 0.03668 0.03691 0.03913 0.039424663
0.03986 0.04946 004996
0.03628 0.03663 0.03686 0.03869 0.038966591
0.03939 0.04766 0.04813 0.04859
0.03632 0.03668 0.03691 0.03869 0.038966591
0.03939 0.04751 0.0479
0.05046 0.04844
Criteria vector f i of expert for each ai alternative are determined by using (2). The estimations of the criteria are denoted by fuzzy numbers according to the codebook illustrated in Fig. 1.
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μf
i
Very low (VL)
1
0
Low (L)
0.25
Medium (M)
0.5
107
Good (G)
Very Good (VG)
0.65
1
fi
Fig. 1. Codebook of the linguistic terms
By using math expression (2), the vector f i is identified. For example, the calculated values for A1,…,A6 are in accordance with the Table 2 rows. Each row describes one alternative, and values of criteria on the first alternative are: f1 = (0.32541; 0.337934404; 0.3437254864) ..... f6 = (0.06397; 0.06477; 0.06557) Results of the a2 are as follows: f1 = (0.42802; 0.4444817688 ; 0.457414646) ..... f6 = (0.04991; 0.05042; 0.05093) Results of the a3 are as follows: f1 = (0.77982; 0.81127466; 0.834865327) ..... f6 = (0; 0.000489; 0.000977) Results of the a4 are as follows: f1 = (0.68454; 0.712025896; 0.732639101) ..... f6 = (0.049459; 0.04996; 0.050461)
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Results of the a5 are as follows: f1 = (0.63324;0.658584255;0.67759421) ..... f6 = (0.047664; 0.048128; 0.048592) Results of the a6 are as follows: f1 = (0.63324;0.658584255; 0.67759421) ..... f6 = (0.047514; 0.047975; 0.048436). For each alternative ϕ1 (ai ), ϕ2 (ai ), ϕ3 (ai ) values are calculated. The subgroups of the importance criteria are described in Table 7. Table 7. Importance rate of criteria Importance rates
Criteria
IR 1 (High) (0.5 0.65 0.7)
f1 f2
IR 2 (Medium) (0.2 0.25 0.3)
f4
IR 3 (Low) (0 0.1 0 .3)
f5 f6
So, φ1 (ai ) =
f 1 + f2 + f3 f 5 + f6 , φ2 (ai ) = f4 , φ3 (ai ) = 3 2
Values for a1 are as follows: φ1 (a1 ) = (0.431839003; 0.442272848; 0.453780.6; 0.8; 0.975); φ2 (a1 ) = (0.03647; 0.03683; 0.03707); φ3 (a1 ) = (0.05223; 0.05279; 0.05342) .
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Obtained values for a2 are as follows: φ1 (a2 ) = (0.483499257;0.495714489; 0.50882); φ2 (a2 ) = (0.03626;0.03662; 0.03685); φ3 (a2 ) = (0.04482;0.04523; 0.04571). Obtained values for a3 are as follows: φ1 (a3 ) = (0.685559559;0.704391376; 0.72376); φ2 (a3 ) = (0.03647;0.03683; 0.03707); φ3 (a3 ) = (0.00547; 0.00507; 0.0046) . Obtained values for a4 are as follows: φ1 (a4 ) = (0.643325393; 0.660620127; 0.6786) ; φ2 (a4 ) = (0.03632; 0.03668; 0.03691) ; φ3 (a4 ) = (0.0443; 0.04469; 0.04516) . Obtained values for a5 are as follows: φ1 (a5 ) = (0.601783424; 0.617866813; 0.63464); φ2 (a5 ) = (0.03628; 0.03663; 0.03686); φ3 (a5 ) = (0.04317;0.04355; 0.04399). Obtained values for a6 are as follows: φ1 (a6 ) = (0.601783424; 0.617866813; 0.63464); φ2 (a6 ) = (0.03632; 0.03668; 0.03691); φ3 (a6 ) = (0.0431; 0.04347; 0.04391). The final aggregate grades for first alternative is calculated using (4): For a1: Agg(a1 ) = (0.431839003;0.442272848; 0.45378)(0.5; 0.65; 0.7)+ (0.03647163;0.036828926; 0.03707)(0.2; 0.25; 0.3) + (0.052227753; 0.052785073;0.05342)(0; 0.1; 0.3) = (0.223213828; 0.30196309; 0.34479 ).
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For the second alternative by applying the same procedure, the final aggregated values were calculated. The value for a2 is shown below: Agg(a2 ) = (0.4835; 0.49571; 0.50882)(0.5; 0.65; 0.7) + (0.03626; 0.03662; 0.03685)(0.2; 0.25; 0.3) + (0.04482; 0.04523; 0.04571)(0; 0.1; 0.3) = (0.249; 0.33589; 0.38094). The value for a3 is shown below: Agg(a3 ) = (0.685559559;0.704391376; 0.72376)(0.5; 0.65; 0.7) + (0.03647; 0.03683; 0.03707)(0.2; 0.0.25; 0.3) + (0.00547; 0.00507; 0.0046)(0; 0.1; 0.3) = (0.32896; 0.43912; 0.48752). The value for a4 is shown below: Agg(a4 ) = (0.643325393; 0.660620127; 0.6786)(0.5; 0.65;0.7) +(0.03632; 0.03668; 0.03691)(0.2; 0.25; 0.3) + (0.0443;0.04469; 0.04516)(0; 0.1; 0.3) = (0.30816; 0.41525; 0.46887). The value for a5 is shown below: Agg(a5 ) = (0.601783424; 0.617866813; 0.63464)(0.5; 0.65; 0.7)+ (0.03628; 0.03663; 0.03686)(0.2; 0.25; 0.3) + (0.04317; 0.04355; 0.04399)(0; 0.1; 0.3) = (0.308147529; 0.41513; 0.4685). The value for a6 is shown below: Agg(a6 ) = (0.601783424;0.617866813; 0.63464)(0.5; 0.65; 0.7)+ (0.03632;0.03668; 0.03691)(0.2; 0.25; 0.3)+ (0.0431;0.04347; 0.04391)(0; 0.1; 0.3) = (0.30816; 0.41513; 0.46849) The distance between the aggregation value of an alternative and very good is determined in accordance with (5) as follows: d (Agg(a1 ), very good ) = |0.295975955 − 0.95833| = 0.662354045 d (Agg(a2 ), very good ) = |0.32892 − 0.95833| = 0.62941 d (Agg(a3 ), very good ) = |0.42882 − 0.95833| = 0.52951 d (Agg(a4 ), very good ) = |0.40634 − 0.95833| = 0.55199 d (Agg(a5 ), very good ) = |0.40619219 − 0.95833| = 0.55213781 d (Agg(a6 ), very good ) = |0.40619 − 0.95833| = 0.55214
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The results obtained are given in Table 8: Table 8. The rank of alternatives Alternative
Distance
(a1 )
0.662354045
(a2 )
0.62941
(a3 )
0.52951
(a4 )
0.55199
(a5 )
0.55213781
(a6 )
0.5521
The smallest distance has a higher rank. So, a3 a4 a6 a5 a2 a1 .
5 Discussion and Conclusion The particular method applied in this article for solving material selection problem is a fuzzy information-based method, which development is based on Zadeh’s ideas and concepts. Determining the best alternative of ferritic stainless steel involves 6 criteria, which helps us to express the relevance of the method. Fuzziness is used for assessment of criteria and criteria importance. The obtained results represents effectiveness of the proposed method.
References 1. Babanli, M.B., Qardashova, L.A., Gojayev, T.L.: Selection of gear material by using fuzzy AHP method. Sci. J. Proc. Azerbaijan High Tech. Educ. Inst. 24(1), 52–59 (2022) 2. Neufill, R.: Materials selection maximizing overall utility. Met. Mater. 4(6), 378–382 (1988) 3. Manninen, T., Säynäjäkangas, J.: Mechanical properties of ferritic stainless steels at elevated temperature. In: Conference: Stainless Steel in Structures - Fourth International Experts Seminar (2012). https://www.academia.edu/9039435 4. Li, Y., et al.: Modelling and analysis of the corrosion characteristics of ferritic-martensitic steels in supercritical water. Materials. 12(3), 409 (2019). https://doi.org/10.3390/ma1203 0409 5. Cashell, K.A., Baddoo, N.R.: Ferritic stainless steels in structural applications. Thin-Walled Struct. 83, 169–181 (2014). https://doi.org/10.1016/j.tws.2014.03.014 6. Honysz, R.: Modeling the chemical composition of ferritic stainless steels with the use of artificial neural networks. Metals 11(5), 724 (2021). https://doi.org/10.3390/met11050724 7. Li-An, X., et al.: Post-fire stress-strain response of structural ferritic stainless steels. J. Constr. Steel Res. 196 (2022). https://doi.org/10.1016/j.jcsr.2022.107389 8. Zhige, W., Justin D.„ Pierre, L., Sébastien, D.: Laser treatment of 430 ferritic stainless steel for enhanced mechanical properties. Mater. Sci. Eng. 831 (2022). doi.org/https://doi.org/10. 1016/j.msea.2021.142205
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9. Aliev, R.A.: Uncertain Computation-Based Decision Theory. World Scientific Publishing, Singapore (2017) 10. Babanli, M.B.: Fuzzy Logic-based Material Selection And Synthesis. World Scientific Publishing Company, Singapore (2019) 11. Zadeh, L.A.: A very simple formula for aggregation and multicriteria optimization. Int. J. Uncertainty Fuzz. Knowl.-Based Syst. 24(6), 961–962 (2016). https://doi.org/10.1142/S02 18488516500446 12. Gardashova, L.A.: Z-number based TOPSIS method in multi-criteria decision making. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Sadikoglu, F.M. (eds.) ICAFS 2018. AISC, vol. 896, pp. 42–50. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-041649_10 13. Babanli, J.M.: Fuzzy approach for evaluation of student’s performance. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 140–147. Springer, Cham (2021). https://doi.org/10.1007/978-3-03064058-3_18
Multicriteria Group Decision Making on Information System Project Selection Using Type-2 Fuzzy Set Aygul Dadasheva(B) Azerbaijan State Oil and Industry University, 34 Azadlig Avenue, AZ1010 Baku, Azerbaijan [email protected]
Abstract. Multicriteria group decision making (MCDM) approach using fuzzy set for Information System (IS) Project Selection evaluation and selection is represented in this paper. The selection of the projects is also considered as the evaluating process for each project’s idea and the idea which has the highest priority has been chosen. In the competitive environment evaluating and selecting the right and reliable IS Projects can be considered as the main factor for the corporate competition ability. Evaluation imprecision which is modeled by trapezoidal fuzzy type 2 set characterizes linguistic term. Information technologies project selection problem is represented to indicate the approach sensitivity with information processing efficiency, system reliability, cost of implementation and three alternatives. Keywords: IT project selection · Multicriteria group decision making · Type- 2 fuzzy set · TOPSIS
1 Introduction Today, in organizations information system (IS) which are related to information technologies, business processes have been rapidly developed [1]. Evaluation and selection of IS projects is a complex and challenging process but effective IS Project could help organizations in understanding the strategy and the using of them for firstly reaching business goals instead of to decide developing the new one. Often this process is based on multiple decision makers, multiple criterial selection [2]. ˙In this paper, as the selection method we used TOPSIS method which presented by type 2 trapezoidal fuzzy sets. For the best possible option selection, we need appropriate justification in which using the structured approach of analysis of the universal performance of options which are available. Multicriteria decision making (MCDM) methods are used in the real-world alternatives ranking. Aim of the MCDM is involved with ranking process of different alternatives. As human preferences have the inherent uncertainty, estimating the alternative with the exact numbers is hard. Developing the system to help decision makers in the IS projects selection, in this article we present an effective multicriteria approach with type- 2 fuzzy set. Modelling of © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 113–121, 2023. https://doi.org/10.1007/978-3-031-25252-5_19
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the human subjectiveness and uncertainty of decision making process, linguistic term are characterized by the trapezoidal type 2 fuzzy numbers [3, 4]. Avoiding the unreliable and complicated comparing process of type-2 fuzzy numbers which is necessary in MCDM, applying the dominance degree concept applied new algorithm is developed. In the following sections, firstly IS project selection type- 2 fuzzy multicriteria group decision making (MCDM) problem is formulated. It is possible to use MCDM also as decision support too; while making the decisions which include multi criterions to evaluate and to select simultaneously. Sequentially, the new created algorithm model has been shown for the type -2 fuzzy MCDM problem solving. The second part represents given preliminaries. Information system project selection problem has been shown in Sect. 3. At the Sect. 4 problem solution which included the numerical example which illustrates applying the new proposed TOPSIS method with trapezoidal fuzzy type 2 sets in IS Project Selection and the main outcomes have been represented. At the result, the ranking of fuzzy numbers is based on the fuzzy sets’ right and left sides areas.
2 Preliminaries Definition 1. A- type-2 fuzzy set in X discourse universe which represented by type-2 membership function. α = {((x, u), μ(x, u) )|∀x ∈ X , ∀u ∈ Jx ⊆ [0, 1], 0 ≤ μ(x, u) ≤ 1} A A A
(1)
In the below mentioned Fig. 1 trapezoidal interval type 2 fuzzy set example has been shown.
H1 ( A1U ) H 2 ( A1U ) H1 ( A1L ) H 2 ( A1L )
0
aiU1
aiL1 aiU1 aiL2
aiL3 aiU3 aiL4 aiU4
Fig. 1. Interval type-2 fuzzy sets
Definition 2. Multicriteria group decision matrix which created by the different decision makers (DM) is determined by Wang method for ranking and comparing of each criterion for every DM and preferring alternative with the maximum value to other options. U˜ = (u1 , u2 , u3 , u4 ; wu ) and V˜ = (v1 , v2 , v3 , v4 ; wv ) are type 2 fuzzy numbers and (m0u , n0u ) and (m0v , n0v ) are these numbers centroid points, then: 1. If m0u m0v (m0u ≺ m0v ) then U˜ V˜ (U˜ ≺ V˜ ),
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2. If m0u = m0v and n0u = n0v , then U˜ ≈ V˜ . 3. If m0u = m0v then, U˜ V˜ (U˜ ≺ V˜ ) is resulted from n0u n0v (n0u ≺ n0v ). Definition 3. If to consider that the A˜ is the given pairwise comparison matrix, it confirms suitable properties (reciprocity and consistency) [5]. In pairwise matrix constraints are described in the following: ˜ A˜ ij A˜ ji = A(1)
(2)
A˜ ij A˜ jk = A˜ ik
(3)
3 Statement of the Problem If to consider that the MC group decision making problem includes 3 criterion – C1 , C2 , C3 and 3 alternatives – A1 , A2 , A3 . C1 - Information processing efficiency; C2 - System Reliability; C3 - Cost of Implementation: In evaluating and the selection of Information System (IS) Project by fuzzy MCDM approach has been used which has been below mentioned [6, 7]. Evaluation imprecision [8] is represented and modelled by fuzzy trapezoidal type-2 numbers which is characterized by linguistic term. In the following problem (A˜ ij ) is represented consistent comparison pairwise matrix and in this matrix all consistency conditions are verified [9]. Using the TOPSIS method we will choose the best alternative. The matrix shown below is pairwise comparative matrix (A˜ ij ): ⎡
1 A˜ 12 ⎢˜ ⎢ A21 1 ˜Aij = ⎢ ⎢. .. ⎢. . ⎣. ˜An1 A˜ n2
⎤ ... A˜ 1n ⎥ ... A˜ 2n ⎥ ⎥ .. ⎥ .. . . ⎥ ⎦ ...
(4)
1
Consistent matrix components met all consistency conditions which are formulated in (1–3). The fuzzy weight for each criterion is calculated with minimizing objective function and the TOPSIS method is applied.
4 Solution of the Problem Step-1: Criteria identification and from the top to the lower levels building the hierarchy by the determination of criterion. Step-2: Pairwise comparison matrices construction which includes all criterions in hierarchy system dimensions. Linguistic variables which used in the pairwise matrices of comparisons and scales in interval fuzzy type-2 are represented in Table 1.
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A. Dadasheva Table 1. Trapezoidal Interval type 2 fuzzy scales of linguistic variables
Linguistic variables
Trapezoidal 2-type Interval fuzzy numbers
Extremely High (EH)
(7,8,9,9;1) (7.2,8.2,8.8,9;0.8)
Very High (VH)
(5,6,8,8;1) (5.2,6.7,8,8;0.8)
Intermediate (I)
(3,4,6,7;1) (3.4,4.2,6,6.8;0.8)
Good (G)
(1,2,4,5;1) (1.4,2.2,3.8,4.8,0.8)
Equal (E)
(1,1,1,1;1) (1,1,1,1;1)
Table 2. The comparison pairwise matrix for the 1st decision maker for the criteria. C1
C2
C3
C1
E
1/G
1/G
C2
G
E
1/G
C3
G
G
E
Table 3. The pairwise comparison matrix for the second decision maker for the criteria. C1
C2
C3
C1
E
E
1/I
C2
E
E
1/I
C3
I
I
E
Table 4. The pairwise comparison matrix for the third decision maker for the criteria. C1
C2
C3
C1
E
1/G
1/G
C2
G
E
1/G
C3
G
G
E
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The pairwise comparison matrices in 2-type interval fuzzy sets are represented in the following (Tables 2, 3 and 4): ⎤ ⎤ ⎡ ⎡ 1 a˜ 12 ... a˜ 1n 1 a˜ 12 ... a˜ 1n ⎢ a˜ 2n 1 ... a˜ 2n ⎥ ⎢ 1/˜a21 ... a˜ 2n ⎥ ⎥ ⎥ ⎢ ⎢ ⎢ ⎥ (5) = A=⎢ . . . ⎥ ⎢ .. . . . .. .. ⎥ ⎣ .. .. . . .. ⎦ ⎣ . ⎦
1/˜an1 1 a˜ n2 ... 1 a˜ n1 a˜ n2 . . . 1 Step-3: Determination of group decision making pairwise matrix. This matrix has been presented in Table 5. Table 5. The pairwise comparison matrix for the group decision making for the criteria. C1
C2
C3
C1
(1,1,1,1:1) (1,1,1,1:1)
(1,0.5,0.25, 0.2;1) (1,0.7,0.45,0.26, 0.2,0.8;0.8)
(1,0.5,0.25,0.2;1) (0.7,0.45,0.26, 0.2;0.8)
C2
(1,2,4,5;1) (1.4.2.2.3.8,4.8;0.8)
(1,1,1,1;1) (1,1,1,1;1)
(1,0.5,0.25,0.2;1) (0.7,0.45,0.26, 0.2;0.8)
C3
(3,4,6,7;1) (3.4,4.2,3, 3.8,0.8)
(3,4,6,7;1) (3.4,4.2,3, 3.8,0.8)
(1,1,1,1;1) (1,1,1,1;1)
Step-4: Construction of consistent pairwise matrix. Table 6. Consistent pairwise matrix C1
C2
C3
C1
(1,1,1,1:1) (1,1,1,1;1)
(1,1,1,1:1) (1,1,1,1;1)
(1,0.5,0.25,0.2;1) (0.7,0.45,0.26, 0.2;0.8)
C2
(1,1,1,1;1) (1,1,1,1;1)
(1,1,1,1;1) (1,1,1,1;1)
(1,0.5,0.25,0.2;1) (0.7,0.45,0.26, 0.2;0.8)
C3
(1,2,4,5;1) (1.4.2.2.3.8,4.8;0.8)
(1,2,4,5;1) (1.4.2.2.3.8,4.8;0.8)
(1,1,1,1;1) (1,1,1,1;1)
Step-5: Calculation the fuzzy weights for each criterion. Fuzzy type 2 matrix expressed in Table 6 by four crisp matrices are defined as below indicated in Table 7, 8, 9 and 10:
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A. Dadasheva Table 7. Crisp matrix 1 C1
C2
C3
C1
1.0
1.0
1.0
C2
1.0
1.0
1.0
C3
1.0
1.0
1.0
Table 8. Crisp matrix 2 C1
C2
C3
C1
1.0
1.0
0.5
C2
1.0
1.0
0.5
C3
2.0
2.0
1.0
Table 9. Crisp matrix 3 C1
C2
C3
C1
1.0
1.0
0.25
C2
1.0
1.0
0.25
C3
4.0
4.0
1
Table 10. Crisp matrix 4 C1
C2
C3
C1
1.0
1.0
0.2
C2
1.0
1.0
0.2
C3
5.0
5.0
1.0
Achievement function is to minimize objective function [10]: ⎤ ⎡ 4 4 (nij + pij )⎦ min ⎣ i=1 j=1
1
wi − wi mij + + (wi − wi mij ) 2 where
1
wi − wi mij + + (wi − wi mij ) pij = 2 nij =
(6)
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Goals and constraints: 1w1 − w1 + n11 − p11 = 0, 1w2 − w1 + n12 − p12 = 0, 0.5w3 − w1 + n13-p13 = 0. 1w1 − w2 + n21 − p21, 1w2-w2 + n22 − p22, 0.5w3 − w2 + n23 − p23. 2w1 − w3 + n31 − p31, 2w2-w3 + − -n32 − p32, 1w3 − w3 + n33 − p33. W1 + W2 + W3 = 1, W1 > 0, W2 > 0, W3 > 0. Bellowed results are obtained by using Linear programming and weights are obtained as: Objective function: Z = min(n11 + p11 ) + (n12 − p12 ) + nij + pij ) = 0. w1 (0.33; 0.25; 0.16; 0.143; 1, 1) (0.29; 0.24; 0.17; 0.15 : 0.8, 0.8) w2 (0.33; 0.25; 0.16; 0.143; 1, 1) (0.29; 0.24; 0.17; 0.15 : 0.8, 0.8) w3 (0.33; 0.5; 0.66; 0.71; 1, 1) (0.41; 0.52; 0.66; 0.71 : 0.8, 0.8) Step-6: Determination of the best alternative using TOPSIS method. The alternative with the best utility is selected [11, 13]. After the construction of normalized matrix, the weighted normalized matrix has been created and the ideal and the negative ideal solutions has been determined. At the next step, the closeness to the ideal solution has been calculated and then the alternatives have been ranked. Table 11 shows the alternatives’ interval type- 2 fuzzy scores of with respect to criteria. Table 11. Alternatives’ interval type- 2 fuzzy scores of with respect to criteria A1
A2
C1
(0.009;0.001;0.007;0.025;1,1) (0.001;0.002;0.006;0.0018;0.8,0.8)
(0.001;0.002;0.011;0.03;1,1) (0.001;0.003;0.006;0.027;0.8,0.8)
C2
(0.011;0.021;0.074;0.17:1,1) (0.013;0.024;0.064;0.14:0.8,0.8)
(0.002;0.005;0.02;0.049:1;1) (0.003,0.006,0.017,0.040;0.8,0.8)
C3
(0.017,0.043,0.16,0.36;1,1) (0.022,0.050,0.14,0.30;0.8,0.8)
(0.012,0.030,0.12,0.29;1,1) (0.015,0.035,0.10,0.23;0.8,0.8)
C1
(0;0.008;0.035;0.01:1,1) (0.004;0.009;0.03;0.078:0.8,0.8)
C2
(0.002,0.004,0.015,0.037;1,1) (0.002,0.004,0.012,0.030;0.8,0.8
C3
(0.005,0.012,0.056,0.15;1,1) (0.006,0.014,0.048,0.12;0.8,0.8)
A3
After the ideal (Si * ) and negative ideal (Si ’ ) solutions’ determination, the separation measures for each alternative have been calculated. The separation of the ideal and negative ideal alternative is below mentioned:
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A. Dadasheva Si *
Si ’
A1
(0.320.340.290.17:1.1) (0.380.330.300.30: 0.8,0.8)
(0.310.130.210.65:1,1) (0.110.150.200.20:0.8,0.8)
A2
(0.310.240.160.18;1,1) (0.250.220.160.14:0.8,0.8)
(0.190.290.410.52:1,1) (0.260.320.410.44:0.8,0.8)
A3
(0.310.270.400.65:1,1) (0.220.310.410.43:0.8,0.8)
(0.320.320.210.17:1,1) (0.360.300.220.18:0.8,0.8)
The results after the relative closeness to the ideal solution (Ci * ) calculation have been shown: Ci * A1
(0.49 0.28 0.42 0.79:1.1)(0.23 0.31 0.41 0.41:0.8, 0.8)
A2
(0.38 0.55 0.72 0.74:1, 1)(0.51 0.59 0.72 0.76:0.8, 0.8)
A3
(0.51 0.54 0.34 0.21:1, 1) (0.62 0.49 0.35 0.30:0.8, 0.8)
The best alternative is second alternative. The ranking method is based on type 2 fuzzy set right and left sides areas.
5 Conclusion The right Information System project selection is the main component of effective management technology. The main purpose of this paper is finding the best alternative with TOPSIS method with fuzzy weights. The effectiveness of the represented TOPS˙IS method is illustrated by the numerical example. Reliable preferences over the choice criteria are shown by fuzzy type-2 set in the represented work. Using the suggested approach, the best alternative has the highest result, and the second alternative has been chosen.
References 1. Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965) 2. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning – I. Inform. Sci. 8(3), 199–249 (1975) 3. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning1. Inform. Sci. 8, 199–249 (1975) 4. Gardashova, L.A.: Application of operational approaches to solving decision making problem using Z-numbers. J. Appl. Math.. 5(9), 1323–1334 (2014). https://doi.org/10.4236/am.2014. 59125 5. Aliev, R.A., Guirimov, B.G., Huseynov, O.H., Aliyev, R.R.: A consistency-driven approach to construction of Z-number-valued pairwise comparison matrices. Iran J. Fuzzy Syst. 18(4), 37–49 (2021)
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6. Huseynov, O.H., Adilova, N.E.: Multi-criterial optimization problem for fuzzy if-then rules. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 80–88. Springer, Cham (2021). https://doi.org/10.1007/ 978-3-030-64058-3_10 7. Huseynova, N.F.: Decision making on tourism by using natural language processing. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 741–747. Springer, Cham (2022). https://doi.org/10.1007/978-3030-92127-9_98 8. Oztaysi, B.: A Group decision making approach using interval type-2 fuzzy AHP for enterprise information system project selection. J. Multiple-Val. Logic Soft Comput. 24(5–6), 475–500 (2015) 9. Dadasheva, A.N.: Analysis of consistency of pairwise comparison matrix with fuzzy type-2 elements. Lect. Notes Netw. Syst. 362, 324–330 (2022) 10. Sadikoglu, G., Dovlatova, Kh. J.: Investigation of preference knowledge of decision maker on consumer buying behaviour. In: Aliev, R., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F. (eds.) 10th International Conference on Theory and Application of Soft Computing, Computing with Words and Perceptions-ICSCCW-2019, AISC, vol. 1095, pp. 613–621. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-35249-3_78 11. Aliyeva, K.: Multifactor personnel selection by the fuzzy TOPSIS method. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Mo., Jamshidi, Sadikoglu, F.M. (eds.) ICAFS 2018. AISC, vol. 896, pp. 478–483. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-04164-9_64 12. Gardashova, L.A.: Z-number based TOPSIS method in multi-criteria decision making. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Mo., Jamshidi, Sadikoglu, F.M. (eds.) ICAFS 2018. AISC, vol. 896, pp. 42–50. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-041649_10 13. Aliyeva, K.R.: Facility location problem by using Fuzzy TOPSIS Method. B-quadrat verlags, pp. 55–59. Uzbekistan (2018). https://doi.org/10.34920/2018.4-5.55-59
Forecasting Demand in the Commodity Market of Food Products Using Neural Networks Mikayilova Rena Nuru1,2(B) 1 Digital Economy and ICT, Azerbaijan State Economic University, Baku 1147, Azerbaijan
[email protected] 2 Azerbaijan State Oil and Industry University, 34 Azadlyg Avenue, Baku 1010, Azerbaijan
Abstract. When opening a new commercial enterprise, a correct predictive estimate of the demand for the goods of this firm should be given. This work is devoted to the use of neural networks for demand forecasting, by determining the demand elasticity coefficient, which will allow commercial enterprises to give a correct predictive estimate of the demand for their goods in the commodity market. It is known that forecasting is a probabilistic scientifically substantiated judgment about the trends of the phenomenon under study in the future. On the other hand, it should be noted that: - demand is an important factor in the study of the commodity market; - when opening a new commercial enterprise, a correct predictive assessment of the demand for the goods of a given company in the commodity market should be given; - demand and supply appear on the commodity market not spontaneously, but are formed and act according to the relevant laws; relevant laws; - human experience and intuition are among the main sources of information for forecasting demand and future market characteristics; - it is impossible to obtain statistical data in advance for a certain period of time. The paper considers the features of forecasting demand in the commodity market and substantiates the relevance of using neural networks (which is more adequate to the market model in the presence of uncertainty factors) for their forecasting than the methods of extrapolation of trends that are actively used in solving economic problems. The issue of choosing the type of neural network for approximating and predicting the elasticity coefficient of demand for food and non-food products is considered. Keywords: Commodity market · Neural networks · Elasticity coefficient of demand · Radial basic neural network · Regression neural networks · Forecasting demand
1 Introduction A very difficult stage in the study and forecasting of the commodity market is the modeling process [1–4]. The main “participants” in the process of modeling the commodity market are supply and demand, and most importantly, the establishment of a balance system. However, the establishment of a balance system between supply and demand in the commodity market is not enough, it is necessary to identify contradictions © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 122–129, 2023. https://doi.org/10.1007/978-3-031-25252-5_20
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between producers and consumers, between sellers and buyers, and thus determine the purposefulness of each element operating in the market. In the economic literature, there are various approaches to the definition of the categories of supply and demand [4–8]. In this work, demand is understood as the quantity of a good or service that will be purchased at a certain price for a certain period. It is useless to try to determine demand without price, since it changes precisely depending on it. The law of demand operates other things being equal, the demand for goods in quantitative terms varies inversely with price. This happens for two reasons: first, when the price drops, the consumer wants to buy more of the good (the income effect); secondly, when the price of a product decreases, it becomes cheaper relative to other goods, and it becomes relatively more profitable to purchase it (substitution effect). Demand and supply appear on the commodity market not spontaneously but are formed and act according to the relevant laws, and thus, demand functions (the volume of goods that customers are able to buy) and supply functions (the volume of goods that are able to sell to customers) are born. The law of demand does not work in three cases: – in case of excessive demand caused by the expected increase in prices; – for some rare and expensive goods (gold, jewelry, antiques, etc.), which are a means of investing money; – when switching demand for better and more expensive goods. The basic point in the study of the process of supply and demand is to determine the point of market equilibrium. Market equilibrium is the balance between the opposite directions of producers and consumers in the system of commercial activity. A balanced price is an important commodity market indicator. Excess or shortage of goods in the commodity market is difficult to determine, and information about prices is available to both producers and consumers. It is important for enterprises to determine the quantitative impact on the magnitude of demand that a change in the price of products, consumer incomes or prices of substitute goods produced by competitors can have. When opening a new commercial enterprise, a correct predictive estimate of the demand for the goods of this firm should be given. It is known that forecasting is a probabilistic scientifically substantiated judgment about the trends of the phenomenon under study in the future. It should be noted that the main sources of information for forecasting demand and future market characteristics are: • extrapolation of tendencies, processes, patterns of development of which in the past and present are quite well known; • model of the process under study, reflecting the expected or desired trends in its development; • human experience and intuition; • The above confirms the fact that: • demand is an important factor in product market research;
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• when opening a new commercial enterprise, a correct predictive estimate of the demand for the goods of this company in the commodity market should be given; • supply and demand appear on the commodity market not spontaneously, but are formed and act according to the relevant laws; • Not in all cases the law of demand is formed and act according to the relevant laws; • Human experience and intuition are among the main sources of information for forecasting demand and future market performance; • It is not possible to obtain statistical data in advance for a certain period of time. Since demand is influenced by more uncertainty factors, we propose the following application of neural networks to predict the demand elasticity coefficient. Recently, neural networks [9] have been used to solve forecasting problems, the application of which is based on the well-known ability of a neural network to approximate arbitrary functions of many variables [10]. Neural networks, due to their approximation abilities, allow solving a wide range of forecasting problems, regardless of their specific content, while being based only on experimental data. When using neural networks, a lot of time and computational resources are spent only at the stage of its training, and the trained neural network finds a solution very quickly, and therefore the method seems to be very promising for practical applications. This work is devoted to the use of neural networks for demand forecasting, in order to determine the demand elasticity coefficient, which will allow commercial enterprises to give a correct predictive estimate of the demand for their goods in the commodity market. The work is structured as follows. The introduction discusses the features of demand forecasting in the commodity market and substantiates the relevance of using neural networks (which is more adequate to the market model in the presence of uncertainty factors) for their forecasting than the trend extrapolation methods that are actively used in solving economic problems. Section 2 describes basic concepts such as demand elasticity, radial basis neuron, and neural networks and regression neural networks. Section 3 discusses the issue of choosing a neural network for approximating and predicting the elasticity coefficient of demand for food and non-food products using data for 2009–2020 [11, 12]. The results obtained are described in the conclusion section.
2 Basic Definitions Let us present the following basic definitions for solving the stated problem. Definition 1. Coefficient of Price Elasticity of Demand. The measure of the response of one value to a change in another is called elasticity. Elasticity measures the percentage change in one economic variable when another changes by one percent. In this regard, it is easy to see that price elasticity of demand, shows how much the quantity demanded for a product will change in percentage terms when its price changes by one percent.
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If we denote the price P, and the quantity demanded Q, then the coefficient of price elasticity of demand Er is equal to: EP =
Q ; P
(1)
where is the change in demand, %; price change, %; The elasticity coefficient is defined as the ratio of the increase in demand to the increase in price: Ep =
P1 − P0 Q1 − Q0 P1 + P0 Q1 − Q0 .100 : .100 = . Q1 + Q0 P1 − P0 (Q1 − Q0 ) : 2 (P1 − P0 ) : 2
(2)
where Q0 , Q1 —the amount of demand before and after the price change, pcs, P0 , P1 — the initial and new price, rub. If the absolute value of the price elasticity of demand is greater than 1, then we are dealing with a relatively elastic demand. In other words, a change in price in this case will lead to a greater quantitative change in the quantity demanded. If the absolute value of the price elasticity of demand is less than 1, then demand is relatively inelastic. In this case, a change in price will entail a smaller change in the quantity demanded. With an elasticity coefficient equal to 1, one speaks of unit elasticity. In this case, a change in price leads to the same quantitative change in the quantity demanded. Definition 2. Radial Basic Neuron. The structure of a radial basic neuron is shown in Fig. 1. A radial basic neuron (RBN) calculates the distance between the input vectors X and the weight vector W, then multiplies it by a fixed threshold B.
Fig. 1. Radial basic neuron
Definition 3. Radial Basic Neural Network (RBNS). Consists of two layers: a hidden radial base layer of S 1 neurons and an output linear layer of S 2 neurons. The elements of the first layer of the RBNS calculate the distances between the input vector and the weight vectors of the first layer. The threshold vector B and the distances are multiplied element by element. The output of the first layer can be expressed by the formula. A1 = radbas(W − X · B),
(3)
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where A1 – is the output of the first layer; the radbas function is the radial basis function; W – is the weight matrix of the first layer of the network; X – is the input vector; B – is the threshold vector of the first layer. According to the formula, radial basic neurons with a weight vector close to X will generate values close to 1. If the neuron has an output of 1, then this value will be transferred to its linear neurons by the weights of the second layer. Radial basic neural networks are trained in three stages. Definition 4. Regression Neural Networks (NRS) have the same first layer as RBNS, but the second layer is constructed in a special way. To approximate functions, generalized regression neuron networks are often used. It has as many neurons as there are target < input vector/target vector > pairs. The weight matrix W is the set of target rows. The target value is the value of the function being approximated in the training set. The main task of developing a neural network solution is to choose the optimal architecture of the neural network. In this regard, for the task we will use the following types of neural networks [9]: radial basic (RBF), and generalized regression (GRNN), which are most often used to solve the problem of approximating experimental data. On the other hand, the choice of neural network architecture, which one will be better and more practical, depends in most cases on the conditions of the problem. According to the above, in the next section, we consider the issues of choosing a neural network solution model for predicting the demand elasticity coefficient.
3 Choosing a Neural Network Architecture for Predicting the Coefficient of Demand Elasticity To solve the forecasting problem, consider the statistical data, which are given in [11–15] and presented in Table 1. When calculating the demand elasticity coefficients, formula 2 of definition 1 was used. From the table and from Fig. 2 the elasticity coefficient of 2016 differs sharply from the rest, the reason is that it was in this year that the forced devaluation of the manat was carried out in the republic. Based on this, we will not consider the statistical data of this year due to its spontaneity. Approximation of the demand elasticity coefficient was carried out using the following methods: 1. Exponential smoothing method. As a result, the following approximation formula is obtained: y = 0.0005x6 − 0.0169x5 + 0.2378x4 − 1.6342x3 + 5.7216x2 − 9.6351x + 6.9855, with Correlation Coefficient (R): = 0.88295 Coefficient of Determination (R2 ) = 0.7796. To approximate the trend line, the Toolkit MS Excel was used. 2. A method using a generalized regression (GRNN) neural network with Correlation Coefficient (R): = 0. 98040 Coefficient of Determination (R2 ) = 0. 96119.
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3. A method using a radial basic neural network, in which Correlation Coefficient (R): = 1.0 Coefficient of Determination (R2 ) = 1.0. Based on the newrb function, a radial basis neural network (RBNN) was created to approximate the points, which are given in Table 1. A fragment of the source code of the constructed network is described below: e = 0.002; % target RMSE (Root mean squared error) Sp = 1; % scatter value of the radial basis neural network. % definition of the sequence of arguments of the approximated function P. P = [99.9000 106.1000 108.7000 100.9000 101.9000 101.8000 105.4000 114.5000 102.0000 102.9000 103.6000; 108.4906 115.6522 119.5489 110.6918 111.9318 111.6751 116.8182 116.8874 105.0992 106.1995 102.0305]; % determination of the values of the approximated function corresponding to P. T = [1.6368 0.9420 0.7306 0.9674 0.8853 0.4276 0.7719 1.8006 1.0872 0.8435 −0.1693]; [net tr] = newerb(P,T,e,sp); % creation of a radial base network. %Next, network operation is emulated. The obtained results show that the best model for approximating and predicting the demand elasticity coefficient is a model built based on a radial basic neural network. Table 1. Statistical data for determining the demand elasticity coefficient Years
In % to the previous year Consumer price index: food and non-food products (percentage)
Trade turnover
Coefficient of elasticity (absolute values)
2009
99.9000
108.4906
1.6368
2010
106.1000
115.6522
0.9420
2011
108.7000
119.5489
0.7306
2012
100.9000
110.6918
0.9674
2013
101.9000
111.9318
0.8853
2014
101.8000
111.6751
0.4276
2015
105.4000
116.8182
0.7719
2016
115.6000
117.5097
15.6391
2017
114.5000
116.8874
1.8006
2018
102.0000
105.0992
1.0872
2019
102.9000
106.1995
0.8435
2020
103.6000
102.0305
−0.1693
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M. R. Nuru
Exponential Smoothing 40
Value
20 0 -20
1
2
3
4
5
6
7
8
9
10
11
Data Point Actual
Forecast
Poly. (Forecast)
Fig. 2. Dynamics of changes in the coefficient of elasticity of demand
4 Conclusion According to the constructed models, a forecast was made for the demand elasticity coefficient for 2022, which once again confirms that the demand elasticity coefficient will be lower than 1. This forecast confirms that a price change will entail a smaller change in demand. This statement says that there is currently an unstable situation in the commodity market, which in turn relates to the economic situation in the world. Further research on this topic should be carried out in the field of diagnosing and forecasting commodity markets based on an integrated approach, where, along with economic indicators and extrapolation methods, it is necessary to consider methods using neural networks.
References 1. Gorbunov, V.K.: Mathematical Modeling Of Market Demand, 212 p. (2018). http://conf. svmo.ru/files/2020/ThesesSaransk2020.pdf. (in Russian) 2. Korolev, A.V.: Economic-Mathematical Methods and Modeling, 255 p. (2016). https://public ations.hse.ru/pubs/share/folder/inbly3btur/202051943.pdf. (in Russian) 3. Blagodatskikh, V.G., Yaroshevich, N.Yu.: Research of the sectoral structure of the industrial products market: a dynamic approach. (in Russian) Izvestia USUE, 6(74), p. 102–115 (2017) 4. Zemskova, A.V.: Modeling the behavior of consumers of services. (in Russian) NRU ITMO J. 3, 183–192 (2014) 5. Anurin, V.F.: Marketing research of the consumer market (in Russian) SPb.: Peter. 270 p. (2006) 6. Evstafieva, S.V.: Forecasting market conditions (in Russian) Saratov: FGBOU,70 p. (2013) 7. Zharikov, A.V., Goryachev, R.A.: Forecasting demand and sales volume (in Russian) N/Novgorod: NGU, 39 p. (2017) 8. Luginin, O.E.: Economic and mathematical methods and models: theory and practice with problem solving (in Russian) Rostov n/D: Phoenix (2009) 9. Beale, M.H., Hagan, M.T., Demuth, H.B.: Neural Network Toolbox. User’s Guide. – Natick: Math Works, Inc., 435 p. (2014)
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10. Hornik, K, Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Netw. 2, 359 (1989) 11. Consumer Price Index (pre-trade, percentage) (in Azerb.). https://www.azstat.org/portal/tbl Info/TblInfoList.do;JSESSIONID=1AD665579B19CAFCD98E7481AF1EB5DF 12. General indicators of trade (in Azerb.). https://www.azstat.org/portal/tblInfo/TblInfoList.do? vw_cd=MT_ATITLE 13. Gardashova, L.A.: Application of DEO method to solving fuzzy multiobjective optimal control problem. Appl. Comput. Intell. Soft Comput. 2014(268), 1–7(2014). https://doi.org/10. 1155/2014/971894 14. Iskandarov, E.K., Ismayilov, G.G., Ismayilova, F.B.: Diagnostic operation of gas pipelines based on artificial neuron technologies. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Mo., Jamshidi, Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 787– 791. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-35249-3_103 15. Aliev, R.A., Aliev, R.R.: Soft Computing and its Application. World Scientific, New Jersey (2001)
Introducing Uncertainty-Based Dynamics in MADM Environments Debora Di Caprio1(B)
and Francisco J. Santos Arteaga2
1 University of Trento, 38122 Trento, Italy
[email protected]
2 Universidad Complutense de Madrid, 28223 Madrid, Spain
[email protected]
Abstract. One of the main problems faced by the literature on Multi-Attribute Decision-Making (MADM) methods, which constitutes an inherent assumption that remains undiscussed through the different publications, is the fact that rankings are definitive. As a result, these models do not account for any of the consequences derived from the uncertainty inherent to the evaluations or the potentially strategic reports delivered by the experts. That is, once the ranking is computed, the decision makers (DMs) should select the first alternative, concluding the applicability and contribution of the corresponding model. There are no potential regret or uncertainty interactions triggered by the quality of the reports or their credibility. However, the results of the ranking are not always those preferred by the DMs, who may have to proceed through several alternatives, particularly if the evaluations provided by the experts fail to convey the actual value of the corresponding characteristics. This problem has not been considered in the MADM literature, which has incorporated fuzziness and imprecision to its models, but not accounted for the consequences of credibility in terms of regrettable choices and the combinatorial framework that arises as soon as this possibility is incorporated into the analysis. We define a MADM setting designed to demonstrate the ranking differences arising as DMs incorporate the potential realizations from an uncertain evaluation environment in their choices. We illustrate the substantial ranking modifications triggered by the subsequent dynamic and regret considerations while introducing important potential extensions within standard MADM techniques. Keywords: Uncertainty · MADM · Regret · Credibility · TOPSIS
1 Introduction We study a scenario where a decision maker (DM) receives a set of evaluations regarding the criteria defining different alternatives. However, as is generally the case, the evaluations received exhibit uncertainty regarding their actual realizations [2, 4]. Given the fact that the alternative selected may not perform according to expectations, the ranking obtained should help determining both the initial choice made by the DM as well as any further one in case of suboptimal performance by the initial alternative selected © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 130–138, 2023. https://doi.org/10.1007/978-3-031-25252-5_21
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[3, 5]. Accounting for the effects of uncertainty regarding the potential realizations of the different characteristics defining the alternatives implies formalizing the capacity of the DM to design an evaluation plan based on the current information available about each alternative, the type of uncertainty considered and the set of potential realizations. The DM must account for the different combinatorial possibilities determined by the number of alternatives that he is willing to evaluate whenever the ranking involves regrettable decisions [1]. These sequential considerations must be implemented when defining the decision process within the corresponding MADM technique. We define an ordering environment where the evaluations assigned to the alternatives acknowledge the uncertainty inherent to the reports of the expert(s). We illustrate the substantial ranking modifications triggered by the dynamic and regret considerations formalized while also introducing important potential extensions within the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) and, mainly, any similar MADM technique.
2 TOPSIS We start by describing the basics of TOPSIS before extending its main structure to incorporate credibility and regret. As a Multi-Attribute Decision-Making (MADM) technique, TOPSIS is generally applied to rank a series of alternatives based on criteria evaluations received from one or more experts. TOPSIS computes two ideal reference points per criterion, a positive and a negative one, and calculates the relative distance between the characteristics defining each alternative and both reference values. The main steps defining the implementation of TOPSIS are described below. The m alternatives evaluated are denoted by A1 , A2 , ..., Am , while the n criteria applied to perform the evaluations are given by C1 , C2 , ..., Cn . The performance evaluation of alternative Ai , i = 1, ..., m, with respect to criterion Cj , j = 1, ..., n, is denoted by xij and summarized through a decision matrix defined as follows: C1
C2
…
Cn
A1
x11
x12
x1n
A2
x21
x22
… …
x2n
Am
xm1
xm 2
…
xmn
W = [ w1 , w2 ,..., wn ]
The terms wj , j = 1, ..., n, represent the importance assigned by the expert(s) to each criterion j. Given the values composing the decision matrix and the fact that criteria can be either positive or negative, the set of alternatives is ranked through the following steps.
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Step 1. The decision matrix is normalized to allow for a direct comparison across criteria. The evaluations received from the expert(s) are normalized via xij rij = i
xij2
, i = 1, ..., m, j = 1, ..., n;
(1)
Step 2. Each column of the decision matrix is multiplied by the weight describing the relative importance of each criterion vij = wj rij , j = 1, ..., n;
(2)
giving place to the weighted normalized decision matrix. Step 3. The criteria used to evaluate the alternatives consist of either positive or negative qualities. Ideal positive, vi+ , and negative, vi− , values are computed for each criterion. The vectors summarizing the ideal criteria values are defined as follows A+ = ν1+ , ..., νn+ (3) with vi+ = maxj (vij )|j ∈ positive criterion
(4)
vi− = minj (vij )|j ∈ negative criterion
(5)
when considering the best positive values, and A− = ν1− , ..., νn−
(6)
where vi− = mini (vij )|j ∈ positive criterion
(7)
vi− = maxi (v ij )|j ∈ negative criterion
(8)
when dealing with the worst negative values. Step 4. The distances between the evaluations reported for each alternative and the ideal values, both positive and negative, are given by di+
⎡ ⎤1/2 n 2
νj+ − νij ⎦ , i = 1, ..., m =⎣
(9)
j=1
di−
⎡ ⎤1/2 n 2
νj− − νij ⎦ , i = 1, ..., m =⎣ j=1
(10)
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Step 5. Given the di+ and di− values obtained for each Ai , the position of an alternative within the ranking is determined by its relative distance from the negative ideal solution Ri =
di−
di+ + di−
i = 1, ..., m
(11)
The highest score that may be obtained by an alternative corresponds to a value of Ri = 1, while the lowest one is given by Ri = 0. If the reports were strategic, the rankings obtained would represent the preferences of the expert(s) providing the evaluations received by the DM.
3 An Illustrative Numerical Exercise The effects derived from the incorporation of sequential regrettable decisions are described numerically, using a simple example to illustrate the behavior of TOPSIS. Consider an evaluation framework consisting of three alternatives and two criteria. The following decision matrix summarizes the main characteristics of the strategic problem analyzed. C1
C2
8
0
A1 A2 A3
4 4 0 8 W = [w1 , w2 ] = [0.5,0.5]
Assume that both criteria are desirable, that is, higher values represent more valuable alternatives. The results derived from this numerical setting can be intuitively inferred before solving the model. Clearly, under the standard assumptions applied when implementing TOPSIS, the three alternatives should be equally ranked by the DM. C1
C2
A1
0.4472
0
A2 A3
0.2236 0
0.2236 0.4472
The weighted normalized decision matrix is given by leading to a value of Ri = 21 , i = 1, 2, 3. That is, the DM should be indifferent between the three alternatives. The above intuition and results prevail when defining an uncertain scenario where the evaluations represent the best potential performance of each alternative per criterion, allowing for the actual realizations to be as high as the values reported to the DM. In this
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case, highly valued alternatives are expected to perform better to the extent reported in the evaluations. Consider the following decision matrix. Whose entries correspond to the expected value of the uncertain realizations conditioned by the evaluations of the expert(s), r xik 1 r xr xik dxik , where xik describes the upper domain limit of the uniform distribution 0
ik
defined by the reports received by the DM, such that, for instance, 8 0
r x11
0 1 8 x11 dx11 .
1 r x11 dx11 x11
=
In this case, the same Ri = 21 , i = 1, 2, 3, would also be obtained for all
alternatives. C1
C2
A1
4
0
A2 A3
2 0
2 4
The uncertainty inherent to the evaluations leads to a natural question: what would happen if the DM could consider the potential results from solving this uncertainty when selecting the current alternative. In this regard, what would happen if the initial choice was not optimal, and the DM had to select a different alternative. The answer given by the above model is simple, it does not matter, since all alternatives are equally ranked, and any choice constitutes a perfectly viable strategy. We illustrate how this is not the case if the DM is allowed to consider the potential consequences from his current choice when selecting a given alternative.
4 Perception-Based Evaluation Intervals We differentiate between the evaluations received from the experts and the potential r ∈ X be the evaluation received realizations that may be observed by the DM. Let xik k r ) contained from the expert regarding alternative i and criterion k. Consider the set W − (xik r in Xk , which includes the whole set of potential realizations xik ∈ [0, xik ] that may be r ∈ X . Any potential observation observed by the DM leading to a lower utility than xik k r of xik must be defined with respect to xik , accounting for the uncertainty inherent to the r ]. potential realizations that may be observed by the DM, i.e. [0, xik r − The set W (xik ), defining the potential worsenings that may be observed relative to r ∈ X , equals xik k (12) where S(μ) defines the support of the corresponding density function μ assigned to the k th criterion.
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A similar intuition should be applied when considering negative criteria, with the set of potential realizations defining the worsening being located above the evaluations provided by the experts. 4.1 Value Functions The following functions define the expected utility values received by the DM when observing realizations from alternative i and criterion k and accounting for the possibility of regretting the initial choice and observing alternative j. The combinatorial regret r process defined involves two alternatives and is conditioned by the relative values of xik r . and xjk r
xik r r V (xik , xjk , xik , xjk ) = 0
⎡ 1 ⎢ r ⎣ xik
xik 0
xr
1 r (xik )dxjk + xjk
jk xik
⎤ 1 ⎥ r r ≤ xjk xjk − c dxjk ⎦dxik , xik r xjk (13)
r
xik r r V (xik , xjk , xik , xjk ) =
⎡ r xik
0
1 ⎢ r ⎣ xik
r xjk
xik 0
1 r [xik ]dxik + xik xr
1 r (xik )dxjk + xjk
jk xik
⎤
(14)
1 ⎥ r r xjk − c dxjk ⎦dxik , xik > xjk r xjk
To simplify the presentation, we have assumed linear utility functions, u(xik ) = xik , ∀i, k. We have also introduced a cost, c, to penalize the DM for not selecting the most suitable alternative as his first choice and having to proceed with the next one. The number of combinations that must be defined by the DM when accounting for three alternatives equals six, a dimension that continues increasing as additional alternatives are incorporated into the analysis. The costs would also have to be incremented accordingly as additional potentially regrettable alternatives are considered by the DM.
5 Analysis Table 1 presents the set of potential combinations that may be defined based on the three alternatives composing the decision problem. The expected utilities obtained per criterion are determined by the pairs of potential realizations that may be observed when penalty costs are either omitted or incorporated to the value function. The resulting weighted decision matrix absent penalty costs, together with the corresponding Ri values, is given by
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D. Di Caprio and F. J. Santos Arteaga Table 1. Combinatorial evaluations and expected utilities.
Alternatives
C1 values
C2 values
V (C1 )
V (C2 )
V (C1 , c)
V (C2 , c)
A1 A2
([0,8], [0,4])
([0], [0,4])
4.333
2
4.308
1.9
A1 A3
([0,8], [0])
([0], [0,8])
4
4
4
3.9
A2 A1
([0,4], [0,8])
([0,4], [0])
4.333
2
4.258
2
A2 A3
([0,4], [0])
([0,4], [0,8])
2
4.333
2
4.258
A3 A1
([0], [0,8])
([0,8], [0])
4
4
3.9
4
A3 A2
([0], [0,4])
([0,8], [0,4])
2
4.333
1.9
4.308
Ri
C1
C2
A1 A2
0.348
0.161
0.5
A1 A3
0.321
0.321
0.856
A2 A1
0.348
0.161
0.5
A2 A3
0.161
0.348
0.5
A3 A1
0.321
0.321
0.856
A3 A2
0.161
0.348
0.5
The following order is defined among the different pairs of alternatives A1 A3 ∼ A3 A1 A1 A2 ∼ A2 A1 ∼ A2 A3 ∼ A3 A2 . The strict order obtained illustrates how the DM prefers to choose the first and third alternatives over any combination including the second one. This is the case despite the positive potential realizations available when the first or third alternative underperform in one of the evaluation criteria. The symmetry in the evaluations follows from the specific design of the model, while that obtained for the A1 A3 and A3 A1 pairs results from the absence of penalty costs. We introduce these costs below and analyze the resulting evaluation differences. Assume that the value functions incorporate a penalty cost equal to c = 0.1. The following weighted decision matrix – with the corresponding Ri values assigned to each pair of alternatives – is obtained.
C1
C2
Ri
A1 A2
0.248
0.109
0.5
A1 A3
0.230
0.224
0.848
A2 A1
0.245
0.115
0.506
A2 A3
0.115
0.245
0.506
A3 A1
0.224
0.230
0.848
A3 A2
0.109
0.248
0.5
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The order of preferences defined among the alternatives is given by A1 A3 ∼ A3 A1 A2 A1 ∼ A2 A3 A1 A2 ∼ A3 A2 . As in the costless scenario, the DM prefers the first and third alternative over any other combination that includes the second one. However, in this case, the DM considers also the second alternative as a potentially more stable choice before proceeding with either the first or the third one. This change in preferences reflects the introduction of costs, which implies that the choice order determines the expected utility received. The rankings obtained in the three scenarios analyzed are summarized in Fig. 1.
Fig. 1. Ri values across alternatives and regret scenarios.
6 Conclusions We have defined an evaluation framework designed to illustrate the ranking differences arising as DMs incorporate the potential realizations from an uncertain environment in their choices. The combinatorial complexity of the model increases in the number of potential alternatives composing the regret path, which limits the applicability of the model when considering long paths. However, when accounting for two or three regrettable decisions per path, the model remains manageable and can be easily applied to a variety of MADM techniques.
References 1. Di Caprio, D., Santos Arteaga, F.J.: Combinatorial abilities and heuristic behavior in online search environments. Oper. Res. Perspect. 8, 100179 (2021). https://doi.org/10.1016/j.orp. 2021.100179 2. Di Caprio, D., Santos Arteaga, F.J.: A novel perception-based DEA method to evaluate alternatives in uncertain online environments. Comput. Ind. Eng. 131, 327–344 (2019). https://doi. org/10.1016/j.cie.2019.04.007 3. Santos-Arteaga, F.J., Di Caprio, D., Tavana, M.: A self-regulating information acquisition algorithm for preventing choice regret in multi-perspective decision making. Bus. Inf. Syst. Eng. 6(3), 165–175 (2014). https://doi.org/10.1007/s12599-014-0322-8
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4. Santos Arteaga, F.J., Tavana, M., Di Caprio, D.: A new model for evaluating subjective online ratings with uncertain intervals. Expert Syst. Appl. 139, 112850 (2020). https://doi.org/10. 1016/j.eswa.2019.112850 5. Tavana, M., Santos Arteaga, F.J., Di Caprio, D.: The value of information as a verification and regret-preventing mechanism in algorithmic search environments. Inf. Sci. 448–449, 187–214 (2018). https://doi.org/10.1016/j.ins.2018.03.032
Analyzing the Digital Marketing Strategies Role in Post Pandemic Recovery Period Khatira J. Dovlatova(B) Azerbaijan State Oil and Industry University, 34 Azadlig Avenue, AZ1010 Baku, Azerbaijan [email protected]
Abstract. Modern information technologies (IT) in business area has brought about important evolution in today’s market place well as formulation of digital markets. Digital markets created new opportunities and chances for various economic businesses and consumers. Utilizing such opportunities require accurate marketing strategies in fuzzy environment according to multi criteria decision making problems. This paper focused on digital marketing strategies within the post pandemic period of organizations in uncertain environment. The article investigated digital marketing strategies within the given criteria for managing the crisis by organizations. The aim of the study is to evolve attribute, methodology how to selecting the most suitable digital marketing tools for a business and market in post pandemic recovery period. To make a decision on given fuzzy problems, multi criteria decision making methods should be used. In this article, fuzzy multi criteria decision making problems with Analytic Hierarchy Process (AHP) and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) methods are applied to choose the best digital marketing strategy. The obtained results of solving the given problem which TOPSIS and AHP fuzzy multi criteria decision making methods can be used to choose the most appropriate strategy for companies in post pandemic recovery period. Applied AHP method gives eigenvectors and using them as weights decision maker can solve problem by using TOPSIS method. Keywords: Fuzzy AHP · Fuzzy TOPSIS · Decision making · Eigenvalue · Eigenvector · Digital marketing
1 Introduction Modern digital communication plays a main role in the development of the market economy, which has prearranged the development of new ways of marketing communications and marketing tools. There are different approaches to digital marketing between researchers and this process influences choosing the best marketing strategy in taking into account the given criteria. But in research scientists did not use fuzzy information for analyzing the given situation. A lot of multi criteria decision techniques as (AHP, Analytic Network Processing - ANP, and TOPSIS), mathematical programming
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 139–146, 2023. https://doi.org/10.1007/978-3-031-25252-5_22
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(Linear Programming, Goal Programming or Mixed-Integer Programming) and others are existed for solution of decision-making problems [1–4]. The Fuzzy TOPSIS method represents comparatively suitable practice samples, particularly in actual problems where individual opinions are obtained by linguistic data. For the mentioned goals a fuzzy multi criteria decision making method, which is an extension of the F-TOPSIS approach is used. This paper is focused as the literature is reviewed as stated by the different criteria and methods used for the digital marketing strategy selection problem in fuzzy environment. The scientific approach of this paper is to take into consideration the given criteria for selection the best digital marketing strategy. To solve problems in digital sphere, alternatives are based on various criteria’s necessary to be selected.
2 Preliminaries Definition 1. The Equation with Fuzzy Numbers [5]: bij = (bij,l , bij,m , bij,u ),
bij = (1, 1, 1) bij,l > 0 i, j = 1, 2......., n
i = j. (1)
The formula summarizes a fuzzy comparison matrix B which constitutes the following elements, 1 1 1 1 , i, j = 1, 2, ...n, i = j. (2) = , , bij = bij,u bij,m bij,l bij Definition 2. Determination of Fuzzy Weights [6]: B ⊗ w˜ = λ˜ l ⊗ w, ˜
(3)
where B, fuzzy mutual comparison matrix of type [n × m]. Components of the fuzzy matrix B, fuzzy vector w˜ and fuzzy eigenvalue λ˜ are assumed as triangular fuzzy numbers which may be demonstrated as positioned by w˜ = (wl , wm , wu ), λ˜ = (λl , λm , λu ). Definition 3. Consistency Index (CI) and Consistency Ratio (CR) [7, 8]: ˜ as described in the previous Given the fuzzy eigenvalue problem B ⊗ w˜ = λ˜ l ⊗ w, part and define the principal fuzzy eigenvalue λ˜ = (λl , λm , λu ) and corresponding fuzzy eigenvectors w˜ = (wl , wm , wu ). For the Bl ,Bm ,Bu matrix calculate the CI and CR according to [9, 10]. Definition 4. Construction of Weighted Normalized Decision Matrix [11]. bij = wj × rij
(4)
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Definition 5. Positive and Negative Ideal Solution. Positive ideal solution F ∗ and negative ideal solution F − for the weighted normalized fuzzy decision matrix can be obtained on base of the weighted normalized grading. Positive ideal solution matrix is defined with formula (5), the negative ideal solution matrix based on formula (6) [12, 13]: F ∗ = (max bij /j ∈ J ), (min bij /j ∈ J [i = 1, 2, 3, ..., m] = {b1∗ , b2∗ , ..., b1n } (5) and the negative-ideal F − solutions are calculated as follows: F − = (min bij /j ∈ J ), (max bij /j ∈ J [i = 1, 2, 3, ..., m] = {b1− , b2− , ..., b1N − } (6) Definition 6. Obtaining the Separation Measures for Each Alternative from Ideal and Negative Ideal Alternative Is: Si∗ = [
2 b∗j − bij ]1/2
Si = [
2 b∗j − bij ]1/2
i = 1, ..., n
(7)
Definition 7. Relative Closeness to the Ideal Solution [7]. Ci∗ = Si /(Si∗ + Si )
(8)
3 Statement of the Problem Digital marketing strategies are influenced by different economical processes. The factors influencing digital marketing strategies are analyzed as attribute that has a main role in the global market environment. In a fuzzy environment the pairwise comparison matrix of attribute is exhibited by linguistic factors which are shown by triangular fuzzy numbers. MCDM problem involves 5 criteria and 5 alternatives for digital marketing A1 , A2 , A3 , A4 , A5 . C1 - Budget; C2 - Marketing strategy goals; C3 - The age of the audience; C4 - The company’s staff preference; C5 - frequency. Table 1. Shows the comparison of attributes (criteria) under competency into triangular fuzzy numbers and final step to obtain consistency ratio of this shown fuzzy matrix (1,2). Aim of this paper use the obtaining eigenvectors from consistent matrix as weights of attributes for ranking alternatives in the given decision matrix [8].
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K. J. Dovlatova Table 1. Fuzzy matrix of the criteria
Attribute C1
C2
C3
C4
C5
C1
(1,1,1)
(2.3,3.33,5)
(3.3,5,10)
(1,1,1)
(0.3,0.5,1)
C2
(0.2,0.3,0.4) (1,1,1)
(0.01,0.02,0.03) (0.55,0.56,0.57) (1,2,3)
C3
(0.1,0.2,0.3) (0.2,0.3,0.4)
(1,1,1)
C4
(1,1,1)
(1.75,1.79,1.81) (1.43,1.67,2)
(1,1,1)
(10,11.11,12.5)
C5
(1,2,3)
(0.33,0.5,1)
(0.08,0.09,0.1)
(1,1,1)
(2.5,3.3,5)
(0.5,0.6,0.7)
(0.2,0.3,0.4)
4 Solution of the Problem In research paper we analyzed the best alternative to take into account the given attribute. Fuzzy pairwise comparison matrix of the attribute for multi-criteria problem is given in Table 1 [10, 14]. Stage 1. First stage express the pair-wise comparison reciprocal fuzzy matrix B bij = for the attribute C1 ,C2 ,…,Cn by evaluating the priority values as fuzzy numbers B divided by three crisp (bij,l , bij,m , bij,u ), (i, j = 1, 2, ..., n). Given the fuzzy matrix matrices Cl , Cm , Cu are defined based on [7] as follows: ⎤ ⎤ ⎡ ⎡ 1 b12,l ... b1k,l 1 b12,m ... b1k,m ⎥ ⎥ ⎢ ⎢ ... ... ⎥ Bm = ⎢ ⎥ Bl = ⎢ ⎦ ⎣ 1/b12,u ⎣ 1 ... b2k,l 1 ... b2k,m ⎦ 1/b12,m 1/b1k,u 1/b2k,u ... 1 1/b1k,m 1/b2k,m ... 1 ⎤ ⎡ 1 b12,u ... b1k,u ⎥ ⎢ ... ⎥ Bm = ⎢ ⎣ 1/b12,l 1 ... b2k,u ⎦ 1/b1k,l 1/b2k,l ... 1 Stage 2. Defined matrices are used for obtaining of a system of fuzzy linear homogeneous equations [15]. Bl wl + Bm wm + Bu wu − λl wl − λm wm − λu wu = 0
(10)
where are:Bl = 2Bl + Bm = 3 Bm = Bl + 4Bm + Bu = 6 Bu = Bm + 2Bu = 3 (11) After using (9) we defined three crisp matrices (Tables 2, 3 and 4): .
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Table 2. Bl and Bl
Bl
Bl
1 0.2 0.1 1 1
2.5 1 0.2 1.75 0.33
3.33 0.01 1 1.43 2.5
1 0.55 0.5 1 0.08
0.33 1 0.2 10 1
3 0.7 0.4 3 4
8.33 3 0.7 5.29 1.17
11.67 0.04 3 4.52 8.33
3 1.66 1.6 3 0.25
1.17 4 0.7 31.11 3
Table 3. Bm and Bm Bm
1 0.3 0.2 1 2
Bm 3.33 1 0.3 1.6 0.5
5 0.2 1 1.67 3.33
1 0.56 0.6 1 0.09
0.5 2 0.3 11.11 1
6 1.8 1.2 6 12
20.83 6 1.8 10.72 3.33
33.33 0.12 6 10.1 20.83
6 3.36 3.6 6 0.54
3.33 12 1.8 66.94 6
25 0.08 3 5.67 13.33
3 1.7 2 3 0.29
2.5 8 1.1 36.11 3
Table 4. Bu and Bu Bu 1 0.4 0.3 1 3
5 1 0.4 1.82 1
10 0.03 1 2 5
1 0.57 0.7 1 0.1
1 3 0.4 12.5 1
Bu 3 1.1 0.8 3 8
13.33 3 1.1 5.42 2.5
Stage 3. Eigenvalues of Bl , Bm and Bu are obtained with MATLAB software program: λl = 15.37; λm = 34.85; λu = 21.63. λl , λm , λu are calculated by given formula: ⎧ ⎧ λ = 2λl + λm ⎪ ⎪ ⎪ ⎨ 15.37 = 2λl + λm ⎨ l −69.7 = −2λl − 8λm − 2λu 34.85 = λl + 4λm + λu ⇔ ×(−2) ⇔ λm = λl + 4λm + λu ⇔ ⎪ ⎪ 21.63 = λm + 2λu ⎩ ⎪ ⎩ 21.63 = λm + 2λu λu = λm + 2λu −48.07 = −2λl − 7λm ⇔ ⇔ λl = 4.96, λm = 5.45, λu = 8.09. (12) 15.37 = 2λl + λm
Stage 4. By homogenous fuzzy linear equations eigenvectors also are obtained (3): Eigenvectors of Bl , Bm and Bu are obtained with MATLAB package: wl =
n n n w l λl wm w u λu , wm = , wu = ; where sl = wi,l , sm = wi,m , su = wi,u . s l λm sm s u λm i=1 i=1 i=1
(13)
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wl = [−0.45, −0.2, −0.13, −0.81, −0.25] Sl = −1.86 wm = [0.45, 0.21, 0.13, 0.8, 0.29] Sm = 1.9 wu = [0.47, 0.23, 0.13, 0.77, 0.32] Su = 1.93
(14)
Applying the mentioned software program, the following eigenvectors are obtained: wl = [0.23, 0.1, 0.07, 0.41, 0.14], wm = [0.24, 0.12, 0.07, 0.42, 0.15], wu = [0.37, 0.17, 0.1, 0.59, 0.25]
(15)
Stage 5. In accordance to [5] consistency index and consistency ratio for B˜ matrix are obtained by using following formulas [5]: CI =
0.11 5.45 − 5 = 0.11, CR = = 0.1, CR = 0.1 ≤ 0.10 5−1 1.12
(16)
Implementing the offered formula, the eigenvalues, CI and CR ratio are obtained. CR is 0.1, the proposed matrix B is consistent. Stage 6. Constructed weighted normalized decision matrix (4) (Table 5 and 6). Table 5. Fuzzy matrix of the attribute Attribute C1 C2 C3 C4 C5 weights (0.23,0.24,0.37) (0.1,0.12,0.17) (0.07,0.07,0.1) (0.41,0.42,0.59) (0.14,0.15,0.25) A1
(1,2,3)
(2,3,4)
(1,1,1)
(4,5,6)
(5,6,7)
A2
(5,6,7)
(3,4,5)
(1,2,3)
(2,3,4)
(6,7,8)
A3
(2,3,4)
(2,3,4)
(2,3,4)
(1,1,1)
(2,3,4)
A4
(1,1,1)
(5,6,7)
(7,8,9)
(5,6,7)
(1,1,1)
A5
(1,2,3)
(1,1,1)
(2,3,4)
(3,4,5)
(3,4,5)
Table 6. Weighted normalized Fuzzy matrix of the attribute A1 A2 A3 A4 A5
C1 w (0.018,0.037,0.085) (0.088,0.110,0.199) (0.035,0.055,0.114) (0.018,0.018,0.028) (0.018,0.037,0.085)
A1 A2 A3 A4 A5
C2 w (0.013,0.024,0.046) (0.02,0.032,0.057) (0.013,0.024,)0.046 (0.034,0.048,0.08) (0007,0.008,0.011)
C4 w (0.1,0.128,0.216) (0.05,0.077,0.144) (0.025,0.026,0.036) (0.125,0.154,0.252) (0.078,0.102,0.18)
C3 w (0.004,0.004,0.006) (0.004,0.009,0.018) (0.009,0.013,0.024) (0.03,0.034,0.055) (0.009,0.013,0.024)
C5 w (0.038,0.049,0.095) (0.045,0.057,0.108,) (0.015,0.024,0.054) (0.015,0.024,0.054) (0.023,0.032,0.068)
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Stage 7. Calculated the relative closeness to the ideal solution (8).
Si*
S i'
A1
0.08 0.09
0.13
A1 0.08 0.14
0.21
A2
0.08 0.08
0.12
A2 0.08 0.15
0.23
A3
0.12 0.15
0.24
A3 0.02 0.06
0.10
A4
0.08 0.10
0.20
A4 0.11 0.14
0.23
A5
0.10 0.10
0.16
A5 0.05 0.10
0.16
Ci∗ = Si /(Si∗ + Si ) = [(0.08/(0.08 + 0.08) + 0.14/(0.14 + 0.09) + 0.21/(0.21 + 0.13)]/3 = 0.57 Ci∗ = (0.57, 0.61, 0.25, 0.56, 0.45) Rank the preference order: A2 > A4 > A1 > A5 > A3 . According to calculation of relative closeness to the ideal solution the best alternative (close to the ideal solution) is A2 for using in the post pandemic recovery period.
5 Conclusion The result of contrasting the features of the market and the selection attribute for digital marketing strategies (budget, marketing strategy goals, audience age, competence of the company’s staff, the frequency of use of tools), the main tools are chosen for the post pandemic recovery period. In this paper we use the development of AHP and TOPSIS multi-criteria methods for fuzzy problem. Applying F-AHP and F-TOPSIS multi-criteria decision-making problem is solved. F-AHP method is characterizes with using the pairwise comparison matrices of the attribute and define eigenvectors for using in F-TOPSIS method which can help to choose the best alternative. The suggested method can be implemented for different issues that associated to solve large decision-making problems in business especially in post pandemic recovery period.
References 1. Ayhan, M.B.: A fuzzy Ahp approach for supplier selection problem: a case study in a gearmotor company. IJMVSC 4(3), 11–23 (2013). https://doi.org/10.5121/ijmvsc.2013.4302 2. Dovlatova, K.J.: Decision making in investment by application of the analytic hierarchy process (AHP). B-quadrat verlags, pp. 226–228 (2018) 3. Vargas,V. R.: Using the analytic hierarchy process (AHP) to select and prioritize projects in a portfolio PMI Global Congress – North America Washington (2010) 4. Huseynova, N.F.: Decision making on tourism by using natural language processing. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 741–747. Springer, Cham (2022). https://doi.org/10.1007/978-3030-92127-9_98
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5. Cabala, P.: Using the analytic hierarchy process in evaluating decision alternatives Oper. Res. Dec. 1(1), 1–23 (2010) 6. Kardi Teknomo’s Homepage. https://people.revoledu.com/kardi/tutorial/AHP/purchase.html 7. Nadaban, S., Dzitac, S.: Neutrosophic TOPSIS: A General View. 6th ICCCC (2016). https:// doi.org/10.1109/icccc.2016.7496769 8. Laarhoven, V., P. J. M., Pedrycz, W.: A fuzzy extension of Saaty‘s priority theory. Fuzzy Sets Syst. 11(1–3), 229–241 (1983). https://doi.org/10.1016/S01650114(83)80082-7 9. Saaty, T.L.: Theory and applications of the analytic network process: decision making with benefits, opportunities, costs, and risks RWS Publications, 3rd edn. (2005) 10. Dadasheva, A.: Analysis of consistency of pairwise comparison matrix with fuzzy type-2 elements. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 324–330. Springer, Cham (2022). https:// doi.org/10.1007/978-3-030-92127-9_45 11. Kumar, Dr. A. A.: Factors influencing customers buying behavior. J. Market. Consumer Res. Int. Peer-reviewed J. 27, 30–34 (2016) 12. Aliyeva, K.: Facility location problem by using fuzzy topsis method. Chem. Technol. Control Manag. 3, 55–59 (2018). https://doi.org/10.34920/2018.4-5.55-59 13. Aliyeva, K.: Multifactor personnel selection by the fuzzy TOPSIS method. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Mo., Jamshidi, Sadikoglu, F.M. (eds.) ICAFS 2018. AISC, vol. 896, pp. 478–483. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-04164-9_64 14. Aliev, R.A.: A consistency-driven approach to construction of Z-number-valued pairwise comparison matrices. Iran J. Fuzzy Syst. 18(4), 37–49 (2021). https://doi.org/10.22111/IJFS. 2021.6175 15. Prascevic, Z., Prascevic, N.: Application of fuzzy AHP method based on eigenvalues for decision making in construction industry. Tehniˇcki vjesnik 23(1), 57–64 (2016). https://doi. org/10.17559/TV-20140212113942
Artificial Intelligence and Digital Economy: Development Prospects Ali Abbasov
and Ramin Rzayev(B)
Institute of Control Systems of ANAS, B.Vahabzadeh Street 9, 1141 Baku, Azerbaijan [email protected], [email protected]
Abstract. The digitalization of the state economy implies the formation of a stable and secure information and telecommunications infrastructure for high-speed transmission; the ability to store and process large amounts of data, accessible to all organizations and households; the use of advanced software by government agencies, local governments, and organizations. Obviously, the main benefits from the digitalization of the economy lie in the plane of solving problems related to productivity growth, cost minimization, automation, and production efficiency. It is possible to analyze levels of data that are beyond human understanding, which in turn allows companies to personalize experiences, customize products (services) and identify growth opportunities with speed and accuracy that were not possible before. However, the implementation of the Digital Economy project is only the first step towards creating the image of the economy of the near future. According to the unanimous opinion of experts, the main “actor” that allows consumers and businesses to get the maximum benefit out of the Digital Economy will be Artificial Intelligence, which will significantly change the world and will be used everywhere in the economy. Companies that do not consider the phenomenon of Artificial Intelligence and do not respond to its penetration into day-to-day life are not capable of innovating and reengineering their business models. At best, these companies will lose their competitive advantage, and at worst, they will simply disappear. Keywords: Artificial intelligence · Digital economy · Productivity · Digital skill
1 Introduction Currently, the place and role of Artificial Intelligence (AI) tools and methods in business and the world economy are topics of stormy discussion among specialists in various fields, as it’s perfectly natural that AI could lead to radical, perhaps unprecedented, changes in the setup and work of people. The current level of development of AI methods and tools is not in its infancy, but a significant part of the synergistic effect from its application is still ahead. Today, AI is actively penetrating our daily lives – literally into all spheres of human life, ensuring safety and increasing productivity, considering the new challenges of the present time it offers new transformation opportunities for consumers, business, and society. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 147–153, 2023. https://doi.org/10.1007/978-3-031-25252-5_23
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AI has enormous potential to influence the development of the entire global economy. Combined with key technologies such as the Internet of Things (IoT) [1, 2], Big Data Analytics (BDA) [2] or Blockchain [3], AI can become the basis for economic growth and thus ensure competitiveness and the creation of new high-tech jobs. According to forecasts, due to the application of AI technologies, the volume of the global economy by 2030 may increase by the additional e13.33 trillion, which is significantly higher than the current combined output in China and India. e5.6 trillion of this amount is expected to come from exponential productivity growth, and e7.73 trillion – from consumption spillovers. One of the latest studies by the McKinsey Global Institute provides an analysis of AI technologies influences on the global economy. In particular, [1] analyzes the behavior of large companies and the dynamics of changes in various sectors of the economy in terms of developing approaches to the implementation and development of AI technologies within the digital economy. However, this analysis considers the probable costs that countries, companies, and workers may meet in the transition to AI. Therefore, based on these prerequisites, it becomes important and relevant to study the prospective impact of AI technologies on the digital economy.
2 Artificial Intelligence: Historical Aspect Many ideas appear and disappear very quickly. Some, like one-day butterflies, die almost immediately, others live for years, and still others for decades. But only very few of them determine the direction of the movement of human thought for many centuries. One of the phenomenal human qualities is the thirst for creativity. The inexplicable desire to reproduce oneself, to see one’s reflection in one’s creations, has its roots in the time of rock paintings. Even though our ancestors had no practical benefit from rock paintings, they decorated their own dwellings with sketches of themselves with enviable persistence. With the development of natural intelligence and the creation of more and more advanced tools and technologies of creativity, man recreated himself in clay, stone, metal, with amazing grace and, most importantly, accurately conveying forms. But how could a man stop there? Man has always dreamed of breathing life into his creations – the ability to think and feel. The period that replaced the thousand-year prehistory of human dreams was called “Dawn” by the famous scientist in the field of AI Patrick Winston. In work “AI in the 1980s and Beyond” (1987) he scaled the time axis as shown in Fig. 1. According to P. Winston, the prehistory of AI began in 1842, with the creation of an analytical (difference) engine by Charles Babbage, which largely anticipated the development of computer techniques. However, many researchers believe that the period of prehistory is not limited to the personality of Ch. Babbage but is rooted deep in the times of myths and legends. The period of prehistory lasted until 1960 (naturally, this and all other dates from Fig. 1 are conditional). By this time, supporters of the “top-down” computer approach to understanding AI had computers at their disposal and a lot of contextual ideas had accumulated. In 1953, American mathematician and philosopher Norbert Wiener had already offered the idea that the processes of control and communication in machines, living organisms and societies are similar. The processes of transmission, storage, and processing of information are common to them.
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Fig. 1. The evolution of approaches to the development of AI.
The “Dawn period” is characterized by excessive promises to make humanity happy with the creation of AI. The search for a semblance of a mechanism capable of displaying intellectual abilities in the logical basis of a computer was unsuccessful and, as a result, the period of the dawn of AI was replaced by stagnation. The revival of general interest in AI is associated with the emergence of applied modeling systems, such as expert systems MYCIN, Prospector, etc., as well as Soft Computing technology, formed based on Fuzzy Logic. The formation of Soft Computing technology became possible after the widespread use of Artificial Neural Networks, which are characterized by their adaptive and approximation abilities. If during the previous stages only specialists in cybernetics and computer technology were mainly engaged in the problems of AI, then the commonwealth period is characterized by the establishment of fruitful contacts between them and researchers from other fields of science, especially linguists and psychologists. Finally, P. Winston preferred to call the next period the time of entrepreneurship when work on AI should be put on a commercial basis and provide an economic synergistic effect from implementation. This idea was expressed a long time ago but remains very relevant.
3 Contribution of AI Technologies to Economic Activity According to [4], in the short term, AI technologies can significantly accelerate the pervasive development of the digital economy in the following five main areas: • Computer vision: [5]. • Natural language. • Intelligent virtual assistants as software agents that can solve problems and/or provide services based on commands given in natural language [6]. • Process automation with a high degree of robotization, as a form of business process automation technology based on bots (metaphorical software robots) or digital workers: [7]. • Advanced machine learning: [8]. According to the most conservative estimates, by 2030, about 70% of global companies can implement at least one of these areas of AI. However, less than half of them can fully reclaim all five categories of AI. At the same time, there are several barriers to the rapid adoption and reclaim of AI technologies. For example, it will be difficult for “laggard companies” to achieve the effect of the introduction of AI technologies, since by that time the leading companies will already have time to take advantage of
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the opportunities of AI, which will significantly reduce the ability to attract high-quality specialists from a limited number of talented people. It should be noted several factors that imply the introduction of innovations and specify a new level of competition under the use of AI technologies, which directly affect the growth of the economy in the context of its digitalization. Increase Productivity with Automation. AI technologies can provide a significant increase in productivity in enterprises that use automation industry. Automation of robotic and cognitive processes, machine learning and natural language processing, multi-agent systems of associativity enable companies to maximize their profits by increasing the synergies of investments (labor, capital, and assets). Capital-intensive industries such as manufacturing and transport are the main beneficiaries of productivity gains. Increase in Consumer Demand. As AI technologies adopt the consumer market, in the near future it is most probably may be visible the increase in consumer demand characterized by the availability of personalized and/or higher quality goods and services. Government revenue from consumer demand is projected to substantially outweigh productivity gains. Implementation of Innovations. By its very nature, AI can actively drive innovation because, when combined with BDA technology it can quickly analyze terabytes of data and create the new knowledge. The innovative activity of companies using AI technologies allows them to reduce the costs of ongoing research and development, as well as create favorable opportunities for conducting promising experiments. It is assumed that the affecting of AI on the global (or national) economy will be nonlinear, but over time it may increase at an increasing rate. By 2030, the contribution of AI to world economic growth could be three times or more higher than in the previous five years. A “sigmoid model” of AI adoption and reclaim is probably. As can be seen from Fig. 1, a slow start is predicted due to the significant costs and investments associated with study and implementing these technologies, and then an acceleration is expected due to the synergetic effect of competition and the emergence of additional opportunities along with the innovation process. It would be a mistake to interpret the “sigmoid model” as a “slow burning” phenomenon as argument that the effect of the introduction of AI technologies will be bounded. The volume of benefits for companies and/or countries that are the first to adopt and implement AI technologies will only grow in subsequent years and, first, at the expense of companies and/or countries that do not pay adequate attention to the development and implementation of AI. The capabilities of AI are significant, but there is no doubt that its infiltration can cause disruptions. AI productivity gains probably will not materialize right away. In time, its influence will increase at an accelerated pace. Therefore, the initial benefits of investing in the development and promotion of AI may not be noticeable in the short term. Laborious patience and long-term strategic thinking are needed (Fig. 2).
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Fig. 2. A “sigmoid model” of AI adoption and reclaim.
4 Projected Gap Between Countries, Companies and Workers According to statistical studies, the leaders in the implementation of AI, which are now post-industrial countries, can dramatically increase their undeniable advantage over developing countries. It is predicted that by the implementation of AI, these countries can receive an additional from 20% to 25% of net economic benefits compared to today, while developing countries can receive only about 5%−15%. Currently, in many economically and institutionally developed countries, where the proportion of the elderly population is quite high, there is a slowdown in GDP growth (recession). This is another very important stimulus for the adoption of AI as an additional option that can push the digital economy to higher growth by increasing the labor productivity. Moreover, over the past decades, high rates of remuneration have been established in industrializing countries. In essence, this is another additional incentive for the accelerated adoption of AI technologies that provide a replacement for manual labor and routine work. In developing countries, where there are relatively low rates of remuneration, other methods of increasing productivity are being used as the main factors in economic growth. First, this is the use of advanced experience of post-industrial countries and the restructuring of their industries. Therefore, these countries may have less incentive to implement AI, which, in any case, may offer them relatively less economic benefit than advanced economies. However, some developing countries may be an exception to this rule. For example, China has its own national strategy to become a global leader in the AI technologies supply chain and is already investing heavily in advancing AI. The other example is Azerbaijan speech technology market based on AI Azerbaijan Language Processing Systems will cover up to 60% of population by 2030 [9]. By 2030, the development of AI technologies may lead to a noticeable bundle between companies relative to productivity. A significant gap is predicted between companies that will fully implement AI tools in their enterprises over the next 5–7 years, and companies that have not adopted AI technologies. Companies that have a strong start-up IT base, are inclined to invest in AI, and have a positive view of the business case for
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AI will get benefit disproportionately. Potentially, these companies can double their net income and further to generate about 6% annual net income growth. Based on the exist cost and revenue model, companies that do not implement AI technologies are expected to experience a decrease in cash income of about 20%. One important factor in their predicted decline in profits will be the presence of strong competitive dynamics from companies using AI, which in turn will naturally provoke debate about the unequal distribution of AI benefits. The widening gap between countries and companies will also affect the level of individual workers. The demand for jobs may shift from routine (repetitive) industries to those associated with social and cognitive processes, which will require more digital skills. By 2030, jobs that perform repetitive manufacturing procedures or require low levels of digital skills could drop from 40% to 30% of total employment. On the contrary, the share of competencies in the field of non-repetitive industries that require digital skills will increase from about 40% to more than 50%. It is obvious that the transformation towards an increase in the share of digital skills in work competencies will affect the wages of workers. It is planned that about 13% of the total wage fund can move into categories requiring high digital skills in production with AI, where revenues will rise markedly. However, the share in the total wage fund for categories with low digital skills will decrease from 33% to 20%. Thus, because of the widening gap between competencies with low and high levels of digital skills, the competition for specialists in the development and use of AI tools will intensify. In addition, there is already an excess supply in the labor market for a relatively large proportion of people who lack cognitive and digital skills needed to interact with AI technologies. Under the current conditions, it is already necessary to pursue a decisive policy to overcome the discomfort of citizens from the impending threat of job loss soon as AI technologies are introduced within the digital transformation of the economy. Companies must also take part in find solutions to the challenge of training and retraining specialists to interact with AI tools. People will have to adapt to a new world, where staff turnover may be higher. They are probably must learn new professions and/or permanently update their skills to satisfy the needs of the dynamically changing labor market. Using historic experience of creating high-tech jobs on the base of exist ones and adjusting for lower labor-productivity ratios to account for the probably labor-saving nature of AI technologies by intelligent automation, new jobs created by investment in AI could increase employment by about by 5%. By 2030, the cumulative productivity effect is expected to have a positive effect on total employment of about 10%.
5 Conclusion In addition to the above factors of AI influence, the economy of Azerbaijan in the context of its digitalization will be influenced by micro factors, such as the pace of implementation of AI technologies, and macro factors, such as global connectivity or the structure of the labor market. To adopt the AI technologies within the Digital Strategy for the sectoral development of the Azerbaijan economy it is necessary to increase the domestic costs, primarily at the expense of all sources of public revenue in accordance with their shares in the GDP. Therefore, in the framework of the economy digitalization,
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it is also necessary to formulate a state strategy for the adoption of Artificial Intelligent, for which it is proposed to solve the following priority problems: • formation of an appropriate system for the legal regulation within the digital economy, based on a flexible approach in each area, and the adoption the digital technologies based civil circulation; • formation of a nationwide infrastructure for storing, processing and transmitting data mainly on the basis of competitive national engineering designs, including AI tools; • training highly qualified personnel in the development and use of AI tools with digital skills in management and production; • ensuring information security mainly on the basis of national developments in the storage, processing and transmission of data that guarantee the protection of the interests of the individual, business and the state; • creation of mainly national developments based end-to-end digital technologies; • adoption of digital technologies and platform decisions in the spheres of public management and rendering of services, including in the favors of the population and SME; • transformation of the socio-economic system of the state, including education, healthcare, agriculture, industry, construction, urban economy, transport and energy infrastructure, financial services by the adoption of digital technologies and platform decisions; • considering venture financing and other development institutions, the formation of a unified system for evaluating and financing projects relative to development and/or adoption of AI technologies and corresponding platform solutions.
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Evaluation of Logistics Services of Airlines in the Azerbaijan Passenger Transportation Market Sevil Imanova1,2(B) 1 Baku Engineering University, Khirdalan AZ010, Azerbaijan
[email protected] 2 Azerbaijan State Oil and Industry University, 34 Azadlyg Avenue, Baku AZ1010, Azerbaijan
Abstract. The high-quality and stable functioning of civil air transport contributes to the full development of the economy of any state and is one of the important indicators of the quality of people life. Nowadays development of the civil air transportation sector of the economy is characterized by excessively fierce competition, especially in the provision of services both directly at airports and during flights. At the same time, the quality of services for the transportation of passengers should, to the maximum extent, satisfy the constantly growing requirements of consumers. The article considers a combined approach to a multi-criteria assessment of the competitiveness of airlines operating in the passenger transportation market in Azerbaijan, based on expert data on the levels of services obtained in the course of surveys of different categories of passengers. Within the framework of this approach and the selected system of indicators of the airline’s competitiveness, a methodology for assessing and ranking airlines is applied, based on the adaptation of the considered expert-fuzzy analysis methods, as well as the methods of comparative analysis of Pareto and Borda. British Airways, Lufthansa, Turkish Airlines and AZAL, which are the most active in the passenger air transportation market in Azerbaijan, are considered as alternatives to be evaluated. Keywords: Airline · Logistic service · Competitiveness factor · Fuzzy set · Fuzzy inference
1 Introduction Information support for effective management and development of operational technologies to improve the quality of service meets the requirements of air passengers requires the use of new scientifically based (innovative) approaches to ensure the permanent growth of the airline’s competitiveness based on a multi-criteria assessment of the level of customer service quality. One of these approaches is the expert-fuzzy analysis of relevant data, which provides the solution of weakly structured problems and describes the behavior of a similar system of a humanistic type. The current level of development of the theory of fuzzy sets and fuzzy logic makes it possible to take into account an increasing number of not only metrizable (quantitative), but also non-metrizable (weakly © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 154–163, 2023. https://doi.org/10.1007/978-3-031-25252-5_24
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structured) parameters that significantly affect the quality of logistics services and offer a modern, more adequate and combined method for assessing the quality of service for air passengers. Based on these prerequisites, the relevance of developing methods for assessing the logistics services of airlines becomes obvious.
2 Statement of the Problem The competence requirements of approaches to the formation and assessment of the level of competitiveness of an airline consist in the study of multidimensional evaluated factors and their use in the formation of airline ratings. In other words, the assessment of the level of competitiveness of an airline is a multi-criteria procedure that implies the application of a compositional rule for aggregating the assessment for each of the selected influence factors. Nowadays, there is no single approach to the methodology for calculating the rating of an airline, as there are different points of view regarding the composition of factors that have a significant impact on the level of competitiveness of an airline. For example, some researchers consider the competitiveness of airlines at the level of airports and, in fact, the airlines themselves. In particular, at the levels of airports and airlines, various authors summarize and classify all external and internal factors that affect the competitiveness of airlines. Including in accordance with the requirements of the International Air Transport Association IATA. In the framework of this research the consumer assessment of the attractiveness of an airline is derived from the consideration that when choosing an airline (provided that there is equilibrium in terms of other indicators), the one with the ratio of the fare to the useful effect received by the passenger is less than in other airlines. However, in practice, the criteria by which a potential passenger evaluates and chooses the airline that suits him include a much larger number of indicators than the size of the air fare. Testing and comparative analysis of the adequacy of the proposed approaches will be carried out on a hypothetical example of a group of airlines, which we will conventionally denote as: a1 , a2 , . . . , a10 . From the point of view of making decisions on the subject of assessing attractiveness, these airlines are alternatives, the level or competitiveness of which is assessed by experts from among different categories of airline passengers according to the above variables: x1 , x2 , . . . , x5 . For evaluation the logistics services of British Airways, Lufthansa, Turkish Airlines and AZAL, we used the Fuzzy Delphi method, where the assessment data of Internet expertise obtained from different categories of air passengers were used as an information base. To evaluate airlines ak (k = 1 ÷ 4) using the Fuzzy Delphi method, the following variable indicators were chosen as the basis: x1 – air ticket price; x2 – airline reliability; x3 – frequency of flights; x4 – service on board; x5 – aircraft type. Based on these indicators as evaluation criteria, a questionnaire was compiled and experts were selected from among different categories of passengers who actively use the services of the listed airlines. Each of the independent experts was asked to individually evaluate each of these airlines on a 100-point scale for its satisfaction with respect to the criteria xi . After that, the expert assessments of the airlines were analyzed for their consistency (or inconsistency) according to the rule: the maximum allowable difference between
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two expert opinions on the airline’s satisfaction with respect to the criterion xi (i = 1 ÷ 5) should not exceed 50 units. In particular, by applying the Fuzzy Delphi method with respect to the criterion “Reliability of the airline” for these airlines, evaluation concepts are formed in the form of corresponding fuzzy sets by means of the identified membership functions in a triangular form, which are shown in Fig. 1. British
Lutfhansa
1,2
1,2
1
90
1
0,8
91
0,8
0,6
Series1
0,6
0,4
0,4
0,2
0,2
0
80 0
20
40
60
100 100
80
Series1
0
120
80 0
20
40
60
Turkish
80
100 100
120
Azal
1,2
1,2
82
1
1
0,8
80
0,8
Series1
0,6
0,6
0,4
0,4
0,2
0,2
0 0
20
40
60
70 80
100 100
Series1
0
120
60 0
20
40
60
80
95 100
Fig. 1. Membership functions of the fuzzy set “Reliability” for airlines.
Based on the application of the Fuzzy Delphi method in [1], for all criteria, aggregated expert estimates of airline logistics services were established, which are summarized in Table 1. Table 1. Aggregated expert assessments of airline logistics services. Airlines
Competitiveness factors Ticket price
Reliability
Frequency
Service
Type of aircraft
x1
x2
x3
x4
x5
a1 – British airways
86
90
88
87
89
a2 – Lufthansa
90
91
92
93
90
a3 – Turkish airlines
92
82
86
89
86
a4 – Azal Avia
85
80
84
86
88
Based on the preliminary results, it is necessary to develop a combined approach to the evaluation of logistics services, taking into account non-metrizable indicators of the competitiveness of airlines in the air transportation market.
3 Estimation of Airlines Using a Fuzzy Inference System Before creating an analytical model for a multi-criteria assessment of the levels of competitiveness of airlines, it is advisable to build an appropriate reasonable gradation scale.
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To build a fuzzy inference system (FIS) regarding the assessment of the satisfaction of airlines ak (k = 1 ÷ 4) for their compliance with the criteria x i (i = 1 ÷ 5) a verbal model was chosen as the basis, formulated in the form of the following information fragments: d 1 : “If the price of the ticket and the reliability of the airline are acceptable, then it is satisfactory”; d 2 : “If, in addition to the above, the frequency of air transportation is acceptable - May, then the airline is more than satisfactory”; d 3 : “If the price of the ticket, the reliability and frequency of air transportation, the maintenance service, and the fleet of airliners are acceptable, then such an airline is impeccable”; d 4 : “If the ticket price, reliability, service, and the fleet of airliners are acceptable, then this airline is very satisfactory”; d 5 : “If an airline’s ticket price, reliability, fleet are acceptable, but the service it offers is unacceptable, then the airline is still satisfactory”; d 6 : “If the price of the ticket, the frequency of air transportation and the fleet of airliners are unacceptable, then the airline is unsatisfactory.” Assuming the set of airlines U = {a1 , a2 , a3 , a4 } to be a universal set, fuzzification of input qualitative characteristics can be carried out using fuzzy sets of the form Ai = {μAi (a1 )/a1 , μAi (a2 )/a2 , μAi (a3 )/a3 , μAi (a4 )/a4 }
(1)
where μAi (ak ) (k = 1 ÷ 4) are the values of the membership functions of the corresponding fuzzy sets Ai , reflecting the qualitative criteria for assessing the satisfaction of airlines. As a membership function that determines the ratio of the airline ak (k = 1 ÷ 4) to the qualitative assessment criterion Ai , a Gauss function of the form is chosen: μAi (ak ) = exp{−[ei (ak ) − 100]2 /σi2 }
(2)
where ei (ak ) is the consolidated assessment of experts regarding the airline ak , made on a 100-point scale for the satisfaction of the airline in terms of the i -th feature x i (i = 1 ÷ 5) (see Table 1); σ i 2 = 1089 is the density chosen empirically, which is the same for all cases of term fuzzification. Taking into account this formulation, based on the verbal model d 1 ÷ d 6 FIS in symbolic form looks like this: d 1 : (x 1 = A1 ) & (x 2 = A2 ) ⇒ (y = S); d 2 : (x 1 = A1 ) & (x 2 = A2 ) & (x 3 = A3 ) ⇒ (y = MS); d 3 : (x 1 = A1 ) & (x 2 = A2 ) & (x 3 = A3 ) & (x 4 = A4 ) & (x 5 = A5 ) ⇒ (y = P); d 4 : (x 1 = A1 ) & (x 2 = A2 ) & (x 4 = A4 ) & (x 5 = A5 ) ⇒ (y = VS); d 5 : (x 1 = A1 ) & (x 2 = A2 ) & (x 4 = ¬A4 ) & (x 5 = A5 ) ⇒ (y = S); d 6 : (x 1 = ¬A1 ) & (x 3 = ¬A3 ) & (x 5 = ¬A5 ) ⇒ (y = YS), where ∀j ∈ J = {0, 0.1, 0.2, …, 1} fuzzy sets from the right parts of the rules are restored by means of the corresponding membership functions [2]: S = satisfactory
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(airlines),M S (j) = j; MS = more than satisfactory, M MS (j) = j(1/2) ; P = perfect, 1, j = 1, VS = very satisfactory, M VS (j) = j2 ; US = unsatisfactory, μP (j) = 0,j < 1; M S (j) = 1 − j. The implementation of the rules using the Lukasiewicz implication μU×J (u, j) = min{1, 1 − μU (u) + μJ (j)} gave the desired functional solution in the matrix form
a1 R = a2 a3 a4
0 0.1647 0.0877 0.2573 0.3074
0.1 0.1647 0.0877 0.2573 0.3074
0.2 0.1647 0.0877 0.2573 0.3074
0.3 0.1647 0.0877 0.2573 0.3074
0.4 0.1647 0.0877 0.2573 0.3074
0.5 0.1647 0.0877 0.2573 0.3074
0.6 0.1647 0.0877 0.2573 0.3074
0.7 0.1647 0.0877 0.2573 0.3074
0.8 0.1647 0.0877 0.2573 0.3074
0.9 0.1647 0.0877 0.2573 0.3074
1 0.1647 0.9429 0.9429 0.8761
,
where, according to [3], the elements of the k-th line, as the values of the membership function of the fuzzy subset of the discrete universe J, form a fuzzy conclusion regarding the satisfaction of the k airline (k = 1 ÷ 4) in the context of consolidated expert assessments for its compliance factors x i (i = 1 ÷ 5). After defuzzification of these conclusions, numerical estimates of the logistics services of airlines were obtained, which are summarized in Table 6.
4 Identification of Weights of Evaluation Criteria The assessment of the attractiveness of an airline is made by experts based on the analysis and comparison of specific values of the criteria of the companies under study. This assessment will be the more accurate, the better the experts know the needs of consumers in this segment of the transportation market. Assume that by independent questioning of 15 passengers from different categories who make permanent trips on certain routes, expert assessments of the degree of importance of airline attractiveness factors x i (i = 1 ÷ 5) are determined. Each expert-passenger is provided with a questionnaire, where he is asked to place the variable xi according to the principle: the most important variable is designated by the number “1”, the next less important - by the number “2” and then in descending order of importance. After checking the rank scores for consistency, in the process of Internet expertise, the values of the normalized scores of the generalized weights of the airline attractiveness variables x i (i = 1 ÷ 5) are set, which are summarized in Table 2. To calculate the average value α i for the i group of normalized estimates of variables x i , an iterative equality of the form [4] weighted by the degrees of expert competence is used: m αi (t + 1) = wj (t)αij (3) j=1
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Table 2. Expert normalized estimates of generalized variable weights x i . Experts
Estimated variables x i (i = 1 ÷ 5) and their normalized values (α ij ) x1
x2
x3
x4
x5
01
0.300
0.250
0.225
0.150
0.075
02
0.300
0.250
0.225
0.075
0.150
14
0.300
0.225
0.250
0.075
0.150
15
0.300
0.250
0.150
0.225
0.075
4.350
3.550
2.800
2.325
1.975
…
where wj (t) is the weight characterizing the degree of competence of the j expert (j = 1 ÷ m) at time t. For each iteration step, the weights that determine the degrees of expert competence are established based on the following equalities: n ⎧ ⎨ wj (t) = [1/η(t)] αi (t) · αij (j = 1, m − 1), i=1 m m ⎩ wm (t) = 1 − wj (t), wj (t) = 1, j=1
j=1
where η(t) is a normalizing factor that ensures the transition to the next iteration step, which is determined by the formula n m η(t) = αi (t)αij . i=1
j=1
The process of determining group estimates of normalized values is iterative in nature, which ends when the following condition is met: {|αi (t + 1) − αi (t)|} ≤ ε, where ε is the allowable accuracy of calculations, which is set in advance by the user. Thus, using (3) in the 3rd approximation, normalized estimates of the generalized weights for groups i = 1 ÷ 5: α 1 (3) = 0.28995, α 2 (3) = 0.23760, α 3 (3) = 0.18721, α 4 (3) = 0.15449, α 5 (3) = 0.13075. The conclusion of the integral assessment of the consumer index, located in the range from 0 to 100, was carried out using the evaluation criterion [4]: R = 100 ×
5 i=1
αi (3)ei /[max{
5 i=1
αi (3)ei }]
(4)
where ei is an expert assessment of the airline’s satisfaction with respect to the i-th factor x i . At the same time, the minimum value of the R index reflects the minimum level of attractiveness of the airline, and vice versa, the maximum value of the index indicates the highest level of its competitiveness. As a result of applying (4), total values were obtained, which are summarized in Table 6.
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5 Estimating Airlines Using the Fuzzy Maximin Convolution Method As criteria for assessing the satisfaction of airlines ak (k = 1 ÷ 4), we use the evaluation concepts “ACCEPTABILITY” as one of the possible terms of linguistic variables x i (i = 1 ÷ 5). Based on (1) and (2), these terms are reflected by the corresponding fuzzy sets of the form Ai on a finite set of estimated airlines {a1 , a2 , a3 , a4 } in the following: • • • • •
ACCEPTABILITY (ticket price): A1 = {0.8353/a1 , 0.9123/a2 , 0.9429/a3 , 0.8133/a4 }; ACCEPTABILITY (reliability): A2 = {0.9123/a1 , 0.9283/a2 , 0.7427/a3 , 0.6926/a4 }; ACCEPTABILITY (frequency): A3 = {0.8761/a1 , 0.9429/a2 , 0.8353/a3 , 0.7905/a4 }; ACCEPTABILITY (service): A4 = {0.8563/a1 , 0.9560/a2 , 0.8948/a3 , 0.8353/a4 }; ACCEPTABILITY (type of aircraft): A5 = {0.8948/a1 , 0.9123/a2 , 0.8353/a3 , 0.8761/a4 }.
Next, a set of optimal alternatives [5–10] A is established by intersecting fuzzy sets containing airline scores according to the ACCEPTABLE criterion in the form:A = A1 ∩ A2 ∩ A3 ∩ A4 ∩ A5 , where the airline with the maximum degree of belonging to the fuzzy set A is considered satisfactory. In this case, the operation of crossing fuzzy sets corresponds to the choice of the minimum value for the alternative ak (k = 1 ÷ 4): μA (ak ) = min{μAi (ak )}. As a result, the set of optimal alternatives is formed as follows: i
A = {min{0.8353, 0.9123, 0.8761, 0.8563, 0.8948}, min{0.9123, 0.9283, 0.9429, 0.9560, 0.9123}, min{0.9429, 0.7427, 0.8353, 0.8948, 0.8353}, min{0.8133, 0.6926, 0.7905, 0.8353, 0.8761}} = {0.8353, 0.9123, 0.7427, 0.6926}. The most competitive airline is determined from the vector of priorities relative to alternative airlines: max{μA (ak )} = max{0.8353, 0.9123, 0.7427, 0.6926, the market of passenger air transportation in Azerbaijan is the airline a2 (Lufthansa), which corresponds to the value of 0.9123. The subsequent ranking of airlines is built in descending order: a1 (British Airways) → 0.8353, a3 (Turkish Airlines) → 0.7427, a4 (AZAL) → 0.6926. In the case of different degrees of importance of indicators x i (i = 1 ÷ 5), defined above as weights α i (3) (i = 1 ÷ 5), the set of optimal alternative airlines {a1 , a2 , a3 , a4 } is determined by intersecting fuzzy sets Ai : A = Aα1 1 ∩ Aα2 2 ∩ Aα3 3 ∩ Aα4 4 ∩ Aα5 5 , where the k-th airline (k = 1 ÷ 4) is considered to be the best, for which the condition: μA (ak ) = max{μA (ak )} Then, taking into account the weighted criteria Ai (a), the set of optimal alternatives is: A = {min{0.83530.28995 , 0.91230.23760 , 0.87610.18721 , 0.85630.15449 , 0.89480.13075 }; min{0.91230.28995 , 0.92830.23760 , 0.94290.18721 , 0.95600.15449 , 0.91230.13075 }; min{0.94290.28995 , 0.74270.23760 , 0.83530.18721 , 0.89480.15449 , 0.83530.13075 }; min{0.81330.28995 , 0.69260.23760 , 0.79050.18721 , 0.83530.15449 , 0.87610.13075 } = {0.94915, 0.97373, 0.93175, 0.91643}. As in the previous case, the most satisfactory airline is found from the expression: max{μA (ak )} = {0.94915, 0.97373, 0.93175, 0.91643}. Among the components of this
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vector, 0.97373 is the largest, which corresponds to the alternative a2 . This means that the best airline in terms of consumer appeal is Lufthansa. The subsequent ranking of airlines is built in descending order as: a1 (British Airways) → 0.94915, a3 (Turkish Airlines) → 0.93175, a4 (AZAL) → 0.91643.
6 Evaluation of Airlines by Pareto Rules and Bord Method The Pareto rule provides for the ranking of alternatives by determining pairwise preferences regarding evaluation criteria. For airlines ak (k = 1 ÷ 4) the results of the comparative analysis are summarized in Table 3. The most preferred airline is a2 , which contains 2 columns that do not contain the “−” character: columns a1 and a4 . Airline a1 contains only one column that does not contain a “−” character: column a4 . The remaining two airlines, namely a3 and a4 , do not contain any columns with a “+” symbol at all. This means that airline a2 is preferred over airlines a1 , a3 and a4 . It is followed by the airline a1 , which includes only one column a4 that does not contain the “−” symbol, which determines the preference for a1 over a3 and a4 . To compare a3 and a4 , the Pareto rule is again applied, which, due to its triviality, quite easily establishes the advantage of a3 over a4 . Table 3. Preference table based on pairwise comparisons of airlines. a1 a2 a3 a4 a3 a1 a2 a4 x1 − − + x1 + + + x2 − + + x2 − − + x3 − + + x3 − − + x4 − − + x4 + − + x5 − + + x5 − − − a2 a1 a3 a4 a4 a1 a2 a3 x1 + − + x1 − − − x2 + + + x2 − − − x3 + + + x3 − − − x4 + + + x4 − − − x5 + + + x5 − − +
Next, Bord’s selective rule is applied, according to which airlines are ranked by each factor x i (i = 1 ÷ 5) in descending order with the assignment of appropriate ranks to them (Table 4) and then the total rank is calculated for each decision (Table 5). The airline with the highest total rank is considered the best. As can be seen from Table 5, Lufthansa received the highest total score, which positions it as the best airline in the five-factor assessment of the selected alternatives.
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S. Imanova Table 4. Airline ranking in descending order.
Ranking
Airline benchmark x1
x2
x3
x4
x5
4
a4
a4
a4
a4
a3
3
a1
a3
a3
a1
a4
2
a2
a1
a1
a3
a1
1
a3
a2
a2
a2
a2
Table 5. Airline ranking using the Borda Method. Airlines
Project comparative evaluation indicators
British airways
x1
x2
x3
x4
x5
3
2
2
3
2
Total points
Order
12
2
Lufthansa
2
1
1
1
1
6
1
Turkish airlines
1
3
3
2
4
13
3
AZAL
4
4
4
4
3
19
4
Table 6. The results of the assessment of airlines in the air transportation market in Azerbaijan. Airlines
Fuzzy Delphi
FIS
Estimate
Estimate
Order
MaxMin convolution: Order
For the For the homogeneous case inhomogeneous case Estimate
Order
Estimate
Order
British Airways
87.87
2
0.9080
2
0.8353
2
0.9492
2
Lufthansa
91.08
1
0.9535
1
0.9123
1
0.9737
1
Turkish Airlines
87.25
3
0.8635
3
0.7427
3
0.9318
3
AZAL
84.17
4
0.8246
4
0.6926
4
0.9164
4
7 Conclusion As a result of applying the Fuzzy Delphi, FIS method, as well as the fuzzy maximin convolution method, integral satisfaction scores for British Airways, Lufthansa, Turkish Airlines and AZAL were obtained for the entire set of criteria x i (i = 1 ÷ 5). A comparative analysis of the results obtained by the three methods is presented in Table 6, from which it can be seen that the results completely coincide with respect to the positions
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of airlines. Moreover, this ranking is also confirmed by the results of evaluating these airlines using the rather trivial Pareto rule and the Borda Method.
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Customer Characteristics in Digital Marketing Model Gunay E. Imanova1(B)
and Gunel Imanova1,2
1 Azerbaijan State Oil and Industry University, 34 Azadlyg Avenue, Baku, Azerbaijan
[email protected], [email protected] 2 Azerbaijan State University of Economics, Istiglaliyyat Street 6, AZ1001 Baku, Azerbaijan
Abstract. Growth in e-commerce marketing and customers’ interest toward online shopping have changed the traditional way of ‘try and buy’ to online ordering of products. As a result, most of the brick and mortar companies and startups tend to strengthen their digital marketing strategies by creating e-commerce sites that appeal to customers. Online seller companies can understand their customers’ needs, wants, and preferences by analyzing the customer characteristics that influence their purchase decisions. In this research, personal characteristics that affect the consumer buying decision in online shopping are identified, weighted and analyzed using triangular fuzzy numbers and fuzzy AHP method. Investigated criteria are provided as customer’s age, occupation, economic situation, lifestyle, and personality and self-concept. Furthermore, based on the research it is identified that personal characteristics of customers have a significant impact in online retailing. Keywords: Digital marketing · Fuzzy AHP · Decision making · Consumer buying behavior · E-commerce
1 Introduction Today, marketing practices are highly affected by the global events such as pandemic, lockdown, economic crisis and following inflation, advanced and accessible technology, digital marketing and so forth. Therefore, dynamic marketing environment makes competition even fiercer, and companies become more customer-oriented. As a result, acquiring timely and relevant information about customer needs, wants and preferences, potential opportunities and threats, and competitive intelligence, need digitalization in marketing. Digitalization offers advantages such as reaching broader customer base and segments without; space restrictions for selling products, and country borders [1]. E-commerce marketing as part of digital marketing is the transaction of product and services and realized through B2B, B2C, B2E, G2C, C2C variations [2]. B2C or business to customer variant is the most popular one in e-commerce, where the companies such as Amazon, Alibaba, eBay, or Spotify sell products and services to the customers. Use of online shopping gained even more popularity after pandemic and lockdowns. Online seller companies should be aware of the several characteristics of customers that © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 164–171, 2023. https://doi.org/10.1007/978-3-031-25252-5_25
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can affect the consumer buying behavior and decision. Main characteristics that affect the consumer behavior can be classified as cultural, social, personal and psychological characteristics [3, 4]. Cultural factors involve sub topics such as culture and social classes [3]. Culture is reflected on customers’ needs and wants through the learned set of beliefs and values. Social factors comprised of factors such as family, groups, social roles and status [3]. Personal factors involve the influences such as customer’s age, occupation, economic situation, lifestyle and personality (and self-concept) [3]. Personal factors and their influence on online shopping behavior will be discussed throughout the research. Psychological factors comprised of factors such as perception, motivation, learning, beliefs and attitudes that further influence the consumer buying decision [3]. In this paper, main aim is to analyze and identify the relative importance of each pair of criteria based on triangular fuzzy numbers and fuzzy AHP method to understand the effect of several customer characteristics on consumer behavior during online shopping. Unfortunately, there are limited number of research about this subject and uncertainty and reliability is not always taken into account. The remaining part of the paper is structured as following. In Sect. 2, preliminary information is presented, and it is followed by the statement of the MCDM problem. In Sect. 4, solution method of the MCDM problem with an illustrative case is provided. Finally, conclusion points for the study are presented in Sect. 5.
2 Preliminaries Definition 1. Fuzzy numbers [5, 6]: Decision making process tends to be uncertain within the real-world environment, regarding the possibility of the given values. Besides, possible degrees of uncertainty or impreciseness related to given values remain unknown to the decision maker, because of the ill-defined data. In a fuzzy set, for each possible value of x, the assigned degree is given as μ(x) [0.1]. x0 ∈ R, where μM (x0 ) = 1
(1)
for any 0 ≤ α ≤ 1, Aα = x, μAα (x) ≥ α is a closed interval, where F(R) Definition 2. Random variables [5]: Random variables can be classified into two groups as continuous random variables and discrete random variables. Continuous variable which can be shown by X, can take infinite numerical outcomes of possible values of x. However, a discrete random variable, X can only be presented with countable distinct values. ˜ l , am , au ) is used to indicate Definition 3. Triangular fuzzy numbers [7] : Triplet A(a the triangular fuzzy number, where the membership is assigned using the formula (2). ⎧ 0, x ∈ (−∞, al ) ⎪ ⎪ ⎪ ⎨ x−al , x ∈ [a , a ] l m al (2) μA˜ (x) = am− c−x ⎪ , x ∈ [a m , au ] ⎪ au− am ⎪ ⎩ 0, x ∈ (au , +∞)
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Definition 4. Fuzzy MCDM model [8]: For multi-criteria decision-making process, DM makes assessments under fuzzy environment, and decisions are made based on multiple criteria in order to select the optimal alternative. Fuzzy sets theory provides the needed flexibility for the evaluation of data under the uncertainty.
3 Statement of the Problem The main aim of this research is to analyze and identify the relative importance of each pair of factors of personal characteristics that influence the online shopping behavior of customers, based on triangular fuzzy numbers and fuzzy AHP method. Companies can use the results of this evaluation to understand their customers in a better way. Moreover, sellers can utilize the results in their digital marketing strategies to increase the traffic in their website. Analyzed research indicate the most important factors that affect the consumer behavior [9] and consumer buying decisions in online markets [4, 10, 11]. Our research is characterized by 5 main criteria C = {c1 , c2 , c3 , c4 , c5 }. After analyzing the related literature, we suggest criteria to be feed based on the personality characteristics of the customers as the following: C1: Age: Age is an important factor that affects the purchase decision. Younger customers tend to use more online shopping than older generations. They are more interested in using the technology and evaluating the products and available information about offers [10]. In the research [4], it is found that age is positively correlated to online buying. C2: Occupation: Occupation is another important factor that affect the consumer buying decision. Customers with different jobs tend to need and want different products and services. For instance, white-collar employees need to wear suits, while workers in the construction sector need distinct apparel and may buy durable phones such as CAT smartphones [3]. C3: Income/Economic situation: Higher income consumers, who earn higher than $75.000 annually, tend to shop more online than lower income earner customers. The main reasons can be stated as the availability of internet, technology, medium for purchase such as computers and higher education levels of customers [4, 10, 11]. On the other hand, nowadays, customers use online shopping for acquiring the same products in the stores with the discounted prices. Therefore, lower income consumers can also prefer online shopping. C4: Lifestyle: Lifestyle is the other personality factor that affects the consumer behavior. Customers’ interests (about fashion, food, shopping), opinions (about business, products, events) and activities (sports, social activities) shape how he/she will act in the society [3, 9]. In the research [10], it is shown that there is a relationship between consumer online buying behavior and lifestyle.
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C5: Personality and self-concept: A customer’s distinct and unique personality affects his or her purchasing decision. Customer characteristics such as self-confidence, defensiveness, sociability, aggressiveness decide what the consumer buy and consume [3]. It can be defined as the complete behavior of an individual in different situations [9]. Consumers tend to buy products/services that match their own self-concept [3]. Decision makers provide the weights for the above given criteria and pairwise comparison matrix is created as it is shown in Table 1, which are defined in triangular fuzzy numbers. Table 1. Pairwise comparison matrix C1
C2
C3
C4
C5
C1
(1.1.1)
(2,3,4)
(1/3.1/2.1/1)
(1,2,3)
(1,2,3)
C2
(1/4, 1/3, 1/2)
(1.1.1)
(1/4.1/3.1/2)
(1/3.1/2.1/1)
(1/3.1/2.1/1)
C3
(1,2,3)
(2,3,4)
(1.1.1)
(1,2,3)
(1,2,3)
C4
(1/3.1/2.1/1)
(1,2,3)
(1/3.1/2.1/1)
(1.1.1)
(1,2,3)
C5
(1/3.1/2.1/1)
(1,2,3)
(1/3.1/2.1/1)
(1/3.1/2.1/1)
(1.1.1)
4 Solution of the Problem In this paper, we analyze the importance of criteria based on triangular fuzzy numbers and suggest the use of fuzzy AHP method [12] for pairwise comparison of the provided criteria and deriving consistency ratio. Step 1: Through evaluating the priority values in fuzzy numbers c˜ ij = (cij,l , cij,m , cij,u ), (i, j = 1, 2, ..., n), pair-wise comparison reciprocal fuzzy matrix indicated as C˜ is created for the given criteria C1 ,C2 ,…,Cn . Three crisp matrices Cl , Cm , Cu are obtained by dividing the fuzzy matrix C˜ as it is given below [13–16].
(3)
Step 2: The acquired matrices are used in order to calculate the system of fuzzy linear homogeneous equations (Tables 2, 3 and 4). Cl wl + Cm wm + Cu wu − λl wl − λm wm − λu wu = 0
(4)
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where: Cl = 2Cl + Cm = 3
Cm = Cl + 4Cm + Cu = 6
Cu = Cm + 2Cu = 3
Table 2. Cl 1
2
0
1
1
0.25
1
0
0
0
1.00
2.00
1
1
1
0.33
1.00
0.33
1
1
0.33
1.00
0.33
0.33
1
Table 3. Cm 1
3
0.5
2
2
0.33
1
0.33
0.5
0.5
2
3
1
2
2
0.5
2
0.5
1
2
0.50
2
0.5
0.5
1
Table 4. Cu 1
4
1
3
3
0.5
1
0.5
1
1
3
4
1
3
3
1
3
1
1
3
1
3
1
0.024
1
Next, we compute the following matrices: Cl = 2Cl + Cm Cm = Cl + 4Cm + Cu Cu = Cm + 2Cu The matrices are given in Tables 5, 6 and 7.
(5)
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Table 5. Cl 3.00
7.00
1.17
4.00
4.00
0,83
3.00
0,83
1.17
1.17
4.00
7.00
3.00
4.00
4.00
1.17
4.00
1.17
3.00
4.00
1.17
4.00
1.17
1.17
3.00
Table 6. Cm 6.00
18.00
3,33
12.00
12.00
2.08
6.00
2.08
3,33
3,33
12.00
18.00
6.00
12.00
12.00
3,33
12.00
3,33
6.00
12.00
3,33
12.00
3,33
2,36
6.00
Table 7. Cu 3.00
11.00
2,50
8.00
8.00
1.33
3.00
1,33
2,50
2,50
8.00
11.00
3.00
8.00
8.00
2,50
8.00
2,50
3.00
8.00
2,50
8.00
2,50
0.55
3.00
Step 3: Eigenvalues λl , λm, λu of Cl , Cm and Cu are acquired using MATLAB software program: λl = 1.49 λm = 5.29 λu = 5.3 Moreover, to obtain consistency index and consistency ratio, the following formulas are used: CI =
λmax − n n−1
(6)
CI RI
(7)
CR =
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5 Conclusion Increasing demand and interest of consumers towards using digital marketing and buying online have changed the marketing and retailing strategies of many companies. Brickand-mortar stores also become online sellers by developing their e-commerce websites to target broader customer base. For effective and efficient online retailing, sellers should also know about the characteristics of customers that influence their online purchase decisions. There are several characteristics of customers, and the main subject of this research is related to personal characteristics. Personal characteristics involve customer’s age, occupation, economic situation, lifestyle, and personality and self-concept. In this research, main aim is to analyze and identify the relative importance of each pair of the mentioned criteria based on triangular fuzzy numbers and fuzzy AHP method. The proposed method can also be applied for different decision-making problems related to consumer behavior and other marketing practices, regarding the uncertainty.
References 1. Teo, T.S., Yeong, Y.D.: Assessing the consumer decision process in the digital marketplace. Omega 31(5), 349–363 (2003) 2. Piñeiro-Otero, T., Martínez-Rolán, X.: Understanding digital marketing—basics and actions. In: Machado, C., Davim, J. (eds.) MBA. Management and Industrial Engineering, pp. 37–74. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-28281-7_2 3. Kotler, P., Armstrong, G., Opresnik, O.M.: Harlow: Principles of Marketing. England, Pearson (2018) 4. Kanchan, U., Kumar, N., Gupta, A.: A study of online purchase behaviour of customers in India. ICTACT J. Manag. Stud. 1(3), 136–142 (2015). https://doi.org/10.21917/ijms.2015. 0019 5. Aliev, R.A., Alizadeh, A., Aliyev, R.R., Huseynov, O.H.: Arithmetic of Z-Numbers, the: Theory and Applications. World Scientific (2015) 6. Zadeh, L.A., Aliev, R.A.: Fuzzy Logic Theory and Applications: Part I and Part II - Singapore: World Sci., 692 p. (2018, 2019) 7. Aliev, R.A., Aliev, R.R.: Soft Computing and Its Application. World Scientific (2001) 8. Dalalah, D., Hayajneh, M., Batieha, F.: A fuzzy multi-criteria decision making model for supplier selection. Expert Syst. Appl. 38(7), 8384–8391 (2011). https://doi.org/10.1016/j. eswa.2011.01.031 9. Gajjar, N.B.: Factors affecting consumer behavior. Int. J. Res. Hum. Soc. Sci. 1(2), 10–15 (2013) 10. Li, N., Zhang, P.: Consumer online shopping attitudes and behavior: an assessment of research. In: AMCIS 2002 Proceedings, vol. 74 (2002). https://aisel.aisnet.org/amcis2002/74 11. Lohse, G.L., Bellman, S., Johnson, E.J.: Consumer buying behavior on the Internet: findings from panel data. J. Interact. Mark. 14(1), 15–29 (2000). https://doi.org/10.1002/(SICI)15206653(200024)14:1%3c15::AID-DIR2%3e3.0.CO;2-C 12. Mehdiyev, N.: Application of fuzzy AHP-TOPSIS method for software package selection. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 827–834. Springer, Cham (2020). https://doi.org/10. 1007/978-3-030-35249-3_109
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13. Dovlatova, K.J.: Estimation of benchmarking influence in buyer’s decision-making process by using fuzzy AHP. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 173–182. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-92127-9_26 14. Prašˇcevi´c, N., Prašˇcevi´c, Ž.: Application of fuzzy AHP method based on eigenvalues for decision making in construction industry. Tehniˇcki vjesnik/Techn. Gaz. 23(1), 57–64 (2016). https://doi.org/10.17559/TV-20140212113942 15. Aliev, R.A., Gardashova, L.A.: Z-set based approach to control system design. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 10–21. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-640 58-3_2 16. Aliyeva, K.R.: Demand forecasting for manufacturing under Z information. Procedia Comput. Sci. 120, 509–514 (2017). https://doi.org/10.1016/j.procs.2017.11.272
Estimation of Countries’ Economic Development by Using Z-Number Theory Rafig R. Aliyev(B) Azerbaijan State Oil and Industry University, Azadlyg Avenue, 20, AZ1010 Baku, Azerbaijan [email protected]
Abstract. The economic development level of countries or regions is main indicator for measuring progress in their economy. This problem has increased attention of the scientists and practitioners in the recent past. The level of countries’ economic development mainly is characterized by the level of GDP. GDP per capita, unemployment rate and others. Both in classical and fuzzy modeling of economic development level of countries unfortunately reliability of available information is not taken into consideration. In this paper Z-rule based method for estimation of economic development level of countries which takes into account bimodal information processing is suggested. The numerical example including six Z-rules is tested. Keywords: Z-set · Z-number · Similarity of Z-sets and Z-numbers · Z-approximate reasoning · Economic development · GDP
1 Introduction In the literature economic development level of countries is considered as a function of macroeconomic factor such as GDP, GDP per capita, population size, unemployment, and others. In [1] economic development of countries is considered. Neural network model is used for predicting the country’s development level. This model describes relationship between economic development and different economic, governance indicators. Also, sensitivity analysis for estimation of relative importance of these factors in prediction is investigated. Local economic development problem is investigated in [2]. Objective analysis of the economic development level of countries is given in [3]. Classifying countries in optimal number of groups which characterizes different level of economic development is performed. Authors propose a composite index for estimation of the level of economic development of countries. Classification of countries into specific groups is based on this suggested index. In [4] authors investigate economic development level of regions and countries with finance and growth nexus. Clustering for dividing countries into groups for identification of the level of development also is considered in [5]. This clustering approach is based on hierarchical clustering using Euclidean distance. Classification of countries into specific group is investigated. In [6] identification of main factors that can be influenced to economic level of countries is considered. Different socio-economic indicators were investigated for construction of relationship between dependent and independent variables. As model of © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 172–179, 2023. https://doi.org/10.1007/978-3-031-25252-5_26
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relationship statistical regression model is used. In the paper [7] author presents powerful approach to model for evaluating the level of economic development of countries and regions. Main advantage of the proposed model is fact that it is based on fuzzy logic and it takes into account vagueness and uncertainty of existing information declared by experts. It is shown that economic division of countries is consequence of the level of different indicators, such as GDP, GDP per capita, unemployment rate, industrial growth, etc. Authors suggest If-Then fuzzy model in which antecedent variables are GDP, GDP per capita, and unemployment rate and consequent variable is economic development level of countries. By using approximate reasoning algorithm country’s economic development level is calculated. Both in classical and fuzzy modeling of economic development level of countries unfortunately reliability of available information is not taken into consideration. To deal with real-life problems that are characterized not only crisp or fuzzy values of variable of interest same time with reliability of them prof. L. Zadeh suggested Znumber conception. Basic objective of this paper is to develop the Z-information-based model to predict the country’s economic level by using some macroeconomic indicators such as GDP, GDP per capita, and unemployment rate (for medium population). The paper is structured as follows: Sect. 2 includes some preliminaries on Z-number theory. In the Sect. 3 statement of the problem is given. In Sect. 4 new approach to solution of stated problem is considered. The final section offers some conclusions.
2 Preliminaries Definition 1. Continuous Z-number. [8–10]. A continuous Z-number is an ordered pair Z = (A, B) where A is a continuous fuzzy number playing a role of a fuzzy constraint on values that a random variable X may take: X is A, B is a continuous fuzzy number with a membership function μB : [0, 1] → [0, 1], playing a role of a fuzzy constraint on the probability measure of A: P(A) = μA (x)p(x)dx is B. R
Definition 2. A discrete Z-number [8, 9]. A discrete Z-number is an ordered pair Z = (A, B) where A is a discrete fuzzy number which describes a fuzzy constraint on values that a random variable X may take – “X is A”, and B is a discrete fuzzy number with a membership function μB : {b1 , ..., bn } → [0, 1], {b1 , ..., bn } ⊂ [0, 1], which describes a fuzzy constraint on the probability measure of A : P(A) is B Definition 3. Z-rules [11]. Rule 1: If X1 is ZX1 ,1 = (AX1 ,1 , BX1 ,1 ) and , … , and Xm is ZXm ,1 = (AXm ,1 , BXm ,1 ) then Y is ZY = (AY ,1 , BY ,1 ).
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Rule 2: If X1 is ZX1 ,2 = (AX1 ,2 , BX1 ,2 ) and , … , and Xm is ZXm ,2 = (AXm ,2 , BXm ,2 ) then Y is ZY = (AY ,2 , BY ,2 ). . . Rule n: If X1 is ZX1 ,n = (AX1 ,n , BX1 ,n ) and , … , and Xm is ZXm ,n = (AXm ,n , BXm ,n ) then Y is ZY = (AY ,n , BY ,n ). Definition 4. Similarity of Z-numbers. Similarity of Z-numbers Z1 , Z2 is computed as follows: S(Z1 , Z2 ) =
1 (S(A1 , A2 ) + S(B1 , B2 ) + S(G1 , G2 )) 3
(1)
where S(A1 , A2 ) and S(B1 , B2 ) are values of Jaccard similarity of fuzzy numbers. S(G1 , G2 ) is similarity of the sets of probability distributions. Definition 5. Jaccard similarity measure [11, 12]. Jaccard similarity measure between Z-number valued vectors is represented as ⎛ m ⎜ 1 ⎜ w Jsi = Z Aw ×⎜ j , Bj K ⎝2 j=1 k=1 K
+
1 K 2 k=1
K
μAi (xk )
2
+
μAi (xk ) · μAid (xk )
k=1 K k=1
μAid (xk )
2
K
−
k=1
μAi (xk ) · μAid (xk )
(2)
⎞
μBi (xk ) · μBid (xk )
⎟ ⎟ k=1 ⎟ K K ⎠
2
2 μBi (xk ) · μBid (xk ) μBi (xk ) + μBid (xk ) − k=1
k=1
Definition 6. Similarity between probability distributions. 1 , S(G1 , G2 ) = 1 + Dset (G1 , G2 ) n
Dset (G1 , G2 ) =
i=1
αi Dset (G1αi , G2αi ) n
(3) αi
i=1
Dset (G1αi , G2αi ) = max{maxp1 ∈Gαi (minp2 ∈Gαi D(p1 , p2 )), maxp2 ∈Gαi (minp1 ∈Gαi D(p1 , p2 ))} 1
2
2
1
αi ∈ (0, 1] D(p1 , p2 ) is computed as 1 (D(p1 , p) + D(p2 , p)), 2 p1 (x) + p2 (x) ,x ∈ X. p(x) = 2
D(p1 , p2 ) =
(4)
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3 Statement of the Problem Given the following Z-rules:
1. If (GDP is (low, very sure)) and (per capita is (low, very sure)) and (unemployment rate is (medium, very sure)), then (the level of economic development is (low, sure)) 2. If (GDP is (medium, very sure)) and (per capita is (medium, very sure)) and (unemployment rate is (low, very sure)), then (the level of economic development is (medium, sure)). 3. If (GDP is (high, very sure)) and (per capita is (medium, very sure)) and (unemployment rate is (medium, very sure)), then (the level of economic development is (medium, sure)). 4. If (GDP is (medium, very sure)) and (per capita is (medium, very sure)) and (unemployment rate is (high, very sure)), then (the level of economic development is (low, sure)). 5. If (GDP is (high, very sure)) and (per capita is (high, very sure)) and (unemployment rate is (low, very sure)), then (the level of economic development is (high, sure)). 6. If (GDP is (medium, very sure)) and (per capita is (high, very sure)) and (unemployment rate is (medium, very sure)), then (the level of economic development is (high, sure)). 7. If (GDP is (low, very sure)) and (per capita is (high, very sure)) and (unemployment rate is (high, very sure)), then (the level of economic development is (medium, sure)).
(5)
and investigated country indicators (GDP, per capita and unemployment rate) find the Z-value of level of economic development of the country. Corresponding to the rules (5) reliability linguistic terms are sure = {0.7, 0.8, 0.9}; very sure = {0.8, 0.85, 0.9}. Codebooks of linguistic terms in (5) are shown in Figs. 1, 2, 3, 4 and 5.
Low
Medium
1
High
0.8 0.6 0.4 0.2 0 -1
1
3
5
7
9
Fig. 1. Membership functions for the level of economic development
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1
Medium
Low
High
0.8 0.6 0.4 0.2 0 0
10000 20000 30000 40000 50000
Fig. 2. Membership functions for GDP per capita
1 Low
Medium
High
0.8 0.6 0.4 0.2 0 0
10
20
30
40
Fig. 3. Membership functions for Unemployment
1
VL
L
ME
H
VH
0.8 0.6 0.4 0.2 0 0
100000 200000 300000 400000 500000 600000 700000 Fig. 4. Membership functions for GDP (Million USD)
Estimation of Countries’ Economic Development by Using Z-Number Theory
Very sure
Sure
1
177
0.8 0.6 0.4 0.2 0 0.7
0.75
0.8
0.85
0.9
Fig. 5. Membership functions for reliability of Z-numbers
4 Solution of the Problem The problem is solved as follows: For each rule in (5) similarity of current observation Z = (ZX 1 , ZX 2 , ZX 3 ) and vector of rule antecedents is computed as a minimum similarity: Sv (Z , Zj ) = mini=1,...,3 S(ZX i ZXi ,j ), j = 1, ..., 6,
(6)
S(ZX i ZXi ,j ) is similarity of Z-numbers. Resulting output (level of economic development) is computed as ZY =
n
wj ZY ,j ,
(7)
j=1
where ZY ,j is the Z-valued consequent of the j-th rule, Sv (Z , Zj ) , wj = n k=1 Sv (Z , Zk )
(8)
j = 1, ..., 6; k = 1, ..., 6 are coefficients of linear interpolation. Taking into account Codebooks given in Figs. 1, 2, 3, 4 and 5 rules can be presented as 1. If (GDP is ((100, 100, 700), (0.8, 0.85, 0.9))) and (per capita is ((0, 0, 30), (0.8, 0.85, 0.9))) and (unemployment rate is ((0, 10, 20), (0.8, 0.85, 0.9))), then (the level of economic development is ((0, 0, 10), (0.7, 0.8, 0.9))) 2. If (GDP is ((100, 300, 700), (0.8, 0.85, 0.9))) and (per capita is ((0, 15, 30), (0.8, 0.85, 0.9))) and (unemployment rate is ((0, 0, 20), (0.8, 0.85, 0.9))), then (the level of economic development is ((0, 5, 10), (0.7, 0.8, 0.9))). 3. If (GDP is ((100, 700, 700), (0.8, 0.85, 0.9))) and (per capita is ((0, 15, 30), (0.8, 0.85, 0.9))) and (unemployment rate is ((0, 10, 20), (0.8, 0.85, 0.9))), then (the level of economic development is ((0,5,10), (0.7,0.8,0.9))). 4. If (GDP is ((100, 300, 700), (0.8, 0.85, 0.9))) and (per capita is ((0, 15, 30), (0.8, 0.85, 0.9))) and (unemployment rate is ((0, 20, 20), (0.8, 0.85, 0.9))), then (the level of economic development is ((0, 0, 10), (0.7, 0.8, 0.9))).
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5. If (GDP is ((100, 700, 700), (0.8, 0.85, 0.9))) and (per capita is ((0, 30, 30), (0.8, 0.85, 0.9))) and (unemployment rate is ((0, 0, 10), (0.8, 0.85, 0.9))), then (the level of economic development is ((5, 10, 10), (0.7, 0.8, 0.9))). 6. If (GDP is ((100, 300, 700), (0.8, 0.85, 0.9))) and (per capita is ((0, 30, 30), (0.8, 0.85, 0.9))) and (unemployment rate is ((0, 10, 20), (0.8, 0.85, 0.9))), then (the level of economic development is ((5, 10, 10), (0.7, 0.8, 0.9))). 7. If (GDP is ((100, 100, 700), (0.8, 0.85, 0.9))) and (per capita is ((0, 30, 30), (0.8, 0.85, 0.9))) and (unemployment rate is ((0, 20, 20),(0.8, 0.85, 0.9))), then (the level of economic development is ((0, 5, 10), (0.7, 0.8, 0.9))). Assume that economic development level of the investigated country is characterized by following information GDP is ((100, 200, 700), (0.8, 0.85, 0.9)) per capita is((0, 20, 30), (0.8, 0.85, 0.9)) unemployment rate is ((0, 5, 15), (0.75, 0.8, 0.85)) In accordance with Sect. 4 similarity between the given data and antecedent vector of rules in (5) is calculated as S(Z , Z1 ) = 0.44, S(Z , Z2 ) = 0.49, S(Z , Z3 ) = 0.44, S(Z , Z4 ) = 0.33, S(Z , Z5 ) = 0.39, S(Z , Z6 ) = 0.44, S(Z , Z7 ) = 0.33. By using (8) interpolation weights are calculated for activated rules. Here threshold level for similarity is 0.4. w1 = 0.24, w2 = 0.27, w3 = 0.24, w6 = 0.24 . Finally resulting information economic development level of considered country is calculated by using (7) Z = w1 Z1 + w2 Z2 + w3 Z3 + w6 Z6
Z = ((1.22, 5, 10), (0.37, 0.44, 0.53))
So economic development level of the considered country is “about 5” with reliability about 45%.
5 Conclusion The estimation of economic development level of regions and countries is challenging problem in the evaluation of their sizes. In existing literature general approach to analysis of this problem is based on statistical and rarely on fuzzy logic methods. Unfortunately, both in statistical and fuzzy approaches to evaluation of countries’ or regions’ economic development level reliability of decision relevant information in existence is not taken into account. Basic objective of this paper was to develop the Z-information-based [13, 14] model to predict the country’s economic level by using some macroeconomic indicators such as GDP, GDP per capita, and unemployment rate (for medium population). The
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suggested method is based on Z-number similarity-based approximate reasoning taking into consideration ambiguity and uncertainty described both fuzzy and probabilistic measures. Numerical example given in the study shows validity of proposed method of evaluation of economic development level of countries.
References 1. Ahmad, Z., Saleem, A.: Predicting level of development for different countries. J. Sustain. Dev. 5(11), 15–31 (2012). https://doi.org/10.5539/jsd.v5n11p15 2. Greenwood, D.T., Holt, R.P.F.: Local Economic Development in the 21st Century: Quality of Life and Sustainability, 232 p. (2014) 3. Nastu, A., Stancu, S., Dumitrache, A.: Characterizing the level of economic development of countries. In: Proceedings of the International Conference on Applied Statistics, vol. 1(1), pp. 343–354 (2019). https://doi.org/10.2478/icas-2019-0030 4. Nguyena, Y.N., Brownb, K., Skullyb, M.: Economic development levels and the finance and growth nexus (2016). https://doi.org/10.13140/RG.2.1.5126.5684 5. Vazquez, S.T., Sumner, A.: Beyond low and middle income countries: what if there were five clusters of developing countries? Poverty and inequality research cluster, p. 404 (2012) 6. Popa, D.I.: Influence factors of the economic development level across European countries. Rom. Stat. Rev. 64(2), 3–16 (2016) 7. Stojic, G.: Using fuzzy logic for evaluating the level of countries’ (regions’) economic development. Panoeconomicus 3, 293–310 (2012). https://doi.org/10.2298/PAN1203293S 8. Zadeh, L.A.: A note on Z-numbers. Inf. Sci. 181(14), 2923–2932 (2011) 9. Aliev, R.A., Huseynov, O.H., Aliyev, R.R., Alizadeh, A.V.: The Arithmetic of Z-Numbers: Theory and Applications. World Scientific, Singapore (2015). https://doi.org/10.1142/9575 10. 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 11. Aliyev, R.R.: Fuzzy logic’s Z-extension-based decision tools and their applications. dissertation work for the degree of Doctor of Philosophy, Baku, Azerbaijan, 104 p. (2021) 12. Aliyev, R.R.: Similarity based multi-attribute decision making under Z-information. bQuadrat Verlag, Germany, pp. 33–39 (2015) 13. Aliev, R.A., Gardashova, L.A.: Z-set based approach to control system design. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 10–21. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-640 58-3_2 14. Nuriyev, A., Baysal, A.B.: Z-Numbers-based approach to hotel service quality assessment. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 85–94. Springer, Cham (2022). https://doi.org/10.1007/ 978-3-030-92127-9_15
Fuzzy Approach to Explainable Artificial Intelligence Alexey Averkin1,2
and Sergey Yarushev3(B)
1 Federal Research Centre of Informatics and Computer Science of RAS, Moscow, Vavilova,
42, Moscow, Russia 2 Educational and Scientific Laboratory of Artificial Intelligence, Neuro-technologies and
Business Analytics, Plekhanov Russian University of Economics, Stremyanny Lane, 36, Moscow, Russia 3 Departments of Informatics, Plekhanov Russian University of Economics, Stremyanny Lane, 36, Moscow, Russia [email protected]
Abstract. The widespread introduction of artificial intelligence systems in all areas of human activity imposes requirements of responsibility on these systems. Systems operating in critical areas such as healthcare, economics, and security systems based on artificial neural network models should have an explanatory apparatus to be able to evaluate not only the recognition, prediction, or recommendation accuracy familiar to everyone, but also to show the algorithm for getting result of neural network working. In this paper, we investigate methods of explainable artificial intelligence for rules extraction from artificial neural networks, which are based on the fuzzy logic. Keywords: Fuzzy logic · Machine learning · Explainable artificial intelligence · Neural networks · Decision tree
1 Introduction Research in the field of explanatory artificial intelligence has been actively conducted since the mass introduction and application of artificial intelligence methods, in particular artificial neural networks, began. The reason was the inability of Artificial neural networks (ANN) to give an answer to a simple question – how was the result achieved? ANN, including deep learning networks, already surpass human capabilities in many tasks, for example, the task of image recognition or the search for regularities. But the mass introduction of such technologies was followed by a few problems, because for the result to be trusted, it is necessary to determine based on which factors ANN made a particular decision. From a legal point of view, restrictions are also imposed, because it is impossible to justify legally accepted decisions by artificial intelligence. To solve these problems, scientists around the world are working on the creation of explanatory artificial intelligence (XAI). One of the approaches to creating models based on ANN is to extract rules from them based on fuzzy logic methods, genetic algorithms, or decision © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 180–187, 2023. https://doi.org/10.1007/978-3-031-25252-5_27
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trees. In this paper, we will consider the operation of decision trees in the problem of extracting rules from ANN. One of the most important fields of application neural networks is the time series forecasting. And here this is extremely important to understand how an artificial neural network made a particular decision. And one of the variations of solving this problem is fuzzy logic theory application. To begin with, let’s say a few words about the time series and importance of rules extraction from ANN when working with time series. The time series is controlled by two main forces - time and events that affect the change in the values of the time series over time. Most of these events are characterized by some uncertainty. Each time series point can be correlated with a fuzzy variable with a certain membership function. Lotfi Zadeh has suggested the fuzzy logic theory in 1965, thanks to which it is possible to describe qualitative fuzzy concepts and knowledge about the surrounding world, and later operate with them to obtain new information. The use of this concept allows us to formalize linguistic information for the construction of mathematical models. The concept of a fuzzy set is based on the proposition that the elements that make up this fuzzy set, as well as having common properties, can possess it and, therefore, belong to this set to varying degrees. Nowadays, XAI is a prominent and fruitful research field where many of Zadeh’s contributions can become crucial if they are carefully considered and thoroughly developed. It is worth noting that about 30% of publications in Scopus related to XAI, dated back to 2017 or earlier, came from authors well recognized in the Fuzzy Logic field. This is mainly due to the commitment of the fuzzy community to produce interpretable fuzzy systems since interpretability is deeply rooted in the fundamentals of Fuzzy Logic. Since 2011, L. Zadeh (Father of Fuzzy Logic, co-inventor of Z-Transform, and AI Hall-of-Fame inductee) had been involved in Z Advanced Computing, Inc. (ZAC) and was one of the ZAC’s inventors. ZAC is the pioneer Cognitive Explainable-AI (Artificial Intelligence) (Cognitive XAI) technologies. The Cognitive Explainable-AI (Artificial Intelligence) approach use the results of Prof. Rafic Aliev, Prof. Ronald Yager, Prof. Mo Jamshidi [1].
2 Review of Fuzzy Rules Extraction Algorithms Research in the development of explanatory systems has been going on for a long time. The current state of research in the development of explanatory artificial intelligence systems can be divided into three stages: the first stage (since 1970) - the development of expert systems, the second stage (mid-1980s) - the transition from expert systems to knowledge-based systems, and the third (since 2010) - the study of deep architectures of artificial neural networks, which required new global research on the construction of explainable systems. The most interesting direction in the development of explanatory AI models is rule extraction using neuro-fuzzy models. Fuzzy rule-based systems (FRBS) developed with fuzzy logic have become a field of active research over the past few years. These algorithms have proven their strengths in tasks such as managing complex systems, creating fuzzy controls. The relationship between both approaches (ANN and FRBS) has been carefully studied and shown to be equivalent. This leads to two important conclusions.
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First, you can apply what was found for one of the models to another. Second, we can translate the knowledge embedded in the neural network into a more cognitively acceptable language - fuzzy rules. In other words, we get a semantic interpretation of neural networks [2, 3]. To get a semantic interpretation of the deep learning black box, neural networks can be used instead of the last fully connected layer. For example, ANFIS (Adaptive Neural Fuzzy System) is a multi-layer feedforward network. This architecture has five layers such as a fuzzy layer, a production layer, a normalization layer, a defuzzification layer, and an output layer. ANFIS combines the advantages of a neural network and fuzzy logic. Below is a classification of the most well-known neuro-fuzzy approaches. There are three techniques for combining artificial neural networks (ANNs) and fuzzy models: [4, 5]: 1. neuro-FIS, in which ANN is used as a tool in fuzzy models. 2. fuzzy ANNs, in which the classical ANN models are fuzzified. 3. neuro-fuzzy hybrid systems, in which fuzzy systems and ANN are combined into hybrid systems. Based on these techniques, neuro-fuzzy models can be divided into three classes [6, 7]. Cooperative neuro-fuzzy models. In this case, part of the ANN is initially used to define fuzzy sets and/or fuzzy rules, where only the resulting fuzzy system is subsequently executed. In the learning process, membership functions are determined, and fuzzy rules are formed based on the training sample. Here the main task of the neural network is to select the parameters of the fuzzy system. Parallel neuro-fuzzy models. The neural network in this type of model works in parallel with the fuzzy system, providing input to the fuzzy system or changing the output of the fuzzy system. A neural network can also be a post-processor of the output data from a fuzzy system. Hybrid neuro-fuzzy models. The fuzzy system uses a training method, as does the ANN, to adjust its parameters based on the training data. Among the presented classes of models, models of this class are most popular, as evidenced by their application in a wide range of real problems [8–11]. Among the most popular hybrid models are the following architectures. Fuzzy Adaptive Learning Control Network (FALCON) [12], which has a five-layer architecture. There are two linguistic nodes per one output variable. The first node works with a training sample (training pattern), the second is the input for the entire system. The first hidden layer labels the input sample according to membership functions. The second layer defines the rules and their parameters. Training takes place based on a hybrid unsupervised algorithm to determine the membership function, the rule base and uses the gradient descent algorithm to optimize and select the final parameters of the membership function. The adaptive neuro-fuzzy inference system ANFIS [13] is a well-known neuro-fuzzy model that has been applied in many applications and research areas [14]. Moreover, a comparison of the architectures of neural fuzzy networks showed that ANFIS shows
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the minimum error in the prediction task. The main disadvantage of the ANFIS model is that it places heavy demands on computing power [15]. The Generalized Approximate Intelligent Reasoning Control (GARIC) [16] system is a neuro-fuzzy system using two neural network modules, an action selection module, and a state assessment module, which is responsible for assessing the quality of the action selection by the previous module. GARIC is a five-layer feedforward network. The Neural Fuzzy Controller (NEFCON) [17] was developed to implement a Mamdani-type fuzzy inference system. Links are defined using fuzzy rules. The input layer is a fuzzifier, and the output layer solves the defuzzification problem. A network is trained based on a hybrid reinforcement learning algorithm and an error backpropagation algorithm. The fuzzy inference and neural network system in fuzzy inference software (FINEST) [18] is a parameter setting system. Tuning of fuzzy predicates, implication function and combinatorial function is performed. The system for automatically building a neural network of fuzzy inference (SONFIN) [19] is in essence like the NEFCON controller, but instead of implementing fuzzy inference of the Mamdani type, it implements the inference of the Takagi-Sugeno type. In this network, the input sample is processed using the aligned clustering algorithm. When identifying the structure of the precondition part, the input space is divided in a flexible manner according to an algorithm based on aligned clustering. The tuning of system parameters is partially implemented using the least squares method, the preconditions are tuned using the backpropagation method. Dynamically developing fuzzy neural network (dmEfuNN) and (EFuNN) [20]. In EFuNN, all nodes are created in the learning process. The first layer passes the training data to the second, which calculates the degree of fit with a predefined membership function. The third layer contains sets of fuzzy rules, which are prototypes of input-output data, which can be represented as hyperspheres of fuzzy input and output spaces. The fourth layer calculates the degree to which the output membership function has labeled the input, and the fifth layer defuzzifies and calculates the numerical values of the output variable. DmEfuNN is a modified version of EFuNN. The main idea is that for all input vectors a set of rules is dynamically selected, the activation values of which are used to calculate the dynamic parameters of the output function. While EFuNN implements Mamdani-type fuzzy rules, dmEFuNN uses Takagi-Sugeno type.
3 Rule Extraction Algorithm Based on Decision Trees The most well-known disadvantage of ANN is that it is impossible to determine how the neural network achieved the result. ANN basically work according to the principle: received a training sample, trained, received input data, processed, and gave the result. What happens inside the neural network and how the neural network makes this or that decision is unclear. Accordingly, as mentioned in previous chapters, these problems impose significant restrictions on the use of artificial intelligence algorithms in real tasks, especially if these tasks are critically important for a person or his health. To solve the problem of extracting knowledge from neural networks, many algorithms have been developed, mainly they work with ANN weights and impose significant restrictions on the neural network architecture.
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In this paper, we will consider an algorithm for extracting rules based on decision trees, which does not impose specific requirements on the neural network architecture. This algorithm builds decision trees from a trained ANN. The advantage of this algorithm is that it can work with absolutely any artificial neural network of any architecture, regardless of the presence of feedbacks, training methods or types of input and output data. The decision tree obtained from the neural network will be a classification tree. 3.1 Rule Extraction Algorithm Using decision trees to extract rules from ANN allows you to extract a humanunderstandable structure from a neural network and convert the output result of the network into a hierarchical sequence of IF-THEN rules. The algorithm classifies the input data in the neural network and analyzes the network itself, thereby extracting classification rules from it separately for each class. The algorithm for constructing a decision tree approximating the operation of a trained artificial neural network looks like this: 1. Build and train the original neural network - “oracle”. 2. Calculate the value q = max (0, minSamples − S), where minSamples is the minimal number of training examples used in each node of the tree, S is the current training sample (respectively S is its volume). Thus, q is the number of additional examples that need to be generated. 3. Based on the evaluation of the distribution of features from S, q new training examples are randomly generated. 4. The “oracle” recognizes that both new examples and old examples from the set S belong to one or another class. 5. Add the generated examples to the set S. 6. We are splitting up a set of buildings as a free algorithm for building buildings. 7. For each of the resulting subsets – recursion from step 2 until the local or global completion criterion of the algorithm is met. The maximum allowable depth of the generated tree is used as a global criterion for the completion of the algorithm. The local stopping criterion is met, if there are examples in this node of the tree that belong to only one class, or the signs that allow further separation to have ended or the test for the consistency of this division has not been passed. After reading the description of the algorithm, the question may arise: why, in fact, use the “oracle”? After all, you can simply build a decision tree based on the available training sample, which already contains an exact indication of which class each example belongs to. Moreover, such an “oracle” as a neural network, no matter how well trained it is, will still make mistakes. The point here is the generalizing ability of artificial neural networks, which allows us to obtain simpler decision trees. In addition, the use of “oracle” makes it possible to compensate for the lack of data, which is observed when constructing decision trees at lower levels. Thus, it is possible to extract structured knowledge not only from extremely simple neural networks, but also from arbitrary classifiers, which makes it possible to apply the described algorithm in a wide range of practical tasks.
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3.2 Rules Extraction from ANN Based on the Decision Trees A thinned tree is much more compact and simpler than an untreated one. In addition to this, the thinned tree has greater classification accuracy. In this regard, we will draw all meaningful conclusions based on a thinned tree. The first meaningful conclusion that can be drawn at first glance is that the work of Sergei Dovlatov is very clearly different in style (here, by style we will understand the frequency response of sentence lengths) from three other writers, and for making such a decision there was enough data that in the text fragment under study there are less than 2 sentences 34 words long and less than 4 sentences 48 words long. Linguistics experts will have to judge why exactly such figures turned out, and such data may be of great value to them. In contrast to the work of S. Dovlatov, the work of A.I. Kuprin is the least clearly distinguished from others. We can see this by the way a lot of records describing his works gradually disintegrate into parts, often close in size. However, such a feature can be caused not only by the peculiarities of the writer’s work, but also by the small number of works (18 in total) that participated in the study. It can be noted that the resulting decision tree does not include all the attributes that were present in the training sample. This leads to an important conclusion that decision trees also allow you to select the most significant characteristics and discard unnecessary ones. This observation is very important for further research in the field of choosing the characteristics most relevant to the individual author’s style. Having made sure that thinning gives a more compact decision tree, it would be interesting to find out: and what threshold level of significance gives the most compact decision tree, without reducing the accuracy of prediction? To answer this question, various threshold levels of significance were checked. Threshold levels of significance from the range [0; 1] were checked, and the threshold level of significance 0 corresponds to the «strictest» thinning, and level 1 corresponds to the complete absence of thinning From this graph after thinning, with a successful choice of the threshold level of significance (the choice can be made using the same technique as was used during testing), the percentage of errors is significantly reduced. In the presented algorithm, there is an additional parameter reflecting the minimum number of training data for each node. Classical algorithms based on decision trees are not capable of achieving such accuracy.
4 Discussion In this paper, the possibility of using algorithms for extracting rules from an artificial neural network based on decision trees was demonstrated. As an example, the task of determining the authorship of classical works of Russian writers based on ANN and decision trees was chosen. Decision trees based on the trained network built its structure. Two more approaches to the extraction of rules and the development of explanatory artificial intelligence systems, such as fuzzy cognitive maps and a mining clustering algorithm, were also considered. Briefly, it should be noted that all the presented algorithms require additional testing and research of their effectiveness as meth odes of extracting rules and knowledge from neural networks, but they can be considered as possible ways of developing explanatory artificial intelligence systems.
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Acknowledgement. The paper is partially supported be the grants RFBR 20-7-00770 “Facing Fundamental Problems of Constructing “Understanding” Cognitive Agents, Multi-Agent Systems and Artificial Societies on the Basis of Synergetic Artificial Intelligence Approaches, Information Granulation Techniques, Dynamic Bipolar Scales and Dialogical Worlds” and RSCF 22-7110112 “Hybrid Decision Support Models Based on Augmented Artificial Intelligence, Cognitive Modeling and Fuzzy Logic in Problems of Personalized Medicine”.
References 1. Zadeh, L.A., Aliev, R.A.: Fuzzy Logic Theory and Applications: Part I And Part II. World Scientific (2018). https://doi.org/10.1142/10936 2. Averkin, A., Yarushev, S.: Hybrid neural networks for time series forecasting. In: Kuznetsov, S., Osipov, G., Stefanuk, V. (eds.) RCAI 2018. CCIS, vol. 934, pp. 230–239. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00617-4_21 3. Pilato, G., Yarushev, S.A., Averkin, A.N.: Prediction and detection of user emotions based on neuro-fuzzy neural networks in social networks. In: Abraham, A., Kovalev, S., Tarassov, V., Snasel, V., Sukhanov, A. (eds.) IITI’18 2018. AISC, vol. 875, pp. 118–125. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-01821-4_13 4. Jin, X.-H.: Neurofuzzy decision support system for efficient risk allocation in public-private partnership infrastructure projects. J. Comput. Civ. Eng. 24(6), 525–538 (2010). https://doi. org/10.1061/(ASCE)CP.1943-5487.0000058 5. Jin, X.-H.: Model for efficient risk allocation in privately financed public infrastructure projects using neuro-fuzzy techniques. J. Constr. Eng. Manag. 137(11), 1003–1014 (2011). https://doi.org/10.1061/(ASCE)CO.1943-7862.0000365 6. Mitra, S., Hayashi, Y.: Neuro-fuzzy rule generation: survey in soft computing framework. IEEE Trans. Neural Netw. 11(3), 748–768 (2000). https://doi.org/10.1109/72.846746 7. Kim, J., Kasabov, N.: HyFIS: adaptive neuro-fuzzy inference systems and their application to nonlinear dynamical systems. Neural Netw. 12(9), 1301–1319 (2004). https://doi.org/10. 1016/s0893-6080(99)00067-2 8. Shihabudheen, K.V., Pillai, G.N.: Recent advances in neuro-fuzzy system: a survey. Knowl. Based Syst. 152, 136–162 (2018). https://doi.org/10.1016/j.knosys.2018.04.014 9. Lin, C.T., Lee, C.S.G.: Neural network based fuzzy logic control and decision system. IEEE Trans. Comput. 40(12), 1320–1336 (1991). https://doi.org/10.1109/12.106218 10. Viharos, Z.J., Kis, K.B.: Survey on neuro-fuzzy systems and their applications in technical diagnostics and measurement. Measurement 67, 126–136 (2015). https://doi.org/10.1016/j. measurement.2015.02.001 11. Naderpour, H., Mirrashid, M.: Shear failure capacity prediction of concrete beam-column joints in terms of ANFIS and GMDH. Pract. Period. Struct. Des. Constr. 24(2) (2019). https:// doi.org/10.1061/(ASCE)SC.1943-5576.0000417 12. Fan, L.: Revisit fuzzy neural network: demystifying batch normalization and ReLU with generalized hamming network. In: 31st International Conference on Neural Information Processing Systems, Long Beach California, USA, pp. 1920–1929 (2017). https://doi.org/10. 48550/arXiv.1710.10328 13. Bherenji, H.R., Khedkar, P.: Learning and tuning fuzzy logic controllers through reinforcements. IEEE Trans. Neural Netw. 3, 724–740 (1992). https://doi.org/10.1109/72. 159061 14. Nauck, D., Kruse, R.: Neuro-fuzzy systems for function approximation. Fuzzy Sets Syst. 101(2), 261–271 (1999). https://doi.org/10.1016/S0165-0114(98)00169-9
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15. Juang, C.F., Lin, C.T.: An online self constructing neural fuzzy inference network and its applications. IEEE Trans. Fuzzy Syst. 6(1), 12–32 (1998). https://doi.org/10.1109/91.660805 16. Nürnberger, A., Nauck, D., Kruse, R.: Neuro-fuzzy control based on the NEFCON-model: recent developments. Soft Comput. 2(4), 168–182 (1999). https://doi.org/10.1007/s00500005 0050 17. Tano, S., Oyama, T., Arnould, T.: Deep combination of fuzzy inference and neural network in fuzzy inference. Fuzzy Sets Syst. 82(2), 151–160 (1996). https://doi.org/10.1016/0165-011 4(95)00251-0 18. Prasad, M., Lin, C., Li, D.: Soft-boosted self-constructing neural fuzzy inference network. IEEE Trans. Syst. Man Cybern. Syst. 47(3), 584–588 (2017). https://doi.org/10.1109/TSMC. 2015.2507139 19. Kasabov, N.: Evolving fuzzy neural networks for supervised/unsupervised on-line knowledgebased learning. IEEE Trans. Syst. Man Cybern. 31(6), 902–918 (2001). https://doi.org/10. 1109/3477.969494 20. Aliev, R.A., et al.: Type-2 fuzzy neural networks with fuzzy clustering and differential evolution optimization. Inf. Sci. 181(9), 1591–1608 (2011). https://doi.org/10.1016/j.ins.2010. 12.014
Z-Numbers Based Evaluation of Expert Opinions on Agricultural Structure G. Imanov1
, A. Aliyev1(B)
, and R. Mikayilova2,3
1 Institute of Control Systems of Azerbaijan National Academy of Sciences, Baku AZ1141,
Azerbaijan [email protected] 2 Azerbaijan State University of Economics, Baku AZ1001, Azerbaijan [email protected] 3 Azerbaijan State Oil and Industry University, 34 Azadlyg Avenue, Baku AZ1010, Azerbaijan
Abstract. This article sets out the methodology for evaluation of expert opinions on agricultural structure of sown areas that is one of main factors constituting food security. For this purpose, the theory and instruments of fuzzy Z-numbers have been employed. The Z-number theory opened a new window of opportunities for many applications, especially in the areas of computation with probabilities and events stated in natural language. From this perspective, Z-numbers theory is an effective tool to make synthesis and analysis of expert opinions. In this paper, we try to determine the best case among expert opinions. Firstly, on the basis of subjective expert evaluations, corresponding Z-numbers are constructed. Then, in order to establish the medium version of expert opinions, addition and averaging operations on Z-numbers have been carried out. As a result, the intermediate of the expert opinions is assessed, then the best case is selected which may be accepted as the desired agricultural structure of sown areas of cereal and leguminous plants in Azerbaijan for the upcoming years. Keywords: Food security · Agricultural structure of sown areas · Z-numbers · Z-average · Z-t-conorm
1 Introduction The world is passing through a very turbulent and challenging time. If you have a look at today’s scene of our planet, you cannot see any pleasant pictures. A pandemic continuing more than two years, conflicts and wars bursting out from time to time, the results of climate change, humanitarian and economic crises attracted attentions on food security problems of world countries. Worsening international relations and trade, increasing risk factors require a new approach to food security problems. Food security is an agenda at public and political debates in many countries, for its urgency in national security, rural and agricultural development, general welfare of the society, poverty reduction, and more. Food security concept is defined as the condition in which people all the time have economic, social and physical access to sufficient and nutritious food that meeting their © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 188–195, 2023. https://doi.org/10.1007/978-3-031-25252-5_28
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dietary needs for a healthful and active life. Built on this definition addressed in the 1996 World Food Summit, the Global Food Security Index takes into account the main issues of Affordability, Availability, Quality and Safety, Natural Resources & Resilience within a group of 113 countries. The index is a dynamic quantitative and qualitative scoring model, generated from 28 particular indicators, that measures different aspects of food security over both developed and developing countries. The general goal of the study is to measure which countries are most and least susceptible to food insecurity based on the categories of Affordability, Availability, Quality and Safety, and Natural Resources & Resilience [1]. Food security index in 2021 was 62.6 with global ranking 56 in Azerbaijan. Affordability sub index was 82.3, availability was 82.3, Quality & Safety was 62.0, and Natural Resources & Resilience was 50.7. Today Azerbaijan meets its wheat demand at 59–60% level [2]. The main factor influencing Availability sub index is considered to be agricultural structure of sown areas. In this paper by application of fuzzy Z-number tools to define optimal agricultural structure two expert opinions are evaluated.
2 Statement of the Problem Two expert opinions have been used in order to outline the current state of agricultural structure of sown areas use. First expert opinion describes the current situation of the agricultural structure of sown areas in Azerbaijan. The second expert opinion as a proposal of an agricultural scientist takes into account liberated areas after II Karabakh war, which is given in Table 1 [3, 4]. Table 1. Structure of sown areas in Azerbaijan №
All categories of farmlands
Expert I
Expert II
X (Thnd. ha.)
P
X (Thnd. ha.)
P
1
Wheat
588.4
0.5949
740
0.64
2
Maize
33.7
0.0341
36
0.03
3
Barley
345
0.3488
350
0.31
4
Rye
0.3
0.0003
0.5
0.00
5
Wild oat
5.8
0.0059
6.0
0.00
6
Spelt
0.0
0.0000
0.0
0.00
7
Millet
0.1
0.0001
0.2
0.01
8
Rice
3.0
0.0030
4.0
0.00
9
Sorghum grain
0.1
0.0001
0.2
0.00
Leguminous
12.7
0.0128
15.0
0.01
10
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The Table 1 illustrates that the wheat and barley are main grown products. They are followed by maize and leguminous plants. The remaining categories of farmland have insignificant percentage (converted to probability (denoted as p) as a proxy). In this paper by employing fuzzy Z-numbers instruments two expert opinions are analyzed and the best structure is selected.
3 The Algorithm and Solution of the Problem In this paper the main purpose is to determine the best case for the structure of sown areas in Azerbaijan taking into account all categories of farmlands. In this regard the algorithm is developed consisting of five steps. The solution procedure includes subjective conversion of crisp data into fuzzy Z-numbers, addition, averaging and t-conorm operations on fuzzy Z-numbers. The algorithm of solution consists of following steps: Step 1. Based on statistical information provided in Table 1 expert opinions on agricultural structure of sown areas can be presented in fuzzy Z-numbers subjectively as following: A1 = 0.63/588.4 + 0.92/33.7 + 0.13/345 + 0/0.3 + 0/5.8 + 0/0.1 + 1/0.1 + 0.95/3.0 + 1/0.1 + 0.58/12.7 B1 = 0.15/0.5949 + 0.02/0.0341 + 0.1/0.3488 + 0.001/0.0003 + 0.01/0.0059 + 0.0001/0 + 0.0001/0.0001 + 0.002/0.003 + 0.0001/0.0001 + 0.001/0.0128 A2 = 0.59/740 + 0.57/36 + 0.24/350 + 0/0.5 + 0/6.0 + 0/0.1 + 1/0.2 + 0.6/4.0 + 1/0.2 + 0.29/15.0 B2 = 0.92/0.6424 + 0.62/0.0313 + 0.008/0.3038 + 0.08/0.0004 + 0.1/0.0052 + 1/0 + 0.33/0.0002 + 0.36/0.0035 + 0.33/0.0002 + 0.09/0.0130 The support of fuzzified data and probabilities have been built based on historical data [4]. Step 2. In this stage, expert opinions converted to fuzzy Z-numbers are added in order to find the average Z-number. For this purpose, the following adding rules as one of binary operations on fuzzy Z-numbers [5, 6] are carried out: Let us consider some binary arithmetic operations (+, −, ×, ÷) on two discrete Znumbers. If we denote * as binary operations, and Z1 = (A1 , B1 ) and Z2 = (A2 , B2 ), + = (Z1+ ∗ Z2+ ) should be estimated: then first Z12 Z1+ ∗ Z2+ = (A1 ∗ A2 , R1 ∗ R2 )
(1)
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The operations on the first part A1 ∗A2 are carried out according to arithmetic rules on fuzzy numbers. R1 ∗R2 is a convolution p12 = p1 ◦ p2 of discrete probability distributions defined as following: p1 (x1 )p2 (x2 ) p12 (x) = (2) x=x1 +x2 + + as Z12 = (A1 ∗A2 , p12 ), which is the first stage in computation As a result, we have Z12 with discrete fuzzy Z-numbers. By definition, a fuzzy Z+ number carries more information than a fuzzy Z-number. This is the reason why it is labelled a fuzzy Z+ number. As will be seen in the sequel, computation with fuzzy Z+ numbers is a portal to computation with fuzzy Z-numbers [7]. In the next stage, it gets obvious that the probability distributions of p1 and p2 are not exactly known for data given as Z-numbers. So fuzzy restrictions on p1 and p2 are taken into account: n1 μA1 (x1k )p1 (x1k ) is B1 , (3) k=1
n2 k=1
μA2 (x2k )p2 (x2k ) is B2 ,
(4)
Thus, Bj , j = 1, 2 is a discrete fuzzy number, that is a soft constraint on probability measure of Aj . Thus, values of bjl ∈ supp Bj , j = 1, 2; l = 1, . . . , m of the discrete fuzzy number of Bj , j = 1, 2 are probability values of Aj , bjl = P(Aj ). In order to evaluate pj the following goal-programming problem must be solved: (5) μAj xj1 pjl xj1 + μAj xj2 pjl xj2 + . . . + μAj xjn pjl xjn → bj Subject to pjl xj1 + pjl xj2 + · · · + pjl xjn = 1 pjl xj1 , pjl xj2 , · · · , pjl xjn ≥ 0
(6)
n j Taking into account the fuzzy restrictions i=1 μAj (xji )pj (xji ) is Bj , probability distributions pj , j = 1, 2 are obtained by solution of the goal programming problems given below: c1 v1 + c2 v2 + · · · + cn vn → bj
(7)
Subject to v1 + v2 + · · · + vn = 1 v1 , v2 , · · · , vn ≥ 0
(8)
where, ck = μAj (xjk ), vk = pj (xjk ), k = 1, . . . , nj It must be noted that to guarantee a unique solution for goal programming problem (7)–(8) the compatibility conditions have to be employed.
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As a result, pjl xjk , k = 1, . . . , n is obtained. Then, solving n linear goal programming problems the fuzzy set of probability distribution pjl is constructed. Membership function values of fuzzy set of convolutions p12s , s = 1, . . . , m2 is found as following: μp12 (p12 ) = max μp1 (p1 ) ∧ μp2 (p2 ) (9) p1 ,p2
Subject to.
nj μAj xjk pj xjk , j = 1, 2 μpj pj = μBj p12s (x) =
(10)
k=1
p1 (x1 )p2 (x2 ), ∀x12 ∈ X12 ; x1 ∈ X1 ; x2 ∈ X2
(11)
x=T (x1 ,x2 )
In the final step P(A12 ) = nk=1 μA12 (x12k )p12 (x12k ) turning into B12 taking into account the membership function μB12 that induces fuzziness, is found as below: μB12 (b12s ) = sup μp12s (p12s ) (12) Subject to b12s =
p12s (xk )μA12 (xk )
(13)
k
Finally, Z12 = Z1 + Z2 = (A12 , B12 ) is obtained. The summing of Z-numbers have been carried out by a special program coded and added as an additional tool in Matlab by the authors of “The arithmetic of Z-numbers” [5]. Step 3. Afterward of addition, the average Z Average = (A, B) of Z1 , Z2 is computed, that is given in Table 2. Step 4. Further, the averaged Z-number is defuzzified according the following rules: The A part of averaged Z-number is defuzzified referring [8] employing the formula given below: μa˜ =
l+m+u (25) 3
where a˜ = (l, m, u) – is a triangular fuzzy number In this stage according to Kang’s method [9], the reliability part B of obtained Z-number is converted into crisp number as given below: xμR˜ (x)dx α= (36) μ∗˜ (x)dx R
˜ is reliability part, μ ˜ (x)- is membership values, x-probability values, μ∗ (x)where RR R˜ is minimum membership function values for B part of Z-numbers (expert I and expert II).
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Table 2. Average of Z-numbers №
Z Average = (A, B)
1
[(568.43, 664.2, 883.7) (0.1368, 0.1516, 0.1928)]
2
[(31.78, 34.85, 39.75) (0.0036, 0.0041, 0.0063)]
3
[(171.63, 347.5, 363.5) (0.0531, 0.0871, 0.1048)]
4
[(0.075, 0.40, 0.4505) (0.00036, 0.000431, 0.000434)]
5
[(1.525, 5.9, 6.1) (0.000397, 0.000537, 0.002184)]
6
[(0, 0.055, 0.11) (0, 0, 0)]
7
[(0.05, 0.15, 0.25) (0, 0, 0)]
8
[(2.1, 3.5, 5.6) (0.000317, 0.000384, 0.000594)]
9
[(0.05, 0.15, 0.25) (0, 0, 0)]
10
[(10, 13.85, 27.15) (0.000356, 0.000427, 0.000753)]
Table 3. Averaged expert opinions №
All categories of farmlands
Average structure of sown areas X (Thnd. ha.)
P
1
Wheat
705,44
0.64
2
Maize
35,46
0.02
3
Barley
294,21
0.30
4
Rye
0,31
0.01
5
Wild oat
4,51
0.01
6
Spelt
0,06
0.00
7
Millet
0,15
0.00
8
Rice
3,73
0.00
0,15
0.00
9 10
Sorghum grain Leguminous
17,0
0.01
Subsequently, the expert opinions given in Z- numbers combined as an average of Z-numbers that is broken down in Table 3 as an optimal structure of sown areas taking into account both expert evaluations. Step 5. Finally, to distinguish expert opinions in Z-numbers, t-conorm operation on the base of rule: T(Z1 , Z2 , Z Average ) = max(Z1 , Z2 , Z Average ) is performed [10–12]. The selected expert opinion as a best case is introduced in Table 4. To sum up, it can be inferred that t-conorm operation on expert opinions (Expert II, and Average version) allows selecting the best case. The selected best case puts forward the highest possible and optimal structure over the all categories of farmlands.
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№
All categories of farmlands
The selected expert opinion X (Thnd. ha.)
P
1
Wheat
740
0.64
2
Maize
36
0.03
3
Barley
350
0.31
4
Rye
0.5
0.01
5
Wild oat
6.0
0.01
6
Spelt
0.06
0.00
7
Millet
0.2
0.00
8
Rice
4.0
0.00
Sorghum grain
0.2
0.00
Leguminous
17
0.01
9 10
4 Conclusions In this paper, we carried out evaluation of expert opinions with the application of the theory and instruments of fuzzy Z-numbers. Concept of Z-numbers is suitable to generalize expert opinions into a single one, on that account we applied Z-number average and t-conorm operator. Taking into consideration that Z-numbers based reasoning is suitable to deal with partially reliable information in economics, it has an advantage over the traditional fuzzy methods in evaluation and selection of expert opinions. The proposed approach can be a piece of help for decision-makers in application to the different aspects of socio-economic systems.
References 1. https://www.unccd.int/resources/knowledge-sharing-system/global-food-security-index 2. https://impact.economist.com/sustainability/project/food-security-index/Index 3. Ibrahimov, I.: Development perspectives of regions and liberated areas. Cooperation, Baku, 240 p. (2022) 4. www.azstat.gov.az 5. Aliyev, R., Huseynov, O., Aliyev, R., Alizadeh, A.: The Arithmetic of Z-numbers. Theory and Applications, 301 p. World Scientific Publishing Co. (2015) 6. Aliyev, R., Huseynov, O., Aliyev, R., Alizadeh, A.: The arithmetic of discrete Z-numbers. Inf. Sci. 290(1), 134–155 (2015). https://doi.org/10.1016/j.ins.2014.08.024 7. Zadeh, L.A.: A note on Z-numbers. Inf. Sci. 181, 2923–2932 (2010) 8. Rahmani, A., Lotfi, H., Rostami, M., Allahviranloo, T.: A new method for defuzzification and ranking of fuzzy numbers based on the statistical beta distribution. Adv. Fuzzy Syst. 2016, Article ID 6945184, 8 p. https://doi.org/10.1155/2016/6945184 9. Kang, B., Wei, D., Li, Y., Deng, Y.: Amethod of converting Z-number to classical fuzzy number. J. Inf. Comput. Sci. 9(3), 703–709 (2012)
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10. Aliyev, R.R., Huseynov, O.H., Aliyeva, K.R.: Z-valued t-norm and and t-conorm operatorsbased aggregation of partially reliable information. Procedia Comput. Sci. 102, 12–17 (2016). https://doi.org/10.1016/j.procs.2016.09.363 11. Gardashova, L.A.: Using fuzzy probabilistic implication in Z-set based inference. In: Aliev, R.A., Yusupbekov, N.R., Kacprzyk, J., Pedrycz, W., Sadikoglu, F.M. (eds.) WCIS 2020. AISC, vol. 1323, pp. 33–39. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-68004-6_5 12. Aliev, R.A., Pedrycz, W., Eyupoglu, S.Z., Huseynov, O.H.: Approximate reasoning on a basis of Z-number-valued ıf-then rules. IEEE Trans. Fuzzy Syst. 25(6), 1589–1600 (2017). IEEE Computational Intelligence Society, USA. https://ieeexplore.ieee.org/document/7572935
Pareto-Optimality-Based Investigation of Quality of Fuzzy IF-THEN Rules Nigar E. Adilova(B) Joint MBA Program, Azerbaijan State Oil and Industry University, 34 Azadlyg Avenue, Baku AZ1010, Azerbaijan [email protected]
Abstract. In recent times, fuzzy IF-THEN rules have been successfully applied to construct conditional statements in decision making, decision analysis etc. The specification of quality criteria of fuzzy IF-THEN rules provides a better model to be used, created alternative cases, and selected one of the important cases among alternatives. Therefore, great number of works have been dedicated to define preferable case of rule base. However, obtaining Pareto-optimality solutions is still considered an important matter to improve quality criteria. In this paper, the author proposes Pareto-optimality-based investigation of quality of IFTHEN rules. As the main part of this work, the mentioned approach is solved by considering the importance of quality criteria. An experimental analysis is carried out regarding the quality criteria assessment for different cases of If-Then model. Keywords: Pareto-optimality · Fuzzy IF-THEN rules · Quality criteria · Complexity · Coverage · Partition · Inconsistency · Accuracy
1 Introduction The existence of imprecise information in multi-criteria decision making is an actual problem, which has been widely spread. It can be concluded with the lack of certainty or distinctness. The usage of optimization methods, or in wide sense, the updating If-Then model can be a reason to apply a better model even in an ambiguous environment. Fuzzy Pareto-optimality is a fundamental theory to obtain Pareto-optimal cases among all possible variants. The main theoretic goal of this method is to define the lowest degree as Pareto optimality case and the highest degree as a strong definition of optimality. Respectively, the lowest degree can be identified with 0, and the highest one can be accepted as 1. A set of these points categorizes as an optimal solution, a small subset points are considered as Pareto front. This classification demonstrates dominance relation among objectives. For the first principle the number of objectives in a solution must be identified to improve the other solution. The second principle is to define the size of each improvement. As a result, “less” and “more” optimal solutions are individualized [1–5]. Widely developed theories on this field with the combination of fuzzy logic tools, multi-objective optimization and decision-making methods are available in the following resources [6–10]. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 196–202, 2023. https://doi.org/10.1007/978-3-031-25252-5_29
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This paper examines an optimal method known as Pareto-optimality to any kind of IF-THEN model. The motivation of the paper is about the investigation of multicriterial optimization problem for fuzzy If-Then rules [11]. An optimal solution can be acquired with the assistance of Pareto-optimality method. Therefore, the rest of the paper is structured as follows: Section 2 offers fuzzy IF-THEN rules and Pareto-optimality-related some preliminary information. Section 3 covers the general description of the problem. The solutional approach based on Pareto-optimality investigation on the specific case is exemplified in Sect. 4. Eventually, Sect. 5 is devoted to the concluding marks.
2 Preliminaries Definition 1. Fuzzy Fuzzy If-Then rules [12]: Fuzzy IF-THEN rules comprehensively identify conditional statements. Considering multi-input case fuzzy IF-THEN rules are shown as below: If (X1 is A1 ), (X2 is A2 ), . . . , (Xn is An ) Then Y is B where Ai determines information granules. Definition 2. Quality criteria of Fuzzy If-Then rules [13, 14]: The quality criteria of Fuzzy If-Then rules must be noticed in: – – – – –
Complexity (comp); Partition (part); Coverage (cov); Inconsistency (Incons); Accuracy (RMSE).
Although the assessment of quality criteria is widely discussed in [13], overall, their measuring formulas are as (1)–(5). r comp = m/ nk
(1)
k=1
parti = 1/(pi − 1)
(2)
⎧ pi ⎪ ⎨ hi (x) = µ(k) (x), if 0 ≤ hi (x) ≤ 1 Xi hi (x)dx i covi = where hi (x) = k=1 ⎪ Ni pi −hi (x) ⎩ otherwise pi −1 ,
Incons(i) =
∑ [1.0 − Cons( R (i), R (k ))] + ∑ 1
1≤ k ≤ N k ≠i
1
[1.0 − Cons( R1 (i), R 2 (l ))],
1≤ l ≤ L i =1,2,..., N
n
1 RMSE = (yi − yi )2 n
(3)
(4)
i=1
(5)
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Definition 3. Pareto-optimality [15]. Assume that two solutions are given: A1 , A2 ∈ A; (A1 is considered to dominate A2 in the Pareto sense for the given conditions) nbF, neF, and nwF are evaluated by the membership degrees of predefined fuzzy sets “greater than 0”, “equal to 0”, “less than 0” respectively. These three parameters are defined as follows: nbF(A1 , A2 ) =
M
µib (fi (A1 ) − fi (A2 )),
(6)
µie (fi (A1 ) − fi (A2 )),
(7)
µiw (fi (A1 ) − fi (A2 )).
(8)
i=1
neF(A1 , A2 ) =
M i=1
nwF(A1 , A2 ) =
M i=1
In the following step, any couple of alternatives do(A1 , A2 ) is obtained as:
0, if nbF ≤ M −neF 2 do(A1 , A2 ) = 2·nbF+neF−M , otherwise nbF
(9)
do(A1 , A2 ) = 1 shows that A1 Pareto dominates A2 ; do(A1 , A2 ) = 0 shows that A1 does not Pareto dominant A2 . Membership functions for i-th objective of “” cases are described in the following (Fig. 1)
=
0
Fig. 1. Membership functions for i-th objective of “ ” cases
3 Statement of the Problem Consider that FRBS (Fuzzy Rule-based System) consists of n number of rules, m number of antecedents and a consequent as given below:
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If X1 is High, X2 is Low, …., Xm is Low, Then Y is Small If X1 is High, X2 is Low, …., Xm is Medium, Then Y is Medium If X1 is High, X2 is Low, …., Xm is High, Then Y is High … n. If X1 is Low, X2 is High, …., Xm is High, Then Y is High The problem is designed to improve FRBS by using multi-criteria optimization method. The solution of the problem must be realized by considering constraints on fuzzy terms, collection of the rules, collection of the terms, quality criteria [14]. To develop FRBS goal functions for 5 quality criteria must be emphasized: comp → max, cov → max, part → max, fincons → min, RMSE → min.
4 Solution of the Problem by Using Numerical Example We will illustrate the main features of the problem by means of a numerical example. The general problem mentioned in the previous section is concretely being solved with the aid of the given rules. The main objective is to find an optimal version of FRBS by applying Pareto-optimality method. Thus, as an experimental analysis, FRBS is a mixture of the following rules and is formed by 3 antecedents and a consequent part (Table 1): Table 1. An example for fuzzy rule-based system Rules
Antecedents
№
X1
X2
X3
Y
Consequent
1
H
L
L
S
2
H
L
M
M
3
H
L
H
H
4
H
M
L
M
5
H
M
M
M
6
H
M
H
H
7
H
H
L
H
8
H
H
M
H
9
H
H
H
H
10
M
L
L
S
…
…
…
…
…
25
L
H
L
S
26
L
H
M
M
27
L
H
H
H
where the mnemonics H, L, M, S represent “High”, “Low”, “Medium”, “Small” linguistic terms which have been marked with triangular fuzzy numbers, respectively. We consider the problem of how to improve FRBS for the quality criteria. Optimal version of FRBS may be obtained as the result of Pareto-Optimality investigation method.
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More extensively, the actuality of multi-criterial optimization matter for the given FRBS regarding to the competitive parameters has been proposed in [11]. However, in this work we have tried to make our contribution to find Pareto-Optimality solutions to this problem. For the current statement of rule base, the calculational result of quality criteria is characterized in Case-1. Other cases are formulated by updating FRBS. The main purpose of the usage of multi-cases is related to the multi-criteria optimization problem solution. Consequently, evaluation of quality criteria using (1)–(5) for the obtained 4 cases is reflected in Table 2. Table 2. Measures of quality criteria for FRBS Cases
Complexity
Coverage
Partition
Inconsistency
RMSE
Case-1
0,045
0,588
0,5
0,0153
8,704
Case-2
0,045
0,584
0,5
0,0178
6,578
Case-3
0,045
0,592
0,5
0,0184
8,824
Case-4
0,045
0,617
0,5
0,017
34,92
First, experiments are initiated with normalizing the parameters described in Table 2. The application of constraints on quality criteria given in [11] helps to construct a better model. For the normalization of positive parameters in the goal function, we will use formula (10), for negative indices formula (11) will be applied. = xinorm j xinorm j
=
xi j − xjmin xjmax − xjmin
,
(10)
xjmax − xi j
(11)
xjmax − xjmin
Correspondingly, a result of normalizing values is summarized in Table 3. Table 3. Normalized values of quality criteria Cases
comp
cov
part
fincons
RMSE
Case-1
0
0.121212121
0
1
0.924988
Case-2
0
0
0
0.193548387
1
Case-3
0
0.242424242
0
0
0.920754
Case-4
0
1
0
0.451612903
0
Then the realization of Pareto-optimality-based investigation will be activated with the given program code:
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After that the degree of optimality (do) is automatically calculated for (6)–(9) equations. Hereby, do result for the given FRBS will be as follows (Table 4): Table 4. The degree of optimality for 4 cases Cases
do
Case-1
1
Case-2
0.0809
Case-3
0.1207
Case-4
0.5965
Diversified series of cases are described as below: Case − 1 Case − 4 Case − 3 Case − 2 It is obvious that the best solution is Case-1 as it has the maximal optimality degree.
5 Conclusion In this paper a method based on the principle of pareto-optimality for optimizing the quality of fuzzy If-Then rules has been investigated and a rule base close to the optimal case has been obtained. Numerical example given in the study reveals validity of proposed investigation method. Results extracted from the experimental analysis reflects Pareto-optimality-based solution to the problem.
References 1. Farina, M., Amato, P.: A fuzzy definition of “optimality” for many-criteria optimization problem. IEEE Trans. Syst. Man Cybern. Part A Syst. Hum. 34(3), 315–326 (2004) 2. Farina, M., Amato, P.: On the optimal solution definition for many-criteria optimization problems. In: Proceedings of the NAFIPS-FLINT International Conference, New Orleans, pp. 233–238. IEEE Service Center (2002) 3. Carlsson, C., Fuller, R.: Multiobjective optimization with linguistic variables. In: Proceedings of the Sixth European Congress on Intelligent Techniques and Soft Computing, EUFIT 1998, Aachen, Verlag Mainz, Aachen, vol. 2, pp. 1038–1042 (1998)
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4. Alizadeh, A.V.: Application of the fuzzy optimality concept to decision making. In: 10th International Conference on Theory and Application of Soft Computing, Computing with Words and Perceptions, pp. 373–382 (2020) 5. Alizadeh, A.V., Musayev, A.A., Aliyev, R.R.: Application of the fuzzy optimality concept to decision making with imprecise probabilities. In: Sixth International Conference on Soft Computing, Computing with Words and Perceptions in System Analysis, Decision and Control, ICSCCW 2011, b-Quadrat Verlag, pp. 373–382 (2012) 6. Aliev, R.A.: Decision making theory with imprecise probabilities. In: Proceedings of the Fifth International Conference on Soft Computing and Computing with Words in System Analysis, Decision and Control (ICSCCW 2009), Famagusta, North Cyprus, p. 1 (2010). https://doi. org/10.1109/ICSCCW.2009.5379425 7. Jabbarova, K.I.: Application of expected utility to business decision making under U-number valued information. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Sadikoglu, F.M. (eds.) ICAFS 2018. AISC, vol. 896, pp. 716–723. Springer, Cham (2019). https://doi.org/10. 1007/978-3-030-04164-9_94 8. Jabbarova, K., Hasanova, N.: An application of the VIKOR method to decision making in investment problem under Z-valued information. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Sadikoglu, F.M. (eds.) ICAFS 2018. AISC, vol. 896, pp. 499–506. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-04164-9_67 9. Gardashova, L.A., Guirimov, B.G.: Decision making problem of a single product dynamic macroeconomic model on base of fuzzy uncertainty. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 237–245. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-35249-3_30 10. Imanova, G.E., Imanova, G.: Some aspects of fuzzy decision making in digital marketing analysis. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 465–473. Springer, Cham (2022). https:// doi.org/10.1007/978-3-030-92127-9_63 11. Huseynov, O.H., Adilova, N.E.: Multi-criterial optimization problem for fuzzy IF-THEN rules. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, Mo., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 80–88. Springer, Cham (2021). https://doi.org/ 10.1007/978-3-030-64058-3_10 12. Novák, V., Lehmke, S.: Logical structure of fuzzy IF-THEN rules. Fuzzy Sets Syst. 157(15), 2003–2029 (2006) 13. Adilova, N.E.: Quality criteria of fuzzy IF-THEN rules and their calculations. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 55–62. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-640 58-3_7 14. Adilova, N.E.: Specificity of fuzzy rule bases. Dissertation work for the degree of Doctor of Philosophy, Baku, Azerbaijan, 160 p. (2022) 15. Aliev, R.A.: Uncertain Computation-Based Decision Theory, 521 p. World Scientific, Singapore (2017)
Predicting Solar Power Generated by Grid-Connected Two-Axis PV Systems Using Various Empirical Models Youssef Kassem1,2,3,4(B) , Hüseyin Gökçeku¸s2,3,4 , Marilyn Hannah Godwin2,4 James Mulbah Saley2,4 , and Momoh Ndorbor Mason2,4
,
1 Faculty of Engineering, Mechanical Engineering Department, Near East University,
Nicosia 99138, North Cyprus [email protected] 2 Faculty of Civil and Environmental Engineering, Near East University, Nicosia 99138, North Cyprus [email protected], {20215601,20213832, 20213467}@std.neu.edu.tr 3 Energy, Environment, and Water Research Center, Near East University, Nicosia 99138, North Cyprus 4 Engineering Faculty, Kyrenia University, Kyrenia 99138, North Cyprus
Abstract. The main goal of this paper is to predict the mean monthly electricity generation (EG) produced by Two-axis solar systems using the Adaptive-Neuro Fuzzy Inference System (ANFIS) and Response Surface Methodology. The Twoaxis solar systems are located in 25 coastal Mediterranean cities. Accordingly, in this study, the geographical coordinates (latitude, longitude, and altitude) and climate conditions (global solar radiation, air temperature, and clearance index) were collected and used as input variables for the models. The results showed that all proposed models were suitable for EG prediction. The results demonstrated that the RSM model has produced the highest value of R-squared (0.956) and lowest value of RMSE (42.672 kWh) compared to the ANFIS model. Keywords: Electricity generation · ANFIS · RSM · Climate conditions · Geographical coordinates
1 Introduction The growth of population and energy demand has led to an increase in the consumption of fossil fuels [1]. Moreover, climate change has forced countries for finding an alternative sources for generating electricity and reducing greenhouse gas emissions [2]. Therefore, utilizing renewable energy as an alternative energy source will help to reduce environmental problems, essentially greenhouse gas emissions and air pollution due to increasing fossil fuel consumption [3, 4]. Renewable energy including solar energy is rapidly increasing due to economically viable and limited environmental impacts [5]. Recently, several studies have investigated the utilization of renewable energy as a clean © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 203–210, 2023. https://doi.org/10.1007/978-3-031-25252-5_30
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energy source in different locations [6–8]. For example, Mansouri et al. [7] estimated the potential of rooftop PV electricity in Lethbridge, Canada using LiDAR data and ArcGIS. The results showed that the developed system has huge potential to offset the energy demand of the city. Generally, geographic location and climate conditions are most factors that affect the performance of the solar system particularly power generated [9]. In recent years, machine learning and mathematical models have been employed to predict the performance of the solar system [9–11]. In this regard, the present paper aims to predict the power generation for Two-axis grid-connected solar system using ANFIS and RSM models. To this aim, the geographical coordinates (latitude, longitude, and altitude) and climate conditions (global solar radiation, air temperature, and clearance index) were collected and used as input variables for the models.
2 Material and Methods 2.1 Study Area and Data In this research, 25 coastal Mediterranean cities located in Libya, Lebanon, Syria, Palestine, Tunisia, and Algeria are taken as a case study for predicting the mean monthly electricity generation produced by a small-scale Two-axis grid-connected solar system. The mean monthly climate parameters and electricity generation of the solar system are collected from Ref. [12]. The statistics summary of the selected variables is tabulated in Table 1. Table 1. Statistical parameters of the collected data. Variable
Unit
Explanation
Lat
◦
Mean
SD
Min.
Max.
Latitude
33.92
2.02
31.19
36.91
Long
◦
Longitude
18.30
11.55
−0.64
36.00
Alt
m
Altitude
31.92
42.23
3.00
204.00
GSR
kWh/m2
Global solar radiation
5.15
1.91
2.01
8.50
AT
◦C
Air temperature
5.15
1.91
2.01
8.50
Cl
–
Clearance index
0.60
0.07
0.46
0.74
EG
kWh
Electricity generation
735.30
188.50
390.40
1125.40
SD: Standard deviation; Min: Minimum; Max: Maximum
2.2 Adaptive-Neuro Fuzzy Inference System (ANFIS) In 1993, Jang has developed the ANFIS as a hybrid of artificial neural network (ANN) and fuzzy inference system (FIS) [13]. ANFIS combines the advantage of ANN learning
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ability and reasoning ability of rule-based FIS that can include past observation in the classification process [14]. In this model, the fuzzy logic definition is used to build the system and the neural network automatically optimizes the system parameters as opposed to manual optimization in building a system in FIS [13–15]. The flexibility and adaptability of the ANFIS model make it a proven approach to dealing with uncertainty that is in addition to its high ability to handle large noisy data from dynamic and complex systems [13–15]. The description of the MFFNN and CFNN models was given in Ref. [16, 17]. In this research, the training (60%), checking, and testing data (other parts) were used to develop and validate the model, respectively. The results of the ANFIS are compared with observed data. 2.3 Response Surface Methodology The RSM is a mathematical and statistical method polynomial model as expressed below [18, 19]. Y = β0 +
n i=1
βi xi +
n i=1
βii xi2 +
n n−1 i
βij xi xj
(1)
i=i+1
where Y is the predicted response, β0 , βi , are related to the main effects and βii and βij to interaction, x i and x j are the independent variables. The main goal of this model is to show the interaction between the input variables and output variables as shown in Eq. (2) EG = f (Lat, Long, Alt, GSR, AT , CL)
(2)
3 Results and Discussion In this study, two models are developed and evaluated to find the suitable model for the mean monthly EG prediction Then, the results of the proposed models are compared with each other. These models are ANFIS and RSM. In this study, the training was done using the mean monthly data for Al khums, Al Ladhiqiyah, Alexandria, Algiers, Annaba, Az Zawiyah, Beirut, Bejaia, Benghazi, Djerba Modoun, Gabes, Gaza Strip, Matrouh, Misratah, and Oran. For checking, mean monthly data for Surt, Sousse, Skikda, Sfax, and Port Said were utilized for checking/validating the model. The developed model was used to predict the monthly EG for Tartus, Tripoli-Lebanon, Tripoli-Libya, Tunis, and Turbruq. 3.1 Modeling with ANFIS ANFIS algorithm is used to estimate the relationship between the EG as geographical coordinates (Lat, Long, and Alt) and climate conditions (GSR, AT, and Cl). In this work, the trial and error method was utilized to determine the number of membership functions, and type of membership for input and output. Table 2 lists ANFIS information.
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Information
Value
Number of nodes
161
Number of linear parameters
64
Number of nonlinear parameters
36
Total number of parameters
100
Number of training data pairs
180
Number of checking data pairs
60
Number of fuzzy rules
64
Number of membership functions for each input
2
Membership grades for input
Triangular-shaped
The output port of each rule use
Linear defuzzifier
Moreover, the hybrid algorithm with the least square method and the backpropagation gradient descent method is employed in ANFIS learning. Figure 1 shows the structure (rules) of the tuned FIS. Furthermore, the rule viewers, which indicate the value of different inputs to the ANFIS model and determining output are shown in Fig. 2. Additionally, Fig. 2 shows the scatter diagram that compared the observed data with the estimated ones by the ANIFS model in the training phase.
Fig. 1. Structure of the ANFIS model
3.2 Modeling with RSM The mathematical equation that was developed using RSM (Eq. (3)) for predicting the EG is expressed as shown below.
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EG = −71317 + 409(Lat) + 59.2(Long) + 17.03(Alt) + 76(GSR) − 931(Cl) + 4.96 Lat 2 − 0.0746 Long 2 + 0.02952 Alt 2 + 7.34 GSR2 + 5067 Cl 2 − 1.473(Lat)(Long) − 0.555(Lat)(Alt) + 2.87(Lat)(GSR) − 86.3(Lat)(Cl) − 0.1038(Long)(GSR) − 0.017(Long)(GSR) − 7.3(Long)(Cl) + 0.0252(Alt)(GSR)
(3)
+ 0.61(Alt)(Cl) − 292(LGSR)(Cl)
EsƟmated data [kWh]
Figure 3 compares the scatter plots of the RSM model versus the observed data in the training and checking phase. It can be noticed that the estimated values are closed to the measured data.
1
Training phase
0.8 0.6 0.4 y = 0.9489x + 0.029 R² = 0.9346
0.2 0 0
0.2
0.4
0.6
0.8
1
Observed data [kWh]
EsƟmated data [kWh]
Fig. 2. Correlation between the observed and predicted data using the ANFIS model.
1 0.8 0.6 0.4 0.2
y = 0.951x + 0.028 R² = 0.9493
0 0
0.2
0.4
0.6
0.8
1
Observed data [kWh] Fig. 3. Correlation between the observed and predicted data using RSM in the training phase.
3.3 Performance Evaluation of ANFIS and RSM The ANFIS’s performance is compared with the RSM to evaluate the performance of the proposed models. The values of R-squared and root mean squared error (RMSE) are listed in Table 3. It is noticed that the maximum R-squared value and minimum RMSE were obtained from the RSM model. Figure 4 illustrates the time series plot for each location used in the testing phase.
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Fig. 4. Time series plot for the locations used in the testing phase
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Table 3. Overall performance evaluation of the models. Statistical indicator R-squared RMSE [kWh]
ANFIS
RSM
0.949
0.956
47.358
42.672
4 Conclusions The prediction of electricity generation from the solar system is very important for the power grid’s secure, stable, and economical operation. Therefore, ANFIS and RSM models were designed and developed to predict the mean monthly electricity generation from the Two-axis solar system located in 25 coastal Mediterranean cities The results showed that all proposed models were suitable for estimating the EG of the solar system. Among the developed models, the RSM model presented significantly better prediction performance based on the value R2 and RMSE.
References 1. Kassem, Y., Çamur, H., Aateg, R.A.F.: Exploring solar and wind energy as a power generation source for solving the electricity crisis in Libya. Energies 13(14), 3708 (2020). https://doi. org/10.3390/en13143708 2. Ghazouani, A., Jebli, M.B., Shahzad, U.: Impacts of environmental taxes and technologies on greenhouse gas emissions: contextual evidence from leading emitter European countries. Environ. Sci. Pollut. Res. 28(18), 22758–22767 (2021). https://doi.org/10.1007/s11356-02011911-9 3. Kassem, Y., Gökçeku¸s, H., Janbein, W.: Predictive model and assessment of the potential for wind and solar power in Rayak region, Lebanon. Model. Earth Syst. Environ. 7(3), 1475–1502 (2020). https://doi.org/10.1007/s40808-020-00866-y 4. Kassem, Y.: Computational study on vertical axis wind turbine car: static study. Model. Earth Syst. Environ. 4(3), 1041–1057 (2018). https://doi.org/10.1007/s40808-018-0461-x 5. Shahsavari, A., Akbari, M.: Potential of solar energy in developing countries for reducing energy-related emissions. Renew. Sustain. Energy Rev. 90, 275–291 (2018). https://doi.org/ 10.1016/j.rser.2018.03.065 6. Yadav, S.K., Bajpai, U.: Performance evaluation of a rooftop solar photovoltaic power plant in Northern India. Energy Sustain. Dev. 43, 130–138 (2018). https://doi.org/10.1016/j.esd. 2018.01.006 7. Mansouri Kouhestani, F., Byrne, J., Johnson, D., Spencer, L., Hazendonk, P., Brown, B.: Evaluating solar energy technical and economic potential on rooftops in an urban setting: the city of Lethbridge, Canada. Int. J. Energy Environ. Eng. 10(1), 13–32 (2018). https://doi.org/ 10.1007/s40095-018-0289-1 8. Kassem, Y., Gökçeku¸s, H., Çamur, H.: Economic assessment of renewable power generation based on wind speed and solar radiation in urban regions. Glob. J. Environ. Sci. Manag. 4(4), 465–482 (2018). https://doi.org/10.22034/gjesm.2018.04.007 9. Kassem, Y., Othman, A. A.: Selection of most relevant input parameters for predicting photovoltaic output power using machine learning and quadratic models. Model. Earth Syst. Environ., 1–26 (2022). https://doi.org/10.1007/s40808-022-01413-7
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10. da Silva Fonseca, J.G., Jr., Oozeki, T., Takashima, T., Koshimizu, G., Uchida, Y., Ogimoto, K.: Use of support vector regression and numerically predicted cloudiness to forecast power output of a photovoltaic power plant in Kitakyushu, Japan. Prog. Photovolt. 20(7), 874–882 (2012). https://doi.org/10.1002/pip.1152 11. Kumar, P.M., Saravanakumar, R., Karthick, A., Mohanavel, V.: Artificial neural networkbased output power prediction of grid-connected semitransparent photovoltaic system. Environ. Sci. Pollut. Res. 29(7), 10173–10182 (2021). https://doi.org/10.1007/s11356-021-163 98-6 12. Kassem, Y., Gökçeku¸s, H., Lagili, H.S.A.: A techno-economic viability analysis of the twoaxis tracking grid-connected photovoltaic power system for 25 selected coastal Mediterranean cities. Eng. Technol. Appl. Sci. Res. 11(4), 7508–7514 (2021). https://doi.org/10.48084/etasr. 4251 13. Tabbussum, R., Dar, A.Q.: Performance evaluation of artificial intelligence paradigms— artificial neural networks, fuzzy logic, and adaptive neuro-fuzzy inference system for flood prediction. Environ. Sci. Pollut. Res. 28(20), 25265–25282 (2021). https://doi.org/10.1007/ s11356-021-12410-1 14. Zaman, M., Hassan, A.: Improved statistical features-based control chart patterns recognition using ANFIS with fuzzy clustering. Neural Comput. Appl. 31(10), 5935–5949 (2018). https:// doi.org/10.1007/s00521-018-3388-2 15. Yue, X., Chen, Y., Chang, G.: Accurate modeling of biodiesel production from castor oil using ANFIS. Energy Sour. Part A Recover. Utili. Environ. Eff. 40(4), 432–438 (2018). https://doi. org/10.1080/15567036.2017.1422058 16. Kassem, Y., Çamur, H., Bennur, K.E.: Adaptive neuro-fuzzy inference system (ANFIS) and artificial neural network (ANN) for predicting the kinematic viscosity and density of biodieselpetroleum diesel blends. Am. J. Comput. Sci. Technol. 1(1), 8–18 (2018). https://doi.org/10. 11648/j.ajcst.20180101.12 17. Kassem, Y., Çamur, H., Esenel, E.: Adaptive neuro-fuzzy inference system (ANFIS) and response surface methodology (RSM) prediction of biodiesel dynamic viscosity at 313 K. Procedia Comput Sci 120, 521–528 (2017). https://doi.org/10.1016/j.procs.2017.11.274 18. Kassem, Y., Çamur, H.: Prediction of biodiesel density for extended ranges of temperature and pressure using adaptive neuro-fuzzy inference system (ANFIS) and radial basis function (RBF). Procedia Comput. Sci. 120, 311–316 (2017). https://doi.org/10.1016/j.procs.2017. 11.244 19. Kassem, Y., Gökçeku¸s, H., Çamur, H.: Prediction of kinematic viscosity and density of biodiesel produced from waste sunflower and canola oils using ANN and RSM: comparative study. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 880–887. Springer, Cham (2020). https:// doi.org/10.1007/978-3-030-35249-3_117
Z-Preferences in Consumer Buying Behavior Khatira J. Dovlatova(B) Joint MBA Program, Azerbaijan State Oil and Industry University, 34 Azadlig Avenue, Baku AZ1010, Azerbaijan [email protected]
Abstract. In recent years one of the main topics in the marketing environment advancing consumer behavior and their decision making process. The research paper focuses on the analysis of variables influence on consumers’ buying behavior and their decision in marketing. Marketing is the process which begins with the consumers’ needs, desires, demands and ends with consumer purchasing decision making. Professional marketing managers attempt to clarify consumers and their feedback, therefore they analyze the main features of their behavior. As the process customer buying behavior comes from identifying needs, collecting information, ranking alternatives and realizing the decision making process. All these steps taken by consumer before making a purchase start the formation of the buyer’s desire to make a purchase. Research papers are related to consumer behavior. Marketers initiate to affect to each marketing decisions by providing information which may form the consumer evaluation. The research paper is dedicated to clarifying the various variables of customer purchasing behavior, which are analyzed by using Z numbers. Decision making process and customer behavior are usually subordinated to uncertainties associated with influences of different determinants. In research paper, the Z-number theory is applying to regulate ambiguous situations in investigating the consumer buying behavior. This paper is useful for marketers to analyze and understand the customers’ interests. Research can also help support their marketing tactics and strategy for clarifying different criteria in buying process. Keywords: Customer buying behavior · Marketing strategy · Consumer decision-making · Purchase decision · Z-numbers · Preferences
1 Introduction For being successful in marketing place one of the main rules is to clarify consumer behavior. Consumer attitudes and marketing strategy are in very closely relationship. Most companies focus on realizing the behavior of their target market. Consumer behavior comprises the psychological processes which consumers go through in clarifying their needs, discovering ways to solve these needs, making buying decision. Research process of consumer behavior initiates not only to understand purchase as the process but also to clarify purchasing motives and reasons. Analyzing consumer behavior is the process of how individually consumers make decision to use their accessible resources © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 211–217, 2023. https://doi.org/10.1007/978-3-031-25252-5_31
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for consumption process. This operation combines the study of different factors and determinants influencing customers buying behavior in Z-environment. There are various uncertainty handling models that are improved the analysis of uncertain data. In marketing fuzzy logic approaches, managerial decision, market segmentation are founded and applied [1–3]. Research papers on consumer buying practices have mainly focused on statistical and fuzzy approach. But modern research information is described by integration of fuzzy and incomplete information. Prof. Zadeh established the Z-number conception as new approach in uncertain computation. Z-number concept can be applied for different sectors, especially in marketing, consumer behavior, risk assessment processes.
2 Preliminaries Definition 1. The Z-number [4, 5]: A couple of two fuzzy numbers A and B is represented by Z = (A, B). The value A is a limitation on the values which the uncertain value characterizes as a real value and the second B component measures the degree of ambiguity of the first A component. Definition 2. A discrete Z-number: A fuzzy number depicts a fuzzy limitation on the values which the random variable Y may take and characterizes first component Z = (A, B). B is a discrete fuzzy number with a membership function μB : {b1 , ..., bn } → [0, 1] that depicts a fuzzy limitation on the probability of A: P(A) is B. Definition 3. Operations using for Discrete Z-numbers: Data Y1 and Y2 are discrete Z-numbers depicting the information concerning values of Z12 = MIN (Z1 , Z2 ) and Z12 = MAX (Z1 , Z2 ). Take into consideration calculation of Z12 = Z1 ∗ Z2 , ∗ ∈ {+, −, ·, /}. The first step is calculation of A12 = A1 * A2 . The next step included obtaining of B12 . As a defining result, Z12 = Z1 * Z2 is constructed as Z12 = (A12 , B12 ). A, Z = (λA1 , B1 ) is defined from the scalar multiplication Z = λZ1 , λ ∈ R [6–8]. Definition 4. Finding a distance between Z-numbers: A Z-number Z = (A, B) is described by fuzzy number A, fuzzy number B and an underlying set of probability distributions G. We offer to determine distance between Z-numbers D(Z1 , Z2 ) as mentioned below: Distance between A1 and A2 is computed as D(A1 , A2 ) = supα∈(0,1] D(Aα1 , Aα2 ), D(Aα1 , Aα2 )
α A11 + Aα12 Aα21 + Aα22 − = . 2 2
(1) (2)
Aα1 and Aα2 denote α-cuts of A1 and A2 relevantly, Aα11 , Aα12 indicate lower and upper borders of Aα1 (Aα21 , Aα22 are those of Aα2 ). Distance between B1 and B2 is calculated analogously.
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3 Statement of the Problem In the decision-making process, consumer purchasing behavior is influenced by various variables. The aim of this study is to analyze the preference of attributes which influence the consumer buying behavior and choose the best alternative for buying process. By using MCDM problem given 4 criteria and 4 alternatives are involved: C1 - hedonism, C2 - shopping experience, C3 - brand perception, C4 - purchasing intention. A1 , A2 , A3 , A4 , Problem of decision making is Z-preference in consumer buying behavior. Four decision criteria are considered: hedonism, shopping experience, brand perception, purchasing intention. Hedonism is an important variable which directly influences consumer buying behavior, represents emotional qualifications and focuses on implementing emotional satisfaction. Shopping experience is defined as customer internal and subjective response to direct and indirect interconnection with the company’s service, product or other offers. One of the main consumers’ ability-brand perception is the process which consumers can define the brand under different situations, as expressed by brand identification or recall performance. Purchasing intention is one of the main variable which marketers use to predict prospective sales and to clarify how the operations they take will influence consumers’ buying process. The given criteria are used for comparing 4 alternatives during uncertainty environment, the decision-appropriate information is described by partial reliability and fuzziness. In this paper we use incompletely dependable preference degrees of the Saaty scale to characterize relative importance of attribute in Table 1. ˜ Table 1. Z matrix of the attribute (A) Criteria (C1 )
(C2 )
(C1 )
(0.99 1 1)(0.99 1 1)
(7 8 9)(0.7 0.8 9)
(C2 )
(0.11 0.13 0.14)(0.7 0.8 0.9) (0.99 1 1)(0.99 1 1)
(C3 )
(0.14 0.17 0.2)(0.8 0.9 1)
(0.2 0.3 0.3)(0.6 0.7 0.8)
(C4 )
(0.33, 0.5, 1)(0.1 0.2 0.3)
(0.14, 0.16, 0.2)(0.5 0.6 0.7)
Criteria (C3 )
(C4 )
(C1 )
(5 6 7)(0.8 0.9 1)
(1 2 3)(0.1 0.2 0.3)
(C2 )
(3 4 5)(0.6 0.7 0.8)
(5 6 7)(0.5 0.6 0.7)
(C3 )
(0.99 1 1)(0.99 1 1)
(2 3 4)(0.7 0.8 0.9)
(C4 )
(0.25, 0.33, 0.5)(0.7 0.8 0.9) (0.99 1 1)(0.99 1 1)
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A 4 × 4 pairwise comparison matrix of Z-numbers with triangular fuzzy numbers (TFNs)-formed on elements is represented below: So, we need to define the best alternative in the given Z-valued information on criteria assessment and significance: Find a∗ ∈ {a1 , ..., a9 } such that a∗ ai , i = 1, ..., 9, where denotes preference. Then we depict the explanation way for issue. Firstly, we will check elements of matrix for constructing a consistent pairwise comparison matrix. Constructed a consistent pairwise comparison matrix, we will calculate its Zvalued eigenvectors to estimate significance weights of criteria. In the following step an ideal alternative will be defined which weight is the highest one between criteria values. As a final solution, alternatives will be compared by using distance results that defined by using (1–2).
4 Solution of the Problem Defined optimal matrix is described by the results of the constraint and objective function [9, 10] (Table 2). Table 2. For original and optimal matrices results of limitations Constraints and objective function
Original matrix
Equal-to-Unity consistency check, constraint
0.0001
Reciprocity consistency check, constraint
9.725
Transitivity consistency check, constraint Overall inconsistency value, objective function
11207.86 1.3836
Optimal matrix 3.2887 16.084 281.09 0.173
We should clarify whether the value of K for the defined matrix (Zij ) exceeds a predefined threshold θK = 0.1. The calculated value of K is K((Zij )) = 0.33 that does not get over θK . So, the defined matrix can be computed as consistent. Then, we normalized the criteria values of the alternatives. The decision table (Table 3) is shown below: In the next step, we defined the weighted values of attribute by using the arithmetic of Z-numbers [11, 12]: Zwj Cij = Zwj ZCij , i = 1, ..., 9, j = 1, ..., 4 (Table 4). We should define the best alternative which is with the highest values of the Z-valued weighted attribute. For this reason, Z-numbers (values of the Z-valued weighted attribute) are converted to fuzzy numbers by using the method suggested by Kang et al. For each weighted criterion, the defined fuzzy numbers are compared to define the highest one. As result, the Z-number, from that the highest fuzzy number was previously defined, is used. The determined ideal alternative a∗ = (Z1∗ , ..., Z4∗ ) is shown in Table 5:
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Table 3. Z-valued criteria evaluations (C1 )
(C2 )
(C3 )
(C4 )
(C1 )
(1.03, 1.04, 1.5) (0.43, 0.44, 0.77)
(1.82, 1.83, 4.01) (0.01, 0.82, 0.83)
(2.16, 2.17, 6.24) (0.93, 0.94, 0.98)
(2.08, 2.28, 4.33) (0.46, 0.51, 0.52)
(C2 )
(0.43, 0.59, 0.6) (0.097, 0.099, 0.1)
(1.061, 1.063, 1.068) (0.49, 0.51, 0.52)
(1.41, 1.44, 1.46) (0.09, 0.76, 0.77)
(1.32, 1.33, 4.03) (0.62, 0.63, 0.99)
(C3 )
(0.2, 0.45, 0.46) (0.98, 0.99, 1)
(0.36, 0.72, 0.73) (0.68, 0.69, 0.99)
(1.03, 1.04, 1.24) (0.14, 0.73, 0.74)
(1.08, 1.09, 2.25) (0.87, 0.93, 0.94)
(C4 )
(0.24, 0.48, 0.49) (0.19, 0.5, 0.51)
(0.38, 0.81, 0.82) (0.38, 0.56, 0.57)
(0.89, 0.95, 0.96) (0.25, 0.85, 0.86)
(0.95, 0.96, 0.963) (0.24, 0.89, 0.895)
Table 4. The weighted attribute values (C1)
(C2)
(C3)
(C4)
(C1)
(0 0.41 1.11) (0 0.43 0.76)
(0 0.44 1.16) (0 0.76 0.77)
(0 0.39 1.25) (0.0013 0.7706 0.7709)
(0 0.41 0.82) (0 0.31 0.48)
(C2)
(0 0.24 0.44) (0 0.097 0.099)
(0 0.26 0.31) (0 0.47 0.489)
(0 0.26 0.29) (0 0.69 0.7)
(0 0.24 0.76) (0 0.37 0.76)
(C3)
(0 0.18 0.34) (0 0.87 0.88)
(0 0.17 0.21) (0 0.65 0.83)
(0 0.19 0.25) (0 0.67 0.68)
(0 0.19 0.43) (0 0.45 0.76)
(C4)
(0 0.19 0.36) (0 0.48 0.51)
(0 0.19 0.23) (0 0.53 0.534)
(0 0.17 0.19) (0 0.77 0.78)
(0 0.17 0.18) (0 0.46 0.81)
Table 5. The ideal alternative
a∗
A
B
A
B
A
B
A
B
0, 0.4, 0.74
0, 0.98, 1
0, 0.24, 0.29
0, 0, 1
0, 0.18, 0.2
0, 0.99, 1
0, 0.18, 0.19
0, 0.5.1
Then, we calculate values of distance between each alternative ai = (ZCi1 , ..., ZCi4 ) (Table 6) and the ideal one a∗ = (Z1∗ , ..., Z4∗ ). The distance is defined as below: 4 ∗ D(ai , a ) = D2 (Zij , Z ∗ ) (3) j=1
, Z ∗ ) is depicted in Definition 4. The determined results are given in Table 6.
where D(Zij As a final solution, at the 4th stage, we compare the alternatives as ai ak if D(ai , a∗ ) ≤ D(ak , a∗ ). ∼ So, the results are given as follow: a3 a2 a4 a1
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D(ai , a∗ )
α1
0.61
α2
0.46
α3
0.44
α4
0.55
5 Conclusion This research paper is dedicated to creating the comparison between criteria as hedonism, shopping experience, brand perception and purchasing intention in consumer buying practice by using the Z-number approach. In research paper we offered method to decision making on consumer buying behavior under Z-valued information. Four alternatives (determinants) are determined. The expressed problem comprises PCM with Z-valued degrees of relative significance of attribute. Pairwise comparison matrix is described by a low degree of consistency. The eigenvector is defined to yield Z-valued importance weights of the criteria. Having defined these significance weights and Z-valued attribute estimates of alternatives (variables), the multi-attribute decision problem is solved. The offered way permits to deal with Z-valued information straightly (by applying essential arithmetic of Z-numbers and the different techniques lately offered by the researches). The suggested method can be used for different areas of Marketing Management and consumer behavior to solve different decision-making problems.
References 1. Kumar, A.A.: Factors influencing customers buying behavior. J. Mark. Consum. Res. Int. Peer Rev. J. 27, 30–34 (2016) 2. Sadikoglu, G.: Modeling of consumer buying behaviour using Z-number concept. IASC 24(1), 173–178 (2018). https://doi.org/10.1080/10798587.2017.1327159 3. Dovlatova, K.J.: Estimation of benchmarking influence in Buyer’s decision-making process by using fuzzy AHP. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 173–182. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-92127-9_26 4. Adilova, N.E.: Quality criteria of fuzzy IF-THEN rules and their calculations. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 55–62. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-640 58-3_7 5. Aliev, R.A., Huseynov, O.H., Serdaroglu, R.: Ranking of Z-numbers and its application in decision making. Int. J. Inf. Technol. Decis. Mak. 15(6), 1503–1519 (2016). https://doi.org/ 10.1142/S0219622016500310 6. Zadeh, L.A.: Methods and systems for applications for Z-numbers. US Patent, 8311973 B1 (2012)
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7. Aliev, R.A., Huseynov, O.H., Aliyev, R.R., Alizadeh, A.V.: The Arithmetic of Z-Numbers. Theory and Applications. World Scientific, Singapore (2015) 8. Aliev, R.A., Alizadeh, A.V., Huseynov, O.H.: The arithmetic of discrete Z-numbers. Inf. Sci. 290, 134–155 (2015). https://doi.org/10.1016/j.ins.2014.08.024 9. Aliev, R.A.: Uncertain Computation-Based Decision Theory. World Scientific, Singapore (2017) 10. Aliev, R.A., Guirimov, B.G., Huseynov, O.H., Aliyev, R.R.: A consistency-driven approach to construction of Z-number-valued pairwise comparison matrices 18(4), 37–49 (2021). https:// doi.org/10.22111/IJFS.2021.6028 11. Shen, K., Wang, J.: Z-VIKOR method based on a new comprehensive weighted distance measure of Z-number and its application. IEEE Trans. Fuzzy Syst. 26(6), 3232–3245 (2018) 12. Aliev, R.A., Guirimov, B.G., Huseynov, O.H., Aliyev, R.R.: Country selection problem for business venturing in Z-information environment. Inf. Sci. 597(6), 230–243 (2022). https:// doi.org/10.1016/j.ins.2022.03.049
Prediction of the Power Output of a 4.5 kW Photovoltaic System Using Three Empirical Models: A Case Study in Nahr El-Bared, Lebanon Hüseyin Çamur1
, Youssef Kassem1,2,3,4(B) , Mustapha Tanimu Adamu1 and Takudzwa Chikowero1
,
1 Faculty of Engineering, Mechanical Engineering Department, Near East University,
Nicosia 99138, North Cyprus {huseyin.camur,yousseuf.kassem}@neu.edu.tr, {20215363, 20215146}@std.neu.edu.tr 2 Faculty of Civil and Environmental Engineering, Near East University, Nicosia 99138, North Cyprus 3 Energy, Environment, and Water Research Center, Near East University, Nicosia 99138, North Cyprus 4 Engineering Faculty, Kyrenia University, Kyrenia 99138, North Cyprus
Abstract. In this paper, Multilayer Feed-Forward Neural Network (MFFNN) and Cascade Feed-forward Neural Network (CFNN) have been used to predict the electricity production (EP) from a 4.5 kW PV system located in Nahr ElBared, Lebanon. Moreover, the accuracy of the proposed models is compared with the response surface methodology (RSM). For this aim, the hourly data of beam irradiance (BI), diffuse irradiance (DI), reflected irradiance (RI), sun height (SH), air temperature (AT), and wind speed (W) were collected and used as input parameters for the proposed models. The results showed that all proposed models were suitable for predicting the EP of the PV system. Among the developed models, the CFNN model presented significantly better prediction performance based on the value R2 and RMSE. Keywords: Nahr El-Bared · Lebanon · PV system · RSM · MFFNN · CFNN
1 Introduction The growth of energy demand, global warming, climate change, and increasing consumption of fossil fuels has led to the transition from conventional fuel to renewable energy resources [1, 2]. According to [3], utilizing renewable energy as an alternative energy source will help to reduce the environmental problems, essentially greenhouse gas emissions and air pollution due to increasing fossil fuel consumption. Renewable energy including solar energy is rapidly increasing due to economically viable and limited environmental impacts [4]. In recent years, many studies have evaluated solar energy’s potential as a clean power source for electricity generation. For instance, Çamur © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 218–225, 2023. https://doi.org/10.1007/978-3-031-25252-5_32
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et al. [5] evaluated the performance of a 5 kW rooftop photovoltaic (PV) system in Nahr El-Bared, Lebanon. The results indicated that the annual generation of electricity could cover the energy demand and reduce the electricity bill in the selected location. Kassem and Abdalla [6] estimated the potential of rooftop PV electricity in the Red Sea State in Sudan. The results showed that the developed system has huge potential to cover the energy demand of households. According to [7], weather parameters, geographic location, and the PV system’s orientation angles are the essential factors that influenced the energy output of the PV system. Moreover, several studies have used machine learning models to predict the power of PV systems as a function of climate parameters [7–9]. Therefore, it needs to develop a model for estimating the output power of PV systems based on the climate parameters. In this regard, the performance of the MFFNN, CFNN, and RSM are developed to estimate the EP of PV system located in Nahr El-Bared, Lebanon. In this study, the hourly data of beam irradiance (BI), diffuse irradiance (DI), reflected irradiance (RI), sun height (SH), air temperature (AT), and wind speed (W) were collected and utilized as input parameters for the developed models. Additionally, the hourly data of the EP from the 4.5 kW PV system was measured using a data logger. The overall flowchart of the current study is illustrated in Fig. 1.
Fig. 1. Flowchart of the current study
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2 Material and Methods 2.1 Study Area and Data One of the largest Palestinian camps in north Lebanon is the Nahr El-Bared camp. It is located near Tripoli city. The climate of Nahr El-Bared is a solid Mediterranean climate with full seasons and a significant difference in temperature in the seasons and regard to rain and the weather in general. In this study, a 4.5 kW PV system is constructed for generating electricity for the residential building located in Nahr El-Bared. For building the system, mono-Si - CS6X-300M manufactured by Canadian Solar and with efficacy of 15.63% is used. In addition, an inverter with a capacity of 5 kW is selected for converting the direct current into alternating current. The hourly data of BI, DI, RI, SH, AT, W, and EP are collected from 01 January 2020–31 December 2020. Table 1 listed the summary statistics of the used parameters. Table 1. Statistical parameters of mean hourly data during 2020. Variable
Unit
Mean
Standard deviation
Coefficient of variation
Minimum
Maximum
PV-power
W
886.3
1284.1
144.88
0
4378.2
BI
W/m2
156.64
258.68
165.14
0
965.47
DI
W/m2
74.85
98.19
RI
W/m2
SH
◦
16.761
AT
◦C
20.33
WS
m/s
2.8104
2.2451
131.19
0
464.61
4.027
143.29
0
13.81
21.981
131.15
0
77.38 37.68
7.01
34.48
0.97
1.2882
57.38
0
8.21
2.2 Machine Learning Models (MLMs) MLMs are utilized as a tool to describe a complex system [10, 11]. Wide ranges of ML models are utilized to solve complex problems in a variety of fields [10, 11]. In this study, MFFNN and CFNN are developed to determine the PV-power of a 4.5 kW PV system. MFFNN is one of the most popular artificial neural network approaches for modeling nonlinear and complex processes in the real world [12, 13]. The description of the MFFNN and CFNN models was given in [14]. The training (70%) and testing data (30%) were used to develop and validate the models, respectively. The results of the MFFNN and CFNN models are compared with observed data.
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2.3 Response Surface Methodology The RSM is a mathematical and statistical method polynomial model as expressed below [15, 16]. Y = β0 +
n i=1
βi xi +
n i=1
βii xi2 +
n−1 n i
i=i+1
βij xi xj
(1)
where Y is the predicted response, β0 , βi , are related to the main effects and βii and βij to interaction, x i and x j are the independent variables. The main goal of this model is to show the interaction between the input variables and output variables as shown in (2) PV − power = f (Bi, DI , RI , SH , AT , W )
(2)
3 Results and Discussion 3.1 Estimating the PV-Power Using MFFNN and CFNN Aforementioned, two machine learning models were utilized to estimate the PV-power of a 4.5 kW PV system. Thus, BI, DI, RI, SH, AT and W are used as input parameters. The best network configuration was found by trial and error method and selected based on the lowest value of mean squared error (MSE). The best function is selected through several trials in the training phase. The training function was TRAINLM. The backpropagation algorithm was used to reduce the MSE value between the measured and predicted values. Table 2 summarizes the best configuration for MFFNN and CFNN. Moreover, the scatter plots of the developed models compared to the observed data is presented in Fig. 2. Table 2. Optimal configuration for MLMs MLM
Configuration
Transfer Function
Number of neurons
MSE
MFFNN
6:1:1
TANSIG
8
3.77 × 10–7
CFNN
6:1:1
LOGSIG
10
9.116 × 10–8
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Predicted data [W]
222
4000 3500 3000 2500 2000 1500 1000 500 0
MFFNN
y = 0.9982x + 0.3245 R² = 0.999996
0
1000
2000
3000
4000
Observed data [W]
Predicted data [W]
4000
CFNN
3000 2000 y = 0.9999x + 0.2064 R² = 0.999997
1000 0 0
1000
2000
3000
4000
Observed data [W] Fig. 2. Comparison of the estimated data with the observed data for PV-power using different MLM models
3.2 Estimating the PV Power Using RSM The mathematical equation that was developed using RSM formula (3) for predicting the PV-power is expressed as shown below. PV − power = −16.18 + 4.9334 · BI + 4.916 · DI − 48.15 · RI − 3.022 · SH + 1.225 · AT + 3.34 · W − 0.001582 · BI 2 + 0.001913 · DI 2 − 17.96 · RI 2 + 0.05164 · SH 2 − 0.03118 · AT 2 − 0.504 · W 2 − 0.000954 · BI · DI + 0.4213 · BI · RI − 0.0702 · BI · SH − 0.012406 · BI · AT + 0.07749 · BI · W + 0.2575 · DI · RI − 0.06495 · DI · SH − 0.01975 · DI · AT + 0.0276 · DI · W + 3.997 · RI · SH − 0.0958 · RI · AT − 2.367 · RI · W − 0.00105 · SH · AT + 0.1215 · SH · WS − 0.0987 · AT · W
(3)
Figure 3 compares the scatter plots of the RSM model versus the observed data in testing phase. It can be noticed that the estimated values are closed to the measured data.
Predicted data [W]
Prediction of the Power Output of a 4.5 kW Photovoltaic System
4000 3500 3000 2500 2000 1500 1000 500 0
223
RSM
y = 0.9993x + 0.8529 R² = 0.99973
0
1000
2000
3000
4000
Observed data [W] Fig. 3. Comparison of the estimated data with the observed data for RSM.
3.3 Performance Evaluation of MFFNN, CFNN, and RSM The performance of MFFNN and CFNN is compared with the RSM to evaluate the performance of the proposed models. The values of R-squared and root mean squared error (RMSE) are listed in Table 3. It is noticed that the maximum R-squared value and minimum RMSE were obtained from the CFNN model. Table 3. Performance evaluation of the models. Statistical indicator RSM
MFFNN
CFNN
R-squared
0.99973 0.999996 0.999997
RMSE*
0.00455 0.00076
0.00049
*RMSE for normalized data
4 Conclusions The PV output power estimation is essential for the power grid’s secure, stable, and economical operation. Therefore, three models, namely, MFFNN, CFNN, and RSM, were developed to determine the EP of a 4.5 kW PV system. The results showed that all proposed models were suitable for estimating the PV-power of the PV system. Among the developed models, the CFNN model presented significantly better prediction performance based on the value R2 and RMSE. In future work, various models with various combinations of parameters including rainfall, relative humidity, and wet-bulb temperature should propose to categorize the most influencing input parameters for predicting the PV-power output value of the PV system.
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References 1. Tercan, E., Eymen, A., Urfalı, T., Saracoglu, B.O.: A sustainable framework for spatial planning of photovoltaic solar farms using GIS and multi-criteria assessment approach in Central Anatolia, Turkey. Land Use Policy 102, 105272 (2021). https://doi.org/10.1016/j.landusepol. 2020.105272 2. Shorabeh, S.N., Firozjaei, M.K., Nematollahi, O., Firozjaei, H.K., Jelokhani-Niaraki, M.: A risk-based multi-criteria spatial decision analysis for solar power plant site selection in different climates: a case study in Iran. Renew. Energy 143, 958–973 (2019). https://doi.org/ 10.1016/j.renene.2019.05.063 3. Neupane, D., Kafle, S., Karki, K.R., Kim, D.H., Pradhan, P.: Solar and wind energy potential assessment at provincial level in Nepal: geospatial and economic analysis. Renew. Energy 181, 278–291 (2022). https://doi.org/10.1016/j.renene.2021.09.027 4. Kassem, Y., Gökçeku¸s, H., Güvensoy, A.: Techno-economic feasibility of grid-connected solar PV system at Near East University hospital, Northern Cyprus. Energies 14(22), 7627 (2021). https://doi.org/10.3390/en14227627 5. Çamur, H., Kassem, Y., Alessi, E.: A techno-economic comparative study of a grid-connected residential rooftop PV panel: the case study of Nahr El-Bared, Lebanon. Eng. Technol. Appl. Sci. Res. 11(2), 6956–6964 (2021). https://doi.org/10.48084/etasr.4078 6. Kassem, Y., Abdalla, M.H.A.: Modeling predictive suitability to identify the potential of wind and solar energy as a driver of sustainable development in the Red Sea State, Sudan. Environ. Sci. Pollut. Res., 1–22 (2022). https://doi.org/10.1007/s11356-022-19062-9 7. Kassem, Y., Othman, A.A.: Selection of most relevant input parameters for predicting photovoltaic output power using machine learning and quadratic models. Model. Earth Syst. Environ., 1–26 (2022). https://doi.org/10.1007/s40808-022-01413-7 8. da Silva Fonseca, J.G., Jr., Oozeki, T., Takashima, T., Koshimizu, G., Uchida, Y., Ogimoto, K.: Use of support vector regression and numerically predicted cloudiness to forecast power output of a photovoltaic power plant in Kitakyushu, Japan. Prog. Photovolt. Res. Appl. 20(7), 874–882 (2012). https://doi.org/10.1002/pip.1152 9. Kumar, P.M., Saravanakumar, R., Karthick, A., Mohanavel, V.: Artificial neural networkbased output power prediction of grid-connected semitransparent photovoltaic system. Environ. Sci. Pollut. Res. 29(7), 10173–10182 (2021). https://doi.org/10.1007/s11356-021-163 98-6 10. Berjawi, A.H., Najem, S., Faour, G., Abdallah, C., Ahmad, A.: Assessing Solar PV’s Potential in Lebanon. Issam Fares Institute for Public and International Affairs (2017) 11. Kassem, Y., Gökçeku¸s, H., Janbein, W.: Predictive model and assessment of the potential for wind and solar power in Rayak region, Lebanon. Model. Earth Syst. Environ. 7(3), 1475–1502 (2020). https://doi.org/10.1007/s40808-020-00866-y 12. Kassem, Y., Gökçeku¸s, H., Maliha, M.R.M.: Identifying most influencing input parameters for predicting chloride concentration in groundwater using an ANN approach. Environ. Earth Sci. 80(7), 1–16 (2021). https://doi.org/10.1007/s12665-021-09541-6 13. Kassem, Y., Gökçeku¸s, H., Alassi, E.: Identifying most influencing input parameters for predicting Cereal production using an artificial neural network model. Model. Earth Syst. Environ. 8(1), 1157–1170 (2021). https://doi.org/10.1007/s40808-021-01148-x 14. Kassem, Y., Gokcekus, H.: Do quadratic and Poisson regression models help to predict monthly rainfall? Desalin. Water Treat. 215, 288–318 (2021). https://doi.org/10.5004/dwt. 2021.26397 15. Kassem, Y., Çamur, H.: Prediction of biodiesel density for extended ranges of temperature and pressure using adaptive neuro-fuzzy inference system (ANFIS) and radial basis function (RBF). Procedia Comput. Sci. 120, 311–316 (2017). https://doi.org/10.1016/j.procs.2017. 11.244
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16. Kassem, Y., Gökçeku¸s, H., Çamur, H.: Prediction of kinematic viscosity and density of biodiesel produced from waste sunflower and canola oils using ANN and RSM: comparative study. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 880–887. Springer, Cham (2020). https:// doi.org/10.1007/978-3-030-35249-3_117
Z-Decision Making for the Selection of IT Engineers Gunay A. Huseynzada(B) Joint MBA Program, Azerbaijan State Oil and Industry University, 34 Azadlig Avenue, Baku AZ1010, Azerbaijan [email protected]
Abstract. The paper deals with IT engineer selection problem in decision making to have comprehensive results for every business. Existing works are devoted to solving this issue through the diverse decision making methods under fuzzy information. In this research we suggest new method for solving ˙IT engineer selection process under fuzzy and partially reliable information formalized by using Z-numbers. The proposed approach that is being described is based on general pairwise matrix on criteria including the distance between Z-vectors and the positive and negative ideal solutions of alternatives. A numerical example is provided to illustrate validity of the proposed approach on multi-attribute decision making for employee selection problem. Final decision alternative is selected according to degree of membership of candidates belonging to the optimal solution. Keywords: Decision making · Z-number · Ideal solution · Distance between Z-vectors · IT engineer selection
1 Introduction Personnel selection is procedure for choosing a candidate from a group of applicants who each satisfy the requirements to perform a particular job in the best possible manner [1]. The advancement of every firm requires the recruitment of skilled staff and their selection The ability of an organization to produce a high-quality product at a fair price and according to schedule is significantly influenced by the abilities of its employees [2]. The most important consideration when hiring new employees is matching the right person with the appropriate position [3]. There are several approaches to the issue of personnel selection problem using Fuzzy logic and various MCDM [4]. Some of these methods are the Analytical Hierarchy Process (AHP) [5, 6] Analytic Network Process (ANP), Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) [5], Multi-criteria Optimization and Compromise Solution (VIKOR) [7], Simple Additive Weighting Method (SAW), Elimination Et Choice Translating Reality (ELECTRE), Preference Ranking Organization METHODS for Enrichment Evaluations (PROMETHEE) [8], Fuzzy expert systems.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 226–233, 2023. https://doi.org/10.1007/978-3-031-25252-5_33
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The literature on employee selection has been analyzed in numerous researches[9]. In paper [10] the issue is simplified to a multicriteria decision-making process taking place in a fuzzy environment. Authors provide a technique for estimating the criteria that allows for the regulation and selection of the best option in accordance with the scenario that best suits the decision-needs maker’s at the moment. Research [11] refers to ANOVA single factor theory. The study’s conclusions demonstrated a link between improved organizational productivity and efficiency and recruiting and selection practices. Article [12] examines modeling of supply and demand dynamics in the employment of information technology experts (IT professionals). On the basis of a fuzzy unbalance scale, methodologies are presented for measuring the structural mismatch in the IT professional labor market and the degree of supply and demand disparity. The fuzzy state classification algorithm of imbalance can assist a variety of parties in making judgments about how to handle the differentiation in the demand for IT workers. Unfortunately, up today there are rare multi-attribute decision-making research under Z-environment. Taking into consideration actual concerns, the Z-number idea was presented by Professor Zadeh. A Z-number is made up of two fuzzy numbers, A and B, where A is a soft constraint on the value of an interest variable and B is a soft constraint on the value of a probability measure of A, acting as a reliability factor for A [13]. In this paper, we suggest a novel strategy called consistency-driven partially reliable preferences. For IT engineer selection using Z-number-valued entries in multi-attribute decision analysis. The paper is set up as follows. We present some background information in Sect. 2, such as definitions of discrete Z-numbers, the distance between Z-numbers, operations over Z-numbers, etc. In Sect. 3 we state the problem of employee selection using information with a Z-number value. The suggested approach to resolving the issue described in Sect. 3 is illustrated in Sect. 4 of this article. Section 5 is conclusion.
2 Preliminaries Definition 1. Z-number [14]. The value of a variable X is expressed as an ordered pair of fuzzy numbers termed a “Z-number,” where A is an imperfect restriction on the values of X and B is an imprecise assessment of the reliability of A and is taken into account as a value of probability measure of A. Z = (A, B) Definition 2. Discrete Z-number Discrete Z-number [15]. An ordered pair Z = (A, B) is referred to as a discrete Z-number if A is a discrete fuzzy number that represents a fuzzy constraint on the possible values of a random variable X: X is A, and B is a discrete fuzzy number with a membership function μB : {b1 , ..., bn } → [0, 1], which describes a fuzzy constraint on the probability measure of A: P(A) is B
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Definition 3. Operations over Discrete Z-numbers [16, 17]: Assume X1 and X2 be discrete Z-numbers describing information about values of X1 and X2 . Whether taking into consideration of the calculation Z12 = Z1 ∗ Z2 , ∗ ∈ {+, −, ·, /}. A12 = A1 ∗ A2 is initial stage. The second stage concerns construction B12 . We identify that in Z-numbers Z1 and Z2 , the ‘true’ probability distributions p1 and p2 are not exactly known. When compared, fuzzy restrictions represented in terms of the membership functions are available n n 1 2 μA1 (x1k )p1 (x1k ) , μp2 (p2 ) = μB2 μA2 (x2k )p2 (x2k ) μp1 (p1 ) = μB1 k=1
k=1
Probability distributions pjl (xjk ), k = 1, .., n probabilistic uncertainty over X12 = X1 + X2 . Given any possible pair p1 , p2 , the convolution p12 = p1 ◦ p2 is computed as p12 (x) = p1 (x1 )p2 (x2 ), ∀x ∈ X12 ; x1 ∈ X1 , x2 ∈ X2 . x1 +x2 =x
Given p12s , the value of probability measure of A12 is computed: P(A12 ) =
n
μA12 (x12k )p12 (x12k ).
k=1
However, p1 and p2 are presented by fuzzy restrictions which coerce fuzzy set of convolutions: μp12 (p12 ) = max{p1 , p2 :p12 =p1 ◦p2 } min{μp1 (p1 ), μp2 (p2 )} Fuzziness of information on p12 induces fuzziness of P(A12 ) as a discrete fuzzy number B12 . The membership function μB12 is described as μB12 (b12 ) = max μp12 (p12 ) according to b12 =
n
μA12 (xi )p12 (xi )
i=1
Consequently, Z12 = Z1 ∗ Z2 is obtained as Z12 = (A12 , B12 ). Definition 4. A distance between Z-numbers [17, 18].
Z-Decision Making for the Selection of IT Engineers
D(Z1 , Z2 ) =
229
n m 1 L L L + R − aR + 1 − bL2α + bR − bR a a1αk − a2α b 1α 2α 1α 1α 2α k k k k k k k n+1 m+1 k=1
k=1
where aαL = min Aα , aαR = max Aα , bLα = min Bα , bRα = max Bα
3 Statement of the Problem Construction of Pairwise Matrix on Criterion for 1st , 2nd , 3rd Experts Take the challenge of selecting an IT engineer using multi-attribute decision-making with information that is valued at a Z-number. Let’s say the firm wants to bring on a new engineer. Three individuals were selected after preliminary screening. A1 , A2, A3 remain for the next evaluation. Three specialists on a committee for the purpose of conducting the interview and choosing the best applicant, E1, E2, and E3 have been developed. The following five criteria are considered [19]. C1 C2 C3 C4 C5
- Emotional steadiness - Oral Communication - Personality - Past experience - Self confidence
Z-numbers analyze all three options in this scenario based on five criteria. As preliminary step there formalized pairwise matrixes on considerations of each expert. Triangle fuzzy numbers and scaled decision matrices are used in Tables 1 and 2 to depict these Z-numbers’ components below. Table 1. First expert’s decision matrix (C1–C5 compared to C1–C3) C1
C2
C3
C1
(0.9 1 1) (0.7 0.8 0.9)
(1.9 2 2.1) (0.7 0.8 0.9)
(2.9 3 3.1) (0.7 0.8 0.9)
C2
(1/2.1 1/2 1/1,9) (0.7 0.8 0.9)
(0.9 1 1) (0.9 1 1)
(1.9 2 2.1) (0.7 0.8 0.9)
C3
(1/3.1 1/3 1/2.9) (0.7 0.8 0.9)
(1/2.1 1/2 1/1,8) (0.7 0.8 0.9)
(0.9 1 1) (0.9 1 1)
C4
(1/4.1 1/4 1/3.9) (0.7 0.8 0.9)
(1/4.1 1/4 1/3.9) (0.7 0.8 0.9)
(1/3.1 1/3 1/2.9) (0.7 0.8 0.9)
C5
(1/5.1 1/5 1/4.9) (0.7 0.8 0.9)
(1/5.1 1/5 1/4.9) (0.7 0.8 0.9)
(1/2.1 1/2 1/1,9) (0.7 0.8 0.9)
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C5
C1
(3,9 4 4,1) (0.7 0.8 0.9)
(4.9 5 5.1) (0.7 0.8 0.9)
C2
(3,9 4 4,1) (0.7 0.8 0.9)
(4.9 5 5.1) (0.7 0.8 0.9)
C3
(2.9 3 3.1) (0.7 0.8 0.9)
(1.9 2 2.1) (0.7 0.8 0.9)
C4
(0.9 1 1) (0.9 1 1)
(2.9 3 3.1) (0.7 0.8 0.9)
C5
(1/3.1 1/3 1/2.9) (0.7 0.8 0.9)
(0.9 1 1) (0.9 1 1)
Analogous matrices were constructed for 2nd and 3rd experts.
4 Solution of the Problem As the next stage, we calculate appropriate values of each experts’ matrixes. Obtained results have been expressed in Tables 3 and 4 presented below [20, 21]. Table 3. Average of obtained Z-numbers (C1–C5 compared to C1–C3) C1
C2
C3
C1
(0.99 1 1) (0.99 1 1)
(0.9 1 1.3) (0.2 0.4 0.5)
(1.6 1.7 1.8) (0.3 0.4 0.5)
C2
(1 1/1.3 1/0.9) (0.2 0.4 0.5)
(0.99 1 1) (0.99 1 1)
(2.4 2.4 2.5) (03. 0.4 0.5)
C3
(1/1.8 1/1.7 1/1.6) (0.3 0.40.5)
(1/2.5 1/2.4 1/2.4) (03. 0.4 0.5)
(0.99 1 1) (0.99 1 1)
C4
(1/1.8 1/1.7 1/1.7) (0.3 0.40.5)
(1/3.1 1/3 1/2.9) (0.6 0.6 0.7)
(1/2.6 1/2.5 1/2.4) (0.5 0.5 0.6)
C5
(1/2.4 1/2.4 1/3.1) (0.3 0.4 0.5)
(1/2.8 1/2.7 1/2.6) (0.3 0.4 0.5)
(1/1.2 1/1.17 1/1.07) (0.3 0.4 0.5)
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Table 4. Average of obtained Z-numbers (C1–C5 compared to C4–C5) C4
C5
C1
(1.7 1.7 1.8) (0.3 0.4 0.5)
(3.1 2.4 2.4) (0.3 0.4 0.5)
C2
(2.9 3 3.1) (0.6 0.6 0.7)
(2.6 2.7 2.8) (0.3 0.4 0.5)
C3
(2.4 2.5 2.6) (0.5 0.5 0.6)
(1.07 1.17 1.2) (0.3 0.4 0.5)
C4
(0.99 1 1) (0.99 1 1)
(1.3 1.36 1.4) (0.3 0.4 0.5)
C5
(1/1.4 1/1.36 1/1.3) (0.3 0.4 0.5)
(0.99 1 1) (0.99 1 1)
Tables 5 contains the Z-valued data on the criteria evaluated for the options [22–24]. Table 5. Z-valued criteria evaluations (C1)
(C2)
(C3)
(C4)
(C5)
A1 (1.26 1.48 1.48) (1.87 1.87 5.11) (1.48 1.48 1.62) (1.28 2.43 4.84) (2.02 3.05 6.25) (0.12 0.34 0.36) (0.85 0.88 0.88) (0.12 0.69 0.78) (0.82 0.82 0.83) (0.29 0.81 0.84) A2 (1.47 2.17 2.17) (1.64 1.64 2.20) (1.33 2.57 2.57) (1.44 2.30 2.30) (271 2.71 2.72) (0.57 0.78 0.78) (0.17 0.17 0.86) (0.91 0.91 0.93) (0.27 0.47 0.47) (0.20 0.20 0.79) A3 (2.62 2.62 7.75) (1.83 1.83 5.29) (1.29 1.68 4.10) (1.38 1.38 3.23) (3.45 3.45 4.17) (0.27 0.78 0.88) (0.04 0.87 0.87) (0.12 0.88 0.88) (0.20 0.67 0.67) (0.13 0.34 0.89)
Following appraisal contains obtained the weighted values of criteria by using the arithmetic of Z-numbers. W1
0.00
2.27
1.82
W2
0.23
−0.18
2.00
W3
6.61
−3.89
0.00
Next, we calculate values of distance between each alternative ai = (ZCi1 , ..., ZCi4 ) and the ideal one a∗ = (Z1∗ , ..., Z4∗ ). The distance is found as follows: D(ai , a∗ ) =
4 j=1
D2 (Zij , Z ∗ )
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G. A. Huseynzada Table 6. The values of distance Alternative
D(ai , a∗ )
a1
0,63
a2
0,74
a3
0,57
According to the obtained values minimum alternative is the most appropriate candidate for IT department.
5 Conclusion Currently when it comes to dealing with interval and fuzzy MADM, several techniques have been created, but there is little study on multi-attribute decision making when dealing with Z-information. In this paper to solve mentioned human resources management problem we apply pairwise matrix on criteria including the Z-vectors and the optimum solution notion are separated by distance. Numerical definition on MADM ˙IT engineer selection problem indicates the quality and effectiveness of offered approach. It is possible to implement the suggested approach to the problem of choosing IT engineers in Z-number based calculation programming system.
References 1. Salehi, K.: An integrated approach of fuzzy AHP and fuzzy VIKOR for personnel selection problem. GJMBR 3(3), 89–95 (2016) 2. Afshari, A.R., Nikoli´c, M., Akbari, Z.: Personnel selection using group fuzzy AHP and SAW methods. JEMC 7(1), 3–10 (2017). https://doi.org/10.5937/jemc1701003A 3. Mammadova, M.H., Jabrayilova, Z.G., Nobari, S.M.: Application of TOPSIS method in support of decisions made in staff management issues. In: IV International Conference (PCI), no. 4, pp. 195–198 (2012) 4. Ersoy, N.: Decision making process for personnel selection under fuzzy environment. SSRJ 6(3), 67–75 (2017) 5. Hashemkhani, S.Z., Antucheviciene, J.I.: Team member selecting based on AHP and TOPSIS grey. Ekonomika Eng. Econ. 23(4), 425–434 (2012) 6. Aliyev, R.R.: Multi-attribute decision making based on Z-valuation. In: ICAFS (2016) 7. Jabbarova, K., Alizadeh, A.V.: Z-decision making in human resources department. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 498–507. Springer, Cham (2021). https://doi.org/10.1007/978-3030-64058-3_62 8. Afshari, A.R., Anisseh, M, Shahraki, M.R., Hooshyar, S.: PROMETHEE use in personnel selection. In: ICTM (2016) 9. Afshari, A.R., Yusuff, R.M, Hong, T.S., Ismail, Y.B.: A review of the applications of multi criteria decision making for personnel selection problem. Afr. J. Bus. Manage. 5(28) (2011) 10. Mammadova, M., Jabrayilova, Z., Mammadzada, F.: Fuzzy multicriterial methods for the selection of IT-professionals. IJISAE 3, 40–45 (2015)
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11. Chaya, J.S., Vanishree, B., Nanjundeswaraswamy, T.S.: Recruitment and selection process in the IT firms. GIS Sci. J. 8(5), 343–356 (2021) 12. Mammadova, M., Jabrayilova, Z., Mammadzada, F.: Fuzzy approach to estimate the demand and supply quantitative imbalance at the labor market of information technology specialists. IJISAE (2015). https://doi.org/10.18201/ijisae.24856.1039 13. Zadeh, L.A.: A note on a Z-number. Inf. Sci. 181, 2923–2932 (2011) 14. Aliev, R.A., Alizadeh, A.V., Huseynov, O.H.: The arithmetic of discrete Z-numbers. Inf. Sci. 290, 134–155 (2015). https://doi.org/10.1016/j.ins.2014.08.024 15. Aliev, R.A., Huseynov, O.H., Aliyev, R.R., Alizadeh, A.V.: The Arithmetic of Z-Numbers. Theory and Applications. World Scientific, Singapore (2015) 16. Aliyev, R.R.: Similarity based multi-attribute decision making under Z-information. In: Eighth International Conference on Soft Computing with Words and Perceptions in System Analysis, Decision and Control, pp. 33–39 (2015) 17. Aliev, R.A., Gardashova, L.A.: Z-set based approach to control system design. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 10–21. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-640 58-3_2 18. Aliev, R.A., Huseynov, O.H., Serdaroglu, R.: Ranking of Z-numbers and its application in decision making. Int. J. Inf. Technol. Decis. Mak. 15(6), 1503–1519 (2016). https://doi.org/ 10.1142/S0219622016500310 19. Agakishiyev, E.: Supplier selection problem under Z-information. In: ICAFS 2016 (2016) 20. Aliev, R.A., Guirimov, B.G., Huseynov, O.H., Aliyev, R.R.: Z-relation equation-based decision making. Expert Syst. Appl. (2021). https://doi.org/10.1016/j.eswa.2021.115387 21. Aliev, R.A., Guirimov, B.G., Huseynov, H., Aliyev, R.R.: A consistency-driven approach to construction of Z-number-valued pairwise comparison matrices. Iran. J. Fuzzy Syst. 18, 37–49 (2021) 22. Jabbarova, K.I.: Multiattribute evaluation of weapon systems under Z-information. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 359–365. Springer, Cham (2020). https://doi.org/10. 1007/978-3-030-35249-3_46 23. Aliyeva, K.: Eigensolution of 2 by 2 Z-matrix. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 758– 762. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-35249-3_98 24. Aliev, R.A., Huseynov, O.H., Aliyeva, K.R.: Toward eigenvalues and eigenvectors of matrices of Z-numbers. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 309–317. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-35249-3_39
Optimal Implicatıon Based Fuzzy Control System for a Steam Generator L. A. Gardashova(B)
and K. A. Mammadova
Department of Computer Engineering, Azerbaijan State Oil and Industry University, Baku, Azerbaijan [email protected]
Abstract. The main advantage of a fuzzy set approach to control engineering is that it can be used to replace very complex and computationally demanding systems of partial differential equations. In this paper, we propose a new method for choosing implications. Proposed method allows to compare six fuzzy implications. The problem of identifying a control system with nonlinearity and operating in uncertain conditions is considered, and the synthesis of the system is carried out according to the operation of fuzzy logic. The development of a fuzzy control algorithm for a highly uncertain control object – a steam generator, the architecture of the fuzzy control system and the definition of its elements are considered. The fuzzy identification of a dynamic object, the analysis of the influence of various fuzzy implications on the process identification and the determination of the optimal implication are carried out using the example of a steam generator of thermal-power-plant (TPP) power units. Keywords: Fuzzy set · Fuzzy relation · Implication · Fuzzy controller · Steam generator
1 Introduction In modern control systems, the use of fuzzy control algorithms, based on artificial intelligence technology, is widespread. The use of a fuzzy control algorithm in the automatic control system makes it possible to obtain higher quality indicators compared to the classical controller. A fuzzy control system reduces resource consumption and energy costs, improves product quality and provides higher resistance to destructive factors compared to a classical automatic control system. When forming mathematical models of systems, the operation of forming uncertainty factors serves as a means of increasing the compatibility (adequacy) of given models with reality, as a result of which the actual effectiveness of the decisions being made is substantiated. At the same time, when creating the system, much attention was paid to the area of mathematically poorly formed or incompletely formed knowledge [1–3]. Such models are called “soft”. They have empirical rules for building knowledge bases; qualitative, heuristic, intuitive, approximate values determined by fuzzy, indefinite intervals. The formation of such information, its processing and management, based on Zadeh’s fuzzy set theory, allows, when describing © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 234–246, 2023. https://doi.org/10.1007/978-3-031-25252-5_34
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fuzzy concepts and procedures, to abandon the “excessive” accuracy brought in by traditional modeling approaches, while maintaining its seriousness. In [2], an approximate mathematical model of a thermal power plant was developed by using real time data on Computer Aided Design and Control software. Authors discuss different controller types being applied to the power plant model. It appears that fuzzy gain scheduled proportional and integral (FGPI) controllers demonstrate better performance than the rest of the controllers considered in the study. The description of information has strong influence on the outcome of the control process. In addition, parameterized operations in the fuzzy domain are legitimately aimed at effective analysis: not at single-purpose or intuitive aspects, but at using the apparatus of fuzzy set theory as reliable sources for obtaining quantitative information. In the [3–8], attention was drawn to the fact that the theory of fuzzy sets (for example, Fuzzy implications) more adequately reflects the essence of the control process. In scientific literature, there are multiple researches considering implications and their applications. In the last few decades, a number of different fuzzy implications have been proposed [9–17]. Fuzzy Implication Axioms, Dependence versus Independence of the Fuzzy Implication Axioms, Robustness of Fuzzy Logic Operators in Fuzzy Rulebased Systems, Fuzzy Adjunctions and Fuzzy Morphological Operations Based on Fuzzy Implications have been presented and currently are applied and discussed in scientific literature [18–26]. It is known that a steam generator, as a control object in energy production, possesses high uncertainty and non-linearity. So obtaining its simple deterministic model and synthesizing the corresponding control system do not meet the requirements for system quality indicators. Sometimes such systems even lead to unstable operation performance. When a control system [27–30] is based on the knowledge of an experienced specialist, control algorithms take uncertainties into account, which ensures high-quality control. The review of scientific literature devoted to the application of optimal fuzzy effects showed that, in the synthesis of fuzzy controllers, the issue of comparative study of optimal fuzzy effects in accordance with the accuracy criteria has not been resolved yet.
2 Statement of the Problem This paper considers the development of a fuzzy control algorithm for a steam-generator object, which embraces the architecture of the fuzzy control system and the definition of its elements. The technical implementation of a fuzzy control system for the channel “fuel consumption - outlet steam temperature” in the steam generator can be described as shown in Fig. 1. In the system described in Fig. 1, (1) is the managed object, which is a oncethrough steam generator. Here, the control action is the amount of fuel, and the controlled variable is a thermocouple (2), which measures the temperature of the steam at the outlet of the generator; (3) is a device that measures the force of thermoelectric motion and converts it into a unified signal; (4) is an analog-to-digital converter (ADC), which function is to convert an analog signal to the digital one; (5) is a comparator, which determines the difference between the required pre-set temperature and the current temperature of the steam generator; (6) is a block that differentiates the input error signal (e); (7) is a
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L. A. Gardashova and K. A. Mammadova
fuzzifier; (F1) – fuzzy error signal (e) turns into a fuzzy set (E). The corresponding fuzzy ∼
sets E˜ and E˙ are determined by introducing the error and the rate of error change into the fuzzifiers (7).
Fig. 1. Scheme for the implementation of a fuzzy ACS of a steam generator
(8) is the logical extraction block, where the fuzzy error and error derivative sets (E˜ ∼
˙ respectively) are extracted based on the fuzzy link composition matrix with and E, maximin composition and the current control fuzzy set (U˜ ) is determined, i.e.,
∼
U˜ = E˜ ◦ (E˙ ◦R(e, e˙ , u))
(1)
µ(u) = max{min(µ(e, e˙ ), µ(e, e˙ , u)}
(2)
u
Here R(e, e˙ , u) is the membership matrix of a fuzzy relation, determined on the basis of an expert table of fuzzy linguistic rules about managing objects, i.e., the knowledge base, and through the optimal fuzzy implication operator. (9)
is a block of knowledge base and fuzzy control database. The definition of a fuzzy knowledge base is an important step in solving the problem of control synthesis and is based on expert assessment. The expert’s judgments about management are defined as linguistic rules in Table 1.
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(10) is a defuzzification block, the fuzzy control outputs a fuzzy value from the set U˜ . The center of gravity method is used as a defuzzification method. (11) is a digital-to-analog converter, which converts the control action being in the form of a binary code into a unified analog electrical signal. (12) is a conversion device that converts an analog unified electrical signal into a unified pneumatic signal. Affects a single (0.2–1 kgQ/sm2 ) pneumosignal (13)-membrane mechanism of action (MMA). MMA, changing the amount of fuel, changes the temperature at the outlet of the steam generator in one direction or another. The knowledge base of the fuzzy control of the steam generator is defined in the form of linguistic rules as follows: If the control error is positive large (e= positive L) and the error change ) then the control will be negative rate is negative medium ( ̇ = small (u= negative S), If the control error has a negative medium (e=NM) and the error change rate is positively small ( ̇ = positive S), then the control will be positive small (u= PS), Also (3) If the control error has a positive medium (e= positive M), and the rate of error change has a negative medium ( ̇ =NM), then the control is zero (u=Z), Also, If the control error is positive medium (e= positive M) and the error change rate is positively small ( ̇ = positive S), then the control is negatively large (u=NL), Also, . .. . . .. . .. . ..
The fuzzy linguistic rules that we have defined are illustrated in Table 1. The following linguistic terms are adopted in this table: NL - negative large; NM-negative medium; NS - negative small; Z-zero; PositiveS - positive small; PositiveM - positive medium; PositiveL - positive large. The values of the control error, the rate of change of errors and modes of membership functions of term-sets output - control effect are shown in Table 1. Table of linguistic rules is stored in memory as a matrix of fuzzy relations in a knowledge base block. All terms represent usage of sigmoid membership functions. For example, µei (e) =
1 1 + [Ce (ei − ei )]2
, i = 1, 15
Membership functions of control error, change rate of error, and term sets of control effect are given in Tables 2, 3, 4, respectively
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L. A. Gardashova and K. A. Mammadova Table 1. Table of Linguistic Rules (TLR).
Table 2. Control error Terms
NB
NM
NS
Z
PosS
PosM
PosB
e˜ i
0,24
0,39
0,68
1,00
0,86
0,49
0,26
Table 3. Change rate of error Terms
NB
NM
NS
Z
PosS
PosM
PosB
e˙ j
0,50
0,67
0,90
0,97
1,00
0,86
0,59
Table 4. Term sets of control effect Terms
NB
NM
NS
Z
PosS
PosM
PosB
u˜ j
0,07
0,15
0,40
1,00
0,50
0,16
0,07
3 Solution of the Problem The solution of the synthesis problem is to determine the structure and parameters of the membership function of the terms of these fuzzy sets - the error (Ei ), the error change ∼
˙ rate E˙ j and the control action (Ul ). Both the error E˜ i and the error rate of change E, as well as the control effect U˜ j , are calculated by the formulas of the corresponding membership functions of fuzzy set terms. From Tables 1, 2 and 3, a fuzzy set of 7 terms is selected for both the error and the error rate of change and control effect in the tentative judgments. Universal set for error E = [−9,9], universal set for error change rate E˙ = [−5,5], for control action U = [−18,0,18], they are described by their values in 15 discrete points; Ei , E˙ j , Ul are elements of fuzzy
Optimal Implicatıon Based Fuzzy Control System for a Steam Generator
239
sets of terms, respectively, such that at these points e = ei , e˙ = e˙ j , u = ul of the membership function µi (e) = 1, µj (˙e) = 1 and µl (u) = 1 Coefficients of membership functions (Ce , Ce˙ , Cu ) are calculated so that the corresponding membership functions of fuzzy term sets are µi (e) ≤ 0.5, µj (˙e) ≤ 0.5, µl (u) ≤ 0.5 [2, 5–7]. In each term, the corresponding -Ce , Ce˙ , Cu - for the fuzzy set take the corresponding values. Based on the table of linguistic rules established on the basis of the knowledge base (Table 1) and the above implications - the logics of Mamdani, ALI1, ALI2, ALI3, Lukashevich and KD, the matrix of fuzzy relations R(ei , e˙ j , ul ) is calculated and stored in memory as a membership matrix. Definition of a matrix of fuzzy relations based on the Mamdani logic based algorithm: Rmamd ei , e˙ j = min(ei , e˙ j ) Imamd ei , e˙ j , ul = min(Rei ,˙ej (ei , e˙ j ) ul ) Rmamd (ei , e˙ j , ul ) = µR (ei , e˙ j , ul ) =
˙ E×E×U
µR (ei , e˙ j ) ∧ µl (u)/(ei , e˙ j , ul )
µi (ei , e˙ j ), µR (ei , e˙ j ) ≤ µl (ul ) , i = 1, n; j = 1, n; l = 1, n µl (ul ), otherwise 7
Rmamd = U Rk (ei , e˙ j , ul ), k = 1, 7,
(4)
k=1
L. Zade’s fuzzy implication (maxmin composition rule) Rzadeh ei , e˙ j = max(min ei , e˙ j , 1 − ei ) Izadeh (ei , e˙ j , ul ) = max(min (Rei ,˙ej (ei , e˙ j ) ul ), 1- Rei ,˙ej (ei , e˙ j )) Rzadeh (ei , e˙ j , ul ) = µi ei , e˙ j ∧ µl (ul ) ∨ (1 − µi (ei , e˙ j ))/(ei , e˙ j , ul )) ˙ E×E×U
i = 1, n; j = 1, n; l = 1, n
(5)
In this work, using the truth value of the disjunction, the logical connector of the logics ALI1, ALI2, ALI3, KD, Lukasiewicz the methods for calculating the matrix of fuzzy relations are defined below. Definition of a matrix of fuzzy relations based on the implication ALI 1: ⎧ ⎨ 1 − ei , ei < e˙ j RALI 1 ei , e˙ j = 1, ei = e˙ j ⎩ e˙ j , ei > e˙ j ⎧ ⎨ Rei ,˙ej ei , e˙ j , Rei ,˙ej < ul RALI 1 ei , e˙ j , ul = 1, µi ei , e˙ j + µj (u) = 1 ⎩ µi ei , e˙ j + µj (u) > 1 µl (u),
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RALI1 (ei , e˙ j , ul ) =
(µ(ei , e˙ j ) ˙ E×E×U
→ µl (ul ))/(ei , e˙ j , ul ),
i = 1, n; j = 1, n; l = 1, n in here, ⎧ ⎨ µi ei , e˙ j , µi ei , e˙ j + µj (u) < 1 1 µi ei , e˙ j ∧ µl (ul ) → µRALI 1 ei , e˙ j , ul == 1, µi ei , e˙ j + µj (u) = 1 ⎩ µl (u), µi ei , e˙ j + µj (u) > 1 7 Rk ei , e˙ j , ul , k = 1, 7 (6) RALI 1 = k=1
Determination of the fuzzy relation matrix based on ALI2 implication: ei ≤ e˙ j 1, RALI 2 ei , e˙ j = min 1 − ei , e˙ j , ei > e˙ j RALI 2 ei , e˙ j , ul 1, RALI 2 ei , e˙j ≤ ul = min 1 − RALI 2 ei , e˙ j , ul , RALI 2 ei , e˙ j > ul
RALI 2 (ei , e˙ j , ul ) = (1 − µ ei , e˙ j , ul )/(ei , e˙ j , ul ) ˙ E×E×U
i = 1, n; j = 1, n; l = 1, n in here, 1 µi ei , e˙ j ∧ µl (ul ) → µRALI2 ei , e˙ j , ul 1, µi ei , e˙ j + µl (ul ) ≤ 1 = min(µi ei , e˙ j , µj (u)), µi ei , e˙ j + µl (ul ) > 1 RALI2 = ∩7k=1 Rk ei , e˙ j , ul k = 1, 7
(7)
Determination of fuzzy relation matrix based on ALI3 implication: 1, ei ≤ e˙ j RALI 3 (ei , e˙ j ) = e˙ j ˙j ei +(1−˙ej ) , ei > e 1, Rei ,˙ej (ei , e˙ j ) ≤ ul e˙ j RALI 3 (ei , e˙ j , ul ) = Re ,˙e (ei ,˙ej )+(1−ul ) , Rei ,˙ej (ei , e˙ j ) > ul i j
RALI3 (ei , e˙ j , ul ) = 1, n in here,
µ(ei , e˙ j ) ˙ E×E×U
→ µ(ul )/(ei , e˙ j , ul ),i = 1, n; j = 1, n; l =
Optimal Implicatıon Based Fuzzy Control System for a Steam Generator
1 µi ei , e˙ j ∧ µl (ul ) → µRALI3 ei , e˙ j , ul ==
241
1, µi (ei , e˙ j ) + µl (u) ≤ 1 1−µ (e ,˙e )
i j , µi (ei , e˙ j ) + µl (u) > 1 1 − µ (e ,˙e i)+µ i i j l (ul )
RALI3 = ∩7k=1 Rk (ei , e˙ j , ul ), k = 1, 7
(8)
Determination of fuzzy relation matrix based on Lukashevich implication: RLukas (ei , e˙ j ) = min(1, 1 − ei + e˙ j ). RLukas (ei , e˙ j , uL ) = min(1, 1 − Rei ,˙ej ei , e˙ j + uL ) RLukas (ei , e˙ j , uL ) = 1, n
µ(ei , e˙ j ) ˙ E×E×U
∧ µ(ul )/(ei , e˙ j , ul ), i = 1, n; j = 1, n; l =
1
µi (ei , e˙ j ) ∧ µl (ul ) → (1 − µi (ei , e˙ j )) ∧ µl (ul ) = max(µi (ei , e˙ j ) + µl (ul ) − 1; 0) RLukasevich = ∩7k=1 Rk (ei , e˙ j , ul ), k = 1, 7
(9)
Determination of fuzzy relation matrix based on KD implication: RKD (ei , e˙ j ) = max(1 − ei , e˙ j ). RKD (ei , e˙ j , uL ) = max(1 − Rei ,˙ej (ei , e˙ j ), uL ) RKD (ei , e˙ j , ul ) =
˙ E×E×U
µ(ei , e˙ j ) ∨ µl (ul )/(ei , ej , ul )
i = 1, n; j = 1, n; l = 1, n 1
µi (ei , e˙ j ) ∧ µl (ul ) → (1 − µi (ei , e˙ j )) ∧ µl (ul ) = min(1 − µi (ei , e˙ j ), µl (ul )) RKD = ∩7k=1 Rk (ei , e˙ j , ul ), k = 1, 7
(10)
Figures 2, 3, 4, 5 and 6 describe the results of computer simulation-modeling of the fuzzy regulation system according to different types of implication operators, i.e., the dependence of the transition process of ACS over time: Relationship matrix on the PD controller of Mamdani implication.
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2
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Fig. 2. Transition process curve of fuzzy ACS using Mamdani implication. (Assignment grade g = 17) 20
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Fig. 3. Transition process curve of fuzzy ACS using ALI1 implication. (Assignment grade g = 17) 20
18
16
14
12
10
8
6
4
2
0 0
20
40
60
80
100
120
Fig. 4. Transition process curve of fuzzy ACS using ALI2 implication (Assignment value g = 17) 12
10
8
6
4
2
0 0
20
40
60
80
100
120
Fig. 5. Transition process curve of fuzzy ACS by KD implication (Assignment value g = 17)
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12
10
8
6
4
2
0 0
20
40
60
80
100
120
Fig. 6. Transition process curve of fuzzy ACS using Lukasevich implication (Task value g = 17)
According to Zade’s maxmin composition, the fuzzy set of control is determined by the formula (1). The defuzzification block determines a fuzzy control signal from the fuzzy control set. Defuzzification can be done in several ways. One of the widely used defuzzification methods in dynamic fuzzy control systems is the formula for finding the centroid center of gravity. N j=1 uj µj (uj ) (11) u(t) = N j=1 µj (uj ) To determine the impact of implications on the quality of the system when using each matrix Rk (ei , e˙ j , ul ), k = 1, 7 the quality criterion of the fuzzy control system is the mean square error (MSE). Jj =
1 N 2 e (t), N = 1, 40 j=1 N
(12)
Table 5 shows the types of fuzzy implications used in the calculation of matrices of fuzzy relations, and the values of the mean square error of control systems. From here, the type of optimal implication is determined based on the minimization of the mean square error. It can be seen from the table that the influence of implication operators on a fuzzy control system with different types of controllers is different. Thus, based on the table, we come to the conclusion that since the ALI1 implication is very effective in astatic and preventive-differentiating control laws, in some cases the ALI2 implication should be considered as the optimal implication in the steam generator control system. Thus, the fuzzy implication operator ALI2 has the smallest mean square error and the best transient process for a system with PD control. Table 5. Root mean square error (J) table Implications
Mamdani
ALI1
ALI2
ALI3
KD
Lukasiewicz
PD controller
14,798.77
2147.62
1625.21
4459.59
4384.85
4459.59
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4 Conclusion When modeling fuzzy objects, a significant influence of the type of optimal implication on the quality of ACS was revealed when calculating the relationship matrix, which is established and determined on the basis of fuzzy linguistic rules. The ACS transient process is stable and aperiodic. The integral quadratic error of ACS (steam generator temperature control) with imitation of a fuzzy PD controller is 1625.21. Temperature adjustment time T = nTd = 5 (n = 10; Td = 0.5), which meets practical requirements. For the above mentioned process fuzzy implication is determined: ALI-2. Our next problem is how to choose the Z implication to be able to describe reliability of information.
References 1. Aliev, R., Aliev, F., Babaev, M.: Fuzzy Process Control and Knowledge Engineerig in Petrochemical and Robotic Manufacturing. Verlag TUV Rheinland, Koln (1991) 2. ˙Ilhan, K., Ertu˘grul, Ç., Hasan, T.: A fuzzy logic controller application for thermal power plants. Energy Conv. Manag. 47(4), 442–458 (2006). https://doi.org/10.1016/j.enconman. 2005.05.010 3. Du, X., Li, P.: Fuzzy logic control optimal realization using GA for multi-area AGC systems. Int. J. Inf. Technol. 12(7), 63–72 (2006) 4. Aiswarya, P., et al.: Comparison of PID and fuzzy-PID control for nuclear steam boiler level control. Int. J. Innov. Technol. Res. 3(2), 1961–1965 (2015) 5. Ali, A.M., Ebrahim, M., Hassan, M.M.: Automatic voltage generation control for two area power system based on particle swarm optimization. Indones. J. Electr. Eng. Comput. Sci. 2(1), 132- 144 (2016). DOI:https://doi.org/10.11591/ijeecs.v2.i1.pp132-144 6. Isamiddin, S., et al.: Algorithms for synthesis of a fuzzy control system chemical reactor temperature. In: III International Workshop on Modeling, Information Processing and Computing.MIP: Computing-2021, pp. 64–70(2021). http://ceur-ws.org/Vol-2899/paper010. pdf 7. Khrystyna, F., Ievgeniia, K., Valery, S.: Optimal design of intelligent control systems of steam turbine using genetic algorithms. Int, Book Series.13, 105–112. http://www.foibg.com/ibs_ isc/ibs-13/ibs-13-p15.pdf 8. Singhala, P., Shah D.N., Patel. B.: Temperature control using fuzzy logic Int. J. Instrum. Control Syst. 4(1), 1–10(2014). https://doi.org/10.5121/ijics.2014.4101 9. Duy, N.T., et al.: Design of Sugeno fuzzy logic controller for resistance furnace. J. Multidiscip. Eng. Sci. Stud. 3(8), 2001–2006(2017). ISSN 2458–925X 10. Tarun Kumar, D., Yudhajit, D.: Design of a room temperature and humidity controller using fuzzy logic. Am. J. Eng. Res. 02(11), 86–97(2013). e-ISSN 2320–0847, p-ISSN 2320- 0936 11. Egoigwe, S.V., Nwobi, Ch., et al.: Application of fuzzy logic temperature controller for water bottle indust. Comput. Eng. Intell. Syst. 10(2), 16–22 (2019). https://doi.org/10.7176/CEIS 12. Kamari, M.L., Isvand, H., Nazari, M.A.: Applications of multi-criteria decision-making (MCDM) methods in renewable energy development: a review. Renew. Energy Res. Appl. 1(1), 47–54 (2020). https://doi.org/10.22044/RERA.2020.8541.1006 13. ˙Ihsan, K., Murat, Ç., Fulya, T.: A comprehensive review of fuzzy multi criteria decision making methodologies for energy policy making. Energy Strat. Rev. 24, 207–228 (2019). https://doi.org/10.1016/j.esr.2019.03.003
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14. Aliev, R.A., Aliev, R.R.: Soft Computing and its Application. World Scientific, New Jersey, London, Singapore, Hong Kong (2001) 15. Aliev, R., Tserkovny, A.: Systemic approach to fuzzy logic formalization for approximate reasoning. Inf. Sci. 181, 1045–1059 (2011) 16. Tserkovny, A.: A t-norm fuzzy logic for approximate reasoning. J. Soft. Eng. Appl. 10, 639–662 (2017). https://doi.org/10.4236/jsea.2017.107035 17. Tserkovny, A.: A fuzzy logic based resolution principal for approximate reasoning. J. Softw. Eng. Appl. 10, 793–823 (2017). https://doi.org/10.4236/jsea.2017.1010045 18. Sinuk, V.G, Panchenko, M.V.: Method of fuzzy inference for one class of MISO-structure systems with non-singleton inputs. IOP Conf. Series: Mater. Sci. Eng. 327 (2018). https:// doi.org/10.1088/1757-899X/327/4/042074 19. Yager, R.R.: On some new classes of implication operators and their role in approximate reasoning. Inf. Sci. 167(1–4), 193–216 (2004). https://doi.org/10.1016/j.ins.2003.04.001 20. Mammadova, K.A.: Construction of fuzzy power generation model of thermal power plants. Sci. Coll. «interconf» 1, 1065–1075 (2021). https://ojs.ukrlogos.in.ua/index.php/interconf/art icle/view/8840 21. Shi, Y., Gasse B., Kerre, E.: Fuzzy implications: classification and a new class. In: Baczy´nski, M., Beliakov, G., Bustince Sola, H., Pradera, A. (eds.) Advances in Fuzzy Implication Functions. Studies in Fuzziness and Soft Computing, vol. 300, pp. 31–51. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-35677-3_2 22. Shi, Y., Ruan, D., Kerre, E.: On the characterizations of fuzzy implications satisfying I(x, y) = I(x, I(x, y)). Inf. Sci. 177(14), 2954–2970 (2007). https://doi.org/10.1007/978-3-642-356 77-3 23. Pei, D.: Unified full implication algorithms of fuzzy reasoning. Inf. Sci. 178, 520–530 (2008). https://doi.org/10.1016/j.ins.2007.09.003 24. Jafarli, M.M., Gardashova, L.A.: Using data mining technology for analysis of hydrogenperoxide decomposition reaction. In: International Conference on Actual Problems of Chemical Engineering Dedicated to the 100th Anniversary of Azerbaijan State Oil and Industry University, pp. 548–553 (2020) 25. Mas, M., Monserrat, M., Torrens, J., Trillas, E.: A survey on fuzzy implication functions. IEEE Trans. Fuzzy Syst. 15(6), 1107–1121 (2007). https://doi.org/10.1109/TFUZZ.2007.896304 26. Mas, M., Monserrat, M., Torrens, J.: The law of importation for discrete implications. Inf. Sci. 179, 4208–4218 (2009). https://doi.org/10.1016/j.ins.2009.08.028 27. Aliev, R.A., Gardashova, L.A.: Z-set based approach to control system design. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) 14th International Conference on Theory and Application of Fuzzy Systems and Soft Computing – ICAFS-2020 . ICAFS 2020. Advances in Intelligent Systems and Computing, vol. 1306, pp. 10–21. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-64058-3_2 28. Ahmadov, S.A., Gardashova, L.A.: Fuzzy dynamic programming approach to multistage control of flash evaporator system. In: Aliev, R., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F. (eds.) 10th International Conference on Theory and Application of Soft Computing, Computing with Words and Perceptions - ICSCCW-2019. ICSCCW 2019. Advances in Intelligent Systems and Computing, vol. 1095, pp. 101–105. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-35249-3_12
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29. Gardashova, L.A.: Synthesis of fuzzy terminal controller for chemical reactor of alcohol production. In: Aliev, R., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F. (eds.) 10th International Conference on Theory and Application of Soft Computing, Computing with Words and Perceptions - ICSCCW-2019. ICSCCW 2019. Advances in Intelligent Systems and Computing, vol. 1095, pp. 106–112. Springer, Cham (2020). https://doi.org/10. 1007/978-3-030-35249-3_13 30. Adilova, N.E.: Quality criteria of fuzzy IF-THEN rules and their calculations. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) 14th International Conference on Theory and Application of Fuzzy Systems and Soft Computing – ICAFS-2020. ICAFS 2020. Advances in Intelligent Systems and Computing, vol. 1306, pp. 55–62. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-64058-3_7
Prediction of Runoff Using Artificial Neural Networks, MLR Regression, and ARIMA Model (A Case Study: Bared River, Lebanon) Youssef Kassem1,2,3,4(B) , Hüseyin Gökçeku¸s2,3,4 , Francis Surfia Dioh2 Marcus Paye Quoigoah2 , and Marilyn Hannah Godwin2
,
1 Faculty of Engineering, Mechanical Engineering Department, Near East University,
Nicosia 99138, North Cyprus, Cyprus [email protected] 2 Faculty of Civil and Environmental Engineering, Near East University, Nicosia 99138, North Cyprus, Cyprus [email protected], {20213607,20213021, 20215601}@std.neu.edu.tr 3 Energy, Environment, and Water Research Center, Near East University, Nicosia 99138, North Cyprus, Cyprus 4 Engineering Faculty, Kyrenia University, Kyrenia 99138, North Cyprus, Cyprus
Abstract. In this paper, Multi-layer perceptron neural network (MLPNN) and Radial basis function neural network (RBFNN) have been used to predict the monthly runoff in Bared River, Lebanon. Moreover, the accuracy of the proposed models is compared with the ARIMA model and Multiple Linear Regression (MLR). For this aim, maximum temperature, minimum temperature, solar radiation, wind speed, soil moisture and were collected and used as input parameters for the proposed models. The results showed that ARIMA and MLPNN models were suitable for predicting the monthly. Among the developed models, the ARIMA has the best performance for runoff prediction. Keywords: Runoff · Bared river · MLPNN · RBFNN · ARIMA · MLR
1 Introduction Climate change is an important factor in the strategic management of water resources in dry and semi-arid countries [1]. Several researchers have studied the effects of climate change on water resources [2, 3]. Thus, investigating the influence of climate change on the hydrologic cycle is vital for hydrology development. Several studies have concluded that climate change is the main indicator related to the changes in runoff in the basin or catchment area [4]. Accordingly, predicting the amount of water in a basin over a period is a very important topic for scientists and engineers for centuries [5]. Additionally, the analysis of runoff is very important for predicting floods and droughts [6]. Moreover, runoff modeling is a useful tool for designing and operating the various components of water resources © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 247–255, 2023. https://doi.org/10.1007/978-3-031-25252-5_35
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projects and water resource planning and management [7]. It also helps to reduce the influence of drought and water resources issues [8]. Recently, several empirical models of runoff series such as machine learning models and mathematical modeling are developed to construct a long-term runoff forecasting model [5–9]. Bared river, the third largest river in the Akkar district of North Lebanon, has a very important strategic position. It is fed by the springs in the mountains. Recently, the heavy rainfall with snow has led to an extreme flood, which caused flooded some streets up to the windows of the houses especially houses built near the river. Therefore, it is necessary to provide a predictive model that can estimate the runoff in the bared river to minimize the effect of floods in the area. In this regard, four empirical models, namely, MLPNN, RBFNN, ARIMA, and MLR are developed to predict the runoff. For this aim, the monthly global meteorological data including maximum temperature, minimum temperature, wind speed, solar radiation, rainfall, and soil moisture are utilized as input variables for the models.
2 Material and Methods 2.1 Data Due to the limitation of available the actual data of climate parameters, global meteorological data are utilized to understand the influence of geographical coordinates on the prediction of precipitation and predict monthly precipitation using various empirical techniques. In this study, global meteorological data were obtained from TerraClimate. TerraClimate dataset offers global monthly meteorological data with high-spatial resolution (1/24°, ~4-km) monthly climate as well as provides the data since the year 1958 to date [10]. The main reasons to utilize TerraClimate were the availability of consistent long-term monthly maximum temperature (Tmax), minimum temperature (Tmin), solar radiation (SR), wind speed (WS), soil moisture (SM), runoff (Q), and rainfall (R), which is allowed considering an eventual change in climate variables. The statistical parameters of the used variables are tabulated in Table 1. Table 1. Statistical parameters of monthly used data for the period of 1958–2021. Variable
Unit
Mean
Standard deviation
Tmax
◦C
24.62
Tmin
◦C
16.35
R
mm
62.57
71.38
114.07
SM
mm
89.87
66.95
WS
m/s
3.44
DR
W /m2
44.63
191.79
Q
mm
11.78
33.17
5.269 5.364
0.6567
Coefficient of variation 21.4 32.81
Minimum
Maximum
12.63
34.27
3.9
25.95
0
407
74.49
15.9
202.2
19.07
1.8
5.44
429.69
-264.98
265.29
281.6
0
341.7
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2.2 Machine Learning Models (MLMs) MLMs are utilized as a tool to describe a complex system [11]. Wide ranges of ML models are utilized to solve complex problems in a variety of fields [11]. In this study, MLPNN and RBFNN are developed to determine the CFPP of Biodiesel. MLPNN and RBFNN are the most popular artificial neural network approaches for modeling nonlinear and complex processes in the real world. Generally, MLPNN is a feedforward neural tool consisting of three layers (input layer, hidden layer and output layer) [12]. Besides backpropagation algorithm is used for training MLPNN. Furthermore, RBFNN is a variant of feed-forward neural network with a hidden interconnected layer. Distinct advantages of RBFNN include universal approximation abilities, no local minimum problem, and a faster learning algorithm over other ANNs based on previous scientific studies [13]. The description of the MLPNN and RBFNN models is given in [11, 13]. In this study, 70% of the data was used for training, while the remaining data were utilized to test the model. The results of the proposed models are compared with observed data. 2.3 ARIMA Model ARIMA model was developed by Box, Jenkins, and Reinsel [14]. It is very widely used in time series modeling. Moreover, it is defined by three terms (p, d, and q). Box–Jenkins algorithms are utilized to finalize the value of p, d, and q. The description of the ARIMA models is given in [15]. 2.4 MLR Model The MLR is a mathematical statistical model for establishing the relationship between independent and dependent variables (Eq. (1)). Q = f (Tmax.Tmin, SM , R, WS, SR)
(1)
MLR can be expressed as Q = A + B(Tmax) + C(Tmin) + D(R) + E(SM ) + F(WS) + G(DR)
(2)
where A = –5.194, B = –4.254, C = 5.152, D = 0.32, E = 0.066, F = 3.401, and G = –0.005
3 Results and Discussion 3.1 Estimating the Runoff Using MLPNN and RBFNN Aforementioned, two machine learning models were utilized to predict the runoff of biodiesel. Thus, Tmax, Tmin, SR, WS, SM, and R, are utilized as input parameters for the models. The best configuration of the network was found based on the lowest value of mean squared error. Moreover, the trial and error method is employed to find the best parameters for the model. Figures 1 and 2 show the architecture model for MLPNN and RBFNN. Additionally, Table 2 lists the summary and parameters for the proposed models. It is found that the root mean squared error (RMSE) is estimated to be equal to 13.73 and 19.04 for MLPNN and RBFNN, respectively.
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Fig. 1. The structure of MLPNN for predicting the runoff.
Table 2. Network information. Model
Layer
Parameters
Value/function
MLPNN
Hidden Layer(s)
Number of Hidden Layers
2
Number of Units in Hidden Layer 1a
4
RBFNN
Number of Units in Hidden Layer 2a
3
Activation Function
Sigmoid
Output Layer
Activation Function
Linear
Statistical indicator for the training phase
R-squared
0.82
MSE [mm]
188.39
RMSE [mm]
13.73
Number of Units
10
Activation Function
Softmax
Hidden Layer Output Layer
Activation Function
Linear
Statistical indicator for the training phase
R-squared
0.66
MSE [mm]
362.58
RMSE [mm]
19.04
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Fig. 2. The structure of RBFNN for predicting the runoff.
3.2 Estimating the Runoff Using ARIMA and MLR As discussed previously, ARIMA and MLR models were utilized to estimate the runoff of Bared River in Lebanon. Moreover, 70% of the data were used for training, and the remaining data for evaluating the model performance. The results showed that ARIMA (1, 0, 12) model has produced a good agreement with the observed data compared to the MLR model. Time series plots of the observed and predicted runoff values in the training phase are shown in Fig. 3.
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Fig. 3 Comparison of the estimated data with the observed data for runoff using ARIMA and MLR models
3.3 Performance Evaluation of Proposed Models The performance of artificial neural network models is compared with the ARIMA and MLR to find the best model for runoff prediction. The values of R-squared and root mean squared error (RMSE) are listed in Table 3. It is noticed that the maximum R-squared value and minimum RMSE were obtained from the ARIMA model followed by MLPNN with a value of 0.816 for R-squared and 10.25 for RMSE. Figure 4 illustrates the time series plots of the observed and estimated monthly values of runoff in the testing phase. Table 3. Evaluation of model performance. Statistical indicator R-squared RMSE [mm]
MLPNN 0.816 10.25
RBFNN 0.688 12.70
ARIMA 0.859 8.56
MLR 0.513 15.91
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Fig. 4. Comparison of the estimated data with the observed data for all developed models.
4 Conclusions In this study, the ability of MLPNN, RBFNN, ARIMA, and MLR models for monthly runoff prediction was investigated. R-squared and RMSE were employed to evaluate the performance of the models. The results showed that ARIMA and MLPNN models were suitable for estimating the monthly runoff. Among the developed models, the ARIMA model presented significantly better prediction performance based on the value R2 and RMSE.
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In future work, various models with various combinations of parameters should be investigated to identify the parameter that influenced the runoff.
References 1. Ostad-Ali-Askari, K., Ghorbanizadeh Kharazi, H., Shayannejad, M., Zareian, M.J.: Effect of management strategies on reducing negative impacts of climate change on water resources of the Isfahan-Borkhar aquifer using MODFLOW. River Res. Appl. 35(6), 611–631 (2019). https://doi.org/10.1002/rra.3463 2. Karimi, V., Karami, E., Keshavarz, M.: Climate change and agriculture: Impacts and adaptive responses in Iran. J. Integr. Agric. 17(1), 1–15 (2018). https://doi.org/10.1016/S2095-311 9(17)61794-5 3. Ayt Ougougdal, H., Yacoubi Khebiza, M., Messouli, M., Lachir, A.: Assessment of future water demand and supply under IPCC climate change and socio-economic scenarios, using a combination of models in Ourika Watershed, High Atlas. Morocco. Water 12(6), 1751 (2020). https://doi.org/10.3390/w12061751 4. Li, Z., Li, Q., Wang, J., Feng, Y., Shao, Q.: Impacts of projected climate change on runoff in upper reach of Heihe River basin using climate elasticity method and GCMs. Sci. Total Environ. 716, 137072 (2020). https://doi.org/10.1016/j.scitotenv.2020.137072 5. Wang, W.C., Chau, K.W., Qiu, L., Chen, Y.B.: Improving forecasting accuracy of medium and long-term runoff using artificial neural network based on EEMD decomposition. Environ. Res. 139, 46–54 (2015). https://doi.org/10.1016/j.envres.2015.02.002 6. Ji, G., Lai, Z., Xia, H., Liu, H.: Wang, Z: Future runoff variation and flood disaster prediction of the yellow river basin based on CA-Markov and SWAT. Land 10(4), 421 (2021). https:// doi.org/10.3390/land10040421 7. Ghumman, A.R., Ghazaw, Y.M., Sohail, A.R., Watanabe, K.: Runoff forecasting by artificial neural network and conventional model. Alexandria Eng. J. 50(4), 345–350 (2011). https:// doi.org/10.1016/j.aej.2012.01.005 8. Tiwari, D.K., Tiwari, H.L., Nateriya, R.: Runoff modeling in Kolar river basin using hybrid approach of wavelet with artificial neural network. J. Water Climate Change 13(2), 963–974 (2022). https://doi.org/10.2166/wcc.2021.246 9. Zhihua, L.V., Zuo, J., Rodriguez, D.: Predicting of runoff using an optimized SWAT-ANN: a case study. J. Hydrol.: Reg. Stud. 29, 100688 (2020). https://doi.org/10.1016/j.ejrh.2020. 100688 10. Abatzoglou, J.T., Dobrowski, S.Z., Parks, S.A., Hegewisch, K.C.: TerraClimate, a highresolution global dataset of monthly climate and climatic water balance from 1958–2015. Sci. Data 5(1), 1–12 (2018). https://doi.org/10.1038/sdata.2017.191 11. Kassem, Y., Gökçeku¸s, H., Janbein, W.: Predictive model and assessment of the potential for wind and solar power in Rayak region, Lebanon. Model. Earth Syst. Environ. 1–28 (2020). https://doi.org/10.1007/s40808-020-00866-y 12. Xu, Y., Li, F., Asgari, A.: Prediction and optimization of heating and cooling loads in a residential building based on multi-layer perceptron neural network and different optimization algorithms. Energy 240, 122692 (2022). https://doi.org/10.1016/j.energy.2021.122692 13. Lin, H., Dai, Q., Zheng, L., Hong, H., Deng, W., Wu, F.: Radial basis function artificial neural network able to accurately predict disinfection by-product levels in tap water: Taking haloacetic acids as a case study. Chemosphere 248, 125999 (2020). https://doi.org/10.1016/ j.chemosphere.2020.125999
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14. Kao, Y.S., Nawata, K., Huang, C.Y.: Predicting primary energy consumption using hybrid ARIMA and GA-SVR based on EEMD decomposition. Mathematics 8(10), 1722 (2020). https://doi.org/10.3390/math8101722 15. Kassem, Y., Gökçeku¸s, H., Çamur, H.: Wind speed prediction of four regions in northern Cyprus prediction using ARIMA and Artificial Neural Networks models: a comparison study. In: Aliev, R., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Sadikoglu, F. (eds.) 13th International Conference on Theory and Application of Fuzzy Systems and Soft Computing — ICAFS2018. Advances in Intelligent Systems and Computing, vol. 896, pp. 230–238. Springer, Cham. https://doi.org/10.1007/978-3-030-04164-9_32 (2018)
Devices with Fuzzy Logic Control of Artificial Lung Ventilation Aynur J. Jabiyeva(B) Biomedical Engineering Research Group at Department of Instrument Engineering, Azerbaijan State Oil and Industry University, Azadlig 20, Nasimi, Baku, Azerbaijan [email protected]
Abstract. This article presents the development of a ventilator and its control algorithm. The main feature of the developed ventilator is compressed by a pneumatic drive. The control algorithm is based on the adaptive fuzzy inference system (ANFIS), which integrates the principles of fuzzy logic. The paper also presents a simulation model to test the designed control approach. The results of the experiment provide verification of the developed control system. The novelty of the article is, on the one hand, the implementation of the ANFIS controller, pressure control, with a description of the training process. On the other hand, in the article presented a draft ventilator with a detailed description of the hardware and control system. Keywords: Pneumatic drive · Artificial lung ventilation · Coronavirus · Fuzzy logic
1 Methods and Models The article uses fuzzy logic as they deal with its uncertainty and inaccuracy. Of the many real problems, it naturally allows control algorithms to be based on human activities, and not on mathematical models [1]. In the presented article, fuzzy logic simulates human thinking and the ability to make a decision based on not very accurate information, which allows the use of a controlled system, such as a high-frequency lung apparatus, in applications compatible with traditional control algorithms based on fuzzy algorithm models. One such area is medical decision making, which involves various factors of varying relative importance in the context of experience [1–6]. Many hospitalized patients on specific grounds, rapid and abrupt deterioration, often accompanied by shortness of breath and lack of individual apparatus. During the pandemic, the information about the patients in the period of equipment failure was taken from the specialists of the National Rehabilitation Institute of Azerbaijan, candidates of sciences and doctors with more than 20 years of experience. This study deals with the development of fuzzy logic for automatically controlling levels oxygen Pressurized Ventilation (PSV) performed in patients with severe lung disease (COPD) [2]. Currently, there is not generally an accepted approach to pulling © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 256–264, 2023. https://doi.org/10.1007/978-3-031-25252-5_36
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the patient away from mechanical ventilation, a clear opinion in the medical community where it is possible somehow algorithmically shape cutting process from a mechanical ventilator. Fuzzy logic seems appropriate for this job because it naturally represents the subjective human concepts used in medical decisions [3]. It is associated with all processed inputs, defines duplicated functionality between input and finally decides the response received. The aim of this study was development of fuzzy logic algorithms to control pressure-assisted ventilation in the intensive care unit patients using Heart rate, tidal volume measurement, respiratory rate, and the involvement of arterial oxygen pressure [4]. Algorithms based on fuzzy logic show the potential to improve the work of medical professionals. This article describes a fuzzy logic algorithm that can help explore the types of tasks that humans are not suited for by mimicking the complexity of human thought processes situations and performing repetitions indeed. In practice, there may not be an exact model for medicine, the situation can be very different when modeling is challenging, fuzzy logic is regarded as the best option as a tool by which the human mind can work with approximate information and extract and produce meaningful information [5]. We retrospectively exemplify its application in 10 patients with severe chronic obstructive pulmonary disease, contrasting the results of the algorithm’s decisions with the actual data outcomes. Unexpected diseases and disasters are becoming major problems that our world is facing. In this article, in addition to using other methods, we also applied the adaptive neuro-fuzzy inference system (ANFIS) [7]. When a patient is presented at the imaging counter, the system will capture their vital signs and include the patient’s physiological state and general appearance as well as their complaints. This data will be managed and analyzed on the data server and the patient’s emergency situation will be immediately informed. Considering the proposed method, it will help to reduce the burden of the emergency doctor, especially in the event of the patient’s lung arrest and serious disaster. Fuzzy inferential clustering was used to find fuzzy rules for the ANFIS model. The results showed that it was evaluated by measuring specificity and sensitivity for binary classification of training data. Therefore, it was chosen as the technique to develop the initial forecasting model.
2 Statement of the Problem and Its Solution The Patient Early Warning System (MEWS) is a proven guideline or bedside assessment tool to that extent successfully used to achieve this goal by locating high-risk patients in an effort to take prompt preventive intervention. In order to arrive at a decision, MEWS analyzes physiological or vital signals such as body temperature, blood pressure (BP), heart rate, respiration rate, oxygen saturation, and blood sugar. Patients having a MEWS score of at least 5 points are transferred right away to the emergency department. If we apply the ANFIS principle, Adaptive Neural Fuzzy Inference System parameters construct a fuzzy inference system (FIS) obtained from training samples, the considered FIS has two inputs x and y with two related membership functions (MFs) and one output (z), two non- A general set of rules with fuzzy if–then rules is represented as the following algorithm (Fig. 1.), Rule 1: if x is A1 and y is B1, then …
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Patient choice
Determining the patient's condition
Yes
Yes
Disconnecting the patient from the ventilation system
No Mild condition
Turning on the ventilator No. 1
No
There is a need for a ventilator
Yes
No
Slightly severe condition
Turning on the ventilator No. 2
Yes
No Serious condition
Turning on the ventilator No. 3
Yes
Turning on the ventilator No. 4
Very serious condition
No
Turning on the ventilator No. 5
Patient status and connection time to the ventilator
Fig. 1. Algorithm based on fuzzy logic for artificial lung ventilation
The multi-ventilator method does not optimize carbon dioxide removal for a variety of reasons, and oxygen levels will be difficult to control and optimize. Patients with COVID-19 seem to respond to PEEP fairly well. Of all, PEEP is only a method to raise mean airway pressure, the primary factor impacting lung function recovery. In severe hypoxemia, reverse Ratio ventilation can be employed to raise the pressure even more in the middle airways. It has been proven that fuzzy logic is able to transfer knowledge from humans and experts employing linguistic expressions, into computer models. Systems for fuzzy inference (FINS) use a set of “if–then-else”, “if–then” regulations created on the basis of the knowledge gained by experts (biomedical engineers in relation to this work), to help in medical diagnosis in conditions or they recommend treatment according to the current situation. Core Principle: Patient independence from the ventilator. Adaptive network-based fuzzy inference systems method [10] a hybrid intelligent system is one of the best solutions in data modeling, capable of reasoning and learning in an uncertain and uncertain environment. It is a combination of two or more mechanical ventilator technologies. This combination was usually done to overcome single smart technologies [7–9]. As a rule, in the hospital, the ventilator is adjusted to the needs of a particular patient. We would not want one patient’s tachypnea to hyperventilate patients on the same
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ventilator with others. Therefore, basically each patient should breathe independently when using a multi-patient ventilator and will not affect the ventilation of other patients connected to the ventilator. This can be achieved as described below. Pressure cycle ventilation is preferred over volume cycle ventilation. Pressure cycle ventilation and volume cycle ventilation have the following advantages [11–14]: • Volumetric ventilation: the benefit is the supply of a volume that is certain of oxygen ( the drawback is the inability to regulate peak pressure). • Pressure cycling ventilation: the advantages are assured peak pressure is limited (the drawback is the absence of an oxygen volume control system). Once you start using the numerous people using a ventilator, thus controversy will to a large extent disappear. There are a few major drawbacks to using volume loop mode: 1. Using Multi-Patient Volume Cycle mode does not provide oxygen volume control for any patient, nor does it provide maximum airway pressure control. 2. The volume cycle mode of patients using the same ventilator should have the same size, the same FiO2, and the same PEEP requirements. Using pressure cycle mode solves the following problems: 1. In pressure cycling: in this mode, we maintain control over the movement pressure and maximum airway pressure. 2. Using the pressure cycling mode avoids harmful interaction between patients. 3. Patients using the same ventilator do not have to be the same size. Continuous mandatory ventilation (CMV) is required, and patients can usually turn on the ventilator to breathe. It’s possible that modern ventilators don’t require constant ventilation. However, the following action will have the same result: 1. Raise the threshold of the lung machine as much as possible so that patients can breathe 2. Respirolytic sedation can be utilized to lessen the patient’s breaths per minute and stop the ventilator from turning on. Ventilation efficiency will be less than fine-drawn. A multi-fan technique will not optimize carbon dioxide removal for a variety of reasons, and oxygen levels will be challenging to regulate and optimize. Patients with COVID-19 seem to respond to PEEP fairly well. Of all, PEEP is only a method to raise mean airway pressure, the primary factor impacting lung function recovery [5, 6]. In severe hypoxemia, reverse Ratio ventilation can be employed to raise the pressure even more in the middle airways. Five ventilators provide individual settings for 10 patients.
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The main disadvantage of the scheme described above is that patients need to be selected due to the relative level of lung damage severity (PEEP and FiO2 requirements) [14]. This problem can be solved in the following way: imagine we installed five fans: • Ventilator 1: settings for minor injuries (FiO2 50%, PEEP 10 cm, peak pressure 20 cm) • Moderate injury settings for Ventilator 2 (FiO2 60%, PEEP 14 cm, peak pressure 26 cm) • Setting for high injury on Ventilator 3 (FiO2 80%, PEEP 18 cm, peak pressure 30 cm). • Ventilator 4 settings for hypoxia (FiO2 100%, PEEP 22 cm, peak pressure 35 cm). • Rescue settings (FiO2 100%, PEEP 22 cm, peak pressure 35 cm, ventilation) for Ventilator 5 is inversely proportional to inspiratory time >> expiratory time).
Fig. 2. Statistical measurement for the input and output variables
Each ventilator can connect 1 to four patients. If patients are deteriorating, they can be changed to more ventilators (e.g., ventilators No. 2–3). Alternatively, as patients improve, they can be switched to fewer ventilators. This system allows multiple ventilators to provide individual settings for multiple patients. This article’s goal is to create a knowledge-based method [15–17] for the treatment of dyspnoea. To achieve this goal, a fan was developed. Fans are called smart fans because they use fuzzy logic to control the status of pneumatic equipment. Currently, there is no generally accepted method for weaning patients off the ventilator, but it is understandable that the medical world believes that this process can somehow be developed algorithmically. For this purpose, fuzzy logic looks apt because it easily describes subjective human concepts used in. The current study’s objective was to create a fuzzy logic system that uses measurements of heart rate, oxygen volume, respiration regulating heart rate and arterial oxygen saturation to support pressure ventilation in intensive care unit patients. The fuzzy logic method is covered in this paper, and ten patients with severe chronic obstructive pulmonary disease are retrospectively evaluated using how it works. We do
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this by comparing many decision-making in medicine processes the system’s predictions what is actually happens. Fuzzy logic’s suggested uses matched the current state on average 70% of the time, and 90% of the time, within 2 cm H2O. When we compared our algorithm’s predictions to cases where degree of pressure supports changes were in fact made by the attending doctor, physicians tended to decrease support levels slightly more aggressively than the algorithm. In the light of continuous observations of the patient’s vital signs, we concluded that our fuzzy algorithm is able to regulate breathing rate with pressure support. Fuzzy logic is used to automatically control mechanical ventilation with pressure support. ANFIS is an example of a hybrid intelligent system that solves these problems [7]. It depends on the data learning rules and membership functions. This Inference Systems model for ANFIS infers from a first-order system to generate an if-on rule to construct a model that maps input to output with high efficiency. tle('Pa ent 1'); text(25,80 3% text(25,77,'\rightarrow Ven lator No.1 opera on'); text(25,74,'\rightarrow Ven lator No.2 opera on'); text(25,71,'\rightarrow Ven lator No.3 opera on'); text(25,68,'\rightarrow Ven lator No.4 opera on'); text(25,65,'\rightarrow Ven lator No.5 opera on'); Len_Pat_1=length(Pa ent_1); a=0; for i=1:Len_Pat_1+1; OX1(i)=a; a=a+1; Pa ent_2=[41 45 48 52 53 51 48 47 44 41 36 31 28 25]; figure (2); plot(Pa ent_2); xlabel('Days'); % Ось ОХ ylabel('Co % Ось ОY tle('Pa ent 2'); text(10,50 1% text(10,49,'\rightarrow Ven lator No.1 opera on'); text(10,48,'\rightarrow Ven lator No.2 opera on'); text(10,47,'\rightarrow Ven lator No.3 opera on'); text(10,46,'\rightarrow Ven lator No.4 opera on'); text(10,45,'\rightarrow Ven lator No.5 opera on'); Len_Pat_2=length(Pa ent_2); a=0; for i=1:Len_Pat_2+1; OX2(i)=a; a=a+1; end; axes2=gca; set(axes2,'XTick', OX2); set(axes2,'YTick',[20 30 40 50 60 70 80 96]); set(axes2,'YTickLabel', {'','Mild','','Slightly severe','Serious','','Very serious','Cri cal'}
Fig. 3. Software computational process of artificial lung ventilation
Previously inputs and outputs were passed to the ANFIS model to extract the rules. The “fuzzification” level is set and adapts the parameters for the selected membership. After that comes the power firing level, which is the IF conditions for setting the rules. Firepower output is normalized in the normalization layer. Before the last layer, there is another adaptation layer that works as a “defuzzification” layer of the rules, where the parameters of the ventilator model are adjusted to get the best match between input and output data. The circuits were tested on a turbine ventilator connecting two test circuits to two patient circuits. Two patients are predicted to weigh 70–75 kg with breaths per minute (RR) 20 m/min, ratio between inhaled and exhaled air (I:E) 1:1 and inhaled oxygen concentration (FiO2) of 100%). Initial inspiratory pressure was 10 cm, and positive
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expiratory pressure (PEEP) was recorded at 15 cm H2O. H2O. The first 15-h study was conducted between two simulated patients under similar conditions -static airway compliance (Cstat) Airway resistance and 50 ml/cm H2O 5 cmH2O/l/s. Measured W in pressure control mode was 953 ml, but to everyone the sick patient was given 470 ml. Then we did two more tests. Our tests support the Technically, it is possible to ventilate two patients at once, but there are challenges and risks involved associated with this arrangement continues. Given current information and data on this topic, this should only be done in emergencies due to mechanical failure. We suggest a schedule (Fig. 2) for initiating type 2 ventilation. Coordination of the patient for compliance and possibly airway resistance is key. Your clinician must be prepared to recognize signs of possible under or over ventilation and be prepared to initiate manual ventilation in case of problems (Fig. 4).
Fig. 4. Membership functions of regulation error, ventilation error with volume cycle and pressure cycle. Information for each patient
The model showed the best results in all 10 statistical measurements for training and unseen data. ANFIS works like a small window in the model to show which parameters affect the prediction result. Membership options have been adapted to provide a better match between input and output during ANFIS training. He changed the form of membership in accordance with the new adapted parameter. The most effective variables are the airway and respiration (variable 1), as its membership pattern changed significantly after exercise compared to the other variables. Some Pressure control (PC) mode was used to assess the experimental circumstances (inspiratory time: expiratory time ratio: 1:2, positive expiratory pressure) (PEEP) (Fig. 3) 12 cmH2O, breathing time to climb 0.1 s). First, conformity for the two test lungs eventually got bigger to 22 cmH2O at peak inspiratory pressure at 25 breaths per minute and then at 15 breaths per minute (10–70 ml cmH2O-1). Then the right Clung was gradually increased and the left was set to 50 ml/.cmH2O-1. In the third case, three concentrations of were injected into right lung during testing pinching the flexible clamp on the tube but was not delivered to the left test lung. The lungs were identical 50 ml
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in each test lung cmH2O-1 and 30 was chosen cmH2O 15 breaths per minute. This investigation was replicated using 70 ml cmH2O-1 on the right and 20 ml cmH2O-1 Clung on the left. Finally, we simulated coughing by manually squeezing the test lungs in a setting with and without a check valve. Each test condition was measured for 1.5 min. VT per calculations for the test lung were the mean of every breath. VT is portrayed in mlkg-1, assuming a patient who has an anticipated body weight of 70–75 kg. With the result obtained of the experiments gave the following results: The presented approach gave satisfactory mechanical results based on the ANFIS ventilation controller. The ventilation was capable to approximately follow the benchmark pressure. Thus, it might be argued that the technique is appropriate for application. Pressure-controlled ventilation, inspiratory/expiratory requirements, and oxygen volume ratio or delivery have been investigated.
3 Conclusions The solution of the given problem is simulated. In the article, we presented a ventilator based on pneumatic systems. Pressure cycling ventilation has been successfully used with positive outcomes. • It is practically a single ventilator can be used to ventilate multiple patients. Most likely, this is possible using basic parameters that protect the lungs. However, this tactic comes at a price: poor ventilation and a lack of control over precise oxygen levels (with high pCO2). • The main purpose prevents one patient from having an adverse effect on other patients. Without allowing any patient to activate the ventilator, this can be accomplished utilizing pressure cycling ventilation. • On a ventilator, patients should be completely unconscious and unresponsive (or, if, paralyzed on a ventilator 5). • The efficiency of each patient’s ventilation can be monitored with end oxygen CO2. • By utilizing a few ventilators with various parameters, it is possible to support a large group of patients with quite individual parameters. The main results are as follows: we have given a detailed description of the new concept of the ventilator, the development of a control algorithm based on an adaptive neuro-fuzzy inference system, graphical representation and experimental analysis of the simulation model. The experiment’s findings demonstrated that the main problem was solved, and the main features were to maintain the PEEP value of the initial pressure. This is due to a leak in the print instrument interface. These phase issues occurred when low pressure levels were present during the reference. The article also presents the results of mechanical ventilation in the assisted ventilation mode, this is exclusively intended to support patients who do not have lung pathology. Biochemical testing of the ventilator is now possible. In the future, these ideas will first be focused on animals. Animal testing will be the focus of future effort. During ventilation the animal’s vital signs will be watched closely. As a result, the results will be examined, and the appropriate adjustments will be made. for human use.
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References 1. Ishola, N.B., et al.: Adaptive neuro-fuzzy inference system-genetic algorithm vs. response surface methodology: A case of optimization of ferric sulfate-catalyzed esterification of palm kernel oil. Process. Saf. Environ. Prot. 111, 211–220 (2017) 2. Jang, J.S.R., Sun, C.T., Mizutani, E.: Neuro-Fuzzy and Soft Computing. Prentice Hall, Upper Saddle River (1997) 3. Al-Hmouz, A., Shen, J., Al-Hmouz, R., Yan, J.: Modeling and simulation of an adaptive neuro-fuzzy inference system (ANFIS) for mobile learning. IEEE Trans. Learn. Technol. 5, 226–237 (2011) 4. Hoehl, S., et al.: Evidence of SARS-CoV-2 Infection in Returning Travelers from Wuhan, China. N. Engl. J. Med. 382, 1278–1280 (2020) 5. World Health Organization: Coronavirus Disease (COVID-19) Pandemic. https://www.who. int/emergencies/diseases/novel-coronavirus-2019. Accessed 29 Apr 2019 6. Wang, D., Zhou, M., Nie, X., Qiu,W., Yang, M., Wang, X., Xu, T., Ye, Z., Feng, X., Xiao, Y.: Epidemiological characteristics and transmission model of Corona Virus Disease 2019 in China. J. Infect. (2020) 7. Lipinski, T., Ahmad, D., Serey, N., Jouhara, H.: Review of ventilation strategies to reduce the risk of disease transmissionin highoccupancy buildings. Int. J. Thermofluids 7, 100045 (2020) 8. Carter, C., Osborn, M.: COVID-19 disease: invasive ventilation. Clin. Integr. Care 1, 100004 (2020) 9. Gattinoni, L., et al.: Lung recruitment in patients with the acute respiratory distress syndrome. N. Engl. J. Med. 354, 1775–1786 (2006) 10. Aliev, R.A., Gardashova, L.A.: Z-set based approach to control system design. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 10–21. Springer, Cham (2021). https://doi.org/10.1007/978-3-03064058-3_2, Das, A., Menon, P.P., Hardman, J.G., Bates, D.G.: Optimization of mechanical ventilator settings for pulmonary disease states. IEEE Trans. Biomed. Eng. (2013) 11. Esteban, A., et al.: Characteristics and Outcomes in Adult Patients Receiving Mechanical VentilationA 28-Day International Study. JAMA (2002) 12. Rezaei, E., Karami, A., Yousefi, T., Mahmoudinezhad, S.: Modeling the free convection heat transfer in a partitioned cavity using ANFIS. Int. Commun. Heat Mass Transf. 39, 470–475 (2012) 13. Hawker, F.H., Torzillo, P.J., Southee, A.E.: PEEP and “reverse mismatch”. A case where less PEEP is best. Chest 99, 1034–1036 (1991) 14. Adilova, N.E.: Consistency of Fuzzy If-Then rules for control system. Adv. Intell. Syst. Comput. 1095, 137–142 (2020). https://doi.org/10.1007/978-3-030-35249-3_17 15. Adilova, N.E.: Quality criteria of fuzzy If-Then rules and their calculations. Adv. Intell. Syst. Comput. 1306, 55–62 (2021). https://doi.org/10.1007/978-3-030-64058-3_7 16. Gardashova, L.A.: Z-set based inference using ALI-2 implication for control system design. Lect. Notes Netw. Syst. 362, 75–84 (2021). https://doi.org/10.1007/978-3-030-92127-9_14 17. Imanov, E., Ozkilic, O., Imanova, G.: Flight information system by using fuzzy expert inference. Procedia Comput. Sci. 120, 304–310 (2017). https://doi.org/10.1016/j.procs.2017. 11.243
Structural Analysis of Piston Machines by Using Computer Software Valeh Bakhshali(B)
, Nail Mardanov , Ismayil Ismayil , and Aygun Bekirova
Department of Mechanics, Azerbaijan Technical University, H. Javid Avenue, 25, AZ1073 Baku, Azerbaijan {v.bakhshali,ismayil_i}@aztu.edu.az
Abstract. The durable and reliable work of compressor-pump stations used in the oil and gas industry has great importance for practice. In reality these areas are characterized by uncertainty information. All structural elements of Piston Machines such as connecting rods, pistons, and piston rings are heavy-duty loaded mechanical systems. The connecting rod of the crank-piston mechanisms of such systems undergo high stresses and wear, and their kinematical couplings are subject to fatigue and failure due to friction, seizure, oscillations, and impact. Friction loss reduction and service life extension remain the main problems in the design and exploitation of reciprocating machinery. The central problems are the optimal design of the crank-piston group and the piston-ring assembly, and the choice of better materials for rubber coupling, leading to a balance between pulsation control and performance. Increasing the efficiency and durability of the piston compressors and pumps directly depends on the correct calculations and design of these elements. By using ANSYS software the structural model of a connecting rod was developed. Using ANSYS software, simulation and stress analysis are performed on the basis of the 405GP15/70 and ARIEL heavy-duty balanced opposed piston compressors used in the Caspian sea - Black sea Region. The article investigated the main causes of failures through the collection and analysis of data from different parts of the machines used for transporting the oil and gas resources. The stress and deformations are analyzed for the connecting rod made of steel material or special aluminum alloy by applying pressure on it in the structural analysis in this article. Structural analysis was performed in ANSYS software. An analysis of static stress and damages due to the application of pressure is presented and analyzed in this work. By observing the analysis results, we can decide whether our designed connecting rod is safe or not under applied load conditions. Investigation of complex problems with respect to friction and wear (clearances), stresses, and strain phenomena in the piston machines gives the opportunity to solve the problems of increasing the durability of these machines. Keywords: Piston compressor · Connecting rod · Thermodynamics · Structural analysis · ANSYS · Uncertainty · Fuzzy angles
1 Introduction The technical security and environmental situation on the oil and gas pipeline are depending on durability and reliability of machines and equipment used in oil industry. Piston © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 265–273, 2023. https://doi.org/10.1007/978-3-031-25252-5_37
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pumps and compressors are widely used for the exploration and transportation of oil and gas. Piston and centrifugal machines are heavy-duty systems that are still failureprone due to high stresses and wear proses. Specialized methods will be developed for the influence of impacts, vibrations, temperature, and film lubrication and unified in a system model. The research efforts will lead to more reliable and efficient design alternatives for reciprocating machines which are used for the transport of oil and gas and will thus contribute directly to the competitiveness of a key industry in the Caspian Sea Black Sea Region, for example in Baku-Tbilisi-Ceyhan (BTC) Main Oil Pipeline, there are 8 pump-compressor stations (2 stations in Azerbaijan, 2 stations in Georgia and 4 stations in Turkey territory). Besides BTC today the region is functioning the Trans Adriatic Pipeline (TAP) which transported Caspian natural gas to Europe. Connecting with the Trans Anatolian Pipeline (TANAP) at the Greek-Turkish border, TAP will cross Northern Greece, Albania, and the Adriatic Sea before coming ashore in Southern Italy to connect to the Italian natural gas network. The energy security of the Black Sea - Caspian Sea Region depends on the technical conditions -reliability and durability of the machines and equipment used in oil and gas pipelines in the Region. The overall goal of the research is the development of an integrated model of the piston machine system that is then used to evaluate and improve the current design and increase the environmental conditions. Providing the technical security of oil and gas pipelines is one of the very important problems of exploitation and transport in the oil and gas industry. All structural elements of Piston Machines (PM) such as connecting rods, pistons, and piston rings are heavy-duty loaded mechanical systems. The main objectives are to investigate and analyze the thermal stress and mechanical stress distribution of pistons in real conditions during the working process of the piston machine. The work describes the stress distribution of the piston by using the finite element method to predict the higher stress and critical region on the component. By using ANSYS software the structural model of a piston will be developed. Compressor-pump stations are used on the oil and gas pipeline for the transport of this mineral resource. Current methods of reciprocating and centrifugal machinery design, see e.g. [1, 2], are based on partial empirical relations and do not take into account many of the factors that are affecting the mechanical and thermodynamic processes in these machines. Till to day, neither applied formulas are available for durability and reliability of the parts, for mechanical losses in the bearings, for energy losses in the kinematical couples of machines used in the oil industry, nor has there been basic research of the impact phenomena in these kinematic couples. On the other hand, very detailed models leading to computer-intensive simulations have recently been developed for piston ring dynamics in the context of blow-by estimation [2], for lubrication conditions of the ring/liner contact, for dynamically loaded bearings, and for stress and failure analysis of assembly parts. However, until now, the insight gained with these models has not found its way into more detailed models for reciprocating machines such as piston and centrifugal compressors. To this end, a modular system modeling approach as described below combined with model reduction is necessary in order to keep the computational efforts at reasonable magnitudes [3].
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2 The Mechanical and Thermodynamically Analysis of the Piston Machines The working process taking place in the cylinder in all PM is the result of three main processes: the thermodynamic process in the cylinder, the heat exchange process between gas and walls of the cylinder, and the hydrodynamic process of gas flux through density in the distribution parts of the cylinder. Analyses of the complex problems depend on friction and wear processes in PM labyrinth sealings making it possible for the all-around solution of increasing its reliability and durability. Such a process as it is known can be determined by four equations of mathematical physics, describing the main laws of the forms of matter existence. They are the system of equations describing gas flux in the channel consisting of the equation of continuity, the equation of motion, the equation of energy (first law of thermodynamics), and the equation of state of gas flux [1–3]. The goal of this work is to determine both total deformation and normal stress distributions of different materials like aluminum alloy, and cast iron piston crowns to improve the mechanical efficiency of piston compressors. Comparisons with results from piston by means of static analysis using ANSYS software. Figure 1 is presented the scheme of the crank-piston mechanism of the piston compressor with the double-acting cylinder with an indicator diagram. Where is showed the gas pressure with respect to the volume of the cylinder, i.e. p = f (V ). Processes of compressing and discharge in the cylinder accepted as polytrophic are subjected to the equation: pV m = const
(1)
where p is gas pressure in the cylinder, V is a volume of the cylinder, m is the polytrophic factor. In accordance with the analyses mentioned above and on the basis of expression (1), the gas pressure compressing on the piston p and p , correspondingly from the upper and lower surfaces of the piston we obtained the following expressions, taking into account the gaps in kinematic couples [2]: p˜ = ⎡
fp pb V0m1
⎤m1 2 ˜ + R2L sin2 ϕ˜ Vhr + (Sp − R(1 − cosϕ) ⎢ ⎥ ⎣ ⎦ ˜ ϕ˜ − ReL1 sinαsin ˜ ϕ˜ + e1 cosα˜ + e2 cos)f ˜ p − ReL2 sinsin
p˜ = ⎡
m2 fp ph Vhr
Vhr +
⎤m2
(2)
2 ⎢ ⎥ ⎣ R(1 − cosϕ) ⎦ ˜ − R2L sin2 ϕ˜ − ReL1 sinα˜ sinϕ˜ f p ˜ sinϕ˜ + e1 cosα˜ + e2 cos ˜ − ReL2 sin
where pb and ph are the pressure of gas in the compressor inlet and outlet branch pipes; ϕ is a fuzzy rotational angle of the crankshaft, m1 and m2 are factors of polytrophic processes of compressing and expanding gas in the cylinder; V 0 is the gas volume at
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Fig. 1. Crank-piston mechanism of the reciprocating compressor
the beginning of compressing process, S p is the piston working displacement, f p is an area of working surface of the piston, R - is the radius of the crankshaft, L is connecting rod length; Vhr is the harmful volume space of the cylinder, e1 and e2 are clearances in kinematic couples of connecting rod, α and Θ are fuzzy angles which characterized the contact points in these clearances. It should be noted that as a result of friction and wear processes in kinematic couples of PM are formed the clearances on it, which are harmful phenomena. For this reason, kinematical couples of machines functioned the impact phenomena with respect to these clearances. For the determination of the volume of the cylinder, we take into account the clearances e1 and e2 in kinematic couples of connecting rod of PM [4, 5]. In accordance with the analyses mentioned above and on the basis of expression (2), the gas pressure compressing on the piston p and p , correspondingly from the upper and lower surfaces of the piston is obtained. For determining of main gas pressures p and p in the cylinder influencing the piston group we divide the period of one working cycle into six identity phases in the limits of each one where the regularity of pressure from both sides of the piston remains unchangeable [6–8].
3 Dynamical Parameters for the Piston Machine The piston and connecting rod play the main role in piston compressors used in the oil industry. Analyses of the failure of the piston group (crank piston mechanism) due to various thermal and mechanical stresses are very important for practice. The working
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condition of the piston group is so worst in comparison to other parts of the machine. The main objective of this work is to investigate and analyze the stress distribution of the piston, and the structural analysis of a piston using two different materials that are used in this work. We created pressure on the piston head at 45 MPa and 10 MPa on these two materials. Finally, we find out which one is a suitable material for the piston in these two materials. The design of the piston is carried out using SolidWorks software, static analysis is performed using finite element analysis (FEA). In multi-stage compressors with crossheads are used double-acting disk pistons. The high-speed compressor pistons shall be extremely light. They are made of aluminum alloys or cast iron, lightweight design with cutouts on the side surface that reduce the weight of the piston and reduce the friction works [9–11]. The equivalent – Mises stress is determined by expression:
(σ1 − σ2 )2 + (σ2 − σ3 )2 + (σ3 − σ1 )2 , (3) σMises = 2 where σ1 , σ2 and σ3 are main normal stresses in the piston. The normal stress and the unit longitudinal deformation in piston are determined as σ = Eε, ε =
du , dy
(4)
where E is the modulus of elasticity of material, ε is the unit longitudinal deformation of piston and u is the absolute total deformation of piston. The mechanical and material properties of crank-piston mechanism of the piston compressor have been provided in Table 1. The mathematical calculation is presented using expressions (3), (4) in ANSYS the maximum stresses and deformations criterion by Mises, based on Mises-Hencky theory using finite element analysis. The stresses on the piston shall not exceed the allowable stresses [12–14].
4 Modeling and Meshing of the Connecting Rod The static analysis for the connecting rod was done by FEA using ANSYS software on the basis of the expressions (3) and (4). For ANSYS simulation the geometry of the solid work is separated into elements. These elements are interlinked to one another at a point called a node. In present examination work, we have used FEA for the Structural analysis of solid works Software is used to prepare the connecting rod. After completing solid works modeling, the model is saved in IGES file then it is imported to ANSYS software for the FEA. In Fig. 2 is shown a meshed model of connecting rod of the double-acting piston. The end hinge of the connecting rod is to be fixed. Using expressions (2) and Table 1 we investigate the structural parameters of PM. The gas pressures p and p in the cylinder influencing the piston group from expression (2) are changing in time. Here we consider the extremal loading of the connecting rod. The load ph = 4.5 MPa is applied on the top and the load pb = 1.01 MPa is applied on the bottom of the piston surfaces as for the first stage of the piston compressor 405GP15/70. The piston is made of different materials such as Carbon steel, Cast iron, Aluminum
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Parameters
Values
The piston stroke, m
Sst = 0.22 m
The radius of crank shaft, m
R = 0.11 m
The thickness of piston ring
a = 0.0115 m
Height of piston ring
b = 0.009 m
Length of connecting rod
L = 0.52 m
Internal diameter of the sealing rings
d1 = 0.05 m
External diameter of the sealing rings
d2 = 0.072 m
Height of the sealing rings
b1 = 0,012 m
Radius of the finger of crank shaft
rA = 0,075 m
Number of the piston rings
z0 = 2
Mass of connecting rod made of cast iron
mcr = 26.4 kg
Mass of piston group made of cast iron
mp = 114.5 kg
Moment of inertia of the connecting rod
Jo = 4.28 kg.m2
Coefficient of friction between piston rings and cylinder wall
μp = 0.1
Coefficient of friction between piston rod and sealing rings
μp = 0.08
The pressure of gas in the inlet branch pipe
pb = 1.01·105 Pa
The pressure of gas in the outlet branch pipe
ph = 4.5 · 105 Pa
The polythrope indicators of the gas in cylinder
m1 = 1.4 (compression), m2 = 1.35 (expansion)
Angular velocity of the crank shaft
n = 500 rpm
a)
b)
Fig. 2. Meshed model of the connecting rod: a – general view, b – across section of piston
alloys, etc. Figure 3 is shown the static analysis of the connecting rod. In an attempt in this article, the connecting rod is modeled by using SolidWorks software, and static analysis is done by using ANSYS Workbench software. There is evaluated the normal
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stresses and total deformations. The Workbench focuses on attaching existing geometry, setting up the finite element model, solving, and reviewing results.
a)
b)
Fig. 3. Static analysis of the connecting rod: a – normal stress diagram, b – total deformation diagram
Figure 3 is shown the static analysis of the connecting rod. In an attempt in this article, the piston is modeled by using SolidWorks software, and static analysis is done by using ANSYS Workbench software. There is evaluated the normal stresses and total deformations. The Workbench focuses on attaching existing geometry, setting up the finite element model, solving, and reviewing results. The novelty of the article is characterized by new theoretical methods for the determination of forces of gas pressure in cylinders of reciprocating machines with taking into account the wear processes and the clearances in kinematic couples of crank-piston mechanisms. The reliability of the received scientific results is provided with the correctness of the statement of tasks and decisions on the basis of laws of physics, mechanics and thermodynamics. The results of the investigation is generalized for any piston machines used in the oil and gas industry.
5 Conclusions On the thermodynamic basis and conditions of the real working process of the piston compressors with a double-acting cylinder have considered and substantiated the gas pressure acting on the piston group and uncertainty information based analytical methods for determining these forces are presented. Structural analysis also was performed in ANSYS software. An analysis of static stress and damages due to the application of
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pressure is presented and analyzed in this work. The structural analysis is done on the connecting rod model using Cast iron and Aluminum alloy. Which material is durable for the manufacturing of the connecting rod is decided by comparing both the material analysis. The results of the investigation can be useful for the design and exploitation of piston machines used in the oil and gas industry.
References 1. Rangwala, A.S.: Reciprocating Machinery Dynamics: Design and Analysis. Marcel Dekker, New York (2001). https://doi.org/10.1115/1.1399378 2. Davitashvili, N., Bakhshaliev, V.: Dynamics of Crank-Piston Mechanisms. Springer, Heidelberg (2016). https://doi.org/10.1007/978-981-10-0323-3 3. Bakhshali, V.I., Mardanov, N.T., Bekirova, A.A., Ismayil, I.A.: Development of methods for processing acoustic emission signals of sensors for the compressor-pump station’s control. In: In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) 11th International Conference on Theory and Application of Soft Computing, Computing with Words and Perceptions and Artificial Intelligence - ICSCCW-2021. Lecture Notes in Networks and Systems, Springer, Cham, vol. 362, pp. 704–710. (2022). https://doi.org/10. 1007/978-3-030-92127-9_93 4. Wittenburg, J. Kinematics.: Theory and Applications. Springer, Heidelberg (2016). https:// doi.org/10.1007/978-3-662-48487-6 5. Bakhshali, V.I.: Nanomechanics and its applications: mechanical properties of materials. In: Proceedings of the International E-Conference on Advances in Engineering, Technology and Management - ICETM 2020. Institute of Research Engineers and Doctors, pp. 77–81. USA (2020). https://doi.org/10.15224/978-1-63248-188-7-15 6. Yan, X., Dai, X., Zhang, K., Li, J., He, K.: Effect of teeth bending and mushrooming damages on leakage performance of a Labyrinth seal. J. Mech. Sci. Technol. 32(10), 4697–4709 (2018). https://doi.org/10.1007/s12206-018-0917-y 7. Hu, D., Jia, L., Yang, L.: Dimensional analysis on resistance characteristics of Labyrinth seals. J. Therm. Sci. 23(6), 516–522 (2014). https://doi.org/10.1007/s11630-014-0736-0 8. Burstein, L, Ingman, D.P.: Pore ensemble statistics in application to lubrication under reciprocate motion. Tribol. Trans. 43(2), 205–212 (2000). https://doi.org/10.1080/104020000089 82330 9. Boyaci, A., Hetzer, H., Seemann, W., Proppe, C., Wauer, J.: Analytical bifurcation analysis of a rotor supported by floating ring bearings. J. Nonlinear Dyn. 57(4), 597–507 (2009). https:// doi.org/10.1007/s11071-008-9403-x 10. Ilie, F.: Modelling of the contact processes in a friction pair with selective-transfer. J. Mater. Res. Technol. 12, 2453–2461. https://doi.org/10.1016/j.jmrt.2021.04.048 11. Sofiyev, A.H., Schnack, E., Demir, F.: Elasto-plastic stability of circular cylindrical shells subjected to axial load, varying as a power function of time. Struct. Eng. Mech. 24(5), 621–639 (2006). https://doi.org/10.12989/sem.2006.24.5.621 12. Wannatong, K., Chanchaona, S., Sanitjai, S.: Simulation algorithm for piston ring dynamics. J. Simul. Model. Pract. Theory 16(1), 127–146 (2008). https://doi.org/10.1016/j.simpat.2007. 11.004 13. Shaheen, W., Kanapathipillai, S., Mathew, P., Prusty, B.: Optimization of compound die piercing punches and double cutting process parameters using finite element analysis. Proc IMechE, Part B: J. Eng. Manuf. 234(1–2), 3–13 (2019). https://doi.org/10.1177/095440541 9855507
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14. Götze, A., Jaitner, D.: Combined experimental and simulative approach for friction loss optimization of DLC coated piston rings. Autom. Engine Technol. (2022). https://doi.org/10. 1007/s41104-022-00115-7
Using of Conventional Neural Network to Diagnose Scabies by Dermoscopy Husam Zendah1(B)
and Kamil Dimililer2
1 Computer Engineering, Near East University, Nicosia, North Cyprus, Via Mersin 10, Turkey
[email protected]
2 Electrical and Electronic Engineering, Applied Artificial Intelligence Research Centre
(AAIRC), Near East University, Nicosia, North Cyprus [email protected]
Abstract. In medicine, particularly dermatology, artificial intelligence has made major advances. The usage of different networks for scabies detection, including such deep learning, has proven to be highly advantageous in terms of overall performance. The goal of this work, however, is to conduct an analytical inquiry for the early diagnosis of scabies using a deep learning system trained using a VGG-16. The objectives of this study were the investigation of deep learning, the collection of quantitative data, the use of the VGG-16 model for both testing and training, as well as the interpretation of results. The method involved reviewing a dataset acquired again for study and using a higher processing machine that boosts the effectiveness of results. VGG-16 model has been trained and tested on the same two different categories. Aside from developments in hardware technology and processing, new categorization approaches based on deep learning have raised the relevance of dermatological applications. Many difficulties may be solved through these programs, such as limited access owing to distance, physical impairment, a lack of dermatologists, jobs, scheduling, and so on. They also assist doctors in making objective and timely diagnostic judgments. As a result, therapies may be administered on time, which is especially critical for life-threatening skin illnesses. Costs can also be decreased. Furthermore, the software for free or less expensive than an in-medical consultation. The VGG-16 model performed exceptionally well in the research, with excellent accuracy of 97.67%. Keywords: CNN · Transfer learning · Scabies · Dermoscopy
1 Introduction The skin is the biggest organ in the human body and serves various functions. Because the skin is exposed to the outside world, illnesses and infections are more common. A lesion area is an infectious patch on the skin. Scabies is a skin infection caused by a human itching mite [1]. The scabies mite burrows into the skin’s top layer, where it lives & lays its eggs. Scabies is characterized by acute itching as well as a pimple-like skin disease. The scabies mite is often disseminated by direct, prolonged skin-to-skin contact with a © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 274–281, 2023. https://doi.org/10.1007/978-3-031-25252-5_38
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scabies person. Scabies is present all across the world and affects people of various ethnicities and socioeconomic backgrounds. Scabies can spread quickly in crowded areas where intimate body and skin contact was common. Scabies outbreaks are common in institutions including nursing homes, long-term care facilities, and prisons. Scabies infestations are very widespread in child-care centers. Despite technological improvements and advances in the domains of medicine, the number of individuals affected by illnesses [2] continues to rise. Worse, most of these diseases remain undiscovered until they are in their latter stages, giving them fewer odds of survival [3, 4]. Deep Learning is an Artificial Intelligence area in which a computer algorithm analyses raw data and learns the discriminating features needed to uncover hidden patterns in it [5–8]. During the preceding decade, there were considerable advances in the ability of DL-based programs to evaluate various types of data, notably photos [9–13]. The most common DL model can be trained by supervised methods, in which datasets comprise inputs (for example, dermoscopy images of skin disorders) and direct contractual labels (for example, diagnosis or skin disease categories such as ‘Normal’ or ‘Abnormal’) [14, 15]. As a result of these factors, constructing image analysis devices becomes a significant area of study [16]. In the hands of unskilled dermatologists, dermoscopy has been shown to improve the diagnosis accuracy of skin disorders. This research examines common skin scabies conditions with distinctive symptoms that may be exploited as image recognition objects. The essential points of this study are stated below. 1. 2. 3. 4.
Find out an appropriate dataset that can be used to train the model. Organize and optimize the data in getting a more accurate prediction result. How the CNN model can be applied in this research? Applying neural network optimization to minimize the function with maximized efficiency.
In Sect. 2, we will be discussing how the model was constructed. In Sect. 3, we demonstrate the result of this research. Finally, Sect. 4 concludes this paper.
2 Materials and Method 2.1 Datasets Dermoscopy picture database collected from TRIPOLI MEDICAL CENTER’s Dermatology Service in Tripoli, Libya. The Dermoscopy pictures were acquired under identical conditions at the Dermatology Service of Hospital using the Dermoscopy, RGB color scheme. This picture database comprises 138 Dermoscopy photos of scabies lesions, comprising 74 abnormal images and 64 Normal images (Fig. 1). 2.2 Data Preparation During the data preparation process, processing time on data pre-treatment techniques is often employed in the image processing phase. This is because pre-processing consumes
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Fig. 1. Scabies/abnormal/normal dermoscopy images
around 50–80% of the time in most deep learning projects, and it includes both pixel value scaling and the usage use of digital image augmentation methods during both training and testing assessment of the model. Dataset Training set should be supplemented most likely including rescaling at random, vertical flips, and luminance, contrast, and color perturbations, in addition to random cropping. Because the photographs in the training dataset were of varying sizes, they would have to be resized before they could be used as model input. 2.3 Data Augmentation Data augmentation is a type of data pre-processing. Frequently, the amount of data available is insufficient to execute the categorization assignment adequately. In these circumstances, we supplement the data. For instance, if we are dealing using a dataset categorizing scabies into two categories, we might not have a sufficient number of photos (since high-quality photos are difficult to get by). augmentation is frequently employed to improve the volume and diversity of training data. Only the training set should be augmented, never the validation set. As you are aware, pooling enhances invariance. If a scabies image is in the image’s upper left corner, you may use pooling to determine if the scabies is a little left/right/up/down in the upper left corner. However, given training data that includes data augmentation such as rotation, cropping, translation, lighting, scaling, noise addition, and so on, the model learns all of these changes. This considerably improves the model’s accuracy. As a result, even if scabies appears in any part the model should be able to reproduce the image and identify it with great accuracy. 2.4 CNN A Convolutional Neural Network is a Deep Learning system that can take an image as input, assign importance (learnable weights and biases) to distinct aspects/objects in the image, and distinguish one from the other. It is a network architecture that learns directly from data, eliminating the need for manual feature extraction. Such as image classification. 2.4.1 Convolutional Layer The Convolution Operation’s goal is to extract high-level information such as edges from the input image; the first ConvLayer is in charge of capturing low-level features such as
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edges, color, gradient direction, and so on. With further layers, the architecture adjusts to the High-Level characteristics as well, resulting in a network with a comprehensive comprehension of the pictures in the dataset. The procedure produces two sorts of results: one in which the dimensionality of the convolved feature was reduced in comparison to the input, and another in which the dimensionality would either be raised or remains constant. 2.4.2 Pooling Layer A pooling layer performs a conventional downsampling operation, reducing the inplane dimensionality of the maps to introduce translation invariance to smaller shifts and distortions and lower the number of future learnable parameters. It is worth noting that there are no learnable parameters in any of the pooling layers, but filter size, stride, and padding are pooling hyperparameters. 2.5 Activation Function The activation function determines whether or not to stimulate a neuron by computing the weighted sum and then adding bias to it. The activation function’s objective is to induce non-linearity into a neuron’s output. 2.5.1 ReLU The ReLU is by far the majority popular and widely employed world activation function. Since then, it has been put to use in Almost all deep learning and deep neural network approaches (Fig. 2).
Fig. 2. ReLU
2.6 Fully-Connected Layer The fully linked layer establishes the association between the location of visual features and a class. Indeed, the input table corresponds to a feature map for a specific feature: the high value shows the position (more or less exact depending on the pooling) of this feature in the picture. If the placement of a feature at a specific point in the image is typical of a particular class, the associated value in the table is given considerable weight.
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2.7 Optimizer Adam When translating inputs to outputs, an optimization method determines the values of the parameters (weights) which minimize the error. These optimization techniques, also known as optimizers, have a significant impact on the correctness of the deep learning model. They also have an impact on the model’s speed training. 2.7.1 Adam Adam represents the adaptive moment estimation which is another way of computing current gradients from earlier gradients. Adam also uses momentum by combining fractions of previous gradients with the current one. This optimizer has gained popularity and is now widely used in neural network training. It’s easy to become overwhelmed by the sophistication of some of these new optimizers. Just keep in mind that they all have the same goal: to reduce our loss function. Even the most complicated methods are fundamentally basic. 2.8 Transfer Learning Transfer learning is a frequent and successful approach for training a network on a small dataset, in which a network is trained on a massive dataset, such as ImageNet, and then reused & applied to the particular task of interest. A fixed feature extraction method is a procedure that removes FC layers from a pre-trained network while keeping the remaining network as a fixed feature extractor, which consists of a succession of convolution and pooling layers referred to as the convolutional base (Fig. 3).
Fig. 3. Transfer learning model
2.8.1 VGG 16 VGG16 is simply a convolution neural network (CNN) design that took first place in the 2014 ILSVR (Imagenet) contest. It is recognized as one of the greatest vision model architectures currently available. The major characteristic of VGG16 is that, rather than a large number of hyper-parameters, they focused on generating the convolution operation of a 3 × 3 filter using a stride 1 and always used the same padding & max pool layer
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of a 2 × 2 filter with such a stride 2. This convolution & max pool layer setup is kept throughout the design. Finally, as an output, it has two FC (fully connected layers) and a softmax. The number 16 in VGG16 refers to its 16 weighted Layers (Fig. 4).
Fig. 4. VGG16 model
3 Experiments 3.1 Experimental Results and Analysis I created CNN model to test the dataset, and the trials revealed that when we utilize Transfer Learning in this scenario, the model would achieve 97.67% accuracy after 20 epochs. More information on the model may be found in the Figure below (Fig. 5).
Fig. 5. Accuracy and loos per epoch of the model
The assessment parameters of the analysis that was trained using the dataset for the two photos are shown in the Fig. 6 below, along with the percentage of accuracy and predictions of the images for each image.
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Fig. 6. Evaluation results of the model
4 Conclusion Convolutional Neural Networks have revolutionized image categorization challenges. As previously noted, dilated CNN has been effectively employed in image detection issues; nevertheless, to the best of our knowledge, this marks the first-time scabies photos have been classified using the CNN approach combined with transfer learning. In this research, we offer a method for developing a classifier that detects whether scabies is normal or aberrant in a Dermoscopy picture. In the ImageNet Large Scale Visual Recognition Challenge, the VGGNet-16, a pre-trained convolutional neural network (CNN) model, is employed as a feature vector extractor for microscopic pictures. Extensive experiments and parameter adjustment revealed that my suggested model performed well when working with a gathered dataset, with 97.67% accuracy using these extracted feature vectors.
References 1. Heukelbach, J., Feldmeier, H.: Scabies. Lancet 367(9524), 1767–1774 (2006). https://doi. org/10.1016/S0140-6736(06)68772-2 2. Dimililer, K., Ever, Y.K., Ugur, B.: ILTDS: Intelligent lung tumor detection system on CT images. In: Corchado Rodriguez, J., Mitra, S., Thampi, S., El-Alfy, E.S. (eds.) Intelligent Systems Technologies and Applications 2016. ISTA 2016. Advances in Intelligent Systems and Computing, vol. 530, pp. 225–235 (2016). https://doi.org/10.1007/978-3-319-47952-1_17. 3. Dimililer, K., Hesri, A., Ever, Y.K.: Lung lesion segmentation using Gaussian filter and discrete wavelet transform. ITM Web Conf. EDP Sci. 11, 01018 (2017). https://doi.org/10. 1051/itmconf/20171101018 4. Waldis, A., Mazzola, L., Kaufmann, M.A.: Concept extraction with convolutional neural networks. In: Proceedings of 7th International Conference on Data Science Technology and Application, pp. 118–129 (2018) 5. Polunin, A., Yandashevskaya, E.: Using of convolutional neural networks for Steganalysis of Digital Images. Proc. Ins. Syst. Program. RAS, 32(4), 55–164 (2020). https://doi.org/10. 15514/ISPRAS-2020-32(4)-11. 6. Dimililer, K.: DCT-based medical image compression using machine learning. Signal Image Video Process. 16(1), 55–62 (2022). https://doi.org/10.1007/s11760-021-01951-0
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7. Dimililer, K., Kavalcıo˘glu, C.: Gaussian noise and haar wavelet transform image compression on transmission of dermatological images. In: Abraham, A., Mauri, J.L., Buford, J.F., Suzuki, J., Thampi, S.M. (eds.) Advances in Computing and Communications. ACC 2011. Communications in Computer and Information Science, vol. 192, pp. 357–364. Springer, Heidelberg. https://doi.org/10.1007/978-3-642-22720-2_37 8. Dimililer, K., Kavalcıo˘glu, C.: Gaussian noise and discrete cosine transform image compression on transmission of dermatological images. In: Abraham, A., Mauri, J.L., Buford, J.F., Suzuki, J., Thampi, S.M. (eds.) Advances in Computing and Communications. ACC 2011. Communications in Computer and Information Science, vol. 192, pp. 357–364. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22720-2_37. 9. Dimililer, K., Kayalı, D.: Image enhancement in healthcare applications: a review. In: AlTurjman, F. (ed.) Artificial Intelligence and Machine Learning for COVID-19. Studies in Computational Intelligence, vol. 924, pp. 111–140. Springer, Cham (2021). https://doi.org/ 10.1007/978-3-030-60188-1_6 10. Dimililer, K., Sekeroglu, B.: Skin lesion classification using cnn-based transfer learning model. Gazi Uni. J. Sci., 36(2) (2023). https://doi.org/10.35378/gujs.1063289 11. Liang, F., Shen, C., Wu, F.: An iterative BP-CNN architecture for channel decoding. IEEE J. Sel. Top. Signa., 12 (1), 144–159 (2018). https://doi.org/10.1109/JSTSP.2018.2794062 12. Kayali, D., Dimililer, K., Sekeroglu, B.: Face mask detection and classification for COVID-19 using deep learning. In: International Conference on INnovations in Intelligent SysTems and Applications, pp. 1–6 (2021). https://doi.org/10.3390/app12189171 13. Yamashita, R., Nishio, M., Do, R.K., Togashi, K.: Convolutional neural networks: an overview and application in radiology. Insights Imaging 9(4), 611–629 (2018). https://doi.org/10.1007/ s13244-018-0639-9 14. Liang, Y., Yang, J., Quan, X., Zhang, H.: Metastatic breast cancer recognition in histopathology images using convolutional neural network with attention mechanism. In: Chinese Automation Congress (CAC), pp. 2922–2926. IEEE (2019). https://doi.org/10.1109/CAC 48633.2019.8997460 15. Qin, Y.: A cancer cell image classification program: based on CNN model. In: 2nd International Seminar on Artificial Intelligence, Networking and Information Technology (2021). https://doi.org/10.1109/AINIT54228.2021.00037 16. Sharma, S., Sharma, S., Athaiya, A.: Activation functions in neural networks. Int. J. Eng. Appl. Sci. 04(12), 310–316 (2020). https://doi.org/10.33564/ijeast.2020.v04i12.054
Determination of the Dynamic and Interactive Event in Exascale Computing Systems via Request Clustering Nigar Ismayilova(B) Azerbaijan State Oil and Industry University, Baku AZ1010, Azerbaijan [email protected]
Abstract. Load balancer is one of the main problems in Exascale Computing system management. The dynamic nature of executed requests and used resources makes the assignment process complicated between requests and machines. In this work fuzzy c-means clustering method for grouping the resources into different clusters with soft borders was proposed. Application of the soft approach allows to cluster requests without hard separation of the request space and consequently to determine the occurrence of the dynamic and interactive event. Keywords: Exascale computing system · Dynamic and interactive event · Requests clustering · Fuzzy C-means
1 Introduction Optimization of load balancer – finding the best assignment between processes and resources represents an important topic to study because of increasing the usage of HPC technologies in various fields of science and industry. The challenges with optimization methods for task scheduling in different type of distributed computing systems are growing with progress of computational resources and scientific inventions. The optimal distribution of tasks between resources in cluster computing systems with the standing quantity of requests and computational machines based on general network optimization methods such as bipartite matching, minimax criteria, finite element methods have been successfully applied [1–3]. On the other hand, for dynamic environments with unstable nature of resources and requests it is necessary to apply new approaches based on artificial intelligence. The purpose of load balancer in cloud computing systems is optimization of comprehensive computing capacity, which differs from the load balancer’s maximization of computing mission in another distributed systems such as cluster computing, grid computing, peer to peer computing and exascale computing [4]. By popularization of modern wireless communications, the necessity of load balancer in fog computing systems grows. The goal of load balancer in such systems is to minimize execution time and energy consumption. Increasing the number of resources used in computing systems and heterogeneity of the solved requests increases the complexity of the load balancer process. As usual, the © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 282–288, 2023. https://doi.org/10.1007/978-3-031-25252-5_39
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main problem in systems with dynamic structures is the recognition and classification of the unlabeled data. AI forecasting method opens wide areas for high-performance load balancer models based on least-connection scheduling algorithms [5, 6]. Progress and intensive usage of heterogeneous computing environments such as grid computing, P2P computing, and cloud computing, as well as challenges in Exascale computing systems demonstrate the necessity and effectiveness of proposed dynamic load balancers for distribution of load [7, 8]. Several investigations have used artificial intelligence techniques to assign requests to suitable resources, where one or both has dynamic nature [9, 10]. In the dynamic and heterogeneous systems the main problem for finding the appropriate assignment between requests and machines is related to occurrence of dynamic and interactive (D&I) event. In this situation different kinds of problems which make necessary to change the load balancer management technique may appear. The first problem appearing in dynamic distributed systems related to the D&I events is to define the moment of D&I occurrence for making decisions about the changing of the load balancer mechanism. For this purpose, analysing of the requests and determination of the D&I occurrence case is the solution of the half problem. Application of fuzzy logic-based solutions gives suitable opportunities for making decisions in uncertain environments as dynamic and heterogenous computing system [11–13].
2 Dynamic and Interactive Event Mechanism of load balancer activity can be modeled by the following formula [12]: Load distribution : Processrequirements → [Resourceattributes ] ∴ (1) ∀Process ∈ HPCProcesses → Scheduled Resourceactivity = 100% Accordingly, this formula describes conditions for optimal load balancer. It is an assignment process of requests to computing machines where each process in the system must be scheduled and the activity of all resources should be 100%. Dynamicity of processes and computing machines and occurrence of dynamic and interactive events makes problems during optimal processing of the load balancer in Exascale computing systems. Two problems remain with the dynamic and interactive (D&I) event’s occurrence: a) determination of the dynamic and interactive events in the computing systems; b) handling of the assignment process between requests and machines. In this work has been proposed approach for the solution of the first case by fuzzy c-means clustering of the requests in the computing system. The limitation of Exascale computing system is mainly related to the dynamic nature of both resources and requests. The dynamicity of requests can be defined as the result of three cases: a) executed request created new processes; b) process needs connection with other executed processes; c) process requires connection with the global space [13].
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3 Grouping of the Requests Using Their Requirements Clustering processes allow us to determine the dynamic and interactive events (D&I) by extracting the unusual situation. It means that, if we observe the process which does not belong to the determined classes of the processes or belongs to them with small membership degrees, then we will assume that D&I has occurred. In this situation, we have two ways: Determination of the new class of processes. Resolve the clustering problem by considering the observed D&I and including the observed situation in one of the existed clusters. Before solving the clustering problem, we need to clarify the vector of request attributes and distance metric for calculating similarities between them. Let’s assume that we have a request vector in distributed Exascale system defined by the following parameters: (2) R = Reqnature , Reqtype , Reqtime , Reqlocation , Reqrequirements . This vector gives information about the request, its nature, type of the process, time required for the execution of the task, source of the process, here Reqrequirements represents technical requirements of the request defined by the following matrix: RIO/time RM /time RF/time Reqrequirements = (3) RIO/value RM /value RF/value Request requirements matrix defines time required by the given process from the computation environment as input/output resource, memory, and file connection, as well as values of these requirements. When in the distributed computing system, we observe requests that can be executed using the computing and processing capabilities of the resources of the system load balancer will work successfully. However, if there appears the request whose requirements are beyond the capabilities of the system’s resources or are very different from the requests’ requirements executed before its appearance, we define it as the D&I and propose new solution methodologies. For the realization of this approach in this work application of the fuzzy c-means clustering technique for clustering of the request based on their attributes vector has been proposed and assumed that if the next request does not belong to one of the found clusters or belongs with the small membership degree then the dynamic and interactive event has occurred. The main problem here is to define the correct distance metric for the calculation of the distances between the requests, as you see from the expressions (2)–(3) request requirements vector contains both categorical and numerical attributes. Considering this fact, we proposed to use distance metric based on a hybrid approach combining cosine distance metric for categorical (attributes’ categories will be converted to discrete numbers) and Euclidian distance (L2 – norm) for numerical attributes. Generally, it is not possible to classify executed processes into different groups using their attributes, but the usage of the fuzzy c-means clustering method allows to group requests into different groups softly without hard borders [13]. This method also
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provides the possibility for determination of the D&I occurrence via clustering even during incomplete information about the request [14, 15]. Based on the fuzzy c-means clustering algorithm for soft grouping of the requests during execution of the dynamic and heterogenous computing system our goal is to minimize the following function: Jm =
C N
2 µm ij Reqi − Cj ,
(4)
i=1 j=1
where m is any real number greater than 1, µij – is the degree of membership Reqi to cluster j, Cj – is the center of cluster, and ∗ is similarity calculated using different metrics as mentioned above, C – number of clusters, N – number of requests. Clustering process realized through the optimization process iteratively by updating membership degrees µij and cluster centers Cj : µij =
C k=1
1 Reqi −Cj Reqi −Ck
N
2 m−1
Cj =
m i=1 µij · Reqi
N m i=1 µij
(5)
These formulas can be explained by the following algorithm: 1. In the first step are defining centers by randomly chosen requests equal to the number of clusters planned for grouping of the requests; 2. Next step defines membership degrees of each request to the cluster centers using the first part of the formula (5), for finding the membership degree of the i-th request to the j-th cluster we find distance between the i-th request and the j-th cluster center by separating the request and the cluster center into two parts: categorical (for this part we use cosine similarity for the distance) and numerical (where we apply Euclidian distance metric) parts, divide it to the distance between i-th request and all cluster centers, then we find its 2/(m-1)-th power and summarize them, m is selected regarding to the degree of fuzziness that significantly affect the result of clustering; 3. Then we recalculate cluster centers by using the second part of the formula (5) by sum of multiplications of the membership degrees to all request and dividing this sum to the sum of all membership functions for the given cluster. Steps 2 and 3 iteratively repeated until finding the minimum of the function described in formula (4). By this way we can define different groups of the familiar processes in distributed computing system before D&I occurrence. The main opportunity of application fuzzy c-means clustering for grouping executed processes is soft borders between request groups. Accordingly, appearance of new unknown request or process can be defined by calculation of the membership degree of the process to the defined clusters, i.e. if the new process does not belong to defined clusters or belongs with very low membership degree leads to D&I occurrence. Thus, one of the significant challenges for optimization of the load balancer process in Exascale Computing System, determination of the D&I event can be solved using proposed approach.
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4 Argument Determination of the D&I events in heterogeneous computing systems is very important for choosing the mechanisms for the management of such systems. D&I appearance leads to changing of the computing system, which requires defining new ways for load balancer, resource discovery, and process migration. Artificial intelligence is one of the main tools for handling uncertainty, determination of unknown cases, and controlling them. Fuzzy logic is the technique that allows increasing the intelligence level of the approach [19–22, 23]. Using this opportunity grouping of the requests for determination of the unknown events, namely D&I events gives chances to manage the computing system with the heterogeneous nature. Traditional algorithms proposed for load balancer such as round robin are not able to define D&I and handle the situation after D&I occurrence [16]. In this case after D&I occurrence, as the server is not familiar with the appeared situation, it will be failed, and we will observe the cascading process in the whole computing system. In this regard, the proposed algorithm allows us to control the computing system after D&I occurrence by determination of the request nature which leads to the D&I occurrence. After the clustering of the requests based on their characteristics, request bringing to the D&I occurrence is determined using the formula (5). If the membership degree for the current request is very low for all clustering groups, it means that we are dealing with the state that was not seen before. In this situation there are two ways for solutions for load balancer, resource discovery and process migration: 1. we can include the request to the cluster for which membership degree is higher than others; 2. we can create the new group of requests by re-clustering. As the group of the unseen request has been defined, load balancer can use one of the previous solutions applied to other requests of the cluster. The advantage of the formula (5) is that, by this formula we can softly group requests based on their characteristics for determination of the particular states.
5 Conclusion Determining the D&I occurrence in Exascale Computing Systems can be considered as a significant step forward in load balancer framework design for managing the dynamic and heterogenous computing systems. By application of the fuzzy c-means clustering algorithm for grouping executed requests and consequently determination of the unknown requests which defines the D&I occurrence case is useful for the next step of the Exascale Computing Systems management, handling D&I event and define the best assignment between requests and available resources.
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Evaluation of Techniques Used in Phenol Removal from Wastewater Using Fuzzy PROMETHEE Method Basil Bartholomew Duwa1,3 , Ay¸seGünay Kibarer3(B) , Berna Uzun1,2,4 Serife ¸ Kaba3 , and Dilber Uzun Ozsahin3,5
,
1 Operational Research Center in Healthcare, Near East University, 99138 Nicosia, Cyprus
{basil.barthduwa,berna.uzun}@neu.edu.tr
2 Statistics Department, Carlos III University of Madrid, Getafe, Madrid, Spain
[email protected]
3 Department of Biomedical Engineering, Faculty of Engineering, Near East University,
99138 Nicosia, Cyprus {aysegunay.kibarer,serife.kaba}@neu.edu.tr 4 Department of Mathematics, Faculty of Applied Sciences, Near East University, 99138 Nicosia, Cyprus 5 Medical Diagnostic Imaging Department, College of Health Sciences, University of Sharjah, Sharjah, United Arab Emirates [email protected]
Abstract. Phenolic chemicals have high toxicity level even at low concentrations, making them a priority contaminant. Conventional and innovative treatment strategies are examined in this review. As reported by the World Health Organization (WHO), around 144 million Olympic-sized swimming pools of wastewater are generated annually around the world. Approximately 48% of that effluent is dumped into the environment untreated. Therefore, to properly treat and remove contaminants such as phenol from wastewater deposits, it is now important to develop innovative treatment methods. This study focuses on evaluating five (5) alternate techniques used in phenol removal from wastewater using decision-making techniques, specifically the Preference Ranking for the Organization Method for Enrichment Evaluation PROMETHEE, a Fuzzy technique in data analysis. These removal techniques employed were distillation, adsorption, chemical oxidation, membrane separation, and biodegradation. Parameters such as duration, safety, ease of operation, side effects, efficiency, affordability, reliability, and energy consumption of each alternative were evaluated using the PROMETHEE, Multi-criteria decision-making paradigm. The representation of the comprehensive individual ranking of all the current alternatives revealed that the Membrane separation method is the optimal choice because it has the highestranking flow representation (0,0621); while the distillation separation method is the second with an optimum net ranking flow of 0,0263. However, the chemical oxidation method is revealed to be the least ranked technique based on the criteria selected. Keywords: Biodegradation · PROMETHEE fuzzy logic · Phenolic chemicals · MCDM · Membrane separation © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 289–296, 2023. https://doi.org/10.1007/978-3-031-25252-5_40
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1 Introduction The flow of untreated wastewater from industries, agricultural, and residential operations into water bodies are the primary cause of the presence of phenolic compounds in water bodies. These substances are revealed to be poisonous, and they are capable of inflicting severe consequences that linger for an extended period on both people and animals. Even in low quantities, they are carcinogenic and cause harm to the red blood cells as well as the liver. When these compounds interact with bacteria, inorganic compounds, or other organic compounds in water, substituted compounds or other moieties can be produced. These substituted compounds or other moieties may be just as dangerous as the original phenolic compounds [1]. The quality of water is imperative for human health, which as well is useful in the quality of aquatic life in the water bodies. Thus, as the human population is becoming increasingly difficult to guarantee that there will always be sufficient quantities of clean water available for everyone [2]. Recently, there has been an increase in the level of concern among decision-makers and scientists on the impacts of human and animal exposure to chemical compounds in the environment, specifically the aquatic environment. In this context, phenolics are some of the chemicals that present the greatest cause for concern because of their propensity to remain in the environment for extended periods, accumulate, and to have harmful effects on both people and animals. Phenolic chemicals can be found in high quantities in nature and are thought to be responsible for the colors of flowers and fruits. Others are synthesized, and their products find use in many different areas of people’s everyday lives [3, 4]. As a consequence of this, a variety of techniques for the treatment of wastewater have been developed and put into practice for the removal of phenolic compounds from industrial, domestic, and municipal wastewaters before their discharge into water bodies. The goal of these techniques is to mitigate the harmful effects that these chemicals have on human and aquatic life as much as possible. Extraction, polymerization, the electroFenton process, photocatalytic degradation, and other similar processes are examples of some of these procedures [5]. Phenolic compounds exhibit a high level of toxicity even when present in low concentrations, which places them as pollutants. This evaluation looks at both traditional treatment methods and cutting-edge approaches to the treatment of wastewater by using advanced mathematical techniques to evaluate the major methods applied in the extraction of phenols in water. 1.1 Techniques Applied in Phenol Removal in Wastewater The major techniques used in separating and extracting phenols in wastewater are explicitly explained individually in this section. Distillation\Evaporation: The removal of phenols from wastewater can be accomplished using several different processes, including evaporation and distillation. It is done by taking advantage of the phenols’ relatively high evaporation rates. Methods that use distillation typically have substantial energy costs and are normally only viable for extremely high concentrations of phenol [6, 7]. Purification can be accomplished using
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steam distillation, depending on how volatile the phenol is. Although the liquid-liquid extraction method is very effective at removing chemicals from wastewater, the process is relatively time-consuming, expensive, and may be associated with injuries due to the huge number of organic solvents (some of which are toxic) that are used in the procedure [8]. Adsorption\Extraction: Adsorption, which makes use of solid consumables like activated carbon, is a typical method for removing phenols. The economics are contingent not only on the cost of the adsorbent but also on the cost of disposing of or recycling it [9]. Therefore, new solutions are being explored including chemical functionalization of the activated charcoal, impregnation by nanoparticles, and the use of chitin/chitosan as limited bio sorbents, which are viable alternatives to extract phenolic chemicals from the environment. Adsorption is considered one of the preferred methods used in removing phenolics from water since it is simple to design and implement. The process creates no hazardous byproducts. [10]. Membrane Separation: The membrane separation method is a special kind of barrier that, when applied to a gas or liquid, can facilitate the separation of different species through a variety of different separation processes, such as diffusion, sieving, or sorption. The semipermeable aspect of the membranes is what ultimately leads to the selective separation that takes place [11]. Chemical Oxidation: The oxidation of phenols and other organics is a tedious process. Traditional oxidizing chemicals such as ozone, chlorine, permanganate, etc., and catalysts and circumstances such as irradiation can all be utilized [12, 13]. Biodegradation: An established and effective way of removing phenols from water is the use of biological treatment. Biodegradation of phenols can be accomplished by the employment of aerobic or anaerobic microbes [14]. The application of enzymes to remove phenolic substances from wastewater has been described in several scientific studies. “Shesterenko and colleagues” work is one of these reports. It was revealed to have removed phenols from water using Agaricus bisporus tyrosinase and inorganic coagulants immobilized on polymer-carriers [15]. Phenolic compounds are regarded to be a priority pollutant since even in small concentrations, they pose a significant risk to human health and the environment. This study compares and contrasts the efficacy of established modern techniques with those that are considered to be on the leading edge of medical innovation. Comparisons are performed between the effectiveness of various therapies that use phenol and many routinely employed derivatives.
2 Materials and Methodology 2.1 PROMETHEE (Preference Ranking Organization Method for Enrichment Evaluations) One of the most difficult aspects of dealing with problems that arise in the real world is gathering accurate data in order to do system analyses. Therefore, advanced simulation techniques such as the Fuzzy-Logic based models are applied in the evaluation of major decision problems. The fuzzy PROMETHEE is a decision-making technique that evaluates and compares decision problems where the conflicting multiple criteria occurs. In
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contrast to other multi-criteria decision-making methods, PROMETHEE has the advantage of enables decision makers determine preference values of each alternative with different types of preference functions assigned to each criterion. The concept of fuzzy logic refers to one variety of many-valued logic. The truth value of variables in this kind of logic can be any real number that is between 0 and 1, inclusive. It is used for the goal of managing the concept of partial truth, in which the truth value may fluctuate between being fully true and being entirely false. This is accomplished through the utilization of this idea management tool. On the other hand, the truth values of variables in Boolean logic can never be anything other than the integer values 0 or 1, as these are the only two outcomes that are even remotely feasible. [16]. The PROMETHEE approach has been successfully applied to a significant number of major applications in a variety of studies, such as in industries, healthcare, water resources, banking and finance, tourism, and business management, among others. The PROMETHEE technique requires two important and different kinds of data: information concerning the criteria weights that are taken into consideration and the preference function of the researcher or the decision-maker when comparing the variables in terms of individual criterion [17]. The notion of fuzzy sets was developed to address the problem of dealing with the unpredictability of human judgment. The formulation and solution of problems that are too complicated or vague to be susceptible to analysis by standard methodologies are developed through the application of fuzzy set theory [18]. The selected importance weights of the criteria are determined by the experts as shown in Table 1. Table 1. Linguistic fuzzy scale. Linguistic scale
Triangular fuzzy scale
Importance ratings of criteria
Very High (VH)
(0.75, 1,1)
Efficiency, safety, reliability
Important (H)
(0.50, 0.75, 1)
Ease of operation, side effects
Medium (M)
(0.25, 0.50,0.75)
Affordability, duration
Low (L)
(0, 0.25, 0.50)
Energy required
Very Low (VL)
(0,0,0.25)
Table 2 shows the data of phenol removal technique. The PROMETHEE MCDM technique was mainly applied in the decision making of the alternatives used in the extraction of phenol in wastewater after the defuzzification process. The Yager index is used as the defuzzification process since it considers all the point in the set to clarify the fuzzy numbers. The Gaussian preference function is assigned to each criterion which considers the difference of the alternatives using the standard deviation of the related data of the criterion.
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Table 2. Datasets for the phenol removal from wastewater techniques Alternative| Criteria
Duration Affordability Safety Easy for Energy Efficiency Reliability Side operation consumption effects
Aim
min
min
max
max
max
max
max
min
Distillation [19]
H
L
VH
YES
L
VH
VH
L
Adsorption [20]
M
M
H
YES
M
H
H
M
Membrane separation [21]
L
L
VH
YES
H
VH
VH
M
Chemical oxidation [22]
H
H
L
NO
L
VH
H
M
Biodegradation M [23]
L
H
YES
L
H
VH
L
3 Results and Discussion In the PROMETHEE Net ranking flow on Table 3, the membrane separation method showed higher result with 0,0621 net ranking flow as the preferred alternative. The distillation separation technique also performed distinctly well with the net ranking of 0,0263; while the Biodegradation method exhibited as the third preferred technique (0,0031). However, other techniques flawed, such as the chemical oxidation method, which was revealed to be the 5th ranked in phenol removal, with −0,0843; while the Adsorption method is preferred than the chemical oxidation method with −0,0072 net ranking flow result. In addition, the positive ranking flow shows the strength of the alternatives, while the negative ranking flow shows the weakness of the alternatives, which subsequently assist in obtaining the complete ranking. Similarly, the pictorial representation of the study analysis, showed both the positive and negative ranking results as seen in Fig. 1. Based on the figure representing the PROMETHEE evaluation results, the membrane separation technique shows the highest positive results above the 0-treshold and the least negative result below the 0-treshold. In contrast, the chemical oxidation method shows the highest negative result below the 0-treshold and the least positive result above the 0-treshold. The most common method that shows high phenol Table 3. Ranking results. Phi
Phi +
Phi-
0,0655
0,0034
Rank
Alternatives
1
Membrane separation
2
Distillation
0,0263
0,0412
0,0149
3
Biodegradation
0,0031
0,0255
0,0224
4
Adsorption
−0,0072
0,0189
0,0261
5
Chemical oxidation
−0,0843
0,0041
0,0884
0,0621
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removal in wastewater in several studies, is the adsorption and the biological methods, Contrary to this study, the researchers did not adopt a modern analytical model, such as the Fuzzy-PROMETHEE MCDM. Therefore, this study is exceptional when compared to other studies, by introducing classical data analytical models (Fuzzy-PROMETHEE).
Fig. 1. PROMETHEE rainbow
4 Conclusion Phenolics are exceedingly dangerous and toxic to all forms of life, including humans, and animals both terrestrial and aquatic. In the presence of chlorine, phenolic compounds can also transform into carcinogenic chlorophenols. Both the U.S Environmental Protection Agency (EPA) and the National Pollutant Release Inventory (NPRI) of the United States of America and Canada, respectively, consider them to be high-priority water pollutants. In many different jurisdictions, there are stringent discharge limitations for phenols that are typically less than 0.5 mg/L. There is a distinct and unmistakable differentiation between which the alternatives are favored and taken into consideration in the process of removing phenol from wastewater at various locations, as determined by the comparative evaluation of the numerous phenol removal techniques used in this research. This study will serve as a blueprint and a guide to many individuals, institutions, research institutes, governmental agencies, and non-governmental organizations that consider protecting the vast water bodies from human disposal.
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18. Sayan, M., Sultanoglu, N., Uzun, B., Yildirim, F.S., Sanlidag, T., Ozsahin, D.U.: Determination of post-exposure prophylaxis regimen in the prevention of potential pediatric HIV-1 infection by the multi-criteria decision-making theory. IEEE, International Journal Advances Science Engineering Technology, pp. 1–5 (2019). https://doi.org/10.1109/ICASET.2019.871 4442 19. Ozsahin, D.U., et al.: Evaluating cancer treatment alternatives using fuzzy PROMETHEE method. Int. J. Adv. Comput. Sci. Appl. 8(10) (2017). https://doi.org/10.14569/IJACSA.2017. 081024 20. Ozsahin, D.U., Isa, N.A., Uzun, B., Ozsahin, I.: Effective analysis of image reconstruction algorithms in nuclear medicine using fuzzy PROMETHEE. IEEE, International Journal Advances Science Engineering Technology, pp. 1–5 (2018). https://doi.org/10.1109/ICASET. 2018.8376892 21. Mohammadi, S., Kargari, A., Sanaeepur, H., Abbassian, K., Najafi, A., Mofarrah, E.: Phenol removal from industrial wastewaters: a short review. Desalin. Water Treat. 53(8), 2215–2234 (2015). https://doi.org/10.1080/19443994.2014.883327 22. Raza, W., Lee, J., Raza, N., Luo, Y., Kim, K.H., Yang, J.: Removal of phenolic compounds from industrial wastewater based on membrane-based technologies. J. Ind. Eng. Chem 71, 1–18 (2019). https://doi.org/10.1016/j.jiec.2018.11.024 23. Lefèvre, S., Boutin, O., Ferrasse, J.H., Malleret, L., Faucherand, R., Viand, A.: Thermodynamic and kinetic study of phenol degradation by a non-catalytic wet air oxidation process. Chemosphere 84(9), 1208–1215 (2011). https://doi.org/10.1016/j.chemosphere.2011.05.049
Research of the Manufacturing Quality of Plastic Details with Complex Forms of Connection Naila A. Gasanova(B) , Agali A. Quliyev , Aynur V. Sharifova , Tamilla U. Khankishiyeva , and Rafiga S. Shahmarova Azerbaijan State Oil and Industry University, Azadlig 34, Nasimi, Baku, Azerbaijan [email protected]
Abstract. This article examines the nature passing of the shrinking deformation of plastic thread elements depending on their size and manufacturing regimes. At the same time, within a wide range of regime parameters, achievable limits of quality indicators of details working in structures of equipment for exploration, drilling and operation in the oil and gas industry are investigated. Mathematical dependencies between quality indicators (shrinkage and strength) of details against pressing temperature are established. The scientific-practical methods for insurance of plastic details quality in oil field equipment based on the mathematical models of their production have been developed. These mathematical models reflect the regularity of influence of production regime and structure of the details on the quality indicators (durability in stretching, hardness, roughness of surface, density and shrinkage for the optimization of their production regimes). In this article the quality of thread details of the oil-field equipment depending on modes of production of their various constructions and composition of press materials were reviewed. By adjusting the operating parameters during production of details are defined quality indicators: tensile strength, hardness of details and others. Keywords: Smooth and threaded plastic parts · Shrinking deformations · Pressing pressures · Pressing temperature · Regime parameters · Size error · Quality indicators
1 Introduction The use of plastic details in various constructions makes it possible to reduce the cost and labor intensity of manufacturing machines and devices, to reduce the weight of constructions while improving their quality and reliability. Researches were carried out with the aim of increasing labor productivity and replacing non-ferrous and ferrous metals with plastic masses. Details for this purpose are selected with a certain characteristic, so that in the future the developed technological process could be used in the oil and gas industry. As is known, in order to ensure a high-quality connection of smooth and threaded details making from various plastics, it is primarily necessary to establish boundaries of the sizes error. The nature passing of shrinking deformation and error in the entire plastic thread elements differs greatly from the smooth details [1]. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 297–304, 2023. https://doi.org/10.1007/978-3-031-25252-5_41
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Threaded parts do not meet the requirements of the 3rd accuracy class, since the screwing is ensured due to the guaranteed clearance, the value scattering of the actual average diameter is practically commensurate with the tolerance for the average thread diameter according to the 3rd accuracy class, and for large diameters it exceeds it.
2 Optimal Control of Technological Regimes To obtain the required accuracy of plastic thread, first of all, the optimal control of technological regimes is required and, as a result of the establishment oscillation limits of shrinkage as the main indicator of manufacturing quality. The analysis of works devoted to the issues of the accuracy making the threading on plastic details revealed that the specified process is much more complicated in its specificity and differs from the accuracy of manufacturing smooth parts from plastics [2]. In our opinion, a complex solution is required to study the issue of the accuracy of thread production on plastic parts, i.e., here it is errors caused by oscillation in shrinkage of native thread elements (d , d1 , d2 , s, α/2) and errors caused by processing regimes must be taken into account. The influence of each regime parameter on the oscillation in the shrinkage of thread elements is studied separately and at the same time the complex influence of the mode parameters on the errors in the manufacture of these elements as a whole is determined for further development of the thread size tolerance. In connection with the above, we are considering the study of the shrinkage process and oscillation in the shrinkage of elements of plastic threaded details with sizes M20 × 2 (valve body). These sizes are often used in the oil and gas industry.
3 Establishing the Mathematical Dependence Between the Quality Indicators (Shrinkage and Strength) of Details on the Pressing Temperature The study of the joint action of all technological parameters on the accuracy of manufacturing individual elements of plastic threaded parts is complex problem, and its solution for both smooth and threaded plastic parts possible only with the use of mathematical modeling. Using the mathematical method, mathematical models of the process of manufacturing plastic parts are determined, while shrinkage, surface roughness and hardness of manufactured parts made of thermosetting plastics are taken as quality indicators. For the mathematical characterization of the dependence of quality indicators on the technological parameters proposed by us, are two models: -the first order polynomial
-the second order polynomial
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where a0 , ai , b0 , bi , bij , bii are the coefficients of the regression equation; k is the number of input variables; xi – values of independent input variables – technological parameters; y– the value of the input parameter of quality indicator. Based on the mathematical description of paired dependencies on technological parameters, the mathematical model describing the process passing shrinkage of plastic threaded details can be written in general form (1) Here Qk − shrinkage k-th element of thread; xi − processing modes (X1 − specific pressure, MPa; X2 − pressing temperature, °C; X3 − holding time, mm/min). For the experiment, the second-order orthogonal plan was used and the number of experimental points was chosen according to the method proposed by Box-Wilson (Tables 1, 2). The plans of experimental shown in Tables 1 and 2 have a number of positive properties. Firstly, this plan can be obtained as a result of completing the first-order plan, which creates convenience for the experimenter when obtaining an inadequate mathematical model of the first order, which makes it possible to go to the second order, adding experiments only at star points and in the center of the plan. Secondly, the arrangement of starry points on the axes does not violate the orthogonally of the first-order columns and interaction effects. This enables the corresponding independent coefficients of the regression equation to be obtained. To determine the coefficients a0 , ai , aij , aii in the regression Eq. (1), we used an algorithm that simplifies the notation system with the introduction of a dummy variable X0 = 1, as a result of which we obtained: X0 = Z0 ; X1 = Z1 ; X2 = Z2 ; X3 = Z3 ; X12 = Z4 ; X22 = Z5 ; X32 = Z6 ; X1 X2 = Z7 ; X1 X3 = Z8 ; X2 X3 = Z9 . In the new designation system, the second-order polynomial is written as a linear homogeneous equation Qi =
q
ai zi
(2)
i=0
Coefficients of the regression Eq. (2) are found by the least squares method, i.e. from the minimum condition 2 q n n 2 Qk − Q = ai zi =0 (3) Qk − k=1
k=1
i=0
min
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Factors
X1 = P, MPa
X2 = t, 0 °C
X3 = τ, min/mm
Shrinkage of thread elements, %
Main level
36
160
0,7
Qi
Upper level
38
175
0,8
Lower level
34
145
0,6
Interval of variation
2
15
0,1
Experiences
X1
X2
X3
Qd
Qd1
Qd2
Qd3
1
+1
+1
+1
0,960
0,890
1,200
1,910
2
+1
+1
−1
0,310
0,420
0,410
1,420
3
+1
−1
+1
0,996
0,920
0,210
1,860
4
+1
−1
−1
0,340
0,580
0,860
1,510
5
−1
+1
+1
0,980
0,980
0,620
1,880
6
−1
+1
−1
0,320
0,480
0,960
1,310
7
−1
−1
+1
1,00
1,040
0,840
1,910
8
−1
−1
−1
0,510
0,680
0,920
2,100
9
+α
0
0
0,890
0,890
0,570
1,610
10
−α
0
0
0,510
0,560
0,880
2,210
11
0
+α
0
0,980
0,920
0,790
1,860
12
0
−α
0
0,880
0,580
0,640
1,860
13
0
0
+α
0,320
0,310
0,830
1,650
14
0
0
−α
0,990
0,860
0,940
1,920
15
0
0
0
0,910
0,660
0,870
1,860
16
0
0
0
0,880
0,780
0,830
1,790
17
0
0
0
0,870
0,840
0,840
1,820
18
0
0
0
0,890
0,910
0,890
1,810
19
0
0
0
0,885
0,920
0,880
1,830
By permutation and simplifying the Eq. (3), we get a system of linear equations with respect to coefficients 9 Qk z1 = a1 9k=1 z1 z1 + a2 9k=1 z2 z1 + ...+a9 9k=1 z9 z1 k=1 9 9 9 9 k=1 Qk z2 = a1 k=1 z1 z2 + a2 k=1 z2 z2 + ...+a9 k=1 z9 z2 ......................................................... ......................................................... 9 9 9 9 k=1 Qk z2 = a1 k=1 z1 z9 + a2 k=1 z2 z9 + ...+a9 k=1 z9 z9
(4)
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Table 2. Size M33 × 3 Material K-18–53 Factors
X1 = P, MPa
X2 = t, 0 °C
X3 = τ, min/mm
Shrinkage of thread elements, %
Main level
36
160
0,7
Qi
Upper level
38
175
0,8
Lower level
34
145
0,6
Interval of variation
2
15
0,1
Experiences
X1
X2
X3
Qd
Qd1
Qd2
Qd3
1
+1
+1
+1
0,410
0,420
0,460
0,700
2
+1
+1
−1
0,510
0,509
0,490
0,680
3
+1
−1
+1
0,460
0,470
0,510
0,650
4
+1
−1
−1
0,620
0,610
0,560
0,810
5
−1
+1
+1
0,540
0,580
0,490
0,920
6
−1
+1
−1
0,680
0,640
0,564
0,960
7
−1
−1
+1
0,560
0,720
0,630
0,740
8
−1
−1
−1
0,710
0,760
0,740
0,980
9
+α
0
0
0,440
0,540
0,550
0,670
10
−α
0
0
0,670
0,720
0,610
0,840
11
0
+α
0
0,650
0,760
0,600
0,760
12
0
−α
0
0,580
0,810
0,760
0,750
13
0
0
+α
0,420
0,450
0,640
0,660
14
0
0
−α
0,630
0,580
0,607
0,810
15
0
0
0
0,640
0,620
0,580
0,850
16
0
0
0
0,570
0,610
0,625
0,840
17
0
0
0
0,560
0,640
0,620
0,830
18
0
0
0
0,580
0,590
0,630
0,860
19
0
0
0
0,590
0,608
0,620
0,870
Determining the coefficients of Eq. (4), it is necessary to apply actions with the matrix, for which Eq. (4) is writing in matrix form B=A+C
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9 9 9 9 2 z1 z2 z1 ... z9 z1 Qk z1 a0 k=1 k=1 k=1 k=1 a 1 9 9 9 9 2 z2 z1 z2 ... z9 z2 Qk z2 a2 A = k=1 ; B = k=1 ; C = ... k=1 k=1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 9 9 9 9 a 9 z9 z1 z2 z9 ... z92 Qk z9 k=1
k=1
k=1
(5)
k=1
The solution to Eq. (5) is to find the elements matrix of column C. As is known from matrix theory, the solution is provided to the following form C=A
−1
+B
−1
where A − is the inverse matrix for solving the system of equations, the program package situated in the work [3] was used. Substituting the calculated values of the coefficients in Eq. (1), we obtain a mathematical model describing the process passing of shrinkage of the plastic threaded details. It consists of 4 equations for each size (M20 × 2, M33 × 3): for shrinkage of outer diameter − Qd , inner diameter − Qd1 , average diameter − Qd2 and pitch − Qs . For size M20 × 2 Qd = 0, 885 − 0, 13X1 − 0, 42X2 − 0, 092X3 + 0, 002X1 X2∗ + +0, 021X1 X3 + 0, 008X2 X3∗ − 0, 061X12 + 0, 024X22 − 0, 042X32 , Qd1 = 0, 870 − 0, 021X1 − 0, 037X2 − 0, 082X3 − 0, 003X1 X2∗ − −0, 005X1 X3∗ − 0, 002X2 X3∗ − 0, 094X12 − 0, 061X22 − 0, 040X32 , Qd2 = 0, 860 − 0, 160X1 − 0, 032X2 − 0, 076X3 − 0, 002X1 X2 + +0, 010X1 X3 − 0, 032X12 − 0, 007X22 + 0, 016X32 , Qs = 1, 840 − 0, 261X1 − 0, 066X2 − 0, 210X3 + 0, 022X1 X2 + +0, 009X1 X3∗ − 0, 002X2 X3∗ + 0, 141X12 + 0, 172X22 + 0, 231X32
(6)
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For size M33×3 Qd = 0, 580 − 0, 0812X1 − 0, 0168X2 − 0, 040X3 + 0, 004X1 X2∗ + +0, 02X1 X3 − 0, 018X2 X3 − 0, 018X12 + 0, 016X22 − 0, 021X32 , Qd1 = 0, 621 − 0, 080X1 − 0, 010X2 − 0, 042X3 + 0, 006X1 X2∗ + +0, 011X1 X3 + 0, 002X2 X3∗ − 0, 018X12 + 0, 012X22 − 0, 015X32 ,
Qd2 = 0, 630 − 0, 074X1 − 0, 014X2 − 0, 042X3 + 0, 006X1 X2∗ +
(7)
+0, 011X1 X3 + 0, 0014X2 X3∗ − 0, 026X12 + 0, 130X22 − 0, 021X32 , Qs = 0, 860 − 0, 182X1 − 0, 038X2 − 0, 076X3 − 0, 0018X1 X2∗ +
+0, 0020X1 X3∗ + 0, 0018X2 X3∗ + 0, 048X12 − 0, 142X22 + 0, 021X32 . The obtained mathematical models describing the process passing of shrinkage of the threaded detail (M20 × 2, M33 × 3) were checked for adequacy. To test the hypothesis about the adequacy the results of experiment with the found relation Eqs. (6) and (7), it is sufficient to estimate the deviation predicted by the regression equation of the output value Qk from the results of experiment Qk at points X k of the factor space. When checking for the adequacy of Eqs. (6) and (7), it was found that they adequately reproduce the investigated process. From the analysis of Eqs. (6) and (7), describing the dependence of the shrinkage elements of the plastic threaded details on technological factors, it can be seen that taking into account the linear effects (in the levels of variation, Table 2) and regime parameters in all cases, the shrinkage decreases and out of the indicated factors the greatest influence is exerted by the pressing pressure, which is confirmed by the results of works [4–8]. The influence of paired interactions X1 X2 , X1 X3 and X2 X3 is almost insignificant, and their coefficients a12 , a13 and a23 , when tested for significance, turned out to be insignificant in the chosen levels of variation of the variables. Of these, only X1 X2 is significant for the shrinkage of the pitch, and X2 X3 is significant for the shrinkage of the outer diameter of the thread (size M33 × 3). It should be noted here that the noticeable effect of the pressing pressure on shrinkage is due to the fact that with an increase in pressure along the entire section of the material, additional latent heat is formed, which increases the pressing temperature, and due to which the shrinkage in step increases in comparison with diameters, since the thickness of the thread profile is much less than the thickness of the part body. On the other hand, at large limits variation of the holding time the temperature is evenly distributed over the outer diameter. As a result, the process passing of chemical shrinkage during molding is almost stopping. In the longitudinal direction, the shrinkage decreases because the direction of pressing coincides with the direction the passing of the shrinkage of the pitch, as a result of which the pressure is completely absorbed by the press-material [6–8]. The influence of square members on shrinkage of thread diameters is negative, i.e. with an increase in these factors to the second degree (at the selected levels), the shrinkage always decreases, and under the shrinkage of the pitch − vice versa, which is associated with the anisotropy of shrinkage, i.e. the shrinkage of the pitch in the longitudinal direction is usually greater than in the transverse direction.
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4 Discussion and Conclusions The obtained mathematical models (6) and (7), describing the dependence of the shrinkage of plastic thread elements with different pitch and diameter on the operating variables, make it possible, solving optimization problems, to establish optimal modes that ensure the minimum shrinkage of all elements, thread elements. Therefore, for plastic threaded connections, a special system of tolerances is provided, which includes, in addition to the existing accuracy classes of threads, new accuracy classes 4 and 5th, as well as threads with an especially large pitch. Mathematical models of the process of manufacturing parts from various engineering plastics are proposed, reflecting the relationship between the components of the vector of quality indicators (shrinkage, strength, accuracy) of plastic parts with regime parameters of processes, composition of materials, designs of parts, in order to optimize quality indicators.
References 1. Kerimov, D.A.: Scientific bases and practical methods of optimization of parameters of quality of plastic details of the oil-field equipment. Dissert. of Doct.techn.sciences., Baku (1985) 2. Braginsky, V.A., Mirzoyev, R.G.: System from fit tolerances of details from plastic. (Review of literary data). Plastics in mechanical engineering and instrument making, MDNP, M. (1965) 3. Kerimov, D.A., Kurbanova, S.K.: Bases of designing of plastic details and press-moulds. Baku: Publishing house “Elm”, 504 (1997) 4. Kerimov, D.A., Gasanova, N.A.: Determination of quality of plastic details under interval uncertainty. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Sadikoglu, F.M. (eds.) ICAFS 2018. AISC, vol. 896, pp. 848–851. Springer, Cham (2019). https://doi.org/10.1007/ 978-3-030-04164-9_111 5. Gasanova, N.A.: Definition of mechanical indicators of plastic details of the oil field equipment. Int. J. Innov. Res. Comp. Sci. Tech. 8(4), 313–314. https://doi.org/10.21276/ijircst.2020.8.4.11 6. Aslanov, J.N., Sultanova, A.B., Huseynli, Z.S., Mustafayev, F.F.: Determination of radial strains in sealing elements with rubber matrix based on fuzzy sets. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 765–773. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-92127-9_101 7. Babanli M.B.: Fuzzy Logic-based Material Selection And Synthesis, World Scientific Publishing Company( 2019). ISBN: 9813276584, 9789813276581 8. Ahmadov, S.A., Gardashova, L.A.: Fuzzy dynamic programming approach to multistage control of flash evaporator system. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 101–105. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-35249-3_12
Tableaux Deduction System for Fuzzy Logic with Estimates of Fuzziness Values Gerald S. Plesniewicz
and Alexey N. Aparnev(B)
National Research Princeton University MEI, Krasnokazfrmennaya, 14, 111250 Moscow, Russian Federation [email protected]
Abstract. Let LZ be Zadeh’s fuzzy propositional logic determined by the norm min{x, y} with implication ϕ → ψ considered as the shorthand ~ ϕ ∨ ψ. A simple estimate for a formula ϕ has he forms ϕ ≥ a, ϕ > a, ϕ ≤ a and ϕ < a where ϕ is a formula of the logic LZ. An composite estimate is a propositional combination of simple estimates. We call the logic of estimates LE the set of all estimates (simple and composite) with their natural semantics determined by fuzzy interpretations for LZ. For the logic LE, some sound and complete inference system, based on the use of analytic tableaux, is presented. Keywords: Fuzzy logic · Estimates · Fuzziness values · Inference rules · Hintikka set
1 Introduction. Main Definitions Let LZ denote Zadeh’s fuzzy propositional logic with a set P of propositional variables. Its syntax is the same as that of classical propositional logic. The semantics of the logic LZ are determined by fuzzy interpretations of formulas. Such interpretations are extensions of interpretations of propositional variables from P. A fuzzy interpretation of propositional variables is simply a function “_”: P → [0,1] (where [0,1] is the unit interval). Fuzzy interpretations of arbitrary formulas of the logic L are defined inductively from the values of “p” (p ∈ P) with using the norm min{x, y}. Note that formula ϕ → ψ is treated as a shorthand for the formula ~ ϕ ∨ ψ. We will consider estimates for fuzzy logic formulas from LZ as expressions with the following syntax: • (p ≥ a), (p > a), (p ≤ a), (p < a) are atomic estimates, where p ∈ P and a ∈ [0,1]; • (ϕ ≥ a), (ϕ > a), (ϕ ≤ a), (ϕ < a) are simple estimates, where ϕ is a formula from LZ; • an arbitrary estimate is propositional combination of simple estimates. An estimate is composite if it contains propositional connectives. Semantics of estimates is determined naturally by interpretations that are extensions of interpretations “_” of formulas from LZ. So, for any estimate λ and a ∈ [0,1] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 305–312, 2023. https://doi.org/10.1007/978-3-031-25252-5_42
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We will consider estimates as sentences of some logic called the logic of estimates LE. We emphasize that LE is a crisp logic, but interpretations of its propositional variables are fuzzy. The logic LE (as every crisp logic) induces a logical consequence relation between estimates. For a set of estimates E and an estimate λ, the logical consequence E |= λ holds by definition if there is no interpretation under which all the estimates from E are true and the estimate λ is false. The concept of logical inconsistency (or non-satisfiability) directly connected to the concept of logical consequence. Generally, a set E of sentences of some logic L is satisfiable if there is an interpretation under which all sentences from E; otherwise, E is called unsatisfiable (or inconsistent). Clearly, if L contains the negation ‘ ~’ then E |= λ ⇔ ‘E ∪ {~λ,}is inconsistent’ for all formula λ from LE. Thus, the problem of logical consequences can be reduced to the problem of recognizing inconsistency. Early, S. Kundu considered estimates of Zadeh’s logic statements, for which he constructed a sound and complete inference system based on the resolution principle [4, 6]. In this paper we present some sound and complete inference system based on using analytic tableaux [2, 3]. Let denote the presented inference system. We can also use the terminology of the theory of knowledge bases. For example, a knowledge base is a finite set estimates (as sentences of the logic LE). Facts are atomic estimates or disjunction of atomic estimates. A fact base is a finite set of facts.
2 Equivalences in the Logic of Estimates LE Estimates λ and μ are equivalent if, under any interpretation, they have the same truth values: λ ≡ μ ⇔df “λ” = “μ” for any interpretation “_”. The following lemma gives a list of equivalences used in proving the soundness and completeness of the system of inference rules . In the lemma, ϕ is a formula of the logic L, and a ∈ [0,1]. Lemma 1. The following equivalences hold in the logic of estimates LE: ~ (ϕ ≥ a) ≡ (ϕ < a), ~ (ϕ > a) ≡ (ϕ ≤ a), ~ (ϕ ≤ a) ≡ (ϕ > a), ~ (ϕ < a) ≡ (ϕ ≥ a), (~ ϕ ≥ a) ≡ (ϕ ≤ 1– a), (~ ϕ > a) ≡ (ϕ < 1– a), (~ ϕ ≤ a) ≡ (ϕ ≥ 1– a), (~ ϕ < a) ≡ (ϕ > 1– a), 1: ((ϕ ∧ ψ) ≥ a) ≡ ((ϕ ≥ a) ∧ (ψ ≥ a)), ((ϕ ∧ ψ) > a) ≡ ((ϕ > a) ∧ (ψ > a)), ((ϕ ∧ ψ) ≤ a) ≡ ((ϕ ≤ a) ∨ (ψ ≤ a)), ((ϕ ∧ ψ) < a) ≡ ((ϕ < a) ∨ (ψ < a)), 2: ((ϕ ∨ ψ) ≥ a) ≡ ((ϕ ≥ a) ∨ (ψ ≥ a)), ((ϕ ∨ ψ) > a) ≡ ((ϕ > a) ∨ (ψ > a)), ((ϕ ∨ ψ) ≤ a) ≡ ((ϕ ≥ a) ∧ (ψ ≥ a)), ((ϕ ∨ ψ) < a) ≡ ((ϕ > a) ∧ (ψ > a)), ((ϕ → ψ) ≥ a) ≡ ((ϕ ≤ 1– a) ∨ (ψ ≥ a)), ((ϕ → ψ) > a) ≡ ((ϕ < 1– a) ∨ (ψ > a)), ((ϕ → ψ) ≤ a) ≡ ((ϕ ≥ a) ∧ (ψ ≥ a)), ((ϕ → ψ) < a) ≡ ((ϕ > a) ∧ (ψ > a)). The first four equivalences are obvious. Proof of 1: “((ϕ ∧ ψ) ≥ a)” = 1 ⇔ “(ϕ ∧ ψ)” ≥ a ⇔ (“ϕ” ∧ “ψ”) ≥ a ⇔ min{“ϕ”, “ψ”} ≥ a. ⇔
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“ϕ” ≥ a and “ψ” ≥ a ⇔ “(ϕ ≥ a)” = 1 and “(ψ ≥ a)” = 1 ⇔ (“ϕ ≥ a” ∧ “ψ ≥ a”) = 1. ⇔ “((ϕ ≥ a) ∧ (ψ ≥ a))” = 1. Hence “((ϕ ∧ ψ) ≥ a)” = 1 ⇔ (ϕ ≥ a) ∧ (ψ ≥ a))” = 1 for any interpretation “_”. Therefore, equivalence 1 is true. Proof of 2: “((ϕ ∧ ψ) ≤ a)” = 1 ⇔ “(ϕ ∧ ψ)” ≤ a ⇔ (“ϕ” ∧ “ψ”) ≤ a ⇔ min{“ϕ”, “ψ”} ≤ a. ⇔ “ϕ” ≤ a or “ψ” ≤ a ⇔ “ϕ ≤ a” = 1 or ψ ≤ a” = 1 ⇔ (“ϕ ≤ a” ∨ “ψ ≤ a”) = 1 ⇔ “((ϕ ≤ a) ∨ (ψ ≤ a))” = 1. Hence “((ϕ ∧ ψ) ≤ a)” = 1 ⇔ (ϕ ≤ a) ∧ (ψ ≤ a)” = 1 for any interpretation “_”. Therefore, equivalence 2 is true. The remaining equivalences are proved similarly.
3 System The system has the inference rules placed in the two tables – Table 1 and Table 2. The rules from the first table are used when building inference trees for knowledge bases written in the logic of estimates LE. The second table contains the rules for detecting contradictions arising in the inference trees that we build for knowledge bases using the system . A pair [λ, μ] of simple estimates is said to be conflicting if there is some inference rule from Table 2 such that applying the rule to the pair [λ, μ] we get as output the contradiction sign X. For example, consider the pair of estimates s = [((p ∧ q) ≥ 0.7), ((p ∧ q) ≤ 0.5)] and the rule 4* (from Table 2). From the antecedents of the rule 4* we get the pair s if we put ϕ: = (p ∧ q), a: = 0.7 and b: = 0.5. Since a = 0.7 > 0.5 = b, the conditions for the applicability of the rule 4* are satisfied, and we can execute this rule. Then we obtain the value X. Therefore, s is a conflicting pair. The first 6 rules from Table 1 are the usual inference rules used in the analytictableaux systems for propositional logic (see, for example, the books [3, 5]). Clearly, classic propositional logic is a fragment of LE since p is equivalent to (p ≥ 1). The rules 1 – 6 are used by algorithms for building inference trees for knowledge bases written in propositional logic. In essence, the same algorithms can be used when constructing inference trees for knowledge bases written in LE logic. In this case, the rules from Table 1 are applied in a similar way as the rules for propositional logic. The rules of Table 1 are divided into conjunctive and disjunctive. A rule is disjunctive if its consequent contains the connective ‘or’; if the consequent contains the connective ‘and’ or contain no connectives, then the rule is conjunctive. Consider an example of building an inference tree T0 for the knowledge base Kb0 = {(((p1 ∨ ~ p3 ) > 0.3) → (p2 ≤ 0.4)), (((p1 ∧ p2 ) ≤ 0.9) → (~p1 ≤ 0.5))}. The vertices of inference trees have right and left labels. For example, the second vertex of the tree T0 (Fig. 2) has the left label “0:” and the right label “[5, 6]”. The label “0:” tells that the corresponding estimate for a vertex belongs to the knowledge base Kb0 , and the label “[5, 6]” tells that rule 6 from Table 1 was applied at step 5 to this estimate. The result of applying this rule was the pair of estimates [5: ~ ((p1 ∧ p2 ) > 0.9),, 5: (~p1 ≤ 0.5)] which as the “fork” was attached to two branches whose ends are
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marked with explanation mark ‘!’ on Fig. 1. (A branch in a tree is a path starting from the root of the tree.) Recall that the sound rules of inference in any crisp logic are those that keep the formulas true. It is easy to see that, thanks to Lemma 1, all the inference rules from Table 1 are sound. Table 1. Inference rules. (Here are λ and μ ∈ LE, ϕ and ψ ∈ LZ) Rule number
Antecedent
Consequent
1
~ ~λ
λ
2
(λ ∧ μ)
λ and μ
3
~ (λ ∧ μ)
~ λ or ~ μ
4
(λ ∨ μ)
λ or μ
5
~ (λ ∨ μ)
~ λ and ~ μ
6
(λ → μ)
~ λ or μ
7
~ (λ → μ)
λ and ~ μ
8
~ (ϕ ≥ a)
(ϕ < a)
9
~ (ϕ > a)
(ϕ ≤ a)
10
~ (ϕ ≤ a)
(ϕ > a)
11
~ (ϕ < a)
( ϕ ≥ a)
12
(~ ϕ ≥ a)
(ϕ ≤ 1– a)
13
(~ ϕ > a)
(ϕ < 1– a)
14
(~ ϕ ≤ a)
(ϕ ≥ 1– a)
15
(~ ϕ < a)
(ϕ > 1– a)
16
((ϕ ∧ ψ) ≥ a)
(ϕ ≥ a) and (ψ ≥ a)
17
((ϕ ∧ ψ) > a)
(ϕ > a) and (ψ > a)
18
((ϕ ∧ ψ) ≤ a)
(ϕ ≤ a) or (ψ ≤ a)
19
((ϕ ∧ ψ) < a)
(ϕ < a) or (ψ < a)
20
((ϕ ∨ ψ) ≥ a)
(ϕ ≥ a) or (ψ ≥ a)
21
((ϕ ∨ ψ) > a)
(ϕ > a) or (ψ > a)
22
((ϕ ∨ ψ) ≤ a)
(ϕ ≤ a) or (ψ ≤ a)
23
((ϕ ∨ ψ) < a)
(ϕ < a) and (ψ < a)
24
((ϕ → ψ) ≥ a)
(ϕ ≤ 1– a) or (ψ ≥ a)
25
((ϕ → ψ) > a)
(ϕ < 1– a) or (ψ > a)
26
((ϕ → ψ) ≤ a)
(ϕ ≥ 1– a) and (ψ ≤ a)
27
((ϕ → ψ) < a)
(ϕ > 1– a) and (ψ < a)
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4 Completeness of the System for Logic of Estimates LE A system of inference rules for a given logic L is complete when, for any knowledge base Kb and any statement λ written the L, the logical consequence Kb |= λ holds if λ is. Derived from Kb by means of the rules of the system . Further, we use the standard terminology accepted in the theory of analytic tableaux [2]. Let B be a branch of an inference tree T and λ is an estimate in T. Then we say that: (i) λ is deployed if some inference rule (from Table 1) has been applied to λ; (ii) B is closed if it ends with the symbol ‘X’; (iii) B is open if it is not closed; (iii) T is closed if all its branches are closed; (iv) B is complete if every its composite estimate is deployed; (v) T is completed if every its branch is complete or closed. Table 2. Rules for closing branches of inference trees. (Here is λ --- μ denotes that the estimates λ and μ belong to the same branch.) Rule number
Antecedents
Consequent
1*
ϕ > a, ϕ < a
X
2*
ϕ ≥ a, ϕ < a
X
3*
ϕ > a, ϕ ≤ a
X
4*
(ϕ ≥ a), (ϕ ≤ b), a > b, (ϕ ≥ a) --- (ϕ ≤ b)
X
5*
(ϕ ≥ a), (ϕ < b), a ≥ b, (ϕ > a) --- (ϕ ≤ b)
X
6*
(ϕ > a), (ϕ ≤ b), a ≥ b, (ϕ ≥ a) --- (ϕ < b)
X
7*
(ϕ > a), (ϕ < b), a ≥ b, (ϕ > a) --- (ϕ < b)
X
Theorem 2. Let Kb be a knowledge base in LE and λ be an estimate written with propositional variables from Kb. It takes place: (I) If Kb |= λ then every completed inference tree for Kb ∪ {~ λ} must be closed; (II) If some completed inference tree for Kb ∪ {~λ} is closed then Kb |= λ. We prove Theorem 2 using the so-called Hintikka sets. A set H of estimates is said to be Hintikka set (in the system ) if (a) H contains no conflicting pairs of atomic estimates; (b) H is downward saturated relatively the rules that correspond to inference rules of the system . Let’s rewrite the rules from the table into corresponding conditions, as can be seen from the following examples: • Rule 1 is rewritten into the condition ‘If ~ ~ X ∈ H then X ∈ H’;
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0: (((p1 p2) ≤ 0.9) → (~p1 ≤ 0.5)) [5, 6] ______________|__________________ | | p3) > 0.3)) [2, 9] ! 1: (p2 ≤ 0.4) [8, 9*] 1: ~ ((p1 2: ((p1 p3) ≤ 0.3) [3, 22] _______|_________ 3: (p1 ≤ 0.3) [14, 16*] | | 3: ( p3 ≤ 0.3) [4, 14] 5: ~ ((p1 p2) ≤ 0.9) [6, 3] 5: (~p1 ≤ 0.5) [9, 14] ! 4: (p3 ≥ 0.7) 6: ((p1 p2) > 0.9) [7, 2] 9: (p1 ≥ 0.5) | 7: (p1 > 0.9) B3 ____|__________________ 7: (p2 > 0.9) [8, 9*] | | 8: x 5: ~ ((p1 p2) > 0.9) [10, 9] 5: (~p1 ≤ 0.5) [11, 14] 10: ((p1 p2) ≤ 0.1) [13,18] 11: (p1 ≥ 0.5) [12, 5*] ____|________________ 12: x | | 13: (p1 ≤ 0.1) [14, 16*] 13: (p2 ≤ 0.1) B1 B2 Fig. 1. Inference tree T0 for the knowledge base Kb0
• • • •
Rule 2 is rewritten into the condition ‘If (X ∧ Y) ∈ H then X ∈ H and Y ∈ H’; Rule 7 is rewritten into the condition ‘If ~ (X → Y) ∈ H then X ∈ H and ~ Y ∈ H’; Rule 10 is rewritten into the condition ‘If ~ (X ≤ a) ∈ H then (X > a) ∈ H’; Rule 18 is rewritten into the condition ‘If ((X ∧ Y) ≤ a) ∈ H then (X ≤ a) or (Y ≤ a).
Lemma 2. Every Hintikka set (in the logic of estimates LE) is satisfiable. Proof. Let P = P(H) be the set of all propositional variables from a Hintikka set H. For each p ∈ P, we write down all atoms from H with p: (p ≥ a1 ), (p ≥ a2 ),…, (p ≥ an ) and (p ≤ b1 ), (p ≤ b2 ),…, (p ≤ bm ), where it is possible that some non-strict inequalities are replaced by strict inequalities. Let pmax = max{a1 , a2 ,…, an } and pmin = min{b1 , b2 ,…, bn }. Note that pmin ≤ pmax . Indeed, suppose that pmin > pmax . Take the indices r and s such that pmin = ar and pmax = bs . Then. we have the pair [(p ≥ ar ), (p ≤ bs )] which is conflicting since ar > bs . This contradicts with the requirement (a) that Hintikka set must not contain conflicting pairs of atoms. “(p ≥ ai )” = 1 ⇔ “p” ≥ ai ⇔ p# ≥ ai , “(p ≤ bi )” = 1 ⇔ “p” ≤ bi ⇔ p# ≥ bi . Thus, “α” = 1 for all atomic estimates from H. We prove by induction on the structure of estimates that the estimates from H are true under this interpretation: “λ” = 1 for all λ ∈ H. Induction base: The statement the “α” = 1 for all atomic estimates from H. Induction transfer. In particular, for the rules 1, 2, 7, 10, 18 we have: Rule 1 (Table 1): ~ ~λ |– λ. By inductive hypothesis, “λ” = 1. We have “~ ~λ” = ~ ~ “λ” = ~ ~ 1 = 1. Hence, “ ~ ~ λ” = 1.
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Rule 2: (λ ∧ μ) |– λ and μ. By inductive hypothesis, “λ” = 1 and “μ” = 1. We have “(λ ∧ μ)” = (“λ” ∧ “μ”) = (1 ∧ 1) = 1. Hence, “(λ ∧ μ)” = 1. Rule 7: ~ (λ → μ) |– λ and μ. By inductive hypothesis, “λ” = 1 and “~μ” = 1. We have “ ~ (λ → μ)” = ~ (“λ” → “μ”) = ~ (1 → 1) = 1. Hence, “ ~ (λ → μ)” = 1. Rule 10: ~ (ϕ ≤ a) |– (ϕ > a). By inductive hypothesis, “(ϕ > a)” = 1. We have “ ~ (ϕ ≤ a)” = 1 ~ ⇔ (“ϕ” ≤ a) = 1 ⇔ “ϕ” > a) = 1 ⇔ “(ϕ > a)” = 1. Hence, “ ~ (ϕ ≤ a)” = 1. Rule 18: ((ϕ ∧ ψ) ≤ a) |– (ϕ ≤ a) or (ψ ≤ a). By inductive hypothesis, “(ϕ ≤ a)” = 1 or “(ψ ≤ a)” = 1. We have “((ϕ ∧ ψ) ≤ a)” = 1 ⇔ “(ϕ ∧ ψ)” ≤ a) ⇔ “ϕ” ≤ a or “ψ” ≤ a ⇔ “(ϕ ≤ a)” = 1 or “(ψ ≤ a)” = 1. Hence, “((ϕ ∧ ψ) ≤ a)” = 1. Proof of Theorem 2 (I). Let the relation Kb |= λ holds, and T be any completed inference tree which was built for the set Kb ∪ {~λ}. Suppose that T is not closed. Let B be an open branch of T. Then B is a Hintikka set. Therefore, B is satisfied set (due Lemma 2). The set Kb ∪ {~λ} is also satisfied since Kb ∪ {~λ} ⊆ B. There is an interpretation “_” which make true all estimates from Kb ∪ {~λ}. In particular, “ ~ λ” = 1, “λ” = 0, and “μ” = 1 for all μ ∈ Kb. Since Kb |= λ, we have “λ” = 1. (Contradiction: “λ” = 0 and “λ” = 1). Proof of (II) Theorem 2 (II). In the book [3] there is the proof of the Theorem 2.67 (page 39) that a complete tableau T built for a formula ϕ (in propositional logic) is unsatisfied if T is closed. This proof can be adapted to the case of the logic of estimates LE.
5 Deduction in the Logic of Estimates LE We will show by example how logical deduction is performed in the logic of estimates LE. Consider again the inference tree T0 (Fig. 2) built for the knowledge base Kb0 . It easy to check that the tree T0 is completed. We see that T0 has 5 branches, of which the third and fourth are closed, and the rest (denoted B1 , B2 , B3 ) are open. Let B be an open branch of an inference tree T. Denote by B the conjunction all atoms lying on the branch B. For example, for T0 we have. B1 = ((p3 ≥ 0.7) ∧ (p1 ≤ 0.1)), B2 = ((p3 ≥ 0.7) ∧ (p2 ≤ 0.1)), B3 = ((p2 ≤ 0.4) ∧ (p1 ≥ 0.5). We can close the open branches of T if adding to T suitable atoms. For example, let us take atom (p2 > 0.4). Then in the tree T0 with (p2 > 0.4), there are conflicting pairs [(p2 > 0.4), 13: (p2 ≤ 0.1)] and [(p2 > 0.4), 1: (p2 ≤ 0.4)] which close the branches B2 and B3 . For finding such conflicting pairs we will use a special bipartite graph (T) whose the left vertices are estimates B (composite, as a rule) and the right vertices are atomic estimates with the variables x i and yi as their boundaries (see Fig. 2). The edges of (T) are pairs of estimates [λ, α] where: (i) α is an atom of the forms (p ≥ x), (p > x), (p ≤ y), (p > y); (ii) α is atom (p ≥ x) and λ contains (p < a) with some a; α is atom (p > x) and λ contains (p ≤ a) with some a; α is atom (p ≤ y) and λ contains (p > a) with some a; α is atom (p ≤ y) and λ contains (p > a) with some a. For
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B1
B2
B3
(p1 > x1 ) / x1 = 0.1 ○ (p1 ≥ x1) (p1 < y1) (p1 ≤ y1) (p2 > x2) / x2 = 0.4 ○ (p2 ≥ x2) (p2 < y2) (p2 ≤ y2) (p3 > x3) (p3 ≥ x3) (p3 < y3) / y3 = 0.7 (p3 ≤ y3) Fig. 2. Graph (T0 )
example, the graph (T) have the edge connecting B2 with (p3 < y3 ) since B2 contains (p3 ≥ 0.7). We see from Fig. 2 that the set C = {(p1 > x 1 ), (p2 > x 2 )} is a minimal (for inclusion) covering of all left vertices of the graph (T). (The estimates from C are marked by circle ◯.) In Fig. 2 after slashes the values of variables x j and yj are written for the vertices with positive degrees. In general case, let V 1 , V 2 ,…, V m be all left vertices connected to the right vertex V = (p < y). Then each conjunction V k contains the atomic estimate (p ≥ aj ), and we set y = min{a1 , a2 ,…, am }. This value is the answer to the query (p ≥ y): Kb. We have that Kb |= (p ≥ min{a1 , a2 ,…, am }).
References 1. Aliseda, A.: Abductive Reasoning. Springer (2006). https://doi.org/10.1007/1-4020-3907-7 2. Agostino, M., Gabbay, D., Hahnle, Possega J.: Handbook of Tableaux Methods. Springer (2001). https://doi.org/10.1023/A:1017520120752 3. Ben-Ari, M.: Mathematical Logic for Computer Science. 3rd edition. Springer (2017). https:// doi.org/10.1007/978-1-4471-4129-7 4. Chen, J., Kundu, S.: A sound and complete fuzzy logic system using Zadeh’s implication operator. In: Ra´s, Z.W., Michalewicz, M. (eds.) ISMIS 1996. LNCS, vol. 1079, pp. 233–242. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-61286-6_148 5. Fitting, M.: First-Order Logic and Automated Theorem Proving. Springer (1996). https://doi. org/10.1007/978-1-4612-2360-3 6. Kundu, S.: An improved method for fuzzy-inferencing using Zadeh’s implication operator. In: Proceedings of IJCAL Workshop on Fuzzy logic in AI, pp. 117–125. Springer (1995)
Research of Bitumen-Based Asphalt Compositions Using Neural Network D. S. Mamed Hasan-zade(B)
, A. I. Babayev , and G. S. Hasanov
Azerbaijan State Oil and Industry University, Ave. Azadlig., 20, AZ1010 Baku, Azerbaijan [email protected]
Abstract. The work is dedicated to the research of the production process of bitumen-based asphalt compositions. The main function of the bituminous binder in pavement mixture is to bind the aggregate particles together by providing adhesion between the components in the composite. Despite that fact that the weight ratio of bituminous binders is low (5–7%) in the mixture, their impact on the operating characteristics of pavement is quite high. The increase in transportation and speed intensity at global and regional scales is making the demand for the performance indicators of pavement more stringent. Thus, it creates the necessity of modifying bitumens used in road construction to bring them to the required parameters. In the article, a new modified asphalt pavement bitumen composition with higher quality binding properties, favorable temperature and tensile properties based on brittle bitumen raw materials melting at high-temperature (110 °C) and technological additives, and preparation of asphalt pavement based on it, optimization of the components used in the process according to the physical and mechanical properties of the commodity product, possible aspects of artificial intelligence relationships in the exploitation process have been investigated. The article deals with the research of bitumen-based asphalt compositions using ANFIS model. Keywords: Asphalt composition · Bitumen · Asphalt pavementneural network · Mass extensibility · Softening temperature · Penetration depth
1 Introduction The creation of solid and durable foundation of asphalt pavement, the quality of which is determined by physical and mechanical properties of the used bituminous binder is one of the topical issues. Since asphalt pavement bitumen used to obtain high-quality asphalt pavement usually does not meet the set requirements, various additives are added to the composition of bitumen compositions. These additives include various industrial wastes, as well as production wastes of polymer materials. In this regard, recently much attention has been paid to the research on changing operating characteristics of bitumen by using wastes in the content of polymer-bitumen compositions. In recent years, bitumen compositions modified with various polymer wastes have been widely used to create practical asphalt pavement. Among them, in particular, © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 313–320, 2023. https://doi.org/10.1007/978-3-031-25252-5_43
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polyisoprene (SKI-3), divinyl styrene elastomers, ethylene-propylene copolymers, highpressure polyethylene, polypropylene production waste, etc. can be shown [1–5]. Bitumen modified with polymers is bituminous is a new type of constructing material with the ability to create bituminous binder, insulating coating layer being subjected to possible transformations due to mechanical mixing of polymer-rubber-containing wastes with bitumen in the form of a solid and liquid solution in various proportions and temperature, pressure of the environment, mixing intensity, time, chemical activity tendencies of the components, thereby improving its properties according to the initial indicators. It is known that bitumen is essentially a complex mixture of hydrocarbon chains with different molecular weights. The proportional change of these components in bitumen significantly affects both its rheological and physical properties. Differences in the bitumen structure, polymer macromolecules subjected to transformations during the process, elastomer-based rubber granules originally vulcanized with sulfur, but most of the double bonds are not used, allow obtaining various materials with needed properties due to the possible transformations between heavy hydrocarbons of various structures (asphaltenes, maltenes, aromatics, resins and saturated) that make up the composition of used oil and bitumen. Bitumen modified with polymers is most often used in the production of pavement and asphalt pavement components. This is related to their effect at high temperature [6, 7]. As it is known asphalt produced from heavy oil residues is natural asphalt. Artificial asphalt is a mixture of minerals such as gravel, sand, sandstone, limestone and viscous binding elements, etc. [8, 9]. Asphalt concrete is a complex mixture of bitumen and mineral materials and is used in road construction, pothole repair, etc. One of the main factors determining the positive operating characteristics of asphalt is the existence of crushed gravel constituting the basis of asphalt mass, soft, flexible, durable adhesive layer that is resistant to oxidation, numerous shocks and vibrations caused by the contact of a tire with coating, and natural biological bacteria. Stringent requirements arising from repeated and enhancing traffic loads further increase the demand for this indicator. Especially recently, the reduction of economic and environmental losses along with sustainability of pavement is becoming a necessity. It is known that the requirements of EURO-6, in addition to fuel, are aimed at improving the operating characteristics of even more vehicles. This, along with other factors, is closely related to the composition, structure, and quality of road construction materials. In order to determine these dependencies, the characteristics of pavement raw materials components, production technology, operating conditions should be considered as a system. The gravel being of the same or different size, the elasticity of the glue that binds them together, have a significant effect on whether the shocks caused by the contact between a tire and road are monotonous or variable, hard or soft, smooth (these indicators are recorded by special sensors and transferred to the electronic control center of the transport). All this is recorded in the artificial intelligence system, and maneuvering characteristics of the vehicles are adjusted according to the operational capabilities of the road. The research work is dedicated to the modification of bituminous binders using various additives and the preparation of new asphalt components for the further use of pavement in order to reduce economic and ecological losses along with the durability of pavement.
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2 Materials Used in Practice According to SS 10585–99, black oil of M-40 characterized by kinematic viscosity at 80 °C of 43 mm2 /s, density at 20 °C of 922.1 kg/m3 , pour point of minus 12 °C was used in the research work. Its decomposition point was 184 °C, the ash content of the mass was 0.0228%, and the mass fraction of sulfur was 0.23% (Table 1). Table 1. Physical and mechanical properties of black oil M-40 used in accordance with SS 10585– 99 № Name
Indicators
1
kinematic viscosity at 80 °C, mm2 /s 43
2
density at 20 °C, kg/m3
3
Installation point, °C
−12
4
Combustion point, °C
184
5
Ash content, %
0.0228
6
Mass fraction of sulfur, %
0.23
7
Mass fraction of water, %
Not
922.1
Bitumen which is characterized by softening temperature of 110 °C, needle penetration depth of 16 x 0.1 mm at 25 °C and stretchability of 3 cm at 25 °C was used as raw material in ring and ball test. High-pressure polyethylene (LDPE) production wastes with a molecular weight of 700–11,000 was used as a modifier in bitumen content, based on published data [10, 11], and crumb rubber with 0.06 mm diameter, a waste product from the production of rubber products, was used.
3 Methodology of Sample Preparation In order to obtain a homogeneous polymer-bitumen composition, bitumen is mixed with black oil of M-40 (SS 10585–99) at temperature of 120 °C. LDPE and rubber crumbs are added to the resulting mixture at the indicated temperature and stirring vigorously. By continuing to stir the bitumen mixture, temperature is raised to 170 °Cand kept at that temperature for 30–40 min. Mineral content of bitumen composition is prepared as follows. Pure river sand was used to conduct experiments. Stone dust is the material obtained as a result of processing river stone in thermal centrifuges. Gravel is a construction material produced by grinding stones and passing them through sieves. Chemical composition of used cement is as follows: 67% calcium oxide, 22% silicon oxide, 5% aluminum oxide, 3% iron oxide and 3% other substances. Depending on the amount of mineral components and bitumen, asphalt compositions are divided into several types: a) sandy (for pavements and pedestrian); b) fine-grained (for roads with heavy traffic), rubber-bitumen for covering stadiums and bicycle roads, etc.
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Asphalt includes petroleum-derived asphalt and asphalt oil. These compounds include asphaltenes, resins, cyclic compounds and saturated hydrocarbons [5]. Bituminous polymer mixtures with optimal operating properties were added to bitumen of BND 60/90 and tested. The tests were carried out according to the standards such as softening temperature (SS 11506–73), penetration (SS 11506–73), tensile strength (SS 11505–75).
4 Results and Discussion Researches were conducted to study the impact of the asphalt content on some qualities of the prepared pavement [12, 13]. Based on the conducted research (Table2) it was determined thatthe change in the amount of each of the components constituting asphalt composition has a noticeable impact on physical and mechanical properties of asphalt. So, keeping the other components practically constant in the samples, the physical and mechanical properties of asphalt compositions at the mass limits of bitumen -30.8, gravel stone -10.3%, softening temperature is 90 °C, needle penetration depth is 75mm, tensile strength is maximum being 13mm. However, these indicators are not achieved at the mass limits of river sand −36.5%, clay −23.4%. Cement is a binder between organic and inorganic substrates due to its composition of oxides. In addition to its direct function, gravel stone creates a mill effect in the course of the technological process, which makes it possible for the components to be evenly distributed in the system. That is, the system itself is quite dynamic. This opens up wide opportunities for the application of artificial intelligence in asphalt production technology. Table 2. Physical and mechanical properties of asphalt compositions N
Name
KiSh, °Csoftening temperature respectively
Needle penetration depth at 25 °C × 0,1 mm
Tensile strength of sm, at 25 °C SS 11505–75
1
Composition: % mass Bitumen – 17.5 Clay – 23.4 River sand – 36.5 Stone dust – 8.8 Cement – 8.8 Gravel stone – 5.0
110
58
8
2
Composition: % mass Bitumen – 14.0 Clay – 23.4 River sand – 36.5 Stone dust – 8.8 Cement – 8.8 Gravel stone – 5.0
115
60
10
3
Composition: % mass Bitumen – 30.8 Clay– 10.5 River sand – 7.7 Stone dust – 20.5 Cement – 10.3 Gravel stone – 10.3
90
75
13
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Comparing the data presented in Table 3, it can be seen that melting temperature of bitumen, which has a high melting temperature (100 °C) and is taken as raw material, decreases by about 2 times in all three cases of addition of additives. That is, the bitumen, which is not suitable for road construction due to its fragility, is modified and turned into a raw material suitable for road construction due to its physical and mechanical properties. While increasing the amount of waste from polyethylene production in the content of the composite from 1.5% to 7.7% does not significantly affect the penetration coefficient, high tensile strength of 13.5 mm is observed at 2.2% of polymer addition. This is explained by the fact that in the amount of 7.7% of polymer, its even distribution does not take place in the content of the composite. Like polyethylene, rubber crumb also shows a high result of 13.5 mm at low tensile strength of 2.2%. Black oil plays an important role in the even distribution of additives in the bitumen mixture. The third sample shows that the reduction of black oil from 22.1% to 11.6% causes the tensile index to decrease from 13.5 mm to 3.0 mm, which is explained by insufficient distribution of the components in the medium. Table 3. Physical and mechanical properties of polymer-bitumen compositions. N
Name
1
2
KiSh, °Csoftening temperature respectively SS 11506- 73
Needle penetration depth at 25 °C x 0.1 mm, SS 11501–73
Tensile strength of sm, at 25 °C SS11505–75
3
4
5
High melting bitumen (raw material)
110
16
3
1
Bitumen composition: % mass Bitumen- 77.5 Rubber crumb – 1.6 LDPE (waste) – 1.5 Black oil 19.4
54
134
9
2
Bitumen composition: % mass Bitumen- 73.5 Rubber crumb - 2.2 LDPE (waste) – 2.2 Black oil- 22.1
47
139
13.5
3
Bitumen composition: % mass Bitumen- 77.6 Rubber crumb - 3.1 LDPE (waste) – 7.7 Black oil - 11.6
43
143
3.0
We use ANFIS model [14–16] (Fig. 1.) to compute Y1, Y2 and Y3. Fragments of the obtained results are given in Fig. 2, 3, 4. These parameters help to increase the durability of pavement achieved by reducing fatigue and thermal cracking, as well as reducing susceptibility to high temperatures (for example, wear rutting, pushing, rockiness) and increased retention of aggregates in applications, for example, chip breakers. These indicators constitute a set of mutually
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confirming and mutually exclusive factors for complex systems, capable of aggregating fuzzy representations [17–19], the mechanism of which is closely related to both the quantitative ratio of components and the technology of their production.
Fig. 1. The structure of neural network
Fig. 2. Mass extensibility (Y1 )
Fig. 3. Softening temperature (Y2 )
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Fig. 4. Penetration depth (Y3 )
5 Conclusion Thus, the following conclusions can be reached within the framework of the conducted research. It was determined that the change in the amount of each of the components constituting the composition of asphalt has a noticeable effect on the physical and mechanical properties of asphalt. Softening temperature, needle penetration depth, tensile index characterizing elasticity have improved to the level that will ensure the production of high-quality consumer products within the mentioned limits. Research show that changing the ratio of the components has an active impact on the results. In the article, neural network was constructed according to the impact of the components on certain properties of the composition was investigated. Depending on the initial data, Mass extensibility (Y1), Softening temperature (Y2), Penetration depth (Y3) were determined through the neural network. These results are satisfactory and show that the used method is correctly applied.
References 1. Leonenko, V.V., Safarov, G.A.: Some aspects, modification of bitumen with polymeric materials. J. Chemistry and Technol. Fuel Oils 5, 43–48 (2001) 2. Nekhroshev, V.P., Rossel, L.P.: Modification of road bitumen properties with plasticizers based on tactical polypropylene. Oil and gas of Western Siberia: a collection of articles of the All-Russian Scientific and Technical Conference. Tyumen: Tyum.SU publishing house (2005) 3. Rozental, D.A., Tobolina, L.S., Fedosova, V.A.: Modification of bitumens with polymer additives. Oil Refining. Thematic Rev. 6, 1–48 (1998) 4. Schulte, W.: Temperatura bsenkungim Asphaltstrabenbau. Asphalt (BRD) (2003). http://yric. az/GTK_Book_1.pdf 5. Muhamatdin, I.I., Galimullin, I.N.: Adhesive additives for paving bitumen. Oil Refining and Petrochemistry 2, 33–37(2017) 6. Heritage Research Group, Firestrone Polymers. LLC (US) US Patent. Method for producing asphalt composition. Patent 2194729, USA (2004) 7. Graves, D., Burner, P., Herjenroter, W., Ris, T., et al.: Modified asphalt binders and asphalt pavement compositions. Patent 6569351, USA (2005)
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8. Federov, V.V., Syroezhko, A.M., Begak, O.Y., Proskuyakov, V.A., Borovikov, G.I.: Journal of Applied Chemistry 75, 1027 (2002) 9. Pozdnyaeva L.V.: Petroleum resin as a modifier of oil road bitumen. M, GP RosDorNil (2003) 10. Khristoforova, A.A., Filippov, S.E., Gogolev I.N.: Development of hard surfaces of career roads with the use of activated crumb rubber.Electronic scientific journal. Engineering Bulletin of the Don 4, 347–350 (2011) 11. Khristoforova, A.A., Sokolova, M.D., Potlov, S.N.: The influence of the mode of mechanical activation of crumb rubber on the most important operational properties of sealing rubbers. Materials Tehcnology, Instruments 13(1), 73–76 (2008) 12. Mamed Gasan-zade, D.S., Babaev, A.I., Hasanov, G.S.: News of Azerbaijan higher technical schools materials. In: II International Conference Reconstruction and Restoration in Postconflict Situations. Baku-2022, 24(2), pp. 179–184 (2022). http://rrpcs2022-conf.asoiu.edu.az 13. Mamed Gasan-zade, D.S., Babaev, A.I., Hasanov, G.S.: Polymer-bitumen composition. Azerbaijanian patent, I 2022 0025 (2022) 14. Aliev, R.A., Fazlollahi, B., Aliev, R.R., Guirimov, B.G.: Linguistic time series forecasting using fuzzy recurrent neural network. J. Knowledge. “Education” Society of Azerbaijan Republic.Series Business: 3–13 (2005) 15. Aliyarov, R.Y., Gardashova, L.A., Hasanli, N.I.: Predicting porosity through fuzzy logic based methods from south caspian basin data. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 268–274. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-64058-3_33 16. Ercan, O.: Artificial neural network based modelling of the Marshall Stability of asphalt concrete. Expert Syst. Appl. 38(5), 6025–6030 (2011). https://doi.org/10.1016/j.eswa.2010. 11.018 17. Aliev, R.A., Gardashova, L.A.: Z-set based approach to control system design. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 10–21. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-640 58-3_2 18. Gardashova, L.A.: Z-Set based inference using ALI-2 implication for control system design. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 75–84. Springer, Cham (2022). https://doi.org/10.1007/ 978-3-030-92127-9_14 19. Aliyeva, K.R.: Demand forecasting for manufacturing under Z information. Procedia Comput. Sci. 120, 509–514 (2017). https://doi.org/10.1016/j.procs.2017.11.272
Logical-Linguistic Model for Reactor Cleaning from Impurities E. A. Melikov(B)
, T. M. Magerramova , and A. A. Safarova
Azerbaijan State Oil and Industry University, Baku, Azerbaijan [email protected], [email protected]
Abstract. The study of one chemical-technological complexes class as a control object and the analysis of the solving state the problem of these complexes optimal control shows that one of the most important tasks is the automating problem the control of the catalytic apparatus that is part of these complexes. Thus, the main and complex apparatus of the chemical-technological complex for the propylene production is the reactor for the hydrogenation of acetylene compounds. It is a complex physicochemical system in which a multiphase, multicomponent, inhomogeneous continuous medium is distributed within the working volume of the catalytic apparatus and changes in time, at each point of which and at the phase boundary there is a transfer of mass, momentum, energy. The operation of the apparatus under study in incomplete information conditions and the complexity of constructing optimal control trajectories leads to the need to develop a reactor control system based on a logical-linguistic current situations description. Due to the variability of the non-stationary process physicochemical characteristics in the reactor, as well as the incompleteness of the rules linguistic table, due to the impossibility of taking into account all possible situations, the article presents a fuzzy control algorithm. It is implemented as a fuzzy logic controller with structural and parametric adaptation, with self-learning elements, which provides an adequate display of the control strategy. This facilitates the effective control of the process under study and ensures the required quality of the resulting propane-propylene fraction at the reactor outlet, and hence commercial propylene at the considered chemical-technological complex outlet. Keywords: Management · Uncertainty · Fuzzy set · Affiliation function · Oil and gas industry · Numerical methods · Static models · Dynamic models
1 Introduction The main difficulty in the management of chemical-technological complex in propylene production is associated with determination of the optimal control trajectory for the process of selective methylacetylene and propadiene hydrogenation. The causes of these complications are as listed: the complexity of identifying the equations describing the physicochemical transformations (these transformations become sophisticated because of short contact time and the © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 321–329, 2023. https://doi.org/10.1007/978-3-031-25252-5_44
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variable content of situational characteristics distribution in the reaction zone of the apparatus as well as contributions due to temperature of acetylene compound hydrogenation process and the active surface of the catalyzer in the reactor); high costs and in some cases impossibility of carrying out experiments. Additionally, the speed at which characteristics of technological processes exacerbates their full compatibility and even, if possible, leads to drastic overcomplication of the apparatus control system with respect to the static error in adequacy.
2 Statement of the Problem In numerous existing scientific works, to identify the internal processes of such contact reactors, preference was given to mathematical models based on the kinetic representation of catalytic transformations, as well as mixed models. The reason for this is search for reliable mathematical models for solving the issue of controlling the reaction apparatus. This model comprehensively describes the work surface and accounts for catalyst activeness loss. However, considering the lack of information on physicochemical transformations in the operating catalytic apparatus, difficulty of determining catalyst activeness, numerous situational variables and presence of complex relationships among them regime parameters and loadings complexity of determining the rate of elementary reactions in the catalytic reactor, the wide range of quantitative and qualitative characteristics variation of the raw materials leads to utilizing impossibility universal regression analysis models. Because of this there is an issue of describing the operation of acetylene hydrogenation reactor through utilizing the information on quality by using the summarization of the staff knowledge and experience. It is worth mentioning that sometimes automatic process control systems specialists need to consider factors that may be impossible or difficult to formalize. The degree of complexity of such technological processes is so high that the application of deterministic and stochastic mathematical models describing their operation fails to give desired characteristics. In these cases, to identify the operating modes of the complex under consideration, it is important to use the apparatus of the theory of fuzzy sets [1–5]. In other words, the construction of adequate mathematical models for control systems can be based on fuzzy set theory, which allow for projection and synthesis of these systems [6]. The preparation of such intellectual control systems is based on logical-linguistic description of technological processes occurring in them. The control of the process in these systems is undertaken through use of fuzzy controllers. What lays in the intellectual fuzzy controllers application basis is using presenting and researching knowledge ways to generate “knowledge”. Thus, the industrial fuzzy controllers creation lately has been relying on the artificial intelligence principles which are undergoing active improvement in the cybernetics field. The essence of fuzzy controller synthesis is the ability to make use of its knowledge base (KB). KB is put forward as a collection of fuzzy control rules and it is presented in a form of fuzzy conditions statements.
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During generation of a KB the fuzzy controller[7–10] is given an objective, ensuring the desired control system transition characteristics, and the information on the control object and technological process. Fuzzy controllers capable of gathering the preliminary regulations collect the knowledge independently without an expert through method of trial and error whilst operating in a form of limited KB. The fuzzy logic control (FLC) synthesis is undertaken via these methods of self-organization. Below the automatic control system of a reactor incorporating use of fuzzy controllers based on fuzzy models and control algorithm application that are shown to be robust and trustable in practice is discussed. The control system of the catalytic apparatus is shown on Fig. 1. The control object operation description in these algorithms and models is done IN /Q IN OUT through both qualitative and quantitative information use. Here QH C3 H4 and TPPF 2 OUT is situational variable, F IN , Q IN , Q IN are control variables, QH PPF C3 H4 C3 H6 are disturbances 2 OUT and QC3 H4 is regulating quantity.
Fig. 1. Acetylene compound hydrogenation reactor control system
Linguistic variables (LV) used to describe the quantity and quality of raw material entering the reactor, regime parameters and quality requirements to final product are utilized in preparing the logical-linguistic description of the reactor. −
IN , Q IN IN Furthermore, Xj 1t (j1 =1, 3) correspond to LV FPPF C3 H4 and QC3 H6 describing OUT describing state, V corresponds to LV Q OUT disturbance, Yt corresponds to LV QH t C3 H4 2 − IN /Q IN OUT describing quantity; Uj 2t j2 =1, 2 correspond to LV QH C3 H4 and TPPF describing 2 − IN OUT controls; Uj 3t j3 =1, 2 correspond to LV (QIN H2 /QC3 H4 ) and TPPF describing
variations of control. Each one of Xj 1t , Yt , Vt , Uj 2t and Uj 3t LV Xj 1t , Yt , Vt , Uj 2t and Uj 3t was specified in the universal set. Then each was transfered to fuzzy divison which defines how many terms there are in the term set. The strength of input space term sets defines the maximum number of fuzzy control rules in the KB. Usually trial and error heuristic procedure is used to select the optimal fuzzy division.
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Here the term sets of LV components are defined as follows: T(Xj 1t ) = T(Yt ) = T(Vt ) = T(Uj 2t ) = T(Uj 3t ) = {NB, NM, NS, VNS, ZE, VPS, PS, PM, PB}. As follows, NB is negative big, NM is negative medium, NS is negative small, VNS is very negative small, ZE is zero, VPS is very positive small, PS is positive small, PM is positive medium, PB is positive big. The membership functions based on research of the discussed technological process are generated according to LV term sets. In addition, an expert specialists group is involved in the work, estimating the values of this process membership functions. The membership function is presented as shown below: μA (u) =
n
ai /ui
i=1
Chainlike membership function allowing for its manipulation through fuzzy calculations is used here: μ(x) = e−a(x−b) , 2
where a is width, b is the angle coordinate of bell shape form. The possible situations description is given in a linguistic table form based on the formalization of the expert knowledge and information coming from the control object and through using LV term sets. The linguistic table of these regulations presented as collection of these linguistic rules is defined as follows: IF disturbance is χt , the control object position is γt , regulating quantity is νt and controls are ωt−1 , THEN the controls variations ωt−1 . Here χt = (χ1t , χ2t , χ3t ), γt , νt , ωt = (ω1t , ω2t ) and ωt = (ω1t , ω2t ) Xt = (X1t , X2t , X3t ), Yt , Vt , Ut = (U1t , U2t ) and Ut = (U1t , U2t ) are corresponding values of LV at the instance t. Each logical regulation defines a situation that may occur in the control object. The linguistic table based on experience and corresponding technological personnel knowledge is shown below (Table 1). When the next state vector of the control object arrives at the FLC input, the linguistic rules values describing the required control actions are determined using the Zadeh compositional rule and transferred to the control object as controls: ωt = χt ◦ γt ◦ νt ◦ ωt−1 ◦ Rt Rt is the current value of the relationship table, “°” means the max-min composition.
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Table 1. Logical-linguistic rules X1t
X2t
X3t
Yt
1
PS
2
PS
3
Vt
U1t ,
U2t
U1t
U2t
PS
PM
PS
PS
PS
PM
PS
ZE
PM
PM
ZE
VPS
PM
PS
PS
ZE
PS
PM
PM
ZE
PB
PM
PM
PS
ZE
4
PM
PM
PM
ZE
PM
PS
PM
ZE
PS
5
PS
PS
PM
PM
PB
PS
PM
ZE
PS
6
PM
PIS
PM
PM
PS
PM
PM
ZE
PS
7
PB
PM
PB
ZE
PS
PB
PS
ZE
PS
8
PS
PM
PM
ZE
VPS
PM
PM
ZE
NS
9
PM
PS
PM
ZE
PS
PM
PM
ZE
NS
10
PM
PM
PM
PM
PB
PS
PM
ZE
PM
11
PB
PB
PM
PS
PS
PS
PS
ZE
PM
12
PM
PM
PS
PS
VPS
PM
PS
NS
ZE
13
PB
PM
PM
PM
VPS
PM
PM
NS
ZE
14
PS
PM
PS
ZE
PS
PM
PM
VNS
VPS
15
PS
PM
PM
ZE
PB
PS
PS
PM
ZE
16
PB
PB
PM
ZE
PM
PS
PS
PS
PM
17
PM
PB
PS
PS
PS
PS
PB
NS
PS
18
PS
PM
PS
ZE
PM
PM
PS
PM
NS
19
PB
PM
PM
ZE
VPS
PB
PM
NS
NM
20
PM
PB
PM
ZE
PS
PS
PS
VNS
PS
21
PM
PB
PS
ZE
VPS
PM
PS
VNS
ZE
22
PB
PB
PM
ZE
VPS
PM
PM
VPS
VPS
23
PM
PS
PS
PM
VPS
PS
PB
NM
VPS
3 Fuzzy Control Algorithm Consider the proposed fuzzy control algorithm that describes the human experience of controlling the reactor under study, implemented on the basis of the developed logicallinguistic model in the form of a FLC with structural-parametric adaptation elements. At stage I, the actual fuzzy controller is implemented, which is determined by a set of rules (1). By introducing a composite variable that is the input vector of the control system At = Xj , Yt , Vt , Ut−1 and, assuming that some vector at comes to its input, the logical inference rule for the FLC in in terms of the membership function is written in the form: μωt = ∨ . . . ∨ ∨ ( ∨ μαt (at ) ∧ μRjt (at × ut ) , a1t ∈A1t
a6t ∈A6t ut ∈U t j∈P
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here μRjt (at × ut ) describes the mapping corresponding to the j-th LCR of the form (1). Here μRjt = ( ∧ μrjit (ait )) ∧ ( ∧ μrjkt (ut )), μαt (at ) = ∧ μαit (ait ), rjit - relation i∈I
i∈I
k∈K
table elements, I = {1, . . . , n}, P = {1, . . . , p}, K = {n + 1, . . . , n + k}. Further, at stage II, the analysis of the obtained solution is carried out. Moreover, if the resulting solution is approximated as undetermined and μαt (at ) ≈ 0 or μαt (at ) μRjt (at × ut ), ∀j ∈ P, then the output FLC is connected to the parametric adaptation block, thus forming a set It of all indexes i, for which μαt (at ) = μωt . If μωt is a unimodal function that allows full interpretation of the fuzzy correspondence ωt , then the output of the fuzzy controller is connected to the control object, otherwise the transition to the structural adaptation block is performed. At stage III, it is checked whether the response of the object νt fell into the allowable region (νt ∈ ϕt ). If this condition is met, then the transition to stage I is carried out (the output of the control object under consideration is closed with a fuzzy controller / ϕt and for the and a control corresponding to the current situation is generated). If νt ∈ term-sets introduced by the operator of the desired control changes ωt the inequality holds: μωt (μt ) ≤ ε, νt (μt−1 + μt ) ∈ ϕt ) then the transition to stage IV (parametric adaptation stage) is carried out. In this case, a set of all indices k is formed, for which: μj0 kt (μt ) ≤ ε, j0 = arg max μat (at ) ∧ μRjt (at × μt ) . j∈P
/ ϕt and μωt (ut ) > ε, then the transition to stage V (the structural adaptation If νt ∈ stage) is carried out. It should be noted that the parametric adaptation of the FLC is implemented at stage IV. The transition to this stage from stage III means that the parametric assignment of / It does not match to the changed knowledge base of the decision the terms ait , ∀i ∈ / It is taken. maker. If the solution is approximated as undefined, then μαt (at ) ≈ 0, ∀i ∈ In this case, the parameters of the membership function are changed so that: μαt (at ) = c0 , where c0 is chosen in such a way that the fuzzy matching approximation ωt with the adapted membership function parameters is no worse than that obtained at stage I. As one of the options for choosing the parameter c0 , we used: c0 = min μait (ait ) . If the transition is carried out from stage III, then it is necessary to solve the following system of equations:
μrjo kt (μt ) = c0 , ∀k ∈ / It . At the same time, structural adaptation is carried out when the current situation on the technological control object does not exist in the relationship table. In this case, μαt (at )
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does not prevent the fuzzy matching interpretation ωt (μαt (at ) > μωt ), however, the solution is approximated by contamination of several or all terms from T(Ur ) (transition from stage II). When moving from step III, the row for which μRt was the maximum is replaced. Replacement is carried out with the consent of the person making the decision. The issue of controlling the methylacetylene and propadiene hydrogenation reactor is governed by stabilization of propane-propylene fraction quality indices obtained at the catalytic reactor exit. These are shortly and fairly described above. Table 2. A fragment of the linguistic rules table obtained as a FLC self-learning result X1t
X2t
X3t
Yt
Vt
U1t ,
U2t
U1t
U2t
24
PM
PS
PS
PM
VPS
PS
PB
NM
VPS
25
PB
PB
PM
ZE
PS
PS
PS
PS
VPS
26
PM
PM
PS
PS
VPS
PM
PS
PM
VNS
27
PM
PS
PM
PS
PS
PM
PS
PM
VNS
28
PB
PS
PB
PS
PS
PM
PS
VNS
VNS
29
PB
PS
PB
PM
PM
PB
PS
VNS
VNS
30
PB
PB
PB
PS
PB
PM
PB
NB
VNS
31
PS
PM
PM
PM
PB
PB
PM
NB
VNS
32
PM
PS
PB
PS
PB
PB
PS
NM
VNS
33
PB
PB
PB
PS
PB
PM
PM
NB
NB
34
PB
PB
PM
PS
PM
PM
PS
NB
VNS
35
PS
PM
PM
PS
PB
PM
PM
NS
NS
36
PM
PS
PB
PM
PB
PB
PS
VNB
VNS
37
PM
PS
PB
PS
PB
PB
PS
NS
VNS
38
PB
PS
PB
PS
PM
PM
PS
ZE
VNS
39
PB
PM
PB
PS
PB
PB
PS
ZE
ZE
40
PB
PS
PB
PS
PB
PB
PS
ZE
NS
41
PB
PB
PM
PM
PM
PM
PS
NM
VNS
42
PM
PB
PB
PM
PB
PM
PM
NM
NS
43
PS
PS
PS
PS
PB
PB
PS
NM
ZE
44
PB
PB
PB
PM
PB
PB
PM
NB
ZE
Due to the variability of the physicochemical non-stationary process in the reactor (in particular, the drop in catalyst activity), as well as the incompleteness of the rules linguistic table, due to the impossibility of taking into account all possible situations, the logical-linguistic description becomes inadequate to the process described by it. It is clear that it is necessary to make changes to the logical-linguistic model, which are associated both with the need to clarify the parametric definition of the components linguistic variables term sets, and with the relationship table structure addition based on
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new knowledge of the technological personnel. In this regard, in the developed reaction apparatus control system with self-learning elements, an adaptive controller is proposed, which is a FLC with structural-parametric adaptation elements. Moreover, this controller consists of a fuzzy controller itself, output feedback blocks, structural adaptation, parametric adaptation, solution analysis, a memory device, as well as a fuzzy-to-clear value converter block. It should be noted that the table of relations at the first 60 steps of the regulator operation was supplemented with 20th rows. The corresponding correction of membership functions parameters a and b for linguistic variables term sets elements has been carried out. In addition, five lines in the rules linguistic table have been replaced. A fragment of the rules linguistic table obtained as a FLC self-learning result is presented in Table 2.
4 Conclusion Thus, the developed and presented logical-linguistic model, developed using the technological personnel knowledge and experience and the relevant measuring instruments readings, makes it possible to quite easily and effectively control the reactor for the selective hydrogenation of acetylene compounds in the propane-propylene fraction. For this, software has been developed that describes the algorithm proposed above for controlling the methylacetylene and propadiene hydrogenation reactor under study in a self-learning and self-configuring automatic control system for this catalytic apparatus, based on a logical-linguistic description of technological situations that arise in the control process. It should be noted that the control of the catalytic apparatus, observed using a FLC with structural-parametric adaptation based on the above logical-linguistic rules table and a fuzzy control algorithm, provides better (optimal) results compared to traditional quality indicators of the propane-propylene fraction, obtained at the reactor outlet, and reduces the low-quality commercial propylene amount to 0.5 ÷ 0.8% of the total volume. Approbation of the developed algorithm and control system in industrial conditions that confirmed their performance and efficiency was carried out.
References 1. Peng, X.T.: Generating rules for fuzzy logic controllers by function. Fuzzy Sets Syst. 36(83– 89), 98–105 (1990) 2. Dushdurova, N.I., Mammadkhanova, S.A.: Modeling of dehydrogenation and oxidative dehydrogenation of isopropyl alcohol over Ti-V-O catalyst. Adv. Intel. Syst. Comput. 1323, 596–603 (2021) https://www.scopus.com/inward/record.uri?eid=2-s2.0-85104847314&doi= 10.1007%2f978-3-030-68004-6_7 3. Aliyeva, A.Z., Mamedova, N.A.: Two-stage catalytic process for producing unsaturated esters of naphthenic acids in ionic liquids. Theor. Exp. Chem., 136–141 (2020). https://doi.org/10. 1007/s11237-020-09647-1 4. Gardashova, L.A.: Synthesis of fuzzy terminal controller for chemical reactor of alcohol production. Adv. Intel. Syst. Comput. 1095 (2020). https://doi.org/10.1007/978-3-030-352493_13 5. Khalafova, I.A.: Research of the composition of gases produced in the catalytic cracking process under the influence of magnetic field. Process. Petrochem. Oil Refin. 1(1), 61–72 (2022)
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6. Melikov, E.A.: Principles of optimizing the control of propylene purification process from acetylene derivatives. In: The 7-th International Conference on Control and Optimization with Industrial Applications – COIA-2020, Azerbaijan, Baku, 26–28 August 2020, pp. 272–274 (2020) 7. Aliev, R.A., Gardashova, L.A.: Z-set based approach to control system design. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., M., Jamshidi, Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 10–21. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-640 58-3_2 8. Ahmadov, S.A., Gardashova, L.A.: Fuzzy dynamic programming approach to multistage control of flash evaporator system. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Mo., Jamshidi, Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 101–105. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-35249-3_12 9. Aliev, R., Aliev, F., Babaev, M.: Fuzzy process control nd knowledge engineering in petrochemical and robotic manufacturing. Verlag TUV Rheinland, Koln (1991) 10. Adilova, N.E.: Construction of fuzzy control system rule-base with predefined specificity. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Sadikoglu, F.M. (eds.) ICAFS 2018. AISC, vol. 896, pp. 901–904. Springer, Cham (2019). https://doi.org/10.1007/978-3-03004164-9_119
Quantitative Assessment of the Risk of Failure and Vulnerability of Oil and Gas Pipelines at Underwater Crossings I. A. Habibov(B)
and S. M. Abasova
Azerbaijan State Oil and Industry University, Azadliq Streed 20, Baku, Azerbaijan [email protected]
Abstract. Currently, several routes are used to transport Azerbaijani energy resources, including the Baku-Novorossiysk, Baku-Supsa, Baku-Tbilisi-Ceyhan oil pipelines and the Baku-Tbilisi-Erzurum and TANAP gas pipelines. In addition, to meet the needs of the population and industrial enterprises within the country, there is a wide branching of the gas transmission system, the total length of which is more than 4,500 km for the transportation of high-pressure gas and about 40,000 km for low and medium pressure gas pipelines. All gas pipelines run along complex routes, including near sea shores, above and below rivers, mountain, steppe, forest and other places. The most dangerous sections of the routes are the places where rivers and sea shores intersect. Failures and damages of gas pipelines are largely determined by technical, technological, operational, geographical and other factors. At the same time, the problem of ensuring the safe functioning of gas pipelines when they cross rivers is of particular relevance. The situation is particularly difficult in mountainous and foothill areas, where the number of pre-emergency situations has recently increased due to the exposure of pipes as a result of general and lateral erosion. Forecasting the depression of the bottom in the cross sections of watercourses by pipelines for various purposes is one of the important tasks in the design of underwater pipeline crossings. This task is still far from being solved due to insufficient knowledge of riverbed erosion. Based on the above, the work is devoted to solving the problem of predicting the process of general erosion and exposure of gas pipelines at underwater crossings, taking into account the time to reach the maximum depth of erosion using linear stochastic differential equations. Keywords: Unified gas supply system · Gas pipeline · Forecasting · Exposure and depth of pipe erosion
1 Introduction The problem of ensuring the safe functioning of oil and gas pipelines when they cross rivers has become particularly relevant in recent years. The situation is particularly difficult in mountainous and pre-mountainous regions, where the number of pre-emergency © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 330–337, 2023. https://doi.org/10.1007/978-3-031-25252-5_45
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situations has increased recently due to the exposure of pipes, due to general and lateral erosion. Forecasting the lowering of the bottom in the intersections of watercourses by pipelines for various purposes is one of the important tasks in the design of pipeline underwater crossings. This task is still far from being solved due to the insufficient degree of knowledge of the erosion of riverbeds. A deeper analysis of the problem and the creation of adequate forecast models are needed to design the structures in question safe, taking into account the reasonable risk of pipeline exposure. The poor reproducibility of the phenomenon of erosion and exposure of gas pipelines, as well as their relationship with the variability of soil characteristics and long-term fluctuations in river flow, makes it appropriate to use probabilistic models and the theory of random process releases [1, 2]. Despite the well-known successes of hydrology in predicting the flow of rivers [3, 4], as well as studies on the permissible non-erosive velocities of the water flow, sediment movement, erosion and other factors (see [5, 6]), the deepening of the pipeline in the underwater crossing are considered too simplistic. When choosing the depth of laying, the risk degree of an unfavorable condition of the pipeline (exposure and rupture), accompanied by significant material [13–16] damage and significant environmental violations, is not taken into account. The main reason for the unreasonable choice of the depth of the pipeline should be considered an incomplete account of the random nature of the process of erosion - exposure of the pipeline. Thus, when choosing a depth margin and determining the risk of an unfavorable (failure) condition, one should first of all take into account the random statistical nature of the erosion (which is a classic example of a random process) and the variable nature of the flow of physical, mechanical and other processes during the erosion of the riverbeds, as well as the responsibility of the object under consideration for the damage caused in case of failure [7]. New opportunities for further risk reduction in assessing the resistance to erosion of riverbeds are hidden in the disclosure of the random nature of the deformation of riverbeds and the factors that cause it.
2 Modeling of the Process of General Erosion Solution of the problem of predicting the process of general erosion and exposure of gas pipelines at underwater crossings, taking into account the time to reach the maximum depth of erosion using linear stochastic differential equations. One of the important tasks in the study of erosion processes is the prediction of the time (period) of its stabilization. Due to the complexity of the process, the prediction of gaps in time has not been fully studied. Only for cohesive soils there is an expression for an approximate time prediction, derived on the basis of the fatigue theory of erosion [8, 9]. To describe changeable random processes of erosion, the methods of the theory of Markov processes, the so-called processes without memory, seem to be the most effective. These include, in particular, stochastic kinetic equations used in physics to study diffusion and other similar processes. In [10], the stochastic differential equation (SDE) was used to describe the erosion process dy = m0 dt + σ dx(t)
(1)
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where y(t) is the defining parameter (in this case, the depth of the fracture); m0 , σ respectively, the average rate of change of the determining parameter and its standard deviation; x(t) is a random component of the Gaussian process. The main task of the analysis of the erosion process is to determine the distribution of time until the greatest depth of the total erosion is reached. This problem is similar to the problem of the first achievement by process (1) of the upper boundary of the region. Obviously, it can be solved if the conditional probability density of the transition of process (1) from one state to another is known. The conditional transition density for a Markov process of diffusion type is described by the Fokker-Planck-Kolmogorov (FPK) equation, which for process (1) is written as σ 2∂ 2P ∂P ∂P + m0 − =0 ∂t ∂y 2∂y2
(2)
The solution of this equation under the boundary conditions corresponding to the case of the monotonic nature of the realizations of the process (1) P(y, t)y=−∞ = P(y, t)y=+∞ = 0 (3) and initial condition P(y, t)|t=o = δ(y)
(4)
where δ(y) – delta function, makes it possible to determine the density f (t) of the distribution of the time of the first achievement by the process of a given threshold H, which is expressed as H f (t) = −∞
∂P ∂y ∂t
(5)
The distribution function of the time of the first achievement by the process (1) of the given boundary H is represented as μ−t (6) P(t) = √ , αμ t where α - is the significance level; μ = H/m0 ; F(Z) - probability integral given tabularly in reference manuals on mathematical statistics. The value of the time t of the first achievement of the process (1) is obtained by resolving the equation with respect to t μ−t √ , in this case, the value of Z is determined from the equality F(Z) = P g , where Z = αμ t Pg - specified acceptable level of non-failure operation (usually Pg = 0,9 is accepted). In the case when the realizations of the random process y(t) are nonmonotonic curves, instead of (6) we have the equality t+μ μ−t 2 − √ . P(t) = (7) √ − exp 2 α μ αμ t αμ t
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However, in practice, the values m0 and σ generally depend on t and y, i.e., the erosion process is described by the stochastic differential equation (SDE) dy = a(t, y)dt + b(t, y)dW (t),
(8)
where a(t, y) and b(t, y) are nonrandom functions; W(t) is the standard Wiener process, dW(t) = V(t)dt, where V(t) is white noise with intensity ν(t) [11]. We will consider a linear SDE, i.e., Eq. (8), in which a(t, y) = α0 + α1 y, b(t, y) = β0 + β1 y
(9)
In this case, Eq. (8) has a unique solution. Under condition (9) and the restriction β1 = const = 0
(10)
the solution of Eq. (8) obeys the normal distribution law. Let’s indicate by U(t) the solution of Eq. (8) under condition (9) and consider the problem of determining the distribution law for the residence time of a Markov random process U(t) in a given region (u1 , u2 ). Let us introduce into consideration the probability density w(τ , y) that at time τ the ordinate of the random function U(t) will be in the interval (y, y + dy) provided that in the time interval (t, t + T) the value of the ordinate has never gone beyond the boundaries of the region (u1 , u2 ), i.e. Let us consider the probability density w(τ, y) that at the moment of time the ordinate of the random function U(t) will be in the interval (y, y + dy) provided that in the time interval (t, t + T) the value ordinate has never gone beyond the boundaries of the region (u1 , u2 ), i.e. u1 ≺ U (t) ≺ u2
(11)
during the time interval (t, τ ), τ = t + T. Then the probability W(τ) of not reaching the boundaries of the region (11) by the time τ = t + T is determined by the equality u2 W (τ ) =
w(τ, y)dy.
(12)
u1
Let’s denote by ƒ 0 (θ ) the probability density of the time of the function U(t) in a given area. Obviously, if by the time τ the ordinate of the function has never reached the forbidden boundaries u1 and u2 , then this means that the time θ of staying in the allowable ∞ area will be at least (τ − t) and the probability of this event is equal to fθ (θ )d θ. On the other hand, this probability is determined by formula (12). Hence ∞
u2 fθ (θ )d θ =
τ −t
τ −t
w(τ, y)dy u1
(13)
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Here, by differentiation with respect to τ we get u2 f0 (θ ) = − u1
∂w(τ, y) ∂W (τ ) |τ =t+θ τ =t+θ dy = − ∂τ ∂τ
(14)
When the moment of crossing the boundary of the region (11) (u1 or u2 ) is taken as the initial moment of time, formula (14) gives the law of time distribution between two successive crossings of the boundaries of the region, i.e. the residence time of the random function U(t) in the allowed area from the moment of entry into this area until the moment of exit. Having a probability density ƒθ (θ), it is possible to calculate the mathematical expectation of the residence time of the function U(t) in the given area: ∞ θ = M (θ ) =
θ fθ (θ )d θ .
(15)
0
Integrating by parts and taking into account that W(∞) = 0, W(t) = 1, we obtain ∞ θ=
W (τ )d τ .
(16)
t
Since under the condition (9) a(t,y) = a(y) and b(t, y) = b(y), then U(t) is a stationary Markov process. In this case w(τ , y) will not depend on t and τ separately, but only on the difference (τ -t) and, therefore, ∂w ∂w =− ∂t ∂τ
(17)
On the other hand, until the boundary of the allowed region is reached, the function w must satisfy the first Kolmogorov equation ∂w 1 2 ∂ 2 w ∂w + a(x) + b (x) 2 = 0 ∂t ∂x 2 ∂x
(18)
where x is the value of U at time t. After simple transformations, taking into account (16) and the condition that the functions a and b are independent of time, from (18) we obtain the equation: d 2θ dθ = q(x) + p(x) 2 dx dx where indicated p(x) = 2a(x)/b2 (x), q(x) = −2/b2 (x). The general integral of Eq. (19) will be [1]: ⎧ x3 x3 x ⎪ p(x1 )dx1 ⎨x3 p(x1 )dx1 }dx3 + c2 θ(x) = e x 2 x2 q(x2 )dx2 + c1 ex ⎪ ⎩ x
x
(19)
(20)
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where x is any value of U taken as the initial value, and the constants c1 and c2 are determined from the boundary conditions θ (u1 ) = θ (u2 ) = 0
(21)
expressing the fact that if at first the ordinate of the random process was equal to one of its maximum allowable values, then the residence time of the random function inside the allowable region is equal to zero. Putting in (20) x = u1 and taking into account (21), we obtain u2 x3 c1 = −
ex
x3 p(x1 )dx1
· q(x2 )dx2 dx3
u1 u1
u2
c2 = 0,
−
e
x2
(22) p(x1 )dx1
u1
dx2
u1
Under conditions (9)–(10) p(x) =
2 (α + α1 x), q(x) β02 0
= − β22 and θ(x) is calculated 0
by formulas (20) and (22) using two-dimensional quadrature formulas [12]. In particular, when α1 = 0 formulas (20) and (22) have analytical expressions: 2α 2α 2 − 20 (x−x ) − 20 (x−x ) β 1 β0 2 1 θ (x) = 1 − e β0 − (x − x1 ) + c1 0 1 − e β0 , (23) 2 α0 a 2α0 2α c1 =
2 β02
−
1 α0
1−e
1−e
−
−
0 (u −u ) 2 1 β02
2α0 (u2 −u1 ) β02
(24)
We apply formulas (23) and (24) to solve the example from [10].
3 Application of the Model Let’s consider an example where it is required to determine how long it will take for an underwater pipeline to become exposed when crossing a river. The limiting depth of erosion H = 2 m and the level of non-failure operation Pg = 0.9 are set. There are data on the estimated depth of erosion (in meters) obtained from observations of the maximum flow of the river: 2000 - 1.35; 2004 - 0.89; 2008 - 1.15; 2012 - 0.90; 2016 1.20. Let’s assume x = 0.89, x = 0.9, u1 = x = 0.89, u2 = 2. By formula (24) we find c1 = 2211.97. Substituting c1 into (23), we get θ (x) = 10.33. Since the initial data are given with a countdown of 4 years, then 10.33 × 4 ≈ 41 years, starting from t = 2012 (which corresponds to x = 0.9). Therefore, the time required to expose the pipeline during washout is 38 years. For comparison, it should be noted that approximately the same time (35.95 years) was obtained from the calculations in [10]. However, the calculations in [10] were made according to the simplified formula Pg = F(z), which is valid only in the case when the process realizations are monotonic curves. In the case
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of non-monotonic realizations of the process (this is the case we are dealing with in the considered example), the required time t will be determined from Eq. (7) at P(t) = Pg . The formulas for calculating the maximum rupture depth H are given in [9] both for cohesive soils and non-cohesive soils, heterogeneous in size and for foundations made of rocks. Satisfactory agreement between the calculated maximum depths of the erosion funnel and the observed ones indicates the acceptability of the H calculation schemes given in [9] and some (not quite strict) assumptions made in this case.
4 Conclusions Thus, designing the depth of oil and gas pipelines at underwater crossings requires the study of the random statistical nature of river erosion. For this purpose, the problem of predicting the process of general erosion is solved in this work, taking into account the time to reach the limiting depth of erosion using linear stochastic differential equations. The proposed assessment of the degree of risk of the onset of an unfavorable state of the pipeline (exposure and rupture) at underwater crossings will contribute to the development and rapid deployment of systems for preventing and eliminating emergency situations. A similar methodology based on the use of stochastic kinetic equations can be used to predict the vulnerable state of territories and objects under the impact of mudflows.
References 1. Sveshnikov, A.A.: Applied Methods of the Theory of Random Functions. 3rd edn, 463 p. Lan, St. Petersburg (2011). (in Russian) 2. Kovyazin, V.F.: Applied Methods of the Theory of Random Functions: Study Guide, 464 p. Lan, St. Petersburg (2016). (in Russian) 3. Ratkovich, D.Ya.: Actual problems of stochastic hydrology. Water Resour. 27(6), 645–654 (2000). (in Russian). https://doi.org/10.1023/A:1026609817870 4. Naidenov, V.I., Shveikina, V.I.: Nonlinear models of fluctuations in river flow. Water Resour. 29(1), 62–67 (2002). https://doi.org/10.1023/A:1013801308608. (in Russian) 5. Begam, L.T., Lishtvan, L.L., Muromov, V.S.: Deformations of Bridge Beds (Ed. “Transport”), p. 200 (1970) 6. Zhuravlev, M.M.: Local erosion at the bridge supports. “Transport”, p. 113 (1984) 7. Mirtskhulava, Ts.E.: Prediction of General Erosion in Bridge Crossings and in Places Where Oil and Gas Pipelines Cross Rivers, Taking into Account Time, p. 39. Academy of Sciences of Georgia, Tbilisi (2001) 8. Grishanin, K.V., Degtyarov, V.V., Seleznev, V.M.: Waterways. Transport, p. 400 (1986) 9. Mirtskhulava, Ts.E.: Fundamentals of Physics and Mechanics of Channel Erosion. Gidrometeoizdat, p. 304 (1988) 10. Mirtskhulava, Ts.E.: Assessment of the risk of failure and vulnerability of oil and gas pipelines at river crossings. Oil Ind. 3, 96–99 (2005) 11. Pugachev, V.S., Sinitsyn, I.N.: Stochastic Differential Systems. Nauka, p. 560 (1985) 12. Kahaner, D., Mowler, K., Nash, S. Numerical Methods and Software. Mir, p. 575(1998)
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13. Aslanov, J.N., Sultanova, A.B., Huseynli, Z.S., Mustafayev, F.F.: Determination of radial strains in sealing elements with rubber matrix based on fuzzy sets. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, Mo., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 765–773. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-921279_101 14. Gasanova, N.A.: Definition of mechanical indicators of plastic details of the oil field equipment. Int. J. Innov. Res. Comput. Sci. Technol. 8(4), 313–314 (2020). https://doi.org/10. 21276/ijircst.2020.8.4.11 15. Ahmadov, S.A., Gardashova, L.A.: Fuzzy dynamic programming approach to multistage control of flash evaporator system. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, Mo., Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 101–105. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-35249-3_12 16. Babanli, M.B.: Fuzzy Logic-based Material Selection And Synthesis, World Scientific Publishing Company (2019). ISBN 9813276584, 9789813276581 17. Sultanova, A.B.: Development of an automatic parking algorithm based on fuzzy logic. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, Mo., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW-2021. LNNS, vol. 362, pp. 428–436. Springer, Cham (2022). https://doi.org/10. 1007/978-3-030-92127-9_58
Prediction of Energy Consumption in Residential Buildings Using Type-2 Fuzzy Wavelet Neural Network Rahib Abiyev1(B)
and Sanan Abizada2
1 Department of Computer Engineering, Near East University, Lefkosa, North Cyprus
[email protected]
2 Department of Electrical and Electronic Engineering, Near East University, Lefkosa,
North Cyprus [email protected]
Abstract. Residential buildings use a significant part of the total energy of the countries. The utilisation of energy is defined by consumer occupancy, construction materials used in buildings. The timely changes of these factors lead to vague and imprecise representations of energy consumption prediction. Fuzzy logic is a more suitable approach for modelling this problem. In this paper, type-2 fuzzy wavelet neural networks (T2-FWNN) is proposed for modelling the energy consumption prediction of residential buildings. The system implements type-2 fuzzy reasoning using wavelet neural network technology. A gradient descent algorithm using a cross-validation approach has been applied for the construction of T2FWNN system. The learning of T2-FWNN system is based on an adaptive procedure that adjusts learning rates for stabilisation of training. The constructed system is used for the prediction of energy demand in residential buildings of Northern Cyprus. The presented comparative results prove the effectiveness of the constructed T2-FWNN model and the suitability of the T2-FWNN in the prediction of energy demand. Keywords: Type-2 fuzzy sets · Energy prediction · Wavelet neural networks
1 Introduction Residential buildings utilize a significant part of the total electricity. Due to lack of financial incentives, this sector is not studied well in comparison to other industrial sectors [1, 2]. Various factors affect energy utilization in residential buildings. Human occupancy, the characteristics of residential buildings and the locations of energy stations have strongly influenced energy utilization. The buildings’ characteristics which are the size of the house, size of rooms, size of windows, number of rooms, number of windows, materials’ type used in the construction of the house are important variables that influence the energy consumption [2]. Also, economical factors such as the income of consumers, the price of energy, the frequency of using electrical appliances are important variables affecting energy consumption. As can be seen, the variables that affect the energy demand © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 338–345, 2023. https://doi.org/10.1007/978-3-031-25252-5_46
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in the building are different and also, the impacts of these factors on energy usage are vague and uncertain. The existence of uncertainties and imprecise information allows the use of fuzzy technology in evaluating the appropriate value of energy consumption. In this paper, we are considering the design of energy consumption using fuzzy set theory. Various approaches were used for the energy load prediction of residential buildings. They can be conditionally divided into physical modelling and data-driven methods [1, 2]. Physical models use thermodynamic rules for energy modelling. These are DOE-2 [3], EnergyPlus [4], ESp-r [5], DeST [6], TRNSYS [7], which can estimate the energy load of buildings. These programs allow to evaluate the effect of physical parameters on energy load. But these programs have a complex structure and need detailed information about residential buildings for the appropriate design of the model. Obtaining the physical parameters is difficult and sometimes substantial differences may occur between predicted model output and actual values [1, 7]. Nowadays, data-driven approaches based on computational intelligence techniques are actively used for modelling and control of industrial and non-industrial processes. These models use historical statistical data for the evaluation of the energy load. Various computational intelligence techniques were implemented for the prediction of energy load. These are ANNs [8], SVM [9], SVR [10]. The integration of different computational intelligence techniques was used to improve the performance of the prediction system [11, 12]. As shown above, energy consumption depends on the characteristics of residential buildings, locations of energy stations and it has strongly influenced by economical and demographic factors. The impacts of these factors on energy consumption are uncertain and vague. To handle these uncertainties, type-2 fuzzy logic is applied. Because type-2 fuzzy logic uses a fuzzy membership function (MP), it can handle uncertainties that existed in the rule base of the problem. Type-2 fuzzy logic was invented by Zadeh [13] and future improved by Mendel [14]. Type2 fuzzy sets are applied to solve many industrial and nonindustrial problems[15–20]. These are time-series forecasting [15, 16], channel equalizations [17], dynamic plant control [18, 19], servo system control [20], credit rating [21]. The development of the type-2 rule base is important for the design of the type-2 fuzzy system. In this paper, we are considering the integration of wavelet neural network (WNN) technology and type-2 fuzzy sets for the construction of the rule base. The design of such hybrid system decreases the design time of the system. In addition, WNN can model the local detail of nonlinear processes [22]. The integration of WNN and fuzzy sets were used for time-series prediction [16], dynamic plant control [19]. In this study, type2 fuzzy sets and WNN are integrated for modelling the energy demands of residential buildings. The paper is written as follows. Section 2 proposes T2-FWNN model used for the buildings’ energy demand. Section 3 describes the simulation of the T2-FWNN prediction system. The conclusions are given in Sect. 4.
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2 T2-FWNN Model for Energy Consumption In the paper, we are using TSK type rules, NN and wavelet technology for the design of T2-FWNN. Wavelet functions with different translation and dilation coefficients can describe various essential behaviors and features of the used nonlinear model. The rule number is also decreased because of this property. The used if-then rules are as follows: If x1 is A˜ j1 and . . . and xm is A˜ jm Then y1 is wjk
m
(1 − zij2 )e− i=1
2 zij 2
(1)
where, zij = (xi −bij )/aij , , (i = 1,..,m; j = 1,…,r). Aij and bij are dilation and translation. A˜ ji are type-2 membership functions (MFs), wij are coefficients, x 1 , x 2 , …, x m and y1 , y2 , …, yr are inputs and outputs, correspondingly. m is the number of inputs, r is the rules’ number, correspondingly. Figure 1 presents T2-FWNN system structure. As shown T2-FWNN consists of six layers. The first layer distributes inputs, the second layer presents MFs. In the paper, Gaussian is used for describing membership functions(mf). We used Gaussian mf with an uncertain mean. The Gaussian MFs μj (x i ) used in this paper are described as μj (xi ) = e
−
(xi −cij )2 σij2
(2)
where, x is the input signal with uncertain mean c ∈ [c1 ,c2 ], cij and σij are the centers and widths of the Gaussians, respectively. The second layer of T2-FWNN calculates upper μj and lower μj membership degrees using interval type-2 fuzzy sets and α-cut. _
μA˜ j (xk ) = μA˜ j (xk ), μA˜ j (xk ) = [μj , μj ] k
k
(3)
k
In rule layer 2, the t-norm operation is utilised to find the fuzzy firing strange of each rule.
Fig. 1. T2-FWNN model
Prediction of Energy Consumption in Residential Buildings
fj = min μA˜ (x1 ), μA˜ (x2 ), . . . μA˜ (xm ) ; m 1 2 f j = min μA˜ 1 (x1 ), μA˜ 2 (x2 ), . . . μA˜ m (xm )
341
(4)
j
where f and f j are upper and lower mfs, correspondingly. In the next layer using input signals the output of wavelet functions is calculated for each fired neuron. Here the number of rules is denoted as r and this value is equal to the number of wavelet functions used Ψj (z) =
zij2 m − 1 aij 2 1 − z 2 e− 2 ; yj = wj j (z) ij
(5)
i=1
where zij = (xi − bij )/aij . In the next fourth and fifth layer, the type-reduction and defuzzification operations [18, 19] is performed in order to find the output uk (k = 1,..,n) of the network. r r r r (6) uk = p f j yjk / fj + q f j yjk / fj j=1
j=1
j=1
j=1
where yjk = wjk ·Ψ j (z), p and q are used to update the upper and lower portions. The design of the T2-FWNN system includes finding the proper values of c1ij , c2ij , sij , wjk , aij , bij , p, q (k = 1,..,n, i = 1,..,m, j = 1,..,r,) variables of the system. In this study, fuzzy clustering and gradient descent algorithms are applied to design T2-FWNN.
3 Simulations The T2-FWNN system is used for modelling energy consumption in residential buildings. For modelling, we used statistical monthly data, between 2004–2020 years, about the energy consumption in the residential building. The data was taken from Kib-Tek electricity company of North Cyprus. Using T2-FWNN model the design of the prediction model is accomplished. The cross-validation approach, gradient algorithms and fuzzy clustering are used for the training of the system. The performance of the designed system is measured using root mean square error (RMSE) and also mean square error (MSE).
2 2 1 N d 1 N d Yi − Yi ; RMSE = Yi − Yi (7) MSE = i=1 i=1 N N The solving of electricity consumption allows to plan electricity production in advance and prevent electricity deficiency problems. Using the dataset we organised training, validation and testing data. At first we used x(t), x(t − 2), x(t − 3), x(t − 8) and x(t − 9) in order to predict three-step ahead prediction x(t + 3). As seen 5-dimensional input vector is used to predict one-dimensional output vector. 10-fold crassvalidation and 200 epochs were used for simulation. Five, eight and ten rules are used for simulation purposes. The training division has been plotted in Fig. 2. With 10 rules, the error values
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of training, validation and testing were obtained as 0.052754, 0.052858 and 0.051163 respectively. Figure 3 depicts the results of the T2-FWNN system. Here solid line depicts the actual, dashed line depicts 3-step ahead prediction result of the T2-FWNN system. Figure 4 depicts a plot of RMSE for test division. Comparison has been done in order to demonstrate the efficiency of T2-FWNN model. Using the same statistical data, the design of the prediction system is implemented using neural networks (NN) and fuzzy neural networks (FNN). Table 1 describes the comparison of the prediction models using different rule numbers. In the second stage, the T2-FWNN system is used for one-step ahead prediction. Input signal was five-dimensional vector that included x(t), x(t − 1), x(t − 4), x(t − 5) and x(t − 11) items, output was x(t + 1). The results were obtained using 10-fold crossvalidation and 200 learning epochs. The RMSE values for training, testing and validation data were determined as 0.05825, 0.059 and 0.05747 correspondingly (Table 2).
Fig. 2. Training division
Fig. 3. Test division. 3-step ahead prediction. Solid line-actual output, dashed line-predicted output
The T2-FWNN model results are compared with the results of NN and fuzzy NN based prediction models. Table 2. Shows the comparative results. The obtained results indicate the efficiency of using T2-FWNN in the prediction of electricity consumption.
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Fig. 4. The error plot
Table 1. Comparative results Rules
MSE
RMSE
Training
Evaluation
Testing
Training
Evaluation
Testing
NN
10
0.00559
0.00613
0.00597
0.07482
0.07831
0.07727
Fuzzy NN
10
0.00471
0.00474
0.00419
0.06865
0.06886
0.06478
T2-FWNN
5
0.00414
0.00416
0.00407
0.06434
0.06450
0.06380
8
0.00304
0.00305
0.00299
0.05515
0.05526
0.05467
10
0.00278
0.00279
0.00262
0.05275
0.05285
0.05116
Table 2. The results of comparisons. MSE
RMSE
Train
Evaluation
Testing
Training
Evaluation
Testing
NN
0.00524
0.00532
0.00523
0.072415
0.072941
0.072334
Fuzzy NN
0.00477
0.00483
0.00471
0.069086
0.69526
0.068672
T2-FWNN
0.00339
0.003482
0.00330
0.058245
0.059007
0.057475
Comparisons of the different models were done in order to prove the efficiency of the proposed T2-FWNN. Multilayer Perceptron that uses backpropagation for learning (MLP), least media Lazy Kstar, squared linear regression(LeastMedSq), Linear regression, Radial basis function networks (RBF) that uses K-means clustering algorithm, radial based function network that uses supervised training, Support vector machine (SMOReg), Random Forest, NN, Fuzzy NN and T2FWNN. The simulations were done for 3- and 1-step ahead predictions (Table 3). Here NN, Fuzzy NN and T2FWNN were simulated using 10 hidden neurons. The results obtained from the comparisons indicate the suitability of using T2-FWNN in the prediction of electricity demand.
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1-ahead prediction
MAE
RMSE
MAE
RMSE
Random Forest
0.0575
0.0783
0.0588
0.082
Bagging
0.0603
0.0834
0.0585
0.0821
Lazy Kstar
0.0636
0.0867
0.0651
0.0927
Linear Regression
0.0593
0.0811
0.0553
0.0766
RBF
0.0836
0.1022
0.0787
0.1001
RBF Regressor
0.0574
0.0779
0.0562
0.0774
SMOReg
0.0562
0.0801
0.0537
0.0775
LeastMedSq
0.0563
0.0798
0.0549
0.0773
MLP
0.07
0.0931
0.0672
0.0917
M5Rules
0.06
0.0821
0.0553
0.0766
NN
0.005971
0.077275
0.00523
0.072334
Fuzzy NN
0.004197
0.064787
0.00471
0.068672
T2FWNN
0.002628
0.051163
0.00286
0.057475
4 Conclusions The paper proposes T2-FWNN model for the energy consumption prediction in residential buildings. The design of the system is implemented using fuzzy classification and gradient descent algorithms. The cross-validation approach is applied to organise learning division. The designed system is applied for energy prediction in residential buildings of North Cyprus. The development of T2-FWNN is performed using statistical data for three- and one-step-ahead prediction. For the comparative purpose, the design of other techniques including NN and FNN is implemented. The comparisons of different models indicate the suitability of using T2-FWNN in the prediction of energy consumption.
References 1. Amasyali, K., El-Gohary, N.M.: A review of data-driven building energy consumption prediction studies. Renew. Sustain. Energ. Rev. 81, 1192–1205 (2018). https://doi.org/10.1016/ j.rser.2017.04.095 2. Tsanas, A., Xifara, A.: Accurate quantitative estimation of energy performance of residential buildings using statistical machine learning tools. Energy .ings 49, 560–567 (2012). https:// doi.org/10.1016/j.enbuild.2012.03.003 3. Simulation Research Group, Lawrence Berkley National Lab, Overview of DOE 2.2 (1998). http://ww.doe2.com/ 4. Crawley, D.B., et al.: EnergyPlus: creating a new-generation building energy simulation program, Energ. Build. 33(4), 319–331 (2001). https://doi.org/10.1016/S0378-7788(00)001 14-6
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5. Strachan, P.A., Kokogiannakis, G., Macdonald, I.A.: History and development of validation with the ESP-r simulation program. Build. Environ. 43(4), 601–609 (2008). https://doi.org/ 10.1016/j.buildenv.2006.06.025 6. Yan, D., Xia, J., Tang, W., Song, F., Hang, X.Z., Jiang, Y.: DeST—an integrated building simulation toolkit part I: fundamentals. Build. Simul. 1(2), 95–110 (2008). https://doi.org/10. 1007/s12273-008-8118-8 7. Fumo, N.: A review on the basics of building energy estimation. Renew. Sustain. Energ. Rev. 31, 53–60 (2014). https://doi.org/10.1016/j.rser.2013.11.040 8. Kumar, R., Aggarwal, R., Sharma, J.: Energy analysis of a building using artificial neural network: a review. Energ. Build. 65, 352–360 (2013). https://doi.org/10.1016/j.enbuild.2013. 06.007 9. Li, Q., Meng, Q., Cai, J., Yoshino, H., Mochida, A.: Applying support vector machine to predict hourly cooling load in the building. Appl. Energ. 86, 2249–2256 (2009). https://doi. org/10.1016/j.apenergy.2008.11.035 10. Hong, W.C.: Electric load forecasting by support vector model. Appl. Math. Model 33(5), 2444–2454 (2009). https://doi.org/10.1016/j.apm.2008.07.010 11. Abiyev, R.H.: Fuzzy wavelet neural network for prediction of electricity consumption. AIEDAM: Artif. Intell. Eng. Des. Anal. Manuf. 23(2), 109–118 (2009). https://doi.org/10. 1017/S0890060409000018 12. Abiyev, R., Abiyev, V.H., Ardil, C: Electricity consumption prediction model using neurofuzzy system. World Acad. Sci. Eng. Technol. 8 (2005) 13. Zadeh, L.H.: The concept of linguistic variable and its application to approximate reasoning. Inf. Sci. 8, 199–249 (1975). https://doi.org/10.1016/0020-0255(75)90036-5 14. Mendel, J.M.: Uncertain Rule-Based Fuzzy Logic System: Introduction and New Directions, 2nd edn, 684 p. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-51370-6 15. Karnik, N.N., Mendel, J.M.: Application of Type-2 fuzzy logic systems to forecasting of time-series. Inf. Sci. 120, 89–111 (1999). https://doi.org/10.1016/S0020-0255(99)00067-5 16. Abiyev, R.H.: A Type-2 fuzzy wavelet neural network for time series prediction. In: GarcíaPedrajas, N., Herrera, F., Fyfe, C., Benítez, J.M., Ali, M. (eds.) IEA/AIE 2010. LNCS (LNAI), vol. 6098, pp. 518–527. Springer, Heidelberg (2010). https://doi.org/10.1007/9783-642-13033-5_53 17. Abiyev, R.H., Kaynak, O., Alshanableh, T., Mamedov, F.: A Type-2 neuro-fuzzy system based on clustering and gradient techniques applied to system identification and channel equalization. Appl. Soft Comput. 11(1), 1396–1406 (2011). https://doi.org/10.1016/j.asoc. 2010.04.011 18. Abiyev, R.H., Kaynak, O.: Type-2 fuzzy neural structure for identification and control of timevarying plants. IEEE T. Ind. Electron 57(12), 4147–4159 (2010). https://doi.org/10.1109/TIE. 2010.2043036 19. Abiyev, R.H., Kaynak, O., Kayacan, E.: A type-2 fuzzy wavelet neural network for system identification and control. J. Franklin Inst.-Eng. Appl. Math. 350(7), 1658–1685 (2013). https://doi.org/10.1016/j.jfranklin 20. Kayacan, E., Oniz, Y., Aras, A.C., Kaynak, O., Abiyev, R.: A servo system control with time-varying and nonlinear load conditions using Type-2 TSK fuzzy neural system. Appl. Soft Comput. 11(8), 5735–5744 (2011). https://doi.org/10.1016/j.asoc.2011.03.008 21. Abiyev, R.H: Credit rating using Type-2 fuzzy neural networks. Math. Probl. Eng. (2014). https://doi.org/10.1155/2014/460916 22. Thuillard, M.: Wavelets in Softcomputing. World Scientific Press, Singapore (2001)
Modeling the Interaction of Components of a Distributed Information and Communication Environment Nodirbek Yusupbekov1(B)
, Nargiza Usmanova2
, and Shukhrat Gulyamov1
1 Tashkent State Technical University, 2 University Street, 100095 Tashkent, Uzbekistan
[email protected] 2 Tashkent University of Information Technologies named after Muhammad Al-Khorezmi,
108 Amir Temur Street, 100200 Tashkent, Uzbekistan
Abstract. The work is devoted to the development of scientific and methodological foundations for improving the efficiency of distributed computing networks and systems by organizing an info-communication network environment for transmitting and processing information. The concept of the study of information processes in network structures based on the principles of the organization of the intermediate software environment, which allows you to explore various mechanisms of intra-system and intersystem information exchange between system components. The principles of development and implementation of associative interaction components of info-communication network structures are proposed. They allow achieving intellectualization of their behavior. A methodological approach to the study and analysis of info-communication network structures and their capabilities is proposed, based on the application of the principles of creating a program description and allowing to determine of a set of objects (distributed elements) under the modes of function and processes of functioning of a distributed information environment from a detailed analysis of the principles and mechanisms for the interaction of services and resources of a distributed networks and ensure effective interplay of network and system components of info-communication systems both for the distributed architecture of the network itself and for interacting resources, services, and interfaces. Keywords: Associative interactions of components · Info-communication network structures · Distributed information environment · Intelligent agents · Distributed information system
1 Introduction A distributed system, which is of fundamental importance in various fields and areas of ICT, is today the object of research by many groups of the world community. These studies are stimulated by the ever-increasing role and the ever-wider development of various networks and technologies (such as the semantic Web, Grid computing, cloud computing, the Internet of things, and others), each of which has its principles and © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 346–353, 2023. https://doi.org/10.1007/978-3-031-25252-5_47
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implementation features. But in general, all these technologies are based on creating a single environment that allows the user to receive services anywhere and anytime. However, in many areas, the capabilities of computing tools are limited due to the nature of information processing and the development of computer system control (for example, in the field of pattern recognition, problem-solving with incomplete information, predicting the results of an intended action and generating control, with real-time process dynamics, etc.). The possibilities of information technology that exist today involve the implementation of new approaches to information processing, united by the general properties of associative or intuitive information processing, which make it possible to process knowledge, carry out logical inference and, thereby, allow the intellectualization of computing systems [1, 2]. To date, despite the existence of enough solid theoretical and practical foundations for studying distributed systems, there are still insufficiently developed tools for describing the evolution in time of both the distributed systems themselves and the populations of programs operating in their structures; this is due to several reasons, among which, first of all, the heterogeneity of the composition and the dynamics of the behavior of the components, including the presence of unpredictably changing structures. Existing methods for describing and studying distributed systems, as an analysis of modern domestic and foreign works shows, are mostly unable to answer many questions in this direction, in particular, how software structures operating in distributed systems and networks can be formed for effective interaction. Components and creating a single distributed environment. In this regard, it is necessary to solve the problems of effective organization of distributed computing, expanding the corresponding functionality and improving the mechanisms for the interaction of many elements (components), taking into account functional processes of an intra- and inter-system nature, as well as complex infrastructure links due to network and system architectures [3, 4].
2 Conceptual Representation of a Behavioral Model of a Distributed Information Space The decomposition of the functional architecture of distributed systems takes into account the component construction of software (in the context of the software architecture, in which various structures are distinguished corresponding to certain aspects of the interaction of components, i.e. class structures, deployment structures, possible interaction scenarios, etc.) of a computing system, properties of components and relations between them. A distributed state information space represents a set of objects associated with or related to processes. At the same time, methodologically, the decomposition in relation to the components and the representation of the state space for various components is carried out in such a way that connections can be defined in the model at one level or another (Fig. 1). Such a representation allows you to define and detail a set of internal structures of a distributed environment, its components, their connections, and possible interactions between components, including the properties of these components, by specifying the corresponding structural elements identified by the interaction interface at various levels
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of abstraction (for example, through the structure software classes, possible scenarios for the interaction of components, etc.) [5]. Along with this, in a distributed space, the implementation of the application is carried out through a set of autonomous processes, it’s represented by a multi-agent system and is supported by the underlying environment, i.e. the proper degree of functionality can be provided at the required level of consideration, which makes it possible through the behavioral model of the distributed environment (space) to move to the programming model, and, accordingly, to the software architecture (SW) or modification of the process of its development. Considering that the behavior of an agent in a multi-agent system is identified by its control system, an agent control scheme is considered, the development of which is an important part of solving the problem.
Fig. 1. Conceptual representation of the behavioral model of the distributed space and its relationship with the model of the environment.
The agent control scheme in the conceptual representation of the distributed space behavioral model is shown in Fig. 2. In the distributed space, depending on the task, a set of objects is formed, the behavior of objects, their properties, the establishment of relations between objects, the interfaces for each object and the implementation of the object are specified. It is important to substantiate the fact that in OOP the computational process is understood as a system assembled from modules that interact with each other and have their own ways of processing incoming messages [6]. Based on sound modeling principles, the implementation of the relevant blocks of the above scheme and the optimization of the behavior of agents takes into account the following factors when modeling: 1. Evolutionary search: a module of communication with other agents (highlighted in the diagram by a dash-dotted line) - a model of an associative environment. 2. Individual learning and action choice: goal and evaluation module - Hopfield neural network model and tensor transformation. 3. Exchange of experience between agents as a result of communications: effective interaction of components in a distributed environment - a model of a multi-agent system based on fuzzy sets.
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At the same time, the implementation of the modeling principles for each of them is determined by the corresponding model, taking into account the principles of multidimensional decomposition.
Fig. 2. Agent control scheme in the conceptual representation of the behavioral model.
Modeling of evolutionary search. Under the provisions of the theory of intelligent systems, the implementation of information processing and control technologies, and, consequently, the organization of the computational process largely depends on the implemented principle of organizing the system in each specific case, on the basis of which models of dynamic objects and processes are presented, as well as from a number of other factors. At the same time, changes occurring as a result of information interactions between sets of elements of the same hierarchy level can be both quantitative and qualitative. The former is characterized by changes within information systems, the latter by changes in the hierarchical structure, as well as changes in relationships and interconnections between sets of information systems at different levels of the hierarchy. For quantitative analysis of information processes, determination of the effective configuration of the interaction of network components, and a detailed assessment of the functioning of information systems, a systematic approach is used that makes it possible to describe information processes based on associative links [7]. The associative environment plays the role of a communication system (Fig. 1); association or associative connection - the establishment of similarity/difference relations between the representations of two or more objects or events, and the defining characteristic of the space of a multi-coordinate associative environment is the implementation in it of the chosen measure of similarity, interpreted as the distance between the analyzed information objects, presented in the form of ordered sets of elements of some sets, based on the introduced space metric. Using the possible manifestations of the properties of
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information objects in the network, based on the concepts of associative environments, one can determine [8]: – information field Q as a set of information about the state space of the information system; – hierarchy level of the information field QL (L- hierarchy level) - information from the information field Q, which can be reflected by information systems of a certain level of organization of the level model in all sets ofcells of the corresponding L-th (not higher) hierarchy level U PK(L) K = 1..Z..X – the layer of the hierarchy level of the information field QJ (L) (J -layer index) - information available to a separate subset of information systems levelof the hierar of a certain chy of sets of elements of the L-th hierarchical level U PK(L) k = 1..Z , U (PK(L) ) . The above provisions are applicable when modeling information processes: when modeling a network graph G(V , R(V )) can be represented by a set of all possible pairs of nodes D0 : D0 = {(s, d )|s, d ∈ V , s = d }, where the first element of the pair will correspond to the source node that initiates some information flow, and the second to the recipient node. Thus, any task associated with information transformation can be described as a set of tasks for the interaction of virtual elements HK(L) , DK(L) and UK(L) of the corresponding network nodes. If V1 are network nodes, represented by a set of virtual objects, characterizing information interactions of information systems of different levels V1 , (V1 ⊂ HK(L) , DK(L) , KK(L) ): N N N c c s s d d min c ∈ Pc i,j=1 Uij Cij + i,j=1 Hij Cij + i,j=1 Dij Cij , i=j
s∈Ps
i=j
d ∈D
i=j
where: N - set of elements of the same level; Pc - processes of the source node; Ps - processes of the receiving node; Cijx - the conditional cost of communication when requesting an information object on element j from element i. It is obvious that the value of Cijx will be determined by the efficiency of management processes for heterogeneous components (objects) in a distributed environment formed by info-communication network structures. The conditions for the execution of this expression can be restrictions on access to a resource, features of the application implementation, etc. It is important to note that in such a representation, two concepts are used to describe the task of information interaction of objects in a distributed environment: data (as a result of information exchange) and calculations (as a process), which are different for different applications. The efficiency of a distributed environment is determined by and depends on the results of managing the processes associated with providing data and performing calculations. The data is described by the attributes of the entities in the environment, and the calculations are related to the behavior of the entities [9]. A formalized description of the system-network connections between the components of a distributed system based on the concepts of associative environments allows, therefore, the most complete mutual mapping of various network architectures, to represent the interaction of network elements, and also to describe the application functionality of various scenarios and solutions for the implementation of services (applications).
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A distributed application is considered to consist of many processes (programs, computing resources, operating systems, and other processes) performing a task, while a communication network passes messages between processes in a coordinated manner to exchange data and information). The functionality of a distributed environment, and, accordingly, its functional architecture, is completely determined by the needs of application processes in the transfer of various types of information. The system model is described by a graph, the vertices of which represent processes, and the edges are directed communication channels. A distributed application (according to the distributed application model and the system model for a software component proposed in the third chapter) consists of a set of p1 , p2 , pi , ..., pn processes that interact via mij message exchange. In general, the set of states of processes and communication channels is the state of distributed computing. For process pi , event x is received as eix ; for message m send and receive events - send (m) and rec(m) respectively. If events occur, this leads to changes in the corresponding processes and channels and a change in the state of the system: an internal event changes the state of the process to which it refers. Events for any process are linearly ordered as they occur: the execution of process pi is a sequence of events ei1 , ei2 , ..., eix , eix+1 , ... denoted as Si , i.e. Si = (si → i), where si is the set of events initiated by process pi , and the relation → i determines the linear sequence of these events [10]. The execution of a distributed application is a set of distributed events (processes), i.e. S = ∪i si . The → relationship between events in distributed computing determines the order of events S = (S, →), that occur depending on the distributed algorithm, as well as the cause-and-effect dependence of the processes involved in distributed computing (the occurrence of events). In general, one can write: ⎧ y ⎪ eix → ei , ⎨ y y y eix →msg ei , ∀eix , ∀ei ∈ S, eix → ej ⇔ ⎪ ⎩ ∃ez ∈ S : ex → ez ∧ ez → ey , j i k k k Using of such relationships, can be written various procedures for the functioning of a distributed object from the point of view of information exchange. For the purpose of modeling a distributed space, the so-called internal model of an agent is developed as a representative of an object (or group of objects) in terms of object-oriented programming. Modeling individual learning and action selection in a distributed environment. To describe the behavior of elements and components of a distributed environment (space), objects (entities) with variable parameters and discrete time are introduced into consideration, on the basis of which certain properties of objects can be studied. In addition, such objects, from the point of view of the mathematical description, are introduced into the neural network space as its nodes interacting according to certain rules and algorithms, depending on the functional purpose of the object in the state space. Such a representation of the structure of the associative environment is close to a model organized according to the object principle. The justification for the transition to such an organization should be the concretization of the concept of an element of the environment, i.e. its states, input and output signals (depending on functions) [11, 12]. Then the associative element of the environment will be the minimum structural element with respect to which the associative environment appears to be homogeneous. At the level of objects, in a structurally
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homogeneous associative environment, functional nodes and blocks can be formed (for example, these can be blocks of basic associative cells). For a distributed associative environment, links between associative elements organize structures of another level. These can be, for example, structures for managing, storing and processing data; the number of internal states of an associative element must be sufficient to implement the functions of memory, interaction, comparison, etc. Associative elements make it possible to implement in the associative environment all the basic functions that the base associative cell has, and if the base associative cell realizes its capabilities due to the presence of functional nodes, then the associative elements implement these capabilities as part of the objects of the associative environment.
3 Conclusion Concepts, principles, and scientific and methodological foundations for solving the theoretical and applied aspects of the implementation of associative interaction in modern info-communication network structures of computer systems have been developed in the work. The proposed and substantiated methodology for the study of info-communication network structures allows, based on a single framework concept, to describe complex functional and information connections of an inter- and intra-system nature and confirms the validity of the initial hypothesis of the study: methods and algorithms of software engineering when fulfilling the postulate of separation and sharing of the potential of distributed information and computing resources in the area of their coordination and coordination, allow for effective interaction of nodes and components of info-communication network structures and optimal real-time control of computing resources, significantly expanding the potential of automated control and expanding the functionality of computing systems. For a formalized description of complex relationships in the organizational structure of an associative environment, the apparatus of neural networks can be used: the process of functioning of an associative environment is described on the basis of the Hopfield network, for which there are two modes: learning and classification; in the learning mode, based on the known vectors, the weight coefficients of the network are selected; in the classification mode, with fixed values of weights and input of a specific initial state of neurons, a transient process occurs. This network can be trained according to various rules; in this case, the training vectors are repeatedly presented until the values of the weights stabilize. Further, the vectors representing the vertices of a distributed network environment are studied on the basis of the concepts of a tensor, which is a multidimensional vector in a certain basis, the directions of the component axes of which are specified by the coordinates of the multidimensional space.
References 1. Soumitra, D., Benat, B.-O.: INSEAD, the global information technology report, 2012: living in a hyperconnected world. INSEAD and the World Economic Forum, Geneva (2012). https:// www3.weforum.org/docs/Global_IT_Report_2012.pdf
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2. Insights to drive stronger performance. http://www.gartner.com/technology/home.jsp. 3. Usmanova, N.: Featuring self-organization in distributed systems: the way to converge toward desired structure/ubiquitous computing and internationalization. Korea 4(1), 1–6 (2012) 4. Usmanova, N.B.: Determination of the optimal structure of telecommunications networks in the context of the introduction of new technologies. J. Prob. Inf. Energy 3, 26–32 (2001) 5. Yusupbekov, N.R., Aliev, R.A., Aliev, R.R., Yusupbekov, A.N.: Intelligent Control Systems and Decision Making. Uzbekiston Milliy Encyclopedia, Tashkent (2014) 6. Akimova, G.P., Soloviev, I.A., Tarkhanov, I.A.: Modeling the reliability of distributed information systems. IT CS 3, 79–86, (2019). 1014357/207186321190307 7. Kasymov, S.S., Usmanova, N.B.: On developing the environment for multiagent system of distributed computing: using the associations. J. Chem. Tech. Cont. Manag. 3, 72–76 (2015) 8. Weiss, G.: Multiagent Systems: A Modern Approach to Distributed Artificial Intelligence. The MIT Press, Cambridge (2000) 9. Moser, T., Mordinyi, R., Winkler, D., Melik-Merkumians, M., Biffl, S.: Efficient automation systems engineering process support based on semantic integration of engineering knowledge. In: International Conference on Emerging Technologies and Factory Automation, pp. 1–8. IEEE Press, New York (2011). https://doi.org/10.1109/ETFA.2011.6059098 10. Broy, M.: A model of dynamic systems. In: Bensalem, S., Lakhneck, Y., Legay, A. (eds.) ETAPS 2014. LNCS, vol. 8415, pp. 39–53. Springer, Heidelberg (2014). https://doi.org/10. 1007/978-3-642-54848-2_3 11. Liang, T.-Y., Shieh, C.-K., Zhu, W.: Task mapping on distributed shared memory systems using Hopfild neural network. In: Proceedings of the Communication Networks and Distributed Systems Modeling and Simulation (1997) 12. Yusupbekov, N.R., Igamberdiev, H.Z., Mamirov, U.F.: Adaptive control system with a multilayer neural network under parametric uncertainty condition. CEUR Workshop Proc. 2782, 228–234 (2020)
Fuzzy Approach to Analysis of the Temporal Variability of the Vegetation in a Specific Area Elchin Aliyev(B)
and Fuad Salmanov
Institute of Control Systems of ANAS, B. Vahabzadeh str. 9, AZ1141 Baku, Azerbaijan {elchin,fuad.salmanli}@sinam.net
Abstract. Existing remote monitoring technologies provide farmers with useful information about the current health status of crops. The ability of remote sensors to detect subtle differences in vegetation makes them indispensable tools for precision farming, providing a quantitative assessment of crops in a particular area of the field. Multispectral data from such sounding allows farmers to obtain the vegetation maps, reflecting the current state of crops. Such vegetation maps allow to analyze the state of plants in dynamics, as well as to predict yields. In precision agriculture, for the numerical interpretation of multispectral data, vegetation indices are used. These indices are obtained empirically, i.e., by conducting experiments with different wavelength ranges in the electromagnetic spectrum. The given article considers the annual dynamics of the development of the plant culture in a particular field by analyzing the corresponding time series of a particular vegetation index. The possibility of predicting the yield of a particular crop based on fuzzy modeling of such time series is considered. Keywords: Multispectral data · Vegetation index · Vegetation map · Fuzzy time series · Forecasting
1 Introduction Most sown crops are distinguished by successive changes in development phases, which are fixed by means of the spectral-reflective features of plants. One of the ways to study seasonal changes in the spectral-brightness characteristics of crops is the vegetation indices for each pixel of the vegetation map, which make it possible to quantify the features of the vegetation cover and the patterns of its change in the dynamics of development. Precision agriculture uses standard algorithms for predicting crop yields based on the analysis and modeling of the dynamics of the spectral-reflective properties of plants, which, as a rule, work with “crisp” averaged multispectral remote sensing data. At the same time, averaging the results of measurements of spectral ranges for calculating vegetation indices is one of the most common empirical operations in systems for collecting and processing multispectral data. However, multispectral remote sensing data, or, more specifically, the wavelength ranges in the electromagnetic spectrum,
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 354–363, 2023. https://doi.org/10.1007/978-3-031-25252-5_48
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should be considered weakly structured, that is, those that are known to belong to a certain interval [1]. For example, the maximum reflection of the cellular structures of plants is fixed in the wave range from 750 nm to 900 nm, which is the near infrared region of the electromagnetic spectrum. However, more adequate ways of reflecting such ranges of the electromagnetic spectrum are evaluative concepts, such as the terms “high”, “low”, etc., which can be formally described by appropriate fuzzy sets [1, 2]. Based on this paradigm, the importance and relevance of studying methods for predicting seasonal changes in the spectral-brightness characteristics of crops using fuzzy time series (FTS) that reflect the dynamics of the vegetation index and the corresponding plant reflection coefficients become obvious.
2 Problem Definition As a rule, the calculation of vegetation indices is based on two ranges of the electromagnetic spectrum of vegetation reflectivity [3]: on the reflection of plants in the red region (RED) of the spectrum (620 nm, 750 nm), which illustrates the greatest absorption of solar radiation by chlorophyll of higher vascular plants, and on the reflection of plants in the near infrared region (NIR) of the spectrum (750 nm, 900 nm), where the region of greatest reflection of the cellular structures of the leaf is concentrated. In the theory of precision farming, the most common indicator for assessing the state of vegetation is the NDVI (Normalized Difference Vegetation Index), which is established by the following formula NDVI =
NIR − RED NIR + RED
(1)
where NIR and RED are the reflection coefficients, which are calculated by mapping the red and infrared regions onto a unit segment [0, 1] by trivial equalities: RED = (λ1 − 620)/(750 − 620), NIR = (λ2 − 750)/(900 − 750), where λ1 ∈ (620, 750) and λ2 ∈ (750, 900). The task is to implement a fuzzy method for predicting seasonal changes in the spectral-reflective characteristics of crops based on the TS of plant reflection coefficients obtained by processing multispectral data for each pixel of the vegetation map. To test the fuzzy approach, appropriate TS were chosen as an example, which, on the scale of one fixed pixel, reflect the temporal variability of the spectral ranges RED and NIR (see Table 1 and Fig. 1) obtained from MODIS images (see Fig. 2) area in Jonesboro (USA, Arkansas) with geographic coordinates (−90.16, 35.81) [4]. Table 1 also summarizes the appropriate NDVI values calculated by (1).
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Fig. 1. NDVI TS as a reflection of the temporal variability of the RED and NIR coefficients.
Table 1. Temporal variability of NDVI. №
Date
NIR
RED
NDVI
№
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
3 FTS: Initial Steps for Building a Predictive Model The existing approaches to modeling and forecasting the FCS imply the sequential implementation of the following steps: 1) construction of a universe covering all data of the TS; 2) TS data fuzzification; 3) identification of internal fuzzy relations and their grouping; 4) establishment of fuzzy outputs (forecasts) of the applied model and their defuzzification. One of the methods for constructing the universe and establishing the optimal number of qualitative criteria for evaluating weakly structured data was proposed in [5]. The essence of this approach is the sequential implementation of the following procedures. Step 1. Assorting all data {x t }t=1÷n into the ascending sequence {x p(i) }, where p is a permutation that sorts the data under condition: x p(t) ≤ x p(t+1) .
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Step 2. Determination of the average (AD) for all pairwise distance between any two consecutive values x p(i) and x p(i+1) (d i = |x p(i) – x p(i+1) |) by following formula: AD(d1 , d2 , ..., dn ) =
n−1 i=1
|xp(i) − xp(i+1) |/(n − 1)
and standard deviation σ AD by following formula n−1 σAD = (di − AD)2 /(n − 1) i=1
(2)
(3)
Step 3. Identification of existing anomalies to be eliminated. For this purpose, the average distance and standard deviation values set in the previous step are applied. Pairwise distances that do not satisfy condition (4) must be removed. AD − σAD ≤ di ≤ AD + σAD .
(4)
Step 4. Recalculation the average AD for the remaining pairwise distance d i . Step 5. Determination the appropriate universe in the form U = [D1 , D2 ], where D1 = Dmin – AD; D2 = Dmax + AD; Dmax is the maximum among the TS data; Dmin is the minimum among the time series data. Step 6. Determination the appropriate number of qualitative criteria for evaluating the TS data by following equality m = [D2 − D1 − AD]/[2 · AD].
(5)
4 Modeling the NDVI FTS Based on the above procedures for the TS relative to NIR and RED reflectance (see Table 1), the final average distance ADNIR = 0.0144 and ADRED = 0.0022 were be established. Then, the universes for each TS are obtained in the form: • U NIR = [0.1106 − 0.0144, 0.8702 + 0.0144] = [0.0962, 0.8846], where 0.8702 and 0.1106 are the maximum and minimum among the NIR TS data, respectively. • U RED = [0.0659 − 0.0022, 0.1623 + 0.0022] = [0.0637, 0.1645], where 0.1623 and 0.0659 are the maximum and minimum among the RED TS data, respectively. Based on the application of formula (5), the optimal values of the number of evaluation criteria for estimation the NIR and RED reflection coefficient were obtained as: mNIR = [0.8846 − 0.0962 − 0.0144]/[2 · 0.0144] = 26.9158 ≈ 27, mRED = [0.1645 − 0.0637 − 0.0022]/[2 · 0.0022] = 22.2444 ≈ 22.
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Fuzzification of NIR and RED reflections is carried out by following trapezoidal membership function ⎧ ⎪ 0, x < akj ⎪ ⎪ x−aj1 ⎪ ⎪ ⎪ ⎨ aj2 −aj1 , aj1 ≤ x ≤ aj2 , μAj (x) = 1,aj2 ≤ x ≤ aj3 , (6) ⎪ aj4 −x ⎪ ⎪ , a ≤ x ≤ a , ⎪ j4 ⎪ aj4 −ak3 j3 ⎪ ⎩ 0, x > aj4 , the corresponding parameters of which are satisfied to following equations: aj2 – aj1 = aj3 – aj2 = aj4 – aj3 (j = 1 ÷ m) and presented in Table 2. As a result, obtained fuzzy analogues for all NIR and RED data are presented in Table 3. The modeling of the FTS provides for the detection of internal relationships, which in our case are reflected in the form of fuzzy implications “If , then ”. Internal fuzzy relationships are grouped by the following rule: • if the fuzzy set Ak is prerequisite for one or more fuzzy sets in the FTS, then the so-called 1st order group is localized relative to Ak ; • if the bunch of fuzzy sets Ai , Ai+1 is prerequisite for one or more fuzzy sets in the FTS, then the so-called 2nd order group is localized relative to Ai , Ai+1 . Groups of the 1st and 2nd orders of identified internal relationships for the NIR and RED TS are presented in Tables 4 and 5, respectively. Table 2. Fuzzy sets as qualitative criteria for evaluation of NIR and RED reflections. NIR TS
RED TS
Fuzzy set Membership function parameters
Fuzzy set Membership function parameters
ai1 A1
ai2
ai3
ai4
bi1
bi2
bi3
bi4
0.0637 0.0659 0.0681 0.0703
A2
0.0962 0.1106 0.1250 0.1394 B1 0.1250 0.1394 0.1537 0.1681 B2
A3
0.1537 0.1681 0.1825 0.1969 B3
0.0726 0.0748 0.0770 0.0792
A4
0.0770 0.0792 0.0814 0.0836
…
0.1825 0.1969 0.2112 0.2256 B4 …
A24
0.7576 0.7720 0.7864 0.8007 B19
0.1435 0.1457 0.1479 0.1501
A25
0.1479 0.1501 0.1524 0.1546
A26
0.7864 0.8007 0.8151 0.8295 B20 0.8151 0.8295 0.8439 0.8582 B21
A27
0.8439 0.8582 0.8726 0.8846 B22
0.1568 0.1590 0.1612 0.1645
0.0681 0.0703 0.0726 0.0748
0.1524 0.1546 0.1568 0.1590
Various approaches are used to determine “crisp” (defuzzified) predicts. The essence of one of them is as follows [6]. If the data for the i-th day is described in the form of the
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359
Table 3. FTS of reflection coefficients NIR and RED. №
NIR TS
№
RED TS
NIR
FS
RED
FS
1
0.2036
A4
0.0958
B7
2
0.3175
A8
0.1445
3
0.3639
A10
4
0.3623
A10
5
0.2219
6 7 8
NIR TS
RED TS
NIR
FS
RED
FS
16
0.8565
A27
0.1452
B19
B18
17
0.8651
A27
0.1453
B19
0.1523
B20
18
0.8702
A27
0.1455
B19
0.1623
B22
19
0.3357
A9
0.1256
B14
A5
0.1025
B9
20
0.1125
A1
0.0678
B1
0.1717
A3
0.0835
B5
21
0.3666
A10
0.1348
B16
0.1676
A3
0.0845
B5
22
0.6051
A18
0.1245
B14
0.1407
A2
0.0765
B3
23
0.5828
A17
0.1463
B19
9
0.1106
A1
0.0659
B1
24
0.4628
A13
0.1354
B16
10
0.1214
A1
0.0689
B1
25
0.3492
A9
0.1158
B12
11
0.1502
A2
0.0815
B4
26
0.3523
A9
0.1233
B14
12
0.1529
A2
0.0813
B4
27
0.3450
A9
0.1389
B17
13
0.1664
A3
0.0855
B5
28
0.2457
A5
0.1125
B11
14
0.4084
A11
0.1324
B16
29
0.2173
A4
0.1045
B9
15
0.5890
A17
0.1356
B16
30
0.2058
A4
0.1056
B10
Table 4. Internal relationships of the 1st order. NIR TS
RED TS
G1 : A1 ⇒ A2 , A10 , A11
G9 : A11 ⇒ A17
G1 : B1 ⇒ B1 , B4 , B16 G9 : B14 ⇒ B1 , B17 , B19
G2 : A2 ⇒ A1 , A2 , A3
G10 : A13 ⇒ A9
G2 : B3 ⇒ B1
G3 : A3 ⇒ A2 , A3 , A11
G11 : A17 ⇒ A13 , A27 G3 : B4 ⇒ B4 , B5
G4 : A4 ⇒ A4 , A8
G12 : A18 ⇒ A17
G4 : B5 ⇒ B3 , B5 , B16 G12 : B18 ⇒ B20
G5 : A5 ⇒ A3 , A4
G13 : A27 ⇒ A9 , A27
G5 : B7 ⇒ B18
G13 : B19 ⇒ B14 , B16 , B19
G6 : A8 ⇒ A10
G6 : B9 ⇒ B5 , B10
G14 : B20 ⇒ B22
G7 : A9 ⇒ A1 , A5 , A9
G7 : B11 ⇒ B9
G15 : B22 ⇒ B9
G8 : A10 ⇒ A5 , A10 , A18
G8 : B12 ⇒ B14
G10 : B16 ⇒ B12 , B14 , B16 , B19 G11 : B17 ⇒ B11
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E. Aliyev and F. Salmanov Table 5. Internal relationships of the 2nd order.
NIR TS
RED TS
G1 : A1 , A1 ⇒ A2 G2 : A1 , A2 ⇒ A2
G15 : A9 , A5 ⇒ A4 G1 : B1 , B1 ⇒ B4 G16 : A9 , A9 ⇒ A9 , A5 G2 : B1 , B4 ⇒ B4
G15 : B14 , B17 ⇒ B11 G16 : B14 , B19 ⇒ B16
G3 : A1 , A10 ⇒ A18
G17 : A10 , A5 ⇒ A3
G3 : B1 , B16 ⇒ B14
G17 : B16 , B12 ⇒ B14
G4 : A2 , A1 ⇒ A1 G5 : A2 , A2 ⇒ A3
G18 : A10 , A10 ⇒ A5 G19 : A10 , A18 ⇒ A17
G4 : B3 , B1 ⇒ B1 G5 : B4 , B4 ⇒ B5
G18 : B16 , B14 ⇒ B19 G19 : B16 , B16 ⇒ B19
G6 : A2 , A3 ⇒ A11
G20 : A11 , A17 ⇒ A27
G6 : B4 , B5 ⇒ B16
G20 : B16 , B19 ⇒ B19
G7 : A3 , A2 ⇒ A1 G8 : A3 , A3 ⇒ A2
G21 : A13 , A9 ⇒ A9 G22 : A17 , A13 ⇒ A9
G7 : B5 , B3 ⇒ B1 G8 : B5 , B5 ⇒ B3
G21 : B17 , B11 ⇒ B9 G22 : B18 , B20 ⇒ B22
G9 : A3 , A11 ⇒ A17 G10 : A4 , A8 ⇒ A10
G23 : A17 , A27 ⇒ A27 G24 : A18 , A17 ⇒ A13
G9 : B5 , B16 ⇒ B16 G10 : B7 , B18 ⇒ B20
G23 : B19 , B14 ⇒ B1 G24 : B19 , B16 ⇒ B12
G11 : A5 , A3 ⇒ A3
G25 : A27 , A9 ⇒ A1
G11 : B9 , B5 ⇒ B5
G25 : B19 , B19 ⇒ B19 , B14
G12 : A5 , A4 ⇒ A4
G26 : A27 , A27 ⇒ A27 , G12 : B11 , B9 ⇒ B10 A9
G26 : B20 , B22 ⇒ B9
G13 : A8 , A10 ⇒ A10
G13 : B12 , B14 ⇒ B17 G27 : B22 , B9 ⇒ B5
G14 : A9 , A1 ⇒ A10
G14 : B14 , B1 ⇒ B16
fuzzy set Ak , which has only relationship within the FTS, say Ak ⇒ Aj , then the fuzzy predict for the next (i + 1)-th day will be the set Aj . If there is a group of fuzzy relations, for example, of the form Ak ⇒ Aj1 , Aj2 , …, Ajp , then the union of fuzzy sets Aj1 ∪ Aj2 ∪ … ∪ Ajp is the fuzzy predict for the (i + 1)-th day. So, the defuzzified value of predict Ak is the abscissa of the middle of the upper base of the k-th trapezoid. For example, for the fuzzy predict A4 , described by the trapezoidal membership function with the parameters indicated in Table 2, the numerical analogue is the abscissa of the middle of the upper base: (0.1969 + 0.2112)/2 = 0.20405. Really, according to the fuzzy set point estimate rule [2], the following formula is used: F(A) =
1 αmax
α max
M (Aα )d α,
(7)
0
where Aα = {u|μA (u) ≥ α, u ∈ U} is the α-level set (α ∈ [0, 1]); M (Aα ) =
1 n
n t=1
ut (uk
∈ Aα ) is the cardinal number of the corresponding α-level set. For the fuzzy output A4 = {0/0.1825, 1/0.1969, 1/0.2112; 0/0.2256} (see Table 2) we have: 0 < α < 1, α = 1, A4α = {0.1969, 0.2112}, M (A4α ) = (0.1969 + 0.2112)/2 = 0.20405.
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361
Then, according to (7), the defuzzified value of the A4 is follows
1
F(A4 ) =
M (A4α )d α = M (A4α ) · α = 0.20405.
0
According to [6], for fuzzy relation Ak ⇒ Ai , Aj , At the numerical predict is obtained as the arithmetical mean value. In particular, the fuzzification of fuzzy output for the date 15.03.2000, which is described as union A1 ∪ A2 ∪ A3 (see Table 2), is provided as following F = [(0.1106 + 0.1250)/2 + (0.1394 + 0.1537)/2 + (0.1681 + 0.1825)/2]/3 = 0.14655. Thus, considering the internal fuzzy relations of the 1st and 2nd orders for the FTS of the NIR and RED, the corresponding predictive models were obtained. Further, desire predictive model for NDVI TS is restored by application of the empirical formula (1) for each day according to the corresponding forecast data NIR and RED, which are obtained on the base of 1st and 2nd order models (M1 and M2). These models are interpreted in the form of Table 6 and Fig. 2. Table 6. NDVI FTS models. №
Date
NDVI
M1
M2
№
Date
NDVI
M1
M2
1 18.02.2000 0.3599
16 25.06.2000 0.7101
0.6722
0.7099
2 26.02.2000 0.3745 0.2951
17 02.07.2000 0.7124
0.6360
0.7099
3 05.03.2000 0.4099 0.4269 0.4269 18 11.07.2000 0.7135
0.6360
0.6343
4 15.03.2000 0.3812 0.4337 0.4034 19 20.07.2000 0.4554
0.6360
0.6343
5 21.03.2000 0.3680 0.5964 0.3887 20 27.07.2000 0.2479
0.3301
0.2748
6 29.03.2000 0.3457 0.3287 0.3482 21 02.08.2000 0.4623
0.5356
0.4765
7 06.04.2000 0.3296 0.4240 0.3482 22 12.08.2000 0.6587
0.5138
0.6591
8 15.04.2000 0.2957 0.4240 0.3177 23 20.08.2000 0.5987
0.6626
0.5948
9 22.04.2000 0.2535 0.3724 0.2748 24 28.08.2000 0.5473
0.6622
0.5523
10 29.04.2000 0.2759 0.5356 0.2748 25 03.09.2000 0.5019
0.4553
0.5005
11 08.05.2000 0.2966 0.5356 0.2920 26 13.09.2000 0.4815
0.3026
0.4724
12 15.05.2000 0.3058 0.2795 0.2920 27 20.09.2000 0.4259
0.3301
0.3094
13 24.05.2000 0.3211 0.2795 0.3482 28 29.09.2000 0.3719
0.3530
0.4028
14 09.06.2000 0.5104 0.4240 0.5045 29 07.10.2000 0.3505
0.2985
0.3314
15 15.06.2000 0.6257 0.6323 0.6247 30 15.10.2000 0.3217
0.4638
0.3124
MSE
0.0137
0.0021
MAPE (%)
25.5716
5.9490
MPE (%)
−0.1161 −0.0182
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Fig. 2. 1st and 2nd order models for NDVI TS forecasting.
As can be seen from the results of NDVI forecasting by the 2nd method, the error value according to the MSE criterion is quite low (0.0137 for M1, and 0.0021 for M2), which cannot be said about the error value according to the MAPE criterion (25.5716 for M1 and 5.9490 for M2). The MPEs for the 1st and 2nd order predictive models are (−0.1161) and (−0.0182), respectively, reflecting a slight bias below the 5% threshold.
5 Conclusion The paper discusses one of the tools of precision farming methodology related to the applying of the NDVI, which allows to identify crop volumes and more accurately estimate the current state of growing. The last statement is relative since the index itself does not reflect the absolute values of plant volumes. Nevertheless, regarding the obtained multispectral data, it is possible to estimate the development of growing plants and predict their perspective yield. It is necessary to consider that the NDVI changes throughout the entire vegetation cycle, that is, during the period of initial growth, the period of flowering and maturation, its indicators differ significantly, in fact, as evidenced by the dynamics of NDVI on the example of given pixel (see Fig. 1). The practice of precision farming has shown that the most active increase in the NDVI occurs during the growing season, during the flowering period, the growth of the crop slows down and halts, and in the process of crop maturation, the index gradually decreases. The fuzzy approaches to forecasting the temporal variability of NDVI proposed in the article can be easily extrapolated onto the processing of multispectral data obtained for all pixels of the corresponding vegetation maps. If vegetation maps used in precision farming allow only visually determining differences in the state of plants, then owing to digitalization it becomes possible to interpret the color range of vegetation from light tones with a low index to dark color with high NDVI.
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–I. Inf. Sci. 8(3), 199–249 (1975). https://doi.org/10.1016/0020-0255(75)90017-1
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3. Andreichikov, A., Andreichikova, O.: Analysis, Synthesis, Planning Decisions in the Economy. Finance and Statistics, Moscow (2000). (in Russian) 4. Vegetation Indices 16-Day L3 Global 250 m MOD13Q1 (LPDAAC). https://goo.gl/maps/YAd domuoXsD4QQN36. Accessed 11 Feb 2022 5. Ortiz-Arroyo, D., Poulsen, J.R.: A weighted fuzzy time series forecasting model. Indian J. Sci. Tech. 11(27), 1–11 (2018). https://doi.org/10.17485/ijst/2018/v11i27/130708 6. Chen, S.M.: Forecasting enrollments based on high-order fuzzy time series. Cybern. Syst. Int. J. 33, 1–16 (2002). https://doi.org/10.1080/019697202753306479
Application of Fuzzy TOPSIS in Server Selection Problem V. H. Salimov(B) Azerbaijan State Oil and Industry University, Baku Azadliq Street 20, Baku, Azerbaijan Republic [email protected]
Abstract. The paper is devoted to the application fuzzy technologies for solving multi-criteria decision making problems. In the information technology era the computer servers play key role. The effectiveness of function information processing centers depends on adequate server selection. The modern servers are characterized by many attributes. There are various methods for solving this problem. One of most used method is TOPSIS (The Technique for Order of Preference by Similarity to Ideal Solution). TOPSIS method is based on the ideal point approach. All stages of the servers selection problem solving on base of TOPSIS method are presented. Keywords: Fuzzy number · Decision making · TOPSIS method
1 Introduction Multi Criteria Decision making (MCDM) [1, 2] is permanently important problem in system analysis. MCDM can be considered as vector optimization problem. MCDM problems can be solved on the basics of preferences of decision makers. There are many methods for solving this problem. These methods can be classified in 2 categories: the methods based on the aggregation of criteria into single criterion and methods based on pairwise comparisons of alternatives. The WGP (weighted average product), WGA (weighted average sum) and their variations [3, 4] are included in first category, AHP, PROMETHEE, ELECTRE, TOPSIS [5–13] are included in second category. The information about popularity of different methods is presented in article [3]. The original TOPSIS has been developed by Hwang for certain data. In 2000 Chen developed fuzzy TOPSIS [4–21] method for problem with uncertain data. The paper is devoted to application of fuzzy TOPSIS method in server selection problem. In the information technology era the computer servers play key role. The effectiveness of functioning of information processing centers depends on adequate server selection. The modern servers are characterized by many attributes. There are various methods for solving multiattribute decision problem. One of most used method is TOPSIS (The Technique for Order of Preference by Similarity to Ideal Solution). TOPSIS method is based on the ideal point approach. All stages of the servers selection problem solving on base of TOPSIS method are presented.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 364–371, 2023. https://doi.org/10.1007/978-3-031-25252-5_49
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2 Fuzzy TOPSIS Method MCDM problem can presented as a linguistic matrix m – alternative’s number n - criteria’s number (Table 1), where X˜ ij = (aij , bij , cij , dij ) is a representation of linguistic terms by fuzzy trapezoidal numbers. Table 1. MCDM problem representation. C1
C2
C3
…
Cn
X˜ 12 X˜ 22
X˜ 13 X˜ 23
…
A2
X˜ 11 X˜ 21
…
X˜ 1n X˜ 2n
A3
X˜ 31
X˜ 32
X˜ 33
…
X˜ 3n
…
… X˜ m1
… X˜ m2
… X˜ m3
…
… X˜ mn
A1
Am
…
The fuzzy TOPSIS method’s stages are presented below: 1. In first stage the linguistic variables for decisions and weights of criteria are presented with fuzzy trapezoidal numbers (Tables 2 and 3).
Table 2. The linguistic variables for the importance of criterion weights. Linguistic Variables
Trapezoidal Fuzzy Numbers
Very Low (VL)
(0, 0.1, 0.2.0.3)
Low (L)
(0.1, 0.3, 0.45, 0.7)
Medium (ML)
(0.4, 0.5, 0.7, 0.8)
High (H)
(0.5, 0.6, 0.75, 0.85)
Very High (VH)
(0.6, 0.7, 0.8, 0.9)
A normalized matrix R˜ = (rij ), i = 1, 2, . . . m; j = 1, 2, . . . n is calculated. The calculation of the normalized matrix is realized by following formulas: aj∗ aj∗ aj∗ aj∗ aij bij cij dij , , , = ( , , , ), j ∈ J1 , j ∈ J , r ˜ r˜ij = ij dj∗ dj∗ dj∗ dj∗ dij cij bij aij dj∗ = maxi dij , j ∈ J , aj∗ = mini aij , j ∈ J1 where J and J1 present the set of maximization criteria and set of minimization criteria respectively.
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V. H. Salimov Table 3. The linguistic variables for the decisions. Linguistic Variables
Trapezoidal Fuzzy Numbers
Very Poor (VP)
(0, 1, 2, 3)
Poor (P)
(1, 3, 4.7)
Medium Poor (MP)
(4, 5, 7, 8)
Good (G)
(7, 8, 9.9.25)
Very Good (VG)
(9, 9.25, 9.5, 10)
2. Calculate of the weighted decision matrix V˜ = vij , i = 1, 2, . . . m; j = 1, 2, . . . n ∼
where v˜ ij =rij ⊗w˜ j ,i = 1, 2, . . . m; j = 1, 2, . . . n, and w˜ j are weights of criteria. 3. Determine of positive and negative ideal solutions: A+ = (˜v1+ , v˜ 2+ , v˜ 3+ , . . . . . . .˜vn+ ), A− = (˜v1− , v˜ 2− , v˜ 3− , . . . . . . .˜vn− ), where v˜ 1+ = (1, 1, 1, 1), v˜ 1− = (0, 0, 0, 0). 4. The distances between positive and negative ideal solutions and actual decisions are calculated by formulas: di+ = nj=1 d (˜vij+ , v˜ j+ ), di− = nj=1 d (˜vij− , v˜ j− ), j = 1,2,……m, where the distance is calculated by formula: 1 ˜ ˜ [(a1 − b1 )2 + (a2 − b2 )2 + (a3 − b3 )2 + (a4 − b4 )2 D A, B = 4 5. Calculate closeness coefficient for all alternatives:
CC i =
di−
di− + di+
, i = 1, 2, . . . .m
6. Determine acceptance level of decisions (Table 4). Table 4. Acceptance criteria. Closeness Coefficient(CCi)
Evaluation
CC i ∈ [0, 0.2)
Not recommended
CC i ∈ [0.2, 0.4)
Recommended with high risk
CC i ∈ [0.4, 0.6)
Recommended with low risk
CC i ∈ [0.6, 0.8)
Acceptable
CC i ∈ [0.8, 1.0)
Accepted and preferred
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7. The decision with maximum of closeness coefficient is selected.
3 Server Selection Problem Solving The are many papers where server selection problems are considered [21, 22]. In this paper we consider this problem with 9 criteria. Some of them are objective criteria so are measurable. The used objective criteria are as follows: • • • • •
Price RAM capacity (GB) Processor speed (GHz) Number of cores Hard disk capacity (TB).
The subjective criteria aren’t measurable like objective ones. They are defined based on human expertise. Subjective criteria: • • • •
Reliability Security Scalability Usability.
The selection problem is implemented in 2 stages: in first stage on base of objective criteria are selected group of acceptable by capacity servers, in second stage are selected optimal server according to subjective criteria. Assume that first stage is completed and the set of acceptable alternatives were formed. In this paper we consider implementation of second stage. The Linguistic decision matrix is shown in Table 5. Table 5. Linguistic decision matrix. C1 , ML
C2 , H
C3 , VH
C4 , H
A1
VG
G
VG
MP
A2
MP
G
G
VG
A3
G
VG
MP
G
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The trapezoidal fuzzy numbers-based values are presented below (Tables 6 and 7): Table 6. The results of conversion linguistic data into trapezoidal fuzzy numbers. C1
C2
C3
C4
A1
(9, 9.25, 9.5, 10)
(7, 8, 9.9.25)
(9, 9.25, 9.5, 10)
(4, 5, 7, 8)
A2
(0.4, 0.5, 0.7, 0.8)
(7, 8, 9.9.25)
(4, 5, 7, 8)
(9, 9.25, 9.5, 10)
A3
(7, 8, 9.9.25)
(9, 9.25, 9.5, 10)
(4, 5, 7, 8)
(7, 8, 9.9.25)
Table 7. Weights of criteria. (0.4, 0.5, 0.7, 0.8)
(0.5, 0.6, 0.75, 0.85)
(0.6, 0.7, 0.8, 0.9)
(0.5, 0.6, 0.75, 0.85)
The results of computations are given in Tables 8, 9, 10 and 11. Table 8. The results of calculations of normalized matrix by corresponding formulas. C1
C2
C3
A1
(0.40, 0.42, 0.43, 0.44)
(0.70, 0.80, 0.90, 0, 93)
(0.9, 0.93, 0.95, 1)
C4 (0.4, 0.5, 0.7, 0.8)
A2
(0.5, 0.57, 0.8, 1)
(0.70, 0.78, 0.88, 1)
(0.7, 0.8, 0.9, 0.93)
(0.9, 0.925, 0.95, 1)
A3
(0.43, 0.44, 0.5, 0.57)
(0.90, 0.74, 0.76, 0.78)
(0.4, 0.5, 0.7, 0.8)
(0.7, 0.8, 0.9, 0.925)
Table 9. The results of weighted matrix. C1
C2
A1
(0.16, 0.21, 0.3, 0.36)
(0.35, 0.48, 0.68, 0.79) (0.54, 0.65, 0.76, 0.9)
C3
A2
(0.2, 0.29, 0.56, 0.8)
(0.35, 0.48, 0.68, 0.79) (0.42, 0.56, 0.72, 0.83) (0.45, 0.56, 0.71, 0.85)
A3
(0.17, 0.22, 0.35, 0.46) (0.45,0.56,0.71,0.85)
(0.24.0.35, 0.56, 0.72)
C4 (0.20, 0.30, 0.53.0.68) (0.35, 0.48, 0.68, 0.79)
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Table 10. The results of calculation distance between decisions and the ideal solutions.
d (A1 , A+ ) d (A2 , A+ ) d (A3 , A+ ) d (A1 , A− ) d (A2 , A− ) d (A3 , A− )
C1
C2
C3
C4
0.75
0.73
0.49
0.99
0.95
0.73
0.62
0.62
1.22
0.62
0.92
0.73
0.52
1.16
1.37
0.92
1.02
1.16
1.25
1.26
0.62
1.26
0.98
1.16
Table 11. The results of closeness coefficients calculations. di+
di−
CC i
Ranking
A1
2.67
4.59
0.63
1
A2
3.02
4.52
0.60
2
A3
3.09
4.46
0.59
3
All alternatives are determined as “Acceptable” (Table 4). The analysis of closeness coefficients shows that optimal decision is alternative A1 .
4 Conclusion Today the computer servers play very important role. The paper is dedicated to the problem of computer server selection. The problem is defined as MCDM. All criteria is divided in two groups: objective and subjective. The selection problem for subjective criteria was solved on base of fuzzy TOPSIS method. All stages of implementation are presented in details.
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Fuzzy Inference Based Quadcopter Flight Regulation Under Overland Monitoring Tunjay Habibbayli1,2(B)
and Murad Aliyev3
1 Institute of Control Systems of ANAS, Vahabzadeh Street 9, AZ1141 Baku, Azerbaijan
[email protected]
2 Institute of Information Technology of ANAS, Vahabzadeh Street 9, AZ1141 Baku, Azerbaijan 3 Intelpro LLC, Jabbarly Street Globe Center 609, AZ1065 Baku, Azerbaijan
Abstract. Some territories where economic activity is carried out are characterized by the presence of mountain and forest tracts. To provide information support for the development of infrastructure and agriculture in these areas, in some cases overland monitoring using unmanned technologies is required. In this regard, an algorithm for the formation of a 3D trajectory of a quadcopter during overland piloting in a mountainous and wooded landscape is proposed, which implies autonomous maneuvering to overcome possible obstacles. As a basic model, it is proposed to use a fuzzy inference system with input characteristics in the form of linguistic variables that reflect fuzzy sectors of space, within which the presence of obstacles and the distance to them are interpreted verbally, that is, in the form of terms of corresponding input linguistic variables. Overcoming obstacles is supposed to be performed based on fuzzy conclusions of the proposed system, formulated as terms of output linguistic variables, which reflect changes in the angle of rotation in the horizontal plane, flight altitude and traverse speed of the quadcopter. The given paper analyzes the results of the model behavior for different scenarios of the terms of the input linguistic variables. Keywords: Quadcopter · Overland monitoring · Fuzzy set · Membership function · Fuzzy inference
1 Introduction The current level of unmanned technologies actualizes the use of drones for overland monitoring of infrastructure and agriculture, characterized by large mountainous and forested areas. For overland monitoring of various objects, it is preferable to use rotarywing drones (quadcopters) [1], which are the most popular among researchers despite their own limitations. The advantage of the quadcopter is that each of its four propellers provides raising force and high flight stability. Nevertheless, as a rather complex technical device, a quadcopter is characterized by flight dynamics that are difficult to formalize due to its “sensitivity” to the influence of external factors [1, 2]. Therefore, solving the problem of controlling a quadcopter for overland monitoring in the presence of natural
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 372–381, 2023. https://doi.org/10.1007/978-3-031-25252-5_50
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obstacles in a mountainous-wooded landscape and hard-to-reach places is interesting both from scientific and practical points of view. In this regard, of particular interest are the technological solutions of DJI, which produces compact quadcopters with intelligent flight modes [3].
2 Problem Formulation In the absence of the necessary information support and, as a result, the impossibility of constructing an accurate mathematical model, the application of fuzzy logic methods in quadcopter control is specified by the capabilities, which provide for compiling heuristic knowledge and using intuitive data. Currently, fuzzy approaches to solving problems of automatic control are considered in two aspects. The first is related to the creation of a classifier of situations that forms the goals and objectives of the functioning of a dynamic system. The second approach involves direct fuzzy regulation of the variables of the control object. Based on these prerequisites, it becomes obvious the importance and actuality of developing software for the autonomous movement of the quadcopter under overland piloting in mountainous and wooded areas, including automatic maneuvering to bypass possible obstacles. In the context of the foregoing, an algorithm is proposed for creating a “smart” obstacle avoidance system for quadcopter autopiloting, based on the use of the fuzzy inference.
3 Fuzzy Inference System for Quadcopter Autopilot Regulation The DJI Mavic 2 quadcopter is equipped with six sensors for detecting obstacles in all directions, which ensures high-quality drone performance even in the most difficult situations. Thanks to the Flight Autonomy autopilot system, all data are transmitted and processed permanently in real time. In [4], an algorithm for forming the flight path of a quadcopter was proposed using a fuzzy inference system based on expert and empirical data analysis. It provides overland autopiloting of a quadcopter equipped with obstacle detection sensors in five frontal viewing sectors (Fig. 1).
Fig. 1. Obstacle visibility sectors: a) side view, b) top view
To form the schedule for overland autopiloting of the quadcopter in five directions, a bounded set of logically consistent rules is considered in the form of the information fragments such as:
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d 1 : “If any obstacle is not detected on the flight path of the quadcopter or it is too far away, then there is no need to change direction, height and to reduce speed”; d 2 : “If the sensor detects an obstacle at a medium distance along the flight path of the quadcopter and the sector on the left is free, then it is necessary to lose velocity to an average value and to turn slightly to the left without changing the height”; d 3 : “If the sensor detects an obstacle at a close distance along the flight path of the quadcopter and the sector on the left is free, then it is necessary to lose velocity to a minimum, and to turn sharply to the left without changing the height”; d 4 : “If the sensor detects an obstacle at a medium distance along the flight path of the quadcopter, there is also an obstacle in the left sector at a not remote distance and the sector on the right is free, then it is necessary to lose velocity to an average value, and to turn slightly to the right without changing the height”; d 5 : “If the sensor detects an obstacle at a close distance along the flight path of the quadcopter, there is also an obstacle in the left sector at a not remote distance and the sector on the right is free, then it is necessary to lose velocity to a minimum, and turn sharply to the right without changing the height”; d 6 : “If the sensor detects an obstacle at an average distance along the flight path of the quadcopter, there are also obstacles in the left and right sectors at a not remote distance, and the upper sector is free, then it is necessary to lose velocity to an average value, and slightly increase the flight altitude (pitch-up) without yaw”; d 7 : “If the sensor detects an obstacle at a close distance along the flight path of the quadcopter, there are also obstacles in the left and right sectors at a not remote distance, and the upper sector is free, then it is necessary to lose velocity to a minimum, and sharply increase the flight altitude without yaw”; d 8 : “If the sensor detects an obstacle at an average distance along the flight path of the quadcopter, there are also obstacles in the left, right and upper sectors at a non-remote distance, and the lower sector is free, then it is necessary to lose velocity to an average value, and slightly reduce the flight altitude (dive) without yaw”; d 9 : “If the sensor detects an obstacle at a close distance along the flight path of the quadcopter, there are also obstacles in the left, right and upper sectors at a not remote distance, and the lower sector is free, then it is necessary to lose velocity to a minimum, and sharply reduce the flight altitude without yaw”; d 10 : “If the sensor detects an obstacle at an average distance along the flight path, and an obstacle is also detected at an average distance to the left, obstacles are detected at a not remote distance to the right, below and above, then it is necessary to lose velocity to an average value while maintaining the course and flight altitude”; d 11 : “If the sensor detects an obstacle at a close distance along the flight path of the quadcopter, and an obstacle is also detected at an average distance to the left, obstacles are detected at a not remote distance to the right, below and above, then it is necessary to lose velocity to a minimum and turn sharply to the left without changing the height”;
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d 12 : “If the sensor detects an obstacle at a medium distance along the flight path of the quadcopter, and an obstacle is detected a close distance to the left, an obstacle is detected at an average distance to the right, and obstacles are detected at a not remote distance from below and above along the course, then it is necessary to lose velocity to an average value and turn sharply to the left without changing the course and height”; d 13 : “If the sensor detects an obstacle at a close distance along the flight path of the quadcopter, and an obstacle is also detected at a close distance to the left, an obstacle is detected at an average distance to the right, and obstacles are detected from below and above along the course at a not remote distance, then it is necessary to lose velocity to minimum and turn sharply to the right without changing the height”; d 14 : “If the sensor detects an obstacle at a medium distance along the flight path, an obstacle is detected at a close distance to the left, an obstacle is also detected at a close distance to the right, an obstacle is detected at an average distance from above, and an obstacle is detected at a not remote distance from below, then it is necessary to lose velocity to an average value and turn sharply to the right without changing the course and height”; d 15 : “If the sensor detects an obstacle at close distance along the flight path of the quadcopter, the obstacles are detected at an average distance to the left and to the right, as well as an obstacle is detected at a not remote distance from above, then it is necessary to lose velocity to a minimum and sharply increase flight altitude without yaw”; d 16 : “If the sensor detects an obstacle at a medium distance along the flight path, obstacles are detected at a close distance to the left, right and higher along the course, and an obstacle is detected at an average distance below the course, then it is necessary to lose velocity to an average value without changing the course and height”; d 17 : “If the sensor detects the obstacles at close distance along the flight path of the quadcopter, as well as to the left, right and above, however, an obstacle is detected at an average distance below the course, then it is necessary to lose velocity to a minimum, sharply reduce the flight altitude without yaw”; d 18 : “If an obstacle is detected at a medium distance along the flight path, obstacles are detected at a close distance to the left, right, above and below the course, then it is necessary to lose velocity to an average value without changing the course and height”; d 19 : “If in all sectors of the view the detected obstacles are at a close distance, then it is necessary to lose velocity to a minimum and turn sharply to the left without changing the height”. Maneuvering to the left (or to the right, which is also appropriate) from the frontal impasse caused by the presence of obstacles in all five sectors of view (Rule d19), the quadcopter continues to move and, thereby, creates a new flight path for itself in accordance with the regulations established by rules d 1 ÷ d 19 . Thus, analysis of all possible scenarios of collision with obstacles made it possible to form a complete set of linguistic variables (Table 1) and rules for forming a Fuzzy Inference System (FIS) that regulates the behavior of a quadcopter during overland piloting.
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T. Habibbayli and M. Aliyev Table 1. Input and output linguistic variables of the FIS and their terms.
Inputs Symbol
Variable name
Universe
Term set
x1
The remoteness of the obstacle in the direction of flight
[0, 1]
{X 11 = significant, X 12 = average, X 13 = unsignificant}
x2
The remoteness of the obstacle to the left of the direction
[0, 1]
{X 21 = significant, X 22 = average, X 23 = unsignificant}
x3
The remoteness of the obstacle to the right of the direction
[0, 1]
{X 31 = significant, X 32 = average, X 33 = unsignificant}
x4
The remoteness of the obstacle to the higher of the direction
[0, 1]
{X 41 = significant, X 42 = average, X 43 = unsignificant}
x5
The remoteness of the obstacle to the lower of the direction
[0, 1]
{X 51 = significant, X 52 = average, X 53 = unsignificant}
y1
Airspeed
[0, 1]
{Y 11 = full, Y 12 = average, Y 13 = zero}
y2
Yaw
[−0.5, 0.5]
{Y 21 = sharply to the left, Y 22 = slightly to the left, Y 23 = is absent, Y 24 = slightly to the right, Y 25 = sharply to the right}
y3
Pitch
[−0.5, 0.5]
{Y 31 = sharply up, Y 32 = slightly up, Y 33 = is absent, Y 34 = slightly down, Y 35 = sharply down}
Outputs
The corresponding FIS is formed by the following rules in symbolic form: d 1 : (x 1 =X 11 ) ⇒ (y1 =Y 11 ) & (y2 =Y 23 ) & (y3 =Y 33 ); d 2 : (x 1 =X 12 ) & (x 2 =X 21 ) ⇒ (y1 =Y 12 ) & (y2 =Y 22 ) & (y3 =Y 33 ); d 3 : (x 1 =X 13 ) & (x 2 =X 21 ) ⇒ (y1 =Y 13 ) & (y2 =Y 21 ) & (y3 =Y 33 ); d 4 : (x 1 =X 12 ) & (x 2 =¬X 21 ) & (x 3 =X 31 ) ⇒ (y1 =Y 12 ) & (y2 =Y 24 ) & (y3 =Y 33 ); d 5 : (x 1 =X 13 ) & (x 2 =¬X 21 ) & (x 3 =X 31 ) ⇒ (y1 =Y 13 ) & (y2 =Y 25 ) & (y3 =Y 33 ); d 6 : (x 1 =X 12 ) & (x 2 =¬X 21 ) & (x 3 =¬X 31 ) & (x 4 =X 41 ) ⇒ (y1 =Y 12 ) & (y2 =Y 23 ) & (y3 =Y 34 ); d 7 : (x 1 =X 13 ) & (x 2 =¬X 21 ) & (x 3 =¬X 31 ) & (x 4 =X 41 ) ⇒ (y1 =Y 13 ) & (y2 =Y 23 ) & (y3 =Y 35 ); d 8 : (x 1 =X 12 ) & (x 2 =¬X 21 )& (x 3 =¬X 31 )& (x 4 =¬X 41 )& (x 5 =X 51 ) ⇒ (y1 =Y 12 ) & (y2 =Y 23 ) & (y3 =Y 32 ); d 9 : (x 1 =X 13 )&(x 2 =¬X 21 )& (x 3 =¬X 31 ) & (x 4 =¬X 41 ) & (x 5 =X 51 ) ⇒ (y1 =Y 13 ) & (y2 =Y 23 ) & (y3 =Y 31 ); d 10 : (x 1 =X 12 ) & (x 2 =X 22 ) & (x 3 =¬X 31 )& (x 4 =¬X 41 )& (x 5 =¬X 51 )⇒ (y1 =Y 12 )& (y2 =Y 23 ) & (y3 =Y 33 );
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d 11 : (x 1 =X 13 ) & (x 2 =X 22 )& (x 3 =¬X 31 )& (x 4 =¬X 41 )& (x 5 =¬X 51 )⇒ (y1 =Y 13 ) & (y2 =Y 21 ) & (y3 =Y 33 ); d 12 : (x 1 =X 12 ) & (x 2 =X 23 )& (x 3 =X 32 ) & (x 4 =¬X 41 ) & (x 5 =¬X 51 ) ⇒ (y1 =Y 12 ) & (y2 =Y 23 ) & (y3 =Y 33 ); d 13 : (x 1 =X 13 ) &(x 2 =X 23 ) & (x 3 =X 32 ) & (x 4 =¬X 41 ) & (x 5 =¬X 51 ) ⇒ (y1 =Y 13 ) & (y2 =Y 25 ) & (y3 =Y 33 ); d 14 : (x 1 =X 12 ) & (x 2 =X 23 ) & (x 3 =X 33 ) & (x 4 =X 42 ) & (x 5 =¬X 51 ) ⇒ (y1 =Y 12 ) & (y2 =Y 23 ) & (y3 =Y 33 ); d 15 : (x 1 =X 13 ) & (x 2 =X 23 ) & (x 3 =X 33 ) & (x 4 =X 42 ) & (x 5 =¬X 51 ) ⇒ (y1 =Y 13 ) & (y2 =Y 23 ) & (y3 =Y 35 ); d 16 : (x 1 =X 12 ) & (x 2 =X 23 ) & (x 3 =X 33 ) & (x 4 =X 43 ) & (x 5 =X 52 ) ⇒ (y1 =Y 12 ) & (y2 =Y 23 ) & (y3 =Y 33 ); d 17 : (x 1 =X 13 ) & (x 2 =X 23 ) & (x 3 =X 33 ) & (x 4 =X 43 ) & (x 5 =X 52 ) ⇒ (y1 =Y 13 ) & (y2 =Y 23 ) & (y3 =Y 31 ); d 18 : (x 1 =X 12 ) & (x 2 =X 23 ) & (x 3 =X 33 ) & (x 4 =X 43 ) & (x 5 =X 53 ) ⇒ (y1 =Y 12 ) & (y2 =Y 23 ) & (y3 =Y 33 ); d 19 : (x 1 = X 13 ) & (x 2 = X 23 ) & (x 3 = X 33 ) & (x 4 = X 43 ) & (x 5 = X 53 ) ⇒ (y1 = Y 13 ) & (y2 = Y 21 ) & (y3 = Y 33 ) To implement the FIS that provides autopiloting of the quadcopter according to the formalized schedule, it is necessary to reflect the introduced linguistic variables to the set of their corresponding real numbers by setting membership functions, that is, fuzzify the terms of all input and output linguistic variables. For this purpose, the advantage of one element over another relative to the property of the given fuzzy subset of the discrete universe U = {0, 0.1, 0.2, …, 1} is estimated. According to the Saaty’s 9-point scale [5], for example, the matrix of paired comparisons of the elements of the universe for identifying the membership function of the fuzzy set “unsignificant” as one of the terms of the input linguistic variable “Remoteness of obstacles” (Table 1) is presented as follows.
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where, if the preference of the i-th number over the j-th has one of the presented values, then the assessment of the preference of the j-th number over the i-th has the inverse value (i, j = 0, 1, 2, …, 10). Finding the eigenvector (μ0 , μ1 , …, μ10 ) from the equation (X 13 – λE)·μ = 0, the values of the membership function μ(ui ) of the fuzzy set X 13 are obtained, which are summarized in Table 2. Each such membership function can be approximated as given in a tabular form and obtain a graphical representation of the corresponding fuzzy set. Table 2. The values of the membership function of the fuzzy set unsignificant. Remoteness 0 0.1 0.2 0.3 μ(ui )
1 1
1
0.4
0.5
0.6
0.7
0.8
0.9
1
0.9865 0.0113 0.0098 0.0064 0.0035 0.0021 0.0008 0.0002
In MATLAB\FIS notation, all membership functions were established empirically. In particular, the input and output characteristics of the model are shown in Fig. 2 and Fig. 3, respectively.
Fig. 2. Terms of input linguistic variable “The remoteness of the obstacle in the course”
Fig. 3. Terms of output linguistic variables: y1 – airspeed, y2 – yaw, y3 – pitch.
As a result, using the interactive window of the graphical interface of the MATLAB\FIS editor (Fig. 4), it was possible to generate the products, which are summarized in Table 3, and different flight scenarios, which is presented in Table 4.
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Table 3. The products generated by MATLAB\FIS editor. №
Inputs
Outputs
x1
x2
x3
x4
x5
y1
y2
y3
1
0.95
0.50*
0.50
0.50
0.50
0.855
0
0
2
0.50
0.95
0.50
0.50
0.50
0.350
−0.200
0
3
0.10
0.90
0.50
0.50
0.50
0.013
−0.411
0
4
0.50
0.50
0.90
0.50
0.50
0.350
0.200
0
5
0.10
0.50
0.90
0.50
0.50
0.013
0.411
0
6
0.50
0.50
0.50
0.90
0.50
0.350
0
0.200
7
0.10
0.50
0.50
0.90
0.50
0.013
0
0.411
8
0.50
0.50
0.50
0.50
0.90
0.350
0
−0.200
9
0.10
0.50
0.50
0.50
0.90
0.013
0
−0.411
10
0.50
0.50
0.40
0.40
0.40
0.350
0
0
11
0.10
0.50
0.50
0.50
0.50
0.013
−0.411
0
12
0.50
0.10
0.50
0.50
0.50
0.350
0
0
13
0.10
0.10
0.50
0.50
0.50
0.013
0.411
0
14
0.50
0.10
0.10
0.50
0.50
0.350
0
0
15
0.10
0.10
0.10
0.50
0.50
0.013
0
0.411
16
0.50
0.10
0.10
0.10
0.50
0.350
0
0
17
0.10
0.10
0.10
0.10
0.50
0.013
0
−0.411
18
0.50
0.10
0.10
0.10
0.10
0.350
0
0
19
0.10
0.10
0.10
0.10
0.10
0.013
−0.411
0
* The absence of obstacles determines the use of the average value 0.5 on the universe [0, 1].
Table 4. Obstacle maneuvering scenarios for quadcopter autopiloting. №
Inputs
Outputs
x1
x2
x3
x4
x5
y1
y2
y3
1
0.433
0.291
0.628
0.076
0.961
0.350
0.055
2
0.611
0.824
0.460
0.862
0.855
0.380
−0.194
0.000
3
0.374
0.622
0.139
0.750
0.702
0.337
−0.154
0.215
4
0.712
0.738
0.568
0.438
0.469
0.854
0.000
0.000
5
0.922
0.535
0.320
0.107
0.102
0.855
0.000
0.000
30
0.605
0.961
0.766
0.756
0.306
0.367
−0.196
0.000
31
0.702
0.644
0.219
0.000
0.740
0.851
−0.001
−0.190
… −0.001 (continued)
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T. Habibbayli and M. Aliyev Table 4. (continued)
№
Inputs x1
x2
x3
x4
x5
y1
32
0.433
0.629
0.741
0.405
0.838
0.350
0.144
0.000
33
0.465
0.793
0.395
0.745
0.086
0.350
−0.200
0.000
34
0.065
0.004
0.789
0.553
0.318
0.013
0.411
0.000
35
0.026
0.245
0.480
0.651
0.787
0.014
0.000
−0.195
Outputs y2
y3
Fig. 4. Graphical interface of the MATLAB\FIS editor for viewing rules.
4 Conclusion Complexity, multicoupling, nonlinearity, the presence of uncertain parameters of such technical objects as a quadcopter necessitates the search for ways to solve control problems alternative to the well-known classical P, PI, PID controllers. The result of the expert-empirical research carried out in this article is to get an idea of how to control quadcopters under overland monitoring of the area, the features of their practical application, advantages, and disadvantages. It seems to us that the improvement of results should be achieved using neural and neuro-fuzzy modeling methods. For example, any membership function given at key points obtained using the Saaty’s 9-point scale can be easily approximated using a three-layer feedforward neural network. Based on the scenarios presented in Table 4, it is possible to form a neuro-fuzzy controller capable of providing overland autopiloting of a quadcopter under different obstacles.
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References 1. Michael, D.S.: Simulation, and control of a quadrotor unmanned aerial vehicle (2011). http:// uknowledge.uky.edu/gradschool_theses/93 2. Sharma, A., Barve, A.: Controlling of quadrotor UAV using PID controller and fuzzy logic controller (2012). https://researchtrend.net/ijeece/pdf/8%20ASTHA%20LNCT.pdf 3. DJI drones: types and capabilities of the brand’s aircraft. https://korabelov.info/2021/11/220 373/drony-dji-vidy-i-vozmozhnosti-letatelnyh-apparatov-brenda/. (in Russian) 4. Neretina, V.V., Nafikov, I.R.: Formation of the UAV trajectory during overland monitoring of forest ecosystems based on the apparatus of fuzzy logic. https://apni.ru/article/845-formirova nie-traektorii-dvizheniya-bpla 5. Saaty, T.L., Vargas, L.G.: The Logic of Priorities. Kluwer Nijhoff Publishing, Massachusetts (1982)
Fuzzy Logic Analysis of Parameters Affecting Students’ Satisfaction with Their Life at University M. A. Salahli1(B)
, T. Gasimzade2 , V. Salahli3 and A. Guliyev4
, F. Alasgarova4
,
1 Department of Computer and Instructional Technology Education, Çanakkale Onsekiz
Mart University, Canakkale, Turkey [email protected] 2 Department of Instrument Making Engineering, Azerbaijan State Oil and Industry University, 20 Azadlig Avenue, AZ 1010 Baku, Azerbaijan 3 Department of Computer Engineering, Odlar Yurdu University, Koroglu Rehimov Street, 13, AZ 1072 Baku, Azerbaijan 4 Department of Information Technology and Natural Sciences, Management University, Koroglu Rehimov Street, 822/23, AZ 1072 Baku, Azerbaijan
Abstract. There has been a rapid increase in the number of universities in recent years. This situation causes an increase in the competition among universities in terms of attracting students. Since the factors that express the satisfaction of the students with the university they are studying have a very serious effect on the university preference, studies on the analysis of these factors are of great importance. In this study, the factors affecting students’ satisfaction with their university life were investigated. These factors are divided into 3 groups as department-related, university-related and city-related factors. In the study, using fuzzy logic methods, the effect of various satisfaction factors on the general satisfaction value of the students was determined. The weight of the factors in the formation of satisfaction levels is expressed with fuzzy values. Fuzzy inference method was applied to determine the relationships between the factors. Keywords: University life of students · Student’s satisfaction · Satisfaction factors · Fuzzy inference rules
1 Introduction With the increase in the number of universities, the competition between universities is also increasing. In this respect, it is very important for universities to increase their opportunities to attract students. One of the ways to increase the attractiveness of universities is to increase students’ satisfaction with the university they attend. In the study [1], 6 satisfaction factors were determined in a scale developed to evaluate student satisfaction. These are satisfaction with social and cultural activities; satisfaction with the management of research and development activities; Satisfaction © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 382–390, 2023. https://doi.org/10.1007/978-3-031-25252-5_51
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with education monitoring, evaluation and quality management; Satisfaction with educational process and practices; Satisfaction with education and instructional design; and Satisfaction with the educational environment and resources. The study [2] examines the role of satisfaction on students’ academic performance and investigates the relationship between satisfaction of students and academic performance and explores other factors that contribute academic performance. The study found that there is strong relationship between satisfaction of students and academic performance, and satisfaction promotes both academic achievement and student retention. The factors affecting student satisfaction analysed in [3]. In the study, the relationship between student satisfaction and teacher-student relationship, teachers’ academic preparation, campus facilities and the experiences provided by the institute to students were investigated. In a study investigating the satisfaction levels of students of a faculty [4], it was determined that the most important factors affecting student satisfaction were equipment and infrastructure, academic staff, catering services and location. Researches have also been conducted on the analysis of various dimensions of student satisfaction. In the [5] the differences in life satisfaction dimensions between on-campus and off-campus indicators related to student housing were analysed and it was determined how life satisfaction factors were formed. The relationship between education service quality and student satisfaction in state universities was investigated in [6]. The results of the study [7] showed that only four factors had a significant positive effect on foreign students’ satisfaction with their higher education. These four factors are: education, security, the image and prestige of the institution and student’s preparation before going abroad. Qualitative assessments are mostly used for satisfaction factors. For this reason, it is seen that fuzzy logic methods, which are quite suitable for qualitative evaluations [8, 9], are widely used in studies to determine the satisfaction levels of students with university life. In the study of [10], the degree of satisfaction of international students with the chosen educational environment was determined by Fuzzy Importance-Performance Analysis. A descriptive analysis of student satisfaction was conducted in [11] to discover the main variables affecting the overall online teaching-learning process using classification trees and fuzzy inference methods. The study [12] aimed to determine the quality level of academic services to students by measuring the satisfaction levels of students with academic services. Mamdani fuzzy inference method was used for the analysis of academic services.
2 Research Problem It is important in several ways to learn the satisfaction levels of university students from the educational institution they study. As said above, the increase in the number of higher education institutions has led to an increase in competition among them. Good education alone is not enough to attract more students. The socio-cultural opportunities of the campuses, where students spend a few years of their lives, and the service facilities they offer are important factors in the school preferences of the students. Investigation of student satisfaction can give important clues about the school choice of students. The results of learning about student satisfaction can give important ideas for increasing the morale and motivation of students. The good psychological state, morale and
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motivation of the students also have a positive effect on their education. It is not possible to think of the university life of the students separately from the city where the university is located. Especially in small cities, students have a great impact on the social and commercial life of the city. Many factors such as the social-cultural structure of the city, quality of life, transportation, rented house prices also have a significant impact on students’ satisfaction. Learning these effects is important for the management of cities. Studies show that the level of satisfaction varies according to personality traits. These features may differ depending on the environment in which the student grew up, family situation, economic conditions, and circle of friends. Another group of factors that determine students’ satisfaction levels is related to the department the student is studying. Having to choose the department that he does not want according to his score, the opportunity to find a job suitable for his branch after graduating from school, the level of communication with the department teachers affects the level of satisfaction. In conclusion, we can say that the concept of satisfaction is a complex concept that can be evaluated by the city of the student, the social, economic, cultural characteristics of the university, the department and the personal characteristics of the student. The aim of this study is to determine the satisfaction levels of the students of the Computer and Teacher Technologies Education Department of the Canakkale Onsekiz Mart University. The study takes into account the characteristics of CEIT departments, having some specific characteristics. Changing the score type in student admissions to CEIT departments, increasing the lower limit of entrance scores to the department, and reducing the quota for appointment of teachers for the field of educational technologies decreased the preference for CEIT departments. CEIT department is not in the first preference list for the majority of department students. Many students chose CEIT because their scores were not enough for the more prestigious computer engineering branch. Of course, this forced choice affects their motivation, indirectly their satisfaction with the department. Computer-oriented courses in CEIT departments are not much easier than Computer Engineering Department courses. Despite this, it is very difficult for CEIT graduates to find a job at the same rate as Computer engineering graduates. The fear of not being able to find a job in the future has a negative impact on the satisfaction levels of CEIT students. The fact that there are no questions about the field in the exams for teacher appointments causes the students to lose their interest in the field courses. They cannot find an answer to the question “If my computer knowledge is not necessary, why should I learn the field courses (for example, programming course) that are more difficult”. This leads to a decrease in student satisfaction.
3 Data Collection and Data Analysis As mentioned above, many factors affect students’ satisfaction levels. It is difficult to consider and analyse all these factors in a study. In this sense, in this study, we tried to consider the factors specific to the CEIT department of Çanakkale OnSekiz Mart University. The effect of the city’s characteristics on the satisfaction levels of university students was evaluated within the scope of the research. We can divide the satisfaction factors considered in the study into 3 groups: The first group of factors is related to the CEIT department and includes: The effect of the department not being one of the students’ first preferences (FD1); Fear of being able
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to find a job in the future(FD2); Computer laboratories and internet (FD3); Prestige of the branch (FD4); Syllabus and course content are difficult for students (FD5); Attitude of department staff to students (FD6); The teaching staff have sufficient knowledge and experience (FD7); Attracting students to participate in projects and scientific activities (FD8). The second group of factors is related to the University and includes: Prestige of the University (FU1); University location (FU2); University staff-student relations (FU3); Library facility (FU4); Cafeteria, canteen, recreation facilities (variety, quality, price, and accessibility) (FU5); Student-oriented activities (FU6). The third group of factors is related to the city and includes: Safety (FC1); Accommodation (dormitory and rental facilities, price, distance from school, accessibility) (FC2); Transport (FC3); Sightseeing, entertainment, social interaction, sportive, cultural activity opportunities (FC4): Service (variety, price, quality, accessibility (FC5). A questionnaire containing these factors was prepared and distributed to the 74 students of the CEIT department. For evaluation. Students were asked to make the following evaluations: – Student satisfaction for each factor (SSF); – Weight of each factor in determining student satisfaction level (WSF); – Students’ level of satisfaction with university life (overall satisfaction value-OS). Students were asked to evaluate the parameters of SSF, WSF and OS in the range of [0, 10]. A value 0 for SSF indicates the lowest satisfaction by factor and 10 indicates the highest. A value of 0 for WSF indicates that the factor is very unimportant and 10 is very important. A value 0 for the OS parameter indicates very low overall satisfaction, and 10 indicates very high overall satisfaction. The values of these parameters were converted to fuzzy values for the application of the fuzzy logic method a given in Figs. 1, 2 and 3.
Fig. 1. Fuzzy expressions of parameters SSF Fig. 2. Fuzzy expressions of parameters WSF
Tables 1 and 2 show that the majority of students were satisfied with the factors FD3, FD6, FD7, and FC1. We can interpret these results as follows. Students can do their homework and research without any problems in the computer laboratories of the department during and outside of class hours. The technical and software facilities of the computers ensure that the courses are carried out effectively. High-speed wired
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Fig. 3. Fuzzy expressions of parameters OS
Table 1. Number of students for each satisfaction score and weight value for the factor group 1. Factor name Factor’s satisfaction score (number of students)
Factor’s weight value (number of students)
Satisfied (S) Not be satisfied Very important Important (I) Less (NS) (VI) Important(LI) FD1
51
23
13
32
29
FD2
20
54
44
29
5
FD3
68
6
32
24
18
FD4
33
41
26
33
14
FD5
15
59
34
26
14
FD6
69
4
26
28
20
FD7
65
9
31
30
13
FD8
32
42
38
32
4
internet and Wi-Fi are available for students to access at the university. In this sense, it is reasonable for the students to give mostly positive answers about the FD3 factor. The data related to the FD6 factor show that the student-academic relations are at a good level in the department. The data on the FD7 factor proves that the academic staff have sufficient knowledge and experience. The fact that it is possible to walk around the city safely at any time of the day, and that negative cases are rarely encountered, showed that the students were highly satisfied with the FC factor. Regarding the FD2 factor, the students mostly expressed their dissatisfaction. The thought that they may have problems in finding a job in the future has a negative effect on the education process of the students. This negatively affects the university life of the students. Students stated that they were not satisfied with the curriculum and course content, so the course content was difficult (factor FD5). This is not because the course content is difficult or incomprehensible. The reason why students give negative answers is that most of them do not have sufficient high school knowledge. The majority of the students expressed their satisfaction with the public transportation in the city. This is due to the expensiveness of public transport and the long waiting times (factor FC3). The
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Table 2. Number of students for each satisfaction score and weight value for the factor group 3. Factor name Factor’s satisfaction score (number of student)
Factor’s weight value (number of students)
Satisfied (S) Not be satisfied Very important Important (I) Less (NS) (VI) important(LI) FC1
71
3
65
9
0
FC2
26
48
32
41
1
FC3
18
56
26
18
30
FC4
36
38
26
18
30
FC5
49
25
29
30
15
answers given by the students to the question “Are you satisfied with your university life” were as follows: 21 students stated that they were very satisfied, 30 students were moderately satisfied, and 23 students were not satisfied.
4 The Analysis Process of Satisfaction Values Using Fuzzy Logic The steps of the analysis process of satisfaction values are shown in the Fig. 4.
Fig. 4. The process of analysis of satisfaction factors values with fuzzy logic
We have explained the first 3 steps shown in Fig. 5 in the previous section. In this section, we will try to explain the next steps. Our aim in the analysis of satisfaction parameters using fuzzy logic is to determine the effect of satisfaction factors on the overall satisfaction value. Concretely, it was aimed to investigate the correlation between the satisfaction levels (SSFF), the weights of the factors (WSF), the overall satisfaction value (OS) and the effect of student evaluation on the overall satisfaction value by the SSFF factor (FS). For this purpose, the Apriori algorithm, which is one of the association rule methods, was used [13]. The method finds items that are frequently used together. Using the Apriori algorithm, we tried to answer the following question: Which value combinations of SSFF, WSF, OS and FS are more common in survey responses? For example, the combination of SSFF = “Satisfied”, WSF = “Very Important”, OS = “High”, and FS =” High” values is frequently encountered. In this case, we can say that if SSFF = “Satisfied”, WSF = “Very Important” and OS = “High”, the probability of FS getting the value of “High” is high.
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We used the results of applying the Apriori algorithm for the fuzzy logic inference method expressed by the IF THEN rules [14–16] as follows: FR1i : If SSF i = Satisfied AND WSF i = Very Important AND OS = High THEN FS i = High FR2i : If SSF i = Satisfied AND WSF i = Very Important AND OS = Medium THEN FS i = High FR3i : If SSF i = Satisfied AND WSF i = Very Important AND OS = Low THEN FS i = Low FR4i : If SSF i = Satisfied AND WSF i = Important AND OS = High HEN FS i = High FR5i : If SSF i = Satisfied AND WSF i = Important AND OS = Medium THEN FS i = High FR6 i : If SSF i = Satisfied AND WSF i = Important AND OS = Low THEN FS i = LOW FR7 i : If SSF i = Satisfied AND WSF i = Less Important AND OS = High THEN FS i = Medium FR8i : If SSF i = Satisfied AND WSF i = Less Important AND OS = Medium THEN FS i = Medium FR9i : If SSF i = Satisfied AND WSF i = Less Important AND OS = Low THEN FS i = Low FR10i : If SSF i = Not satisfied AND WSF i = Very Important AND OS = High THEN FS i = Low FR11i : If SSF i = Not satisfied AND WSF i = Very Important AND OS = Medium THEN FS i = Low FR12i :If SSF i = Not satisfied AND WSF i = Very Important AND OS = Low THEN FS i = High FR13i : If SSF i = Not satisfied AND WSF i = Important AND OS = High THEN FS i = Low FR14i : If SSF i = Not satisfied AND WSF i = Important AND OS = Medium THEN FS i = Low FR15i : If SSF i = Not satisfied AND WSF i = Important AND OS = Low THEN FS i = High FR16 i : If SSF i = Not satisfied AND WSF i = Less Important AND OS = High THEN FS i = Low FR17 i : If SSF i = Not satisfied AND WSF i = Less Important AND OS = Medium THEN FS i = Low FR18i : If SSF i = Not satisfied AND WSF i = Less Important AND OS = Low THEN FS i = Medium. The implementation of fuzzy inference rules on the FisPro application is given in Fig. 5. FisPro (Fuzzy Inference System Professional) application [17] was used to create fuzzy inference rules. FisPro is an open source portable software. It allows to create fuzzy inference systems and to use them for reasoning purposes. In accordance with the sample values in the Fig. 5, if the student’s satisfaction factor is 5, the weight of this factor is 3.8, and the overall satisfaction is 5, the overall satisfaction effect of this factor will be 4.432.
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Fig. 5. The implementation of fuzzy inference rules on the FisPro application (screen shoot)
5 Conclusion In the study, a questionnaire was applied to determine the satisfaction of the students from their university life in a university department. Parameters affecting satisfaction were expressed with fuzzy values. By applying fuzzy inference rules, satisfaction factors, the weight of the factors and the effect of these factors on overall satisfaction were investigated. For this purpose, fuzzy inference open source software application FisPro was used. Student opinions about a concrete university, department and city were reflected in the survey data. In this sense, it is possible to come up with completely different results within the scope of another research. The results of the research can help university, faculty and department managers and academicians to pay more attention to which subjects to increase student satisfaction and to take measures in this direction.
References 1. Sim¸ ¸ sek, H., Islim, Ö.F., Öztürk, N.: Student satisfaction as an indicator of quality in higher education: a scale development study. Trakya J. Education 9(3), 380–395 (2019). https://doi. org/10.24315/tred.441397 2. Dhaqane, M.K., Afrah, N.A.: Satisfaction of students and academic performance in Benadir University. J. Edu. Pract. 7(24), 59–63 (2016). https://doi.org/10.7176/JEP 3. Siming, L., Gao, J., Xu, D., Shaf, K.: Factors leading to students’ satisfaction in the higher learning institutions. J. Edu. Pract. 6(31), 114–118 (2015). https://doi.org/10.7176/JEP 4. Bakır, N.O., Arslan, F.M., Gegez, A.E.: Factors affecting satisfaction levels of university students: a research on marmara university business administration faculty students. Marmara Uni. J. Econ. Adminis. Sci. 38(1), 93–125 (2016). https://doi.org/10.14780/iibd.69451 5. Muslim, M.H., Karim, H.A., Abdullah, I.C.: Satisfaction of students’ living environment between on-campus and off-campus settings: a conceptual overview. Procedia - Social Behav. Sci. 68, 601–614 (2012). https://doi.org/10.1016/j.sbspro.2012.12.252 6. Muchiri, K.A., Tanui, E.K., Kalai, J.M.: Quality of academic resources and students’ satisfaction in public universities in Kenya. Int. J. Learn., Teach. Educ. Res. 15 (2016). https:// doi.org/10.26803/ijlter
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7. Ngamkamollert, T., Ruangkanjanases, A.: Factors influencing foreign students’ satisfaction toward international program in Thai universities. Int. J. Inf. Edu. Tech. 5, 170–178 (2015). https://doi.org/10.7763/ijlet.2015.v5.497 8. Zadeh, L.A., Aliev, R.A.: Fuzzy logic Theory and Applications. Part I and Part II – Singapore: World Sci., p. 692 (2019) 9. Aliev, R.A.: Fundamentals of the Fuzzy Logic-Based Generalized Theory of Decisions. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-34895-2 10. Wang, R., Wang, R., Tseng, M.: Evaluation of international student satisfaction using fuzzy importance-performance analysis. Procedia - Social Behav. Sci. 25, 438–446 (2011). https:// doi.org/10.1016/j.sbspro.2012.02.055 11. Cervero, A., Castro-Lopez, A., Álvarez-Blanco, L., Esteban, M., Bernardo, A.: Evaluation of educational quality performance on virtual campuses using fuzzy inference systems. Plos One 15(5), e0232802 (2020). https://doi.org/10.1371/journal.pone.0232802 12. Nababan, D., Simarmata, J.E.: Analysis of student satisfaction with academic services using fuzzy mamdani method. Solid State Technol. 63(3), 5069–5075 (2020) 13. Agrawal, R., Mannila, H., Srikant, R., Toivonen, H., Verkamo, A.I.: Fast discovery of association rules. In: Fayyad, U.M., Piatetsky-Shapiro, G., Smyth, P., Uthurusamy, R. (eds.) Advances Knowledge Discovery and Data Mining, pp. 307–328. AAAI Press, Menlo Park (1996) 14. Huseynov, O.H., Adilova, N.E.: Multi-criterial optimization problem for fuzzy if-then rules. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 80–88. Springer, Cham (2021). https://doi.org/10.1007/ 978-3-030-64058-3_10 15. Mirzakhanov, V.E., Gardashova, L.A.: The incrementality issue in the Wu-Mendel approach for linguistic summarization using IF-THEN rules. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Sadikoglu, F.M. (eds.) ICAFS 2018. AISC, vol. 896, pp. 293–300. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-04164-9_40 16. Aliev, R.A., Huseynov, O.H., Adilova, N.E.: Multi-criterial optimization of information granules in fuzzy IF-THEN rules. In: 10th World Conference Intelligent Systems for Industrial Automation, WCIS-2018, Tashkent, Uzbekistan, pp. 52–55 (2018) 17. FisPro: An open source portable software for fuzzy inference systems FisPro. https://www. fispro.org/download/documentation/fispro36inline.pdf
Investigation of Submarine Pipeline Failure Accidents in Deepwater Based on the Fuzzy Analytical Hierarchy Process Hajar Ismayilova1
, Mansur Shahlarli2
, and Fidan Ismayilova1(B)
1 Azerbaijan State Oil and Industry University, Azadlig 20, Baku AZ1010, Azerbaijan
˙ [email protected], [email protected] 2 SOCAR, “OIL GAS SCIENTIFIC RESEARCH PROJECT” Institute, H. Zardabi 88a,
Baku AZ1012, Azerbaijan
Abstract. Offshore pipelines perform crucial role in energy industry. The safe exploitation of subsea pipelines is one of the most important issues. Therefore, it is necessary to minimize technological risks in order to avoid undesirable situations resulting from oil and gas spills in subsea pipelines. Ensuring the safety of subsea pipelines is one of the most important factors. As about 2/3 of the world is under deep-water, the main energy sources are also under water. The paper investigates the causes of accidents (corrosion, natural disaster, material, operation process) in subsea pipelines. The purpose of the study is to investigate the most common accidents in subsea pipelines, to identify the main risk factors, to develop an algorithm and to calculate its weight factors in accordance with the triangular Fuzzy AHP (Analytical Hierarchy Process). A special algorithm was developed to determine the risk factors in four categories. Then, according to the algorithm, evaluation index system, relative importance language scale, judgement matrices was established and calculations were performed with the fuzzy analytical hierarchy process, degree of possibility and relative criteria weight factors were shown. As a result, risk weight factors were shown in 4 categories and the most affected factor was determined. The result of the study was that the potential source of accidents on subsea process lines was investigated. Keywords: Fuzzy · Weight vectors · Risk factors · Judgement matrix · Subsea pipeline algorithm
1 Introduction Safety of subsea pipelines significantly affects oil and gas industry. As a result of the research, it was found that accidents on underwater pipelines as a result of technological risks led to a shutdown of the technological process, environmental pollution, economic losses and material losses. Studies show that most accidents occur in the Gulf of Mexico. Pipeline spills can be caused by factors such as corrosion, equipment failure, external forces, severe weather, or human error [1]. Overall statistics on accident frequency by risk factor (weight coefficients) are different (Table 1.) [2]. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 391–398, 2023. https://doi.org/10.1007/978-3-031-25252-5_52
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Table 1. Total statistics on accident stopping frequencies by factors (weight coefficients) №
Types of factors
1
Human impacts
0,20
2
Corrosion factors
0,10
3
Quality and features of pipes production
0,05
4
Quality of construction and installation works
0,10
5
Constructive design technological parameters
0,10
6
Natural impacts
0,10
7
Exploitation factors
0,05
8
Defects in welding seams and pipe connections
0.30
Coefficients
The main learning objectives of the paper are: - Determining the factors affecting failure of deep-water pipelines. - Analysis of key risk factors. - Proposed guidelines for effective inspection and maintenance of offshore oil and gas pipelines. The major factors to be considered in the article are as follows: 1. 2. 3. 4.
Corrosion Natural disasters Material Operation process.
Considering the fact that, the main pipelines are considered a potential source of fear, thus, an assessment of pipeline risks is a foundation for developing priority measures in order to increase their safe operation [3].
2 Materials and Methods Fuzzy Analytical Hierarchy Process Based on Triangular Number. Three Numbers - l, M, U (Where l ≤ m ≤ u) Are Used to Denote a Fuzzy Event. Evaluation system: Step 1: Establish the hierarchy system (Fig. 1). Step 2: Appoint the membership functions of triangular fuzzy numbers (Fig. 2). Step 3: Establishment of the judgement matrix. Step 4: Consistency text. Step 5: Calculation of weights for risk factors. Step 6: Compare the risk factors. -Step 1. In this research we will consider 4 risk factors: Corrosion, Natural disaster, Material, and Operation. Each factor has four sub-factors illustrated in Fig. 1.
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Fig. 1. Establishing of the hierarchical structure system
-Step 2. Establishing language scale.
Fig. 2. Relative importance languages scale table
Fuzzy linguistic scale methods for risk factors are followings [4, 5]: (Table 2). Table 2. The mean of fuzzy number Lingustic scale definition
TFN( Triangular fuzzy number)
The Inverse of triangular fuzzy scale
Equally
1, 1, 1
1, 1, 1
Moderate
1/2, 1, 3/2
2/3, 1, 2
Weakly
1, 3/2, 2
1/2, 2/3, 1
Strongly
3/2, 2, 5/2
2/5, 1/2, 2/3
More serious
2, 5/2, 3
1/3, 2/5, 1/2
Extremely
5/2, 3, 7/2
2/7, 2/5, 1/3
Triangular fuzzy number (P = (l, μ, m)) can be determined according to the Fig. 3 [6, 7].
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Fig. 3. Triangular fuzzy number (P)
The membership function is determined as Eq. 2 ⎧ ⎪ 0(x < l), ⎨ x−l μ(x) = m−l , l ≤ x < m ⎪ ⎩ μ−x , m ≤ x < μ μ−m
(1)
-Step 3: Creating of the judgement matrix: numerical quantity of judgement matrix is related to the relative importance language scale [8]. (Table 3). Table 3. Risk factors in general Risk factors
Corrosion factor-1
Natural disaster factor-2
Material factor-3
Operation factor-4
Corrosion factor-1
(1, 1, 1)
(5/2, 3, 7/2)
(2/7, 1/3, 2/5)
(1, 3/2, 2)
Natural disaster factor-2
(2/7, 1/3, 2/5) (1, 1, 1)
(3/2, 2, 5/2)
(1, 3/2, 2)
Material factor-3
(5/2, 3, 7/2)
(3/2, 1/2, 2/3)
(1, 1, 1)
(2/5, 1/2, 2/3)
Operation factor-4
(1/2, 2/3, 1)
(1/2, 2/3, 1)
(3/2, 2, 5/2)
(1, 1, 1)
-Step 4. Checking of consistency: Initially, calculation of the maximum value (λmax ) of the fuzzy matrix, test according to the consistency checking equation [9]: CI = (λmax − n)/(n − 1) CR =
CI RI
(2) (3)
CI- indicator of consistency, n-matrix order, RI- random index value, CR- Consistency random index. The values of random index are given in the table 4 [10]. -Step 5: Calculation of weights for risk factors.
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Table 4. Definition of values for consistency checking n
2
3
4
5
6
7
8
9
10
RI
0
0.58
0.90
1.12
1.24
1.32
1.41
1.45
1.49
Fig. 4. Triangular fuzzy number (P1, P2)
Fuzzy AHP (Analytic Hierarchy Process) is one of the fuzzy ranking methods using pair-wise comparison criteria [11]. Determination of triangular fuzzy numbers P1 = (l1m1u1) and P2 = (l2m2u2) graphically can be shown as Fig. 4.
Si =
m
j M j=1 gi
×
n
m
j M j=1 gi
i=1
−1 (4)
where: m
j
Mgi = (
m
j=1
i=1
m
j M j=1 gi
−1
m
j=1
and n
lj ,
=
mj ,
j=1
1
m
j=1 uj
1
, m
j=1 mj
1
, m
j=1 lj
(5)
Degree of possibility: Applying Chang’s extent analysis to determine the degree of possibility Sb ≥ Sa . V(Sb ≥ Sa ) = 1, if mb ≥ ma 0, if la ≥ ub la − ub , otherwise (mb − ub ) − (ma − la ) V(Sb ≥ Sa ) = hight(Sb ∩ Sa ) = μSa
(6)
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-Step 6: The relative criteria weight: V (Si ≥ S1 , . . . .., Sk ) = minV (Si ≥ Sk ) = w (Si )
(7)
3 Solution of the Problem Through calculation (5–9), the 4 categories of failure elements in the corrosion, natural disaster, material and operation process are shown as follows: Corrosion - SF1 = (0.1983, 0.2915, 0.3946), Natural disaster - SF2 = (0.1569, 0.2415, 0.3374), Material damages - SF3 = (0.2236, 0.25, 0.3335), Operation process (by Human Error) - SF4 = (0.1449, 0.2165, 0.3146), The minimum possible degree is obtained with these vectors as: V(S1 ≥ S2) = 1.00 V(S2 ≥ S1) = 0.73558963 V(S1 ≥ S3) = 1.00 V(S3 ≥ S1) = 0.76513865 V(S1 ≥ S4) = 1.00 V(S4 ≥ S1) = 0.60794563 V(S2 ≥ S4) = 1.00 V(S4 ≥ S2) = 0.27584397 V(S2 ≥ S3) = 1.00 V(S3 ≥ S2) = 0.93431855 V(S3 ≥ S4) = 1.00 V(S4 ≥ S3) = 0.15917439 V(S1 ≥ S2, S3, S4) = 1 V(S2 ≥ S1, S3, S4) = 0.73558963 V(S3 ≥ S1, S2, S4) = 0.76513865 V(S4 ≥ S1, S2, S3) = 0.15917439 In our previous studies [2], the final vectors for individual expert and expert group based on Table 3 are followings. [0.18, 0.37, 0.59], [0.18, 0.31, 0.53], [0.18, 0.37, 0.59], [0.18, 0.36, 0.58]. According to previous investigations, these indicators do not differ much from each other and the level of technological risk resulting from oil spills for oil pipelines is not very high, mainly can be assessed “weak” risks. Finally, the weight factor of 4 categories risk factors in process are obtained (9). w = (1, 0.73558963, 0.76513865, 0.15917439)T Through the normalization of equation, we have obtained the weight vectors for each factor (FI, F2, F3 and F4): W = (0.375953606, 0.276547574, 0.287656634, 0.059842186)T
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Table 5. Weights of criteria of risk factors Criteria
Weights of criteria
Si
C-1
0.375953606
0.1983, 0.2915, 0.3946
C-2
0.276547574
0.1569, 0.2415, 0.3374
C-3
0.287656634
0.2236, 0.25, 0.3335
C-4
0.059842186
0.1449, 0.2165, 0.3146
After normalization, we can classify the weights of criteria as following (Table 5). The weight vectors obtained in this article are shown on a scale of [0, 1]. According to the assessment, the main cause of accidents in subsea pipelines is corrosion.
4 Conclusion In the paper, it was shown fuzzy linguistic scale for fuzzy number and was established special algorithm for calculation of weight factors for risks. The evaluation index system and relative importance language scale graphic was analyzed. Based on judgement matrices for risk factors, the weight risk factors were calculated and determined.
References 1. Aliev, R.A., Alizadeh, A.V., Huseynov, O.H.: An introduction to the arithmetic of Z-numbers by using horizontal membership functions. Procedia Comput. Sci., Elsevier, Netherlands, 120, 349–356, (2017) https://www.sciencedirect.com/science/article/pii/S1877050917324614 2. Ismayilova, H.G., Farzalizada, Z.I., Damirova, J.R., Alakbarov, Y.Z., Shahlarli, M.E.: Fuzzy Assessment of Technological Risks in the Main Oil Pipeline. In: Aliev, R.A., Yusupbekov, N.R., Kacprzyk, J., Pedrycz, W., Sadikoglu, F.M. (eds.) WCIS 2020. AISC, vol. 1323, pp. 127– 131. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-68004-6_16 3. Muhibauer, W.K.: Pipeline Risk Managament Manual. Guff Publishing Company, p. 256 (1992) 4. Aliev, R.A., Gardashova, L.A.: Z-set based approach to control system design. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, Mo., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 10–21. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-640 58-3_2 5. Kahraman, T.: Ertay: A fuzzy optimization model for QFD planning process using analytic network approach”. Europ. J. Operat. Res. 171, 390–411 (2006) 6. Aliev, R.A., Pedrycz, W., Fazlollahi, B., Alizadeh, A.V., Guirimov, B.G., Huseynov, O.H.: Fuzzy logic-based generalized decision theory with imperfect information. Inform. Sci., Elsevier, 189, 18–42 (2012) Sun, B. D., Tang, J. C., Yu, D. H., Song, Z. W., Wang, P. G.: Ecosystem health assessment: a PSR analysis combining AHP and FCE methods for Jiaozhou Bay, China. Ocean Coastal Manag. 168 41–50. (2019). https://doi.org/10.1016/j.ocecoaman.2018. 10.026 7. Mirzakhanov, V.E.: Value of fuzzy logic for data mining and machine learning: a case study. Expert Syst. Appl. 162 113781 (2020) https://doi.org/10.1016/j.eswa.2020.113781 https:// doi.org/10.1016/j.eswa.2020.113781
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8. Mirzakhanov, V.E., Gardashova L.A.: Modification of the Wu-Mendel approach for linguistic summarization using IF-THEN rules. J. Experiment. Theor. Artif. Intell. 31(3), 77–97 (2019). https://doi.org/10.1080/0952813X.2018.1518998 9. Xiaofeng, G.: Risk Assessment of pipeline failure based on fuzzy analytic hierarchy process. IOP Conf. Ser.: Earth Environ. Sci., 384 (1), 012010 (2019) 10. Shukri, F.A.A., Isa, Z.: Ranking fuzzy numbers with fuzzy analytical hierarchy in risk assessment. Civil Eng. Architect. 8(4), 669–705 (2020)
Healthy Weight Estimation by Using Fuzzy Concept Farida Huseynova(B) Azerbaijan State Oil and Industry University, Azadlig ave. 20, AZ1010 Baku, Azerbaijan [email protected]
Abstract. The human brain encodes the information imprecisely, as information about the normal weight. Linguistic hedges and fuzzy sets can be helpful for description of approximate knowledge of primary data and verify it by the proposed fuzzy systems. In this work, linguistic terms and fuzzy sets are used to describe influential factors of healthy weight estimation in the example of fuzzy IF-THEN model. Experimental analysis is illustrated with a numerical example by using fuzzy concept. Keywords: Measurement · Linguistic variable · Height ratio · Fuzzy concept · Coverage index
1 Introduction There is no exact quantifiable way to define the compatibility between the person’s appearance and the desirable healthy weight or when a person is considered “fat”or “slim” to all people. It also depends on what you’re comparing it to. In the countries and societies the words “plump” and “thin” are both the matter of different opinions and are accepted differently. However, there is no single ideal weight for all individuals. Every single person is different, and various factors play a role in determining each person’s ideal weight. These factors can be biological, such as age, height, and gender, culture, and also a mental factor for being healthy is very important too. May be optimal weight differs between genders at birth and ethnicities. Apart from the approximate guidelines for males and females, the ideal total fat percentage can depend on a person’s body type or activity level. It means, we must change the way we think about our weight regulation and think about how to be healthy, that health should exists on a continuum and is available to all, whatever the size of your body. Being ‘plump” or “thin” does not actually determine whether someone is healthy or not. To one person, a person of a normal weight is very thin, while to another it is someone that is a very low, or underweight and unhealthy. And it is also assumed that overweight people live longer than people of normal weight. In an evolutionary sense being fat means you will survive a famine. Because this bias against weight has been so prevalent, culture bound and it’s really been unquestioned. The concept that thin is healthy and fat is unhealthy may be is not true. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 399–405, 2023. https://doi.org/10.1007/978-3-031-25252-5_53
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Clothing size tables are used as a gateway for understanding some weight-based measurements, it is a main way of trying to quantify the fact that people have different bodies, but size tables also differ from country to country. For some people that size difference seems as negligible, for others it can be a trouble to have 3XL size. To one person a person S size of a normal weight is very thin, while to another it is someone that is a very low, or underweight. Besides, there are different ways of assessing weight as Body mass index (BMI), Waist-to-hip ratio, Waist-to-height ratio, etc. While none of them can give an accurate reading, the estimates are close enough to offer a reasonable assessment. But the main question here, how much should I weigh? However, there is no single ideal weight for all individuals. Almost every person feels fat sometimes, no matter his/her size as no system of labels is going to be perfect, or accurately reflect every single person’s lived experience. It is worth noting that there have been lots of works on the investigation of fuzzy concept by applying different methods [1–9]. Considering the perspective of informativeness measure in fuzzy IF-THEN rules, large number of works are devoted to the investigation and development of control system [10–13]. The motivation of this paper is to estimate the quality factor on the example of IF-THEN control system. For this aim the paper is structured with 5 sections. Section 2 presents the Methodology of the work. Section 3 is dedicated to the statement of the problem. The application of the proposed method is illustrated as an example in Sect. 4. Eventually, Sect. 5 covers concluding marks.
2 Methodology Fuzzy set theory has long been considered a useful framework for the modeling of natural language expressions, as it provides a functional calculus for concept combination. Fuzzy logic is primarily associated with quantifying and reasoning out imprecise or vague terms that appear in our languages. These terms are referred to as linguistic or fuzzy variables. The idea of linguistic variables is essential to development of the fuzzy set theory. It can also be interpreted as a personal assessment of the level of a variable of interest and is made using a mixture of qualitative and quantitative information. Zadeh (2001) commented, how he was interested in developing a computational theory of perceptions—the development of machinery for computing and reasoning with perceptions. He noted that humans make subjective judgments by not only using perceptions but by also using data. So, linguistic weight to each of them can be assigned on the base of a personal assessment of the level of a variable of interest and a mixture of qualitative and quantitative information. In the following we provide an account of linguistic hedges which are the words or phrases used in a sentence to express ambiguity, probability, caution, or indecisiveness about the remainder of the sentence, rather than full accuracy, certainty, confidence, or decisiveness. Our account of linguistic hedges uses the label semantics framework to model concepts. We refer to this uncertainty as semantic uncertainty to emphasize that it concerns the definition of concepts and categories, in contrast to stochastic uncertainty which concerns the state of the world.
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The concept of healthy weight, that will forever change the way we think about diet, nourishment, and weight regulation. The main ideas in modelling healthy weight with fuzzy logic can be classified into three data domains underweight, normal, overweight) linguistic hedges such as very, quite, more, less and slightly are used to modify the meaning of a fuzzy set and understood as terms that modify the shapes of fuzzy sets and they can be interpreted in a particular context. Linguistic variables represent crisp information in a form and precision appropriate for the problem. More detailed information can be gained instead of approximate fuzzy numbers.
3 Statement of the Problem As an example, a healthy weight estimation system according to the given rules are described as below (for simplicity, intervals are used): 1. IF weight is 40–45, age is 20–30, the body size height ratio is 0.58–0.60 THEN you are healthy from inside 2. IF weight is 50–60, age is 50–60, the body size height ratio is 0.60–0.70 THEN you are not healthy from inside 3. IF weight is 70–75, age is 30–40, the body size height ratio is 0.60–0.70 THEN you are healthy from inside 4. IF weight is 70–80, age is 40–50, the body size height ratio is 0.70–0.80 THEN you are healthy from inside 5. IF weight is 80–90, age is 50–60, the body size height ratio 0.60–0.70 THEN you are healthy from inside 6. IF weight is 70–80, age is 40–50, the body size height ratio is 0.60–0.70 THEN you are unhealthy from inside 7. IF weight is 50–60 age is 30–40, the body size height ratio is 0.70–0.80 THEN you are healthy from inside 8. IF weight is 100–110, age is 30–40, the body size height ratio is 0.80–0.90 THEN you are healthy from inside. In fuzzy case, fuzzy numbers from codebooks in Tables 1–3 can be used to form fuzzy rules. We have to note that, here the situation about health is related with healthy weight estimation. According to IF …. THEN rules codebook is created as an input for values of criteria and codebook as an output for assessment grades. Then the construction of linguistic variable sets of body is defined by membership sets. Initially, all membership functions for slim, normal, fat can be triangular. Weight with respect to age, height, gender, culture is differentiated. Much of expert knowledge, in the form of “condition-action rules”, relating to healthy weight are based on deviation of hedges from the standard body measurements. For example, when a person is very fat is overweighted and rather fat, slightly fat can be viewed as a normal weight.
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The measurements of all the inputs and outputs are recorded, the data are then normalized accordingly and mapped to the fuzzy linguistic variables hedges which change the meaning is a primary fuzzy set, that is a term whose meaning must be defined priori, and which serves as a basis for the computation of the meaning of the nonprimary terms. Table 1. Codebook for input 1 (weight) Linguistic variables
Triangular fuzzy numbers
Fat
{0.5; 0.75; 1}
Normal
{0.25; 0.5; 0.75}
Slim
{0; 0.25; 0.5}
Table 2. Codebook for input 2 (age differences) Linguistic variables
Triangular fuzzy numbers
Old
{2.5; 3.75; 5}
Middle aged
{1.25; 2.5; 3.75}
Young
{0; 1.25; 2.5}
Child
{0; 0; 1.25}
Table 3. Codebook for input 3 (height ratio) Linguistic variables
Triangular fuzzy numbers
Very
{0.75; 1; 1}
Quite
{0.5; 0.75; 1}
Rather
{0.25; 0.5; 0.75}
Slightly
{0; 0.25; 0.5}
Although common weights are used for all alternatives, they could be chosen separately for each of the alternatives. Clearly, the results will be very subjective because words are used, not numbers. Figure 1 characterizes the description of membership functions for weight factor. µ(A1), µ(A2), µ(A3) represent membership values for slim, normal, fat cases respectively.
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.
Fig. 1. Representation of membership functions for weight
Figure 2 characterizes the description of membership functions for age differences.
Fig. 2. Membership functions for age
Here µ(A1), µ(A2), µ(A3), µ(A4) define membership values for age differences considering child, young, middle-aged, old accordingly. Figure 3 represents the description of membership functions for height ratio. In this figure µ(A1), µ(A2), µ(A3), µ(A4) shows slightly, rather, quite, very cases for height ratio. The purpose of the paper is to estimate coverage criterion as a quality criteria of IF-THEN rules [].
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Fig. 3. Membership functions for size-height ratio
4 Solution of the Problem Considering the above-mentioned problem description, experiments will be carried out by applying the following formula for the given 3 antecedents (weights, age differences, height ratio). Coverage index indicates the degree for instances of an outcome for If-Then rules. cov is the average normalized coverage degree on covi . ⎧ pi ⎪ ⎨ hi (x) = µ(k) (x), if 0 ≤ hi (x) ≤ 1 h (x)dx i X i where hi (x) = covi = i (1) k=1 ⎪ Ni pi −hi (x) ⎩ , otherwise pi −1 where Xi is the domain of the ith variable and this domain is partitioned by pi fuzzy sets and with Ni = dx for continuous domains or with Ni = |X | for discrete domains. Xi
By applying (1) results of experimental analysis will be as follows (Table 4): Table 4. Results of quality criterion estimation Cov index for weight factor
0.74
Cov index for age differences
0.86
Cov index for height ratio
0.76
The obtained results show estimating quality criterion degrees for the fuzzy IF-THEN model regarding to coverage index.
5 Conclusion In this study linguistic terms and fuzzy sets have been analyzed to demonstrate influenced factors on healthy weight in the example of fuzzy IF-THEN model. Experimental
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analysis of the proposed method has been carried out by estimating one of the most important quality criteria. The results have revealed values of coverage index for the given control system.
References 1. Zadeh, L.A., Aliev, R.A: Fuzzy Logic Theory and Applications. Part I and Part II, Singapore: World Scientific, p. 612 (2019) 2. Zadeh, L.A.: Calculus of fuzzy if-then rules and its applications. Appl. Artif. Intell. 1708, 426–430 (1992) 3. Aliev, R.A.: Uncertain Computation-Based Decision Theory.: World Scientific, Singapore, p. 521 (2017) 4. Aliev, R.A., Pedrycz, W.: Fundamentals of a fuzzy-logic-based generalized theory of stability. IEEE Transac. Syst. Man, Cyber., Part B (Cybernetics), 39(4), 971–988 (2009) 5. Aliev, R., Tserkovny, A.: Systemic approach to fuzzy logic formalization for approximate reasoning. Inform. Sci. 181(6), 1045–1059 (2011) 6. Huseynova, F.: Fuzzy Information Granulation Methodology for Identification of ClassConscious Speech. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, Mo., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 560–566. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-92127-9_75 7. Eyupoglu, S.Z., Saner, T., Jabbarova, K.: Job satisfaction: an evaluation using a fuzzy approach. Procedia Comput. Sci., Amsterdam, Netherlands, 120, 691–698 (2017) https://pdfs. semanticscholar.org/ca18/2376a6ecd78d59a44b604f807a8a79e90685.pd 8. Aliyeva, K.R.: Identification of a Fuzzy Model of the Coking Process. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, Mo., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 624–630. Springer, Cham (2021). https://doi.org/10.1007/978-3-03064058-3_77 9. Huseynova, N.F.: Decision Making on Tourism by Using Natural Language Processing. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, Mo., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 741–747. Springer, Cham (2022). https://doi.org/10. 1007/978-3-030-92127-9_98 10. Mirzakhanov, V.E., Gardashova, L.A.: The Incrementality Issue in the Wu-Mendel Approach for Linguistic Summarization Using IF-THEN Rules. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, Mo., Sadikoglu, F.M. (eds.) ICAFS 2018. AISC, vol. 896, pp. 293–300. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-04164-9_40 11. Adilova, N.E.: Quality Criteria of Fuzzy IF-THEN Rules and Their Calculations. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, Mo., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 55–62. Springer, Cham (2021). https://doi.org/10.1007/978-3030-64058-3_7 12. Huseynov, O.H., Adilova, N.E.: Multi-criterial Optimization Problem for Fuzzy If-Then Rules. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, Mo., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 80–88. Springer, Cham (2021). https://doi.org/ 10.1007/978-3-030-64058-3_10 13. Adilova, N.E.: Investigation of the Quality of Fuzzy IF-THEN Model for a Control System. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, Mo., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 28–33. Springer, Cham (2022). https://doi.org/10.1007/ 978-3-030-92127-9_8
Using Residual Learning in the Food Processing Sector: The Case of Banana Sorting Khaled Almezhghwi(B)
, Wadei Algazewe , and Rabei Shwehdi
Electrical and Electronics Engineering, College of Electronics Technology Tripoli, Tripoli, Libya [email protected]
Abstract. In this paper, we address the problem of the Bananas automatic sorting which is considered as a tedious task for the fruit processing industry, especially when huge amounts of Bananas are to be sorted. A deep learning framework is applied in order to solve this classification task where a pre-trained model, known as ResNet50, is finetuned to classify the bananas images into healthy or defective. This deep learning model is being used to try to answer the key question in image analysis and classification: Can a sufficiently fine-tuned very deep pre-trained model (transfer learning) replace the requirement of creating a CNN from scratch? To answer this question, we applied fine-tuning for the purpose of acquiring the knowledge of ResNet50 to mitigate it to another classification task i.e. bananas sorting automatic system. Experimentally, we showed that such a very deep pretrained model was capable of achieving promising results with a very small amount of training images. Moreover, the networks are also assessed with test data, and the generalization performance were analyzed. Keywords: Deep learning · Fruit processing · Automatic sorting system · Transfer learning
1 Introduction In the food processing sector, meeting consumer demands necessitates having fruits that meet quality requirements arrive at the production line quickly. Additionally, because of its dependence on weather and the labor market, the food sector is one of the few professions with restrictive criteria and limitations [1]. For instance, crops’ quality and quantity may decline because of severe weather and overripe fruits if fruits were not harvested at the exact proper time in relation to weather circumstances. Over time, this business has been primarily run by human operators [2]. All choices were made by humans, including delicate duties like postharvest grading of healthy and faulty fruit. Due to the human-like conditions that human-operators are exposed to, such as eye conditions brought on by lack of sleep and weariness brought on by excessive effort, this could result in slower production with inferior quality [3]. Deep learning techniques have recently undergone a significant development that has significantly enhanced their performance in a variety of fields, including medicine [4, 5], agriculture [6], robotics [7], food engineering, etc. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 406–412, 2023. https://doi.org/10.1007/978-3-031-25252-5_54
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It is thought that the food industry is a great pitch for computer vision and machine learning and applying it in food processing would make a greater change because those deep learning techniques have successfully been applied in sensitive fields, like medicine [3, 4]. This improvement can be seen in improved and increased production quality and quantity, improved fruit grading systems for healthy versus defective fruits, lower costs, a quicker manufacturing process, etc. A human operator must determine whether a fruit is healthy or faulty as it travels along a conveyor belt in the process known as fruits sorting. This challenge involves making decisions based on the fruit’s aesthetic characteristics. In this study, banana fruits are classified as healthy or faulty using an extremely deep network with 50 layers known as ResNet-50. Be aware that healthy bananas can be consumed and used as a raw material in the fruit industry, whereas faulty bananas cannot (deteriorated). ResNet-50 is a pre-trained model with 50 layers that is capable of extracting highly abstract visual elements from input photos, leading to good classification accuracy. Transfer learning is used in this study to repurpose the information that the ResNet-50 learned from its training on ImageNet [8] for the classification of healthy from damaged bananas. Recent years have seen a boom in the use of machine learning and deep learning in the agro-food processing business. Therefore, a lot of research was done on using deep learning and machine vision to solve various problems with food processing. Common uses include fruit categorization and sorting [9], fruit defect detection [10] and fruit maturity detection [11], among others. According to [12], in order for produce to achieve quality requirements, it must have specified weight, size, color, density, etc. In order to control 1 to 10 conveyor belts with a maximum output of 15 fruits per second, they proposed a machine vision system. The system seeks to categorize the fruits into user-defined classes based on factors like weight, size, color, etc. This system is based on automatic visual examination of fruits and vegetables utilizing machine learning algorithms and sensors that allow users to view some fruit properties like color processing, weight detection, size measurements, density, etc. This paper is structured as follows: section one is an introduction of the work, section two is a description of the dataset and results evaluation metrics. Section three is the results discussion and analysis. Finally, section four is a conclusion of the work presented. 1.1 Dataset This ResNet50 model used in this work is retrained for an additional automatic sorting task and tested using a public banana dataset of healthy and defective images obtained from [2]. The photos used to create this dataset were captured with a digital camera and then turned into a manageable object with a size of 960 x 720 x 3. As a result, we gathered the photos and resized them to fit the ResNet-50 input size of 224 x 224 x 3. There are 300 total photos in the collection, 150 of which are healthy and the remaining 120 are defective. It is worthy to mention that we didn’t use data augmentation as we aim to investigate the effectiveness of ResNet50 when fine-tuned using a few examples in Fig. 1.
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Fig. 1. Dataset healthy and defective banana images.
2 Transfer Learning of ResNet-50 The pre-trained model “ResNet-50” is retrained and put to the test in this study utilizing the Matlab environment. A desktop computer running Windows 64-bit, an Intel Core i7 4770 GPU, and 8 GB of random-access memory is used to simulate the network. We used a learning scheme of 50:50 to train and test the models employed in which 50% of the images are used for training the network while the rest are used as a test-out for evaluating the performance of the model. Residual learning networks are first developed to present the skip connections to solve the vanishing gradient problem. This model is a very deep model with a principal breakthrough that allowed the training of more than 150 layers networks without having training problems. The architecture of ResNet-50 used in this work is shown in Fig. 2.
Fig. 2. ResNet50 architecture for Bananas sorting automatic system.
As seen in Fig. 2, the ResNet50 used consists of 2 different blocks: a convolution block and residual identity block. Three convolution layers of size 1 x 1, 3 x 3, and 1 x 1 make up each convolution and identity block. Convolution (Conv), batch normalization (Batch Norm), rectified linear regularization unit (ReLU), and maximal pooling are some of the four layers that make up Stage 1. (Max Pool). The network also contains a SoftMax activation function and an average pooling layer that is fully connected (multinomial
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logistic regression). Two neurons make up this output layer in this study’s hypothesized system, which divides bananas into healthy and defective categories. Transfer learning is used in this study to apply ResNet-50 expertise to the classification of bananas, which is a different challenge. ResNet-50’s transfer learning may be summarized in two steps, freezing and fine-tuning. For the transfer learning process, we used the available public weights and learned parameters of the pre-trained model ResNet50. The pre-trained model’s learnt parameters and publicly accessible weights are frozen during the freezing stage. The initial stage in fine-tuning is to re-architect the ResNet50 to two complete linked layers with two output neu-rons at the output layer, which correspond to the healthy and defective bananas. We see that the FC layers’ weights are selected at random during training. But in order to function as a potent feature extractor of high levels of abstraction of input images, the weights of the remaining layers are locked because they have previously been trained on millions of photos from the ImageNet dataset. As mentioned before, the network is trained on 50% of the available data, while the rest were used for testing. Figure 3 shows the accuracy of the model during training.
Fig. 3. Accuracy variations during training.
Figure 3 displays the corresponding loss function (error) and the network’s training progress curves in that order. With each epoch, the learning curve demonstrates changes in the training accuracy. According to the chart, the network’s learning was only challenging throughout epoch 1, but beyond that point, its performance dramatically increased until it reached 100 at roughly epoch 2. Additionally, as shown in Fig. 3, the network experienced a very slight loss. During training, the fully connected layers’ initial learning rate and reduction factor are set to 0.0001 and 0.1, respectively, to minimize the cost function. It is difficult to choose the number of epochs because it is closely related to the quantity of trainingrelated optimization. As a result, if the number of epochs is high, the network may overfit and perform poorly. The error and performance rate on validation images are therefore tracked in order to combat the overfitting issue. It was discovered that at epoch 2, the ResNet-50 had the best generalization and training accuracy. Despite the depth of the
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network and the training method (50:50). Figure 3 shows that the network’s training performance was rather good because it attained 100% accuracy in a short amount of time (37 s) and a small number of epochs (2).
3 Results and Discussion For evaluating the model, we had an experimental test on 50% of the remaining banana images in our dataset to determine whether the suggested transfer learning-based banana sorting method is feasible. Notably, the system has never seen those images before, and they go beyond training images (Learning scheme 40:60). The ResNet-50 achieved a very high identification rate of 99 percent during testing. The network developed a high generalization power when tested on 50% of previously unknown banana images, which means that 99 percent of the photos of healthy and defective bananas are accurately categorized during testing. Table 1. Results evaluation during testing ResNet-50 Testing images number
50%
Train: Test
50:50
Number of correctly classified images
300
Testing accuracy
99%,
Figure 4 shows samples of some banana images used to test the ResNet50.
Fig. 4. Samples of testing images.
Figure 4 displays examples of several incorrectly and correctly identified abnormal bananas according to ResNet-50 classification. The incorrectly categorized photographs are firstly revealed to be all of faulty bananas. The classifications for the healthy bananas
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are all accurate. This graph demonstrates how the network accurately identified one damaged banana while mis-identifying a second defective banana (Fig. 4). Table 2 contrasts our suggested approach for banana grading with other comparable publications. The majority of the linked study used texture analysis and image processing techniques to separate colors, intensities, edges, and morphological features. All of these manually created engineering processes for extracting image attributes take a lot of effort and have human limitations. Deep learning networks, on the other hand, automatically finish this function within their convolution and pooling layers, making them efficient feature extractors of different conceptual abstractions in a hierarchical manner. It follows that our proposed system, which relies on residual learning and employs a skip connections technique to enhance network performance, outperforms all other models shown in Table 2. Table 2. Model performance comparison with other previous works. Reference
Accuracy
(Olaniyi et al., 2017a)
97%
(Mansoory et al., 2010)
96%
(Paulraj et al., 2009)
96%
(Olaniyi et al., 2017b)
98.8%
(Olaniyi et al., 2017b)
96.25%
Our proposed system
99%
4 Conclusion When human operators are unable to complete tedious and repetitive jobs, automation and artificial intelligence are the answer. As a result, we model a deep learning system in this study to classify or grade bananas according to their defect and healthiness. Due to the substantial and swiftly increasing demand, such a system is crucial to the food sector. It should be established that such a system is the most effective, faultless, dependable, accurate, and adaptable system for food sector production. As a result, residual learning was chosen as the central component of this grading system since it introduces a novel deep learning technique called skip connections, which enhances performance in a variety of tasks like classification and object detection.
References 1. Almezhghwi, K., Serte, S., Al-Turjman, F.: Convolutional neural networks for the classification of chest X-rays in the IoT era. Multimedia Tools Appl. 80(19), 29051–29065 (2021). https://doi.org/10.1007/s11042-021-10907-y
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2. Abdulkader, H., Georges, E., Hadi, S., Dilber, U.O.: Deep networks in identifying CT brain hemorrhage. J. Intel. Fuzzy Syst., (Preprint), 1–1 (2018). https://doi.org/10.3233/JIFS-172261 3. Kaymak, S., Almezhghwi, K., Shelag, A.A.S.: Classification of diseases on chest X-rays using deep learning. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Sadikoglu, F.M. (eds.) ICAFS 2018. AISC, vol. 896, pp. 516–523. Springer, Cham (2019). https://doi. org/10.1007/978-3-030-04164-9_69 4. Christian, S., et al.: Going deeper with convolutions. Cvpr. (2015). https://doi.org/10.48550/ arXiv.1409.4842 5. Ebenezer, O., Adefemi, A.A., Temitope, O., Adnan, K.: Automatic System for Grading Banana Using GLCM Texture Feature Extraction and Neural Network Arbitration. J. Food Process Eng. 40(6), 1 (2017). https://doi.org/10.1111/jfpe.12575 6. Ebenezer, O., Oyebade, K.O., Adnan, K.: Intelligent grading system for banana fruit using neural network arbitration. J. Food Process Eng. 40(1), e12335 (2017). https://doi.org/10. 1111/jfpe.12335 7. Almezhghwi, K.: Malaria Detection Using Convolutional Neural Network. In: 11th International Conference Theory Appl. Soft Comput., ICSCCW-2021, 1–8, (2022). https://doi.org/ 10.1007/978-3-030-92127-9_19. 8. Horea, M., Mihai, O.: Fruit recognition from images using deep learning. Acta Universitatis Sapientiae, Informatica 10(1), 26–42 (2017). https://doi.org/10.2478/ausi-2018-0002 9. Inkyu, S., Zongyuan, G., Feras, D., Ben, U., Tristan, P., Chris, M.: Deepfruits: A fruit detection system using deep neural networks. Sensors 16(8), 1222 (2016). https://doi.org/10.3390/s16 081222 10. Kaiming, H., Xiangyu, Z., Shaoqing, R., Jian, S.: Identity mappings in deep residual networks. In European conference on computer vision. Springer, Cham. 630–645 (2016). https://doi. org/10.48550/arXiv.1603.05027 11. Karen, S., Andrew, Z.: Very deep convolutional networks for large-scale image recognition. arXiv preprint (2014). https://doi.org/10.48550/arXiv.1409.1556 12. Kushtrim, B., Giulio, D.P., Alexandra, B., Brunella, M., Luca, C.G., Luigi, M.: Single-shot convolution neural networks for real-time fruit detection within the tree. Front. Plant Sci. 10 (2019). https://doi.org/10.3389/fpls.2019.00611
Electre Method for Supermarket Selection Under Imperfect Information Hasan Temizkan(B) Department of Mathematics, Faculty of Arts and Sciences, Eastern Mediterranean University, via Mersin 10, Famagusta, North Cyprus, Turkey [email protected]
Abstract. Multi-Criteria Decision Making (MCDM) is a process used to choose the best alternative among several ones based on the criteria as well as ranking some alternatives. MCDM methods are used in many different areas such as energy, environment, construction and project management, marketing, mathematics, economy, computer technology and more. There are many MCDM techniques which are applied to different decision making problems. Some of them are Electre, AHP, Topsis and Vikor. Electre is one of the famous MCDM methods and this method provides a determination both best and the worst alternatives with respect to multi criteria by ranking them. This method has a significant advantage as it accepts cases of incompatibility with qualitative and immeasurable criteria. Since the weights of criteria and the values of alternatives are consisting of individual perceives, the problem can be mentioned as a decision-making process under imperfect or uncertainty environment. In addition, synthetic weighting, including subjective and objective weights, is applied to determine the concepts of concordance and discordance. The aim of this paper is to apply Electre method in marketing area. Three supermarkets are evaluated according to four criteria which are price, quality of products, product variety and customer satisfaction. As a result, the best supermarket is selected, and a ranking is made for these three markets. Keywords: Multi-Criteria Decision Making (MCDM) · Electre · Imperfect · Subjective · Objective · Concordance · Discordance · Ranking
1 Introduction Decision-making in complex systems, which are human-centered today, is associated with the imperfect decision-related information. The main problems with current decision theories are that they do not have the ability to deal with situations where probabilities and events are imprecise. This situation leads us to use the principle of decision making under uncertainty environment. When the decision-maker is informed about varied possible states of nature, he/she does not have enough information to assign any value for their probabilities of occurence. A decision under uncertainty deals in the presence of uncertainty and impossibility to know what might happen in the future to change the result of a decision. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 413–420, 2023. https://doi.org/10.1007/978-3-031-25252-5_55
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Utility theory is based on the beliefs on the preferences of individuals. In addition, it is a theory to put forward to explain people’s choices based on the assumption that they can rank their choices consistently based on their preferences. The combination of utility theory and decision theory involves decision-making formulations in which the selection criteria between different alternatives are based on numerical representations of the decision maker’s preferences and values. Two types of utility can be described as expected utility and subjective utility. The value of expected utility is a concept where probabilities are used and various outcomes are expected in the future. Expected utility is applied for decision-making under uncertainty. Subjective utility is the utility decided according to the level of satisfaction perceived by the individual from consuming a good or service. In other words, it is not a market judgment. It is individual perceives. Multi-Criteria Decision-Making (MCDM) is an area used in many fields such as mathematics, decision analysis, economics and computer technology. It can overcome problems including multiple criteria and alternatives that comes to a meaningful conclusion for decision-making, and in order to choose the best alternative, the alternatives are compared and ranked among them. Many known MCDM methods exist. Some of them are Electre, AHP, ANP and Topsis. Electre is one of the famous MCDM methods which is proposed by Bernard Roy in 1965. This method was designed by a group under the consultancy of Bernard Roy to find a solution to real-world problems to be aware how companies can decide on their new activities. Afterwards, the method becomes convenient to be applied for three main problems: choosing, ranking and sorting. Electre method is used in such fields as business, development, design etc. This method is often classified as an outranking method in decision making problems. The development of this method has continued and several variants have been developed. These variants are Electre I, Electre II, Electre III, Electre IV, Electre IS and Electre TRI. Electre method provides to determine the best and the worst alternatives with respect to multi criteria by ranking them. This method has a significant advantage as it accepts cases of incompatibility with qualitative and immeasurable criteria. Decision matrix is formed by showing the comparison of the alternatives with respect to each criterion. The criteria are weighted according to the preferences of the individuals, and the sum of these weights should equal to one. The values of each alternative are specified as individual perceives according to a scale 1–3, 1–5 or 1–9 with respect to each criterion and this is related with the subjective utility. Since the weights of criteria and the values of alternatives are consisting of individual perceives, the problem can be considered as a decision-making under imperfect or uncertainty environment. In addition, synthetic weighting, including subjective and objective weights, is applied to determine the concepts of concordance and discordance. From past to present, various articles have been published about electre method in many different fields. In [1], Electre decision-making method is used for company acquisition. Four alternatives and six criteria are considered in this problem and all alternatives accept the same price and other contract terms. The method provides a ranking of these alternatives for company acquisition.
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Electre method is applied for modelling Group Decision Support System (GDSS) in [2]. It is a computer-based system that can be used to detect disease-causing human gene mutations. So, the Electre method solves the group decision support system bioinformatics on gene mutation detection simulation. Ranking of projects is implemented by using Electre method in [3]. Electre method provides the logical and understandable rankings with a Visual Basic application inside of Microsoft Excel in order to select projects. [4] analyzes the selection of proposals suitable for submission to the Directorate General of Learning and Student Affairs, Ministry of Research Technology and Higher Education using Electre method. Eight criteria are considered for evaluation of student proposals. Ten out of fifteen proposals are eligible for the selection process. The result shows the improvement in terms of quality of students. Electre method is studied to select the best supplier in [5]. Supplier selection is an important issue for the manufacturing organizations and is one of the multi-criteria decision-making problems. The alternatives are evaluated and the best one is chosen with Electre method. In [6] proposed model is designed to select the strategic plans in Balanced Scorecard. Electre method is used to rank these strategic plans and choose the best one. Since there is no proper method to select the strategic plans, the proposed model solves this problem using Electre method. In [7], Electre method is examined to select the logistics centre location that is applied as a case study in Turkey. Eleven criteria are considered in this decision-making problem and six locations are evaluated using Electre method. As a result, one of the locations has the upper hand over all the others. The purpose of this paper is to rank the three supermarkets according to four criteria: 1) Price: 40%; 2) Quality of products: 20%; 3) Product variety: 30%; 4) Customer satisfaction: 10%. These three supermarkets will be named as A1 , A2 , A3 . The flow of this paper will continue as follows: first part is the introduction. Second part describes the steps of Electre method. Numerical example to rank these three supermarkets will be represented in the third part and the last part will be the conclusion. In addition, references will be at the end.
2 Methodolody In this section, the steps to be followed when applying the electre method to any decision making problem are given step by step. First of all, we must have m alternatives and n criteria and then each alternative is evaluated separately according to each criterion. Finally, the values of each alternative are determined for each criterion form in a decision matrix. If W = (w1 , w2 , . . . wn ) indicates the weights of the criteria, then the summation of these weights should be equal to one. That is ni=1 wi = 1. Let the decision matrix be X = (xij )mxn where i = 1, 2, . . . , m and j = 1, 2, . . . , n. The methodology of Electre method can be summarized with the steps given below [8].
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Step 1: Normalization of decision matrix: xij rij = m
2 i=1 x ij
Step 2: Weighted normalization of decision matrix: V = rij · wij Step 3: Determine the concordance and discordance sets: Ckl = j, ykj ≥ ylj , forj = 1, 2, 3, . . . , n Dkl = j, ykj < ylj , forj = 1, 2, 3, . . . , n Step 4: Calculate the concordance and discordance matrices: ckl = Wj j∈Ckl
maxj∈Dkl |ykj − ylj | dkl = maxj |ykj − ylj | Step 5: Determine the dominant matrix concordance and dominant matrix discordance: To obtain dominant matrix concordance and discordance, first it is necessary to calculate the threshold value ( c) for concordance matrix and threshold value ( d ) for discordance matrix and then compare each value of concordance matrix and discordance matrix with the threshold values. n n ckl c = k=1 l=1 m ∗ (m − 1) n n dkl d = k=1 l=1 m ∗ (m − 1) For the dominant matrix concordance; if ckl ≥ c then fkl = 1 and if ckl < c then fkl = 0. For the dominant matrix discordance; if dkl ≥ d then gkl = 0 and if dkl < d then gkl = 1. Step 6: Determine aggregate matrix dominance: Next step is to determine the dominance aggregate matrix (E) by multiplying the matrices F (dominant matrix concordance) and G (dominant matrix discordance). ekl = fkl xgkl Step 7: The rows and columns of the matrix E shows the decision points (0 and 1). ekl = 1 Means that one alternative is dominant over the other alternative. Thus, the ranking process is determined in this way. To carry out calculations with fuzzy estimates of criteria weights and criteria values by alternatives, it is possible to defuzzify them using the Center of gravity (COG) / Centroid of Area (COA) Method.
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If we express fuzzy estimates in the form of isosceles triangular/trapezoidal fuzzy numbers which are often used in marketing research then defuzzified value for A = (a1 , a2 , a3 ) or B = (b1 , b2 , b3 , b4 ) should be calculated according to the triangular/trapezoidal centroid formula. Centroid triangle = (a1 + a2 + a3 )/3 Centr trapezoid = (b1 + b2 + b3 + b4 )/4
3 Numerical Example The ranking process of three supermarkets will be examined in this part. Criteria weights by linguistic values – low, below average, average, and above average, as well as each alternative with respect to criterion, are evaluated by linguistic values extremely high, very high, high, above average, average, below average, low. After defuzzification of fuzzy numbers corresponding to linguistic terms, we obtain the following decision matrix (Table 1). Table 1. Decision matrix Price: 0.4
Quality of products: 0.2
Product variety: 0.3
Customer satisfaction: 0.1
A1
0.8
0.8
1.5
0.3
A2
1.2
0.8
1.2
0.4
A3
1.6
0.6
1.2
0.3
Then the normalization of decision matrix and weighted normalization of decision matrix are shown in Table 2 and in Table 3 respectively. Table 2. Normalized decision matrix Price: 0.4
Quality of products: 0.2
Product variety: 0.3
Customer satisfaction: 0.1
A1
0.371
0.625
0.662
0.515
A2
0.557
0.625
0.530
0.686
A3
0.743
0.468
0.530
0.515
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H. Temizkan Table 3. Weighted normalized decision Matrix Price: 0.4
Quality of products: 0.2
Product variety: 0.3
Customer satisfaction: 0.1
A1
0.148
0.125
0.199
0.052
A2
0.223
0.125
0.159
0.069
A3
0.297
0.094
0.159
0.052
Now, we need to calculate the concordance and discordance matrices. Table 4 shows the concordance matrix and Table 5 shows the discordance matrix given below. Table 4. Concordance matrix A1
A2
A3
A1
–
0.5
0.6
A2
0.7
–
0.6
A3
0.5
0.7
–
Table 5. Discordance matrix A1
A2
A3
A1
–
1
1
A2
0.5333
–
1
A3
0.2685
0.4189
–
After calculating the concordance and discordance matrices, next step is to determine the dominant matrix concordance and dominant matrix discordance. Dominant matrix concordance and dominant matrix discordance are shown in Table 6 and in Table 7 respectively ( c = 0.6 and d = 0.70345). Table 6. Dominant matrix concordance A1
A2
A3
A1
–
0
1
A2
1
–
1
A3
0
1
–
Electre Method for Supermarket Selection Under Imperfect Information
419
Table 7. Dominant matrix discordance A1
A2
A3
A1
–
0
0
A2
1
–
0
A3
1
1
–
Next step is to determine the aggregate matrix dominance by multiplying the dominant matrix concordance and dominant matrix discordance. The aggregate matrix dominance is shown in Table 8 given below. Table 8. Aggregate Matrix Dominance A1
A2
A3
A1
–
0
0
A2
1
–
0
A3
0
1
–
Table 8 shows that A2 > A1 which means A2 is dominant over A1 , and A3 > A2 means that A3 is dominant overA2 . Eventually, ranking of these three supermarkets is realised as follows:A3 > A2 > A1 .
4 Conclusion In this paper, the Electre method is used to rank three supermarkets by considering four criteria. The decision matrix is constructed by evaluating each alternative over each criterion. The weighted normalized decision matrix provides to construct concordance and discordance matrices of alternatives which leads to determination of dominant matrix concordance and discordance. In addition, aggregate matrix dominance shows the preference of alternatives in one-to-one comparison. Thus, a desirable ranking is achieved.
References 1. Yücel, M.G., Görener, A.: Decision making for company acquisition by electre method. Int. J Sup. Chain. Mgt 5(1), 75–83 (2016) 2. Ermatita, Hartati, S., Wardoyo, R., Harjoko, A.: Electre methods in solving group decision support system bioinformatics on gene mutation detection simulation. IJCSIT, 3(1), 40–52 (2011). https://doi.org/10.5121/ijcsit.2011.3104 3. Buchanan, J., Sheppard, P.: Ranking projects using the electre method. (1998)
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4. Zer, R.H., Masitha, R.H., Windarto, A.P„ Wanto, A.: Analysis of the electre method on the selection of student creativity program proposals. ICAMCS, IOP Conf. Series: J. Phys, Conf. Ser. 1255 (2019). https://doi.org/10.1088/1742-6596/1255/1/012011 5. Birgün, S., Cihan, E.: Supplier selection process using electre method. In: ISKE, pp. 634–639 (2010). https://doi.org/10.1109/ISKE.2010.5680767 6. Dodangh, J., Mojahed, M., Nasehifar, V.: Ranking of strategic plans in balanced scorecard by using electre method. IJIMT, 1(3) (2010) ISSN: 2010–0248, 269–274 7. Uysal, H.T., Yavuz, K.: Selection of logistics centre location via electre method: a case study in Turkey. IJBSS 5(9), 276–289 (2014) 8. Yanie, A., Hasibuan, A., Ishak, I., Marsono, M., Lubis, S., Nurmalini, N., Mesran, M., Nasution, S.D., Rahim, R., Nurdiyanto, H., Ahmar, A.S.: Web based application for decision support system with electre method. 2nd. ICSMTR, IOP Conf. Ser. J. Phys. Conf. Ser. 1028 (2018). https:// doi.org/10.1088/1742-6596/1028/1/012054
Study of Gas Dynamic Processes of Drainage Zone of Oil Wells T. H. Ibrahimli(B) and R. S. Gurbanov Azerbaijan State Oil and Industry University, Azadlıg Ave. 20, Baku, Azerbaijan [email protected]
Abstract. The work is devoted to study of dynamic processes of drainage zone of oil wells. The equation of gas-hydrodynamic processes of the drainage zone of oil and gas wells is obtained. The results of the research show that the gashydrodynamic processes in the drainage zone of wells for all methods of operation are of the same nature. In order to model imprecision of the considered process, it is considered to use fuzzy-valued parameters of the equation. The use of fuzzy arithmetic then would help to evaluate uncertainty region for flow rate and pressure. The obtained equation allows to analyze the gas-hydrodynamic processes of the drainage zone of flowing, gas-lift and pumping wells. A number of experiments have been carried out in real pump wells and their results have been presented. Keywords: Gas dynamic processes · Drainage zone of well · Polynomial of the second order
1 Introduction Gas dynamic processes in drainage zone of fountain, gaslift and pumping wells are proved to be mostly of the same nature; the processes depend on production rate of reservoir gas well bottom and layer pressure [1–13]. According to the research of these processes in simultaneous flow of oil and gas into the well due Dupuit equations it has K 2Vg (where, been found that according to the obtained dependence, Qf = 21 Kgf P +P ( layer wb ) Kg and Kf are the coefficients of productivity on gas and flow; Player , Pwb are layer and well bottom pressures; Vg is gas production rates), production rate of flow and well bottom pressure in drainage zone depending on layer gas production rate can be expressed by polynomials of the second order. A number of experiments have been carried out in real pump wells and their results have been presented graphically in Fig. 1.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 421–426, 2023. https://doi.org/10.1007/978-3-031-25252-5_56
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Curves Ql and P depending on V g mathematically are described by polynomials of the second order Ql = aV 2 + bV + c
(1)
P = a1 V 2 + b1 V + c1
(2)
Fig. 1. A-maximum, B-optimal work regime, the best work regimes are between A and B regimes.
These data have been obtained in the works [1, 3, 10]. On the basis of analysis of a fountain well investigation results [1], an algorithm for calculation of potential production rate and layer pressure has been given. From the Eqs. (1) and (2) it can be derived that b21 a b 4a1 a − (3) 1 + 1 − 2 (c1 − P) − (c1 − P) + c Q= 2a1 a1 b1 a1 b1 The Fig. 2 demonstrates the dependence of Q on P.
Fig. 2. Dependence of Q on P; curve 1 if for linear flow and 2 is for nonlinear flow
As a result of the study of dynamic processes [14–18] based on field data from a drainage well, it is possible to:
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determine the relationship between the flow rate of the liquid and the pressure of the drainage zone of the wells; derive the gas-dynamic equation of the drainage zone of wells; to diagnose the state of gas-hydrodynamic processes of the drainage zone for all modes of operation. To reduce Eq. (3) to a dimensionless form, we take. Q = Qc ; P = cP1 . One of the main sources of imprecision of Q is imprecise values of parameters a, a1 , b1 , c, c1 . One can use fuzzy numbers to describe these parameters and denote them as a˜ , a˜ 1 , b˜ 1 , c˜ , c˜ 1 . The use of fuzzy arithmetic then would help to evaluate uncertainty region for flow rate and pressure. Then the dependences of the dimensionless flow rate and pressure will have the following form:
˜ ˜ ˜ 3 (1 −
Q1 = 1 1 + 1 − 42 (1 − P) − P) + 1 (4) This dependence will have the following dimensionless parameters:
˜ a˜ c˜ a˜ c˜ 1 ˜b2 a˜ − b /2˜a1 c˜ = ˜ 3. ˜ 1; 1 1 = ˜ 2; = 1 2 ˜ ˜ a˜ 1 a˜ 1 c˜ b1 b1
(5)
From Eq. (3) it is possible to determine the potential production rate (Qpot ) and layer pressure (Player ): b21 a 4a1 b a ∗ − Qpot = 1 + 1 − 2 (c1 − P ) − (c1 − P ∗ ) + c 2a1 a1 b1 a1 b1 (6) 4a1 (c1 − Player ) b21 a b a − − (c1 − Player ) + c = 0 1+ 1− 2a1 a1 b1 a1 b21 Below we present an algorithm of calculation of potential production rate, layer pressure of wells for an example data, which is given in Table 1. Table 1. Data on a fountain well with layer pressure 7.15 MPa. Oil production Bottom hope Wellhead rate, m3 /day, Q pressure, MPa, pressure, Pbot MPa, Pwh
Layer gas production rate, m3 /day, V
Pbot-Pwh/ Player- Pbot
Productivity factor, Km3 / MPa/day
21,1
3,0
1,75
7125
0,301
5,57
18,8
4,0
2,25
4500
0,556
5,97
13,1
5,0
2,88
3200
0,986
6,09
7,5
6,0
3,56
1875
2,122
6,52
0
7,15*
4,38
375
–
–
The result of processing data in Table 1 is presented in Table 2.
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Table 2. Dependences of flow rate, pressure and the ratio of constant coefficients of the studied well Dependences for flow rate and pressure on formation gas flow rate Q = −0, 8941 · 10−6 V 2 + +0, 01126955V − 13, 8 P = 0, 98925 · 10−7 V 2 − −0, 00153096V + 8, 985
Ratio of constant coefficients Eqs. (1) and (2) With linear inflow into the well
With non-linear inflow into the well a = K1 = 15 a1 b − = K2 = 16, 5 b1 c − = K3 = 8, 88 c1 −
K = a/a1 = 9, 038; K = b/b1 = 7, 36; K = −(−13, 8)/8, 985 = 7, 52 Average value of K is 7,97
Average value of K is 10,3
The Fig. 3 and Fig. 4 demonstrate dependence of P/Q on Q (to determine constants A and B) and Q on P [3], respectively.
Fig. 3. The results of processing experimental data to determine the constants A and B Depending on the non-linear inflow
To determine the potential flow rate and reservoir pressure using formulas given above, we find the bottomhole pressure and the value: Pwb ≤ 0, 5(Player + Pwh )≤ 0, 5(7, 15 + 2, 25) ≤ 4, 7 choose a value P ∗ equal to 3.65 and calculate the terms of the formulas: b21 2a1 a a1
= 11, 846; − 4ab12c1 (1 − =
b b1
≈ 15, 7;
1 b21 2a1
− aa1 (c1 − 3, 65) =
( aa1 −
3,65 8,985 )
=
−0,98925·10−7 ·8,985 (1 − 0, 406) (0,00153096)2
b b1 ) = 0 −6 − −0,8941·10 (8, 985 − 3, 65) 0,98925·10−7
= 0, 901 < 1
3
m = 48, 21 day . 3
m The potential flow rate of the drainage zone will be Q = 48, 21 − 13, 8 = 34, 41 day , and the layer pressure is 7.47 Mpa. The found reservoir pressure is 4% higher than the measured pressure.
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Fig. 4. Nonlinear indicator dependence of a flowing well
Note that similar to Table 1 and Fig. 1 with a comparison of the calculation results using formulas (1) and (2) are empirical, are not universal in nature and describe real data in some approximation and the degree of compliance with the inflow equation, i.e. formulas (1) and (2) must be verified in each specific case.
2 Conclusions As a result of the study, the equation of gas-hydrodynamic processes of the drainage zone of oil and gas wells was obtained. The results of the research confirmed that the gas-hydrodynamic processes occurring in the drainage zone of wells for all methods of operation are of the same nature. The resulting equation can be used to analyze the gas-hydrodynamic processes of the drainage zone of flowing, gas-lift and pumping wells, i.e. a new type of indicator dependence has been obtained. Similar to Table 1 and Fig. 1 with a comparison of the results of calculation by (1) and (2) with the initial data, showing that the given relationships are empirical, are not universal in nature and describe real data in some approximation. The degree of compliance of the inflow equations described by formulas (1) and (2) must be checked in each specific case.
References 1. Silash, A.R.: Dobicha i transport nefti i gaza. M: Nedra, p. 375 (1980) 2. Gurbanov, R.S., Gurbanova, T.G.: O povishenii effektivnosti prochessa jtkachki shtanqovimi skvajinnimi nasosami. Neftepromislovoe delo 10, 58–60 (2014) 3. Gurbanova, T.G.: Razrabotka gazogidradinamicheskix metodov ekspluatachii skvajin, rabotayushix nasosnim sposobom. Phd. Baku, p. 175 (2018) 4. Gurbanov, R.S., Gurbanova, T.G.: Noviy metod issledvaniya skbajin ANX. Baku 10, 38–42 (2013) 5. Gurbanov, R.S., Gurbanov, S.R., Nasibov, N.B.: Optimizachiya rejimov paboti gazliftnix skvajin Texnika. Baku 10, 76–81 (2003)
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6. Gurbanov, R.S., Gurbanov, S.R., Gurbanova, T.G., Nabiev, N.A.: Pakernoe ustroystvo dlya requlirovaniya zatrubnoqo gaza Patent№U20170021 (2015) 7. Gurbanov, R.S., Nasibov, N.B.: Optimizachiya rejima raboti gazliftnix skvajin na osnove dannix debita pritoka gaza i zaboynoqo davleniya Trud, N˙I˙I «Geotexnologicheskix problemi nefti, gaza i ximiya» Baku, t.XII , p. 6 (2003) 8. Gurbanov, R.S., Nasibov, N.B.: Sposob ekspluatachii skvajin. Patent № A2015200056, Baku: 1 (2007) 9. Gurbanov, R.S., Gurbanova, T.G.: Metod integralnogo modelirovaniya neftegazovoy sistemi Trud, N˙I˙I «Geotexnologicheskix problemi nefti, gaza i ximiya» Baku, t.XV, pp. 250–259 (2014) 10. Mamedova, Z.E.: Vibor naiviqodneyshego rejima ekspluatachii shtangonasosnix skvajin s visokim gazovim faktorom. ANX (2), 31–36 (2003) 11. Mamedova, Z.E.: Ob ustanovlenii rachionalnogo rejima ekspluatachii gazopeskoproyavlyayushix nasosnix skvajin / Trudi 2-oy Mejdunarodnoy nauchno-prakticheskoy konferenchii molodix uchenix. Kazaxistan, pp. 147–151 (2002) 12. Mamedova Z.E. Ustanovlenie nailuchshego rejima ekspluatachii gazoproyavlyayushix nasosnix ckvajin. Phd., Baku, 2007, 158 p. 13. Sharifov, M.Z.: ˙Issledovanie i optimizachiyaa rejimov ekspluatachii gazliftnix skvajin Phd., Baku, p. 105 (1991) 14. Ahmadov, S.A., Gardashova, L.A.: Fuzzy dynamic programming approach to multistage control of flash evaporator system. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 101–105. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-35249-3_12 15. Gardashova, L.A.: Synthesis of fuzzy terminal controller for chemical reactor of alcohol production. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 106–112. Springer, Cham (2020). https:// doi.org/10.1007/978-3-030-35249-3_13 16. Aliev, R.A., Pedrycz, W., Kreinovich, V., Huseynov, O.H.: The general theory of decisions. Inform. Sci. 327(10), 125 -148 (2016) https://www.sciencedirect.com/science/article/abs/pii/ S0020025515005885 17. Aliev, R.A., Huseynov, O.H.: Decision Theory with Imperfect Information, p. 444. World Scientific, Singapore (2014) https://www.worldscientific.com/worldscibooks/https://doi.org/ 10.1142/9186 18. Alizadeh A.V.: Application of the fuzzy optimality concept to decision making. Adv. Intell. Syst. Comput. 1095, 542–549 (2019) https://doi.org/10.1007/978-3-030-35249-3_69
Appling Fuzzy Inference Logic System to Dynamic Model of Gross Domestic Product (in Case of Azerbaijan) Yadulla Hasanli1,2(B)
, Shafizade Elnure3
, and Guliev Fariz3
1 Scientific-Research Institute of Economic Studies, Azerbaijan State University of Economics
(UNEC), Istiqlaliyyat Str .6, AZ1001 Baku, Azerbaijan [email protected] 2 Institute of Control Systems, Ministry of Science and Education Republic of Azerbaijan, Bakhtiyar Vahabzadeh Street 68, AZ1141 Baku, Azerbaijan 3 Azerbaijan State University of Economics (UNEC), Istiqlaliyyat Str .6, AZ1001 Baku, Azerbaijan {elnure_sh,f.guliyev}@unec.edu.az
Abstract. The main criteria and source of economic development is economic growth. Economic growth is a sustainable increasing tendency of the main indicators of national theory production – gross national income (GNI) and gross domestic product (GDP). Furthermore, absolute value and per capita growth are also considered. In economics and statistics, various indicators are used to measure the amount of national production. The most important of these is gross domestic product. GDP is expressed by monetary unit of the final products and services produced in the economy. Here, it should be taken into account that GDP is comprised of final products and services produced within the particular country. In this work, fuzzy inference logic system was applied to the dynamic model that demonstrates the dependence of GDP on currency and oil price in case of Azerbaijan economy. To solve this dynamic problem some coefficients, need to be defined. Fuzzy inference logic method was suggested to define these coefficients. Fuzzy inference logic method was realized by MATLAB Software Package. Keywords: Gross domestic product · Dynamic model · Fuzzy logic · Fuzzy inference logic method · Model of the optimal trajectory of GDP
1 Introduction The main criteria and source of economic development is economic growth. Economic growth is a solid stimulant for the growth of the main indicators of national production (GDP, GNI). Furthermore, absolute value and growth per capita is also kept in mind. In economic theory and statistics, various indicators are used to measure the volume of national production. The most important of these is gross domestic product (GDP) [1]. GDP is an expression in monetary unit of the final products and services produced in © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 427–434, 2023. https://doi.org/10.1007/978-3-031-25252-5_57
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the economy. This refers to the final products and services produced within the borders of a particular country. Three main methods are used to calculate GDP [1]: – Added value method (method of production). GDP is equal to the difference between the total output of goods and services and intermediate consumption. Total added value reflects the generation of primary income in the production process. – By costs. Using this method, the volume of GDP is calculated as the sum of consumption expenditures, investment expenditures, government expenditures, and net exports, in other words, the difference between exports and imports; – Calculation of GDP by revenue - the main factors of production receive income in proportion to the share of value added: labor force - as wages; entrepreneur - as a profit; capital - as interest and depreciation allowances; land - as renta. It turns out that it is possible to get the amount of value added by accumulating the income of the main factors of production. The relationship between economic growth factors within the national economy is becoming more complicated. In such a situation, the main goal of the state is the effective use of existing economic factors to promote economic growth to benefit the general populace [2]. There are many factors that affect the increases in GDP. The richness of Azerbaijan’s oil and gas reserves, the near-absolute share of oil production and exports in the country’s exports, and the large inflow of foreign currency reserves from oil and gas exports give us basis to take the currency and oil prices as driving factors to achieve the desired GDP growth. So, in this work, fuzzy inference logic method was applied to the dynamic model that demonstrates the dependence of GDP on currency and oil price in case of Azerbaijan economy. To solve this dynamic problem some coefficients need to be defined. Fuzzy inference logic method was suggested to define these coefficients.
2 The Dynamic Model of GDP with Two Controls Consider the following task: what currency and oil price should be in a certain year to achieve the desired level of GDP after a certain period of time [2, 3]. To do this, consider the following task: 2 2 u1i → min + u2,i+1
(1)
xi+1 = Fxi + G1 u1i + G2 u2,i+1 + v, i = 0, n − 1
(2)
x(0) = x0
(3)
J =
N i=0
(xdesi − xi ) + 2
N −1 i=0
where, xi is the amount of GDP in the i-th year; xdesi -the desired amount of GDP in the i-th year;
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u1i is currency in the i-th year; u2i -the oil price in the i-th year; F, G1 , G2 , v-are defined numbers. Suppose xdesi = 0 for i = 0, N − 1 and xdesN = xdes . Then formula (1) can be written as the following form: J = (xdes − xN )2 +
N −1
2 2 xi2 + u1i → min + u2,i+1
(4)
i=0
(4) can be written in general form as following: J =
N −1 1 1 2 2 2 q(xdes − xN )2 + k0 xi + k1 u1i → min + k2 u2,i+1 2 2
(5)
i=0
xi+1 = Fxi + G1 u1i + G2 u2,i+1 + v, i = 0, N − 1
(6)
x(0) = x0
(7)
Here, q > 0, k0 ≤ 0; k1 , k2 > 0 are coefficients, F, G1 , G2 , v was defined with least square method, and N is the number of years. For this, we construct an extended criterion of quality J [2, 4]. To do this, we add systems of equations with coefficients λ(i)[1, 3, 4] to function J: J = +
N −1 i=0
1 q(xdes − xN )2 2
1 2 2 2 k0 xi + k1 u1i + λi+1 Fxi + G1 u1i + G2 u2,i+1 + v − xi+1 (8) + k2 u2i 2
We use the following notation: φ(x(N )) = Hi =
1 q(xdes − xN )2 2
1 2 2 2 k0 xi + k1 u1i + λi+1 Fxi + G1 u1i + G2 u2,i+1 + v + k2 u2i 2
We can rewrite (8) as such: J = +
N −1 i=1
1 q(xdes − xN )2 − λN xN 2
1 2 2 2 k0 xi + k1 u1i + k2 u2,i+1 + λi+1 Fxi + G1 u1i + G2 u2,i+1 + v − λi xi + H 0 2
We get the following problem: J =
1 q(xdes − xN )2 − λN xN 2
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1 2 2 2 k0 xi + k1 u1i + k2 u2,i+1 + λi+1 Fxi + G1 u1i + G2 u2,i+1 + v − λi xi + 2 H 0 → min (9) xi+1 = Fxi + G1 u1i + G2 u2,i+1 + v, i = 0, N − 1 x(0) = x0
(10)
(11) To solve the problems (2.9)–( 2.11), i.e. to find the valuesλi , i = 0, n + 1 , uji , i = 0, n − 1, j = 1, 2 and xi , i = 0, n , we need to solve the system of equations [2, 4]. We have to define coefficients k0 ≤ 0, k1 , k2> 0. Here, our main goal is to find such values of uji , i = 0, n − 1, j = 1, 2 and xi , i = 0, n that would be more realistic. We’ll apply fuzzy inference logic method for defining these coefficients [5–12]. At the first, we define output and input linguistic variables. So, linguistic variables are: coefficient of GDP, coefficient of currency, coefficient of oil price, GDP, currency and oil price. Input variables of them are: GDP, currency and oil price; output variables are: coefficient of GDP, coefficient of currency, coefficient of oil price. Suppose let us denote these linguistic variables such as: • • • • • •
coefficient of GDP- k0 ; coefficient of currency- k1 ; coefficient of oil price- k2 ; GDP- x; currency -u1 ; oil price- u2 . GoodBadTerm sets of these variables is given in the Table 1. Table 1. Term sets of input and output linguistic variables.
Linguistic variables
Variables
Coefficient of GDP
Output variables
Term sets
Coefficient of currency
k0
Bad
Good
Not too bad
Coefficient of oil price
k1
Bad
Good
Not too bad
k2
Bad
Good
Not too bad
Input variables GDP
x
Bad
Good
Not too bad
Currency
u1
Bad
Good
Not too bad
Oil price
u2
bad
Good
Not too bad
Interval values of these variables correspondingly their term sets is given in the Table 2.
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Table 2. Interval values of input and output variables correspondingly their term sets. Variables
Term sets Bad
Good
Not too bad
k0
[0.05941 -0.28]
[0.05941 -0.14]
[0.05941 0]
k1
[5.097e + 06 10]
[5.097e + 06 1.5e + 07]
[5.097e + 06 3e + 07]
k2
[1699 1]
[1699 5001]
[1699 1e + 04]
Output variables
Input variables x
[2.888e + 10 1]
[2.888e + 10 8.5e + 10
[2.888e + 10 1.7e + 11]
u1
[0.5777 2.36e-17]
[0.5777 1.7]
[0.5777 3.4]
u2
[50.96 -1.776e-15]
[50.96 150]
[50.96 300]
Then, it is implemented as fuzzy sets fuzification. Membership function for these fuzzy sets are constructed as Gaussian function. The next step is to construct logical rules on the base of expert reasoning. For example, expert reasoning can be written as the following form: • If GDP is bad and currency is bad and oil price is bad then coefficient of GDP is bad, coefficient of currency is bad, coefficient of oil price is bad; • If GDP is good and currency is good and oil price is good then coefficient of GDP is good, coefficient of currency is good, coefficient of oil price is good; • If GDP is not too bad and currency is not too bad and oil price is good then coefficient of GDP is not too bad, coefficient of currency is not bad, coefficient of oil price is not bad); • If GDP is bad and currency is good and oil price is very good then coefficient of GDP is bad, coefficient of currency is not bad, coefficient of oil price is not bad; • If GDP is bad and currency is bad and oil price is very good then coefficient of GDP is bad, coefficient of currency is not bad, coefficient of oil price is not bad; • If GDP is not too bad and currency is not too bad and oil price is good then coefficient of GDP is not too bad, coefficient of currency is not bad coefficient of oil price is not bad and etc. Then fuzzy inference logic rules will be in the following form: • If (x is bad) and (u1 is bad) and (u2 is bad) then (k0 is bad)(k1 is bad)(k2 is bad); • If (x is good) and (u1 is good) and (u2 is good) then (k0 is good)(k1 is good)(k2 is good); • If (x is not_too_bad) and (u1 is not_too_bad) and (u2 is very_good) then (k0 is not_too_bad)(k1 is not bad)(k2 is not bad); • If (x is bad) and (u1 is good) and (u2 is very_good) then (k0 is bad)(k1 is not bad)(k2 is not bad);
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• If (x is bad) and (u1 is bad) and (u2 is very good) then (k0 is bad)(k1 is not bad)(k2 is not bad); • If (x is not_too_bad) and (u1 is not_too bad) and (u2 is good) then (k0 is not_too_bad)(k1 is not bad)(k2 is not bad); • If (x is good) and (u1 is bad) and (u2 is good) then (k0 is bad)(k1 is not bad)(k2 is not bad); • If (x is good) and (u1 is good) and (u2 is good) then (k0 is not bad)(k1 is good)(k2 is not bad); • If (x is good) and (u1 is not_too_bad) and (u2 is very_good) then (k0 is not bad)(k1 is not_too_bad)(k2 is not bad); • If (x is bad) and (u1 is bad) and (u2 is bad) then (k0 is not bad)(k1 is bad)(k2 is not bad); • If (x is not_too_bad) and (u1 is not_too_bad) then (k0 is not bad)(k1 is not_too_bad)(k2 is not bad); • If (x is good) and (u1 is bad) and (u2 is good) then (k0 is not bad)(k1 is bad)(k2 is not bad); • If (x is good) and (u1 is bad) and (u2 is bad) then (k0 is not bad)(k1 is bad)(k2 is not bad); • If (x is good) and (u1 is good) and (u2 is very_good) then (k0 is not bad)(k1 is not_too_bad)(k2 is not bad); • If (x is bad) and (u1 is not_too_bad) and (u2 is very_good) then (k0 is not bad)(k1 is bad)(k2 is not bad); • If (x is good) and (u1 is good) and (u2 is good) then (k0 is not bad)(k1 is not bad)(k2 is good); • If (x is bad) and (u1 is bad) and (u2 is bad) then (k0 is not bad)(k1 is not bad)(k2 is bad); • If (x is not_too_bad) and (u1 is not_too_bad) and (u2 is very_good) then (k0 is not bad)(k1 is not bad)(k2 is not_too_bad); • If (x is good) and (u1 is good) and (u2 is bad) then (k0 is not bad)(k1 is not bad)(k2 is bad); • If (x is good) and (u1 is good) and (u2 is very_good) then (k0 is not bad)(k1 is not bad)(k2 is not_too_bad); • If (x is good) and (u1 is bad) and (u2 is bad) then (k0 is not bad)(k1 is not bad)(k2 is bad); • If (x is good) and (u1 is not_too_bad) and (u2 is very_good) then (k0 is not bad)(k1 is not bad)(k2 is not_too_bad); • If (x is bad) and (u1 is good) and (u2 is good) then (k0 is not bad)(k1 is not bad)(k2 is bad); • If (x is not_too_bad) and (u1 is bad) and (u2 is very_good) then (k0 is not bad)(k1 is not bad)(k2 is bad); So the rules are constructed with support of linguistic variables for coefficients of GDP, currency and oil price. Transforming the above rules, we’ll get fuzzy sets for the endogenues variables k0 , k1 , k2 on the base of each rule. The composition method, gives a fuzzy set which is the range of values of fuzzy output variables and by the centroid method, we obtain a crisp numerical solution.
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Fuzzy inference logic method was realized by MATLAB Software Package [13]. As the solution of this problem for each linguistic variable we obtain the following crisp values: • If x = 5*1010 and u1 = 1.7 and u2 = 110 and then k0 = –0.14, k1 = 1.5*107 , k2 = 5.4*103 . The dependence of k0 on x and u1 is shown in the Fig. 1.
Fig. 1. Fuzzy inference for defining coefficients of GDP (k0 ), currency (k1 ) and oil price (k2 ).
3 Conclusion When solving the problem (9)–(11), we have to determine the coefficients k0 , k1 , k2 . These coefficients should be chosen so that the results are close to real values. We encounter many errors when selecting and working with these coefficients at random, and this process takes us a long time. However, when using the fuzzy inference logic method, it is possible to get the desired result with minimal errors in a very short time. In our future work, we intend to study this approach in more detail and get more appropriate results.
References 1. Hasanli, Y.: Modeling of intersectoral relations of Azerbaijan economy., Baku, p. 170 (2011) 2. Shafizade, E.R.: The dynamic model of the optimal trajectory to achieve the desired level of GDP for Azerbaijan. In: Proceedıngs of the 7th International Conference on Control and Optımızatıon with Industrial Applications. Baku, Azerbaijan, vol. 2, pp. 353–355 (2020). COIA20_V2.pdf (coia-conf.org) 3. Hasanli, Y., Hasanov, R.: Application of Mathematical Methods in Economic Research, Baku, p. 303 (2002)
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4. Bryson, A., Ho, Y.-C., Siouris, G.M.: Applied optimal control: optimization, estimation, and control, Waltham, MA: Blaisdell, p. 367 (1979) https://doi.org/10.1109/TSMC.1979. 4310229 5. Tsekouras, G.E.: Fuzzy rule base simplification using multidimensional scaling and constrained optimization. Fuzzy Sets Syst. 297, 46–72 (2016). https://doi.org/10.1016/j.fss.2015. 10.009 6. Hudec, M.: Fuzziness in Information Systems: How to Deal with Crisp and Fuzzy Data in Selection, Classification, and Summarization, p. 210 (2016) 7. Bˇelohlávek, R., Dauben, J.W., Klir, G.J.: Fuzzy Logic and Mathematics: A Historical Perspective, p. 545 (2017) 8. Shankar S., De Silva, C.W.: Intelligent Control : Fuzzy Logic Applications, p. 368 (1995). https://doi.org/10.1201/9780203750513 9. Zadeh, L.A., Yager, R.R.: An Introduction to Fuzzy Logic Applications in Intelligent Systems, p. 357. Springer US (1992). https://doi.org/10.1007/978-1-4615-3640-6 10. Shafizade, E.R., Shikhlinskaya, R.: Application of fuzzy inference rules to a model for optimizing the production and sectoral structure of agriculture to ensure food security. Actual Prob. Econ. 1(103), 286–294 (2010) 11. Shafizade, E.R., Shikhlinskaya, R.Y., Gasimov, B.M.: Fuzzy model of profit maximization for e-shop. In: Proceeding of ICAFS, Lisbon, Costa da Caparica, Portugal, pp. 185–192, (2012) 12. Shikhlinskaya, R.Y., Shafizadeh, E.R.: Profit optimization in virtual business applying fuzzy logic. J. Automation Inform. Sci. 47(1), 77–87 (2015). https://doi.org/10.1615/JAutomatInfS cien.v47.i1.70 13. Leonenkov, A.: Fuzzy modeling in MATLAB and fuzzy TECH, St. Petersburg. BHV, Petersburg, p. 725 (2003)
Analysis of Knee Osteoarthritis Grading Using Deep Learning Serag Mohamed Akila1
, Elbrus Imanov2(B)
, and Khaled Almezhghwi3
1 Department of Biomedical Engineering, Near East University, Mersin-10, Northern Cyprus,
Turkey 2 Department of Computer Engineering, Near East University, Mersin-10, Northern Cyprus,
Turkey [email protected] 3 Electrical and Electronics Engineering, College of Electronics Technology Tripoli, Tripoli, Libya
Abstract. Knee osteoarthritis severity grading from plain radiographs and magnetic resonance (MR) images is of great significance in the diagnosis of osteoarthritis (OA). Recently, deep learning had a great impact on improving the Kellgren and Lawrence (KL) grading scheme of Knee osteoarthritis KOA using models that acquire the contextual features spontaneously without the need for any conventional high computational spatial configuration modeling. In this study, we review the state-of-the-art deep learning methods that enhanced the knee osteoarthritis severity KL grading. Pre-trained models such as Resnet18, VGG, DenseNet, Convolutional Siamese neural network, ResNet34, Squeeze-and-excitation ResNet (SE-ResNet) were found to be employed to extract valuable data for clinical images in the surveyed papers. The survey concludes that some very significant sophisticated deep learning methods were employed in some studies to grade KOA, which may also work on grading other diseases. Moreover, we show that applying Vision Transformer (ViT) for this specific task can be a better option than most of the convolutional neural networks (CNNs) based models. Keywords: Knee · Severity · Radiographs · Grading · Models · Feature
1 Introduction Osteoarthritis is generally identified as arthritis that tear-and-wear, it is also a state where the regular cushioning between joints that is, the cartilage wears out. The bones of the joints rub more strictly touching one another with fewer of the shock-absorbing aids of cartilage. This close rubbing results in stiffness, pain, swelling, etc. Osteoarthritis which is the well-known arthritis can affect the knee which is referred to as degenerative arthritis of the knee. The major causes of osteoarthritis of the knee are weight, age, and heredity. Aside from surgery where arthroplasty, osteotomy and arthroscopy are applied, the osteoarthritis of the knee can be treated by consolidating the muscles closed to the knee usually stabilizes joint. It also goes along way in reducing the pain. Stretching © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 435–443, 2023. https://doi.org/10.1007/978-3-031-25252-5_58
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drills aid in keeping the knee joint mobile and flexible. Moreover, losing weight can significantly reduce knee pain from osteoarthritis. However, physicians usually apply physical examination to diagnose the osteoarthritis of the knee. To check the severity and get the picture of the affected joint, a physician might recommend an imaging test where an X-ray is applied to reveal the cartilage loss and as well show bone spurs around a joint. Magnetic resonance imaging (MRI) also utilizes a magnetic field to give detailed images of the soft tissues, cartilage, and bone. The reliability of physicians might not be enough in assessing the severity of knee OA using a five-point scale of Kellgren & Lawrence (KL) grades. Therefore, the need to automatically predict KL grades from radiograph images to assess and diagnose the severity of knee OA in the early progressive stages is important. Grading the knee OA and measuring the severity of knee OA is important for clinical judgement, forecasting disease advancement and pathology [1]. Osteophytes (bone spurs) formation and joint space narrowing (JSN) are known to be the crucial pathological structures of knee OA [2], which can be understood simply with radiographs [1]. The evaluation and diagnosing of knee OA severity has been on the traditional approach as an image problem which can be solved using classification [3], with the KL grades being the ground truth for classification. A computer-aided analysis is expedient in radiographic features detection, quantifying knee OA severity and predicting the upcoming expansion of knee OA [3]. Learning feature representations of knee OA images using deep learning can be extra effective in assessing the severity condition than when hand-crafted features are used. The feature learning methods give a prospective technique for capturing cues by using a large number of neurons, whereas computer vision features traditionally are designed for simple class acknowledgment. It may also remove many useful cues in the course of feature extraction [4]. Recently, feature representations learning is preferred to features crafted by hands, mainly for fine-grained sorting, since rich presence and shaped features are important for relating subtle variances between classes [4] Over the past 2.5 decades, medical image study methods have been the popular research area in the field of image processing and computer vision. A substantial amount of systems have been recommended for precise description and measurement of knee osteoarthritis [5]. Surveyed the contemporary progress in the improvement of present computer vision techniques for medical applications driven by deep learning and focused on therapeutic imaging. Deep learning is an algorithm capable of extracting data from medical images which are unidentifiable by human analyses to gain information on prognosis, molecular status or treatment sensitivity [6]. It entails multilevel neural networks that carries deep features for disease organization, speech understanding, etc. Deep neural networks, deep Boltzmann machines, stacked auto-encoders and convolution neural networks (CNN) are the common deep learning algorithms. Moreover, Deep learning systems have newly been recognized to extract partial features and have increased the effectiveness of exploring medical images. The influence of the classification method mainly depends on the effectiveness of the resulting features that describe the main characteristics of medical images [1]. Related to conventional methods, the specificity of CNN classifiers is significantly greater, ultimate with radiologists for all surgical exercises. The research was carried out to analyze medical images using deep learning [7]. Also, machine learning [8], fuzzy
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neural network, deep learning [9, 10]and artificial intelligence AI in general have been applied as diagnostic tools in the field of medicine. In this paper, the reader is going to be familiarized with the key guidelines of deep learning techniques on the diagnosis and grading severity of knee osteoarthritis. In addition, it will also objectively highlight the deficiencies and impending thoughts in the application at scientific practice. This assessment is distributed into three sections. Section 2 presents the materials and techniques used in the survey on the severity of knee osteoarthritis. Section 3 presents the results of the reviews where the most common deep learning methods and algorithms used in grading severity of knee osteoarthritis are illustrated. Section 4 discusses the potential of deep learning as well as the future directions related to grading severity of knee osteoarthritis with concluding remarks [11].
2 Materials and Methods Various studies surveyed or overviewed the significance of deep learning in medical imaging [12]. A substantial physique of work has been published in a deep learningbased severity of knee osteoarthritis diagnosis. However, reviewing will be difficult without embracing a systematic methodology to scale down to the most appropriate work associated with this subject. This part describes the scheme embraced for this purpose. To the best of our knowledge, this is the first survey on knee osteoarthritis severity grading using Deep learning. [13], and [14] are some of the related studies that surveyed knee articular cartilage segmentation from MR images and segmentation of knee cartilage respectively. However, their surveys did not explain deep learning explicitly. Figure 1 illustrates the channel of knee severity grading on the knee X-ray radiograph. Google Scholar, Scopus, Science Direct, ISI Web of Knowledge, PubMed and IEEE Xplore were the databases used during the review. The term used for searching was “severity of knee osteoarthritis” and (“medical imaging) and “deep learning”. We involved the articles printed in peer-reviewed magazines, conferences, book chapters, and symposiums. Also, we surveyed the lists of reference of the nominated journals, and the correlated work was involved in retrieving other related journals. We left out articles that are centered on the titles but were not related to our review.
3 Results In the knee osteoarthritis grading using pre-trained models, advanced analytical models have been adopted relatively by the OA field compared to other fields. As confinement of joints was a vital duty in the reported X-ray applications. Several methodologies of varying intricacy were applied, these are customized one-stage YOLO v2 network, the Sobel horizontal image gradients, non-maximal suppression (NMS), Bone Finder tool, Linear SVM etc. Currently, several studies are emphasizing on developing machine learning forecasting models for KOA founded on medical imaging such as magnetic resonance imaging (MRI), X-ray. These Imaging technologies were integrated into the mainstream of innovative logical models to forecast the severity of knee Osteoarthritis with precisions varying from 70%–93%. Deep convolutional neural networks (CNN), Siamese model, Deep Siamese CNN and ResNets were selected because of their efficacy
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and projecting performance. The Deep Siamese CNN learning algorithm achieved 93% using the ResNet34 as the feature extractor [23]. In addition, the test, validation, and training sets included and 5,960; 2,957 and 18,376 respectively. The synopsis of the above-mentioned studies is shown in Table 1. Table 1. Knee Osteoarthritis Grading using pre-trained models Authors
Year
Learning Algorithm
Validation
Results
Bin Liu, Jianxu Luo, Huan Huang [15]
2020
Fast R-CNN
Fivefold-CV
A mean average precision is 82%, sensitivity >78% and specificity >94%
H.H. Nguyen, S. Saarakkala, A. Tiulpin [16]
2020
Siamese model
Considered 4 data settings: 50, 100, 500 and 1000 knee radiographs per KL-grade
Achieved better performance on SL setting compared to the reference scheme’s in theen tire data scenarios
Pingjun Chen, 2019 Linlin Gao, Xiaoshuang Shi, Kyle Allen, Lin Yang [17]
Deep convolutional neural networks (CNN)
The loss consequence weight among neighbor rating is 1, 2, and 3 correspondingly
Achieved 0.858 mean Jaccard index and 0.922 recall under the same Jaccard index threshold of 0.75
Joseph Antony, Kevin McGuinness, Noel E O’Connor, Kieran Moran [18]
2016
Pre-trained and The Data was divided fine-tuned CNN into training (0.60), validation (0.10) and test (0.30) sets for fine-tuning
Matthew D. Li, Ken [19]
2020
ImageNet. ResNets-18, 34,50, 101, and 152
Increase in accuracy and reduction in loss demonstrates that the fine-tuning is active and marks the CNN structures more discriminative, which improves classification accuracy
Same number of (AUCs) of up to 0.90 combined input retinal photographs were sampled at random with the same or dissimilar plus disease classification for both validation and training (continued)
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Table 1. (continued) Authors
Year
Learning Algorithm
Validation
Kevin A. Thomas [20]
2020
169-layer convolutional neural network
32,116 images were Simple average F1 score used to train the model of 70% and an accuracy and tuned it with 4,074 of 71% were obtained images, finally evaluated it with a 4090 image set
Aleksei Tiulpin, 2018 [23]
Deep Siamese CNN
Training, validation and Achieved AUC of 0.93 test sets were 18,376; 2,957 and 5,960 images respectively
Dong Hyun Kim [22]
CNN
9:1 ratio for the training 69% obtained as the and validation set in AUCs of the DL proportion to KL grade algorithm in diagnosing KL image data alone and 75% for the grouping of image data
2020
Results
Currently, several studies are emphasizing on developing machine learning forecasting models for KOA founded on medical imaging such as magnetic resonance imaging (MRI), X-ray. These Imaging technologies were integrated into the mainstream of innovative logical models to forecast the severity of knee Osteoarthritis with precisions varying from 69.5%–99%. 3D CNN architecture, R-CNN and LSTM-the attention mechanism from Nauta’s repository were selected because of their competence and predictive performance [21]. [24] utilized two V-net designs and the 3D architecture applied to BMEL 2-class and gave an accuracy of 0.795. Moreover, [25] achieved an The AUC standards of LSTM for the KL = 1, 2, 3, and 4 are 81%, 91%, 99%, and 98% respectively with 10-fold cross-validation. In this paper, a Transformer-based classification approach is applied for the KL grading of Knee Osteoarthritis grading using plain X-ray radiographs. We used the base ViT developed in [26] in order to transfer its knowledge into a new classification task which is the KL KOA severity grading. This employed ViT has recently shown great potentials in image processing and classification by achieving comparable results while requiring fewer computational resources. This is mainly due to its multi-head attention mechanism [18], that allows it to significantly improve the convergence of the model, hence enhancing the performance and generalization capabilities in case of classification [18]. As seen in Fig. 1, knee X-ray images are fed into the Transformer as inputs of size 224 * 224 * 3 pixels and they are then divided into 16 * 16 patches with 16 stride and no overlapping patches, as in the original base ViT [26]. Those patches are then flattened, and lower-dimensional linear embeddings are produced from these flattened patches. Therefore, the model was trained using the Adam optimization algorithm with a gradient decay factor of 0.9. The initial learning rate was set to 0.001 while the regularization
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Fig. 1. Vision Transformer Illustration for Knee Osteoarthritis KL grading. The ViT consists of several blocks such as: Patches and Embedding, Transformer Encoder, and MLP Head
factor was set to 0.0001. Each model was trained for 50 epochs with a mini-batch size of 16 due to memory limitations. Figure 2 shows the testing confusion matrix (right) of the Transformer. This figure shows that the performance of our model differs from one grade to another which is more likely because the imbalance between grades in addition to complexity and variability of features of every grade. In Table 2 we provide a full breakdown of the testing performance of the best model. The breakdown includes performance metrics such as: Precision, F1-Score, and Accuracy. It is seen that the achieved a significant generalization capability with mean Precision, F1-Score, and Accuracy of 71.2%, 71.2%, and 70%, respectively. It must be noted that the model showed such promising generalization power of accuracy equals to 70%, when tested on both original and augmented X-ray radiographs which may contain different images inspired by the complexities found in the original knee X-ray plain radiographs.
Fig. 2. Confusion matrix of the testing phase.
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Table 2. Knee Osteoarthritis Grading using proposed approach KL grades
Precision
Recall
F1-Score
Accuracy
0
0.86
0.71
0.78
0.70
1
0.41
0.52
0.46
0.53
2
0.60
0.72
0.66
0.57
3
0.81
0.83
0.82
0.86
4
0.88
0.80
0.84
0.94
71.2%
71.6%
71.2%
72%
Mean
4 Discussion This literature assessment defined the contemporary practice of deep learning methods in KOA severity diagnosis and prediction experiments. Table 1 shows an increasing trend of deep learning-related studies and papers in the field of KOA severity signifying the necessity for improving our understanding of the severity of the disease and also the new data-driven tools that could help in early diagnosis and prediction of KOA severity. Deep learning could play an important part concerning the directions in extracting valuable knowledge from various types of clinical data especially images. Data is one of the most important assets in health care diligence. In KOA severity research, some data sources have been taken as inputs establishing powerful multidimensional training and testing data sets. Medical imaging is one of the leading data sources in the area. MRI and X-ray images being classically employed in the bulk of the papers in our survey where 12 out of the 13 used X-ray and only 1 used the MRI. CNN was employed in eight (8) out of the thirteen (13) papers in the survey as a learning algorithm. The selection of CNN could be credited due to its computational effectiveness in high dimensional spaces and the fact that it generalizes well in practice. Finally, we show that a Vision Transformer can be a suitable and better option for grading KOA than most of convolutional neural networks-based method.
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Navigation of a Mobile Robot Based on Fuzzy Images in an Uncertain Environment A. B. Sultanova1,2(B) 1 Azerbaijan State University of Oil and Industry, Baku, Azerbaijan
[email protected] 2 Institute of Control Systems of ANAS, Azerbaijan, Baku AZ1010, Azerbaijan
Abstract. The main goal of scientific research on the development of intelligent object management systems is to ensure that the system can process not only data of a numerical type, but also various types of data, such as image, writing, speech, and operator-controlled systems are replaced by objects that have intelligent management. The increased performance of modern information systems makes it possible to use more complex algorithms for processing and analyzing digital images. The article proposes a fuzzy approach to the processing of images. Descriptive information and the concept of description are mainly covered by uncertainty. Fuzzy logic is a good mathematical basis for working with uncertain information. Using this methodology, the uncertainty in image concepts was manipulated. The increase in the computing power of visual sensors, as well as the ability to process large amounts of information from the scene of an accident, allows for mapping, localization, autonomous navigation, route tracking, etc. this was the main tool for creating visibility in applications such as. The mobile robot is mentioned as the basis for making decisions based on fuzzy visual information, and intelligent algorithms used in robotics have been considered. During the initial preparation of the image for recognition, the main problems, as well as their solutions are considered. Keywords: Computer vision · Fuzzy logic · Fuzzification · Mobile robot · Brightness characteristics · Image processing · Edge detection
1 Introduction The robot is a typical representative of mechatronic products. Nowadays, computer vision technologies have become widely used in many industries and services. The robot is controlled by a human operator. In this case, a person is required to control the robot and constantly monitor its movements. Work that requires increased attention and accuracy leads to rapid fatigue of the operator in the process of complex control and, as a result, to an increase in the probability of erroneous actions. A person cannot always correctly assess the situation and make an adequate decision based on telemetry data. It also slows down the optimal movement and flexibility of the robot. There is a need to create an intelligent robot system that allows it to function independently using fuzzy visual © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 444–451, 2023. https://doi.org/10.1007/978-3-031-25252-5_59
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information in an uncertain external environment with minimal human involvement. In the development of robotics, computer technology and image processing technologies, the use of machine vision has become more widespread. Recent research and development is aimed at developing systems that allow a mobile robot to act independently, make decisions. It is used in mechanical engineering, microelectronics, robotics, on industrial conveyors, in operations for quality control of parts and detection of defects, in detection of underwater processes, etc. image processing technology is used. By using machine vision to obtain data about the robot’s environment, it can improve the identification, localization and interaction of the robot with multiple machines, as well as increase its flexibility. The mobile robot, using its vision, receives visual information, calculates geometric parameters and the position of the target [1]. Machine vision uses video information and visual data as input data for the study and analysis of reliable data in images and videos [2]. In the process of obtaining an image, the camera usually picks up all kinds of noise and interference, so it is necessary to process the image [2, 3]. Receiving information about the environment through a robotic visual system, visual information with the help of computer analysis performs a number of actions or certain actions, receiving information about the environment related to the image [3, 4]. Depending on the working environment, machine vision systems are conditionally divided into two types. The first working environment is a known working environment, and the second is an undefined working environment. Currently, thanks to machine vision, the working environment is a known environment, and the environment is unknown and has uncertain facts [4]. The robot perceives the information contained in the working environment or the information it is interested in through a visual system and records it as a basis for decision-making. Robot vision technology is mainly used in the management of the robot: the description of scene information is a visual control system required to determine the location of the goal or motion data, for example, a visual search and location system, a visual tracking system, etc. to ensure [5]. The relevance of fuzzy image processing is explained by: – Fuzzy methods are powerful tools for knowledge representation and processing; – Fuzzy methods allow you to effectively manage uncertainty and ambiguity; – In many image processing applications, we have to use expert knowledge to overcome difficulties (for example, object recognition, scene analysis).
2 Visual Image Processing The essence of image processing is to bring the image of the initial image into a form that allows solving the problem of recognizing its objects. Image processing refers to signal processing, in which input signals are reflected in the form of images or video recordings. As a result, a transformed version of the input description or a set of characteristic features or parameters associated with this description can be determined. The computer revolution that has taken place over the past 20 years has led to great achievements in the field of digital visualization. The purpose of this article is to present the problem of robot navigation using visual illustrations. Robotics is based on visual sensors, such as a webcam, and any other sensors [5, 6]. Experts and scientists hope to completely
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simulate human vision by artificial means. With the development of research, machine vision gradually developed, and in the environment of computer modeling, the visualvisual function of a person is realized. Machine vision uses video and image data to study, extract and analyze reliable data from images and videos [6]. Processing of visual information with the use of technical vision system (TVS) is the processing of visual organs using computer instead of visual sensors. The processing of visual information in a machine vision system largely depends on image processing methods-image transformation, image compression, encoding, storage, primary processing, image enhancement and reproduction, image segmentation [3]. Image obtained directly from devices - 2D images are loaded with a lot of random noise and artifacts. The elimination of noise, distortion and adjustments is necessary in order to make the right action plan to increase the detection bandwidth and minimize data-related information, remove functions, image segmentation, compliance and recognition reliability [4]. Thus, useful information is preserved, useless information is compressed, and image quality is improved. In the process of image processing, the main goal is not to extract information from the image, but to remove misleading and not very valuable information. 2.1 Fuzzy Image Processing Fuzzy set theory is an extension of conventional set theory that deals with the concept of partial truth. Originally introduced by Lotfi Zadeh of the University of California Berkeley in 1965, fuzzy logic aims to model the vagueness and ambiguity in complex systems. In recent years the concept of fuzzy logic has been extended to image processing by Hamid Tizhoosh and others at the Pattern Analysis and Machine Intelligence (PAMI) research group at the University of Waterloo (Waterloo, ON, Canada). The concept of fuzzy logic has been formulated by many studies on its application in various fields of digital image processing, such as image quality assessment, edge detection, image segmentation, etc. In the past, researchers have proposed many methods for detecting boundaries based on fuzzy logic [3–9]. Fuzzy Logic has found many commercial applications in machine vision and imaging. Objective quality criteria are used in image processing. For example, an image with a small uncertainty showing high contrast may be “good”. But people may not perceive these results well, because such judgments are subjective. This difference between objectivity and subjectivity is the first big problem in humanmachine interaction. Another difficulty is related to the fact that different people may judge the image quality differently. This interpersonal difference is also primarily related to the subjectivity of a person. In recent years, the theory of fuzzy sets has been successfully applied to the issues of image processing and pattern recognition [10]. Fuzzy methods offer a mathematical apparatus for combating uncertainty and uncertainty [11]. Processing of fuzzy image is a nonlinear type of transformation, the difference from other well-known methods is that it is carried out by mastering the functions of belonging to pixels reflecting the image to fully describe the features of the image.
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Fuzzy image processing refers to the totality of all approaches to processing their segments and elements using the theory of fuzzy image clusters. Presentation and processing depend on the selected fuzzy method and the problem being solved. The processing of fuzzy image consists of three stages: the blurring of the image, the change of the belonging value, and the improvement of the image. Thus, the first stage of processing is phasification-generation of the corresponding prices of the membership function. At the phasification stage, the base values can often be interpreted as the type of encoding of the input data, which is necessary because it is incomplete and/or inaccurate. The use of fuzzification and defuzzification stages is due to the fact that we do not have a fuzzy hardware supply. Therefore, we process the image through fuzzy methods. The main advantage of processing fuzzy images is that we cannot change the affiliation values. After converting the image data from the gray level plane to the affiliation plane (fazzification), the corresponding fuzzy methods change the values of the affiliation. This can be fuzzy clustering, rules-based fuzzy approach, fuzzy integration approach. Fuzzy image processing involves the use of various fuzzy approaches, such as comprehension, representation, image processing, segments and fuzzy clusters. The algorithm developed for preliminary fuzzy processing within the framework of the problem being solved can be presented in the following sequence: – capture an image using a webcam; – converting a color image to a gray image; – fuzzy image processing. Processing of fuzzy drawings is a useful technology for the detection of boundaries and the formation of expert knowledge, as well as the combination of inaccurate information from various sources. It is a laxative to present the image fuzzy to obtain fuzzy signs from the digital image. Fuzzy features should be expressed in terms of fuzzy clusters and characterized by membership functions Q to this cluster. To get fuzzy clusters, it is necessary to translate the image into a fuzzy form, that is, the points reflecting the image must be represented in a fuzzy form. A fuzzy description is a description of points reflecting an image using membership functions of fuzzy sets. The fuzzy description is written as follows: M = Kf [F]. where Kf − the conversion operator. Discrete case, µ(x, y) = Kfn [f (x, y), F]. In it, µ(x, y)-is the function of belonging of the pixels of the image. Xj - as a fuzzy feature, some features of the X digital image are understood.
Many types of membership functions are known. Among them, it is necessary to choose those that provide the following conditions:
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Pixel classification is a processing method that segmented the image by classifying each pixel according to certain pixel characteristics. Noise and other sources of uncertainty can make pixel classification difficult. The use of fuzzy plural helps to overcome such uncertainty. Suppose the image X is given as a fuzzy array of size N × M . Each of the elements of this array has an accessory value P, which reflects the brightness of the image; (p = 0, 1, 2…P – 1), (p = 0 ÷ 255 - density range). Using fuzzy plural numbers in their notation, we can write:
where, 0 ≤ µmn ≤ 1, m = 1, 2…M, n = 1, 2…N. The used fuzzy logic rules have been improved for image edge detection. Using 25 fuzzy samples, let’s change their field to a fuzzy field, and then using a mask it is easy to highlight the image, determine the degree of distortion or intuitively a fuzzy index, determining the largest value of the discrepancy between each sample and the original. By selecting the minimum discrepancy values for each pixel, we convert it back to the original domain (0 – 255) and must set the limit value taking into account the following array of 25 pixels, as shown below. Now we scale the above values to get the membership functions of each of the given pixels, as shown below (Fig. 1).
Fig. 1. Pixels and membership functions values. (Note: Scaled pixel membership values can be obtained by dividing the pixel intensity by 255).
Now we can write the pixel intensity µ0 as: µ0 = (µ1 + µ2 + µ3 + µ4 )/4
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A fuzzy logical approach to image processing allows you to use membership functions to determine the degree of belonging of a pixel to the extreme points of an image or a universal area. The extreme points of the image are the contour between two universal areas. We can detect edges by comparing the intensity of neighboring pixels. However, since universal fields are not given with precision, small differences in intensity between two individual pixels do not always represent the extreme points of the image. Instead, the difference in intensity may represent a shadow effect.
3 Simulation of the System Fuzzy image processing consists of three main stages: fuzzification of images F, fuzzy inference system M on membership values and defuzzification of images D. The main fuzzy image processing is in the middle step (fuzzy inference system M). After transferring the image data from the gray level to the fuzzification, the fuzzy output system is determined by the membership values. Fuzzification – encoding of image data and defuzzification – decoding of results that allow processing images with fuzzy methods. This article presents the navigation task for an underwater robot in an unknown environment. The environment containing various types of obstacles is completely unknown to the robot, and all surrounding information must be detected by proximity sensors mounted on the robot body. An underwater robot was taken to solve this problem. An algorithm for image processing of an underwater robot based on the theory of fuzzy clusters is proposed in the following steps: 1. the input form is loaded and its dimensions are determined: M = width, n = height. 2. if image is color image convert it to grayscale. Iterate the pixels of the image and let’s write the intensity of the pixel µ0 in the form µ0 = (µ1 + µ2 + µ3 + µ4 )/4 3. Iterate the pixels for each image and calculate the edge membership function. Let’s recall the function of belonging to the maximum price, which appears in the figure (max.). 4. For each pixel, change its ownership by dividing it by the maximum value. 5. create a structure. Determine the value of the gray intensity using the formula for each pixel: I(i, j) = (L − 1) × µedge (I(i, j)) A jpeg. file was used with the image sizes used (m = 290, n = 174) pixels. The maximum intensity obtained is 202, µopt = 0, 55 The proposed object detection method was modelled using MATLAB. Images created in a fuzzy way look smoother, have less noise, and have a full set of fuzzy conditions (Fig. 2 and 3). The presented image is a grey image, and the information can vary from 0 to 255. Zero data belongs to the black pixel of the image, and 255 data belongs to the entire image. To implement a fuzzy algorithm, the data should only be in the range [0–1].
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Fig. 2. a) ˙Input image b) fuzzy image
Fig. 3. a) Input and output Membership b) original image function graph using FIS editor.
The simulation results demonstrate that the proposed method has great potential for solving the navigation problem. These results allow (Fig. 4.) us to conclude that the implemented FIS system provides greater resistance to changes in contrast and illumination, in addition to avoiding double edges. This has a constant effect on the smoothness and straightness of the lines, for curved lines it gave a good roundness. At the same time, the angles become sharper, and they can be easily identified.
Fig. 4. Image pixels
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4 Conclusion In this article, we presented a navigation algorithm based on a fuzzy image, and showed during the simulation that this algorithm can guide a mobile robot with a calibrated camera in an unknown external environment to a more passable area without encountering obstacles. Fuzzy logic was used to determine the boundaries of the detected image using computer vision. The resulting images can be used to control the robot using digital and fuzzy algorithms. At the same time, image enhancement methods using fuzzy cluster theory were used in the image processing process. The pattern recognition process helps the robot to receive the control signal necessary to act in a certain way, as well as to determine the next action to be performed at the end of the task. The advantage of this method over other methods is that adaptability is achieved here by changing the values of the description. The reliability of the results of the proposed method is better compared to the results obtained through the linear operators of Sobel Robert and Canny.
References 1. Aliev, R.A., Fazlollahi, B., Aliev, R.R.: Soft Computing and its Applications in Business and Economics. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-44429-9 2. Aliev, R.A., Huseynov, O.H.: Fuzzy geometry-based decision making with unprecisiated visual information. Int. J. Inf. Tech. Decis. 13(05), 1051–1073 (2014) 3. Aborisade, D.O.: Fuzzy logic based digital image edge detection. Global J. Comp. Sci. Tech. 10, 78–83 (2010) 4. Xu, L.M., Yang, Z.Q., Jiang, Z.H., Chen, Y.: Light source optimization for automatic visual inspection of piston surface defects. Int. J. Adv. Manufac. Tech. 91(5–8), 2245–2256 (2017) 5. Schroder, T., Kruger, K., Kummerlen, F.: Image processing-based deflagration detection using fuzzy logic classification. Fire Saf. J. 65, 1–10 (2014) 6. Gupta, M.M., Knopf, G.K., Nikiforuk, P.N.: Computer vision with fuzzy edge perception. In: International Symposium on Intel. Control, Philadelphia, USA, pp. 271–278 (1987) 7. Khan, A.R., Thakur, K.: An efficient fuzzy logic based edge detection algorithm for gray scale image. Int. J. Emerg. Tech. Adv. Eng. 2(8) (2012) 8. Sultanova, A.B., Safarov, T.A.: The detection of minefield in spectral mapping with using of UAV. J. RS Glob. https://doi.org/10.31435/rsglobal_ws/28022022/7765 9. Aslanov, J.N., Sultanova, A.B., Huseynli, Z.S., Mustafayev, F.F.: Determination of radial strains in sealing elements with rubber matrix based on fuzzy Sets. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 765–773. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-92127-9_101 10. Gardashova, L.A.: Using fuzzy probabilistic implication in z-set based inference. In: Aliev, R.A., Yusupbekov, N.R., Kacprzyk, J., Pedrycz, W., Sadikoglu, F.M. (eds.) WCIS 2020. AISC, vol. 1323, pp. 33–39. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-68004-6_5 11. Aliev, R.A., Gardashova, L.A.: Z-set based approach to control system design. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 10–21. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-640 58-3_2
Comparison of Oil Quality of Various Fields Based on Fuzzy Cluster Analysis G. Efendiyev1(B)
, S. Abbasova2
, G. Moldabayeva3
, and O. Kirisenko1
1 Institute of Oil and Gas, Azerbaijan National Academy of Sciences, Baku 1000, Azerbaijan
[email protected]
2 Azerbaijan State Oil and Industry University, Baku 1010, Azerbaijan 3 Satbayev University, Satpayev 22a, Almaty 050013, Kazakhstan
Abstract. The article is devoted to modeling relationship between oil properties and difficulty of oil extraction. Data on the properties, composition and conditions of oil occurrence in the fields of Azerbaijan and Kazakhstan have been collected. Clustering has been performed using a fuzzy cluster analysis algorithm based on a set of features characterizing the properties and conditions of oil occurrence and oil quality assessment. Oil density, oil viscosity, permeability of occurrence conditions, as well as oil composition are considered as classification features of various oil types of in the fields of Azerbaijan and Kazakhstan. A brief analysis of existing works on classification and assessment of oil quality of fields with hard-to-recover reserves showed the necessity to divide the total sample (set) into homogeneous groups according to a set of classification features characterizing the composition, properties and conditions of oil occurrence. A generalized parameter characterizing the composition of oil is proposed. Keywords: Oil field · Classification · Fuzzy cluster analysis · Hard-to-recover oils · Sulfur concentration · Density · Viscosity · Permeability
1 Introduction In recent years hard to recover reserves take a significant place in the total volume of oil produced, which creates a number of different problems of a technological and economic nature at various stages of their production, transportation and processing. The expansion of the volumes of processing of the considered oils, characterized not only by abnormal properties, but also by complicated geological conditions of occurrence, makes the problem of studying the qualitative features of hard-to-recover oils urgent. The relevance of the problems noted is especially important for the most comprehensive estimates of the factors that make it difficult to recover oil. In this regard, this article presents the results of the analysis of the properties and composition of various oil types representing Azerbaijan fields. First, a grounding is given for the necessity of a new approach to the tasks of classifying hard-to-recover reserves based on previous work performed. The need to divide the total sample into homogeneous groups according to the complex of classification features is shown and cluster analysis is most suitable © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 452–458, 2023. https://doi.org/10.1007/978-3-031-25252-5_60
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for it [1–5]. In this regard, this we consider the main essence and results of the cluster analysis using the example of earlier work on the fields data of Kazakhstan [13], as well as Azerbaijan [14] and provides a comparative assessment of the difficulty degree in extracting reserves.
2 Brief Analysis of Existing Works According to work [12], the geography of heavy oils and bitumen is quite wide around the world: from the basins of Western Canada, Eastern Venezuela (including the Maracaibo region), to the North Caspian, the Volga-Ural region of Russia, and Kazakhstan. The first two (Western Canada and Eastern Venezuela), of these regions account for 42% and 38%, respectively, of the total reserves of heavy oil and bitumen [12]. It should be noted that various studies present different definitions of hard-to-recover oil reserves, hence, as a result, the difficulties associated with their classification. So, in most cases, for example, according to [6–8, 10, 11], «… Oil reserves represented by sedentary oil are hardly recoverable. (particularly with high viscosity or density and high wax solids content), oils with high (more than 500 m3 /t) or low (less than 200 m3 /t) gas saturation or in the presence of aggressive components in dissolved and/or free gas (hydrogen sulfide, carbon dioxide) in quantities requiring the use of special equipment in well drilling and oil production». Such oils are classified as oils with abnormal physical and chemical properties. This group also includes oils with a high content of metals due to an increase in their degree of environmental hazard. Thus, it should be noted that none of the physicochemical classifications of oil can be recognized as universal. In addition, the classification should also take into account the oil occurrence conditions, and all the marked signs should be covered simultaneously. All this leads to the uncertainty of the classification conditions, in connection with which it is necessary to consider and review this circumstance when solving classification problems. To solve this problem, it is necessary to attract approaches based on the use of methods that presuppose the presence of uncertainties in advance, with the implementation of mutual complementation of methods of mathematical statistics and fuzzy logic.
3 Application of Fuzzy Clustering to Modeling Relationship Between Oil Properties and Difficulty of Oil Extraction As it is noted in the relevant literature, to date, a large number of works have been accumulated in which various clustering algorithms have been proposed, among them hierarchical and non-hierarchical cluster analyses, fuzzy clustering are distinguished [1–7, 9–11]. In recent years, these methods have been widely applied in various fields. At the same time, the principles of the algorithms of “traditional cluster-analysis methods” and their difference from unconventional, i.e., fuzzy clustering methods are described and the advantages of fuzzy clustering are shown, [4, 5]. [1–3] shows the solution of the classification problem of geological objects using cluster analysis.
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a)
b)
c)
d) Fig. 1. Membership functions for different clusters of: a) permeability (logarithm), b) converted viscosity, c) density of reservoir oil, d) corresponding values of oil extraction difficulty.
Comparison of Oil Quality of Various Fields Table 1. Limit values of classification attributes by clusters
Kazakhstan IF Chloride’s concentration Clusters Quant. Quality 1 Cl ≥ 0,08 high 2 Cl ≤ 0,03 low AND
Azerbaijan IF Permeability (logarithm) Clusters Quant. Quality 1 Kper ≤ 1,8 low 2 Kper ≥ 2,2 high 1,8 < Kper < 3 medium 2,2 AND
S* = Converted sulfur concentration log (S x 1000)
ν* = Converted viscosity log (ν x 10)
3
0,03 < Cl < 0,08
medium
Clusters 1 2 3
Quant. Quality S* ≥ 3 high 2 < S* < 3 medium S* ≤ 2 low AND ν* = Converted viscosity log (ν x 10) Clusters Quant. Quality 1 ν* ≥ 1,7 high 2 ν* ≤ 1 low 3 1 < ν* < 1,7 medium AND ρ* = ρ/ρwater - oil to water density ratio Clusters Quant. Quality 1 ρ* ≥ 0,88 high 0.78 < ρ* < 2 medium 0,88 3 ρ* ≤ 0,78 low THEN Oil extraction difficulty Clusters Quant. Quality 1 K ≥ 2,2 high 2 1,7 < K < 2,2 medium 3 K ≤ 1,7 low
Clusters 1 2 3
Quant. ν* ≥ 1,8 0,8 < ν* < 1,8 ν* ≤ 0,8
Quality high medium low
AND Density of reservoir oil Clusters Quant. Quality 1 ρ ≥ 0,89 high 0,85 < ρ < 2 medium 0,89 3 ρ ≤ 0,85 low THEN Oil extraction difficulty Clusters Quant. Quality 1 K ≥ 1,4 high 1a year
Yes
Positive
107
107
Yes/No
Yes/No
Positive
>a year
Biopsy
>107
Yes
Yes/No
Negative
>a year
At Risk
>107
No
No
Negative
>a year
Healthy
>107
Yes/No
Yes
Negative
107
Yes
No
Negative
107
No
No
Negative
17
Yes/No
Yes/No
Positive
>a year
Biopsy
>107
Yes
Yes/No
Negative
>a year
At Risk
>107
No
No
Negative
>a year
Healthy
>107
Yes/No
Yes
Negative
0, m = 1)
(21)
which is provided by β +α > −1 1−m
(22)
has a solution: ⎡ y(t) = ⎣
λ
β+α m−1
+1
β+αm m−1
⎤1/ (m−1)
⎦ +1
· t (β+α)/ (1−m)
(23)
Under condition (22), the relation holds y(t) ∈ Cγ −α [0; ∞), where C γ −α [0,∞] are spaces of functions y(t) defined on [0,∞], for which the product t^(γ − α)*y(t) is bounded by the norm of the space of continuous on [0,∞] functions; i.e.. In this case, the function y(t) represented by (23) is the solution of the weighted Cauchy problem [8], in which (21–22) is considered depending on α under the initial condition lim [t 1−α y(t)] = 0
t→0+
(0 < α < 1)
(24)
or the initial condition (0 Dtα−k y)(0+) = 0, (α > 0, k = 1, ..., n = −[−α])
(25)
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−n The initial condition (24) for Eq. (19) will be satisfied since N˜ O2 (0) = NO∞2 conn dition (22) takes the following form 0 < υd n−1 < 1 in this case. From (15) we get −1/ n NO2 (t) = NO∞2 − N˜ O2 (t)
(26)
where ⎤n/ (1−n) d ·n 1 − υn−1 υd ·n ⎦ · t n−1 N˜ O2 (t) = ⎣ υd n · kd 1 − n−1 ⎡
(27)
3 Results of Experimental Studies Figure 1 shows the results of calculations of kinetic curves for four types of PAASO polymers with T c = 623 K: PAASO -1 – f = 2,6, υ d = 0,6, n = 3,27, d’s = 0,88; kd = 0, 204 · 10−2 h−1 ; PAASO -2 – f = 2,64, υ d = 0,64, n = 3,193, d’s = 0,912; kd = 0, 201 · 10−2 h−1 ; PAASO -3 – f = 2,84, υ d = 0,84, n = 2,866, d’s = 1,072; kd = 0, 547 h−1 and PAASO -4 – f = 2,78, υ d = 0,78, n = 2,953, d’s = 1,024. kd = 0, 536 h−1 .
Fig. 1. Kinetic curves of auto-delayed
Figures 2 and 3 show kinetic curves of a mixed type, while the curves in Fig. 2 correspond to the transition from the auto-delayed mode (PAASO-1-curve 1 and PAASO–2 -curve 2) to the auto-accelerated mode (PAASO-3-curve 3 and PAASO-4 curve 4), and in Fig. 3 transitions from auto-accelerated to auto-delayed mode. The transition times are shown in Figs. 2 and 3.
Simulation of Fractal Kinetics of Thermooxidation
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Fig. 2. Mixed type kinetic curves corresponding to the transition of auto-slow type curves (1 and 2) to auto-accelerated type curves (3 and 4)
Fig. 3. Mixed type kinetic curves corresponding to the transition of auto-accelerated type curves (3 and 4) to auto-slow type curves (1 and 2)
4 Conclusion Usually, within the framework of fractal kinetics, a differential equation of the whole order (equal to one) is used to describe the dependencies of the amount of oxygen absorbed on time during the thermal oxidation of polymers. Instead of the latter, we propose to consider as the fractal kinetics equation of the process of thermos oxidative destruction of polymer melts a fractional differential equation. In addition to the above two modes of thermal oxidation, mixed modes may also occur in polymer melts, appearing during the transition from the auto-delayed to the auto-accelerated mode, and vice versa. As a result of each of these transitions, an S-shaped kinetic curve is formed, for the construction of which estimates of the transition time from one thermal oxidation regime to another are given in the work. Moreover, the above two modes of thermal oxidation, mixed modes may also occur in polymer melts, appearing during the transition from the auto-delayed to the autoaccelerated mode, and vice versa. As a result of each of these transitions, an S-shaped kinetic curve is formed, for the construction of which estimates of the transition time from one thermal oxidation regime to another are given in the work.
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References 1. Kozlov, G.V., Zaikov, G.E.: Structure of Polymer Amorphous State, 465 p. Brill Academic Publishers, Utrecht-Boston (2004) 2. Vilgis, T.A.: Flory theory of polymeric fractals – intersection saturation, and condensation. Phys. A 153(2), 341–354 (1988) 3. Kozlov, G.V., Dolbin, I.V., Zaikov, G.E.: Phisical Chemistry of Low and Flight Molecular Compounds, pp. 107–118. In: Zaikov G., Dalinkevich A. (Eds.) Nova Science Publishers, Inc. New York (2004) 4. Oldham, K., Spanier, J.: Fractional Calculus, 412 p. Academic Press, London – New York (1973) 5. Sahimi, M., McKarnin, M., Nordarl, T., Tirell, M.: Transport and reaction on diffusion-limited aggregates. Phys. Rev. A 32(1), 590–595 (1985) 6. Mikitaev, A.K., Kozlov, G.V., Zaikov, G.E.: Polymer Nanocomposites: Variety of Structural Forms and Applications, 319 p. Nova Science Publishers, Inc., New York (2008) 7. Klymko, P.W., Kopelman, R.: Fractal reaction kinetics: exaction fusion on clusters. J. Phys. Chem. A 87(23), 4565–4567 (1983). https://doi.org/10.1021/j100246a006 8. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations, vol. 204, 540 p. Elsevier (2006). https://www.elsevier.com/books/theory-andapplications-of-fractional-differential-equations/kilbas/978-0-444-51832-3 9. Babanli, M.B.: Fuzzy Logic-based Material Selection And Synthesis. World Scientific Publishing Company (2019). ISBN: 9813276584, 9789813276581 10. Aliev, R.A., Huseynov, O.H.: Fuzzy geometry-based decision making with unprecisiated visual information. Int. J. Inf. Tech. Decis. 13(05), 1051–1073 (2014) 11. Ahmadov, S.A., Gardashova, L.A.: Fuzzy dynamic programming approach to multistage control of flash evaporator system. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M.O., Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 101–105. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-35249-3_12 12. Sultanova, A.B.: Development of an automatic parking algorithm based on fuzzy logic. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M.O., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 428–436. Springer, Cham (2022). https://doi.org/10. 1007/978-3-030-92127-9_58
Fuzzy Models for Calculation of Oil and Gas Reserves I. Y. Bayramov , A. N. Gurbanov , I. Z. Sardarova(B) and S. V. Abbasova
, G. G. Mammadova ,
Azerbaijan State Oil and Industry University, Baku, Azerbaijan [email protected]
Abstract. In this article, methods for estimating the parameters of the gas-bearing layer are proposed based on the results of hydrodynamic studies of wells, considering the accuracy of geological and geophysical information. Considering the accuracy of geological and field information, gas reserves were assessed with the balance method. As an example of estimating reserves based on inaccurate data, the membership function for gas reserves has been established and its schedule is shown. Also, the calculation of oil reserves under uncertainty (by integrated valuation, differential and balance methods) was considered. In this case, the theory of fuzzy sets and the integration of information were used. Keywords: Fuzzy · Parameters · Boundary points · Construction · Balance method · Function · Property functions
1 Introduction The development of constructive methods for monitoring and managing complex oil and gas production systems under uncertainty lags far behind the requirements of practice, which makes it difficult to use all the opportunities provided by technology and significantly reduces their efficiency and reliability. Oil and gas production systems are characterized by large errors in field data, information on individual parameters and their diversity. The lack of reliable primary geological and mining information makes it pointless to use more complex mathematical models to analyze and predict the process. When the deterministic model is extrapolated to the description of an inaccurate system of events distributed in space and time, the approximation errors become large, and the calculations become very difficult or completely impossible. In such a situation, oil and gas industry professionals want to use simplified small-scale models and modeling systems to reduce the uncertainty of the situation and achieve sustainable results without using “strange” decisions. According to the principle of integrity, a complex oil and gas production system cannot be accurately described in a single way. Therefore, its analysis at different levels requires different methods and models. It is not enough to use traditional deterministic approaches to describe field development processes. Thus, in most cases, when creating © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 493–501, 2023. https://doi.org/10.1007/978-3-031-25252-5_65
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software for the management of oil and gas complexes, the Monte Carlo method and the simplest calculations, in many cases, separate software packages are used. Incompleteness of data on complex oil and gas production systems and their individual elements requires the development of mathematical structures for their description and modeling, which allow the complex to use all kinds of multidisciplinary data on the structure and operation of such systems. Thus, a fundamental step in formal methods of describing the sharing of all types of information, especially qualitative information previously lost simply in mathematical modeling, is to use the concept of a fuzzy set.
2 Problem Statement 1. Equilibrium estimation of gas reserves using the theory of fuzzy sets. Determination of gas reserves based on field data can be carried out based on another balancing method, considering the dynamics of the formation pressure drop and the data on the total gas production from the field [1, 2]. The developed algorithms allow to consider several inaccurate parameters, including data on the process of gas field irrigation and fuzzy estimation of the volume of incoming water. However, for simplicity, we consider only the gas mode [2]: V =
Qt 1 − Pt /Pb
(1)
where Qt - total gas production at the current time t, Pb - the initial weighted formation pressure reduced at the initial moment, Pt - the current weighted average weighted formation pressure. In real conditions, it is impossible to accurately calculate gas reserves according to the norm (1), because Pt parameter is obtained by measuring the layer pressure at the site (an inaccurate and indefinite procedure due to different measurement rules) and Qt parameter is measured with a significant error. For the calculation of gas reserves with a drop in reservoir pressure, we consider ˜ t as fuzzy quantities with the function of the volume of gas the total gas production Q produced for (1) with respect to the subset of the allowable values: μ(Qt ) = 1 − (Qt − a)2 /b2 , a − b ≤ Qt ≤ a + b And with a reduced mean P˜ t pressure membership function (MF) μ(Pt ) = 1 − (Pt − c)2 /d 2 , c − d ≤ Qt ≤ c + d where, a, and b characterize the maximum degree of the relation function, and c, d characterize the degree of scattering of the parameter. We use a direct analytical method to find the results of algebraic operations to determine the fuzzy amount of gas reserves. To do this, we (−1/Pb ) first hit: μ1 (Pt ) = 1 − (Pt Pb + c)2 /d 2
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Then we get the following expression for the denominator of formula (1): μ2 (Pt ) = 1 − ((Pt − 1)Pb + c)2 /d 2 = 1 − (Pt − 1 + c/Pb )2 Pb2 /d 2 For the division operation, we use the following equation 1 − (VPt − a)2 /b2 = 1 − (Pt − 1 + c/Pb )2 pb2 /d 2 From this we obtain the following expressions Pt = φ1 (V ) = (ad − bc + bPb )/(dV + bPb ), Pt = φ2 (V ) = (ad + bc − bPb )/(dV − bPb ). Considering the combination of the resulting sets, we finally get the following expression: 2 2 c d / V +b μ(V ) = μ2 (φ1 (V )) = 1 − a − V 1 − Pb Pb An example of estimating reserves on the basis of inaccurate data is constructed with μ(V ) MF values for gas reserves a = 2 · 1011 , b = 5 · 109 , c = 126, d = 3, 8, Pb = 138, 5 and is shown in Fig. 2 using (2) [3]. Thus, the use of the theory of fuzzy sets to evaluate technological parameters in the presence of inaccurately defined values in the equations provides ample opportunities for obtaining a quantitative characteristic of the uncertainty of technological parameters and making informed decisions.
3 Calculation of Oil Reserves Based on the Theory of Fuzzy Sets a) Integrated evaluation method To calculate oil reserves based on fuzzy set theory, let’s first use the integrated estimation method. To do this, consider the formation layer. Let’s use a known equation to calculate oil reserves by the volume method based on average prices, so that all or some quantities of this equation can be given vaguely. This equation can be expressed as follows [3]: Qe = F · he.n.l.h · ka.m.em.. · kn.d .em. · θ · ρ where, Qe - primary oil reserves; F- oil field; he.n.l.h - effective oil line height; ka.m.em.. - open porosity coefficient; ·kn.d .em. - oil coefficient; θ - recalculation coefficient taking into account oil compression; ρ- oil density under standard conditions.
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We replace all calculated parameters with their corresponding MF [4–7]: μ(F), μ(he.n.l.h ), μ(ka.m.em.. ), μ(kn.d .em. ). μ(F) the boundary points for the MF are determined by the internal and external contours of the oil or by the error of the value of the F-field. In the lithological heterogeneity of the deposits, μ(he.n.l.h ), μ(ka.m.em.. ), μ(kn.d .em. ) the MF are determined by the wells falling into the productive zone, the area F and, accordingly, μ(F) the MF by the zone of the strata. From the equation shown by performing algebraic operations on fuzzy quantities, we obtain the following for the resultant MF for oil reserves: μ0 (Qe ) = max[μ(F) ∧ μ(he.n.l.h ) · μ(ka.m.em.. ) · μ(kn.d .em. )] U
U = {(F, he.n.l.h , ka.m.em.. , kn.d .em. )|F · he.n.l.h · ka.m.em.. · kn.d .em. · θ · ρ = Qe } We find the MF μ0 (Qe ) by the inverse numerical method with the data of Table 1. Table 1. Initial data for the calculation of oil reserves Parameters The minimum value of the Prices closest to reality The maximum value of the parameter parameter F, m2
1920 · 106
1960 · 106
2000 · 106
he.n.l.h
8.8
9.7
11
ka.m.em..
0.09
0.1
0.12
·kn.d .em.
0.75
0.8
0.9
Based on the data in the table, it is possible to construct a triangular membership function for each parameter. Based on the inverse numerical method μ0 (Qe ), „ an r-level set is calculated for the function (Table 2). In this case, μ(F), μ(he.n.l.h ),μ(ka.m.em.. ), μ(kn.d .em. ) the membership function takes the value 1, and therefore the fraction [0,1] is divided into r − levels (line 1 of table 2). μ(F), μ(he.n.l.h ),μ(ka.m.em.. ), μ(kn.d .em. ). The results of the second stage of the algorithm for μ(F), μ(he.n.l.h ),μ(ka.m.em.. ), μ(kn.d .em. ) belonging functions are placed in columns 2–5 of the table, respectively. θ and ρ the final result is placed in column 6 of Table 2, taking into account the multiplication of the constants. Table 2. r-Level sets calculated for the function μ0 (Qe ). R(r) σr (F),
σr (he.n.l.h ),
σr (ka.m.em.. ),
σr (kn.d .em. )
μ0 (Qe )
[0.09, 0.12]
[0.75, 0.9]
[843.4, 1757] · 106
0
[1920, 2000] · 106 [8.8, 11]
0.5
[1940, 1980] · 106
[9.25, 10.35] [0.095, 0.11]
[0.775, 0.85] [997, 1416.9] · 106
1
1960 · 106
9.7
0.8
0.1
1124.75 · 106
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b) Differential method Let us use the differential method of calculating oil reserves using the theory of fuzzy sets. The data are not calculated on average. In the first stage, the missing initial data are clarified and calculated, and the initial values are presented in the form of fuzzy quantities. To calculate some missing rates, the closest rate option is approximated. To find the approximate values, a certain number of values are partially sorted according to the degree of importance. The rating procedure and selection of rates are carried out by an expert before the start of the calculation. The criterion can be expressed both for quality and quantitative values. This can be a point, interval, or fuzzy rate. The omission of criteria leads to the inclusion of less correlated values in the sample. It increases the degree of uncertainty but allows obtaining such a value in the absence of information. Preliminary data can be taken not only for a specific area, but also for some well-studied areas. There are several options for describing values as fuzzy quantities [1, 2]: 1) The uncertainty given by the measurement error can be considered. For example, the measurement error provided by a measuring device. Such an error is shown in the passport data of this or similar measuring device. Another example would be the values of the upper or lower parameters of the joints, which can be determined. So, we can draw a triangular membership function (Fig. 1).
Fig. 1. The exact value of the membership function measured with an error of 5%
2) It is also possible to construct a triangular membership function according to the maximum, minimum and numerical average value of the sample (Fig. 2).
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Fig. 2. Construction of the membership function with three points
3) If expressed samples of values are 15 or more, we compile the mf (Fig. 3).
Fig. 3. Construction of membership function based on empirical distribution data
In the second stage of inventory calculation, complex parameters are calculated: ˜ ijj = h˜ ij ∗ k˜n.dij ∗ k˜mij , where i = 1, n, j = 1, m, D Thus, m is the number of wells, h˜ ij -the height of the well, k˜n.dij -saturation with oil, ˜kmij -porosity. In the third stage, the volume of reserves of each layer l assigned to the k ˜ lj = F˜ lj ∗ (D ˜ ij ) ∗ ρ˜lj ∗ θ˜lj ,as, k − l represents the number of layers in the layer, well j Q i=1
˜ ij is taken from the previous stage. μ(Fl ) The border (μ(Fl ) points for the membership D function are determined by the external and internal contour of the oil or the estimation error of the area F l of the l layer. F˜ lj The value of the field is calculated from the sum of ˜
F the fields F l . It can be defined as the average area per well: F˜ l1 = F˜ l2 = ... = F˜ lml = mljl so, l = 1, n, represents the number of n-layers, ml - the number of wells using the llayers. Another approach is to select the value of the fields in proportion to any of the parameters. In the fourth stage, the volume of reserves of each layer l is calculated:
˜l = Q
ml j=1
˜ lj Q
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In the fifth stage, the total reserves of the field are calculated: ˜ = Q
n
˜ l. Q
l=1
The calculation of the volume of oil reserves for the hypothetical field using the proposed algorithm gave the following results (Figs. 4 and 5).
Fig. 4. Volume of C1 category oil reserves
Fig. 5. Volume of C2 category oil reserves
The above method allows you obtaining a result faster than the standard method. c) Balance method Let us use information integration by the balance method. Qb = Qc·n·m (1 + βn p) / βm·e + βn )p where Qc.n..m - total current oil production. βn - oil compression ratio. βm.e. - compression factor of rock pores. p - change of average weight layer pressure. In real conditions, it is also impossible to accurately estimate oil reserves using this equation, because p the parameter is obtained by measuring the formation pressure
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in the field, Qc.n..m is measured with a significant error. We will consider the change in total oil production with a given membership function μ(Qc.n..m ), the average weighted reservoir pressure with a given membership function μ(p). Both analytical and numerical methods can be used to determine the fuzzy rate of oil reserves. Thus, r-level sets μ(Qb ) for a function can be calculated based on the inverse numerical method. The result is shown in Fig. 6 (graph 2). The approach simplifies calculations and reduces the uncertainty zone (the hatched area in Fig. 6 (3)).
Fig. 6. Membership functions for oil resources: 1 - estimation of reserves by the volume method; 2 - assessment of reserves by the balance method; 3 - Coordinated assessment of reserves in two ways
4 Conclusion The use of any specific mathematical apparatus to make decisions under uncertainty allows the model to adequately reflect only certain types of information and other types causes loss of information. So, the simultaneous presence of different types of uncertainty makes it necessary to use the theory of fuzzy sets for decision-making.
References 1. Ahmadov, S.A., Gardashova, L.A.: Fuzzy dynamic programming approach to multistage control of flash evaporator system. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M.O., Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 101–105. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-35249-3_12 2. Krasnov, O.S.: Theory and practice of probabilistic assessment geological risks and uncertainties in the preparation of oil and gas reserves. Oil and gas geology. Theory and practice: Electr. Sci. J. VNIGRI 2 (2007). http://www.ngtp.ru/rub/3/8_2009.pdf 3. Bayramov, I.Y., Gurbanov, A.N., Mirzayev, O.M., Sardarova, I.Z.: Numerical determination of gas and oil reserves. In: 11th International Conference Theory and Application of Soft Computing with Words and Perceptions and Artificial Intelligence - ICSCCW-2021, pp. 522– 529 (2022). https://link.springer.com/bookseries/15179 4. Mirzakhanov, V., Gardashova, L.A.: Wu–Mendel approach for linguistic summarization: practical considerations and solutions. In: 2019 IEEE International Conference Fuzzy System (FUZZ-IEEE), pp. 1–8 (2019). https://doi.org/10.1109/FUZZ-IEEE.2019.885899850
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5. Adilova, N.E.: Investigation of the quality of fuzzy IF-THEN model for a control system. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M.O., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 28–33. Springer, Cham (2022). https://doi.org/10.1007/ 978-3-030-92127-9_8 6. Aliev, R.A., Alizadeh, A.V., Huseynov, O.H.: An introduction to the arithmetic of Z-numbers by using horizontal membership functions. Procedia Comput. Sci., Elsevier, Netherlands 120, 349–356 (2017). https://www.sciencedirect.com/science/article/pii/S1877050917324614 7. Alizadeh A.V.: Application of the Fuzzy Optimality Concept to Decision Making. Adv. Intell. Syst. Comput., Springer, Cham. 1095, 542–549 (2019) https://doi.org/10.1007/978-3-03035249-3_69
Vendor Selection by Using Ideal Solution Methodology with Fuzzy Numbers K. R. Aliyeva(B) Department of Instrument-Making Engineering, Azerbaijan State Oil and Industry University, 20 Azadlig Avenue, AZ1010 Baku, Azerbaijan [email protected]
Abstract. Selection of the right vendor is a very hard task. Vendors have different characteristics which need deep evaluation before ranking. This is a complex process that involves many subjective and objective factors that must be considered before achieving the benefits of vendor selection. An ideal solution methodology is used for the evaluation and ranking of a given set of vendors, applying different attributes. To manage the subjectivity of the decision-maker’s evaluation, an ideal solution with fuzzy numbers was used for ranking alternatives in the considered supplier selection problem. This vendor selection method permits decision makers to identify ideal and negative ideal solutions and separation distances of each alternative from this positive and negative ideal solutions. The better vendor will be a vendor whose separation distance from the ideal solution is minimal and from negative ideal solution is maximal. Keywords: Fuzzy numbers · Vendor selection · Ideal solution
1 Introduction Vendor selection is a very important process for any company to start the production process fluently in the supply chain. Vendor selection based on performance appraisal is a decision of strategic significance to the production. Choosing the right supplier for the company meets customer requirements, creates profits to the organization and helps to meet different attributes such as technical characteristics, cost, delivery speed, and quality. Therefore, a systematic vendor selection process needs to be developed to identify and prioritize relevant criteria and to evaluate the exchanges between technical, economic and performance criteria. In a supply chain management strategy, selecting suitable suppliers is a challenging task because it requires evaluation attributes characterized by complexity, uncertainty, and uncertainty in nature. In recent years, identifying suitable suppliers in the supply chain has become a key strategic issue. Some authors [1–9] have represented that the problem of vendor selection includes several conflicting attributes, both tangible and intangible, and they have offered different methods for supplier selection. Pang and Bai [2] improved a supplier selection approach based on the fuzzy ANP evaluation. The subjective preferences of decision makers have a basic effect on AHP results [10–14]. The decision-makers needs for estimating alternatives always © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 502–506, 2023. https://doi.org/10.1007/978-3-031-25252-5_66
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contain uncertainty. To model such uncertainty in the human selection, fuzzy sets can be combined with binary comparisons, such as the expansion of AHP. The fuzzy AHP method allows a more accurate description of the decision-making process [11]. The fuzzy Ideal solution methodology is another widely used method used over the years in decision-making to prioritize alternatives [12, 13]. In this paper, the fuzzy the Ideal solution method has been developed. Ideal solution is used to sort important criteria for vendor selection from those identified by the staff. This paper is designed as follows. Section 2 introduces the basic steps of the fuzzy Ideal solution methodology that is used in this problem. Section 3 proposed a method of the Ideal solution methodology with fuzzy numbers for the vendor selection problem. Section 4 presents the basic results developed in this article.
2 Preliminaries One of the widely used methodologies of multi-criteria decision making is the Ideal solution technique. Some of the advantages of this method are simplicity, rationality, comprehensibility, well computational efficiency and the ability to measure the relative performance of each alternative in a simple mathematical form. The chosen alternative should have the shortest distance from the ideal solution and the farthest from the negative-ideal solution. The main steps in fuzzy multi-criteria decision-making[15–19] are the following: Step1. Constructing the normalized decision matrix.The normalized decision matrix is calculated using the elements of matrix A and using the following formula: rij =
aij m k=1
(1) 2 akj
Step 2. Constructing weighted normalized decision matrix as follows. ⎤ ⎡ w1 r11 w2 r12 . . . wn r1n ⎢w r w r ... w r ⎥ n 1n ⎥ ⎢ 1 21 2 22 ⎥ ⎢ . ⎥ ⎢. Vij = ⎢ ⎥ ⎥ ⎢. . ⎥ ⎢ ⎦ ⎣. . w1 rm1 w2 rm2 . . . wn rmn
(2)
Step 3. Calculate positive ideal-a∗ and negative ideal-a− solutions. The ideal solution methodology assumes that each evaluation factor-criterion has a monotonically increasing or decreasing feature. The calculation of the ideal solution set is given in the following formula:
a∗ = {(max vij |j ∈ J ), (min vij j ∈ J ) } a∗ = {v1∗ , ..., vn∗ } (3) i
i
Here J and J are sets of indexes of benefit and cost criteria respectively.
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The set of negative ideal solutions selects the largest of the column values in the V matrix (the largest if the appropriate criterion is maximization). The calculation of the set of negative ideal solutions is given in the following formula:
a− = {(min vij |j ∈ J ), (max vij j ∈ J ) } a− = {v1− , ..., vn− } (4) i
i
Step 4. Determining the seperation measures: Ideal separation measure. 2 n ∗ vij − vj∗ Si =
(5)
j=1
Negative- ideal separation measure 2 n vij − v− S− = i
(6)
j
j=1
Step 5. Determining the relative closeness to the ideal solution. Ci∗ =
Si−
(7)
Si− + Si∗
Step 6. Ranking the preference order. In this paper we consider decision problem with criteria weights and evaluations described by fuzzy numbers. Formulas (1)–(7) are used for this case accordingly.
3 Statement and Solution of the Problem Suppose that a multi attribute decision problem involves 4 criteria - C1 , C2 , C3 , C4 and 3 alternatives a1 , a2 , a3 . C1 - Flexibility, C2 - Reliability; C3 - Technology support and C4 Capacity. The weight of each attribute represented by triangular fuzzy numbers (TFNs), such as, w1 = (0.14, 0.2, 0.31), w2 = (0.08, 0.17, 0.28), w3 = (0.32, 0.4, 0.55), w4 = (0.2, 0.25, 0.38). The decision matrix of performance rating in the form of TFNs is presented in Table 1. Table 1. Decision matrix of performance rating C1
C2
C3
C4
w1
w2
w3
w4
(0.14, 0.2, 0.31)
(0.08, 0.17, 0.28)
(0.32, 0.4, 0.55)
(0.2, 0.25, 0.38)
a1
(0.07, 0.25, 0.97)
(0.25, 0.88, 2.64)
(0.33, 0.70, 1.71)
(0.11, 0.24, 0.92)
a2
(0.21, 1, 3.13)
(0.12, 0.53, 2.03)
(0.03, 0.05, 0.09)
(0.11, 0.4, 1.45)
a3
(0.14, 0.4,1.45)
(0.12, 0.18, 0.78)
(0.6, 1.5, 1.62)
(0.23,1,2.37)
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Table 2. Weighted decision matrix C1
C2
C3
C4
a1
(0.01, 0.05, 0.3)
(0.02, 0.15, 0.74)
(0.10, 0.28, 0.96)
(0.02,0.06,0.35)
a2
(0.03, 0.2, 0.97)
(0.01, 0.09, 0.57)
(0.01, 0.02, 0.05)
(0.02, 0.1, 0.55)
a3
(0.02,0.08,0.45)
(0.01,0.03,0.22)
(0.18,0.6,0.91)
(0.04,0.25,0.9)
Solution of this problem and selection better vendor by using ideal solution consists of next steps: Step 1. Construct the weighted decision matrix (Table 2). Step 2. Determine the ideal and negative-ideal solutions: a∗ = {(0.03, 0.2, 0.97), (0.02, 0.15, 0.74), (0.18, 0.6, 0.96), (0.04, 0.25, 0.9)} a− = {(0.01, 0.05, 0.3), (0.01, 0.03, 0.22), (0.01, 0.02, 0.05), (0.02, 0.06, 0.35)} Step 3. Calculate separation measure for each alternative: For example, separation measure for first alternative can be calculated as Sa∗1 = {[(0.01, 0.05, 0.3) − (0.03, 0.2, 0.97)] 2 × [(0.02, 0.15, 0.74) − (0.02, 0.15, 0.74)]2 ×[(0.10, 0.28, 0.96) − (0.18, 0.6, 0.96)]2 × [(0.02, 0.06, 0.35) − (0.04, 0.25, 0.9)]2
1/ 2
= (0.09, 0.4, 1.42)
Sa∗1 = (0.09, 0.4, 1.42),
Sa−1 = (0.08, 0.3, 1.05)
Similarly, for second and third alternatives Sa∗2 = (0.18, 0.6, 1.96),
Sa∗3 = (0.17, 0.60, 2.03),
Sa−2 = (0.03, 0.17, 0.78)
Sa−3 = (0.03, 0.18, 0.72)
Step 4. Calculate relative closeness to the ideal solutions: Ca∗1 =
Sa−1
Sa1 + Sa−1
Ca∗2 =
=
Sa− 2 ∗ Sa +Sa−2 2
(0.09, 0.39, 1.41) = (0.04, 0.4, 5.8) (0.09, 0.28, 1.04) + (0.09, 0.39, 1.41) = (0.01, 0.2, 3.9), Ca∗3 =
Sa− 3 ∗ Sa +Sa−3 3
= (0.06, 0.8, 10.4)
By comparing values of relative closeness of alternatives to the ideal solution, a3 is found as best alternative: a3 > a1 > a2 .
4 Conclusion Vendor selection problem can be characterized with different factors such as, flexibility, reliability, technology support and capacity. To make decision on vendor selection, the methodology of an ideal solution with fuzzy numbers is used in this article to describe high uncertainty in the considered problem.
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References 1. Petroni, B., Braglia, M.: Vendor selection using principal component analysis. J. Supply Chain Manag.: Glob. Rev. Purchas. Supply 36(2), 63–69 (2000) 2. Pang, B., Bai, S.: An integrated fuzzy synthetic evaluation approach for supplierselection based on analytic network process. J. Intell. Manuf. 24(1), 163–174 (2013) 3. Weber, C.A., Current, J.R., Benton, W.C.: Vendor selection criteria and methods. Eur. J. Oper. Res. 50(1), 2–18 (1991) 4. Weber, C.A., Ellram, L.M.: Supplier selection using multiobjective programming: a decision support system approach. Int. J. Phys. Distrib. Logistics Manag. 23(2), 3–14 (1993) 5. 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), 89–301 (2006) 6. Hwang, C.L., Yoon, K.: Multiple Attributes Decision Making Methods and Applications. Springer, Berlin (1981). https://doi.org/10.1007/978-3-642-48318-9 7. Kahraman, C., Cebeci, U., Ulukan, Z.: Multi-criteria supplier selection using Fuzzy AHP. Logist. Inf. Manag. 16(6), 382–394 (2003) 8. Lin, C.: Application of Fuzzy Delphi method (FDM) and fuzzy analytic hierarchy process (FAHP) to criteria weights for fashion design scheme evaluation. Int. J. Clothing Sci. Tech. 25(3), 171–183 (2013) 9. Liao, C.-N., Kao, H.-P.: An integrated Fuzzy TOPSIS and MCGP approach to supplier selection in supply chain management. Expert Syst. Appl. 38(9), 10803–10811 (2011) 10. Chang, D.Y.: Applications of the extent analysis method on Fuzzy AHP. Eur. J. Oper. Res. 95(3), 649–655 (1996) 11. Kabir, G., Hasin, A.A.: Comparative analysis of AHP and fuzzy AHP models for multicriteria inventory classification. Int. J. Fuzzy Logic Syst. 1(1), 1–16 (2011) 12. Dickson, G.W.: An analysis of vendor selection systems and decisions. J. Purchas. 2(1), 5–17 (1966) 13. Liu, J., Ding, F.Y., Lall, V.: Using data envelopment analysis to compare suppliers for supplier selection and performance improvement. Supply Chain Manag.: Int. J. 5(3), 143–150 (2000) 14. Amid, A., Ghodsypour, S.H., Brien, C.O’.: Fuzzy multiobjective linear model for supplier selection in a supply chain, Int. J. Prod. Econ. 104(2), 394–407 (2006) 15. Gardashova, L.A.: Z-number based TOPSIS method in multi-criteria decision making. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Sadikoglu, F.M. (eds.) ICAFS 2018. AISC, vol. 896, pp. 42–50. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-041649_10 16. Aliyeva, K.: Multifactor personnel selection by the fuzzy TOPSIS method. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Sadikoglu, F.M. (eds.) ICAFS 2018. AISC, vol. 896, pp. 478–483. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-04164-9_64 17. Aliev, R.A., Pedrycz, W., Alizadeh, A.V., Huseynov, O.H.: Fuzzy optimality based decision making under imperfect information without utility. Fuzzy Optim. Decis. Mak. 12(4), 357– 372 (2013). https://doi.org/10.1007/s10700-013-9160-2 18. Aliev, R.A., Hajiyev, H.G., Huseynov, O.H.: Optimal decision making for well interventions under uncertainty. TWMS J. Pure Appl. Math. 9(1), 73–81 (2018). http://static.bsu.az/w24/ TWMS%20V9%20N1/pp73-81.pdf 19. Nuriyev, A.M.: Fuzzy MCDM models for selection of the tourism development site: the case of Azerbaijan. F1000 Res. 11(310), 1–24 (2022). https://doi.org/10.12688/f1000research.109 709.1
Selection Core Banking System by Using Fuzzy AHP and Fuzzy TOPSIS Hybrid Method Nihad Mehdiyev(B) Azerbaijan State Oil and Industry University, 20 Azadlig Avenue, 1010 Baku, Azerbaijan [email protected]
Abstract. The core banking system is the back-end system that processes daily banking transactions and publishes updates to accounts and other financial records. Core banking systems typically include payment, deposit, and loan processing capacities with interfaces to basic general recording systems and reporting tools. New core software can clean up the clutter currently created by outdated technology. This is choosing a new core banking system. Basic banking financial services propose banks and their customers several benefits. With advanced data analytics, bank administrators can improve their return on investment by keeping customer satisfaction at an optimal level. Modern core banking system solutions will protect the data of the company and customers from hackers. The goal of this paper is to make group decision-making by using a hybrid method of fuzzy AHP and fuzzy TOPSIS. Hybrid methods AHP and TOPSIS can be used to select the best candidate among the alternatives available Firstly, by using a fuzzy extension of the AHP method weights of criteria in core banking system software selection problems have been determined. Then, the fuzzy TOPSIS technique is used to determine the most suitable alternative regarding company’s goals in uncertain conditions. The researchers generally determine the degrees of importance of each decision maker according to the special characteristics of each decision maker as subjectivity. Keywords: Fuzzy AHP · Multi-criteria decision making · Fuzzy TOPSIS · Core banking system
1 Introduction Core banking technology is the master archive of a giant database of customer balances, deposits, credit accounts, financial transactions, interest, and more. It is also synced with mobile banking apps, internet banking, branches, automated machine tellers, etc. In other words, banking functions come to a pause, and the worst nightmare for banks becomes a reality due to the failure of core banking technology. Core banking technology software selection considered a very important research issue in business intelligence [1], but it has not yet received much attention in research, as research on this subject is necessary. The state of the art is very rich by different methods suggested for the selection problem [2] such as AHP, ANP, PROMETHEE, ELECTRE, TOPSIS etc. Wei et al. [3] offered © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 507–513, 2023. https://doi.org/10.1007/978-3-031-25252-5_67
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the AHP technique for presenting priority in software selection. Yigit et al. [4] used an interactive model using AHP to a selection of web-based object software. Behzadian et al. [5] suggested a TOPSIS based model for multi attribute decision making. Lengacher and Cammarata [6] used a DEA technique to evaluate and choose a portfolio. Liu [7] suggested a weighted linear programming method for the software selection of the problem. Guo et al. [8] offered a genetic algorithm for the optimization of the software selection. Flintsch et al. [9] presented the ANN method for software project selection. Eldrandaly and Naguib [10] suggested an integrated approach of expert systems and AHP to select the best information system software. Zaidan et al. [11] offered a methodology based on integrated AHP and TOPSIS for the selection of software packages. Hybrid of fuzzy AHP and TOPSIS methods are used in this paper. The fuzzy AHP method is a very good technique for core banking system selection problems. It is used to determine the weight of selected attributes [12], and the TOPSIS technique is used for ranking the alternatives on the base of their performance. The paper is organized as follows: The introduction describes a short overview of the decision-making techniques. Section 1 represents the AHP and TOPSIS steps. Section 2 gives the statement of the problem. The solution to the problem by using AHP and TOPSIS techniques steps are described in Sect. 3. Finally, conclusions are represented in the result section.
2 Preliminaries The AHP is a multi-attribute decision-making method and was offered by Saaty [13]. This method is very robust and flexible decision-making tool for working with complex decision problems. The basic steps in AHP method are the following [14]: Step 1. In first step by using pairwise comparison of attributes decision makers state decision matrix as is shown in (1). ⎡ ˜k d11 k ⎢ d˜ 21 A˜ k = ⎢ ⎣··· d˜ k
n1
k d˜ 12 k d˜ 22 ··· d˜ k
n2
k ⎤ · · · d˜ 1n k ⎥ · · · d˜ 2n ⎥ ··· ···⎦ · · · d˜ k
(1)
nn
Step 2. If the size of decision makers will be more than one, so preferences of each decision maker (d˜ ijk ) are averaged and (dij ) are determined by using (2). K
d˜ ijk =
i=1
d˜ ijk
K
(2)
Step 3. The geometric mean r˜i of fuzzy triangle values for each attribute is determined as represented in (3). ⎛ ⎞1/ n n r˜i = ⎝ d˜ ij ⎠ , i = 1, 2, · · · , n j=1
(3)
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Step 4. For determining the fuzzy weight of attribute i(w˜ i ), multiply each r˜i with this reverse vector. w˜ i = r˜i ⊗ (˜r1 ⊕ r˜2 ⊕ · · · ⊕ r˜n )−1 = (lwi , mwi , uwi )
(4)
Then for ranking alternatives we use the TOPSIS method. The basic steps of this multi-criteria decision-making technique are the following [15–19]: Step 1.Constructing the normalized decision matrix which allows comparison across attributes by using formula (2). Step 2.Constructing weighted normalized decision matrix by using formula (4). Step 3: Determining positive (A∗ ) and negative ideal (A− ) solutions. Positive (A∗ ) ideal solution calculated by using the following model: ∗ , A∗ = v1∗ , v2∗ , . . . , vn∗ . A = max vij j ∈ J , min vij j ∈ J (5) i
i
Negative ideal (A∗ ) solutions are calculated by using the following model: − A = , A− = v1− , v2− , . . . , vn− . min vij j ∈ J , max vij j ∈ J
(6)
Step 4: Determining the seperation measures: Ideal separation measure. 2 n ∗ Si = vij − vj∗
(7)
i
i
j=1
Negative- ideal separation measure. 2 n − Si = vij − vj∗
(8)
j=1
Step 6: Determining the relative closeness to the ideal solution Ci∗ =
Si−
Si− + Si∗
(9)
Step 7. Ranking the preference order.
3 Statement of the Problem Methods fuzzy AHP and fuzzy TOPSIS are used for the core banking system software selection problem. This multi-attribute decision-making problem contains different and conflicting attributes. Suppose that a multi-attribute decision making problem involves three criteria-C1 , C2 , C3 , and three alternatives-A1 , A2 , A3 . C1 -Functionality,
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Interpretation
1, 1, 1
j and k equally important
1, 3, 5
j is slightly more important than k
3, 5, 7
j is strongly more important than k
5, 7, 9
j is very strongly important than k
Table 2. Comparison matrices for criteria Criteria
Functionality
Vendor synergy
Technology alignment
Functionality
(1, 1, 1)
(3, 4, 5)
(4, 5, 6)
Vendor synergy
(1/3, 1/4, 1/5)
(1, 1, 1)
(2, 3, 4)
Technology alignment
(1/4, 1/5, 1/6)
(1/2, 1/3, 1/4)
(1, 1, 1)
C2 -Vendor synergy, C3 -Technology alignment. The relative importance of the two criteria is measured according to a numerical scale represented in Table 1. Linguistic performance rating between different criteria is represented in Table 2. The geometric mean of fuzzy triangle values for each attribute is determined as represented in (3). For example, capacity attribute r˜1 -geometric mean of pairwise comparison numbers is calculated as ⎛ ⎞1/ n n 1 1 1 ˜ ⎝ ⎠ = (1 ∗ 3 ∗ 4) 3 ; (1 ∗ 4 ∗ 5) 3 ; (1 ∗ 5 ∗ 6) 3 = [2.3, 2.7, 3.1] dij r˜i = j=1
In the next step, for the capacity attribute the fuzzy weight of w˜ 1 is determined by using Eq. (4). w˜ 1 = [(2.3 ∗ 0.23); (2.7 ∗ 0.25); (3.1 ∗ 0.27)] = [0.53; 0.68; 0.84] w˜ 2 = [(0.87 ∗ 0.23); (0.91 ∗ 0.25); (0.93 ∗ 0.27)] = [0.20; 0.23; 0.25] w˜ 3 = [(0.5 ∗ 0.23); (0.4 ∗ 0.25); (0.35 ∗ 0.27)] = [0.11; 0.1; 0.094] Total numbers and the inverse numbers (power of −1) and increasing order are also represented in Table 3. In the next part of applying the hybrid method, we use fuzzy TOPSIS method steps. At first, we construct the normalized decision matrix represented in Table 4. In the next step we construct the weighted normalized decision matrix represented in Table 5. Determine positive and negative ideal solutions: A∗ = {(0.11, 0.24, 0.42), (0.05, 0.09, 0.15), (0.07, 0.072, 0.073)}
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Table 3. Geometric means of fuzzy comparison numbers Criteria
r1
Functionality
2.3
2.7
3.1
Vendor synergy
0.87
0.91
0.93
Technology alignment
0.5
0.4
0.35
Total
3.67
4.01
4.38
Reverse (power of −1)
0.27
0.25
0.23
Increasing Order
0.23
0.25
0.27
Table 4. Normalized decision matrix C1 (0.53, 0.68, 0.84)
C2 (0.20, 0.23, 0.25)
C3 (0.11, 0.1, 0.09)
A1
(0.08, 0.25, 0.6)
(0.25, 0.4, 0.64)
(0.35, 0.49, 0.61)
A2
(0.2, 0.35, 0.5)
(0.13, 0.35, 0.5)
(0.13, 0.25, 0.39)
A3
(0.15, 0.4, 0.55)
(0.22, 0.37, 0.52)
(0.6, 0.72, 0.81)
Table 5. Weighted normalized decision matrix C1
C2
C3
A1
(0.04, 0.17, 0.5)
(0.05, 0.09, 0.15)
(0.04, 0.05, 0.06)
A2
(0.11, 0.24, 0.42)
(0.03, 0.08, 0.12)
(0.01, 0.025, 0.035)
A3
(0.08, 0.27, 0.46)
(0.04, 0.09, 0.13)
(0.07, 0.072, 0.073)
A− = {(0.04, 0.17, 0.5), (0.03, 0.08, 0.12), (0.01, 0.025, 0.035)} In the next step, by using formulas (7) and (8) we determine separation from an ideal solution and separation from a negative ideal solution. For example, for alternative A SA∗ = 1
n
Aij − A∗
2
= [(0.04, 0.17, 0.5) − (0.11, 0.24, 0.42)]2
j=1
+ ∗ [(0.05, 0.09, 0.15) − (0.11, 0.24, 0.42)]2 + [(0.04, 0.05, 0.06) − (0.11, 0.24, 0.42)]2 n 2 − SA = Aij − A− = [(0.04, 0.17, 0.5) − (0.04, 0.17, 0.5)]2 1
j=1
+ ∗ [(0.04, 0.17, 0.5) − (0.04, 0.17, 0.5)]2 + [(0.04, 0.17, 0.5) − (0.04, 0.17, 0.5)]2
!1
!1 2
2
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The relative closeness to the ideal solution CA∗1 =
SA−1
SA−1
+ SA∗1
For other alternatives − CA∗2 =
S
A2 ∗ SA− +SA2 2
=
(0.09, 0.4, 1.43) = (0.04, 0.44, 5.86) (0.09, 0.4, 1.43) + (0.09, 0.3, 1.06)
= (0.02, 0.23, 3.97), CA∗3 =
SA− 3 − SA +SA∗ 3 3
= (0.06, 0.89, 10.45) ,
After the comparing of obtained triangular fuzzy numbers C Ai we have the following results: CA∗3 > CA∗1 > CA∗2 After ranking alternatives, we determine that alternative A3 is better than other alternatives.
4 Conclusion Hybrid methods AHP and TOPSIS can be used to select the best candidate among the alternatives available. AHP involves a pair-wise comparison between alternatives with respect to each attribute for determining weights. TOPSIS is a very useful and easy method for ranking alternatives of banking system with respect to each attribute. In this paper multi-attribute decision making problem involves three criteria-functionality, vendor synergy and technology alignment, and three alternatives-A1 , A2 , A3 . After ranking alternatives, by using the hybrid method of fuzzy AHP and TOPSIS we determine that one alternative A3 is better than the other alternatives.
References 1. Simitsis, A., Vassiliadis, P., Dayal, U., Karagiannis, A., Tziovara, V.: Benchmarking ETL workflows. In: Nambiar, R., Poess, M. (eds.) TPCTC 2009. LNCS, vol. 5895, pp. 199–220. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-10424-4_15 2. Amiri, M.P.: Project selection for oil-fields development by using the AHP and fuzzy TOPSIS methods. Expert Syst Appl. 37(9), 6218–6224 (2010) 3. Wei, C.-C., Chien, C.-F., Wang, M.-J.: An AHP-based approach to ERP system selection. Int J Prod Econ. 96(1), 47–62 (2005) 4. Yigit, T., Isik, A.H., Ince, M.: Web-based learning object selection software using analytical hierarchy process. IET Softw. 8(4), 174–183 (2014) 5. Behzadian, M., Otaghsara, S.K., Yazdani, M., Ignatius, J.: A state-of the-art survey of TOPSIS applications. Expert Syst Appl. 39(17), 13051–13069 (2012) 6. Lengacher, D., Cammarata, C.: A two-phase data envelopment analysis model for portfolio selection. Adv. Decision Sci., 1–9 (2012) 7. Liu, X.: The site selection of distribution center based on linear programming transportation method. In: Proceedings of the 10th World Congress on Intelligent Control and Automation, pp. 3538–3542 (2012) 8. Guo, J., White, J., Wang, G., Li, J., Wang, Y.: A genetic algorithm for optimized feature selection with resource constraints in software product lines. J. Syst. Softw. 84(12), 2208–2221 (2011)
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9. Flintsch, G., Zaniewski, J., Delton, J., Medina, A.: Artificial neural network based project selection level pavement management system. In: 4th International Conference on Managing Pavements, pp. 451–464 (1998) 10. Eldrandaly, K., Naguib, S.: A knowledge-based system for GIS software selection. Int. Arab. J. Inf. Technol. 10(2), 153–160 (2013) 11. Zaidan, A.A., Zaidan, B.B., Al-Haiqi, A., Kiah, M.L.M., Hussain, M., Abdulnabi, M.: Evaluation and selection of open-source EMR software packages based on integrated AHP and TOPSIS. J. Biomed. Inf. 53, 390–404 (2015) 12. Lin, M.C., Wang, C.C., Chen, M.S., Chang, C.A.: Using AHP and TOPSIS approaches in customer-driven product design process. Comput. Ind. 59(1), 17–31 (2008) 13. Saaty, T.L.: The analytic hierarchy process—what it is and how it is used. Math. Model. 9(3–5), 161–176 (1987) 14. Dovlatova, K.J.: Estimation of benchmarking influence in buyer’s decision-making process by using fuzzy AHP. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 173–182. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-92127-9_26 15. Hwang, C.L., Yoon, K.: Multiple Attribute Decision Making: Methods and Applications, p. 269. Springer-Verlag, Berlin (1981). https://doi.org/10.1007/978-3-642-48318-9 16. Zadeh, L.A., Aliev, R.A.: Fuzzy logic Theory and Applications. Part I and Part II, p. 610. World Science, Singapore (2019) 17. Aliyeva, K.R.: Facility location problem by using fuzzy TOPSIS method. B-Quadrat verlags, Uzbekistan 3, 55–59 (2018). https://doi.org/10.34920/2018.4-5.55-59 18. Aliyeva, K.: Multifactor personnel selection by the fuzzy TOPSIS method. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Sadikoglu, F.M. (eds.) ICAFS 2018. AISC, vol. 896, pp. 478–483. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-04164-9_64 19. Nuriyev, A.M.: Fuzzy MCDM models for selection of the tourism development site: the case of Azerbaijan. F1000 Res. 11(310), 1–24 (2022). https://doi.org/10.12688/f1000research.109 709.1
Performance Analysis of Machine Learning Algorithms for Medical Datasets Fahreddin Sadikoglu1(B)
, Boran Sekeroglu2
, and Deborah Amaka Ewuru3
1 Department of Electrical and Electronic Engineering, Near East University, Nicosia, Cyprus,
99138 Mersin 10, Turkey [email protected] 2 Applied Artificial Intelligence Research Center, Near East University, Nicosia, Cyprus, 99138 Mersin 10, Turkey [email protected] 3 Department of Biostatistics, Faculty of Medicine, Near East University, Nicosia, Cyprus, 99138 Mersin 10, Turkey
Abstract. Medical applications using machine learning have gained importance; therefore, research on the applicability and adequacy of algorithms has also gained momentum. Investigating the performance of the algorithms is crucial for the reallife implementation of classification systems as diagnostic or decision support systems. This paper analyzes the performance of six machine learning algorithms, Decision Tree, Random Forest, Gradient Boosting, Extreme Gradient Boosting, Support Vector Machine, and Logistic Regression, on three medical datasets to demonstrate the weaknesses and strengths of the algorithms. Three experiments in two stages, hyperparameter tuning and performance evaluation are performed. Binary classification and multi-class evaluation are considered in order to analyze the performance of the models with varied challenges. Gradient Boosting and Logistic Regression achieved superior results in binary classification experiments, while Random Forest produced superior results in the multi-class experiment. The results suggested that different machine learning algorithms might obtain unstable performances or stable and consistent results. Keywords: Gradient boosting · Logistic regression · Random forest · Medical dataset · Performance evaluation
1 Introduction Machine learning (ML) is a broad field that is also used as a tool in every field of life and science for two decades. ML algorithms have the ability to establish a relationship within the attributes and instances using statistical, probabilistic, and optimization methods [1]. The algorithms detect the most informative patterns or features based on their characteristics, and each ML algorithm provides several strengths for different problems. Different research studies have been conducted that analyze the classification abilities of machine learning algorithms for different tasks [2]. Six machine learning algorithms, Logistic Regression (LR), Decision Tree (DT), Naive Bayes (NB), K-Nearest Neighbors © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 514–521, 2023. https://doi.org/10.1007/978-3-031-25252-5_68
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(KNN), Support Vector Machines (SVM), and Random Forest (RF), were analyzed in [2] for heart disease and hepatitis diagnosis. The authors concluded that the RF outperformed other algorithms. However, the diversity, complexity, amount of information, and size of datasets directly or indirectly affect the success of machine learning algorithms [3]. It is therefore challenging to determine the superior classifier for all or most applications. Therefore, revealing the strengths and weaknesses of particular models would contribute to further research for specific application areas. The application areas of machine learning and particularly supervised algorithms include sports sciences, social sciences, security applications, and sustainability studies [3–6]; however, medicine and healthcare implementations are the most common areas in which ML is used [7, 8]. The value of human life requires the development of more accurate, bias-free, stable, and consistent systems for machine learning applications to be applied in real life. Developing systems that could support medical doctors in diagnosis and decision-making would be possible when algorithms’ capabilities, deficiencies, and strengths can be generalized. This study aims to measure the classification abilities of machine learning algorithms on medical datasets and to show the behavior of the algorithms based on the data. For this reason, six machine learning algorithms were studied on three different numerical medical datasets. The experiments were carried out as binary classification and multiclass experiments on datasets of different sizes, and the results were obtained with double 5-fold cross-validation. The rest of the paper is organized as follows: Sect. 2 introduces the considered datasets, employed machine learning algorithms, and the experimental details. Section 3 presents the obtained results in detail, and Sect. 4 discusses the results. Finally, Sect. 5 concludes the remarks of the study.
2 Materials and Methods This section introduces the considered datasets, machine learning models, and the experimental design within this study. 2.1 Datasets Three medical datasets are considered in this study. Breast Cancer Coimbra Data Set [9] (BCC) and Cervical Cancer Behavior Risk Data Set [10] (CCBR) are used for the binary classification analysis and the Maternal Health Risk Data Set [11, 12] (MHR) for the performance observation for the multi-class problem. The BCC dataset included ten attributes with 116 instances for both breast cancer patients and the control group. The number of patients within the dataset is 64 (55.17%) since the control group has 52 (44.83%) persons. CCBR dataset consisted of 19 attributes and 72 instances (21−with cervical cancer and 51 with no disease) to diagnose if the patient has cervical cancer or not. The dataset is highly imbalanced, while the number of patients with cervical cancer is 21 (29.16%), and the number of the control group is 51 (70.84%).
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The MHR dataset consisted of 7 attributes for 1014 instances to predict the maternal health risk levels as low (406 patients, 40.03%), mid (336 patients, 33.14%), and high (272 patients, 26.83%) [12]. Table 1 presents the properties of the considered datasets in detail. Table 1. Properties of datasets considered in this study.
Patients
BCC dataset
CCBR dataset
MHR Dataset
64
21
1014 (3 risk levels)
Control
52
51
–
Attributes
10
19
7
2
2
3
Labels
2.2 Machine Learning Models This paper studies six machine learning models, Decision Tree, Random Forest, Gradient Boosting, Extreme Gradient Boosting, Support Vector Machine, and Logistic Regression, on the considered datasets. The following sections briefly introduce the basics of the considered machine learning models. Decision Tree (DT). A DT constructs sequential chart-like nodes where the initial node is the root node, internal nodes are the selections of the dataset’s attributes, and each leaf or decision node represents labels. It is a simple, fast, and efficient way for both classification and regression tasks [13]; however, constructing the most informative or decisive tree is the primary problem in decision trees [13]. Random Forest (RF). RF [14] is a tree-based ensemble method. It constructs several individual decision trees during the training and ensembles them. It is frequently used for classification and regression studies. For classification tasks, the output of the RF is the label selected or voted by most trees (majority) constructed during the training. Gradient Boosting (GradBoost). GradBoost [15] is another tree-based ensemble algorithm that uses boosting the constructed weak learners to minimize the obtained loss. The additional or modified tree is added based on the calculated loss to reduce the total loss using a gradient descent algorithm. Extreme Gradient Boosting (XGBoost). Extreme Gradient Boosting [16] is also an ensemble tree method and applies the boosting principle of weak learners similar to GradBoost. However, some enhancements, such as regularization models, reduce computational costs and avoid overfitting. Additionally, the built-in cross-validation is included in each iteration to determine the exact number of iterations on a single run.
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Support Vector Machine (SVM). Support Vector Machine [17] is one of the most common classifiers, particularly for the limited number of data. It chooses the closest data points of labels (classes) as support vectors and aims to maximize the decision gap between the labels. Furthermore, different kernel functions could be used to map the data points into high-dimensional spaces and perform non-linear tasks. Logistic Regression (LogR). Logistic Regression models the probability of given input variables. The logistic (Sigmoid) function distinguishes the samples or determines the probability of assigning inputs to the proper classes. It is one of the most common and fundamental statistical methods that is used for classification problems [18].
2.3 Design of Experiments and Evaluation In the study, experiments were carried out by dividing the datasets into two groups considering their properties: Binary classification and multi-class experiment. Binary classification experiments were performed for BCC and CCBR datasets, while multiclass experiments were performed using MHR datasets. All experiments for both groups were performed in two stages. The first stage is used for hyperparameter tuning, and the best parameters of each machine learning algorithm were determined using 5-fold cross-validation and grid search for each fold. In the second stage, the final classification abilities of the algorithms were obtained using 5fold cross-validation with the parameters in which the best results were obtained in the first stage. Three evaluation metrics were considered in order to analyze the performance of the machine learning algorithms for the experiments: The receiver operating characteristic area under the curve (ROC AUC) score, Sensitivity (Recall), and Specificity were used for binary classification experiments, and the macro-averaged F1 score, Recall, Precision were considered in the multi-class experiments. The accuracy metric was not considered in this study due to the imbalanced datasets. After the grid search in the first stage, the SVM was implemented using the linear kernel with C = 1 × 10–4 and γ = 1 × 10–3 . The DT was trained using entropy. The number of estimators was set to 250 in RF, GradBoost, and XGBoost, and the learning rates were used as 0.1 and 0.3 in the GradBoost and XGBoost, respectively. The LogR was employed using the lbfgs solver. The Decision Tree and tree ensemble algorithms were considered in the multi-class experiments.
3 Results This section presents the obtained results for both binary and multi-class classification experiments. As mentioned in the previous section, the mean ROC AUC score for binary classification experiments and the macro-averaged F1 score for the multi-class experiment are considered evaluation metrics.
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3.1 Results of Binary Classification Experiments In the BCC dataset, the DT produced the lowest mean ROC AUC score (0.740), followed by the LogR (0.742). Even though the SVM obtained higher results than DT and LogR, it could not outperform tree ensemble methods, and the highest result was achieved by the GradBoost (0.845), followed by RF (0.833). Similar to the BCC dataset, the DT obtained the lowest mean ROC AUC score in the CCBR dataset (0.812), followed by the GradBoost. The SVM, LogR, RF, and XGBoost produced close results (0.965, 0.971, 0.961, and 0.940, respectively); however, the highest result was achieved by the LogR for the CCBR dataset. Table 2 presents the mean ROC AUC Scores, Sensitivity, and Specificity results of the machine learning algorithms for the binary classification experiments. Figure 1 and Fig. 2 show the ROC curves of worse and best folds for the BCC and CCBR experiments. Table 2. The results of the BCC and CCBR experiments. ML algorithm
BCC dataset
CCBR dataset
ROC AUC
Sens. (%)
Spec. (%)
ROC AUC
Sens. (%)
Spec. (%)
Decision tree
0.740
73.43
75.00
0.812
76.19
86.27
SVM
0.760
78.12
75.00
0.965
95.23
98.03
Logistic reg.
0.742
71.87
76.92
0.971
95.23
100
Random forest
0.833
90.62
76.92
0.961
95.23
96.07
Gradient boosting
0.845
85.34
92.18
0.873
85.71
90.19
XGBoost
0.788
78.44
81.25
0.940
90.47
98.03
3.2 Results of Multi-class Experiments Even though the LogR and SVM could be implemented for multi-class problems, they were excluded in the multi-class experiments due to their binary classification nature. The multi-class experiment was performed on the MHR dataset. The close results were obtained in the multi-class experiments; however, the lowest macro-averaged F1 score was produced by GradBoost (0.81). The DT and XGBoost obtained 0.841 and 0.850 macro-averaged F1 scores; however, they could not outperform the RF, where the superior result was achieved (0.859). Table 3 presents the obtained macro-averaged F1 scores for the multi-class experiment.
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Fig. 1. ROC curves of folds for the BCC experiment, (a) worse fold, and (b) best fold.
Fig. 2. ROC curves of folds for the CCBR experiment, (a) worse fold, and (b) best fold.
Table 3. Macro-averaged results for the multi-class MHR experiment. ML algorithm
F1 score
Recall (%)
Precision (%)
Decision tree
0.841
84.24
84.78
Random forest
0.859
85.59
85.85
Gradient boosting
0.810
80.97
81.36
Extreme gradient boosting
0.850
85.32
85.08
4 Discussions Obtained results showed that ML algorithms could be used with high accuracy in classifying medical datasets. However, more stable results are needed to use the developed artificial intelligence or machine learning-based systems for diagnostic purposes in real life. Logistic Regression and SVM, which produced lower results in the BCC dataset with a higher number of instances with fewer attributes, produced superior results in the CCBR dataset with an increased number of attributes and decreased number of instances. Even though the characteristics of the datasets have a significant effect on the machine learning algorithms, it has been observed that the number of attributes and instances is
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an important indicator for LogR and SVM in medical datasets. The decision tree, which classifies with a single tree, obtained the lowest results in binary classification experiments; however, it outperformed the GradBoost algorithm in multi-class experiments. While different results can be obtained each time DT is created, unstable and inconsistent results limit DT use, especially in medical datasets. The GradBoost produced unstable results in this study. While GradBoost can produce the best and worst results, XGBoost and RF have produced stable results in binary classification experiments and are superior in multi-class experiments. Implementing the hyperparameters of the algorithms by choosing the best of the five folds in the first stage, ignoring the other parameters, and making the final experiments could be a reason for the instability in the algorithms, which is the limitation of this study. Applying the best hyperparameters determined in each fold with the hold-out method could improve the obtained results. Additionally, the analysis of Logistic Regression and Support Vector Machine responses for the multi-class class experiments could provide valuable knowledge for further research that would study the considered datasets.
5 Conclusion This study analyzed the performance of six machine learning algorithms using three different medical datasets to determine the models’ strengths and weaknesses. Experiments were performed as binary classification and multi-class experiments. Random Forest, SVM, and XGBoost were stable algorithms, while GradBoost performed better with a higher number of samples but was unstable for other datasets. Logistic Regression achieved superior results with a lower amount of data. The decision tree was the lowest-performing model. Our study has again shown that comparative studies in any machine learning application are still the most valuable method for choosing the superior model. Meanwhile, more comprehensive data and analyzes are needed for machine learning algorithms to be applied in real-time systems. Our future work is to investigate the training of different medical datasets and their use to support the diagnosis of other diseases.
References 1. Uddin, S., Khan, A., Hossain, M.E., Moni, M.A.: Comparing different supervised machine learning algorithms for disease prediction. BMC Med. Inf. Decis. Mak. 19, 281 (2019). https:// doi.org/10.1186/s12911-019-1004-8 2. Ul Hassan, C.A., Khan, M.S., Shah, M.A.: Comparison of machine learning algorithms in data classification. In: 2018 24th International Conference on Automation and Computing (ICAC), pp. 1–6. (2018). https://doi.org/10.23919/iconac.2018.8748995 3. Dogruyol, K., Sekeroglu, B.: Absenteeism prediction: a comparative study using machine learning models. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 728–734. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-35249-3_94
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4. Nourani, V., Andalib, G., Sadikoglu, F.: Multi-station streamflow forecasting using wavelet denoising and artificial intelligence models. Procedia Comput. Sci. 120, 617–624 (2017). https://doi.org/10.1016/j.procs.2017.11.287 5. Sharghi, E., Nourani, V., Soleimani, S., Sadikoglu, F.: Application of different clustering approaches to hydroclimatological catchment regionalization in mountainous regions, a case study in Utah State. J. Mt. Sci. 15(3), 461–484 (2018). https://doi.org/10.1007/s11629-0174454-4 6. Demilew, F.A., Sekeroglu, B.: Ancient Geez script recognition using deep learning. SN Appl. Sci. 1(11), 1–7 (2019). https://doi.org/10.1007/s42452-019-1340-4 7. Alpan, K.: Performance evaluation of classification algorithms for early detection of behavior determinant based cervical cancer. In: 2021 5th International Symposium on Multidisciplinary Studies and Innovative Technologies (ISMSIT), pp. 706–710 (2021). https://doi.org/10.1109/ ISMSIT52890.2021.9604718 8. Adweb, K.M.A., Cavus, N., Sekeroglu, B.: Cervical cancer diagnosis using very deep networks over different activation functions. IEEE Access 9, 46612–46625 (2021). https://doi. org/10.1109/ACCESS.2021.3067195 9. Patrício, M., et al.: Using resistin, glucose, age and BMI to predict the presence of breast cancer. BMC Cancer 18(1) (2018) 10. Sobar Machmud, R., Wijaya, A.: Behavior determinant based cervical cancer early detection with machine learning algorithm. Adv. Sci. Lett. 22, 3120–3123 (2016). https://doi.org/10. 1166/asl.2016.7980 11. Ahmed, M., Kashem, M.A., Rahman, M., Khatun, S.: Review and analysis of risk factor of maternal health in remote area using the internet of things (IoT). In: Kasruddin Nasir, A.N., et al. (eds.) InECCE2019. LNEE, vol. 632, pp. 357–365. Springer, Singapore (2020). https:// doi.org/10.1007/978-981-15-2317-5_30 12. Ahmed, M., Kashem, M.A.: IoT based risk level prediction model for maternal health care in the context of Bangladesh. In: 2020 2nd International Conference on Sustainable Technologies for Industry 4.0 (STI), pp. 1–6 (2020). https://doi.org/10.1109/STI50764.2020.9350320 13. Hussain, S.A., Cavus, N., Sekeroglu, B.: Hybrid machine learning model for body fat percentage prediction based on support vector regression and emotional artificial neural networks. Appl. Sci. 11, 9797 (2021). https://doi.org/10.3390/app11219797 14. Breiman, L.: Random forests. Mach. Learn. 45, 5–32 (2001). https://doi.org/10.1023/A:101 0933404324 15. Friedman, J.: Greedy function approximation: a gradient boosting machine. Ann. Stat. 29, 1189–1232 (2001) 16. Chen, T., Guestrin, C.: Xgboost: a scalable tree boosting system. arXiv:1603.02754 (2016) 17. Cortes, C., Vapnik, V.: Support-vector networks. Mach. Learn. 20(3), 273–297 (1995) 18. Cox, D.: The regression analysis of binary sequences. J. Roy. Stat. Soc.: Ser. B (Methodol.) 20(2), 215–232 (1958)
Difference Between Digital Marketing and Traditional Marketing Models Gunay E. Imanova(B) Azerbaijan State Oil and Industry University, 34 Azadlyg Avenue, Baku, Azerbaijan [email protected]
Abstract. Marketing practices should be changed and adapted as the technology and the preferences of the customers shift constantly. Automating marketing operations become one of the prominent processes to deal with the increased demand, fast consumption, and changing customer needs and wants. Nowadays, the traditional marketing approaches are not enough to satisfy the customers and to survive in a highly competitive market. Therefore, effective use of digital marketing and its tools such as Social Media Marketing, SEO, PPC, and others are crucial for today’s marketing. In this paper, state-of-art research related to traditional versus digital marketing practices, is conducted. Furthermore, the relative importance of each pair of criteria related to advantages of digital marketing over traditional marketing is identified and analyzed based on triangular fuzzy numbers and fuzzy AHP method. Keywords: Digital marketing · Traditional marketing · Triangular fuzzy numbers · Fuzzy AHP · Social Media Marketing · Digitalization
1 Introduction Marketing and its practices should start by understanding the needs, wants, and demands of customers and satisfying them through finding better solutions than the competitors do. One of the ways to deliver better value is to follow and adopt technological changes in the dynamic marketing environment. In this way, companies can achieve a competitive edge over competitors due to better customer analysis, efficient and effective customer targeting strategies, and long-term customer relations [1]. Understanding and satisfying the customer needs accordingly require good marketing research information, which is the heart of marketing. Today, marketing information is relatively easier to gather as the marketing processes become automated. Dozens of big data are stored to be used for understanding and forecasting customer needs and wants even better than customers themselves. Different data resources can be used in order to acquire this information. Thanks to advanced technology, this data comes from everywhere, from social media channels such as Facebook, Instagram, and Twitter, to direct call records, and should be wisely evaluated using automated marketing tools [2]. In order to analyze the marketing environment related data and provide good customer insights there are several digital marketing tools, which will be discussed throughout the research. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 522–529, 2023. https://doi.org/10.1007/978-3-031-25252-5_69
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Buying preferences tend to change as the access to internet and digital marketing increases. Therefore, it is important to adopt and apply the digital marketing technologies besides traditional marketing practices to satisfy the changing customer preferences [2, 3]. The main purpose of this paper is to analyze the literature for the differences between digital and traditional marketing practices and strategies, and the advantages of digital marketing over traditional one. Then, the criteria based on advantages of digital marketing are analyzed and the relative importance of each pair of the criteria based on triangular fuzzy numbers and fuzzy AHP method is identified. The remaining of the paper is structured as follows. Section 2 provides preliminaries. Section 3 identifies differences between traditional and digital marketing concepts, which is followed by advantages of digital marketing over traditional marketing. Section 4 provides the problem statement, followed by its solution in Sect. 5. Finally, conclusion points are presented.
2 Preliminaries Definition 1. Fuzzy Numbers [4]: Decision making process is usually uncertain in the real-world, regarding the possibility of the given values. In addition, possible degrees of uncertainty or impreciseness related to given values are remain unknown to the decision maker, because of the ill-defined data. In a fuzzy set, for each possible value of x, the assigned degree is given as μ(x)[0, 1]. x0 ∈ where μM (x0 ) = 1 for any 0 ≤ α ≤ 1, Aα = x, μAα (x) ≥ α is a closed interval, where F(R).
(1)
˜ (a1 , a2 , a3 ) is used to repDefinition 2. Triangular Fuzzy Numbers [4]: Triplet A, resent the triangular fuzzy number, where the membership is assigned using the equation: ⎧ 0 x(−∞, a1 ) ⎪ ⎪ ⎪ ⎨ x−a1 x[a1 , a2 ] 2− a 1 μA˜ (x) = ac−x (2) ⎪ x[a 2 , a3 ] ⎪ ⎪ a3− a2 ⎩ 0 x(a3 , +∞)
3 Difference Between Digital Marketing and Traditional Marketing Concepts 3.1 Traditional Marketing Model Traditional marketing is the marketing model that most of the customers face every day. Newspaper and magazine commercials, eye-catching billboard ads are still common and highly used by marketers to attract customers. Some of the traditional marketing practices are listed below [5];
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• Telemarketing: is a marketing practice that try to convince customers to buy product or services by providing sales information through telephone conversations. Text messages can also be used for this practice. • Print marketing: is a marketing practice of publishing ads on newspapers, magazines, etc. which convey information about the product or service to be distributed to customers. • Broadcast marketing: is a marketing practice of attracting customer through virtual TV or radio broadcast. • Direct mail marketing: is a marketing practice of using postal mail to send printed materials such as brochures, postcards, catalogs, to increase the awareness about the product or service. • Direct sales at customers’ homes or offices, tradeshows especially in B2B marketing, and referral or word-of-mouth marketing are the other traditional marketing practices to be mentioned. 3.2 Digital Marketing Model With the basic definition, digital marketing is the promotion of product and services via digital channels to attract the customers all around the world [4]. Thanks to the advanced information technology, more and more people, around the globe, reach internet and use social media channels. Because of the dynamic marketing environment, buying behavior and preferences of customers tend to change. To cope with the constant change digitalization in marketing is required [3]. One of the main advantages of digital marketing is the availability of mutual or twoway communication with customers. Digital marketing enables companies to reach the customer in a right way at the right time through the digital marketing technologies such as social media channels and search engines [6]. Nowadays, companies actively use several important digital marketing practices. Some of them are search engine optimization, social media marketing, email marketing, content marketing, and affiliate marketing.
Tradi onal marke ng •Telemarke ng •Print marke ng •Broadcast marke ng •Direct mail marke ng •Direct sales •Tradeshows •Referral marke ng (WOM)
Digital marke ng •Search Engine Op miza on (SEO) and Pay-Per-Click (PPC) •Social Media Marke ng (SMM) •Email Marke ng •Content Marke ng •Affiliate Marke ng
Fig. 1. Traditional versus digital marketing tools
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Search Engine Optimization (SEO) and Pay-Per-Click (PPC): SOE is as a digital marketing technique that is based on organic traffic. It identifies the optimal keywords to make the webpage easily found on the search engines at the top positions. Therefore, besides the visibility of the website, sales of products and services may also increase [7]. The aim of SEO is to match the target customer with the search engines as they search for some information [8]. In contrast, Search Engine Marketing (SEM) aids in marketing and ranking websites through paid search engine advertising and uses paid advertising mechanisms such as Pay-per-click (PPC) in order to increase the visibility of the website [8]. A certain amount of fee is paid for the search engines such as Google. Accordingly, websites will pay the fee only if the ads are clicked and the potential customer is directed to the page [6, 7]. Social Media Marketing (SMM): Today, many people have access to the internet, and social media is actively used by many populations. With this knowledge, companies utilize Social Media Marketing for boosting their sales. SMM became a part of the marketing strategies of many companies. Social media can reveal a wide range of data about customers’ buying preferences, needs and wants, personality traits, brand loyalty, and so forth. The acquired information can be used to serve the target audience in a more effective way [9]. Table 1 presents the popular social media channels and the active user numbers, based on a survey [10]. Through these social media platforms, companies can gain customer-related information, which is used for marketing decisions and strategies. Different tools can be used to analyze the information acquired through these channels. For example, sentiment analysis, neural network-based tools, social bots, and AI are some of the methods in order to analyze the data provided [11]. Table 1. Popular social networks worldwide, 2022 [10] Social Media
Active users (in millions)
Facebook
2910
YouTube
2562
WhatsApp Instagram
2000 1478
Facebook Messenger Twitter
988 436
Email Marketing: Email marketing is a digital marketing practice in which, different segments of customers receive commercial messages via email [12]. According to research [13], sending the optimal number of emails to customers is crucial for long-run profitability. Although the difficulties such as less customer attention toward the emails received, or not opening the emails sent, successful email marketing campaigns can provide a higher ROI, repeat sales, up and cross-selling of products, and better customer insights [12, 13]. Selecting the optimal length of text message, related subject and images of an email are very important topics to be considered [6].
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Content Marketing: Content marketing is one of the essential tools of digital marketing that organizations create and share with the target audience to tell their stories. It shows the values of the company. The main purpose is to inform the target segment of customers about the company and its offers and create a prerogative customer relationship and loyalty through effective promotion [14]. Content can be created in various formats such as blogs, case studies, forums, how-to guides, question and answer-based articles, images, podcasts, videos, banners, infographics, social media sites, and so forth [15]. Affiliate Marketing: Affiliate marketing is the part of digital marketing that is based on a performance-based marketing type. The publisher or affiliate, who is a potential marketing partner, will be paid for the customers brought through their own marketing effort to generate the orders [16]. An affiliate will provide the seller a space to promote the product or services. Eventually, the company will increase its sales and conversations in return for the commission paid to the affiliate [14]. Besides, affiliate marketing is particularly beneficial for startups, which can gain more traffic through giant publisher companies such as Amazon, Alibaba, eBay, and so forth.
4 Statement of the Problem In this research, the relative importance of each pair of factors related to the advantages of digital marketing, is identified and analyzed based on triangular fuzzy numbers and fuzzy AHP method. Digital marketing provides several advantages over traditional marketing. Main privileges are listed below. This research is characterized by 5 main criteria C = {c1 , c2 , c3 , c4 , c5 }. After analyzing the related literature, criteria to be fed are identified as follows. Table 1 deploys the pairwise comparison for the identified criteria. C1: Communication: One of the obvious benefits is related to two-way communication with customers [6]. The use of interactive media enables better communication with customers which in turn helps to improve customer loyalty. C2: Cost: Cost becomes lower through less labor requirements and advertising opportunities. For example, with traditional marketing tools it is much more expensive to target the larger customer segments with effective advertising than promoting through social media, which constitutes little or no cost [5]. C3: Personalized offers: Digital marketing enables customized marketing based on individual profiles and preferences of customers. For instance, new and related offers can be created to appeal to customers according to their purchase history [2]. C4: Time: With traditional marketing, creating TV or printed magazine ads will require a longer time and higher cost than creating digital ads. On the other hand, it is less costly and much easier to update and share the digital content with a broad audience to inform them about new company offerings [5]. C5: Broad information: Digital marketing provides the opportunity to place lots of information on the website about the product or service sold. On the other hand, traditional marketing provides limited ability to share related information due to time and space restrictions related to traditional ads [2, 5].
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Table 2. Pairwise comparison matrix C1
C2
C3
C4
C5
C1
(1,1,1)
(1,2,3)
(1,2,3)
(1,2,3)
(2,3,4)
C2
(1/3,1/2,1/1)
(1,1,1)
(1,2,3)
(1,2,3)
(1,2,3)
C3
(1/3,1/2,1/1)
(1/3,1/2,1/1)
(1,1,1)
(1,2,3)
(1,2,3)
C4
(1/3,1/2,1/1)
(1/3,1/2,1/1)
(1/3,1/2,1/1)
(1,1,1)
(1,2,3)
C5
(1/4,1/3,1/2)
(1/3,1/2,1/1)
(1/3,1/2,1/1)
(1/3,1/2,1/1)
(1,1,1)
5 Solution of the Problem In this research, we analyze the importance of criteria based on triangular fuzzy numbers and propose the use of the fuzzy AHP method for pairwise comparison of the provided criteria and deriving consistency ratio. Step 1: By evaluating the priority values in fuzzy numbers c˜ ij = (cij, l , cij, m , cij, u ), (i, j = 1, 2, ..., n), pair-wise comparison reciprocal fuzzy matrix indicated as C˜ is developed for the given criteria C1, C2,…,Cn. Three crisp matrices Cl , Cm , Cu are acquired by dividing the fuzzy matrix C˜ as it is given below [17–21]. ⎡
1 c12,l ⎢ ⎢ Cl = ⎢ ⎢ ⎣ 1/c12,u 1
...
c1k,l
... ...
c2k,l
1/c1k,u 1/c2k,u ...
⎤
⎡ 1 c12,m ⎥ ⎢ ⎥ ⎢ ⎥Cm = ⎢ ⎥ ⎢ ⎦ ⎣ 1/c12,m 1
... ... ...
1/c1k,m 1/c2k,m ...
1
c1k,m c2k,m
⎤
⎡ 1 c12,u ⎥ ⎢ ⎥ ⎢ 1/c12,l 1 ⎥Cu = ⎢ ⎥ ⎢ ⎦ ⎣
...
c1k,u
⎥ c2k,u ⎥ ⎥ ⎥ ⎦
... ...
1/c1k,l 1/c2k,l ...
1
⎤
1
(3) Step 2: The acquired matrices are used to calculate the system of fuzzy linear homogeneous equations. Cl wl + Cm wm + Cu wu − λl wl − λm wm − λu wu = 0 Cl = 2Cl + Cm = 3
Cm = Cl + 4Cm + Cu = 6
Cu = Cm + 2Cu = 3
Table 3. Cl
Table 4. Cm
1
1
1
1
2
1
2
2
2
3
0,33
1
1
1
1
0,5
1
2
2
2
0,5
1
2
2
0,33
0,33
1
1
1
0,5
0,33
0,33
0,33
1
1
0,5
0,5
0,5
1
2
0,25
0,33
0,33
0,33
1
0,33
0,5
0,5
0,5
1
(4)
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G. E. Imanova Table 5. Cu
Table 6. Cl
1
3
3
3
4
3,00
4,00
4,00
4,00
7,00
1
1
3
3
3
1,17
3,00
4,00
4,00
4,00
1
1
1
3
3
1,17
1,17
3,00
4,00
4,00
1
1
1
1
3
1,17
1,17
1,17
3,00
4,00
0,5
1
1
1
1
0,83
1,17
1,17
1,17
3,00
Table 7. Cm
Table 8. Cu
6,00
12,00
12,00
12,00
18,00
3,00
8,00
8,00
8,00
11,00
3,33
6,00
12,00
12,00
12,00
2,50
3,00
8,00
8,00
8,00
3,33
3,33
6,00
12,00
12,00
2,50
2,50
3,00
8,00
8,00
3,33
3,33
3,33
6,00
12,00
2,50
2,50
2,50
3,00
8,00
2,08
3,33
3,33
3,33
6,00
1,33
2,50
2,50
2,50
3,00
Step 3: Cl , Cm and Cu eigenvalues are obtained with MATLAB software program: λl , λm , λu are founded as λl = 9.07, λm = 3.53, λu = 8.77. Finally, the consistency index and consistency ratio are obtained by using the following formulas: CI =
CI −n , CR = n−1 RI
λmax
6 Conclusion As the world becomes more digital, marketing practices also shift towards digitalization. Traditional marketing practices such as telemarketing and broadcast ads continue to take place in the daily lives of customers. However, as more and more people access the internet and use e-commerce and social media platforms, companies tend to promote their offerings via digital marketing channels. In this paper, traditional and digital marketing channels are compared, and the advantages of digital marketing over traditional ones are identified. Furthermore, the relative importance of each pair of criteria related to the advantages of digital marketing is identified and analyzed based on triangular fuzzy numbers and the fuzzy AHP method. Regarding uncertainty, the proposed method can be applied to various decision-making problems in digital marketing.
References 1. Kotler, P., Armstrong, G., Opresnik, O.M.: Harlow: Principles of Marketing. England, Pearson (2018)
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2. Todor, R.D.: Blending traditional and digital marketing. Bulletin of the Transilvania University of Brasov. Econ. Sci. Ser. V 9(1), 51 (2016) 3. Tiago, M.T.P. M.B., Veríssimo, J.M.C.: Digital marketing and social media: Why bother? Bus Horizons. 57(6), 703–708 (2014). https://doi.org/10.1016/j.bushor.2014.07.002 4. Aliev, R.A., Aliev, R.R.: Soft Computing and Its Application. World Scientific (2001) 5. Lawrence, S., Deshmukh, S., Navajivan, E.: A comparative study of digital marketing vs. traditional marketing. IIBM’S J. Manag. Res. 3(1–2), 112–121 (2018). /https://doi.org/10. 33771/iibm.v3i1-2.1098 6. Durmaz, Y., Efendioglu, I.H.: Travel from traditional marketing to digital marketing. Global J. Manag. Bus. Res. 16(2), 34–40 (2016) 7. Chen-Yuan, C., Bih-Yaw, S., Zih-Siang, C., Tsung-Hao, C.: The exploration of internet marketing strategy by search engine optimization: A critical review and comparison. Afr. J. Bus. Manage. 5(12), 4644–4649 (2011) 8. Green, D.C.: Search engine marketing: why it benefits us all. Bus. Inf. Rev. 20(4), 195–202 (2003) 9. Tuten, T., Solomon, M.: Social Media Marketing, 1st ed. Pearson, Harlow, Essex, UK (2014) 10. Statista: Most popular social networks worldwide as of January 2022, ranked by number of monthly active users. Retrieved from: https://www.statista.com/statistics/272014/global-soc ial-networks-ranked-by-number-of-users/ 11. Imanova, G.E., Imanova, G.: Some aspects of fuzzy decision making in digital marketing analysis. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 465–473. Springer, Cham (2022). https:// doi.org/10.1007/978-3-030-92127-9_63 12. Bawm, Z.L., Nath, R.P.D.: A conceptual model for effective email marketing. In: 2014 17th International Conference on Computer and Information Technology (ICCIT), pp. 250–256. IEEE (2014). https://doi.org/10.1109/ICCITechn.2014.7073103 13. Salehi, M., Mirzaei, H., Aghaei, M., Abyari, M.: Dissimilarity of E-marketing VS traditional marketing. Int. J. Acad. Res. Bus. Soc. Sci. 2(1), 510–515 (2012) 14. Baltes, L.P.: Content marketing-the fundamental tool of digital marketing. Bulletin of the Transilvania University of Brasov. Econ. Sci. Ser. V 8(2), 111 (2015) 15. Bala, M., Verma, D.: A critical review of digital marketing. A Critical Review of Digital Marketing. Int. J. Manag. IT Eng. 8(10), 321–339 (2018) 16. Duffy, D.L.: Affiliate marketing and its impact on e-commerce. J. Consumer Marke. 22(3), 161–163. https://doi.org/10.1108/07363760510595986 17. Prašˇcevi´c, N., Prašˇcevi´c, Ž.: Application of fuzzy AHP method based on eigenvalues for decision making in construction industry. Tehniˇcki vjesnik/Technical Gazette 23(1), 57–64. https://doi.org/10.17559/TV-20140212113942 18. Dovlatova, K.J.: Estimation of benchmarking influence in buyer’s decision-making process by using fuzzy AHP. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 173–182. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-92127-9_26 19. Aliev, R.A., Aliev, B.F., Gardashova, L.A., Huseynov, O.H.: Selection of an optimal treatment method for acute periodontitis disease. J. Medical Syst. 36(2), 639–646 (2012). https://doi. org/10.1007/s10916-010-9528-6 20. Adilova, N.E.: Quality criteria of fuzzy IF-THEN rules and their calculations. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 55–62. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-640 58-3_7 21. Babanli, M.B.: Fuzzy Logic-based Material Selection And Synthesis. World Scientific Publishing Company (2019)
Determination of Green Field Plants Most Suitable for Geographical Features of Places with Fuzzy Logic Methods Rü¸stü Ilgar1
, Vugar Salahli2 , Yagub Sardarov3(B) and Zhala Jamalova3
, Zarifa Imanova3
,
1 Department of Geography Teaching, Çanakkale Onsekiz Mart University, Çanakkale, Turkey 2 Department of Computer Engineering, Odlar Yurdu University, Koroglu Rehimov Street, 13,
AZ1072 Baku, Azerbaijan 3 Department of Computer Engineering, Azerbaijan State University of Oil and Industry,
Baku, Azerbaijan [email protected]
Abstract. Greening is of great importance in improving people’s living environments. One of the main problems in greening is to consider the geographical characteristics of the greening region in the selection of plants for greening purposes. In this study, the problem of selecting plants suitable for the greening region is considered as a classification problem. For this purpose, a prediction model based on the J48 algorithm was created and the suitability of the plants for the greening region was estimated with this model. In addition, it has been tried to determine the suitability level of plants for the region with fuzzy inference rules that take into account heat resistance, cold resistance and drought resistance characteristics. Keywords: Classification problem for greening · Decision tree · Fuzzy logic · Prediction model
1 Introduction The world is experiencing the largest wave of urban growth in its history. More than half of the world’s population, about 73% of the European population and 75.1% of the Turkish population live in cities. With the increasing population it is predicted that two-thirds of the world’s population and 95% of Turkey’s population will live in cities in the nearest future [1]. This situation brings big problems with it. One of the most important of these problems is the lack of green space, which causes serious health problems. In this sense, greening in big cities is of great importance. One of the main greening problems is the determination of plants suitable for the geographical characteristics of the greened area. As a result of the use of plants that are not suitable for the geographical structure and climate of the region for greening, these plants either dry out or require high cost maintenance. There have been many studies on the importance of greening [2, 3].The World Health Organization (WHO) emphasizes the importance of green spaces on welfare and © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 530–538, 2023. https://doi.org/10.1007/978-3-031-25252-5_70
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public health [4, 5]. One of the most common problems of cities is air pollution. In this concept greening also plays an important role in the fight against pollution [6]. Some studies investigate the effects of the city’s geographical-climatic characteristics and ecology factors on the arrangement of green areas. In [2] the characteristics of green agriculture in sensitive ecological areas are analyzed based on the relationship between ecological environmental factors and the method of structuring the vegetation in the landscape of the parks is discussed. The study highlights that choosing appropriate plant species can prevent soil erosion, help restore ecosystems, and improve the landscape value of parks. Climatic factors play an important role in the growth of plants. The study [7] aimed to produce maps showing the upper and lower temperature limits necessary for the production of fruit, vegetables, ornamental plants and forest trees. In this study, the values of low and high temperature parameters were determined with the data taken from 250 climate stations between 1975 and 2010, and on the basis of these values, 18 classes of plant hardiness zones and 10 classes of plant heat zone maps reflecting the topography and altitude effects of Turkey were produced. In many parts of the world, extreme winter cold is an important determinant of the geographic distribution and successful cultivation of perennial plant species. In the United States, the U.S. Department of Agriculture (USDA) Plant Resilience Zone Map (PHZM) is the primary reference for the horticultural and nursery industries, home gardeners, agro meteorologists, and plant scientists to describe geospatial patterns of extreme winter cold. In the [8] the approaches followed for updating the USDA PHZM, the last version of which was published in 1990 have been described. The study [9] investigates the characteristics of drought-tolerant plants. Although plant cold and heat tolerance maps are an important guide indicating whether plant species can be cultivated in certain areas in the open field, using them without additional information about the climate of that region can lead to many inconveniences. Precipitation, air and soil temperature, air and soil moisture, sunshine duration and intensity, wind, etc. are climatic factors [10]. The literature review on the subject shows the necessity of considering many geographical-climatic parameters in the selection of plants for greening purposes. Maps containing information on drought, temperature and cold resistance by regions are important data sources for the selection of plants.
2 Purpose of the Research The aim of the study is to determine the greening plants suitable for the climatic conditions of Canakkale city center of the Republic of Turkiye. Canakkale is city in Turkiye in Çanakkale Province on the southern shore of the Dardanelles at their narrowest point. Çanakkale’s climate is generally mild. It shows a transition climate characteristic between the Mediterranean climate and the Black Sea climate. Precipitation is high in winter and spring. Annual precipitation is between 600–1200 mm. It is frosty for about a month a year. The temperature hovers between –10° and + 38 °C. Due to the increasing influence, the need for green space is increasing in Canakkale, as in other world cities. Although it has suitable climatic conditions for greening, green areas are not enough in Çanakkale city center. Thus, while it is recommended to have 10 m2 of green space per capita in urban areas, the amount of green space per person
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in Canakkale is 9.5 m2 . This is an indication that the greening problem is important for Canakkale. For greening, plants that grow in the region and adapt to the climate and soil of the region are preferred. In addition, plants that are not characteristic for the region but attract attention with their appearance, ornamental or not requiring much maintenance are also used for the greening of parks and avenues. In these cases, some plants selected for greening are not suitable for the geographical features of the region, so they require much more expense and in many cases dry out. For this reason, choosing the suitable plants for greening in cities is an important problem. Many geographical and climatic parameters have positive or negative effects on the development of plants. These parameters are as follows: drought resistance, maintenance need, moisture resistance, light resistance, soil type, sunlight requirement, water requirement, nutrient requirement, climate type. The effect of these parameters on the selection of plants can be very serious or very weak. Various methods are used to solve the problem of choosing greening plants, that ordinary data mining method, classification. The purpose of this study is to use decision tree classification method and fuzzy logic method for the problem of selection of plants suitable for Çanakkale region.
3 The Research Method The study used two methods to investigate the suitability of greening plants for Çanakkale climate. First, the decision tree method was used. 3.1 Classification by Decision Tree Method The effectiveness of classification depends on the size of the dataset and the correct selection of features. The choice of classification model often affects the speed of operation of the model when very large data are used. The large number of patterns and features in the dataset will increase the precision of classification. However, the high number of features in datasets consisting of a limited number of patterns makes the classification model lose its generalization feature. Such an approach was followed in selecting the dataset for classification. – It was determined based on which features of the plants the classification would be made; – Based on the sources and expert opinions, the list of plants that are definitely suitable for the Canakkale region and the list of plants that are definitely not suitable for this region were determined; – For the plants in the first list, we set the class label “suitable” and the other class “not suitable”. The dataset consisting of these two lists was used as a learning and test set in the prediction model. The separation of the dataset into learning and testing subsets depends on the methods used in the application of the models. After the learning process, if the
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predictive precision of the model is above the desired value, it is the situation that indicates that the model has learned. We apply the prediction model to determine the class of a plant that does not grow in the region and for which there is no definite data about its suitability for the region, that is, a plant whose class label is unknown. In the study, 38 plant species were investigated according to 13 parametric characteristics. It was understood that some features were not strictly suitable for the geographical conditions in Çanakkale or had little effect on the decision-making process, and they were excluded from the learning data set. Thus, the number of features has been reduced from 13 to 9. The suitability of the plants for the region was chosen as the class label. In the data set, which was created as a learning set, there were vegetation patterns that were definitely suitable for Çanakkale climatic conditions and were not suitable for Çanakkale climatic conditions. A prediction model based on decision tree method was developed by using J48 algorithm on WEKA application. J48 algorithm is one of the best machine learning algorithms to examine the data categorically and continuously. Weka is a collection of machine learning algorithms for data mining tasks. It contains tools for data preparation, classification, regression, clustering, association rules mining, and visualization. Based on the learning data set, “suitable” and “unsuitable” plants were estimated for Çanakkale region. The accuracy rate was 84.21%. The application results of the J48 decision tree algorithm show that the care needs, sunlight resistance and drought resistance of the plants are effective in plant selection. Of the 38 plants, 13 were found to be unsuitable and 25 were found to be suitable. By increasing the number of learning set and test data, it is possible to use the model not only in Çanakkale, but also in the problem of choosing suitable plants for greening in other areas. The results of the classification process performed with the J48 algorithm in the Weka application are given. The last 5 rows in the table represent the characteristics of the plants for which the class label has not been determined. The prediction model predicted the class labels of these plants. According to the research findings, plants with high resistance to sunlight are “suitable”, while plants with medium and low values are “not suitable” for the Canakkale regon. It has been understood that the plants with medium and high drought resistance are “suitable”, while those with low drought resistance are “not suitable”. If the plant’s need for maintenance is low and medium, its resistance to sunlight is high, and its resistance to drought is medium and high, this plant belongs to the “suitable” class for greening. If the plant needs a lot of care, its resistance to sunlight is low and medium, and its resistance to drought is low, it is included in the “not suitable” class for greening. 3.2 Fuzzy Application Our second study on the selection of plants was the application of fuzzy logic inference rules to solve the problem. There are two reasons for using fuzzy logic method. 1) Comparing the results obtained by the decision tree method with the results obtained by another method;
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2) Class properties and class label are expressed with fuzzy values instead of expressing them with exact values. This is very important in decision making. In the decision tree method, 9 characteristics of the plants were used for classification. In the decision tree method, 9 characteristics of the plants were used for classification. In the fuzzy logic application, we were satisfied with only 3 features (resistance to cold, resistance to heat and resistance to drought). The reason for this is that with the increase in the number of features, the number of inference rules also increases and causes the complexity of the system. The values of the hardness and heat resistance parameters were determined based on the maps prepared by the General Directorate of Meteorology of the Republic of Turkey [10]. These maps indicate which hardness and heat zones the provincial centers belong to, in accordance with 13 hardness zones and 8 heat tolerance zones. According to these maps, plant hardiness zones and plant heat tolerance zones in Turkey were determined as follows (Table 1–2, respectively). Table 1. The hardiness zones and temperature values (temperature values are given with the Fahrenheit temperature scale. Hardiness zone
4a
4b
5a
5b
6a
6b
Temperature – 30, –25 range
– 25, –20
– 20, –15
– 15, –10
– 10, –5
-5, 0 0,5 5,10
Hardiness zone
8b
9a
9b
10a
15,20
20,25
25,30
30,35
8a
Temperature 10,15 range
7a
7b
Table 2. Plant heat tolerance table Zones
2
3
4
5
6
7
8
9
Sunny Days >1–7 >7–14 >15–30 >30–45 >45–60 >60–90 >90–120 >120–150
The drought map of the Turkiye was taken as a basis for the drought values [6]. The drought values of the zones were calculated with the SPI index method. In Table 3, drought zones and SPI values for these zones are given [11].
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Table 3. Drought zones and SPI values Number of drought zones
1
Name of Except. drought Dry zones SPI values of drought zones
2
– 1,60– – 1,30– -0,80– -1,99 – 1,59 −1,29
On the basis of these data, hardiness, plant heat tolerance and drought tolerance fuzzy variables were determined. We used the FisPro open source application to express fuzzy variables and create fuzzy inference rules. Fuzzy variable hardiness can obtain tree fuzzy values –extremely cold, very cold, and cold. Fuzzy variable Heat tolerance can obtain tree fuzzy values –few, moderate, and many. Fuzzy variable Drought can obtain tree fuzzy values –dry,normal,hamid. Trapezoidal form of the input variables is given in the Figs. 1–3. According to the number of drought zone, the fuzzy variable drought takes values in the range of [1, 11]. These values represent 11 drought zones. As can be seen from Table 1, the temperature values of hardiness zones are between –30 °F and 35 °F. As seen in Table 2, the number of sunny days for zones varies between 1 and 160. We evaluated the suitability of the plants to the region in the range of [1, 10]. We decided that the fuzzy variable of suitability could take three fuzzy values:-not suitable, less suitable, and suitable. Fuzzy inference rules [ 12–16] were created to determine the suitability of a plant for the Çanakkale region. These rules were developed based on the results of our study with the decision tree method and expert opinions. Graphical presentation of the input variables (hardiness, heat tolerance, and drought) and of output variable of the system- suitability to Çanakkale region with given attribute values, obtained from Fispro application, were shown in Figs. 1, 2, 3 and 4.
Fig. 1. Drought linguistic valuable
Fig. 2. Heat tolerance linguistic valuable
The screen sheet of the fuzzy inference rules used to determine suitabiliy plants to the regionis is given in Fig. 5. .
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Fig. 3. Hardiness linguistic valuable
Fig. 4. Suitability linguistic output variable
Fig. 5. Fuzzy inference rules
The fuzzy inference rules determine the suitability of a plant for the Canakkale region in the given values of the hardiness, heat and drought characteristics of a plant. In the application example in Fig. 6, the suitability of a plant with a drought value of 6, a heat of 80 and a hardiness of 8,35 for the Çanakkale region was calculated as 7.85 by the fuzzy inference system. This value received because of the defuzzification process. Since the value of the membership function of the suitability is much higher for “suitable” than “less suitable”, we can say that the plant is suitable for the Canakkale region.
Fig. 6. Fuzzy inference rules
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4 Conclusion In the study, the selection of plants for greening purposes in Çanakkale city center of the Republic of Turkey was investigated. Considering the climatic characteristics of Çanakkale and the characteristics of greening plants, 2 methods were used to select the most suitable plants for Çanakkale climate. The classification of plants was made based on 9 feature values with the J48 decision tree algorithm. For this purpose, Weka data mining application was used. Fuzzy inference rules were developed that express the dependence between the three important property values of plants and the suitability level of that plant for a particular region. For this purpose, FisPro fuzzy inference application was used. The methods proposed in the research can be used in studies conducted for the greening of cities. More plant samples are needed to get more precise and practical solutions.
References 1. The official website of the Ministry of Environment, Urbanism and Climate of the Republic of Turkey. http://www.csb.gov.tr/projeler/sehirciliksurasi (Accessed 24 March 2020) 2. Li, Z.: Analysis of Greening Ecology in Landscape Reconstruction of Construction Waste Dump in Wind-sand .:rnational Conference on Energy, Environment and Materials Science, Hulun Buir, China (2020) 3. Ilgar, R.: Perceptıon and awareness of people lıvıng In Çanakkale Cıty related to urban Green Areas. Electronic J. Social Sci. 21(82), 459–479 (2022) 4. Gardashova, L.A., Ilhan, U., Kilic, K.: UAV using Dec-POMDP model for increasing the level of security in the company. Procedia Comput. Sci. 102, 458–464 (2016). https://doi.org/ 10.1016/j.procs.2016.09.427 5. Morar, T., Radoslav, R., Spiridon, L.C., Pacurar, L.: Assessing accessibility to green space using gis. Transylvanian Rev. Administrative Sci. 42, 116–139 (2014) 6. https://www.urbanespora.es/en/the-8-benefits-of-spreading-green-spaces-in-cities/ 7. Pe¸skircio˘glu, M., et al.: Mapping the plant hardiness and heat zone at Turkey scale by geographic information system. J. Field Crops Central Res. Inst. 11–25 (2016) 8. Daly, C., Widrlechner, M.P., Halbleib, M.D., Smith, J.I., Gibson, W.P.: Development of new USDA plant hardiness zone map for the United States. J. Appli. Meteorol. Climatol. 51, 242–264 (2012) 9. Passioura, J.B.: Drought and drought tolerance. Plant Growth Regul 20, 79–83 (1996). https:// doi.org/10.1007/BF00024003 10. Official website of the General Directorate of Meteorology of the Ministry of Environment, Urbanism and Climate Change of the Republic of Turkey, https://mgm.gov.tr/tarim/plantkisoguga-ve-sicaga-dayaniklilik.aspx?g=a 11. McKee, T.B., Doesken, N.J., Kleist J.: The relationship of drought frequency and duration to time steps, Preprints. In: 8th Conference on Applied Climatology, Anaheim, California, pp. 179–184 (1993) 12. Aliev, R.A., Gardashova, L.A.: Z-set based approach to control system design. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Mo., Jamshidi, Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 10–21. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-640 58-3_2
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13. Ahmadov, S.A., Gardashova, L.A.: Fuzzy dynamic programming approach to multistage control of flash evaporator system. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 101–105. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-35249-3_12 14. Adilova, N.E.: Investigation of the quality of fuzzy IF-THEN model for a control system. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 28–33. Springer, Cham (2022). https://doi.org/10.1007/ 978-3-030-92127-9_8 15. Aliev, R.A., Pedrycz, W., Huseynov, O.H.: Behavioral decision making with combined states under imperfect information. Int. J. Inform. Tech. Decision Making 12(3), 619–645 (2013) https://doi.org/10.1142/S0219622013500235
Z-Information Based MCDM Model for Assessing Green Energy Resources: A Case of Resort and Tourism Areas Mahammad Nuriyev1
, Aziz Nuriyev2(B)
, and A. N. Mahamad3
1 Khazar University, Mehsety Str 41, AZ1069 Baku, Azerbaijan
[email protected]
2 Azerbaijan State Oil and Industry University, Azadlyg Ave., 20, AZ1010 Baku, Azerbaijan
[email protected] 3 French-Azerbaijani University, Nizami Str, 183 Baku, Azerbaijan
Abstract. The use of green resources found in resort and tourism spots demands special attention to the preservation of the landscape, image, and scenery. Considering the significance of this issue, for renewables selection, we are using the more advanced approach, based on Z-numbers use. The generally accepted set of criteria is expanded, and specifics of the resort area are taken into consideration in the decision model. The objective of the paper is to develop model and solution procedures allowing to compromise priorities of the resort area preservation and energy resources use and consider task-related information uncertainty and reliability. For the problem solution Z-numbers-based ORESTE and TOPSIS models are developed. Z-numbers application allows to formalize experts’ opinions and the reliability of their estimates. The solution procedure is based on direct calculations with Z-numbers. The final solution provides information on decision variables and their reliability. According to the results obtained from the Azerbaijan resort areas-based case, solar energy, followed by biogas, hydropower, and wind, has the priority in the researched regions. Results confirm the efficiency of the approach and its applicability in other areas/regions. Keywords: Tourism areas · Renewable energy resources · Z-number · MCDM · Z-ORESTE · Z-TOPSIS
1 Introduction Clean energy and environmental sustainability are inseparable parts of the world economic development. This topic becomes especially sensitive when potential renewables like solar, wind, hydro, and biogas are available in resort and tourism areas, and renewables development in these areas must be performed while leaving no negative impacts on landscape and scenery. In such circumstances, it is necessary to complement resources assessment and criteria selection by taking the scenery, landscape, and image of the region criteria into consideration. Moreover, it must be emphasized that with reasonable © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 539–548, 2023. https://doi.org/10.1007/978-3-031-25252-5_71
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approach solar and wind plants, biogas and small hydro stations can be used as tourism attractions as well. Energy source selection is a multi-criteria decision-making task and has a rich history. Researchers, based on task peculiarities and personal preferences, are using pairwise comparison, outranking, distance-based, scoring methods, and a combination of these methods or other approaches. Emerged as conventional decision-making methods, these approaches were later extended by researchers to solve decision-making tasks with fuzzy constraints and objectives. Comprehensive reviews [1, 2] of the multi-criteria decision-making (MCDM) methods applications in the energy sector show that researchers are applying both conventional and fuzzy methods. Energy sources assessment and decision selection are based on subjective, incomplete, and imprecise information, and in such circumstances, applications of the fuzzy models in such subject areas were expected to extend the traditional MCDM methods. The acceptability of different types of renewable energy sources for resort and tourism areas was studied in [3–6]. It should be emphasized that the fuzzy models only partially resolve the issues associated with deficiency and subjectivity of the information, used in MCDM methods. In the classical versions of the fuzzy models, the issue of information reliability is not considered, and decision-makers (DM) get solutions not containing any information about the reliability of the results. Z-numbers allow resolving this problem. Solutions, based on Z-information, provide DM with fuzzy values of the decision variables and their reliability. At present, there are a limited number of publications, related to the use of the Z-numbers in energy sources assessment and selection [7–9], and these approaches are mostly based on the transformation of the Z-numbers. In this paper, we developed the Z-number-based MCDM model for renewable energy resources assessment and selection in the resort areas. The approach, used for the problem solution, is directly operating with Z-numbers, preserves fuzzy values of the decision variables, and fuzzy estimates of confidence in these values in all stages of calculations. It also provides an exact solution within the given initial data. Respectively, the final solution provides decision makers with the fuzzy values of decision variables and the degrees of reliability of these values.
2 Definitions and Operations with Z-numbers Definition 1. Z-Numbers Ranking Based on the Fuzzy Pareto Optimality Principle [10]. Two Z-numbers are compared as multi-attribute alternatives by calculating the degrees of optimality do(Z 1 ) and do(Z 2 ). These degrees are determined based on the number of components for which one Z-number dominates over another Z-number. Calculation of do(Z i ) is a multi-stage process. At the first stage, A parts are normalized. Then intermediate functions nbest (Z i , Z j ), nequal (Z i , Z j ), and nworst (Z i , Z j ) are calculated, estimating how much one Z-number is superior, equivalent, or less with respect to the components A and B. Then, value of d(Z i ,Z j ) is calculated according to below formula. 0, ifnbest Zi , Zj ≤ 1 − O.5, nequal Zi , Zj (1) d(Zj , Zj ) = 2nbest (Zi ,Zj )+nbest (Zi ,Zj )−2 nbest (Zi ,Zj ) If d(Z i ,Z j ) = 1, then Z i is Pareto-dominated over Z j . If d(Z i ,Z j ) = 0, Z i is not Paretodominated over Z j . Based on the values of the function d the degree of optimality of Z j
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is calculated by the formula. do(Zj) = 1−d (Zj , Zj )
(2)
do (Z i ) determines the degree of how much one Z-number is over than another. In other words. Z i > Z j , if do (Z i ) > do (Z j ), Z i < Z j , if do (Z i ) < do (Z j ), Z i = Z j , if do (Z i ) = do (Z j ). Definition 2. Distance Between Z-Numbers [11]. The distance between two Znumbers Z1 and Z2 , whose parts were expressed by fuzzy numbers A1 , B1 , A2 , B2 and underlined set of probability distribution functions (PDF) G, is defined as follow. D(Z1 , Z2 ) = βD(A1 , A2 ) + (1 − β)Dtotal (B1 , B2 )
(3)
here Dtotal (B1 ,B2 ) is a distance for reliability restriction computed as follow: Dtotal = w D (B1 ,B2 ) + (1- w) D (G1 , G2 ) β,w [0,1] are importance degrees assigned by DM, D(A1 ,A2 ) and D(B1 ,B2 ) are distances between fuzzy numbers A1 and A2 , B1 and B2 , respectively. D(G1 ,G2 ) is distance between the sets G1 and G2 of PDFs p1 and p2 underlying Z 1 and Z 2 . 2.1 Z-Number-Based ORESTE Method ORESTE method has been used for renewable energy source selection due to its efficiency in the solution of the ranking and selection tasks [12–14]. The peculiarity of this method is that it can be applied without direct assessment of the criteria weights. Moreover, since criteria weights or various preference parameters are not necessary, this is suitable when experts cannot exactly estimate criteria weights. This method has been successfully used with classical fuzzy models [15–17]. Below, we are introducing the Z-number-based extension of this method and details of the calculation procedure. Step 1. Determining the weak order of criteria. The weak order of criteria is defined based on their relative importance according to the degree of optimality. C j C k C i … C n . Step 2. Obtaining the weak order of the alternatives for each criterion. After constructing of a decision-matrix, the weak order of the alternatives for each criterion is obtained, based on the degree of optimality. C 1 :Ai Ak Ai . ……. Cn: Ak Ai Aj. Step 3. Ranking of the criteria. The rank of a criterion is determined based on its place in the data set, calculated at the first step. If more than one criterion is found to have the same rank, the average rank is used for both values. Step 4. Ranking of alternatives. The ranking of alternatives is determined according to the rank of each alternative in the initial ranking of alternatives for each criterion.
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Step 5. Calculation of the projection distances. Projections combine alternatives ranks and criteria ranks into a number d. The projection distances correspond to the relative positions of the alternatives. dji = (1− ∝)rji + ∝ r j
(4)
here r j is the rank of j-th criterion and rji is the rank of alternative i with respect to j-th criterion, α [0, 1] is coefficient defined by researcher. Projection distances are calculated in such way, that if an alternative a1 is preferred to alternative a2 (a2 a1 ) for criterion j, then d j (a1 ) < d j (a2 ), i. e. the smaller projection distance, the better is the position of the alternative. Step 6. Ranking of the projections and obtaining the global ranks. A mean global rank r j (ai ) is assigned to all the projection distances from the lowest to the highest ones. Smaller r j (ai ) indicates a better position of the alternative. Step 7. Calculation of the mean ranks. For each alternative, a mean rank is computed by the summation of their global ranks over the entire set of criteria using the following formula: r(ai ) =
n
rj (ai )
(5)
j=1
These mean ranks are simply sorted to increasingly determine the global weak order of the alternatives. We can also apply an alternative approach for the problem solution, based on ideas presented in [17], as well. In this case, there is no need to crisp criteria weights, and we operate only with elements of the conceptual apparatus of Z-numbers. Revised steps 3–6 are presented below. Step 3a. Determination of the criterion with a higher degree of optimality (do), and determination of the alternative with a higher degree of optimality for each criterion. Step 4a. Obtaining the dominance-based distance d j from each criterion to the criterion with higher do (j = 1,…,m – number of criteria), and the distances d ij from each alternative to alternative with higher do under each criterion (i = 1,…,n – number of alternatives), according to the formula (1). Step 5a. Computation of the global preference score according to the formula. D(Aij ) = [0.5(dij )2 + 0.5(dj )]1/2
(6)
Step 6a. Computation of the preference score and ranking of alternatives. The preference score of alternative ai is defined as the average of the global preference score of aij 1 D(Aij ) m m
D(Ai ) =
(7)
j=1
According to the preference score, we can obtain the order of alternatives. If D(Ai ) > D(Ak ), then Ai Ak , if D(Ai ) = D(Ak ), then Ai ≈ Ak .
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3 Results We are analyzing the renewable energy resources ranking and selection in resort and tourism areas. As an example, the northeastern region of Azerbaijan was selected. This is a coastal tourist region with many sunny days, wind potential, the presence of hydro resources, as well as developed animal husbandry. The country‘s energy resources endowment in resort areas predetermines four alternatives for the energy resources that are of interest: solar energy, wind, hydro, and bio. Alternatives are analyzed for six criteria: Social acceptance (C1 ); Labor impact (C2 ); Cost Efficiency (C3 ); Landscape and Scenery effects (C4 ); Resource availability (C5 ); Global environmental impact (C6 ). Experts provided the Z-number-based estimation of the criteria weights, and alternatives with respect to the criteria. In estimates, linguistic terms Poor (P), Below Average (BA), Average (A), Above Average (AA), Good (G), Very Good (VG), Low (L), Medium Low (ML), Medium (M), Medium High (MH), High (H), and Very High (VH) are used for weights, criteria, and alternatives evaluations. Criteria importance is defined by the Znumber-based swing weighting method [18]. According to this method, Z-number-based values of criteria weights are. C 3 , C 6 - VH, VH; C 4 , C 5 - H,H; C 1 , C 2 - MH,H The normalized Z-number-based values of weights are. C 1 = (0.121 0.149 0.188)(0.326 0.628 0.946) C4 = (0.138 0.167 0.208)(0.5 0.719 0.947) C 2 = (0.121 0.149 0.188)(0.326 0.628 0.946) C5 = (0.138 0.167 0.208)(0.5 0.719 0.947) C 3 = (0.155 0.184 0.208)(0.366 0.69 0.943) C 6 = (0.155 0.184 0.208)(0.366 0.69 0.943) The Z-number-based evaluations of the alternatives with respect to the various criteria provided by experts are shown in Table 1. Table 1. Z-number-based evaluations of alternatives (decision matrix) Expert
Alternative
C1
C2
C3
C4
C5
C6
E1
Solar
G,VH
AA,H
G,VH
A,H
G,VH
BA,VH
Wind
G,H
AA,H
AA,H
A,MH
AA,VH
A,H
Hydro
AA, H
A, MH
G,VH
BA, H
A,H
A, H
Biogas
G, VH
G,H
GA,H
BA, MH
G,VH
BA, VH
…
…
…
…
…
…
…
…
E5
Solar
AA,VH
A,H
A,VH
AA,VH
AA,VH
A, VH
Wind
G, H
AA,H
AA,H
AA, H
A,H
A, H
Hydro
AA, H
A,M
A,VH
BA,VH
A, H
BA, H
Biogas
G, H
G,H
AA,H
BA, H
G, VH
BA,VH
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C4 and C6 are cost criteria. For further calculations on the next step, we aggregate the expert opinions and normalize the decision matrix (Table 2). Table 2 is used for calculations both for Z-TOPSIS and Z-ORESTE methods. Table 2. Z-number based normalized decision matrix Crite rion
Alternatives
Part A of Z-number based value
Part B of Z-number based value
C1
Solar
0.792
0.676
0.896
0.896
1
0.901
0.901
0.97
Wind
0.792
0.896
0.896
1
0.557
0.753
0.753
0.97
Hydro
0.771
0.875
0.875
0.979
0.618
0.82
0.82
0.97
Biogas
0.792
0.896
0.896
1
0.579
0.787
0.787
0.97
…
…
…
…
…
…
…
…
…
…
C6
Solar
0.722
0.839
0.839
1
0.753
0.959
0.959
0.959
Wind
0.65
0.743
0.743
0.867
0.557
0.753
0.753
0.964
Hydro
0.667
0.765
0.765
0.897
0.618
0.818
0.818
0.963
Hydro
0.667
0.765
0.765
0.897
0.618
0.818
0.818
0.963
Biogas
0.722
0.839
0.839
1
0.673
0.888
0.888
0.959
3.1 Application of Z-numbers Based ORESTE According to the calculation procedures of Z-ORESTE, the Z-number-based values of criteria and values of alternatives from Table 2 are ranked based on optimality degree. The results are presented in the next table.
Table 3. Optimality degree -based ranking of alternatives for each criterion Criteria
Rank of alternative
Criteria Rank
Criteria
Rank of alternative A1
A2
A3
Criteria Rank
A1
A2
A3
A4
A4
C1
4
1
2
3
5.5
C4
1
2
4
3
3.5
C2
2
3
1
4
5.5
C5
4
2
1
3
3.5
C3
4
1
3
2
1.5
C6
4
1
2
3
1.5
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Results of calculation of steps 5–7 are presented in the Table 4. Table 4. Projection distances, global ranks of projections and mean ranks Criteria
Projection distances
Global ranks
A1
A2
A3
A4
C1
4.75
3.25
3.75
4.25
A1 1.5
10.5
6.5
3.5
C2
3.75
4.25
3.25
4.75
6.5
3.5
10.5
1.5
C3
2.75
1.25
2.25
1.75
14.5
23.5
18.5
21.5
C4
2.25
2.75
3.75
3.25
18.5
14.5
6.5
10.5
C5
3.75
2.75
2.25
3.25
6.5
14.5
18.5
10.5
C6
2.75
1.25
1.75
2.25
14.5
23.5
21.5
18.5
62
90
82
66
Sum of global ranks
A2
A3
A4
In accordance with ranking presented in Table 4, the best alternative is A1 , followed by A4 , A3 , and A2 . Calculations with alternative Z-ORESTE method gives the same results. The results for steps 3a-6a are shown in the Tables 5 and 6. Table 5. Dominance-based distances between criteria and alternatives Criteria
Distance to the alternative with the max do for each criterion A1
A2
A3
Distance to the criterion with the max do
A4
C1
0
0.298
0.28
0.246
0.51
C2
0.651
0.527
0.866
0
0.51
C3
0
0.68
0.288
0.463
0
C4
0.56
0.821
0
0.18
0.17
C5
0
0.659
0.874
0.113
0.17
C6
0
0.699
0.585
0.238
0
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M. Nuriyev et al. Table 6. Dominance-based distance between alternatives for each criterion
Alternative
C1
C2
C3
C4
C5
C6
Preference score
Rank
A1
0.361
0.585
0
0.414
0.12
0
0.247
1
A2
0.418
0.518
0.481
0.593
0.481
0.494
0.497
4
A3
0.411
0.711
0.204
0.12
0.629
0.413
0.415
3
A4
0.4
0.361
0.327
0.175
0.144
0.168
0.263
2
Alternative version of the Z-ORESTE gives the same results. 3.2 Application of the Z-TOPSIS According to the procedures of Z-TOPSIS [18–20], the Z-number-based normalized weighted decision matrix and closeness to ideal solutions are calculated. The results are presented in Table 7. Table 7. Z-TOPSIS calculations results Alternatives
Distance Z-PIS
Distance Z-NIS
Closeness
Solar
14.8115
9.1885
0.382854
Wind
15.476
8.524
0.355167
Hydro
15.66
8.34
0.3475
Biogas
14.9805
9.0195
0.375813
The values of relative closeness to ideal solution for alternatives are: A1 = 0.382, A2 = 0.355, A3 = 0.347, A4 = 0.375. According to the relative closeness, the best alternative is A1 , then A4 and A2 and A3 . Rankings obtained on the basis of the methods used differ only in the third and fourth ranks. Both Z-ORESTE and Z-TOPSIS methods confirmed computational effectiveness.
4 Discussions and Conclusion Green energy programs developers when resources with high production capacities are available in resort and tourism areas. This specific and sensitive case demands special attention of the researchers and energy resources developers. In this paper, such case was analyzed for resort areas of Azerbaijan Republic and the Z-number-based approach for the problem solution is proposed. Z-information-based MCDM model was developed for assessing and ranking green energy sources in the resort and tourism areas. Z-formalism, used in the model, allows for formalizing uncertainties inherent to the decision-making task and at the same time
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describes the degree of confidentiality of the experts in the information they are providing. For the task solution, two different methods are applied: Z-ORESTE and Z-TOPSIS. The application of methodologically different two techniques increase the reliability of the solution derived. Direct calculations with Z-numbers, by applying specialized Z-Calc software, provide the decision maker with exact solutions based on fuzzy information and information reliability. Solutions obtained by application of both methods provided similar rankings for renewables. Results obtained show that Z-number-based MCDM methods, based on direct calculations with Z-numbers, can be successfully applied for the solution of the other MCDM tasks in the energy sector and other fields.
References 1. Kaya, I., Çolak, M., Yildiz, F.T.: A comprehensive review of fuzzy multi criteria decision making methodologies for energy policy making. Energ. Strat. Rev. 24, 207–228 (2019) 2. Rigo, P.D., et al.: Renewable Energy Problems: Exploring the Methods to Support the Decision-Making Process. Sustainability 12(23), 1–27 (2020) 3. Pröbstl, U., Jiricka, A., Hindinger F.: Renewable energy in winter sports destinations desired, ignored or rejected? Journal: IGF-Forschungsberichte (Instituts für Interdisziplinäre Gebirgsforschung) 4, 309–318 (2011) 4. Karabu˘ga, A., Yakut, M. Z., Yakut, G., Selba¸s, R., Üçgül, ˙I.: Renewable energy solutions for tourism. Europ. Scient. J. 11(9) (2015) 5. Petrevska, B., Cingoski, V., Serafimova, M.: Sustainable tourism and hotel management in Meacedonia through the use of renewable energy source. UTMS J. Econom. Univ. Tourism Managem. Skopje 7(1), 123–132 (2016) 6. Guozhong, Z., Xiao,W.: The comprehensive evaluation of renewable energy system schemes in tourist resorts based on VIKOR method, Energy 193(C) (2020) 7. Chatterjee, K., Kar, S.: A multi-criteria decision making for renewable energy selection using Z-numbers in uncertain environment. Technol. Econ. Dev. Econ. 24(2), 739–764 (2018) 8. Rathore, N., Singh, M.P.: Selection of Optimal Renewable Energy Resources in Uncertain Environment Using ARAS-Z Methodology. In: International Conference on Communication and Electronics Systems (ICCES), 17–19 July 2019. INSPEC Accession Number: 19379542 9. Nuriyev, M.: Z-numbers based hybrid MCDM approach for energy resources ranking and selection. Int. J. Energy Econom. Policy 10(6), 22–30 (2020) 10. Aliev, R.A.: Uncertain computation-based decision theory, World Scientific Publishing, p.531, (2017) 11. Aliev, R.A., Pedrycz, W., Huseynov, O., Aliyev, R.R.: Eigensolutions of partially reliable decision preferences described by matrices of Z-numbers. Int. J. Inf. Technol. Decision Making (IJITDM) 19(06), 1429–1450 (2020) 12. Pastijn, H., Leysen, J.: Constructing an outranking relation with ORESTE. Math. Comput. Model. 12(10–11), 1255–1268 (1989) 13. Adali, E.A., Isik, A.T.: Ranking web design firms with the ORESTE method. Ege Acad. Rev. Ege Univ. Facul. Econ. Administrative Sci. 17(2), 243–254 (2017) 14. Arjun Raj, A.S., Vinodh, S.: A case study on application of ORESTE for agile concept selection. J. Eng. Design Technol. 14(4), 781–801 (2016) 15. Zhang, C., Wu, X., Wu, D., Liao, H., Luo, L., Herrera-, E.: An intuitionistic multiplicative ORESTE method for patients’ prioritization of hospitalization. Int. J. Environ. Res. Public Health 15(4), 777 (2018)
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16. Zheng, Q., Liu, X., Wang, W.: An extended interval Type-2 fuzzy ORESTE method for risk analysis in FMEA. Int. J. Fuzzy Syst. 23(5), 1379–1395 (2021). https://doi.org/10.1007/s40 815-020-01034-1 17. Liao, H., Wu, X., Liang, X., Yang, J.-B., Xu, D.-L., Herrera, F.: A continuous interval valued linguistic ORESTE method for multi-criteria group decision making. Knowl.-Based Syst. 153, 65–77 (2018) 18. Nuriyev, A.M.: Fuzzy MCDM models for selection of the tourism development site: the case of Azerbaijan. F1000 Res. 11, 310 (2022) doi: https://doi.org/10.12688/f1000research.109 709.1 19. Aliev, R.A., Kacprzyk, J., Pedrycz, W., Mo., Jamshidi, Sadikoglu, F.M. (eds.): ICAFS 2018. AISC, vol. 896. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-04164-9 20. Gardashova, L.A.: Z-Number based TOPSIS method in multi-criteria decision making. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Mo., Jamshidi, Sadikoglu, F.M. (eds.) ICAFS 2018. AISC, vol. 896, pp. 42–50. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-041649_10
Assessing the Impact of Innovations on the Volume of Production of the Final Product in a Fuzzy Information Environment V. J. Akhundov1(B)
and ˙I. S. Rustamov2
1 Research Laboratory of Intelligent Control and Decision Making Systems in Industry
and Economics, Azerbaijan State Oil and Industry University, 20 Azadlig Avenue, AZ1010 Baku, Azerbaijan [email protected] 2 Faculty of Economics and Management, Azerbaijan State Oil and Industry University, 20 Azadlig Avenue, AZ1010 Baku, Azerbaijan
Abstract. A whole set of factors has a significant impact on the economic development of the region. The aim of the study is, taking into account these factors, to build a model that allows calculating the value of the gross regional product both in the form of classical statistical procedures and based on fuzzy modeling. This allows to determine a more adequate prediction price of the final product by region by comparing the results. The object of analysis is the regions of the Azerbaijan Republic. The problem of forecasting the regional final product is solved using the fuzzy Cobb-Douglas model. Keywords: Innovation activity · Fuzzy model · Innovation index
1 Introduction The impact of innovation at the macroeconomic level has been relevant for many decades. Particular interest in it is manifested during various economic crises, which are associated with the search for new directions of development. Of practical importance are the studies of the German scientist G. Mensch [1]. He tried to draw a parallel between the rate of economic growth and cyclicality with the advent of fundamental innovations. The key idea of Mensch’s metamorphosis model is the relationship between depression (stagnation) and innovation. American economist N. Rosenberg examined innovation clusters, distinguishing between T-clusters and M-clusters. T-clusters are associated with “technical processes, while M-clusters are clusters of general incentives for increasing demand or other convenient macroeconomic conditions” [2]. Ch. Freeman and C. Perezargued described clusters of basic innovations [3]. They emphasized that the diffusion of the so-called techno-economic paradigm is accompanied by a major crisis of the structural regulator. The ideas of Norton (J. Norton) and Bass (F. 32 Bass) made it possible to make the transition from a theoretical analysis of the processes of the impact of innovations on the economy to their mathematical formalization [4]. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 549–556, 2023. https://doi.org/10.1007/978-3-031-25252-5_72
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In 2006, the Japanese economist M. Hirooka proposed the idea of synthesizing the above ideas about the nature of the influence of various factors on economic development [5]. A feature of Hirooka’s approach is that he considers the dynamics of scientific and technological progress as a relatively independent factor in economic development that forms the actual economic trends. Hirooka was the first researcher to identify and analyze the developmental. trajectory. M.Kalecki reinforces the idea of a cyclical trend effect that “innovations have on the investment function” [6]. In the models discussed above, aggregate demand was assumed to be known. However, uncertainty in aggregate demand can affect aggregate investment. R. Costrell proposes a model that includes both definite and uncertain demand [7]. In [8] authors showed the application of the fuzzy modeling method in solving the problem of scenario forecasting of regional development. The basis of this analysis is the coordination of the data of expert assessments with the data of regional statistics. Despite the abundance of empirical studies, as many authors note, there are certain difficulties associated with the interpretation of the results of these studies. Until now, there is no generally accepted approach to the economic and mathematical modeling of innovation processes in macroeconomic systems.
2 Calculation of the Final Product of the Region Using a Production Function that Takes into Account the Innovation Factor In the process of assessing the use of resources in the manufacturing sector using the Cobb-Douglas production function, it is necessary to take into account the factor of technical progress. It should be noted that other factors also affect the change in the cost of production, such as changes in the level of management and changes in relative prices over time. Technical progress must be taken into account in the form of a time trend (t), which is part of a specific time function. Taking into consideration the factor of technical progress, the Cobb- Douglas production function takes the following form: Y = A × Lα × Kβ × eλt
(1)
where, A is the technological coefficient; α, β are coefficients of elasticity of capital and labor resources; t-time, λ characterizes the impact of scientific and technological development on the growth of the final product over time, L and K show labor payments, and the cost of fixed assets (average annual cost of fixed assets). We apply the methodology proposed in [9]. The economic zones of Azerbaijan were taken as the object of study. When determining the innovation index, indicators of scientific and technological development and the socio-economic environment and their interaction were considered. The indicators are grouped by characteristics. 19 indicators were used here, uniting 3 groups: resources, the intensity of innovation activity, and indirect conditions. The growth rate of technological progress is defined as the increase in labor productivity in year t + 1 compared to year t. This kind of production function is the simplest kind of dynamic
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551
production function. According to the applied methodology [9], the final innovation index was determined. The algorithm for determining the innovation index and based on it the calculation of the pace of scientific and technical progress is shown in stages (here G is an indicator that characterizes innovation and innovation processes, chosen by the author according to certain criteria for calculating the innovation index): Stage 1. Initial data entry for group. Stage 2. Calculation of Gij indicators (Gij is the i-th indicator in the j-th group). i −Gmin Stage 3. Normalization of indicators Gij, i = 1,n; j = 1,m; Gijnor = GGmax −Gmin Stage 4. Calculation of special indicators ; Gi = ˙ = Stage 5. Calculation of the innovation index Ii
n
i=1 Gij , i = 1, n; j n Gi , i = 1, n. n
= 1, m.
Stage 6. Calculation of the final innovation index; ˙I = n i , i = 1, n. We propose to add stage 7: Stage 7. Calculation of the impact of innovation on the growth rate of the final t 1q ˙ product; λreq = I : = t , here, t = 1,n; i = 1,n. (t–the years under consideration, q – growth rate of the final product). In stage 7 a formula for determining the coefficient of the “influence of innovations on the growth rate of the final product” is proposed. Table 1 shows the calculated “innovation index” (I) for the regions of Azerbaijan and the “impact of innovation on the growth rate of the final product” (λreq) indicator determined on its basis. Table 1. Regional innovation index and the coefficient of the impact of innovations on the growth rate of the final product Regions
˙Innovation index (I)
Coefficient of the impact of innovations on the growth rate of the final product (λreq )
Sheki-Zagatala
0.091283
0.082062
Guba-Khachmaz
0.130358
0.122528
Ganja-Gazakh
0.167315
0.121339
Absheron
0.176137
0.141449
Aran
0.112921
0.103055
Lankaran
0.13629
0.126332
Nakhchivan Autonomous
0.23837
0.215472
Mountainous-Shirvan
0.180792
0.16747
Baku city
0.380019
0.364197
The value of the technical progress component e0,141 in the function indicates that about 15.3% of the increase in final production in the Ganja-Gazakh region is provided by technical progress, while in Sheki-Zagatala this figure does not exceed 9%. Using the above table and indicators of the Azerbaijan State Statistical Committee for the period from 2010 to 2020, we determine the values of α and β in Eq. (1). In the
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course of the study, calculations were made for each region that makes up the economy of Azerbaijan. Thus, the goal in the first part of the study is to build an econometric model to explain the impact of innovation on the production of final products in the regions of Azerbaijan. For example, using the data in Table 1, the value of the final product in the Ganja-Gazakh region was determined. The calculation results are given in Table 2. Table 2. Results of calculations for the Ganja-Gazakh region Years
Actual values of the final product (Y)
The value of the final product determined by the Gradient method (Yı )
2010
1835.53
2259.70
2011
2230.55
2672.69
2012
2561.73
2935.22
2013
2734.36
3168.87
2014
2689.16
3307.31
2015
2757.39
3237.50
2016
3005.08
3359.41
2017
3699.75
3432.10
2018
3724.21
3443.02
2019
4150.72
3713.03
2020
4348.45
3779.34
To obtain more accurate results in the forecasting process, one should take into account the uncertainty of the data, their inaccuracy, statistical errors, etc. (the second group of factors). Therefore, in the second stage of the study, according to the constructed model, the variances of random deviations were determined.
3 Estimation Results of Output (Y) Using the Fuzzy Cobb-douglas (Innovation) Model To obtain a more adequate forecast of the final product by region, it is necessary to take into account a large number of impact factors and other data [10]. ˙It is possible to determine the fuzzy prices of gross output based on the fuzzy prices of fixed assets, wages and the use of innovations in the field of production. Taking into account these factors, when predicting the final product for the regions of the Republic of Azerbaijan, a fuzzy Cobb-Douglas model was used: ˜ α˜ ˜ K · L˜ β · eλ Y = A˜ ·
(2)
˜ α, ˜ L, ˜ where the values of K, Y and parameters A, ˜ β˜ and λ˜ are described by fuzzy numbers. Using fuzzy data, on the basis of fuzzy estimates of fixed assets, labor payments and
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the rate of scientific and technological progress, we calculate fuzzy prices for the final product of the region. In r-cuts one has: The calculation results are given (3) Table 3 shows fuzzy estimates (in form of triangular fuzzy numbers, TFN) of the average annual cost of fixed assets and the average number of employees of in the regions, taking into account possible devations (deviations) in 2010–2020. Using this table, construction of Cobb-Douglas production function under fuzzy information (described by Eq. (2) is based on a solution to the following optimization problem: (4) d Y˜ , Y → min years
˜ ≤ A˜ ≤ ·A· A
(5)
α˜ ≤ ·α· ˜ ≤ α
(6)
Y˜ denotes fuzzy reduced values of end product (Table 3), Y is a fuzzy value of func˜ α, tion (2), A, ˜ β˜ and λ˜ are the fuzzy parameters for the fuzzy Cobb-Douglas production ˜ function, A, A˜ and α, ˜ α, β, β, λ˜ , λ are the boundary conditions of the ranges of these parameters. Distance between fuzzy numbers d is adopted from [11]. ˜ K, ˜ L˜ L, ˜ Y ˜Y ˜ for the Ganja-Gazakh economic region Table 3. Fuzzy estimates of K Years
Average annual cost of fixed assets, (thousand manats) ˜K ˜ K
labor payments (thousand manats) L˜ L˜
The volume of the final product (thousandmanats) ˜Y ˜ Y
2010
(546.3; 563.2; 580.1)
(2222.3; 2291.0; 2359.7)
(1668.7; 1835.5; 2019.1)
2011
(750.4; 773.6; 796.8)
(2681.0; 2763.9; 2846.8)
(2027.8; 2230.6; 2453.6)
2012
(890.7; 918.2; 945.8)
(3036.2; 3130.1; 3224.0)
(2328.8; 2561.7; 2817.9)
2013
(1041.2; 1073.4; 1105.6)
(3183.4; 3281.9; 3380.4)
(2485.8; 2734.4; 3007.8)
2014
(1112.7; 1171.2; 1229.8)
(3201.3; 3369.8; 3538.3)
(2379.8; 2689.2; 3038.8)
2015
(1051.0; 1106.3; 1161.6)
(3306.5; 3480.5; 3654.6)
(2440.2; 2757.4; 3115.8)
2016
(1111.7; 1170.2; 1228.7)
(3609.8; 3799.8; 3989.8)
(2659.4; 3005.1; 3395.7)
2017
(1141.7; 1201.8; 1261.9)
(3874.4; 4078.3; 4282.2)
(3274.1; 3699.8; 4180.7)
2018
(1124.3; 1183.5; 1242.6)
(4178.6; 4398.5; 4618.4)
(3238.4; 3724.2; 4282.8)
2019
(1307.6; 1376.5; 1445.3)
(4421.0; 4653.7; 4886.4)
(3609.3; 4150.7; 4773.3)
2020
(1346.8; 1448.2; 1549.5)
(4163.9; 4477.3; 4790.8)
(3781.3; 4348.5; 5000.7)
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V. J. Akhundov and ˙I. S. Rustamov ˜
˜ α, ˜ eλ that minimize d between fuzzy data The problem is to find such values of A, ˜ β, ˜ α, (Table 3) and fuzzy values of Cobb-Douglas production function constraints. A, ˜ β˜ and λ˜ parameters are taken for the studied Ganja-Gazakh economic region as follows: ˜ A=(294.12;300;306), α=(0.098;0.1;0.102), ˜ α=(0.882;0.9;0.918), A=(0.098;0.1;0.102), ˜ ˜ β=(0.098;0.1;0.102), β=(0,882;0,9;0,918), λ=(0.008;0.01;0.012), λ=(0.64;0.8; 0.96). ˜ ˜ ˜ By solving problem (4)–(6), the fuzzy parameters A, α, ˜ β and λ for the investigated ˜ Ganja-Gazakh economic region production as follows: A=(0,359; 0,367; 0,374), α˜ = ˜ λ=(0,115; 0,116; 0,120). (0,869; 0,872; 0,874), β=(0,126; 0,128; 0,131), The obtained value of the solution was 222,25 thousand manats, which is of approx 7,23% accuracy. Thus, the obtained results can be used for modeling of production in the regions with acceptable accuracy. The corresponding values of Cobb-Douglas production function Y are shown in Table 4. Table 4. Results of calculations for the Ganja-Gazakh region Years TFN-based values of production function, Y 2010
(1531.367; 1699.636; 1884.523)
2011
(1875.994; 2084.828; 2314.61)
2012
(2135.741; 2375.289; 2639.083)
2013
(2269.578; 2525.454; 2807.389)
2014
(2299.709; 2613.337; 2962.646)
2015
(2348.418; 2668.52; 3025.014)
2016
(2552.539; 2901.534; 3290.37)
2017
(2723.499; 3096.64; 3512.498)
2018
(2902.86; 3301.085; 3744.977)
2019
(3107.104; 3535.226; 4012.735)
2020
(2960.369; 3440.44; 3980.039)
The fuzzy values [12–15] of end product and those of Cobb-Douglas production function Y are shown graphically below (Fig. 1. The lower bound. The core and the upper bound of the TFNs are shown). Thus, the forecast prices of the final product were calculated using classical statistical procedures and fuzzy inference rules for the Ganja-Gazakh economic region (Table 2 and Table 4). The standard deviation of the results obtained by these two methods, relative to the actual indicator, was 17% and 7.23%, respectively. These shows that the results obtained using the theory of fuzzy logic (standard deviation 7.23%) can be used to model final product in regions with acceptable accuracy.
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Fig. 1. Fuzzy Cobb-Douglas function graph (solid curve) and imprecise data (dashed curve).
4 Conclusion An analysis of the calculation of the volume of the final product by region based on classical statistical procedures and fuzzy modeling showed that the calculations should take into account the influence of scientific and technological development on the growth of the final product. When calculating the volume of the final product by region based on classical statistical procedures, an algorithm was used to determine the impact of innovation on the growth rate of the final product. The solution of the problem of forecasting the regional final product is carried out using the fuzzy Cobb-Douglas (innovation) model. The results obtained confirm applying fuzzy modeling within the framework of the task.
References 1. Mensch, G.: Stalemate in Technology - Innovations Overcome the Depression. Ballinger Publishing Company, p. 241 New York (1979) 2. Rosenberg, N. Frischtak, C.: Technological innovation and long waves. Cambridge J. Econ. 8(1), 7–24 (1984). https://www.jstor.org/stable/23596671 3. Freeman, C., Pérez, C.: Structural Crises of Adjustment, Business Cycles and Investment Behavior. In: G. Dossi, et al., Eds., Technical Change and Economic Theory, pp. 39–62. London (1988). https://doi.org/10.2307/3502005 4. Norton, J.A., Bass, F.M.: A Diffusion Theory Model of Adoption and Substitution for Successive Generations of High-Technology Products. Manage. Sci. 33, 1069–1086 (1987). https:// doi.org/10.1287/mnsc.33.9.1069 5. Hirooka, M.: Innovation Dynamism and Economic Growth. A Nonlinear Perspective. Cheltenham. UK - Northampton. MA: Edward Elgar, p. 448 (2006). https://doi.org/10.14441/eier. 4.2076. 6. Kalecki, M.: Observations on the Theory of Growth. Economic Journal. 72, 134–153 (1962). https://doi.org/10.2307/2228614 7. Costrell, R.: Profitability and aggregate investment under demand uncertainty. Econ. J.93, 166–181 (1983). https://doi.org/10.2307/2232171 8. Lee, C.F., Tzeng, G., Wang, S.: A fuzzy set approach for generalized CRR model: an empirical analysis of S&P 500. Index Options. Rev. Quant. Finan. Acc. 25, 255–275 (2005). https:// doi.org/10.1007/s11156-005-4767-1 9. Lisina, A.N.: Method of assessment of the level of innovation development of the region. World of Econ. Manag. 12(1), 115–126 (2012). https://lib.nsu.ru/xmlui/handle/nsu/ 3069
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10. Aliev, R.A., Fazlollahi, B., Aliev, R.R.: Soft Computing and Its Applications in Business and Economics. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-44429-9 11. Zhang, X., Chen, W.M.: New Similarity of Triangular Fuzzy Number and Its Application. Adv. Inform. Tech. 1–7. (2014). https://doi.org/10.1155/2014/215047 12. Aliev, R.A., Pedrycz, W., Fazlollahi, B., Alizadeh, A.V., Guirimov, B.G., Huseynov, O.H.: Fuzzy logic-based generalized decision theory with imperfect information. Inform. Sci., Elsevier, 189, 18–42 (2012) https://www.sciencedirect.com/science/article/abs/piiS002002.5511. 006128 13. Aliev, R.A., Pedrycz, W., Alizadeh, A.V., Huseynov, O.H.: Fuzzy optimality based decision making under imperfect information without utility. Fuzzy Optimization and Decision Making, Springer, Germany. 12(4), 357–372, (2013) https://link.springer.com/article/10.1007/s10 70001391602 14. Aliev, R.A., Huseynov, O.H.: Decision Theory with Imperfect Information. World Scientific, Singapoure, p. 444 (2014) https://www.worldscientific.com/worldscibooks/10.1142/9186 15. Nuriyev, A.M.: Fuzzy MCDM models for selection of the tourism development site: the case of Azerbaijan. F1000Research, 11(310), 1–24 (2022). https://doi.org/10.12688/f1000r esearch.109709.1
Application of WASPAS Method to Data Platform Selection Under Z-Valued Information K. I. Jabbarova(B) Department of Computer Engineering, Azerbaijan State Oil and Industry University, 20 Azadlig Avenue, 1010 Baku, Azerbaijan [email protected]
Abstract. The business sector requires highly available, reliable and flexible platform for high-capacity storage data with high computational complexity. It needs a real-time data processing platform with a high degree of data security. Platform has to be simple to utilize with a large users support. Nowadays, there are many data analytics platform. Therefore, in this paper WASPAS method under Z information is applied to the selection of platform of data analytics. Each criteria’s values are described with Z-numbers. The received results demonstrate reasonableness and effectiveness of the offer method. Keywords: MCDM · WASPAS method · Z-number
1 Introduction Data analytics relates to a set of modern technologies, which are developed to efficiently operate and support data that are not only large, but also characterized by great variety and speed [1]. The selecting of the data analytics platform would be help to find patterns and useful insights from big data [1]. MCDM is mostly used in ranking alternatives from the set of accessible alternatives. In [1] studies the technologies of big data and given a comparing analysis of the selecting analytics platforms of data. Also, in [1] demonstrated the application of an AHP method to selection of the data analytics platform. Apache Hadoop, Cloudera, Hortonworks, Pivotal, MapR, and etc. are most widely used platforms of big data analytics [2]. In [2], the use of the fuzzy TOPSIS method for choosing a data analysis platform is demonstrated which can be used by public sector institutions as well as enterprises to solve MCDM problems. The WASPAS method is a new multi-index method of decision which has good computational efficiency and capability to measure the performance of each alternative in a easy mathematical form. It was accepted and applied in many areas [3]. In [3] researches identified and assessed the risks of a construction project in Iran. The results demonstrated the inappropriateness of quarries, the loss of key labor during the life cycle of the project, the involvement of the inexperienced subcontractors are of the most essential risks among the established risks. Besides in [3] WASPAS method was proposed as a suitable method with greater precision among MCDM techniques for evaluating of risks in a real situation. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 557–563, 2023. https://doi.org/10.1007/978-3-031-25252-5_73
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[4] explores the suitability of the WASPAS method as successful tool of MCDM for solving some problems of decision making of manufacturing. It is noted that this method has the ability of correctly ranking the alternatives in all the reviewed problems of selection. The goal of [5], is to establish a WASPAS based ranking approach for MCDM in an environment of PFS. In order to illustrate the practicality and validity of the proposed method, a scenario study is presented in reality, including the selection of an appropriate air conditioning system. The recommended method executes well compared to other existing classifier strategies, according to results of testing acquired for a real-life problem [6]. In this article we regard the application WASPAS method to the selection problem of data analytics platform. This problem with Z-number- valued information. Prof. Zadeh proposed the Z-number concept [7–10]. The paper consists of the following parts: In Sect. 2 is given prerequisite material. In Sect. 3, we apply Z-number based WASPAS method to proposed problem. The conclusion is given in Sect. 4.
2 Preliminaries Definition 1. A discrete Z-number [7–10]. A discrete Z-number is an ordered pair Z = (A, B) where A is a discrete fuzzy number playing a role of a fuzzy constraint on values of a random variable X : X isA. Is a discrete fuzzy number with a membership function μB : {b1 , . . . , bn } → [0, 1]{b1 , . . . , bn } ⊂ [0, 1] [0, 1], playing a role of a i=1 fuzzy constraint on the probability measure of A: P(A) = μA (xi )p(xi ) is B. n
Definition 2. Operations over Discrete Z-numbers [7–10]: Let X1 and X2 be discrete Z-numbers describing information about values of X1 and X2 . Consider computation of Z12 = Z1 ∗ Z2 , ∗ ∈ {+, −, ·, /}. The first stage is computation of A12 = A1 ∗ A2 . The second stage involves construction of B12. We realize that in Z-numbers Z1 and Z2 , the ‘true’ probability distributions p1 and p2 are not exactly known. In contrast, fuzzy restrictions represented in terms of the membership functions are available μp1 (p1 ) = μB1
k=1
μA1 (x1k )p1 (x1k ) , μp2 (p2 ) = μB2
n1
k=1
μA2 (x2k )p2 (x2k )
n2
Probability distributions pjl xjk , k = 1, .., n induce probabilistic uncertainty over X12 = X1 + X2 . Given any possible pair p1 , p2 , the convolution p12 = p1◦ p2 is computed as. p12 (x) = p1 (x1 )p2 (x2 ), ∀x ∈ X12 ; x1 ∈ X1 , x2 ∈ X2 . x1 +x2 =x n k=1
Given p12s , the value of probability measure of A12 is computed:P(A12 ) = μA12 (x12k )p12 (x12k ).
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However, p1 and p2 are described by fuzzy restrictions which induce fuzzy set of convolutions: μp12 (p12 ) =
max
{p1 ,p2 :p12 =p1 ◦p2 }
min{μp1 (p1 ), μp2 (p2 )}
Fuzziness of information on p12 induces fuzziness of Z + as a discrete fuzzy number B12 . The membership function Z2+ = (A2 , R2 ) is defined as μB12 (b12 ) = max μp12 (p12 ) subject to b12 =
n
μA12 (xi )p12 (xi )
i=1
As a result, Z12 = Z1 ∗ Z2 is obtained as Z12 = (A12 , B12 ). A scalar multiplication Z = λZ1 , λ ∈ R is a determined as Z = (λA1 , B1 ). Definition 3 Fuzzy Pareto optimality (FPO) principle-based comparison of Znumbers [11]. Fuzzy Pareto optimality (FPO) principle allows to determine degrees of Pareto Optimality of multiattribute alternatives. We apply this principle to compare Z-numbers as multiattribute alternatives – one attribute measures value of a variable, the other one measures the associated reliability. According to this approach, by directly comparing Z-numbers Z1 = (A1 , B1 ) and Z2 = (A2 , B2 ) one arrives at total degrees of optimality of Z-numbers: do(Z1 ) and do(Z2 ). These degrees are determined on the basis of a number of components (the minimum is 0, the maximum is 2) with respect to which one Z-numbers dominates another one. Z1 is considered higher than Z2 if do(Z1 ) > do(Z2 ). Let us consider a MCDM problem under Z-valued information. Definition 4 [12] A distance between Z-numbers. The distance between Z-numbers Z1 = (A1 , B1 ) and Z2 = (A2 , B2 ) is defined as. D(Z1 , Z2 ) =
n m
1 L L L + R − aR + 1 R a1αk − a2α b1αk − bL2αk + bR a1αk 2αk 1αk − b2αk k n+1 m+1 k=1
k=1
where aαL = min Aα , aαR = max Aα , bLα = min, Bα bRα = max Bα
3 Statement of the Problem and a Solution Method Let us given MCDM problem under Z-information [13–15], where it is necessary to choose the best platform for data analytics. The considered problem consists of three alternatives and five criteria: availability and fault tolerance: C1; scalability and flexibility: C2; performance: C3; distributed storage capacity:C4; data security: C5. [2]. The
560
K. I. Jabbarova Table 1. Evaluations of criteria with Z-number-valued
C1 f1 f2 f3
0
0
0.77
1
0 0.95 1
0
0 1 0.61 0.77 0.92 0
0 1 0.77 0.95 1
0
C2
0 1 0.6 0.7 0.8
0
0
0
0 1 0.6 0.7 0.8
0 1 0.6 0.7 0.8
0
0
0 1 0.71 0.89 0.99
0.56
1
0.7
0
0
0.87
0 1 0.77 0.95 1
0
0
f2
0
f3
0 1 0.7 0.8 0.9
0 1 0.7 0.8 0.9
C3
f1
C4
0 0.89 0.99
0
0 1 0.8 0.9 1
0
0 1 0.66 0.89 0.97
0
0 1 0.8 0.9 1
0
0 1 0.66 0.82 0.97
0
0
0 1 0.59 0.65 0.72
0
0.71
0
1
0 1 0.77 0.95 1
0
0 1 0.7 0.8 0.9
0 1 0.8 0.9 1
0.77
1
0 0.99 1
0
0 1 0.7 0.8 0.9 0 1 0.7 0.8 0.9
0 1 0.7 0.8 0.9
C5 f1 f2 f3
0 0
0
0 1 0.77 0.95 1
0 1 0.66 0.82 0.97 0
0 1 0.77 0.95 1
0 1 0.8 0.9 1
0 0
0 1 0.8 0.9 1
0 1 0.8 0.9 1
values of criteria are described with Z-numbers fij = (Aij , Bij ) (see Tables 1). The criteria’s importance weights are given with crisp. For solving problem is used WASPAS method. It is a joint of WSM and WPM. Steps in WASPAS method are given below [4]: Step 1: Initialize the matrix for solving the selection problem: The criteria’s importance weights are given as: w1 = 0.2, w2 = 0.15, w3 = 0.2, w4 = 0.2; w5 =0.25 Step 2: Calculate the total relative importance based on WSM method with Eq. (1) (1) Qi
=
n
Zfij · wj (2)
(1)
j=1
Zfij are the Z-valued of criteria of each alternative. The obtained results are shown in Table 2. Step 3: Calculate the total relative importance based on WPM method with Eq. (2) (2)
Qi
=
n j=1
Zfij wj
(2)
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(1)
Table 2. The results of Qi
Qi(1)
f1 f2 f3
0
0 1 0.73 0.93 1
0
0
0 1 0.63 0.77 0.93
0
0 1 0.76 0.95 1
0 1 0.32 0.45 0.6
0 0
0 1 0.32 0.42 0.59
0 1 0.33 0.45 0.58
The derived results are presented in Table 3. (2)
Table 3. The results of Qi
Qi(2)
f1 f2 f3
0
0 1 0.75 0.93 1
0
0 1 0.64 0.78 0.93
0
0 1 0.77 0.95 1
0
0 1 0.23 0.37 0.54
0 0
0 1 0.23 0.37 0.54
0 1 0.23 0.37 0.54
Step 4: In order to have improved ranking accuracy and helpfullness of the decision making process. In the WASPAS method, a more general equation for formative the total relative significance of alternatives is given by Eq. (3) Qi = λ · Qi(1) + (1 − λ) · Qi(2) , λ = 0, 0.1, 0.2, . . . , 1
(3)
Qi = Qi(1) When λ = 1 (2)
Qi = Qi When λ = 0 In this case we will take as λ = 0.5. All result are given in Table 4. Finally, the alternatives are ranked on the Q values based. The best alternative would be select with the highest Q value (see Table 5).
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K. I. Jabbarova Table 4. Qi ’s results
Qi f1 f2
f3
0
0 1 0.75 0.94 1
0
0 1 0.64 0.78 0.94
0
0 1 0.77 0.96 1
0
0 1 0.15 0.27 0.43 0
0
0 1 0.15 0.27 0.44
0 1 0.16 0.28 0.43
Table 5. The ranking result Ranking
f3 f1
f2
The results that f3- is the best alternative.
4 Conclusion In this article, the suitability and usefulness of the WASPAS method as a tool of decisionmaking is tested as an illustrative example. This problem includes 3 alternatives. At the time each alternative is characterized with five criteria. Where all value of criteria are given by Z-information. The reliability of the WASPAS method has been proven, which will help its wide application as an effective MCDM tool.
References 1. Lnˇeniˇcka, M.: AHP Model for the big data analytics platform selection. Acta Inform. Pragensia 4(2), 108–121 (2015). https://doi.org/10.18267/j.aip.64 2. Uddin, S., Rahman, M., Hasan, S., Irfan Rana, S.M., Allayear, Sh.M.: A Fuzzy TOPSIS Approach for Big Data Analytics Platform Selection. J. Adv. Comp. Eng. Technol., 5(1), 49–56 (2019) 3. Badalpur, M., Nurbakhsh, E.: An application of WASPAS method in risk qualitative analysis: a case study of a road construction project in Iran. Int. J. Constr. Manag. 21(9), 910–918 (2021). https://doi.org/10.1080/15623599.2019.1595354 4. Chakraborty, S., Zavadskas, K.E.: Applications of WASPAS method in manufacturing decision making. Informatica 25(1), 1–20 (2014). https://doi.org/10.15388/Informatica.201 4.01
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5. Senapati, T., Chen, G.: Picture fuzzy WASPAS technique and its application in multi-criteria decision-making. Soft. Comput. 26(9), 4413–4421 (2022). https://doi.org/10.1007/s00500022-06835-0 6. Jabbarov, T.G., Gurbanov, N.A.: Synthesis of Optimal Technological Parameters of “IronCast-Glass” Grinding Composite Materials Using Fuzzy Logic and Big Data Concepts. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 254–259. Springer, Cham (2021). https://doi.org/10.1007/ 978-3-030-64058-3_31 7. Zadeh, L.A.: Fuzzy sets and commonsense reasoning. Berkeley: Institute of Cognitive Studies report, 21, University of California (1984) 8. Zadeh, L.A.: Fuzzy sets as a basis for the management of uncertainty in expert systems. Fuzzy Sets Syst. 11, 199–227 (1983) 9. Zadeh, L.A.: A computational theory of dispositions. In: Proc. of 1984 Int. Conference on Computation Linguistics. Stanford, pp. 312–318 (1984) 10. Zadeh, L.A.: A note on Z-numbers. Inform. Sci. 181, 2923–2932 (2011) 11. Zadeh, L.A.: Generalized theory of uncertainty (GTU) – principal concepts and ideas. Comput. Stat. Data Anal. 51, 15–46 (2006) 12. Aliev, R.A., Alizadeh, A.V., Huseynov, O.H.: The arithmetic of discrete Z-numbers. Inform. Sci. 290, 34–155 (2015). https://doi.org/10.1016/j.ins.2014.08.024 13. Nuriyev, A.M.: Fuzzy MCDM models for selection of the tourism development site: the case of Azerbaijan. F1000Research, 11(310), 1–24 (2022). https://doi.org/10.12688/f1000r esearch.109709.1 14. Aliev, R.A.: Uncertain computation-based decision theory.: World Scientific, Singapore, p. 521 (2017) 15. Zadeh, L.A., Aliev, R.A.: Fuzzy logic Theory and Applications. Part I and Part II. Singapore: World Sci., p. 610 (2019)
Using Deep Learning Algorithm for Prediction and Detection of Covid-19 Elbrus Imanov1(B)
and Vidura Lakshitha Liyanagamage2
1 Department of Computer Engineering, Near East University, Via Mersin 10, North Cyprus,
Mersin, Turkey [email protected] 2 Research Assistant of Computer Engineering Bambarawana, Maththaka 800080, Sri Lanka
Abstract. As the Covid-19 puts the great impact on the world health and economic situations, which directly leads toward the crisis. Prediction helps us to take precaution accordingly. Currently, more than 293 million of positive cases have been detected and more than 5.4 million deaths have been recorded. To prevail the spread of virus many countries open sourced datasets of Covid-19 positive cases for scientists to predict the curve. Therefore, countries can take the measures accordingly. It helps to obtain a rough idea about the pandemic end date, which is very difficult to predict because of its uncertainty. This article takes the dataset of many countries and predicts the curve of positive cases of the top 10 countries. We used this data to integrate it with logistic regression model to have a future view of pandemic. The article consists of two parts. First part includes the prediction by using logistic regression. This function used Python programming, Panda’s machine learning library, whereCovid-19 dataset has been taken from the open-source dataset available on the internet. Second part includes the detection of Covid-19 using Deep Learning Convolution neural network method. CNN method is used by training the model with the dataset of X-ray Images. CNN can detect the virus at early stages because of its powerful deep learning multiple layers ‘algorithm. There are several stages of detection such as processing image datasets and applying image-processing techniques to have a clear understanding of features in X-ray images. Keywords: Artificial neural network · Machine learning · Deep learning · Convolutional neural network · Artificial intelligence · Polymerase chain reaction
1 Introduction Since January 2019, Sars Covid-19 spreads like a wildfire in all over the world. Researchers are still trying to find out the better cure for this disease, as number of cases increases exponentially and death rate also increasing, it is impossible to test each, and every person expected to the time and cost points. Applying machine learning to call Covid-19 in patients will curtail the time defer for the outcomes of the medical analysis and inflect health corps to accord appropriate medical analysis to them and the preparation for future crises can be done easily. Currently, Antigen and Polymerase chain © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 564–571, 2023. https://doi.org/10.1007/978-3-031-25252-5_74
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reaction (PCR) are generally used to detect the Covid-19, despite the facts, PCR and Antigen have very less sensitivity of detection as Covid-19 shows its internal effects after 2 to 3 days. Also, both tests are expensive and time taking as well. So now here comes the machine learning that plays a necessary role to detect Covid-19 from chest X-ray. Correspondent to the place for action discipline and avoidance, up 10 million adult pneumonia carrier are infected each year in the world, with about 250,000 individuals dying from the disease [1]. Chest X-rays, according to the WHO, are the best accessible methods of diagnosing pneumonia. Even professional radiologists find it difficult to diagnose pneumonia since its symptoms appear to be identical to those of other pulmonary diseases. As a result, various algorithms for this aim have been developed [2]. Neural network, competitive, and a deep neural network were employed in paper to identify chest ailments using the CXR dataset, with deep learning outperforming the others [3]. Deep neural network models have recently considered being a successful method in the range of medicine for the interpretation of anatomy, including lung anatomy that is the subject of this research as well as for the identification of other medical disorders. [4, 5]. Machine learning considers around the belief behind artificial systems that extract knowledge from pictures [6].A convolutional neural network from the ocular background research neo cognition in 1980 [7]. A major milestone in convolutional neural networks was in 1998 when they introduced the LeeNet-5 design which is currently frequently used for handwritten recognition tasks [8]. To detect Covid-19 pneumonia on an individual chest tomography check image, a basic 2D deep learning system termed the first-track Covid19 analysis network [9]. To recognize Covid-19 in chest X-ray pictures, an iteratively pruned deep learning model ensemble [10]. The Covid-Net network uses a means of diagnosing Covid-19 and no Covid-19 pneumonia [11]. For the screening of Covid-19 pneumonia from alternative kinds of growing pneumonia, a consideration based deep 3D different item learning technique [12]. An AI system uses CXR pictures to predict Covid-19 pneumonia [13]. Classified Covid-19 from CT images using removal learning and semi supervised adversarial detection [14]. CorNet, a deep convolutional neural network based on the Xception building for Covid-19 infection detection utilizing CXR pictures [15]. The use of CXR and CT images to detect Covid-19 disorders using deep removal learning. In an optimization, access was used to create a hybrid CNN for recognizing Covid-19 [16]. Described a deep learning approved technique for Covid-19 diagnosis.
2 Machine Learning Algorithm Finding pattern by training and improving structure and flow of data is called as machine learning in easy words. The patterns are discovered by having some peripheral data. Machine learning is the technique for recognizing pattern that can be applied to medical images. Machine learning generally starts from the identification of images features, classification by using ML algorithm. ML algorithm compute the features of images that are believed to be the important for training and learning purpose. After deep training the machine system is able to predict and diagnose the disease. The flowchat of Machine learning process illustrated in the Fig. 1.
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Machine Learning
Clustering Unsupervised
Dimensionality Reduction
Fig. 1. Machine learning process.
Too freshly, deep learning has initiated to be used; the present approach has the aid that it does not lack image feature description and computation as a first stride; comparatively features are rational as an item of the learning action. A CNN operative on a row of assign and also accept few hidden row convolution, merge and perfectly related films are pattern related invisible rows [17]. There are two main categories of Machine learning, unsupervised and supervised. Unsupervised learning is when the data is not known unlabelled, or output is not predictable because of the variety of continuous changes. In supervised learning, all patterns in the dataset are a couple of an input point and an extraneous output point that we are arduous to call. A complete task is arising through investigating the training lay under a supervised learning method. Logistic Regression: Before dive into logistic regression take a step back and review linear regression in another as linear regression some data weight (X) and size (Y) then fit that into a line and with that line could do a lot of things for example calculate the R2 and determine its weight (X) and size (Y) are correlated, large values imply a large effect calculate a p value to determine if the R2 Value is statistically significant use the line to predict weight (X) and size (Y).Deep learning perception: The fundamental building block of deep learning is a single neuron called as forward propagation perception.
3 Methodology of the Process Deep learning has a very deep application in medicine and healthcare so where we can take these raw images of X-Ray and scans of patient and learn to detect things like pneumonia cancer and Covid-19 etc. Datasets for Covid-19 prediction, GitHub live repository have been used that contain data of more than 100 countries and up to date. So, the current result and graphs are according to the updated data up till 4th of January 2022. Covid-19 is a dynamic pandemic that increases and decreases over time, even daily. As a result, it does likely that time will have a role in Covid-19 mortality. The episode date, a derived variable in the dataset, relates to the earliest accessible date from symptom start, laboratory specimen collection date. For prediction algorithm, Python programming and its libraries (Numpy, Pandas, Matplotlib) have been used. Python library that includes a two-dimensional representation item, various derived objects, and a variety of routines for performing fast array processes. Pandas are a Python library that adds rapid, versatile,
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and expressive data design for working with comparative or termed data. As an outcome, it adds an open origin opportunity to Matlab. Prediction model, flow of prediction model has been described for the understanding the flow of program. After calling data set of all the countries we took top 10 countries according to the number of cases and arrange them in ascending order. Two functions have been defined to plot the graph according to the number of cases and second function to plot the regression graph of country. Curve fitting Logistic regression is a prominent machine learning approach because of its ability to generate probabilities and classify fresh samples using continuous and discrete measurement. The way the line is fitted to the data is a significant distinction between linear and logistic regression. This is slightly fancy a machine learning If we will compare normal regression using weight to predict size logistic regression function has been used from Panda’s library. Dataset and data structure: Images from infected and aseptic persons should be possessed in a dataset in order to progress active infection executive and a changing early detection capability against COVID-19. This urgent requirement is fixed as follows in the COVID-19 picture data compilation: Imagine if all of the practitioners and radiologist were infected, and there was no one to advise us speedily. This study employed 130 sample chest X-ray training pictures and 18 pattern chest X-ray analysis images from the Joseph Paul Cohen and Paul Morrison and Lan Dao COVID-19 image data compilation, which is open-source data. Training of Dataset: The model was trained using 130 photos from the training data that apply to two distinct account also 18 images from the test data that apply to two disconnect account. We have used Tensor flow library to perform Deep learning CNN method. First of all, we initialize the images by sequential function and then 2D convolution is used in order to map and detect features. 3 by 3 matrices of images have been created for convolution. Stepwise algorithm for detecting COVID-19 is as follows. Input: Chest X-ray Images dataset (D) Extraction: Feature extraction matrix CNN algorithm vector includes the following steps: Initialization of sigmoid function by weights, extracting of feature of each image, 2D convolution, overall CNN feature implication and the end training images and testing images, output result COVID-19 or normal.
4 Result of Prediction and Detection For prediction, after obtaining the data set of all the countries we took the top 10 countries according to the number of cases and arranged them in an ascending order. Two functions have been defined to plot the graph according to the number of cases and second function to plot the regression graph of country. Curve fitting logistic regression function has been used from panda’s library that makes easier to apply logarithmic function. R2 Value and curve fitting regression line R2 is 0.985826and results are shown in Fig. 2.
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Fig. 2. R2 value and curve fitting regression line.
Actual data regression and projection of prediction for Turkey after 100 days are shown in Fig. 3.
Fig. 3. Actual data regression and projection of prediction.
Future prediction of Turkey Covid-19 cases, regression score, number of cases and weekly increased cases are shown in Fig. 4.
Fig. 4. Regression score, number of cases and weekly increased of cases.
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Receiver operating characteristic of Covid-19 with positive true and positive false rate are shown in Fig. 5.
Fig. 5. ROC of Covid19.
Receiver operating characteristic of normal X-ray with positive true and positive false rate are shown in Fig. 6.
Fig. 6. ROC of Normal X-ray.
Below demonstrates the result of occurrence of Covid-19 detection with deferent evaluating at steps and validation loss, detailed evaluation of test X-ray images results illustrated in Fig. 7.
Fig. 7. Detailed Evaluation of test X-ray images.
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5 Conclusion This article focuses on the COVID-19 prediction by applying logistic regression model to have a future view of pandemic, this function used Panda’s library in the first part. Second section is about COVID-19 detection from X-ray dataset by using Deep learning CNN method. Prediction enables us to take the appropriate precautions. Nearly tens of millions of fatalities and approximately 300 million positive cases have currently been detected and identified. For prediction algorithm, Python programming and its Panda’s library have been used, that include a two-dimensional representation item, various derived objects, and a variety of routines for performing fast array processes. Deep Learning made our life much easier in every phase of life, especially in the medical field. By taking the help of Deep Learning, we can detect cancer, viruses, etc. at very early stages. CNN’s potent deep learning multiple layers algorithm allows it to identify the virus at a preliminary phase. The X-ray images can detect the COVID-19 at early stages because this virus first attacks on lungs. During pandemic, if the virus is infecting millions of people daily, then it is a daunting task to test this amount of people. Therefore, the machine learning plays its role by detecting the virus from X-ray images.
References 1. Pneumonia Home CDC. https://www.who.int/news-room/facsheets/detail/pneumonia 2. World Health Organization: Standardization of interpretation of chest radiographs for the diagnosis of pneumonia in children. World Health Organization. (2001). https://doi.org/10. 1590/S0042-96862005000500011 3. Abiyev, R., Ma’aitah, M.K.S.: Deep convolutional neural networks for chest diseases detection. J. Healthc. Eng. (2018) https://doi.org/10.1155/2018/4168538 4. Abiyev, R., Arslan, M., Bush, I. J., Sekeroglu, B., Ilhan, A.: Identification of epileptic EEG signals using convolutional neural networks. Appl. Sci. Res. 10(12), 4089 (2020) https://doi. org/10.3390/app10124089 5. Abiyev, R., Arslan, M.: Head mouse control system for people with disabilities. Expert Syst. 37(1), e12398 (2020). https://doi.org/10.1111/exsy.12398 6. Imanov, E., Alzouhbi, A.K.: Machine Learning Comparative Analysis for Plant Classification. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, Mo., Sadikoglu, F.M. (eds.) ICAFS 2018. AISC, vol. 896, pp. 586–593. Springer, Cham (2019). https://doi.org/10.1007/978-3030-04164-9_77 7. Fukushima, K.: Neocognitron: A self-organizing neural network model for a mechanism of pattern recognition unaffected by shift in position. Biol. Cybern. 36(4), 193–202 (1980). https://doi.org/10.1007/978-3-642-464669_18 8. LeCun, L., Bottou., L., Bengio, Y., Haffner, P.: Gradient-based learning applied to document recognition, IEEE, 86(11), 2278–2324, (1998) https://doi.org/10.1109/5.726791 9. Ko, H., Chung, H., Kang, W.S.: COVID-19 pneumonia diagnosis using a simple 2d deep learning framework with a single chest CT image: model development and validation. J. Med. Internet Res. 22(6), 1–13 (2020). https://doi.org/10.2196/19569 10. Rajaraman, S., Siegelman, J., Alderson, P.O., Folio, L.S., Folio, L., Antani, S.K.: Iteratively pruned deep learning ensembles for COVID-19 detection in chest X-Rays. IEEE 8, 115041– 115050 (2020). https://doi.org/10.1109/ACCESS2020.3003810 11. Gunraj, H., Wang, L., Wong, A.: COVID Net-CT: a tailored deep convolutional neural network design for detection of COVID-19 cases from chest CT imaes. Front. Med. 7, 1–12 (2020). https://doi.org/10.3389/fmed.2020.608525
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12. Han, Z., Wei, B., Hong, Y.: Accurate screening of COVID-19 using attention-based deep 3D multiple instance learning. IEEE T Med. Imaging. 39(8), 2584–2594 (2020). https://doi.org/ 10.1109/TMI.2020.2996256 13. Abiyev, R., Arslan, M., Idoko, J.C.: Sign language translation using deep convolutional neural networks. KSII T. Internet Inf. 14(2), 631–653 (2020). https://doi.org/10.3837/tiis.2020. 02.009 14. Wang, S.H., Nayak, D.R., Guttery, D.S., Zhang, X., Zhang, Y.D.: COVID-19 classification by CCSHNet with deep fusion using transfer learning and discriminant correlation analysis. Inform Fusion 68, 131–148 (2021). https://doi.org/10.1016/j.inffus.2020.11.005 15. Ezzat, D., Hassanien, A. E., Ella, H.A.: An optimized deep learning architecture for the diagnosis of COVID-19 disease based on gravitational search optimiztion, Appl Soft Comput., 98, Article ID 106742, (2020). https://doi.org/10.1016/j.asoc.2020.106742 16. Nayak, S. R., Nayak, D. R., Sinha, U., Arora,V., Pachori, R. B.: Application of deep learning techniques for detection of COVID-19 cases using chest X-ray images: a comprehensive study, Biomed. Signal Proces. 64, Article ID 102365, (2021). https://doi.org/10.1016/j.bspc. 2020.102365 17. Imanov, E., Shah, Z.: Applying Multi-layers Feature Fusion in SSD for Detection of SmallScale Objects. Int. Conf. Theory Appl. Soft Comput., Computing with Words and Perceptions, pp. 552–559. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-92127-9_74
Fuzzy Logic-Based Planning of the Behavior of Autonomous Vehicles A. B. Sultanova1,2(B) 1 Azerbaijan State University of Oil and Industry, Baku, Azerbaijan
[email protected] 2 Institute of Control Systems of ANAS, Azerbaijan, Baku AZ1010, Azerbaijan
Abstract. The article suggests a fuzzy approach to safe navigation when changing lanes in a road scenario. The approach is to create a module for making informed decisions during lane changes by several agents in order to avoid collisions. The price libraries used in this model help to make decisions when changing lanes. The article describes two modules two fuzzy modules, a fuzzy target control module, and a fuzzy collision avoidance control module are designed to perform these two tasks. As a result, with the help of dynamic fuzzy clustering methods, adaptive driving of an unmanned vehicle (DUV) management is supported, which allows for minimizing the risks of road accidents (accidents involving DUV) and maximizing traffic (total output flow) in conditions of intense traffic flow. In the article, the simulation of a robot car moving along the lane and changing the lane of the Road is implemented in the Matlab environment. Keywords: Autonomous vehicles · Motion planning; fuzzy logic · Evolutionary fuzzy inference systems · Traffic simulation · Multi-robot motion planning · Unmanned transport systems · Intelligent transport system · Simulation modeling · Fuzzy logic
1 Introduction The development of technologies for controlling robotic vehicles in the modern era (CRV) proves that the introduction of robotic vehicle systems is one of the main directions of the development of the automotive industry. However, in recent years, more and more attention has been paid to the development of algorithms for driving a car for a more distant perspective, when a person will be completely excluded from the process of driving an unmanned vehicle (DUV) [1–3]. Since the end of the 20th century, intelligent vehicle traffic has evolved from lane centralization on public roads to real speed, the ability of lane changes [3–9]. Many researchers have shown that he has an excellent ability to drive on public roads. However, vehicle recognition, decision-making, and intelligent traffic planning have not yet reached the level of people with the status of good drivers. Collision prevention for several vehicles is the subject of heated debate in academic circles [2]. The earliest studies focused on two-dimensional planning of the safety Road © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 572–578, 2023. https://doi.org/10.1007/978-3-031-25252-5_75
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in the context of a cluster of autonomous vehicles trying to move around fixed objects. Researchers have recently focused on the need to prevent car collisions. In some cases [3] for each vehicle, other vehicles are considered as dynamic obstacles. Car-like mobile robots have been extensively researched with the aim of using them in applications such as industry, the military, mining, planetary exploration, etc. [4]. Such robotic systems are considered as vehicles, the kinematic models of which are close to the mobility of the car. Following the trajectory is one of the most important tasks of movement for robots, when the robot tries to reach a geometric trajectory (represented as a set of oriented waypoints from a given initial configuration) and follow it without human intervention. When it comes to planning, safe navigation for autonomous vehicles depends on many factors. In general planning, the structure can be divided into movement planning, mission planning, and behavior planning. Motion planning generates the desired trajectory of the vehicle, taking into account the dynamic parameters and the output of the steering and throttle. Mission planning consists of optimizing the path to reach various control points, taking into account the arrival time, distance, or various required maneuvers. Behavior planning allows you to make tactical decisions about driving in relation to such things as keeping a distance, changing lanes, and interacting with neighboring vehicles [8]. Autonomous cars must evolve in a completely undefined dynamic motion. Uncertainty can be recorded either as uncertain indicators of sensors of the same range, or another object moving on the road. In conditions of such uncertainties, it is necessary to eliminate the corresponding uncertainties in order to drive the car safely and effectively. For example, it should make decision-making modules more precise, use available information correctly and maintain correct driving strategies, etc. We have noted that the driving environment of autonomous vehicles IE (AV) is dynamic and completely uncertain. Uncertainty can also be found in the movement of pedestrians crossing the road, in the practice of driving a vehicle driver on an oncoming road, and in the future behavior of other participants. Autonomous vehicles can be replaced in life-threatening conditions and used in military operations and in health care. Ground vehicle management is proof that people are more reliable, more intelligent human drivers, in general, able to understand the environment more quickly and react quickly to sudden changes. Thus, we do not model the interaction between people, we focus only on the interaction between the robot car and the driver. Various methods can be used to control the vehicle. But fuzzy logic has a number of advantages in this area [1]. One of them is Linguistics, where it is possible to evaluate a person’s knowledge and experience by certain values. Fuzzy logic in the management of autonomous vehicles is used to solve navigation problems.
2 Models and Methods In recent years, the multi-agent system has become a very well-known field used in many applications, such as e-commerce, e-health applications, network intrusion detection systems, telematics and transportation systems, as well as robotic systems. Indeed,
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several researchers have used a multi-agent system in the development of a robotic system [4, 6]. A multi-agent system is very useful in the case of several robots that perform different tasks that need to be coordinated with each other [5]. A multi-agent system (MAC, English Multi-agent system) – or multi-agent systems - is a branch of artificial intelligence that uses systems consisting of many interacting agents to solve a complex task or problem. MAC refers to self-organizing systems [5, 10], since they seek the optimal solution to the problem without external intervention. The main advantage of MAC is flexibility. A multi-agent system can be supplemented and modified without rewriting a significant part of the program. ˙In many works, the neural prediction controller is used to track the path the idea of the prediction controller is to calculate future control effects based on the output values predicted by the model [6]. Neural networks are an attractive way to model complex nonlinear systems due to their inherent ability to approximate an arbitrary continuous function. Represents a model-based predictive controller (MPC) based on a multilayer backpropagation neural network mode [7]. As shown in Fig. 1, the two main sources of value for the learning network are the desired states with the control vector and the measured states.
Fig. 1. The main sources of value for the learning network.
Some researchers recommend an in-depth teaching algorithm to control robot behavior. In some cases, this training is used in planning robot behavior, as more effective results are achieved in reinforcement learning (RL) [10]. There are three main groups of reinforcement learning, these are dynamic programming methods (DP), Monte-Carlo (MC) methods, and time difference methods (TD) [11]. They are divided into two factors: environment models and bootstrapping. In the RL system, the bootstrap is used to update the evaluation of state values and action values based on the evaluation of later states. DP requires both bootstrapping and a complete environment model. The MC and TD methods do not require an environment model, and the TD methods should do bootstrap, but the MC methods do not. It is difficult to use DP methods based on models of the well-known environment since the work environment is the real world and it can change frequently. The position and orientation of the main body of the robot and the angle of rotation of the steering wheels depend on the configuration of the robot. To achieve this task, in the classical approach, stationary obstacles and the configuration of the mobile robot are presented on a two-dimensional map, waypoints are generated by the planner, which must take into account the geometric structure and kinematics of the robot. The generated path contains waypoints with acceptable curvature that allow you to avoid collisions
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with obstacles. (Table 1). Preliminary trajectory change is effective for a robotic system since it is much easier for robots to achieve autonomous movement in a pre-known and well-modified environment, robots can move without receiving additional visual information or range information. In addition, creating smooth trajectories avoids awkward movement, which can lead to wheel slippage and reduce the robot’s ability to count. Using a multi-agent system is convenient for solving such a problem. Thus, we have developed a structure consisting of four agents designed for perception, navigation, static, and dynamic obstacle avoidance. These agents interact through a coordination system. Table 1. The created roads are strong points to avoid collisions with obstacles Waypoints
X(m)
Y(m)
V(m/s)
A (car1)
53.5 39.2 25.8 10.9
0.8 0 −0.5 −0.2
30 30 30 30
B (car2)
2.1 13.2 24.4 38.8
−2.5 −2.7 −2.7 −2.7
30 30 30 30
C (car3)
23.9 33.9 35.6 32.7
−25.7 −12.2 −0.6 9.6
30 30 30 30
D (car4)
17.6 22.8 26.1 15
13.5 6.9 −4.4 −20.4
30 30 30 30
The table shows the speed and coordination of each car. In this case, the drive of each car was taken equally (v = 30 m/s). The speed is regulated during collisions.
3 Statement of the Problem and Simulation of the System In this article, we consider planning the behavior of an autonomous car in a multi-agent environment with perception uncertainties. To conduct experiments with the model of a fuzzy controller created by means of the MATLAB programming environment, a model of traffic at an intersection was built. The complete map consists of several roads that intersect at intersections [12, 13]. The complete route of the vehicle consists of a number of roads/intersections, along which it must follow in strict Fig. 2 shows the intersection of two roads. Four cars are approaching the intersection. At time t, car A (car 1- blue), B (car 2- green), C (car 3- purple), D (car 4- yellow) which intend to cross the intersection in straight order.
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Fig. 2. ˙Initial situation. Description of the intersection of two roads
As can be seen from the figure, traffic in each of the possible directions is organized in a separate lane. This scheme was chosen for the reason that by changing the input parameters, namely the number of cars approaching the intersection in each of the lanes, you can change the configuration: by setting the number of cars to zero, you can exclude one or another lane from the model. This creates an arbitrary configuration intersection model. In the created model, in order to simplify calculations, traffic is discretized in such a way that for each given period of time, the number of cars waiting for passage on each of the lanes increases by one with some probability. At the same time, for each specified interval of the Gorenje signal, the number of cars waiting at the stop line in the corresponding lane decreases by one. Consider the case shown in Fig. 3(a). Cars approaching from below and to the right are moving in a straight direction, and from above and to the left – to the left and to the right, respectively. The order of departure, in this case, is determined unambiguously – only the purple car on the left has no interference, so the intersection passes first. The orange car is not moving, since the green one is a hindrance to it on the right. The yellow car cannot turn left and passes the purple one moving from the opposite direction. The blue car similarly waits until the interference on the right disappears. When cars start moving, each car agent calculates the optimal path received from the regulator when exchanging information about the predicted situation on the roads. Regulatory agents provide this information based on the results of their own forecasting system, which collects and analyzes the information received by it during the entire period of the agent’s work. The agent-car transmits information about its location during the movement to the regulatory agency and at this moment transmits it to the guidebook. Based on the overall assessment of the speed and location of all cars approaching it, the regulator decides to change the traffic light signal.
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Fig. 3. Movement of cars at a crossroad. a) normal traffic of cars at the intersection. b) collision event.
4 Conclusion The methods we offer are a behavior planning system for vehicles. Using this method, it is possible to change the lanes of independent vehicles at intersections, without colliding with obstacles on the roadway. The main component of the design is a fuzzy controller and lidar. The article suggests a fuzzy approach to safe navigation when changing lanes in road scenarios. The approach is to create a module for making informed decisions when changing lanes by several agents in order to avoid collisions. The price libraries used in this model help to make decisions when changing lanes. The article describes two fuzzy modules, a fuzzy target management module and a fuzzy collision prevention management module. As a result, with the help of dynamic fuzzy clustering methods, adaptive control of an unmanned vehicle (UAV) is supported, which allows for minimizing the risks of road accidents (accidents involving UAV) and maximizing traffic (total output flow) in conditions of intense traffic flow. In the article, the simulation of a robot car moving along the roadway and changing lanes is implemented in the MATLAB environment.
References 1. Aliev, R.A., Fazlollahi, B., Aliev, R.R.: Soft Computing and its Applications in Business and Economics. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-44429-9 2. Naranjo, J.E., González, C., García, R., de Pedro, T.: Lane-change fuzzy control in autonomous vehicles for the overtaking maneuver. IEEE Trans. Intell. Transp. Syst. 9, 438–450 (2008)
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3. Bentalba, S., El Hajjaji A., Rachid A.: Fuzzy parking and point stabilization: application car dynamics model. In: 5th IEEE Mediterranean Conference on Control and Systems (1997) 4. Frese, C.; Beyerer, J.: A comparison of motion planning algorithms for cooperative collision avoidance of multiple cognitive automobiles. In: Proceedings of the 2011 IEEE Intelligent Vehicles Symposium, Baden-Baden, Germany, pp. 1156–1162 (2011) 5. Wei, J., Snider, J.M., Kim, J., Dolan, J.M., Rajkumar, R., Litkouhi, B.: Towards a viable autonomous driving research platform. In: IEEE Intelligent Vehicles Symposium (IV), pp. 763–770. IEEE (2013) 6. Kuwata, Y., Karaman, S., Teo, J., Frazzoli, E., How, J.P., Fiore, G.: Real-time motion planning with applications to autonomous urban driving. IEEE Trans. Control Syst. Technol. 17, 1105– 1118 (2009) 7. Anderson, S.J.; Karumanchi, S.B.; Iagnemma, K. Constraint-based planning and control for safe, semi-autonomous operation of vehicles. In: Proceedings of the 2012 IEEE Intelligent Vehicles Symposium, Madrid, Spain, pp. 383–388 (2012) 8. Pandey, A., Sonkar, R.K., Pandey, K.K., Parhi, D.R.: Path planning navigation of mobile robot with obstacles avoidance using fuzzy logic controller. In: Intelligent Systems and Control (ISCO) (2014). https://doi.org/10.1109/ISCO.2014.7103914 9. Katrakazas, C., Quddus, M., Chen, W.-H., Deka, L.: Real-time motion planning methods for autonomous on-road driving: state-of-the-art and future research directions. Transp. Res. Part C Emerg. Technol. 60, 416–442 (2015). https://doi.org/10.1016/j.trc.2015.09.011 10. Ahmadov, S.A., Gardashova, L.A.: Fuzzy dynamic programming approach to multistage control of flash evaporator system. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 101–105. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-35249-3_12 11. Gardashova, L.A., Ilhan, U., Kilic, K.: UAV using Dec-POMDP model for increasing the level of security in the company. Procedia Comput. Sci. 102, 458–464 (2016). https://doi.org/ 10.1016/j.procs.2016.09.427 12. Huseynov, O.H., Adilova, N.E.: Multi-criterial optimization problem for fuzzy if-then rules. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 80–88. Springer, Cham (2021). https://doi.org/10.1007/ 978-3-030-64058-3_10 13. Zadeh, L.A., Aliev, R.A.: Fuzzy Logic Theory and Applications. Part I and Part II, 610 p. World Scintific, Singapore (2019)
Digitization of Centrifugal Compressor Asset as One of Key Elements of Overall Digitized Industrial Plant Nodirbek Yusupbekov1(B)
, Farukh Adilov2
, and I. Arsen2
1 Tashkent State Technical University, Tashkent, Uzbekistan
[email protected]
2 LLC “XIMAVTOMATIKA”, Tashkent, Republic of Uzbekistan
{Farukh.Adilov,Arsen.Ivanyan}@himavtomatika.uz
Abstract. Compressors are used to transport the gases and to increase pressure of gases in process plants, power plants, and other industries. Compressor performance has a significant impact on overall plant performance in terms of energy usage, efficiency, and throughput. Centrifugal compressors are also known as turbo-compressors belong to the roto-dynamic type of compressors. This is one of commonly used types of compressors which as asset category investigated by authors together with another centrifugal equipment types such as centrifugal pumps and fans. Digitized model of centrifugal compressor helps to create full simulation of some typical industrial process units such as cracking or reforming units in refining industry, as well as in many petrochemical and gas-chemical applications. This paper continues cycle of researches devoted to development of multi-aspect digital twin of universal digitized industrial plant and contributes to the branch of mathematical modelling of appropriate types of industrial assets which can be used as part of further engineering design and software development works as well as individual results of applied science. Keywords: Centrifugal compressor · Digitization · Flow · Pressure · Impellers · Process performance · Surge · Performance curve · Fault tree
1 Introduction Centrifugal compressors are rotary continuous-flow machines in which the rapidly rotating element accelerates the fluid as it passes through the element, converting the velocity head into pressure, partially in the rotating element and partially in stationary diffusers or blades [1]. Centrifugal compressors are also known as turbo-compressors belong to the rotodynamic type of compressors. In these compressors, the required pressure rise takes place due to the continuous conversion of angular momentum imparted to the gas vapor by a high-speed impeller into static pressure. As shown in Fig. 1 below, low-pressure gas enters the compressor through the eye of the impeller. The impeller consists of a number of blades, which form flow passages for gas. From the eye, the gas enters the © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 579–587, 2023. https://doi.org/10.1007/978-3-031-25252-5_76
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flow passages formed by the impeller blades, which rotate at very high speed [2]. As the gas flows through the blade passages towards the tip of the impeller, it gains momentum, and its static pressure also increases. From the tip of the impeller, the gas flows into a stationary diffuser. In the diffuser, the gas is decelerated and as a result the dynamic pressure drop is converted into static pressure rise, thus increasing the static pressure further. The vapor from the diffuser enters the volute casing where further conversion of velocity into static pressure takes place due to the divergent shape of the volute. Finally, the pressurized gas exits the compressor from the volute casing [3].
Fig. 1. Centrifugal Compressor’s working principle.
Centrifugal compressors and pumps are the categories of centrifugal equipment considered as objects of our research for digital twin implementation and are presented in cycle of authors’ papers published or to be published recently. The objective and originality of the paper is to describe innovative technology of industrial digitalization associated with increasing the efficiency of real categories of process equipment. This paper is one from the set of papers in our focus which as per our scientific-research plan will create fully digitized portfolio of solutions for the entire set of process equipment assets of chemical and petrochemical industries [4].
2 Description of Scientific-Technical Solution The following measured parameters are monitored by digital twin of centrifugal compressor as they have the following impact on performance and health of the centrifugal compressor if it is not operating within its operating range [5]: – Suction Temperature: Increase in suction temperature reduces the feed density which increases the volumetric flow rate to be compressed for delivery of the same amount of discharge mass. At the same time, lower suction temperature may lead to condensation of vapor feed which can lead to increase in vibration and trip scenario – Suction Pressure: Decrease in suction Pressure indicates the low feed to compressor which can lead to critical asset health condition like surging, also a lower suction pressure may also increase the pressure ratio across the compressor if the discharge pressure is controlled, which can lead to surging.
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– Discharge Temperature: Higher discharge temperature indicates the upset in overall operations of the equipment and may lead to trip scenario. Example, it may be because of low coolant flow, high coolant temperature, high bearing temperatures, or drop in efficiency, etc. – Discharge Pressure: Higher discharge pressure indicates the upset in overall operations of equipment and may lead to trip scenario. It may be due to some different reasons like, obstacles in downstream operations, aftercooler is fouled, etc. – Speed: It is direct indication of load on compressor. – Antisurge Valve Opening and flow: Surge is an unstable and undesirable operating condition of the compressor, occurring when the flow through it is less than surge flow. This causes a momentary flow reversal, reducing line pressure and causing erratic behavior. For ensuring safety of equipment, an antisurge controller maintains flow near the control line. Additional circulation beyond the control line is operational loss due to excess compression. The bearing temperature, vibration and displacement readings are monitored for Compressor, motor, and gearbox. The rise in the bearing temperature and vibration indicates improper alignment between rotating parts. The rise in Lube oil temperature increases the viscosity of the lube oil which reduces the strength of the oil film on the bearings and may lead to high vibrations [6]. Nearly all compressors require a form of lubricant to either cool, seal or lubricate key internal components such as gears, bearings, and seals. The lube oil system supplies oil to the compressor and driver bearings and to the gears and couplings. – Tank level: Loss in lube oil tank level can lead to loss of lubrication and compressor trip scenario. The reservoir may be pressurized or vented. – Supply pressure and temperature: Temperatures and pressures are measured at all important locations in the system, including temperatures from oil sumps, return lines from bearings, gears and other mechanical components. Temperatures and pressures are often recorded on the suction and discharge sides of each compression stage to offer the operator a sense of the health of the system. The readings can be taken locally or transmitted to a monitoring station. The flow of oil to each bearing is regulated individually by orifices, particularly important for lubrication points requiring different pressures. – Return temperature: Heat generated by friction in the bearings is transferred to the cooling medium in the oil coolers. Air-cooled oil coolers may be employed as an alternative to water-cooled oil coolers. – Differential pressure across Filters: Filters clean the lube oil before it reaches the lubrication points, and a differential pressure gauge monitors the degree of fouling (flow restriction) of the filters. The seal oil system supplies the mechanical contact and floating ring seals with an adequate flow of seal liquid at all times, correctly ensuring proper function. The oil in the overhead tank is in contact with the reference gas pressure via a separate line, with a static head providing the required pressure differential.
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– Tank Level: The oil in the overhead tank compensates for pressure fluctuations and serves as a rundown supply if pressure is lost. If the level in the tank falls excessively, a level switch shuts down the compressor. A moderate oil temperature is maintained by a constant flow of oil through the overhead tank. – Seal Pressure: The seal oil supply system must be capable of supplying higher seal oil pressure than the highest possible compressor process pressure inboard of the oil seal - which may include settle out, or compressor discharge pressure. The seal pressure at supply and at all important locations of the seal system. The scientific-technical method used in our research is based on mathematical model engine embedded and running in the special software environment which is Digital twin of objected typical centrifugal compressor. This digital twin uses above measure parameters described and generates key performance indicators (KPI) which are parameters of compressor’s effectiveness [7]. These KPIs can be divided to 2 subcategories: energy monitoring KPIs (which are to be monitored to optimize energy consumption) and performance monitoring KPIs (which shows the effective utilization and overall performance of the compressor). Energy monitoring KPIs are: – Degradation losses: This KPI represents the additional power consumed due to excessive power utilized by the compressor when compressor is running at low efficiency. Degradation losses = (DeviationPolyEff / ExpectedPolyEff) ∗ OperatingShaftPower
(1)
– Operational losses: This KPI represents the additional power consumed due to excessive power utilized by the compressor when compressor is running with recirculation. Operational losses = (AntiSurge_Flow / Inlet1_Volume Flow Rate) ∗ OperatingShaftPower
(2)
– Power deviation: This KPI represents the deviation of Operating Power with Expected Power at current operating conditions. Power Deviation % = (OperatingShaftPower − ExpectedShaftPower) / ExpectedShaftPower ∗ 100 (3) – Degradation losses in $ value: This KPI represents the additional expense incurred due to excessive power utilized by the compressor when compressor is running at low efficiency. Degradation losses in $ value = Degradation Loss(in KW) ∗ Energy_Cost_per_KW
(4)
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– Operational losses in $ value: This KPI represents the additional expense incurred due to excessive power utilized by the compressor when compressor is running with recirculation. Operational losses in $ value = Operational Loss (in KW) (5) ∗ Energy_Cost_per_KW Degradation and Operational loss KPIs are aggregated for the calendar date to facilitate daily basis analysis. Performance monitoring KPIs are: – Operating Polytropic Efficiency. Polytropic Efficiency is a process whereby compression is divided into numerous small steps with the steps contain similar isentropic efficiency. Operating Polytropic efficiency is defined as the ratio of the Operating Polytropic Head(m) to the Operating Head(m). Operating Polytropic Efficiency (%) = (Operating Polytropic head / Operating Head) ∗ 100 HPolyo ηPolyo = × 100 HM
(6) (7)
where – Operating Head (m) = HM = (Discharge enthalpy (kJ/kg) – Suction enthalpy (kJ/kg)) / 9,81; −H1 – HM = H2M 9,81 ; – H 2M (kJ/kg) = Discharge enthalpy at Operating discharge temperature and pressure. This can be calculated using the thermo module the fluid discharge conditions T2 and P2; – H 1 (kJ/kg) = Suction enthalpy at Operating suction temperature and pressure. This can be calculated using the thermo module the fluid suction conditions T1 and P1; 1 1545n1 T1 Z1 P2 n1 −1 . – Operating Polytropic Head (m) = HPolyo = MG P1 – n1 =
P log P2 1 T Z log T2 Z2
;
1 1
P1 = Pressure at suction (barg); P2 = Pressure at discharge (barg); Z1 = Compressibility at suction; T1 = Temperature at suction (Deg C); MG = Gas molecular weight (kg/kmole). – Expected Polytropic efficiency. Expected Polytropic efficiency is derived from the compressor performance curve at current volumetric flow rate and speed. Expected polytropic efficiency (%) = Efficiency from updated polytropic curves data = ηE = ηPolyE
(8)
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– Efficiency Deviation. This KPI represents the deviation of Operating efficiency with expected Efficiency at current operating conditions. It indicates excess power consumed by compressor. % Efficiency Deviation = ((Operating Efficiency − Expected Efficiency) / Expected Efficiency) ∗ 100
(9)
– Operating Head. Operating head is defined as the difference between the operating discharge enthalpy and the operating suction enthalpy. Operating Head (m) = HM = (Discharge enthalpy (kJ/kg) − Suction enthalpy (kJ/kg))/9, 81
(10)
– Expected Head. Expected head (m) is defined as the ratio of the expected polytropic head to expected polytropic efficiency. Get Expected polytropic head from map data at expected polytropic efficiency and expected speed from performance curves data. This will be equal to measured isentropic head. Use the corrected speed and head in the interpolation. HPolyE (m) = Expected polytropic head from Performance Curve
(11)
Expected Head = Expected polytropic head (m) / Expected polytropic efficiency (%) (12) HE = HPolyE /ηPolyE
(13)
– Head Deviation. This KPI represents the deviation of Operating head with Design Head at current operating conditions. % Head Deviation = ((Operating Head − Expected Head) / Expected Head) ∗ 100
(14)
– Operating Power. Operating power (kW) is defined as the ratio of the operating head to the operating efficiency. P0 =
H0 × vaporflow × MW , η0 × 3600
where – – – –
H0 = Operating Head (m); MW = Gas Molecular Weight (kg/kmol); η0 = Operating Efficiency (%); Vaporflow is in Kmol/hr.
(15)
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– Expected Power. Expected power is defined as the ratio of the Expected head to the Expected efficiency. Pe =
He × vaporflow × MW , ηe × 3600
(16)
where – He = Expected Head (m); – ηe = Expected Efficiency (%). – Power Deviation. This KPI represents the deviation of Operating Power with Design Power at current operating conditions. % Power Deviation = ((Operating Power − Expected Power)/Expected Power) ∗ 100
(17)
– Index Calculations Fouling Index = (Operating Shaft Power − Design Shaft Power) / Operating Shaft Power
(18)
Here, Power is in kW Energy Index = Abs (Percent Deviation Shaft Power) /100
(19)
Performance Index = Operating Poly Eff (%) /100
(20)
– Capacity losses CapacityLoss = ((InVolumeFlowRate / ExpectedVolumeFlow) − 1) ∗ 100 (21) Here, expected volumetric flow rate is derived from performance curve at measured speed and pressure ratio. – Antisurge Valve opening duration It indicates total duration (min) for which Antisurge valve is opened (24 h basis) [8]. The Fig. 2 below shows the several KPIs filtered in the screen of digital twin application software and demonstrates the way for user to understand how the modelled compressor interacts to real asset and correlates further operation and maintenance of this asset in order to increase its’ effectiveness [9]. And the Fig. 3 is the overall view of Digital twin visualized in used software environment.
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Fig. 2. Filtered KPIs of Centrifugal Compressor’s performance in Digital Twin model.
Fig. 3. Digital twin of Centrifugal Compressor visualized in used software environment.
3 Conclusion This research creates the basis to implement working solution in real industrial facility and achieve clear percentage of its optimization increase in terms of both energy consumption savings and performance optimization. Our research continues the cycle of digital twin modelling for all types of industrial equipment and assets [10]. From the scientific-technical point of view it contributes to our research program of creating complete digitization matrix of a large industrial plant.
References 1. Sahoo, Dr.: Centrifugal Compressor Failure, pp. 219–243 (2021). https://doi.org/10.1002/978 1119615606.ch13 2. Sultanian, B.: Centrifugal compressors. In: Fluid Mechanics and Turbomachinery (2021). https://doi.org/10.1201/9781003053996-9 3. Kollmann, K., Douglas, C., Gulen, S.: Basic theory of centrifugal compressors. In: Turbo/Supercharger Compressors and Turbines for Aircraft Propulsion in WWII: Theory, History and Practice—Guidance from the Past for Modern Engineers and Students (2021). https://doi.org/10.1115/1.884676_ch3 4. Yusupbekov, N., Abdurasulov, F., Adilov, F., Ivanyan, A.: Concepts and methods of “digital twins” models creation in industrial asset performance management systems. In: Kahraman, C., Cevik Onar, S., Oztaysi, B., Sari, I. U., Cebi, S., Tolga, A. C. (eds.) INFUS 2020, pp. 1589– 1595. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-51156-2_185
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5. DeSa, D.: Surge control of centrifugal compressors. In: Instrumentation Fundamentals for Process Control (2019). https://doi.org/10.1201/9780203750698-18 6. Wilkes, J., et al.: Centrifugal compressors. In: Compression Machinery for Oil and Gas (2019). https://doi.org/10.1016/B978-0-12-814683-5.00003-1 7. Yusupbekov, N., Abdurasulov, F., Adilov, F., Ivanyan, A.: Improving the efficiency of industrial enterprise management based on the forge software-analytical platform. In: Arai, K. (ed.) Intelligent Computing. LNNS, vol. 283, pp. 1107–1113. Springer, Cham (2022). https://doi. org/10.1007/978-3-030-80119-9_74 8. Yusupbekov, N., Isakova, S., Abdurasulov, F., Adilov, F., Arsen, I.: Simulation of turbines technological process on power generation in 3D environment of Unisim design. In: 13th International Scientific Conference CPS 2018 “Control of Power Systems 2018”, pp. 99–103. High Tatras, Slovak Republic (2018) 9. Yusupbekov, N., Abdurasulov, F., Adilov, F., Arsen, I.: Increase of effectiveness of industrial enterprise based on forge software-analytical platform. In: 5th International Proceedings on Hybrid and Synergetic intelligent systems HSSS’2020, pp. 23–30. BFU, Zelenogradsk (2020) 10. Yusupbekov, N.R., Abdurasulov, F.R., Adilov, F.T., Ivanyan, A.I.: Application of cloud technologies for optimization of complex processes of industrial enterprises. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M.O., Sadikoglu, F.M. (eds.) ICAFS 2018. AISC, vol. 896, pp. 852–858. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-04164-9_112
Investment Decision Making by Using Natural Language Processing Nigar F. Huseynova(B) Azerbaijan State Oil and Industry University, 34 Azadlig Ave., Baku AZ1010, Azerbaijan [email protected]
Abstract. The use of natural language data can improve decision-making. Classical considerations suggest that language may have developed because it improves decision-making which justifies the study of natural language’s contribution to decision-making. The study of data-based decision-making within the context of evolution provides a view of data use that permits us to both describe the phenomenon of information use as well as to make clear the way of its application. The paper deals with investment decision making through Natural Language Processing. The private citizen tries to invest to his best interest. To arrive at his decisions, he met group of experts to decide which investment option he should partake in. Linguistic terms extracted from the text conveyed by experts’ group are interpreted into fuzzy numbers and Fuzzy Inference Analysis is applied based on the data. According to the results conveyed by FIS the best alternative for investment is determined. Keywords: Natural Language Processing · Group decision making · Decision making under uncertainty · Fuzzy If-Then rules · Fuzzy Inference Systems
1 Introduction In modern world computing with words has become as an important direction in science and technology. In a reversal of long-standing attitudes, manipulation of perceptions and words which identify them is destined to gain in respectability. This is certain to happen because it is becoming increasingly clear that in dealing with real world problems there is much to be gained by exploiting the tolerance for imprecision, uncertainty and partial truth [1–3]. Natural Language Processing (NLP) emerged with the aim of creating a balance between computer science and linguistics, for decades it fulfilled a mission for understanding and interpreting the languages [4]. Natural language generation (NLG) techniques are used in decision making to cope with this challenge as they reduce the cognitive effort to clearly understand decision situations [5]. Natural language processing and natural language generation can summarize and normalize structured and unstructured data from different sources to support the analysts to efficiently assess investment options [6]. Analysts can save time spent on collecting data, instead focusing on analyzing data
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 588–594, 2023. https://doi.org/10.1007/978-3-031-25252-5_77
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with a higher potential for insights. Sophisticated technologies can convey in human language the rationale behind Artificial Intelligence engine–supported investment decisions [7]. These insights can be used for client communications and regulatory purposes and improving Artificial Intelligence decision algorithms [8]. Implementation of these technologies has the potential to significantly help the analysts to spend less time for collecting and understanding information [3]. Because sometimes they were gathering information for a long time without even knowing whether the information useful. Analysts sometimes spend their time for researching, but the shift would be to working with data that has higher potential for insight. In decision making process, NLP performs the precisiation before analysts spend time on evaluation [8] what. Successful investment decision making is main part of corporate survival and sustainable success. Those decisions support company’s future developments and develop competitive advantage by influencing, among other things, its technology, its processes, its working practices, and its profitability. Implementing a comprehensive investment research sometimes seems complicated and hard. But the award of a soundly based decision will be worth the effort put to learn the process and collect the required information. An investment decision involves a commitment today, with a reward from this commitment in the future. This return is often unpredictable at the time the investment decision is made. When assessing such investment opportunities, a private citizen therefore needs to make a prediction about the relative likelihood of the different future possible outcomes.
2 Preliminaries Definition 1. Fuzzy number [10, 11]: A fuzzy number is a set A on R which has the following features: a) A is an ordinary fuzzy set; b) A is a convex fuzzy set; c) α− cut of A, Aα is a closed interval for each α ∈ (0, 1]; d) the support of A, A+0 is bound-ed. Definition 2. Fuzzy If-Then rules [10, 11]: Fuzzy if-then rule representations are generally used to indicate the conventional statements that fuzzy logic possess. A general fuzzy if-then rule is conveyed as follows: If x is A then y is B where A and B define linguistic values interpreted by fuzzy sets. Multi-input multi-output fuzzy system is formulated in the following form If X1 is A1 and X2 is A2 and ... and Xn is An Then Y1 is B1 and Y2 is B2 and ... and Ym is Bm where Ai and Bi are data pieces.
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3 Statement of the Problem In the following problem a private citizen Müller has considerable amount of capital that he tries to invest to his best advantage. His goal is to decide which investment options he should partake in. For it he consults with 5 specialists to make a decision. He asks them the question: “How will be my benefit for the mentioned investment options and economic situations? In order to arrive at decision, they must first rate each of the investment options (to buy obligations, to buy stocks of enterprise, to deposit money) for each of the four states of economy: rapid economic growth, average economic growth, static economic situation, economic recession. First he asked if he invested in obligation or stocks what would be his benefit. The experts adviced that if he invests in obligation, stocks and deposit in rapid economics growth his benefit will be very good. Then he discussed the investment options in average economic growth. The specialists advised him if he invests in obligation or stock the benefit will be neutral, but if he invests in deposit the profit will be good. The specialists analized the investment options in static economic situation and they came to conclusion that if he invests in obligation if he profit ill be neutral and in deposit the benefit will be good but if he invests in stocks the benefit will be bad. The experts advised him that if he invests in obligation in economic recession the benefit will be bad, in stocks the benefit it will be very bad but if he invests in deposit it’ll be neutral. We have to tranform the text given in NLP to machine understanding as profit of Müller is determined by linguistic terms as very good, good, neutral, bad, very bad. These language expressions are transfered to fuzzy numbers. The solution of the problem is given in the next section.
4 Solution of the Problem 1. The following set of rules could be established based on the specialists’ answers: If the private citizen invests in obligations and the state of economy is rapid economic growth Then the profit is very good If the private citizen invests in stocks and the state of economy is rapid economic growth Then the profit is very good If the private citizen invests in deposit and the state of economy is rapid economic growth Then the profit is very good If the private citizen invests in obligations and the state of economy is average economic growth Then the profit is neutral If the private citizen invests in stocks and the state of economy is average economic growth Then the profit is neutral If the private citizen invests in deposit and the state of economy is average economic growth Then the profit is good If the private citizen invests in obligations and the state of economy is static economic situation Then the profit is neutral
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If the private citizen invests in stocks and the state of economy is static economic situation Then the profit is bad If the private citizen invests in deposit and the state of economy is static economic situation Then the profit is good If the private citizen invests in obligations and the state of economy is economic recession Then the profit is very bad If the private citizen invests in stocks and the state of economy is economic recession Then the profit is very bad If the private citizen invests in deposit and the state of economy is economic recession Then the profit is neutral 2. Then linguistic terms are conveyed to fuzzy numbers. The following codebooks for states of economy and for profit have been constructed (Tables 1 and 2). Table 1. Codebook for states of economy Linguistic terms
Triangular fuzzy numbers
Rapid economic growth
{0.75; 1; 1}
Average economic growth
{0.5; 0.75; 1}
Static economic situation
{0.25; 0.5; 0.75}
Economic recession
{0; 0.25; 0.5}
Table 2. Codebook for profit Linguistic terms
Triangular fuzzy numbers
Very good
{11.6; 13.3; 15}
Good
{8.2; 9.9; 11.6}
Neutral
{4; 6.5; 8.2}
Bad
{1.3; 3.1; 4.8}
Very bad
{−2; −0.3;1.5}
3. The Fuzzy Inference System analysis for three investment areas: obligation, stocks and deposit was applied. The analysis is based on the data extracted from the text and If Then rules (Figs. 1, 2, 3, 4, 5 and 6).
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Fig. 1. Fuzzy Partition for states of economy
Fig. 2. Fuzzy Partition of profit
Fig. 3. If then rules in FIS for stocks
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Fig. 4. FIS analysis on the first investment area: Obligation
Fig. 5. FIS analysis on the second investment area: Stocks
Fig. 6. FIS analysis on the third investment area: Deposit
5 Conclusion The paper analyses natural language processing approach to explain the investment analysis on a decision situation. The aim of our natural language Processing approach is to reduce the cognitive complexity to access, understand and interpret the uncertainties on a decision situation. We discovered that linguistic data collected through text could
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be effective in decision making. It’s much more convenient and reliable for people to make decisions through NLP. In this paper according to calculations made in FIS it becomes clear that the most profitable investment alternative for decision maker is deposit (9.9). The other alternatives obligation (6.23) and stock (3.06) are less profitable. The key contribution of this paper is that all the data extracted from text, from words of experts and based on that analysis we learn which investment area decision maker should partake in. Our results show that the NLP approach is particularly beneficial for difficult interpretational tasks.
References 1. Losee, R.M.: Natural language processing in support of decision-making: phrases and partof-speech tagging, 37(6), 769–787 (2001).https://doi.org/10.1016/s0306-4573(00)00061-3 2. Zadeh, L.A.: From computing with numbers to computing with words- from Manipulation of Measurements to Manipulation of Perception. In: Wang, P. (eds.) Computing with Word, pp. 35–67. Wiley (2001). https://doi.org/10.1109/81.739259 3. Aliev, R.A.: Fundamentals of the Fuzzy Logic-Based Generalized Theory of Decisions. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-34895-2 4. Huseynova, F.: Computing with words in natural language processing. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 621–625. Springer, Cham (2020). https://doi.org/10.1007/978-3030-35249-3_79 5. Wulf, D., Bertsch, V.: A natural language generation approach to support understanding and traceability of multi-dimensional preferential sensitivity analysis in multi-criteria decision making. Exp. Syst. Appl. 83, 131–144 (2017). https://doi.org/10.1016/j.eswa.2017.04.041 6. Henry, P., Krishna, D.: Making the investment decision process more naturally intelligent 7. Mendel, J.M., Wu, D.: Perceptual Computing Aiding People in Making Subjective Judgments. Wiley (2010) 8. Mendel, J., et al.: What computing with words means to me, 5(1), 20–26 (2010). https://doi. org/10.1109/mci.2009.934561 9. Dovlatova, K.J.: Application of the combined state concept to behavioral investment decisions under interval-valued information. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Sadikoglu, F.M. (eds.) ICAFS 2018. AISC, vol. 896, pp. 774–780. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-04164-9_102 10. Dovlatova, K.J.: Estimation of consumer buying behavior for brand choosing by using fuzzy IF-THEN rules. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M.B., Sadikoglu, F.M. (eds.) 10th International Conference on Theory and Application of Soft Computing, Computing with Words and Perceptions - ICSCCW-2019, pp. 805–812. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-35249-3_106 11. Adilova, N.E.: Quality criteria of fuzzy IF-THEN rules and their calculations. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) 14th International Conference on Theory and Application of Fuzzy Systems and Soft Computing – ICAFS-2020, pp. 55–62. Springer International Publishing, Cham (2021). https://doi.org/10. 1007/978-3-030-64058-3_7
Multi-attribute Decision Making Under Z-Set Valued Uncertainty Rafig R. Aliyev1
and Akif V. Alizadeh2(B)
1 Research Laboratory of Intelligent Control and Decision-Making Systems in Industry and
Economics, Azerbaijan State Oil, and Industry University, Azadlyg Avenue, 20, 1010 Baku, Azerbaijan 2 Department of Electronics and Automation, Azerbaijan State Oil and Industry University, 20 Azadlig Avenue, 1010 Baku, Azerbaijan [email protected], [email protected]
Abstract. In real-life decision problems it is usually we know the gain (outcome value) corresponding to given set of alternatives with some uncertainty. Instead of numerical value of this outcomes, there is set of possible values of outcomes. In this paper, we consider decision making under Z-set valued uncertainty. In situation when consequences of decision making is Z-set to define a fair price for a participation in such decision to select more appropriate alternatives is investigated. For this in the paper fair price approach is used. A real-word application is considered to demonstrate the usefulness of the proposed approach. Keywords: Z-set · Decision making · Fair price
1 Introduction Set-valued decision making is challenging scientific problem in existing literature. In [1] authors consider decision making problem under interval and set-valued uncertainty. They suggest way to define a fair price for a participation in such a decision. Definitions of fair price under interval, set-valued uncertainty, also fuzzy and Z-set valued uncertainty are given. Theorems on fair price under mentioned above set-valued uncertainty are suggested and proofed. In [2] authors extend decision making problem under closed set to more general case, when considered sets are not closed. Description of assigning fair price to not closed sets is given. In [3] set-valued uncertainty and set-valued uncertainty process are considered. Uncertain sets when their main feature is their variation over time are investigated. In [4] set-valued capacity is investigated and Choguet and the concave integrals are defined. In [5] the set-valued information and decision-making system are introduced. Authors define fuzzy preference relation for interval and set-valued decision-making systems. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 595–607, 2023. https://doi.org/10.1007/978-3-031-25252-5_78
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Fair price assigning in case of different type of uncertainty such as p-boxes, twin intervals, fuzzy values is considered in [6]. It is needed to mention that works in existing literature on set-valued, specially on Z-set valued decision making are scare. In this paper we consider Z-set-valued decision making by using fair price approach. Rest of paper is organized as follows. Section 2 includes some preliminaries. The third section describes the statement of the Z-set-valued decision-making problem and its solution method. In Sect. 4 numerical example is given. The final section offers same conclusions.
2 Preliminaries Definition. Z-numbers [7]. Decisions are based on information. To be useful, information must be reliable. Basically, the concept of a Z-number relates to the issue of reliability of information. A Z-number, Z, has two components, Z = (A, B). The first component, A, is a restriction (constraint) on the values which a real-valued uncertain variable, X, is allowed to take. The second component, B, is a measure of reliability (certainty) of the first component. Typically, A and B are described in a natural language. The concept of a Z-number has a potential for many applications, especially in the realms of economics, decision analysis, risk assessment, prediction, anticipation and rule-based characterization of imprecise functions and relations. Definition. Z-sets [1]. By a Z-set under set-valued p-uncertainty, we mean a pair (S,P) consisting of a bounded closed set S and a bounded closed set P ⊆ (0, 1]. Definition. Fair price [1]. By a fair price under interval uncertainty, we mean a function P([u, u]) that assigns, to every interval, a real number, and which satisfies the following properties: • u ≤ P([u, u]) ≤ u for all u (conservativeness); • if u = v and u < v, then P([u, u]) ≤ P([v, v]) (monotonicity); • for all u, u, v, and v, we have P([u + v, u + v]) = P([u, u]) + P([v, v]) (additivity). Definition. Fair price under Z-set [1]. By a fair price under Z-number uncertainty, we mean a function P(s, p) that assigns, to every pair of two fuzzy numbers s and p such that p is located on an interval [p0, 1] for some p0 > 0, a real number, and which satisfies the following properties: • if a fuzzy number s is located between u and u, then u ≤ P(s, 1) ≤ u (conservativeness); • if w = u + v and r = p ・ q, then P(w, r) = P(u, p) + P(v, q) (additivity); • if for all α, we have s− (α) ≤ t − (α) and s+ (α) ≤ t + (α),
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3 Statement of the Problem and a Solution Method Assume that A = {A1 , A2 , ..., An } is a set of alternatives and C = {C1 , C2 , ..., Cm } is a set of attributes. As we deal with Z-information valued decision environment, characteristics of alternative Ai , i = 1, n on attributes Cj j = 1, m is described by the form Ai = (Z(Ai1 , Bi1 ), Z(Ai2 , Bi2 ), ..., Z(Aij , Bij ), Z(Aim , Bim ) where Z(Aij , Bij ) is evaluation of an alternative Ai with respect to attribute Cj . Hence, we can represent decision matrix Dnm as (Table 1): Table 1. Decision matrix Dnm C1
C2
···
Cm
A1
[Z(A11 , B11 )]
[Z(A12 , B12 )]
···
[Z(A1m , B1m )]
A2
[Z(A21 , B21 )]
[Z(A22 , B22 )]
···
[Z(A2m , B2m )]
.. .
.. .
.. .
.. .
.. .
An
[Z(An1 , Bn1 )]
[Z(An2 , Bn2 )]
···
[Z(Anm , Bnm )]
The problem is given: alternatives Ai , i = 1,…,n to find best alternative[8–12] Ai . In first step we applied Z-Hurwicz approach. In second step, for comparation alternatives we applied Fair Price approach. 3.1 Hurwicz Approach Alternative Ai is characterized by ZCi = αH ∗ max(Zi1 , Zi2 , ..., Zin ) + (1 − αH ) ∗ min(Zi1 , Zi2 , ..., Zin )
(1)
3.2 Fair Price Approach [1] Z-valued fair price is defined as FP(Z(A, B)) = +
1 0
1
K − (α)A− (α)d α +
0
L− (α) ln(B− (α)d α
+
1 0
1
K + (α)A+ (α)d α
0
L+ (α) ln(B+ (α)d α
,
(2)
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were K ± (α) and L± (α) are appropriate fuzzy functions. In a special case, as K · A can be taken part A of the index characterizing the alternatives, ZCi, i.e., ZCi.A. And L can be taken as the core of the fuzzy number ZCi.A, i.e. core(ZCi.A).
4 Numeric Example Assume that one wants to choose one of three available alternatives: buy shares of the company (A1), put investment in the bank for deposit (A2), and to buy bonds (A3). The economic situation of the country for one year is characterized four possible states of nature: rapid economic growth, average economic growth, stable state of the economy, and economic recession. The rate of return as a percentage of the invested amount is given in Table 2. Let us assume than decision matrix D giving as: ⎡ ⎤ Z11, Z12, Z13, Z14; ⎢ ⎥ D = ⎣ Z21, Z22, Z23, Z24; ⎦, Z31, Z32, Z33, Z34 were. Z11 = (Z11.A;Z11.B) == (trimf([10.0,12.0,13.0]);trimf([0.8,0.9,1])); Z12 = (Z12.A;Z12.B) == (trimf([7.0,8.0,9.0,]);trimf([0.7,0.8,0.9])); Z13 = (Z13.A;Z13.B) = (trimf([5.0,6.0,8.0,]);trimf([0.7,0.8,0.9]); Z14 = (Z14.A;Z14.B) = (trimf([2.0,3.0,5.0]);trimf([0.7,0.8,0.9])); Z21 = (Z21.A;Z21.B) = (trimf([14.0,15.0,17.0]);trimf([0.8,0.9,1])); Z22 = (Z22.A;Z22.B) = trimf([6.0,7.0,8.0]);trimf([0.7,0.8,0.9])); Z23 = (Z23.A);Z23.B) = trimf([1.0,3.0,5.0]);trimf(Z23.Bs,[0.7,0.8,0.9])); Z24 = (Z24.A;Z24.B) = (trimf([0.0,1.0,2.0]);trimf([0.7,0.8,0.9])); Z31 = (Z31.A;Z31.B) = (trimf([6.0, 7.0, 9.0]);trimf(Z31.Bs,[0.8,0.9,1])); Z32 = (Z32.A;Z32.B) = (trimf([5.0, 6.0, 8.0]);trimf([0.7,0.8,0.9])); Z33 = (Z33.A;Z33.B) = (trimf([4.0, 5.0, 7.0]);trimf([0.7,0.8,0.9])); Z34 = (Z34.A;Z34.B) = (trimf([2.0,4.0,5.0]);trimf(Z34.Bs,[0.7,0.8,0.9])); In first step, for calculate Hurwiz’s index for alternatives defined as: Ci = αH ∗ max(Z1 , Z2 , ..., Zn ) + (1 − αH ) ∗ min(Z1 , Z2 , ..., Zn ) were Zmaxi(1) = (trimf(10,12,13); Zmaxi(1).B).
Rapid economic growth
(trimf([10.0,12.0,13.0]); trimf([0.8,0.9,1]));
(trimf([14.0,15.0,17.0]); trimf([0.8,0.9,1]));
(trimf([6.0, 7.0, 9.0]); trimf(Z31.Bs,[0.8,0.9,1]));
Alternatives
Shares
Deposit
Bonds
(trimf([5.0, 6.0, 8.0]); trimf([0.7,0.8,0.9]));
trimf([6.0,7.0,8.0]); trimf([0.7,0.8,0.9]));
(trimf([7.0,8.0,9.0,]); trimf([0.7,0.8,0.9]));
Average economic growth
(trimf([4.0, 5.0, 7.0]); trimf([0.7,0.8,0.9]));
trimf([1.0,3.0,5.0]); trimf(Z23.Bs,[0.7,0.8,0.9]));
(trimf([5.0,6.0,8.0,]); trimf([0.7,0.8,0.9]);
Stable state of the economy
Table 2. Rates of return
(trimf([2.0,4.0,5.0]); trimf(Z34.Bs,[0.7,0.8,0.9]));
(trimf([0.0,1.0,2.0]); trimf([0.7,0.8,0.9]));
(trimf([2.0,3.0,5.0]); trimf([0.7,0.8,0.9]))
Economic recession
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Zmaxi(1).B is shown in Fig. 1
Fig. 1. Membership function of Zmaxi(1).B
Zmaxi(2) = (trimf(14,15,17); Zmaxi(2).B). Were Zmaxi(2).B) described as shown in Fig. 2
Fig. 2. Membership function of Zmaxi(2).B
Zmaxi(3) = (trimf(6,7,9); Zmaxi(3).B), were Zmaxi(2).B) described as shown in Fig. 3
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Fig. 3. Membership function of Zmaxi(3).B
Zmin respect to first row of matrix D defined as. Zmini(1) = (trimf(2,3,5); Zmin(1).B), were Zmin(1).A, and Zmin(1).B are shown in Figs. 4, 5:
Fig. 4. Membership function of Zmin(1).A
Fig. 5. Membership function of Zmin(1).B
Zmin respect to second row of matrix D defined as.
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Zmini(2) = (trimf(0,1,2); Zmin(2).B), were Zmin(2).A and Zmin(2).B are shown in Fig. 6 and Fig. 7:
Fig. 6. Membership function of Zmin(2).A
Fig. 7. Membership function of Zmin(2).B
Zmini(3) = (Zmin(3).A; Zmin(3).B), were Zmin(3).A and Zmin(3).B are shown in Figs. 8, 9:
Multi-attribute Decision Making Under Z-Set Valued Uncertainty
Fig. 8. Membership function of Zmin(3).A
Fig. 9. Membership function of Zmin(3).B
Coefficient of realism ZalfaH is Z-number defined as: ZalfaH = (trimf([0.6,0.7,0.8]); trimf([0.8,0.9,1])). (1-ZalfaH) defined as shown in Fig. 10 and Fig. 11:
Fig. 10. (1-ZalfaH).A
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Fig. 11. (1-ZalfaH).B
Now we can calculate decision for every alternative by using following formule: Ci = ZαH ∗ max(Zi1 , Zi2 , ..., Zin ) + (1 − ZαH ) ∗ min(Zi1 , Zi2 , ..., Zin ). Results are shown in Figs. 12, 13, 14, 15, 16 and 17. (Ci(1).A, Ci(1).B) defined as shown in Figs. 12, 13:
Fig. 12. Ci(1).A
Fig. 13. Ci(1).B
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(Ci(2).A, Ci(2).B) defined as shown in Figs. 14, 15.
Fig. 14. Ci2).A
Fig. 15. Ci(2).B
(Ci(3).A, Ci(3).B) defined as shown in Figs. 16, 17.
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Fig. 16. Ci(3).A
Fig. 17. Ci(3).B
By using (2) fair price for each alternative is calculated: FairPrice = ZfpM(Ci) = [12.8575609753846; 16.8542362988717; 8.73417984111302]. So, second alternative is better alternative.
5 Conclusion Set-valued decision analysis is challenging scientific problem in existing literature. Studies on decision making in set-valued, specially on Z-set-valued uncertainty situation are scare. In this paper we have investigated Z-number-based approach to decision making by using Z-number-based Hurwitz extension and fair price for Z-set. The considered in the study approach is demonstrated by solving real-world investment problem.
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References 1. Lorkowski, J., Kreinovich, V., Aliev, R.: Towards decision making under interval, setvalued, fuzzy, and z-number uncertainty: a fair price approach. In: 2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) Beijing, China (2014) 2. Bokati, L., Kosheleva, O., Kreinovich, V.: How much for a set: general case of decision making under set-valued uncertainty. In: Rayz, J., Raskin, V., Dick, S., Kreinovich, V. (eds.) NAFIPS 2021. LNNS, vol. 258, pp. 52–61. Springer, Cham (2022). https://doi.org/10.1007/ 978-3-030-82099-2_5 3. Ghaffari-Hadigheh, A.: Set-valued uncertain process: definition and some properties (2021) 4. Lehrer, E.: Set-valued capacities: multi-agent decision making (2020) 5. Wang, H.: Attribute reduction in interval and set-valued decision information systems (2013) 6. Kreinovich, V.: Decision making under interval (and more general) uncertainty: monetary vs. utility approaches. Departmental Technical Reports (CS), vol. 950 (2015) 7. Aliev, R.A., Huseynov, O.H., Aliyev, R.R., Alizadeh, A.V.: The Arithmetic of Z-numbers. Theory and Applications. World Scientific, Singapore (2015) 8. Gardashova, L.A., Salmanov, S.: Using Z-number-based information in personnel selection problem. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 302–307. Springer, Cham (2022). https:// doi.org/10.1007/978-3-030-92127-9_42 9. Huseynov, O.H., Adilova, N.E.: Multi-criterial optimization problem for fuzzy if-then rules. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 80–88. Springer, Cham (2021). https://doi.org/10.1007/ 978-3-030-64058-3_10 10. Nuriyev, A.M.: Fuzzy MCDM models for selection of the tourism development site: the case of Azerbaijan. F1000 Res. 11(310), 1–24 (2022). https://doi.org/10.12688/f1000research.109 709.1 11. Aliyeva, K.R.: Multi-criteria house buying decision making based on type-2 fuzzy sets. Procedia Comput. Sci. 120, 515–520 (2017). https://doi.org/10.1016/j.procs.2017.11.273 12. Aliyeva, K.: Fuzzy type-2 decision making method on project selection. In: Aliev, R.A., Yusupbekov, N.R., Kacprzyk, J., Pedrycz, W., Sadikoglu, F.M. (eds.) WCIS 2020. AISC, vol. 1323, pp. 180–185. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-68004-6_23
Fuzzy Processing of Hydrodynamic Studies of Gas Wells Under Uncertainty Salahaddin I. Yusifov , Imran Y. Bayramov , Azar G. Mammadov , Rza S. Safarov(B) , Rashad G. Abaszadeh , and Elmira A. Xanmammadova Azerbaijan State Oil and Industry University, 16/21 Azadlig Avenue, Baku City, Azerbaijan [email protected]
Abstract. The methodology for constructing membership functions in decisionmaking in a complex multi-level hierarchical control system based on the theory of fuzzy sets, algorithms for identification of fuzzy parameters of models have been developed, technological and geological-field parameters have been calculated and identified based on indirect information. Keywords: Membership functions · Identification · Fuzzy · Parameters · Gas wells
1 Introduction Real oil and gas production systems are characterized by the simultaneous presence of various types of information: – – – –
point measurements and parameter values; permissible intervals of their change. statistical distribution laws for various quantities. linguistic criteria and restrictions gotten from experts, etc.
Attempts to use any special mathematical apparatus (interval analysis, statistical methods, game theory, deterministic models, etc.) to make decisions under conditions of uncertainty allow only certain types of data to be adequately reflected in the model and lead to irretrievable loss of other types of information. One can achieve stability of algorithms, i.e., their insensitivity to small deviations from the assumptions (for example, about non-stationarity of a regime) by using the fuzzy set apparatus, by considering conditions of existence of models and features of Zadeh’s minimax operations.
2 Statement of the Problem There is a quite sharp increase in errors in initial data for multi-level hierarchical control systems, depending on the control level, at which the calculation is performed. The © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 608–615, 2023. https://doi.org/10.1007/978-3-031-25252-5_79
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correct choice for the appropriate control level of the model and the amount of data transmitted for calculations is extremely important. The complexity of the mathematical model, which takes into account a large number of measured parameters, leads to a decrease in the error introduced by the model. However, due to the large size of the models and the inaccuracy of the applied analytical and numerical methods, the component of errors gets a big value. Solving a problem of large size may be unacceptable while solving in real time. The complexity of a mathematical model also requires an increase in the amount of data transmitted from the lower level and also leads to an increase in the corresponding component of the error. Therefore, it is required to find a reasonable compromise between these factors depending on the control level.
3 Method One of the most widespread hydrodynamic methods for the study of gas wells is research in stationary filtration regimes. Processing of an indicator curve by traditional methods is reduced to finding the filtration resistance coefficients A and B according to the straight-line graph [3]. y = ax + b; y =
P2r.p. − P2b.p. Q
; x=Q
(1)
where Q is the flow rate of a gas well; Pr.p. is a reservoir pressure. Pb.p. is a bottomhole (bottom- hole) pressure. a, b are the filtering resistance coefficients. It is known that the basis of the least-squares method used to estimate the parameters is the following assumptions [5]: 1) 2) 3) 4)
The independent variable xi is not a random variable. Measurements of the dependent variable yi are statistically independent. The conditional distribution of y is normal for the given xi. The dispersion of the measurement error is equal to the dispersion of the dependent variable yi. In practice, violation of these conditions usually consists of the following:
– the independent variable xi is a random variable and it is measured with a certain error; – measurement errors of yi are statistically independent; – the variation interval of the independent variable xi is very small, and measurement errors of y are very large, so variation of the dependent variable is proportional to its measurement error; – dispersions of the variables xi and y may depend on their absolute quantities. In the general case, when the dependent and independent variables are random quantities, the problem of estimating the regression parameters is not practically solved [4],
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because the resulting system of equations is nonlinear, which makes it difficult to be visually solved, even for exponential distribution functions. Let us consider one of the methods of estimating fuzzy parameters of Eq. (1), for example, considering that other methods of estimation can be found by giving narrower allowable ranges of the parameters. Suppose that the initial quantities for gas flow are measured with an error of 5% and for pressure with an error of 0.2%. Using interval operations [6] for the measurement of the quantity y, we have found that the error is 6.5% for the real values of pressures and gas flows. Then, the set of possible values, that the parameters xi and yi can take with the known measurements of xi and yi , can be determined by exponential membership functions. μ(xi ) = exp{−(xi − xi )2 /δx2 }, μ(yi ) = exp{−(yi − yi )2 /δy2 } where δx and δy are the maximum allowable measurement errors. Let us consider the membership function for the joint distribution of a and b as a representation of the results of n measurements when the intersection operation is accepted as multiplication: ⎧ ⎪ ⎨ y1 = ax1 + b n μ(α, β) = max[ μ(xi )μ(yi )], (x1 , y1 , ..., xn , yn ) ... . ⎪ U i=1 ⎩ yn = axn + b
4 Results Taking into account the one-to-oneness of the considered representation and the forms of the initial membership functions, the following results are obtained: μ(α, β) = max[ {xi }
n
μ(xi )μ(axi + b)]
i=1
n
= exp[−( (axi + b − yi )2 )/(δy2 + aδx2 )]
(2)
i=1
The function μ(a, b) is quite difficult to be studied. However, it is possible to define such a function μ∗ (a, b) that the following inequality is satisfied in the real domain of possible values of the coefficient a: μ∗ (a, b) ≥ μ(a, b) For this, it is enough to take the value of a* in the denominator of the exponent, which is greater than the maximum allowed. In order to determine the membership functions for each coefficient separately, it is necessary to project the function μ∗ (a, b) onto the corresponding axes: μ(b) = C · exp{−b − b0 )2 /δb2 }; μ(a) = C · exp{−a − a0 )2 /δa2 }
(3)
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n n 2 b0 = xi yi − xi yi / n x2i − xi ; i=1 i=1 i=1 i=1 i=1 i=1
n n 2 n n n xi yi − xi yi / n x2i − xi ; a0 = n i=1 i=1 i=1 i=1 i=1
n n 2 n 2 2 2 2 2 2 xi / n xi − xi ; δb = (δy + a∗ δx ) i=1 i=1 i=1 n 2 n 2 2 2 2 2 2 xi − xi . δa = (δy + a∗ δx )n / n
where
n
n 2
n
n
i=1
i=1
The constant C is equal to the maximum value of the function μ∗ (a, b). It comes from expressions (3), that with the increase in the number of measurements, the allowed interval for the values of a and b decreases at the indicated level r. So, using a different number of points, it is possible to calculate the filtering resistance coefficients with different degrees of accuracy. σr (a) and σr (b) sets of r-level are analogues of confidence intervals. Graphically, such intervals for r-level sets have rectilinear boundaries. Let us consider development of indicator curves for one of the wells in the field to study the accuracy of calculating coefficients a and b. Results are shown in Table 1. Figure 1 shows that 6–8 measurements and a wider range of flow rate changes are necessary for more reliable determination of the filtering resistance coefficients. Table 1. Evaluation of fuzziness while processing of indicator curves for one well. N
δb δy2 +a∗2 δx2
δa δy2 +a∗2 δx2
2
5,15
0,0129
3
2,8
0,0076
4
1,99
0,0052
5
1,54
0,0042
6
1,17
0,0029
7
1,07
0,0025
8
1,02
0,0022
For the well bottomhole pressure recovery curves, we look at the following equation: y = α + βx
(4)
2 (t) and the rectilinear area The coefficients of this equation are determined by Pb.p. of the curve in the lnt coordinates. It is assumed that the dispersion of the experimental point values satisfies the normal distribution law [2]. Using different numbers of points, we construct multiple sets of straight lines with different inclination angles (Fig. 2).
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Row Row
n Fig. 1. The graph of the change of the ratio error while calculating coefficients a and b (δb /b0 – row 1, δa /a0 –row 2).
The inaccuracy of a bottomhole pressure measurement is characterized by the following exponential membership functions: μ(yi ) = exp[−((yi − yi )2 )/(δ 2 )], i = 1,n 2 ; δ is the allowable where yi is a scalar quantity of measurement of the pressure Pb.p. measurement error.
Fig. 2. Values of the pressure recovery curve with a fuzzy graph for discrete levels: 1 - 0.8; 2 0.6; 3 - 0.2
The membership function for the joint distribution of α and β as a representation of results of n measurements: n μ(α, β) = max[ μ(yi )], U = {yi |yi = α + β xi ; i = 1,n} U
i=1
Taking into account the one-to-oneness of the representation, we can get the following: n n 2 2 μ(α, β) = μ(α + βxi ) = exp −( (α + βxi − yi ) )/(δ ) i=1
i=1
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In order to determine membership functions [7–10] for each coefficient, it is necessary to project the joint function μ(α, β) onto the corresponding axes. Firstly, on the axis α: μ(α) = max μ(α, β) β
β:
We find the partial derivative of μ(α, β) with respect to β then the dependence for
−2(
n
(α + βxi − yi )xi )/(δ 2 ) = 0
i=1
β=(
n
yi xi − α
i=1
n
xi )/(
i=1
n
x2i )
i=1
If we consider the last expression in the expression for μ(α, β), then we get: ⎡
(a − (
⎢ μ(α) = C · exp⎢ ⎣−
n
i=1
yi
n
x2i −
n
yi xi
n
xi )/(n
i=1 i=1 i=1 n n (n x2i )2 δ 2 /(n x2i )2 i=1 i=1
n
x2i − (
n
x)2 ))2
i=1 i=1 n n − ( x i )2 x2i ) i=1 i=1
⎤ ⎥ ⎥ ⎦
where C ≤ 1 is a constant quantity equal to the maximum value of the function μ(α). Analogously, we find partial derivative with respect to α, then α and μ(β): n n n
−2( (α + βxi − yi ))/(δ 2 ) = 0, α = ( yi − β x)/(n) i=1
i=1
⎡
⎢ μ(β) = C · exp⎢ ⎣−
(β − (n
n
xi
i=1
n i=1
yi −
n i=1
n2 δ 2 /(n2
yi
n
i=1
n
i=1
xi )/(n
i=1
x2i − (
n
n i=1
x2i − (
n i=1
x i )2 )
x)2 ))2
⎤ ⎥ ⎥ ⎦
i=1
So, μ(α) get their maxima at the following points:
n and μ(β) n n n n n 2 yi xi i − yi xi xi / n x2i − ( xi )2 ; α0 = i=1
i=1
i=1
β0 = n
n
i=1
yi xi −
i=1
n
i=1
i=1
yi
n
i=1
xi / n
i=1
n
i=1
x2i
−(
n
xi )
2
i=1
So, finding the values of α 0 and β 0 is equivalent to finding them by the least-squares method. Using a different number of points, one can calculate the coefficients α and β (i.e. the equation of a straight line) with different degrees of accuracy.
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5 Discussion With the increase in the number of measurements, the allowed interval for the values α and β decreases at the constant level r. For a concrete example of defining the errors δα2 and δβ2 of the pressure recovery curve depicted in Fig. 2, Fig. 3 shows the ratio error when calculating the coefficients α and β as a percentage. The change range of the function is close to errors of the initial data for the number of measurements n = 10 ÷ 15 for the coefficient α, and n = 20 ÷ 25 for the coefficient β.
Fig. 3. Graphs of ratio errors when calculating the coefficients α and β
6 Conclusion Statement of the problem in a fuzzy form significantly reduces the possibility of obtaining inappropriate solutions in the calculation and optimization process. Construction of models within a fuzzy approach allows to compare models and assign a precise meaning to concepts such as “significant” and “insignificant”. It becomes possible to formalize inaccurate knowledge about the subject area, to include information about the incompleteness of information into the model.
References 1. Bayramov, I.Y, Gurbanov, A.N., Mirzayev, O.M., Sardarova, I.Z.: Numerical determination of gas and oil reserves. In: 11th International Conference on Theory and Application of Soft Computing, Computing with Words and Perceptions and Artificial Intelligence - ICSCCW2021, pp. 522–529 (2022). https://link.springer.com/bookseries/15179 2. Ahmadov, S.A., Gardashova, L.A.: Fuzzy dynamic programming approach to multistage control of flash evaporator system. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 101–105. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-35249-3_12 3. Vasilyev, F.P.: Chislenniye metodi resheniya ekstremalnikh zadach, p. 518. Nauka, Moscow (1980). (in Russian)
Fuzzy Processing of Hydrodynamic Studies of Gas Wells Under Uncertainty
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4. Dementyev, L.F., Kirsanov, A.N., Laperdin, A.N.: Otsenka tochnosti opredeleniya osnovnykh geologo-promislovykh i tekhnologicheskykh parametrov Medvejyego i Urengoyskogo gazovykh mestorojdeniy. – Trudi VNIIEgazproma, Moscow 1(10), 16–23. (in Russian) 5. Himmelblow, D.: Analiz processov statisticheskimi metodami, p. 468. Mir, Moscow (1973). (in Russian) 6. Shokin, I.Y.: Intervalniy analiz, p. 112. Nauka, Novosibirsk (1981). (in Russian) 7. Gardashova, L.A.: Synthesis of fuzzy terminal controller for chemical reactor of alcohol production. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 106–112. Springer, Cham (2020). https:// doi.org/10.1007/978-3-030-35249-3_13 8. Aliev, R.A., Pedrycz, W., Alizadeh, A.V., Huseynov, O.H.: Fuzzy optimality based decision making under imperfect information without utility. Fuzzy Optim. Decis. Making 12(4), 357–372 (2013) https://doi.org/10.1007/s10700-013-9160-2 9. Alizadeh, A.V.: Application of the fuzzy optimality concept to decision making. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 542–549. Springer, Cham (2020). https://doi.org/10. 1007/978-3-030-35249-3_69 10. Aliyeva, K.R.: Identification of a fuzzy model of the coking process. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 624–630. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-64058-3_77
Fuzzy Modeling for Marketing Plan Development Seving R. Mustafayeva(B) Azerbaijan State Oil and Industry University, Azadlig Avenue 20, Baku, Azerbaijan [email protected]
Abstract. In this paper the fuzzy modeling for marketing plan development is considered. Fuzzy clustering is the basic algorithm used in data mining. In marketing, customers can be grouped into fuzzy clusters based on their needs, brand choices, psycho-graphic profiles, or other marketing related partitions. The main practical significance lies in the ability to determine demand, which in turn allows budget planning and cost reduction. Keywords: Time series · Forecasting · Fuzzy modeling · Clustering · c-means
1 Introduction The task of forecasting is aimed at predicting future values of the measured characteristics of the object under study based on observational data, i.e., making a forecast for a certain period of time. Several different forecasting methods have now been developed and substantiated. A prediction market is a market where people can trade contracts that pay off based on the outcome of unknown future events. The market prices generated by these contracts can be seen as a kind of collective prediction of market participants. These prices are based on individual expectations and the willingness of investors to risk their money to meet those expectations. Predictive analytics is often discussed in the context of big data. Technical data, for example, comes from sensors, instruments, and connected systems around the world. Business system data in a company may include transaction data, sales results, customer complaints, and marketing information. Increasingly, companies are making data-driven decisions based on this valuable information. Successful corporate governance depends on effective strategic and operational planning. Mistakes in planning often result in huge costs and, in some cases, reputational damage. Reliable forecasts make an important contribution to effective planning. Demand forecasting is a very important factor for doing business right. It is critical for a company to ensure effective operations management planning, as all organizations will deal with uncertainty going forward, some error between forecast and actual demand should be expected. The goal of an accurate demand forecast is to minimize the deviation between actual demand and forecast. Therefore, due to the uncertainty of demand from customers, they often face obstacles © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 616–619, 2023. https://doi.org/10.1007/978-3-031-25252-5_80
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to overcome the size and the smallest quantity of ordered goods. If there is a shortage, it can be detrimental to the company in terms of costs, while excess inventory can have an adverse effect on further investment. This proves the importance of forecasting consumer demand. The c-means fuzzy model method is more suitable due to the use of precise and imprecise data in demand analysis [1, 2].
2 Fuzzy c-means Method In this method, the sequence of calculations can be expressed as follows: The Fuzzy C-Means algorithm tries to minimize the sum of quadratic errors [3]. The algorithm is based on iterative minimization of the following objective function. k n wi.jp dist(xi , cj )2 J (W , C) = j=1
i=1
The following condition is satisfied for the general degree of membership of a given element x i in all clusters: k wi,j = 1 j=1
In each cluster, the following condition is satisfied by the sum of the degrees of membership of all elements: n 0< wi,j < n i=1
The corresponding center Cj for the cluster cj is defined as follows: n p i=1 wi,j xi c j = n p i=1 wi,j The fuzzy split update formula can be obtained by minimizing the objective function with a weight limit of 1: 1
wi,j = k
(1/dist(xi , cj )2 ) p−1
q=1 (1/dist(xi , cq )
1
2 ) p−1
3 Statement of the Problem and Solution For predicting of demand[4–7] in automobile industry (sales of economy class cars) here uses c-means method simulation in MATLAB. We have the initial data in the form of time series, which are presented at the table below: Based on these data, the capabilities of Data Mining technology were used to study the forecasting of consumer demand. Using the FCM clustering method, clusters were obtained from the above input data and a fuzzy model was built. The clustering method was used to obtain knowledge from the data. The clusters were obtained by the above method and a calculations were performed. Fragment of code is listed below.
618
S. R. Mustafayeva Table 1. Sales of cars 2018
2019
56
46
54
65
67
75
111
70
99
78
63
80
133
88
79
91
87
93
71
49
86
65
135
63
load(’data1.dat’); [center,u,obj_fcn]=fcm(seva1,3,2); center kl1mfs=u(1,:); kl1mf=kl1mfs’; a1=max(kl1mf); kl2mfs=u(2,:); kl2mf=kl2mfs’; a2=max(kl2mf); kl3mfs=u(3,:); kl3mf=kl3mfs’; a3=max(kl3mf); a=[kl1mf kl2mf kl3mf ]
Table 2. Fuzzy numbers for linguistic values of input and output variables Supply of the 1 year Fuzzy number Supply of the 2 year Fuzzy number Predicted demand 66
(59,66,72)
70
(63,70,77)
75
103
(93,103,113)
93
(84,93,102)
65
81
( 73,81,89)
86
(78,86,94)
95
Based on the results of clustering, a fuzzy model was built, consisting of the following set of rules. If the proposals of the previous two years are nearly 66 and 70 Then the predicted demand is nearly 75. If the proposals of the previous two years nearly 103 and 93 Then the predicted demand is nearly65. If the proposals of the previous two years nearly 81 and 86 Then the predicted demand is nearly 95.
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4 Discussion and Conclusion The reason for choosing this method is that it has a number of advantages over other methods. For example, this method is more like the k-means method. The main difference is that in the “Fuzzy-Means” cluster, each point has a certain degree of membership in a certain cluster, so the point is not included in the “cluster” as long as its weak Fuzzy-C Means is slower than the K method. -averages, because this method had more calculations. Each point is evaluated for each cluster, and more operations are performed on each evaluation. K-Means is purely based on distance calculations and this method does not calculate the degree of affiliation, i.e. it is impossible to work with inaccurate data, or there is a strong connection with the cluster.The fuzzy c-means method is more appropriate because it uses accurate and inaccurate data when forecasting consumer demand.
References 1. Aliev, R.A., Fazlollahi, B., Aliev, R.R.: Soft Computing and Its Applications in Business and Economics. Springer Berlin Heidelberg, Berlin, Heidelberg (2004) 2. Yaakob, A., Gegov, A.A.: A fuzzy rule approach with z-numbers for choosing alternatives using TOPSIS. In: Proceedings of the IEEE International Conference on Fuzzy Systems, Istanbul, pp. 1–8 (2015) 3. Khalif, K., Gegov A., Bakar, A.: Z-TOPSIS approach for evaluating effectiveness using fuzzy similarity. In: Proceedings of the IEEE International Conference on Fuzzy Systems, Naples, pp. 1–6 (2017) 4. Imanova, G.: Identification and Ranking of Key Factors for Pattern of Consumer Buying Decisions in Digital Marketing. In: Aliev, R.A., Yusupbekov, N.R., Kacprzyk, J., Pedrycz, W., Sadikoglu, F.M. (eds.) WCIS 2020. AISC, vol. 1323, pp. 237–245. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-68004-6_31 5. Imanova, G.E., Imanova, G.: Digital Marketing Technologies Selection Under Z-Environment. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 378–387. Springer, Cham (2021). https://doi.org/10.1007/ 978-3-030-64058-3_47 6. Imanova, G.E., Imanova, G.: Some Aspects of Fuzzy Decision Making in Digital Marketing Analysis. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 465–473. Springer, Cham (2022). https://doi. org/10.1007/978-3-030-92127-9_63 7. Sadikoglu, G., Adilova, N.E., Anene, P.I.: The Impact of Store Environment on Purchase Intention in Supermarkets. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 237–245. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-92127-9_34
Solving Employee Selection Problem Under Fuzzy-Valued Information Aynur I. Jabbarova1
and K. I. Jabbarova2(B)
1 Department of Mathematics and Statistics, Azerbaijan State Economic University,
Baku, Azerbaijan 2 Department of Computer Engineering, Azerbaijan State Oil and Industry University,
20 Azadlig Avenue, AZ1010 Baku, Azerbaijan [email protected]
Abstract. The approach of TOPSIS was employed to consider the personnel selection problem. The value of the selection criteria is presented by fuzzy numbers. Finally, ranking of alternatives was performed for selection the best one. Keywords: MCDM · TOPSIS method · Fuzzy number · Employee selection
1 Introduction The selection of personal the initial process that defines the success and stability of a company [1]. In this process, successful and reliable selection tests are the key. The level of expertise and academic skill of prospective employees are very essential factors in selection process. In [1] for solving this type of problem uses SAW method. The study results area in the form of prospective test applications employee selection facilitate the process of selecting employees according to their necessity. The aim of [2] to suggest an integrated MCDM model to support the selection of skilled personnel in the different area. The integrated method of AHP and TOPSIS was used in the problem of selection of personnel. At first, the AHP method was used to determine the weights of the criteria. Then to rank alternatives was performed by using TOPSIS. The offered model was applied into a logistics company to select the best deputy manager. Also the goal of [3] is to suggest the use of MCDM techniques in selection of the personnel. Therefore, for the determination of the criteria weights was used SWARA method. The CoCoSo method then helps to rank the alternatives for selection best candidate. The article parts are listed as below: The prerequisite material is given in Sect. 2. In All stages of the calculation of the consider problem are presented in Sect. 3. The next section of the study provides a conclusion.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 620–625, 2023. https://doi.org/10.1007/978-3-031-25252-5_81
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2 Preliminaries Definition 1. Triangular Fuzzy Number [4]. A˜ = (a, b, c) is called triangular fuzzy number if its membership function is given by ⎧ 0, x < a; ⎪ ⎪ ⎪ ⎪ ⎪ x−a ⎪ ⎪ , a ≤ x ≤ b; ⎨ b−a . µA˜ (x) = c−x ⎪ ⎪ , b ≤ x ≤ c; ⎪ ⎪ ⎪ c−b ⎪ ⎪ ⎩ 0, x > c, Definition 2. If A˜ = (a1 , b1 , c1 ), B˜ = (a2 , b2 , c2 ) are two triangular FNs then [4, 5] ˜ B) ˜ := 1 [(a1 − a2 )2 + (b1 − b2 )2 + (c1 − c2 )2 ]. d (A, 3
3 Statement of the Problem Employee selection defines the input level of quality of employees. Problem of employee selection has been analyzed widely [6]. Selecting the best employee between many alternatives is a problem of MCDM. Therefore, we consider the MCDM [6–10] problem, where there are five alternative and four criteria: C1-job responsibilities, C2-work discipline, C3-work quality, C4- behavior. The criteria’s values are presented with fuzzy numbers (see Tables 1 and 2). Table 1. Criteria evaluations with fuzzy-valued information C1
C2
C3
C4
a1
(3.6, 4, 4.4)
(2.7, 3, 3.3)
(3.6, 4, 4.4)
(3.6, 4, 4.4)
a2
(4.5, 5, 5.5)
(3.6, 4, 4.4)
(2.7, 3, 3.3)
(2.7, 3, 3.3)
a3
(2.7, 3, 3.3)
(3.6, 4, 4.4)
(4.5, 5, 5.5)
(3.6, 4, 4.4)
a4
(3.6, 4, 4.4)
(3.6, 4, 4.4)
(2.7, 3, 3.3)
(2.7, 3, 3.3)
a5
(4.5, 5, 5.5)
(3.6, 4, 4.4)
(4.5, 5, 5.5)
(3.6, 4, 4.4)
622
A. I. Jabbarova and K. I. Jabbarova Table 2. Importance weights of the criteria N
Weights
w1
0.34
w2
0.26
w3
0.2
w4
0.2
4 Solution of the Problem TOPSIS method helps to solve this problem which is described in Sect. 3 [4]. The TOPSIS algorithm consists of five stages. All these stages are listed below: Stage 1: The normalized fuzzy decision matrix (NFDM) is calculated using the following equations (see Table 3):
aij bij cij , ∗ , ∗ and cj∗ = max cij (benefit criteria) r˜ij = ∗ i cj cj cj or
r˜ij =
aj− aj− aj−
, , and aj− = min aij (cost criteria). i cij bij aij
Table 3. The NFDM with fuzzy-valued C1
C2
C3
C4
f1
(0.65, 0.72, 0.8)
(0.61, 0.68, 0.75)
(0.65, 0.72, 0.8)
(0.82, 0.91, 1)
f2
(0.82, 0.91, 1)
(0.82, 0.91, 1)
(0.49, 0.55, 0.6)
(0.61, 0.68, 0.75)
f3
(0.49, 0.55, 0.6)
(0.82, 0.91, 1)
(0.82, 0.91, 1)
(0.82, 0.91, 1)
f4
(0.65, 0.72, 0.8)
(0.82, 0.91, 1)
(0.49, 0.55, 0.6)
(0.61, 0.68, 0.75)
f5
(0.82, 0.91, 1)
(0.82, 0.91, 1)
(0.82, 0.91, 1)
(0.82, 0.91, 1)
Stage 2. The weighted normalized fuzzy decision matrix (WNFDM) is computed. For calculation is used below equation (see Table 4): V˜ = v˜ ij , where v˜ ij = r˜ij × wj . Stage 3. Fuzzy Positive Ideal Solution (FPIS) and Fuzzy Negative Ideal Solution (FNIS) are computed with the following equation (see Table 5).
A∗ = v˜ 1∗ , v˜ 2∗ , . . . , v˜ n∗ , where v˜ j∗ = max vij i
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Table 4. Fuzzy-valued WNFDM C1
C2
C3
C4
a1
(0.22, 0.25, 0.27)
(0.16, 0.18, 0.2)
(0.13, 0.15, 0.16)
(0.16, 0.18, 0.2)
a2
(0.28, 0.31, 0.34)
(0.21, 0.24, 0.26)
(0.1, 0.11, 0.12)
(0.12, 0.14, 0.15)
a3
(0.17, 0.19, 0.2)
(0.21, 0.24, 0.26)
(0.16, 0.18, 0.2)
(0.16, 0.18, 0.2)
a4
(0.22, 0.25, 0.27)
(0.21, 0.24, 0.26)
(0.1, 0.11, 0.12)
(0.12, 0.14, 0.15)
a5
(0.28, 0.31, 0.34)
(0.21, 0.24, 0.26)
(0.16, 0.18, 0.2)
(0.16, 0.18, 0.2)
Table 5. FPIS and FNIS C1
C2
C3
C4
FPIS
(0.28, 0.31, 0.34)
(0.21, 0.24, 0.26)
(0.16, 0.18, 0.2)
(0.16, 0.18, 0.2)
FNIS
(0.17, 0.19, 0.2)
(0.16, 0.18, 0.2)
(0.1, 0.11, 0.12)
(0.12, 0.14, 0.15)
A− = v˜ 1− , v˜ 2− , . . . , v˜ n− where v˜ j− = min vij i
Stage 4. For calculation the distance from each alternative to the FPIS and to the FNIS is used the following equations (Table 6): di∗ =
n n
d v˜ ij , v˜ j∗ , di− = d v˜ ij , v˜ j− j=1
j=1
Table 6. The results of Stage 4. di−
di∗ a1
0.16031
0.142608
a2
0.119008
0.183868
a3
0.123917
0.179959
a3
0.181486
0.121402
a5
0
0.302876
Stage 5. The closeness coefficient CC i for each alternative is computed using below equation as follows (see Table 7): CCi =
di−
di−
+ di+
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A. I. Jabbarova and K. I. Jabbarova Table 7. The results of CCi . CCi a1
0.47078
a2
0.607073
a3
0.590865
a3
0.400815
a5
1
Stage 6. Finally, ranking of the alternative is performed. The obtained result shows that fifth alternative is the best: a5 a2 a3 a1 a4.
5 Conclusion The TOPSIS is an important method for assessing alternatives with respect to criteria of selection in problems of MCDM. Therefore, in this study we use the suggest method to employee selection with fuzzy-valued based information. The obtained results show the validity this approach.
References 1. Sutrisno, S., Sutikno, W.H., Bastari, A., Suharyo, O.S.: Application of fuzzy multiple criteria decision making (MCDM) in selection of prospective employees. J. Anal. Sist. Ris. Operasi. 10(1), 10–16 (2019). https://doi.org/10.37875/asro.v10i1.86 2. Nong, N.-M.T., Ha, D.-S.: Application of MCDM methods to qualified personnel selection in distribution science: case of logistics companies. J. Distrib. Sci. 19–8, 25–35 (2021). https:// doi.org/10.15722/jds.19.8.202108.25 3. Popovi´c, M.: An MCDM approach for personnel selection using the CoCoSo method. J. Process Manag. New Technol. 9(3–4), 78–88 (2021). https://doi.org/10.5937/jouproman210 3078P 4. N˘ad˘aban, S., Dzitac, S., Dzitac, I.: Fuzzy TOPSIS: a general view. Procedia Comput. Sci. 91, 823–831 (2016). https://doi.org/10.1016/j.procs.2016.07.088 5. Chen, C.T.: Extension of the TOPSIS for group decision-making under fuzzy environment. Fuzzy Sets Syst. 114, 1–9 (2000). https://doi.org/10.1016/S0165-0114(97)00377-1 6. Robbi, R. et al.: TOPSIS method application for decision support system in internal control for selecting best employees. J. Phys.: Conf. Ser. 1028(1), 012052 (2018). https://doi.org/10. 1088/1742-6596/1028/1/012052 7. Gardashova, L.A., Salmanov, S.: Using Z-Number-Based Information in Personnel Selection Problem. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 302–307. Springer, Cham (2022). https:// doi.org/10.1007/978-3-030-92127-9_42 8. Huseynov, O.H., Adilova, N.E.: Multi-criterial Optimization Problem for Fuzzy If-Then Rules. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 80–88. Springer, Cham (2021). https://doi.org/ 10.1007/978-3-030-64058-3_10
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9. Nuriyev, A.M.: Fuzzy MCDM models for selection of the tourism development site: the case of Azerbaijan. F1000Research 11(310), 1–24 (2022) https://doi.org/10.12688/f1000research. 109709.1 10. Aliyeva, K.R.: Multi-criteria house buying decision making based on type-2 fuzzy sets. Procedia Comput. Sci. 120, 515–520 (2017). https://doi.org/10.1016/j.procs.2017.11.273 11. Aliyeva, K.: Fuzzy Type-2 Decision Making Method on Project Selection. In: Aliev, R.A., Yusupbekov, N.R., Kacprzyk, J., Pedrycz, W., Sadikoglu, F.M. (eds.) WCIS 2020. AISC, vol. 1323, pp. 180–185. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-68004-6_23
The Use of Fuzzy Numbers for the Rational Choice of the Structure of the Distribution Channel of Goods Alekperov Ramiz Balashirin1,2(B) 1 Department of Computer Engineering, Odlar Yurdu University, Baku AZ1072, Azerbaijan
[email protected] 2 Azerbaijan State Oil and Industry University, Baku AZ1010, Azerbaijan
Abstract. Effective management of the system of distribution channels of goods is impossible without a preliminary analysis and evaluation of other channels of distribution of goods existing today. In this regard, this statement becomes relevant if the system of distribution channels is established by a company that, along with the existing product, wants to put on sale a new product line. When determining and choosing the structure of the distribution channel for goods, it is necessary to take into account a large number of criteria, which are mainly qualitative, have a fuzzy character and are based on the experience and intuition of enterprise managers and employees of the enterprise marketing department. To solve this problem in the article, taking into account the characteristics of a particular product and company, an algorithm is proposed that is based on the use of fuzzy numbers, allowing to take into account the experience and intuition of managers and the management of the enterprise in order to rationally choose the structure of the goods distribution channel. The algorithm is based on determining the distances between fuzzy numbers and their ranking, after which a rational option is selected from the evaluated options that is closest to the real state of the company and product, for which it is required to determine the structure of the distribution channel. Keywords: Fuzzy sets theory · Fuzzy numbers · Marketing activities · Distribution channel of goods · Method for rational choice · Wholesale trade
1 Introduction An industrial, trade or service enterprise forms a complex distribution channel structure to ensure its activities, including, in addition to suppliers and consumers of various levels, a large number of intermediaries, which are divided into trade, institutional, banks, advertising, etc. [1–3]. Effective management of the distribution channel system is impossible without a preliminary audit of existing distribution channels, as a result of which it is possible to get an answer to the question of whether the current distribution strategy really corresponds to the product being sold and the target audience. Also, the audit will determine © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 626–633, 2023. https://doi.org/10.1007/978-3-031-25252-5_82
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the functionality of existing distribution channels, in particular, whether they make it possible to inform the target audience of the true value of the product, while spending a minimum of money. The latter becomes the most relevant if a system of distribution channels is established by a company which, in addition to the existing product, wants to launch a new product line on sale. When determining the structure of the distribution channel of goods, a large number of criteria must be taken into account. General recommendations for channel selection are given in [3]. The analysis of these factors shows that: - Determining the criteria for the structure of the distribution channel of goods is a time-consuming task and the information obtained is incomplete and not entirely accurate. The criteria are mainly qualitative, have a fuzzy character and are mainly based on the experience and intuition of managers and employees of the marketing department of enterprises. But on the other hand, they are usually expressed as a score given by one or more experts. After the score, they are converted into numerical values and aggregated into one numerical indicator, and this overall score is used in the process of ranking alternative choices [3]. In practice, employees of marketing departments and business leaders usually rely on their experience and intuition to determine the channels of distribution of goods. Experts. Based on the foregoing, we have proposed an approach using fuzzy numbers [4–6], which allows you to use the experience and intuition of employees of marketing departments and business leaders in determining the structure of the distribution channel of goods. The work is structured as follows. The introduction substantiates the relevance of the considered problem. Section 2 describes basic concepts such as fuzzy numbers, operations on fuzzy numbers, distances between fuzzy numbers, ranking of fuzzy numbers. Section 3 describes in detail the algorithm for choosing the structure of a product distribution channel using fuzzy numbers. Section 4 gives an example of solving the problem of choosing the structure of a product distribution channel with specific characteristics. The results obtained are described in the conclusion section.
2 Basic Definitions Definition 1. A fuzzy number is a normalized and convex fuzzy set [4, 5] defined on the set of real numbers. R, which membership functions μA (x), where: 1. max μA (x) = 1 fuzzy number normalized; x∈R
2. μA (λx1 + (1 − λ)x2 ) ≥ min(μA (x1 ); μA (x2 )) the number is convex. Definition 2. The value of the membership function of a triangular fuzzy number is (Fig. 1.b), a - the average calculated using the formula μA (x) = max 0; 1 − |x−a| d value of the fuzzy number, d is a value of the spread relative to a. Symmetric triangular fuzzy numbers are denoted as A = (a;d,d) = (a;d). If the values of the spread from the mean value are different, then the following designation is introduced A = (a; d1 , d2 ).
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Fig. 1. Membership function of a triangular fuzzy number.
Definition 3. Basic operations on fuzzy numbers [4, 6]. Let and be fuzzy numbers. For an arbitrary operation, in accordance with the principle of generalization, we have the general formula: C = A ◦ B ⇔ μC (z) = max (μA (x) ∧ μB (y)) x, y z=x◦y
The following formula is used to multiply a fuzzy number by a crisp number: μη·A (y) = max μA (x) = μA (y η) · η > 0. x·y=η.x
(1)
(2)
Definition 4. Distance Between Fuzzy Numbers. There are several methods for calculating the distance between fuzzy numbers: - Voxman’s fuzzy distance measure [7], Fuzzy distance given by Hajjari [8], - Improved centroid distance method [9], - Cheng’s distance method [10], - Fuzzy distance given by Shan-Huo Chen et al. [11], - Fuzzy distance given by Chen and Wang [12], - Fuzzy distance given by Guha and Chakraborty [13], - Sadi-Nezhad et al.’s fuzzy distance measure [14]. In our case, to calculate the distance between fuzzy numbers, we used the method proposed in [15], according to the following formulas: Let A = (a1, a2, a3) and B = (b1, b2, b3) are two triangular fuzzy numbers and distance between A and B is denoted by DistAB where DistAB = (d1, d2, d3). We calculate d1, d2 and d3 as follows: |a1 − b3 |, a2 ≥ b2 , d1 = |b1 − a3 |, a2 < b2 d2 = max{|a2 − b2 |, d1 }, 0 a3 = b3 d3 = { max(b3 − a1 , a3 − b1 )}, a3 = b3
(3)
Definition 5. Ranking of Fuzzy Numbers. The ranking of fuzzy numbers is carried out through the determination of the centers of gravity of these triangles. According to the centroid method [16] and taking into account that normalized triangular numbers are considered a special case of generalized trapezoidal triangular numbers, the center of gravity of a normalized triangular number (Fig. 1) is calculated by the following formula (for a normalized triangular fuzzy number, it is assumed that ω = 1): P(A) =
7ω(2a1 + 14a2 + 2a3 ) 324
(4)
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3 Method for the Rational Choice of the Structure of the Distribution Channel of Goods To implement the proposed method, we propose the following algorithm for choosing a distribution channel for goods according to the characteristics of a particular company and its product (Table 1, column “Product K”): 1. Determining the criteria for choosing a distribution channel for goods (Table 1). The distribution channels of goods are characterized by factors that should take into account the characteristics of the product, the characteristics of the company, to which the product belongs, as well as the characteristics and opportunities for selling goods: – Characteristics of the buyer: C1-Multiple B2B - the principle of reducing the number of contacts plays an important role, C2- High concentration - low costs per contact, C3- Large purchases (B2B, B2G) - the costs of establishing contacts are quickly amortized, C4- Irregular purchases - increased costs for frequent and small purchases, C5- Operational supplies - availability of stocks near points of sale; – Characteristics of the goods: C6- Expendable products - the need for fast delivery, C7Large volumes - minimization of transport operations, C8- Techniques are uncomplicated - low maintenance requirements, C9- Non-standard - the goods must be adapted to specific consumers, 3. Characteristics of the company: C10 - Limited financial resources - marketing costs are proportional to sales volume, C11 - Full range the company can offer a full service, C12 - Good control is desirable - minimizing the number of intermediaries, C13 - Widespread fame - the greatest coverage of consumers. 2. Determination of weight coefficients of criteria for choosing a distribution channel for goods. Using the recommendations of the enterprise managers, the values of the weighting coefficients of the criteria were determined (Table 1 column W). 3. Determination of the membership function of fuzzy numbers, with the help of which the degree of satisfaction with the set selection criteria is evaluated. The desirable (market assessment) features should be considered when evaluating alternative options. The following symmetric fuzzy numbers were used for the market assessment of the criteria for the structures of goods distribution channels (Table 1): Low compatibility (LC), where LC = LS = (0.3;0.1,0.1) = (0.3;0.1), Average compatibility (AC): AC = S = (0.5; 0.2, 0.2) = (0.5; 0.2), Very compatibility (VC) VC = VS = (0.8;0.2,0.2) = (0.8;0.2), respectively, with the following membership functions: |x − 0.3| |x − 0.5| , μAC (x) = max 0; 1 − μLC (x) = max 0; 1 − 0.1 0.2 |x − 0.8| , μVC (x) = max 0; 1 − 0.2
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4. A preliminary weighted assessment of ideal options for alternatives is being carried out - the structure of distribution channels for goods, the results of which are fuzzy numbers Rj , j = 1, n, where n is the number of options for the structure of goods distribution channels.
Table 1. Choosing a distribution channel for goods Criteria of choice. opportunistic assessment of criteria (C)
Customer characteristics C1
Product characteristics
Firm characteristics
Criteria weight (W)
Alternative options for the structure of the distribution channel of goods
Characteristics of a particular product and company regarding features to consider when choosing
Direct channel
Short indirect channel
Long indirect channel
V1
V2
V3
Product K
C1
0.05
LC
AC
VC
S
C2
0.07
AC
VC
LC
S
C3
0.07
VC
AC
AC
LS
C4
0.05
LC
AC
VC
VS
C5
0.03
LC
AC
VC
VS
C6
0.1
LC
AC
VC
LS
C7
0.09
VC
AC
LC
LS
C8
0.1
LC
AC
VC
VS
C9
0.07
VC
AC
LC
VS
C10
0.1
LC
AC
VC
VS
C11
0.05
VC
AC
LC
S
C12
0.1
VC
AC
LC
LS
C13
0.12
LC
AC
VC
LS
Let there be a set of goods distribution channel structure V = {v1 , v2 , . . . , v n } and a set of criteria C = {C1 , ..., Cn }. At the same time, the assessment of the j-th alternative by the i-th criterion is represented by a fuzzy number Rij , and the relative importance of the criterion is determined by the coefficient of importance - ωi (weight coefficients), which can be either a fuzzy number or an ordinary clear number. The weighted estimate of the -th alternative is calculated by the formula: Rj =
n i=1
ωi Rij
(5)
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5. A weighted assessment is carried out for the proposed product variant, the results of which are a fuzzy number K. The fuzzy number K is determined, also according to formula 5. 6. It is calculated the distance (Definition 4) between fuzzy numbers K and Rj , j = 1, n, whose results are fuzzy distances, in the form of fuzzy numbers Dist(K)i , i = 1, n. 7. The ranking of fuzzy numbers Dist(K)i is carried out; for this, their centers of gravity are determined (Definition 5). 8. As a rational option, Dist(K)i , i = 1, n, with the smallest value, is chosen.
4 An Example for the Rational Choice of the Structure of the Distribution Channel for the Company’s Product with Certain Characteristics Using the data given in Table 1 and taking into account the characteristics of a particular product and company (the last column of Table 1, option K), according to the algorithm proposed above, we will make a rational choice of the distribution channel structure. In accordance with step 5 of the proposed algorithm, to begin with, it is necessary to carry out a weighted assessment of alternatives, due to the market assessment of the criteria. According to formula 5 and based on the rules of fuzzy number arithmetic [17–21], we have for the structure of the direct channel for the distribution of goods: RV1 = ω1 ∗ LC + ω2 ∗ AC + ω3 ∗ VC+ω4 ∗ LC + ω5 ∗ LC + ω6 ∗ LC + ω7 ∗ VC + ω8 ∗ LC + ω9 ∗ VC + ω10 ∗ LC + ω11 ∗ VC + ω12 ∗ VC + ω13 ∗ LC = 0.05 ∗ (0.3; 0.1) + 0.07 ∗ (0.5; 0.2) + 0.07 ∗ (0.8; 0.2) + 0.05 ∗ (0.3; 0.1) + 0.03 ∗ (0.3; 0.1) + 0.1 ∗ (0.3; 0.1) + 0.09 ∗ (0.8; 0.2) + 0.1 ∗ (0.3; 0.1) + 0.07 ∗ (0.8; 0.2) + 0.1 ∗ (0.3; 0.1) + 0.05 ∗ (0.8; 0.2) + 0.1 ∗ (0.8; 0.2) + 0.12 ∗ (0.3; 0.1)) = (0.015; 0.005) + (0.035; 0.014) + (0.056; 0.014) + (0.015; 0.005) + (009; 0.003) + (0.03; 0.01)+ (0.072; 0.018) + (0.03; 0.01) + (0.05 + 0.014) + (0.03; 0.01) + 0.04; 0.01) + 0.08; 0.02) + 0.036; 0.012) = (0.504; 0.145). RV2 = (0.521; 0.2) and RV3 = (0.589; 0.162). Are defined similarly. A weighted estimate is also made for RK = (0.509; 0.152). RK = (0.509; 0.152). Furthermore, according to definition 4, the distance between K and alternative variants of the distribution channel structure for the product is calculated. As a result, we obtain the following fuzzy distances: Dist(K)v1 = (0.292, 0, 292, 0.302); Dist(K)v2 = (0.34, 0, 34, 0.364); Dist(K)v3 = (0.234, 0, 234, 0.394).
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We carry out the ranking of the calculated fuzzy distance numbers. To do this, we use step 6 of the proposed algorithm and obtain the following results: Pv1 = 0.113987654320988; Pv2 = 0.133259259259259; Pv3 = 0.0979135802469136; We rank distance fuzzy numbers: Pv3 < Pv1 < Pv2 . V3 is chosen as the best option, the structure is the long indirect distribution channel of goods, which is the smallest among them and closest in distance to K, for which you want to select a distribution channel.
5 Conclusion The analysis of the obtained results shows that due to the fact that the company - the owner of the product K will conduct numerous B2B, there are low costs for 1 contact with customers, the product is sold irregularly. There are stocks near the points of sale, and the company has little fame and limited financial resources. It would be better to attract other distributors (provide the opportunity to sell goods for sale) to improve the sale of goods. This method is very simple and effective in which considers the experience and intuition of marketing managers when evaluating alternative choices, as opposed to a simple scoring. The further research to solve this problem is proposed to be carried out to consider all options for the distribution channels of goods, for example, it is necessary to consider criteria for e-commerce, etc. This method can be used by marketing departments of retailers and wholesalers.
References 1. Nepomnyashchiy, E.G.: Economics and Business Management. TSURE Publishing House, Taganrog (1999) (in Russian) 2. Alesinskaya, T.V.: Fundamentals of Logistics. Functional Areas of Logistics Management Part 3: Publishing House of TTI SFU, Taganrog, p. 116 (2010). (in Russian) 3. Shishlo, S.V.: Distribution of Goods. BSTU, p. 115, Minsk (2014). (in Russian) 4. Zadeh, L., Aliev, R.A.: Fuzzy Logic Theory and Applications: Part I and Part II. World Scientific Publishing Company (2018) 5. Hanss, M.: Applied Fuzzy Arithmetic: An Introduction with Engineering Applications. Springer, Berlin (2005) 6. Ramiz, A.: The Method of Ranking Business Processes on Weaknesses Based on the Theory of Fuzzy Sets. In: Kahraman, C., Tolga, A.C., Cevik Onar, S., Cebi, S., Oztaysi, B., Sari, I.U. (eds) Intelligent and Fuzzy Systems. INFUS 2022. Lecture Notes in Networks and Systems, vol 504. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-09173-5_17 7. Voxman, W.: Some remarks on distances between fuzzy numbers. Fuzzy Sets Syst. 100, 353–365 (1998) 8. Hajjari, T.: New Approach for Distance Measure of Fuzzy Numbers. In: International Conference on Operations Research and Optimization, IPM, Tehran, Iran (2011) 9. Abbasbandy, S., Hajjari, T.: An improvement for ranking fuzzy numbers, J. Sci. I.A.U (JSIAU) 20(78/2) (2011) 10. Cheng, C.H.: A new approach for ranking fuzzy numbers by distance method. Fuzzy Sets Syst. 95, 307–317 (1998)
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11. Chen, Sh.-H., Wang, Ch.-Ch.: Fuzzy distance Using Fuzzy Absolute Value. In: Proceeding of the eighth International Conference on Machine Learning and Cybernetics, Baoding, pp. 12– 15 (2007) 12. Chen, Sh.-H., Wang, Ch.-Ch.: Fuzzy distance of trapezoidal fuzzy numbers. In: Proceeding of International Conference on Machine Learning and Cyberneting (2007) 13. Guha, D., Chakraborty, D.: A new approach to fuzzy distance measure and similarity measure between two generalized fuzzy numbers. Appl. Soft Comput. 10, 90–99 (2010) 14. Sadi-Nezhad, S., Noroozi, A., Makui, A.: Fuzzy distance of triangular fuzzy numbers. J. Intell. Fuzzy Syst. 25(4), 845–852 (2012) 15. Alibeigi, M., Hajjari, T., Khani. E.G.: A new index for fuzzy distance measure. Appl. Math. Inform. Sci. 9(6), 3017–30253025 (2015) 16. Rao, P.P.B.: Ranking generalized fuzzy numbers using area, mode, spreads and weight /P.P.B. Rao, N.R. Shankar. Int. J. Appl. Sci. Eng. 10(1), 41–57 (2012) 17. Gardashova, L.A., Allahverdiyev, R.A., Saner, T., Eyupoglu, S.Z.: Analysis of the job satisfaction index problem by using fuzzy inference. Procedia Comput. Sci. 102, 45–50 (2016). https://doi.org/10.1016/j.procs.2016.09.368 18. Adilova, N.E.: Consistency of Fuzzy If-Then Rules for Control System. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 137–142. Springer, Cham (2020). https://doi.org/10.1007/978-3030-35249-3_17 19. Huseynov, O.H., Adilova, N.E.: Multi-criterial Optimization Problem for Fuzzy If-Then Rules. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 80–88. Springer, Cham (2021). https://doi.org/ 10.1007/978-3-030-64058-3_10 20. Aliev, R.A., Pedrycz, W., Fazlollahi, B., Alizadeh, A.V., Guirimov, B.G., Huseynov, O.H.: Fuzzy logic-based generalized decision theory with imperfect information. Inform. Sci., Elsevier 189, 18–42 (2012) https://www.sciencedirect.com/science/article/abs/pii/S00200255110 06128 21. Aliev, R.A., Huseynov, O.H.: Decision Theory with Imperfect Information, p. 444, World Scientific, Singapore (2014). https://www.worldscientific.com/worldscibooks. https://doi. org/10.1142/9186
“Dede Korkud” Epos in Light of Fuzzy Logic Kamal Abdulla1
and Rafik A. Aliev2,3(B)
1 Azerbaijan University of Languages, 134 Rashid Behbudov Street, Baku, Azerbaijan
[email protected]
2 Georgia State University, Georgia, USA
[email protected] 3 State Oil and Industry University, 34 Azadlig Ave, 1010 Baku, Azerbaijan
Abstract. Fuzzy thinking got accumulated in a scientific line called “fuzzy logic” and has actually been formed as an extension of Aristotle’s formal logic that had governed our consciousness until then. This logic is a mode of thinking far beyond the categoricalness, and close to both the human being and his/her principles of the realization and acknowledgement of the world. Natural languages offer ways to express uncertainty in deep knowledge in texts expressed by linguistic terms characterized as fuzzy concept. In this paper fuzzy uncertainties detection in the text of “Dede-Korkud” epos is investigated. Keywords: Fuzzy Logic · Main Facets of Fuzzy Logic · Fuzzy Sets · “Dede-Korkud” text
1 About Fuzzy Logic Facets [1, 2] There are four reliable facets in the fuzzy logic theory: 1) the logical facet; 2) the fuzzy-set-theoretic facet; 3) the epistemic facet 4) the relational facet. These facets shape fuzzy thinking preceding from the system of various relations. The logical facet is a generalized form of multivalued logic. It spans a bridge between “true” and “false”, “the earth” and “the sky”. The law of excluded middle (or third) in classic logic does not work in this facet. The law of the excluded third suggests that there can be no interim case between two opposing poles. However, the formal logic (Aristotle’s logic) stating that there is only a gap between “either… or” does not often turn up to be true. The main aim of the fuzzy-set-theoretic facet of the fuzzy logic is that everything, every phenomenon in the world except the God has a degree. If we view a fuzzy set, then all the elements in the universium have a belonging, degree of membership to this set. The epistemic facet of fuzzy logic is associated with the description of the knowledge introduced in the texts, the semantics of natural language, the analysis of the information in the texts. Fuzzy epistemology facilitates to define (to drive away) the complexity, uncertainty (the cloud) in the text. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 634–636, 2023. https://doi.org/10.1007/978-3-031-25252-5_83
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The fourth facet of fuzzy logic is the facet of fuzzy relations. This incorporates fuzzy relations, more precisely, the fuzzy interdependence of cause and effect. Fuzzy phrases (variables) and the relations based on the scheme “If…, then…” built on their grounds comprise the basics of this facet.
2 Evaluating Fuzzy Uncertainties in “Dede-korkud” Text This paper embodies a systematic view of the world of “Dede Korkut” in the light of the theory of fuzzy logic. Thus, we happen to learn the efficacy, effectiveness of the mechanism of transition from fuzzy theory to a certain literary-artistic text (in our case, the text of “The Book of Dede Korkut”) [3–5]. The text of “Dede Korkut” states that “in those times” the heroes of the Oghuz would sleep seven days and seven nights when they fell asleep, and meanwhile, by no means it was possible to wake the Oghuz hero up. Salur Kazan and Kanturali “experience” such a state. This state was called “a tiny death”. That is neither a genuine life nor a genuine death. Yet the reality inbetween should be named. The name is: “the tiniest death!” This name is approved by modern medicine too. The scientific name of that state is “coma”. Again fuzzy logic, the uselessness of the law of excluded third. It is sometimes easy and sometimes difficult to define the degrees between an ordinary state and maximal state. For instance, there is a desire to generate a vision of a big, very big ship through some phrase. The language potential of the text allows to describe it as follows. The text would say, “The water making the big wooden ships dance”. However, the ship in the vision is not merely big. ˙It is unconvincingly big. Therefore, we read in the text, “the water making big-big wooden ships dance”. The phrase “bigbig” is an effort here to imagine the enormous size of bigness. This is where fuzzy logic starts. The bright example related to the third epistemological facet of fuzzy logic in the text of “The Book of Dede Korkut” is the situation encountered by Salur Kazan and his team while hunting. Salur Kazan goes hunting with a small group of his people taking his son Uruz with him in order to familiarize him with the sites where he displayed his feat as a knight. The spy of the infidel spies it, and thus, Salur Kazan is assaulted by his enemy’s army of 16 thousand men. The text reads, “Sixteen thousand infidels adorned in black mounted their horses. They assaulted Kazan. They watched and noticed (those who watched and noticed were Salur Kazan and his people) that six big dusts landed. Someone uttered: it is the dust of wild animals. Someone said: it is the dust of an enemy. Kazan uttered: “If it were wild animals, it could consist of one or two parts. You should know that this is the foe coming.” Kazan does not see the foe, as there is a cloud of dust all over. Based on his previous experience, Salur Kazan guesses that by the sign of the cloud of dust – the parts of dust being more than two. In a fuzzy mode Kazan “estimates” a foe – an image he has never seen, but imagined. ˙It so happens that one of the infidels reveals the information the author tries “to conceal”.
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We often encounter the mode of expression formed on the basis of “If… Then…” scheme and transfirmed to a sentence structure in the epos “The Book of Dede Korkut”. There are even such structures which are in the shape aleniated from the initial scheme. As if these structures had been exposed to “harakiri”. Let us focus on such an example: “In those days sons would not go against their fathers’ word. If he had, no one would look at that son’s face.” There is no doubt that the scheme “if…, then…” stands in the substructure of the mode of thinking which generated this sentence. If we are willing to bring the sentence to its initial substructure, we need to expose it to some “operation”. Following “the operation”, the sentence would acquire such a state: “If in those days the sons went against their fathers’ word, then that son would be disrespected.” This substructural variant is easier, more favorable, whereas there is no doubt that the latest variant has been through some literary adornment.
3 Conclusion “The unfolding” of the concealed layers of the epos “Dede Korkut” in the light of fuzzy logic originates it to the earlier periods of the awakening of artistic mindset. Antiquity, particularly, the prehistoric mythological antiquity is visually animated before our eyes. We can build the most necessary generalization as follows. ˙In “The Book of Dede Korkut” a democratic way of thinking may have found its manifestation in our ancestor’s mind which must have been represented unconsciously and that can be considered deep moral-ideological foundations of fuzzy logic. This way of thinking is not a coincidence, it regulates our ancestor’s behaviour peculiar to him since the antiquities, his attitude to himself and his surroundings, and as a whole it displays clearly the formation of our nation as a tolerant, loyal nation which cherishes a love within herself towards the surroundings. The application of fuzzy logic to our key book “The Book of Dede Korkut” has been providing this knowledge in initial approach.
References 1. Zadeh, L.A.: Is there a need for fuzzy logic? Inform. Sci. 178, 2751–2779 (2008). https://doi. org/10.1016/j.ins.2008.02.012 2. Zadeh, L.A., Aliev, R.A.: Fuzzy logic Theory and Applications. Part I and Part II. World Sci., Singapore, 610 p. (2018) 3. Abdulla, K.: Introduction to “Dede-Korkud Book” poetics. Baku, RS Poliqraf (in Azerb.), 320 p. (2017) 4. Abdulla, K.: From myth to writing. Baku, Mutarjim (in Azerb.), 370 p. (2009) 5. Arasli, H., Tahmasib, M. (eds.): “Dede-Korkud Book”. Baku, Azerneshr (in Azerb.), (1962)
Toward Z-Number-Based Classification of Dataset R. R. Aliyev1
, O. H. Huseynov2(B)
, and Babek Guirimov3
1 Department of Mathematics, Eastern Mediterranean University, Turkish Republic of Northern
Cyprus, Via Mersin 10, Gazima˘gusa, Turkey [email protected] 2 Research Laboratory of Intelligent Control and Decision Making Systems in Industry and Economics, Azerbaijan State Oil and Industry University, 20 Azadlig , 1010 Baku, Azerbaijan [email protected] 3 State Oil Company of Azerbaijan Republic, SOCAR, SOCAR Tower, 121, H. Aliyev, 1029 Baku, Azerbaijan
Abstract. Nowadays, a lot of classification techniques including probabilistic and fuzzy methods exist. The works devoted to dealing with fusion of probabilistic and fuzzy uncertainties of information are scarce. In view of this, partial reliability of information that stems from uncertainty and complexity of real datasets is of interest. Prof. Zadeh introduced a concept of Z-number to describe reliability of information under fuzziness and probabilistic uncertainty. In this work, an approach to Z-number-valued classification of dataset is outlined. The is aim is to describe partial reliability of knowledge expressed by classification. A benchmark data set is used is considered to illustrate the proposed approach. Keywords: Fuzzy set · Z-number · Classification · Clustering · Reliability
1 Introduction Classification is a one of the main data mining problems. It concerns building a model that describe relationship between data attributes vector (x) and class labels (y). When class labels are unknow, one deals with clustering – unsupervised classification method. A series of traditional, advanced fuzzy and probabilistic classification methods exist [1–3]. Traditional classification generates partition of data into mutually exclusive groups. In fuzzy classification, degrees of membership to several classes are determined. In probabilistic methods, values of probability of belonging to existing classes are computed. In [4], they propose a novel probabilistic approach to dynamic clustering. A method based on probabilistic distributions of attributes values is proposed in [5]. An improvement of probabilistic method is proposed in [6]. The authors introduce a probability density function-based distance measure. Multivariate normal and Student-t distributions are considered.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 637–644, 2023. https://doi.org/10.1007/978-3-031-25252-5_84
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In the field of fuzzy clustering, type-1, type-2 and intuitionistic fuzzy methods exist [7–13]. A novel robust fuzzy method for partitioning imprecise data is introduced in [14]. The method is based on Huber’s M-estimators and Yager’s OWA operators. A comparative analysis shows its performance over other robust fuzzy classification methods [15] is devoted to combination of objective function used in k-means and fuzzy c-means methods to choose an optimal level of fuzziness of the class. The authors also improve segregation ability of clustering by formulating a penalty problem. The algorithm is adjusted to reach a global optimum of clustering problem. In [16], they propose human meta-cognitive learning principles-based fuzzy C-means (FCM) method. Advantages of the method as compared to existing approaches are illustrated in several benchmark problems and a real-world application. Self-organizing maps-based interval type-2 fuzzy method is proposed in [11]. Several works are devoted to fusion of fuzzy and probabilistic methods [3, 17–21]. In [17] fuzzy and probabilistic methods are applied to huge data sets. In [3], entropy measure introduced by Renyi is used to analyze similar features of fuzzy and probabilistic methods of clustering. Fuzzy clustering on the basis of Gaussian probability distributions is considered in [18]. The authors claim that this approach outperforms FCM. A novel method for comparison of soft classification methods, based on application of Earth Mover’s distance measure and ordered weighted average is suggested in [19]. A thorough analysis of semi-supervised hard and soft classification algorithms is done in [20]. A method that integrates fuzzy, probabilistic, and collaborative classification [22] is proposed in [21] to partitioning of mixed data vectors. Nowadays, a series of works on the use of fuzzy and probabilistic methods exist [23–26]. In order to describe partial reliability of information, Prof. Zadeh introduced a concept of Z-number, Z = (A, B) [27]. The component A is a restriction on the values of a real-valued random variable X. The component B is a measure of reliability of A. Both A and B are typically represented by fuzzy numbers. The concept of Z-number [28–30] provides an intuitive basis for summarization of data sets characterized by combination of probabilistic and fuzzy uncertainties. In [30] an approach to data partitioning in form of Z-number-based clusters is proposed. In this paper, we use this approach for description of data sets by using Z-numbers.
2 Statement of Problem Consider a problem of partitioning dataset X = {x1 , ..., xN } ⊂ RD into Z-number valued parts Zj = Aj , Bj , j = 1, ..., C. We propose to consider this problem as an optimization problem with two objectives. A compound objective function J = Jm , Jp is used as a combination of fuzzy C-means objective function Jm and the probabilistic clustering objective function Jp . The main challenge is related to handling imprecision related to true probabilities of membership pj (xi ), xi ∈ X. This requires to consider Jp in a generalized form as a parametric family of Jp = Jp (m2 ), where the range of m2 is represented as a fuzzy set with membership function µm˜ 2 . In view of this, the construction of Z-number-valued classes Zj , j = 1, ..., C may be described as follows [30]:
Toward Z-Number-Based Classification of Dataset
J = Jm , Jp = ⎛
639
⎞
⎟ ⎜ ⎟ ⎜ N C N C ⎟ ⎜ m1 2 m ˜2 xi − vj ⎟ → min xi − vj , =⎜ u ⊗ p ij ij ⎟ ⎜ ⎟ ⎜ i=1 j=1 ⎠ ⎝ ⊕ ⊕ i=1 j=1
(1)
s.t. uij =
xi −vj
C k=1
pij =
1
xi −vj
k=1
2 m1 −1
(2)
xi −vk
C
C
1
1 m ˜ 2 −1
(3)
xi −vk
pij = 1, i = 1, ..., N
(4)
j=1
pij ≥ 0
(5)
vj ∈ X is a center of j-th Z-class, uij = uj (xi ) is a degree of membership of i-th data point to the j-th fuzzy class, pij = pj (xi ) is a probability that i-th data point belongs to the j-th probabilistic class. m1 is a numerical fuzzifier used to obtain fuzzy classes, and m ˜ 2 is a fuzzy number used to obtain a fuzzy set of probability distributions. The objective function (1) is used to compound fuzzy partition Jm and probabilistic partition [4] Jp criteria for construction of Z-classes. Jm is based on the use of squared Euclidean distance, Jp is based on normal Euclidean distance [9]. Decision variables are ˜ 2 the solution to (1)–(5) is represented by a set of pairs uij and pij . For fixed m2 ∈ m uij , pij , j = 1, . . . , C. A family of problems (1)–(5) is induced by a fuzzy set m ˜ 2 . The solution that corresponds to this family is represented as bimodal membership degrees: (uij , {(µpj (pj (xi ))/pj (xi ))|xi ∈ X}), j = 1, ..., C, Fuzzy restriction µpj is induced by µm˜ 2 : µpij (pij ) = sup µm˜ 2 (m2 ), m2
where pij is a solution to (1)-(5) for m2 ∈ m ˜ 2. In what follows, we present the solution procedures for the considered problem.
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3 Solution Approach Z-number-valued classes are formed by using probability measure of fuzzy sets. The first part, A, of a Z-number-valued class is obtained by using FCM method. The B part of a Z-number-valued class, is obtained as a fuzzy restriction imposed on a value the probability measure of A. The of the solution procedures are as follows. stages Stage 1. A set of pairs uij , pij , j = 1, . . . , C are obtained by solving problem (1)– ˜ 2 . Given pj (xi ), probabilities pj (xi ) of membership of different points (5) for each m2 ∈ m xi , i = 1, ..., N to j-th class are found: pj (xi ) =
pj (xi ) , xi ∈ X N pj (xi )
(6)
i=1
This results in condition
N i=1
pj (xi ) = 1.
Thus, a bimodal distribution (µAj , pj ), is obtained, where µAj (xi ) = uij and pj (xi ) is defined by (6), i = 1,…, N. Stage 2. Fuzzy restriction µpj over distributions pj is computed: µpj (pj ) =
min µpj (pj (xi )) sup {(pj (x1 ),...,pj (xN ))} i=1,...,N
(7)
subject to (6). Thus, Z-number-valued classes (µAj , µpj ) are obtained. Stage 1. Projections of (µAj , µpj ) on the axes of D-dimensional space, (µAd ,j , µp ) d ,j are obtained. µAd ,j is obtained as usual. µd ,pj is built as follows µp (pd ,j ) = µpj (pj )
(8)
d ,j
pd ,j (xi,d ) =
xi,1 ,...,xi,d −1 ,xi,d +1 ,...,xi,D
pj (xi ),
(9)
where xi = (xi,1 , ..., xi,d , ..., xi,D ) Stage 4. Fuzzy reliability Bd ,j on the basis of µAd ,j and µp is obtained: d ,j
µBd ,j (bd ,j ) =
sup min µp (pd ,j ) d ,j pd ,j
(10)
s.t. bd ,j =
N
µAd ,j (xd ,i )pd ,j (xd ,i )
(11)
i=1
where bd ,j is a value of probability measure of Ad ,j computed on the basis of one possible probability distribution pd ,j . Thus, Z-numbers Zd ,j = (Ad ,j , Bd ,j ), j = 1, ..., C are obtained for each dimension d = 1, ..., D. To solve problem (1)–(5), we propose to apply the Differential Evolution Optimization.
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4 An Application Consider a dataset on Parkinson’s disease (available at https://archive.ics.uci.edu/ml/ machine-learning-databases/parkinsons/). The attributes of data are 22 sound-based characteristics of patients. Two classes exist: the patients having the disease (class label value “1”) and healthy patients (class label value “0”) There are 147 data lines with status = “1” and 48 lines with status = “0”. Consider Z-number-based partitioning of the data to two groups. At first, the values ˜ 2 (Fig. 1) and the number of ofm1 = 2, m C = 2 are set. Next, optimization clusters problem (1)–(5) was solved and degrees ui , pij,k , j = 1, 2 are computed. The centers vj of the clusters are shown in Table 1.
1 0.8 0.6 0.4 0.2 0
0
1
2
3
4
5
Fig. 1. Fuzzifier m ˜ 2.
Table 1. The clusters (classes) centers Characteristics
1
2
…
17
…
23
v1
140
183
…
1
…
0.24
v2
178
213
…
0
…
0.13
) are obtained based on degrees Further, bimodal distributions (µAj , pj,k ui , pij,k , j = 1, 2, k = 1, ..., K. Soft restriction µpj over possible distributions pj,k is obtained by using (7). Thus, Z-number-valued clusters (µAj , µpj ) are formed. Projections (µAd ,j , µd ,pj ), d = 1, ..., 23 are obtained by using (8)-(9). Finally, Z-numbers Zd ,j = (Ad ,j , Bd ,j ), d = 1, ..., 23, j = 1, 2 are derived. The results for dimension d = 17 of the clusters are shown in Figs. 2 and 3. Let us compare these results with those obtained by FCM by using rate of true classification (RT). The number of classes (clusters) is 2: the class of patients with disease (attribute #17 is equal to 1), and the class of healthy patients (attribute #17 is equal to 0). The results are shown in Table 2. Thus, Z-number-valued clustering attains better classification rate and provides information about reliability of the results.
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0.2
0.4
0.6
0.8
1
0.79
0.8
0.81
(a) 1 0.8 0.6 0.4 0.2 0 0.76
0.77
0.78 (b)
Fig. 2. Z-number Zd =17,j=1 = (Ad =17,j=1 , Bd =17,j=1 ) as cluster 1 projection on dimension 17: (a) Ad =17,j=1 , (b) Bd =17,j=1
1 0.8 0.6 0.4 0.2 0 0
0.2
0.4
0.6
0.8
1
(a) 1 0.5 0 0.76
0.77
0.78
0.79
0.8
0.81
(b)
Fig. 3. Z-number Zd =17,j=2 = (Ad =17,j=2 , Bd =17,j=2 ) as cluster 2 projection on dimension 17: (a) Ad =17,j=2 , (b) Bd =17,j=2
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Table 2. Comparison Of FCM and the proposed method on the disease data Algorithm
Number of true classifications
Number of false classifications
RT
FCM
188
7
96.4%
Proposed method
195
0
100%
References 1. Gosain, A., Dahiya, S.: Performance analysis of various fuzzy clustering algorithms: a review. Procedia Comput. Sci. 79, 100–111 (2016). https://doi.org/10.1016/j.procs.2016.03.014 2. Pedrycz, W.: Fuzzy equalization in the construction of fuzzy sets. Fuzzy Sets Syst. 119(2), 329–335 (2001). https://doi.org/10.1016/S0165-0114(99)00135-9 3. Wang, S.T., Chung, K.F., Shen, H.B., Zhu, R.Q.: Note on the relationship between probabilistic and fuzzy clustering. Soft. Comput. 8, 523–526 (2004). https://doi.org/10.1007/s00500-0030309-8 4. Ben-Israel, A., Iyigun, C.: Probabilistic d-Clustering. J Class, 25, Article no. 5, https://doi. org/10.1007/s00357-008-9002-z 5. Bakhtiarifar, M.H., Bashiri, M.: A probabilistic clustering method for data elements with normal distributed attributes. Commun. Stat. Simul. C. 46(4), 2563–2575 (2017) 6. Rainey, C., Tortora, C., Palumbo, F.: A Parametric Version of Probabilistic Distance Clustering. In: . Greselin, F., Deldossi, L., Bagnato, L., Vichi, M., (eds.) Studies in Classification, Data Analysis, and Knowledge Organization, F Statistical Learning of Complex Data, pp, 33–43 .Springer, Cham (2017) 7. Patel Bhaskar, N., Prajapati Satish, G., Lakhtaria Kamaljit, I.: Efficient classification of data using decision tree. Bonfring Int. J. Data Mining 2(1), 6–12 (2012) 8. Kaur, P., Soni, A.K., Gosain, A.: Robust Intuitionistic Fuzzy C-means clustering for linearly and nonlinearly separable data. IEEE Image Proc., 1–6 (2011) 9. Aliev, R.A., et al.: Type-2 fuzzy neural networks with fuzzy clustering and differential evolution optimization. Inform. Sci. 181, 1591–1608 (2011) 10. Golsefid, S.M.M., Zarandi, M.H.F., Turksen, I.B.: Multi-central general type-2 fuzzy clustering approach for pattern recognitions. Inform. Sci. 328, 172–188 (2016) 11. Comas, D.S., Pastore, J.I., Bouchet, A., Ballarin, V.L., Meschino, G.J.: Interpretable interval type-2 fuzzy predicates for data clustering: A new automatic generation method based on self-organizing maps. Knowl. Syst. 133, 234–254 (2017) 12. Chaira, T.: A novel intuitionistic fuzzy c means clustering algorithm and its application to medical images. Appl. Soft Comput. 11, 1711–1717 (2011) 13. Zhang, H.M., Xu, Z.S., Chen, Q.: On clustering approach to intuitionistic fuzzy sets. Cont. Decis. 22(8), 882–888 (2007) 14. Pierpaolo, D., Jacek, M.L.: Fuzzy clustering of fuzzy data based on robust lost functions and ordered weighted averaging. Fuzzy Sets Syts. 389, 1–280 (2019) 15. Tong, W., Yican, Z., Yanni, X., Deanna, N., Feiping, N.: Modified fuzzy clustering with segregated class centroids. Neurocomputing 361, 10–18 (2019) 16. Kumar, S.V.A., Harish, B.S., Mahanand, B.S., Sundararajan, N.: An efficient Meta-cognitive fuzzy C-Means clustering approach. Appl. Soft Comput. 85,(2019) 17. Hathaway, R.J., Bezdek, J.C.: Extending fuzzy and probabilistic clustering to very large data sets. Comput. Stat. Data An. 51(1), 215–234 (2006) 18. Nefti, S., Oussalah, M.: Probabilistic-fuzzy clustering algorithm. IEEE Syst., Man Cyber. 4786–4791 (2004)
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19. Anderson, D.T., Zare, A., Price, S.: Comparing fuzzy, probabilistic and possibilistic partitions using the earth mover’s distance. IEEE Trans. Fuzzy Syst. 21(4), 766–775 (2013) 20. Miyamoto, S., Obara, N.: Algorithms of crisp, fuzzy, and probabilistic clustering with semisupervision or pairwise constraints. IIEEE Int. C. Granular Comput. 225–230 (2013) 21. Pathak, A., Pal, N.R.: Clustering of mixed data by integrating fuzzy, probabilistic, and collaborative clustering framework. Int. J. Fuzzy Syst. 18(3), 339–348 (2016). https://doi.org/ 10.1007/s40815-016-0168-y 22. Pedrycz, W.: Collaborative fuzzy clustering. Pattern Recogn. Lett. 23(14), 1675–1686 (2002) 23. Gardashova, L.A., Allahverdiyev, R.A., Saner, T., Eyupoglu, S.Z.: Analysis of the job satisfaction index problem by using fuzzy inference. Proc. Comput. Sci. 102, 45–50 (2016). https://doi.org/10.1016/j.procs.2016.09.368 24. Mirzakhanov Vugar E.,. Gardashova Latafat A.: Modification of the Wu-Mendel approach for linguistic summarization using IF-THEN rules. J. Experim. Theoret. Artifi. Intell. 77– 97(2019).https://doi.org/10.1080/0952813X.2018.1518998 25. Mirzakhanov V., Gardashova L.: Wu–Mendel approach for linguistic summarization: practical considerations and solutions. In: 2019 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), pp. 1–8.( 2019). https://doi.org/10.1109/FUZZ-IEEE.2019.885899850 26. Ahmadov, S.A., Gardashova, L.A.: Fuzzy dynamic programming approach to multistage control of flash evaporator system. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Mo., Jamshidi, Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 101–105. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-35249-3_12 27. Zadeh, L.A.: A note on Z-numbers. Inform. Sciences 181, 2923–2932 (2010) 28. Gardashova, L.A.: Application of operational approaches to solving decision making problem using Z-numbers. J. Appli. Mathem. 5(9), 1323–1334 (2014). https://doi.org/10.4236/am. 2014.59125 29. Aliev, R.A., Huseynov, O.H., Aliyev, R.R., Alizadeh, A.V.: The Arithmetic of Z-numbers. World Scientific, Theory and Applications. Singapore (2015) 30. Guirimov, B.G., Huseynov, O.H.: A new compound function-based Z-number valued clustering. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Mo., Jamshidi, Sadikoglu, F.M. (eds.) ICAFS 2018. AISC, vol. 896, pp. 840–847. Springer, Cham (2019). https://doi.org/10.1007/978-3030-04164-9_110
Application of Enterprise Solution Software for a Hotel Chain Serdar Oktay(B) University of Kyrenia, 99320 Kyrenia, Cyprus [email protected]
Abstract. International hotel chains include a large number of hotels. A hotel chain manages many hotels in different locations. Some hotels are managed by the franchising method. Other hotels are managed by themselves. The franchising agreement contains the rules to be followed by the hotel. By implementing these rules, hotels use the brand of the hotel chain. In the other model, the hotel company buys or rents a hotel, and manages the hotel with its own staff. This model is called management. In both methods, the head office of the hotel chain aims to maintain the profitability and reliability of its own brand by monitoring all hotels in its structure in a very serious manner. This study attempts to find out how “Enterprise Solution Software” contributes to international hotel chains. As a result of the study, it was revealed that for more than one reason, hotel chains use the same software in all hotels. It was determined that they could reach their management strategies and profitability goals easily through the common software. Keywords: Lodging software · Hotel Management · Chain hotels · Hospitality · Enterprise solution
1 Introduction Market share for international chain hotels; Global hotel industry demand is driven by economic growth and an increasing trend for domestic and global travel. Over the long term, the lodging industry has grown broadly in line with Gross Domestic Product (GDP) [1]. International chain Hotel Company is a global organisation with a broad portfolio of many hotel brands that operates hotels in three different ways as a franchisor, as a management, and as an owned basis [2]. International chain hotel companies support their property around the globe by balancing local and personalised service. In this way the head office can manage any of the chain’s hotels anywhere in the world [3]. One of the characteristic elements that contribute to getting the competitive advantage is represented by IT technologies [4]. Information is crucial to the management of all types of organisations. PMS can contribute more than technical applications and can be part of the management approach emphasising quality services in the hotel business [5].
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 645–652, 2023. https://doi.org/10.1007/978-3-031-25252-5_85
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Technology continues to have a multifaceted and substantial impact on our industry. In the modern age of computerisation, hotel management is becoming very important to provide efficient, effective and reliable services to the guest with the optimum use of technology. The computerisation of the hotel management is a part of the Enterprise solution software, wherein all the departments of a hotel are linked to the mainframe [6]. Technology will continue to have a multifaceted and substantial impact on the global hotel industry In the long-term. Computer applications are central to hotel operations in today’s modern hotels. For hotels, computers are being integrated into everyday operations to assist in providing hospitality to guests [7]. Enterprise solution software used by many departments at hotels. Computer applications include routinely processing reservations as well as handling registrations, guest charges, guest check-out, night audit, housekeeping, sales and marketing, banquet, purchasing, store control, cost control, accounting. The electronic sharing of data provides information flows to departments. Shared information accelerates hotel management [6]. The accelerators provide speed accessing the financial tasks. Thus, the head office accounting department can make real time consolidation [8]. A process of Revenue management planning to achieve maximum room rates and most profitable guests encourages managers to target sales periods and develop sales programs that will maximise profit for the hotel [9]. While yield management varies prices relative to demand, the rate to individual customers is fixed; hotels set the price and potential guests accept their offer or stay elsewhere. Managers can find solutions by using yield management [10]. The PMS can support the business to maximise its full potential. PMS provides many data’s for Revenue Management [11]. International hotel chains use software brands such as Opera, Suite8, OnQ, EuroProtel, eZee, Fidelio. These software brands were written with long research and sectoral experience by various IT software companies, and they are updated continuously [1]. Apart from Property Management Software (PMS), hotels solve technical problems effectively by using Computerised Facilities Maintenance Management Systems (CFMS) [12].
2 Materials and Methods Ten largest international hotel companies in the world were determined to collect data for the study. The results presented in this study come from the processing of official figures provided by the chains themselves, complemented by statistics from the MKG Consulting worldwide database (MKG Consulting, 2020) [13]. In order to determine this, the official reports of international hotel companies that they published in the Q2 period of 2019 were used. There are all kinds of pieces of data we picked up from hotel chain financial reports. According to the Q2 data of 2019, the hotel chains in the top ten were determined (Table 1), and a phone conversation with the regional management offices of these chains was held. The purposes and benefits of software usage were tried to be understood in the conversations. The question of “Why do they use single model software in all their hotels” was asked to the hotel companies in the study. The answers of the companies were divided into groups, and the questions which were responded by all companies identically at a rate of 90% were combined under the main headings, and the aims were analysed (Table 2).
Application of Enterprise Solution Software for a Hotel Chain Table 1. International hotel chains’ rooms count International hotel chain
Hotels count
Rooms count
Data sources
Marriott International
5,878
1152,253
2019 Q2 earnings release
Hilton Worldwide
4,727
775,866
20169 Q2 earnings release
InterContinental
5,070
726,876
IHG 2019 Q2 report
Wyndham Hotel Group
7,876
683,276
Wyndham 2019 Q2 report
Jin Jiang International
6,425
619,284
Jin Jiang 2019 Q2 investor report
ChoiceHotels
6,429
509,556
Choice 2019 Q2 report
Accor Hotels
3,900
500,366
Accor 2019 Q1 report
BestWestern International
3,903
303,768
HNN graphic Nov 2019
Home Inns Hotel Group
2,787
311,608
HNN graphic Nov 2019
CarlsonRezidor
1,092
172,234
HNN graphic Nov 2019
Hyatt Hotels
633
170,239
Hyatt 2019 Q2 report
Source: MKG Hospitality Data [13]
3 Research Findings and Results Table 2. Common headings of the answers given by hotel management companies; 1. We control the Average Daily Rate (ADR) of all our hotels from the centre 2. We control the Revenue per Available Room (REVPAR) of all our hotels from the centre 3. We monitor the occupancy percentage of all our hotels from the centre 4. We consolidate all hotel revenues in the region on a daily, weekly, and monthly basis 5. We consolidate food and beverage (F&B) revenue analysis for all hotels 6. We consolidate other revenues of hotels 7. We take sales analyses of all hotels to plan sales activities 8. In order to make a central purchase, we take the consumption analysis of all the hotels in the region 9. We check the budgets of all hotels in order to interfere immediately in budget differences 10. We use the same software in all of the hotels of the chain in order to provide the inspection standard 11. We use the same software in order to reduce the cost of personal training in orientations
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The findings indicate that there were several common competitive strategies being practised by the companies. They are innovative positioning, keeping costs low, expanding quickly, continuously innovating, highlighting quality and consistency and extensive training, plus some other indigenous operation practices [14]. In the hotel industry, hoteliers took multi-unit organisation form as an effective way to overcome the weakness of fragment and to acquire economies of scale. Some researchers already pointed out the effect of economies of scale on the efficiency and profitability rate in the hospitality industry [15]. Marketing Management; Marketing management is defined as the analysis, planning, implementation and control of programs designed to create, build and maintain beneficial exchanges with target buyers for the purpose of achieving organisational objectives [16]. The most important sales material in the hotel is the rooms. The hotel manager momentarily checks the hotel’s room sale prices. The primary goal is to sell the rooms at the highest price according to market conditions. Various sales techniques are used for room sales. Target markets and strategies are determined in order to sell rooms according to market conditions [17]. Separate price levels are used for each target market because a wholesale tour operator demands a lower price since it will buy many rooms at a time. The individual market remains at a high price level because of the small number of demands [18]. While selling rooms to these markets at different prices every day, the hotel follows the level of the price with the Average Daily Rate (ADR). By checking ADR continuously, it will be easier to overcome possible problems in advance (Table 2–1). Several industry metrics are widely recognized and used to track performance, including Revenue per Available Room (RevPAR) and rooms supply growth. The RevPAR indicator shows the hotel’s total room sales revenue per room. The daily revenue obtained from rooms is divided into the total room capacity of the hotel. Making efficient sales according to the hotel’s room capacity is monitored by this indicator. The rooms not sold as much as the rooms sold are also cost factors for the hotel [19]. The rooms that remain empty and are not sold on that day cannot be sold on the next day. This method does not apply to the hotel. The hotel has to sell the rooms on a daily basis. With the RevPAR formula, it is accepted as the most accurate method to follow the price balance on a daily basis. By determining whether the correct and good sales figures have been reached with the RevPAR analysis, the control of room prices is ensured (Table 2–2). The occupancy rates of the rooms that are sold weekly; monthly and quarterly in advance will allow managers to plan the number of staff, costs, and consumables correctly [19]. In this way, the purchase quantity and payment amount of the materials consumed continuously by the hotel can be determined in the long term. In the same way, the number of personnel working in the hotel may be planned according to the high or low occupancy that will occur in the future (Table 2–3). Consolidating the revenues of hotels: all revenues of hotels are consolidated locally in regional centres and also in the head office. Although the hotel chain company is a hotel management company, it also operates as an investment company. Consolidation of revenues online is the most critical data that will be presented by the senior managers of the company to the company partners. These data also display the board of directors’
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capital power for planned new investments, or suddenly emerging good opportunity investments [20]. In the commercial market, appropriate investment opportunities, which sometimes emerge suddenly, are evaluated quickly if the available capital is made up of up-to-date data. In order to benefit from these opportunities, the real capital power of the company is required to be known through the consolidation of the revenues of hotels on a daily, weekly, and monthly basis (Table 2–4). Consolidating F&B revenues: room sales come at first in the main activities of hotels. The second significant activity is F&B sales [21]. Restaurants and snack foods are served, contribute to this function. The bar areas of hotels are the income centres where guests can spend their free time comfortably. Gala halls are one of the income centres where organisations such as seminars, congresses, weddings, and New Year’s dinners are held [22]. These revenues are consolidated by head offices, and F&B analyses of hotels are obtained. As a result of the analysis, the cost and profit rates of the hotel for F&B are revealed. F&B profit rates are an important indicator in determining the renovation needs of F&B areas that will be performed in the hotel in the coming years. If the hotel’s F&B revenues are high, renewal and expansion needs will be included in the budget in the coming years. If the hotel’s F&B revenues are low, it means that renewal and expansion are unnecessary (Table 2–5). Room sales and F&B revenues are the first two income sources of hotels. According to the locations of hotels and the markets to which they aim to serve, Other Revenue items may come at the third place in the revenues of hotels. Except for revenues of room sales and F&B, some hotels have other places and services that provide revenue. These are called other incomes. Meeting halls, pool memberships, beach memberships, SPA, laundry, tennis courts, golf tee time, Auto Park, and event area are included under the heading of other income [1]. These revenues, which are under the heading of other income, are analysed by the head office and in the following years, and it is aimed to make better income by making investments to these units of the hotel. Investment and renovation budgets are made accordingly (Table 2–6). Consolidation of sales analysis: in each hotel, all kinds of sales made are consolidated, and analysis tables are prepared. The data collected in a database are used by all sales teams. When the cost of sales and marketing activities included in these analysis tables is analysed, the result displays that some activities can be made jointly [23]. When marketing activities are performed regionally or as a single hotel, it will be paid several times for the same promotion. (Table 2–7). Central purchasing and consumption analyses: Firms often adopt e-procurement slowly due to a lack of knowledge, skills, and trust, and erroneous risk perceptions [24]. There are many products that are bought by hotels daily and monthly. These products are food and beverage materials that are always used. In addition to food and beverage materials, cleaning products and auxiliary materials are also purchased for the comfort and safety of the guests staying in the hotel. The consumption data are consolidated to make this activity efficient. Every hotel in the hotel chain needs to use quality products that are appropriate to the company’s principles and brand [25]. Every hotel will spend time and money to buy a quality product. Through consolidation, common needs are determined, and saving is provided by spending time and money at a time (Table 2–8).
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Large hotel companies have many investor partners. The shares of these companies are traded on the stock exchange. The hotel company continuously informs its investor partners about the general budget. The company’s shares in the stock market gain or lose value, according to the information given [26]. The head office checks whether there is any progress suitable to the targets by periodically consolidating the budgets of the hotels affiliated to it. If there is a hotel that negatively affects the budget, it interferes immediately to correct it. Thus, it is attempted to protect the profitability and prestige of the parent company (Table 2–9). International hotel companies continuously inspect all hotels within their structures. These inspections can be made by the auditors working in the head office of the company or by companies providing audit services externally [27]. Auditors, who audit many hotels during the year, use the menus in the standard software to get instant access to the information they want in each hotel they audit (Table 2–10). Every company wants to work with qualified and experienced staff. The first objective of human resources departments is to find the personnel with these characteristics. The second objective of the human resources department is to train the personnel who are well aware of the company policies and gain the trained workforce to the company [28]. Based on these objectives, the company staff are subjected to orientation training by HR departments in a planned way. Through the use of the common software, the company staff that go to orientation start to work in their new hotel actively without experiencing any problem because the same software is also used in the hotel where the personnel have worked previously. The personnel know how to use the software to obtain data [29]. The efficiency of personnel will decrease while trying to train the personnel well. For these reasons, large hotel companies prefer to use the same software in every hotel, regardless of where it is in the world (Table 2–11).
4 Conclusion The head office of companies that operate hotel chains aims to maintain the profitability and reliability of its own brand by auditing all the hotels in its structure very seriously. The first method used to perform this auditing is to use the same software in all its hotels. In this way, it has the power to monitor and control hotels online. In addition to being able to perform audits from the centre through the common software, the audit staff of the head Office, who go to hotels, also do not need to make extra effort to reach the information they want. The ease of instant access to information shortens the process of taking new decisions by the head office and also helps it to take measures by identifying inefficient hotels immediately. IT helps to meet the demands for timely and accurate information by customers and the IT diffusion in the tourism and hospitality industries has recently increased at an unprecedented rate [30]. According to our research data; the number of chain hotels in the top 10 that use a common hotel software program (Fig. 1). Enterprise Solution software minimizes the risk of making mistakes by undertaking manual control works in hotels. At the same time, it is seen that it enables senior executives to be more central to managerial control by offering a wider audit area for their responsibilities. In this sense, the head office can easily follow all the processes of the guests such as accommodation, eating/drinking and entertainment from the moment the
Application of Enterprise Solution Software for a Hotel Chain
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Hotel Count 15,000 10,000 5,000 0
Hotel Count
Fig. 1. The number of chain hotels that use unique “Enterprise Solution Software”
reservations occur. We see that “the head office” analyses guest data and is using it to create a better guest satisfaction. Today, “distance working” has become a necessity due to COV˙ID-19 and when we look at the issue from this perspective, hotels that use Enterprise Solution Software have been advantageous. Hotel employees who use this technology can perform operations from the device they want wherever they are.
5 Conflicts of Interest The author has no conflicts of interest.
References 1. Stutts, A., Wortman, J.F.: Hotel and Lodging Management. Wiley, New Jersey (2006) 2. Rutherford, D.G., O’Fallon, M.J.: Hotel Management and Operations. Wiley, New Jersey (2010) 3. Karppinen, M.: Strategic Marketing Plan for A Hotel. Vaasa University of Appl. Sci. Degree Programme of Hospitality Manage. Master theses. (2011). Corpus ID: 168036539 4. Dana, O. F.: An empirical research regarding information technology in the hospitality industry: a case study from Mures County. J. Knowl. Manag. Econ. Inf. Technol. 3(6) (2013). doi:https://doi.org/10.1016/S2212-5671(14)00622-4 5. Law, R., Jogaratnam, G.: A study of hotel information technology applications. Int. J. Contem. Hospitality Manag., 17(2), (2005) https://doi.org/10.1108/09596110510582369 6. Baker, S., Bradley, P., Huyton, J.: Principles of Hotel Front Office Operations. South-Western, London (2000) 7. Benli, T., Kızgın, Y.: Konaklama ˙I¸sletmelerinde Bilgi Teknolojisi Kullanımının Önemi Üzerine Bir Alan Çalı¸sması: Mu˘gla ˙Ili Örne˘gi. Mevzuat Dergisi. 5(52) (2002) 8. Lashley, C., Rowson, B.: Getting IT right: Exploring information technology in the hospitality curriculum. Int. J. Contemp. Hospital. Manag. 17(1) (2005). doi:https://doi.org/10.1108/095 96110510577716 9. Yeoman, I., Beattite, M.U.: Revenue Management and Pricing. South-Western. London. (2004). ASIN:B008AU8XPG 10. Litvin, S., Crotts, J. C.: A framework for online sales negotiations of hospitality and tourism services. Information Technology in Tourism. 6(2) (2003). doi:https://doi.org/10.3727/109 830503773048200
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11. Law, R., Leung, R., Buhalis, D.: Information technology applications in hospitality and tourism: a review of publications from 2005 to 2007. J. Travel Tourism Market. 26(5–6) (2009). doi:https://doi.org/10.1080/10548400903163160 12. Stinpanuk, D. M.: Hospitality Facilities Management and Design. AHLA. Michigan (2002) 13. MKG 2020. MKG Consulting worldwide hospitality, published its exclusive survey of hotel chains worldwide, with supply statistics, business results and the ranking of groups and chains in terms of number of rooms. (2020). https://www.mkg-consulting.com/ Reached June/2021 14. Qin, Y., Adler, H., Cai, L.A.: Successful Growth Strategies of Three Chinese Domestic Hotel Companies. J. Manag. Strategy. 3(1) (2012). doi:https://doi.org/10.5430/jms.v3n1p40 15. Lafferty, G., Fossen, A.V.: Integrating the tourism industry: problems and strategies. Tourism Manag 22(1), 11–19 (2001). https://doi.org/10.1016/S0261-5177(00)00021-2 16. Oktay, S.: An analytical study to identify and determine the usage frequency of sales and marketing strategies for 5 star hotels in the antalya region. 9th ICSCCW-2017 Book Ser. Proc. Comput. Sci., 120, 862–870. (2017). doi:https://doi.org/10.1016/j.procs.2017.11.319 17. Lovelock, C., Wirtz, J.: Services Marketing. Pearson Prentice Hall, New Jersey (2007) 18. Reid, R.D., Bojanic, D.C.: Hospitality Marketing Management. Wiley, New Jersey (2016) 19. Baardi, J.A.: Hotel Front Office Management. John Wiley & Sons Inc., New Jersey (2007) 20. Page, S. J., Connell, J.: Tourism: A Modern Synthesis. South – Western. London (2009) 21. Oktay, S., Bahçelerli, N.: Konaklama Operasyonu. Der yayınevi. Istanbul (2018) 22. Lillicrap, D., Cousins, J.: Food and Beverage Service. Hodder Arnold Press, London (2012) 23. Kotler, P., Bowen, J.T., Makens, J.C.: Marketing for Hospitality and Tourism. Pearson Prentice Hall Press, New Jersey (2006) 24. Sigala, M.: e-Procurement diffusion in the supply chain of foodservice operators: an exploratory study In Greece. Inf. Technol. Tourism 8(2), 79–90 (2006). https://doi.org/10. 3727/109830506778001438 25. Sanders, E.E., Hill, T.H., Faria, D.J.: Understanding Foodservice Cost Control. Pearson Prentice Hall, New Jersey (2008) 26. Keiser, J.R.: Principles and Practices of Management in The Hospitality Industry. Van Nostrand Reinhold, New York (1989) 27. Martin, W.B.: Quality Service. Prentice Hall Press, New Jersey (2002) 28. Hayes, D.K., Ninemeier, J.D.: Human Resource Management in the Hospitality Industry. John Wiley & Sons Inc., New Jersey (2009) 29. O’Connor, P.: Online consumer privacy: an analysis of hotel company behaviour. Cornell Hotel Restaurant Administration Q. 48(2), 183–200 (2007). https://doi.org/10.1177/001088 0407299541 30. Singh, A.J., Kasavana, M.L.: The impact of information technology on future management of lodging operations: a delphi study to predict key technological events in 2007 and 2027. Tour. Hosp. Res. 6(1), 24–37 (2005). https://doi.org/10.1057/palgrave.thr.6040042
Fuzzy Logic Modelling of the Relationship Between Attitudes Towards Military Services and Soldiers’ Self-esteem Konul Memmedova(B)
and Banu Ertuna
Department of Psychological Counselling and Guidance, Near East University, Lefko¸sa, North Cyprus, Turkey [email protected]
Abstract. This research examines the relationship between soldiers’ attitudes towards military service and their self-esteem. The attitudes toward military life and associating it with self-esteem is an important factor in the efficiency of military service and the development of military skills. In this study, the soldiers’ self-esteem is measured using Rosenberg’s self-esteem scale. Attitude toward military services is measured with the measurement scale developed by the authors. Application of fuzzy inference instated of statistical inference allows handling imprecision and uncertainty inherent in statistical inference. Keywords: Military service · Attitude · Self esteem · Fuzzy logic · Fuzzy inference
1 Introduction Over time, socio-cultural, economic, political, and technological changes shape peoples’ personal and environmental views. The necessity of the concept of self-esteem comes to the forefront in adapting to the changing conditions. Self-esteem refers to how individuals perceive and value themselves [1]. These changes also affect attitudes towards military service, one of Turkish culture’s basic values. The military environment, which has a different structure from the civilian environment, has unique stressors. The most important stress factors in the military environment are being separated from families due to the deployment of units and institutions and being ready for duty 24 h a day, 365 days a year [2]. Although in certain areas, they may overlap, the military environment contains certain stress factors that are not present in the civilian environment [3]. Everyone approaching the military age adopts an attitude over many years toward various living conditions. When it comes to military service, many different attitudes are present. In [4], the authors stated that cadets with higher private and public self-esteem have higher personal and lower levels of depression. The study by Ebrinc [5] showed that even the self-esteem of soldiers who commit military offences is lower than those who do not, thus revealing the effect of self-esteem on military operations. The study [6] stated that © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 653–661, 2023. https://doi.org/10.1007/978-3-031-25252-5_86
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as self-esteem increases, self-confidence also increases and positively benefits soldiers’ academic success. Again, the research conducted by [7] in military service concluded that young people see military service as the ultimate hero model and that it is a necessity for normal citizens. In another study examining the effects of attitudes towards military service, it was revealed that the difficulties in fulfilling an important role in the army, the threat of being deprived of self-expression, and the thoughts about not being able to fulfil the given duties create anxiety about military service [8]. It is known that attitudes towards social systems are shaped through self-esteem. Self-esteem is an identifying factor in predicting people’s emotions, thoughts, and behaviours. The negative and positive feelings people have as a result of their life experiences are defined as self-esteem [9]. Self-esteem, which develops as a result of people’s experiences, helps predict specific psychological periods [10]. Attitude. Attitude is the tendency to respond positively or negatively to a specific object, situation, institution, concept, phenomenon, or another person that develops over time, which is learned, permanent and continuous [11]. The research on attitudes shows that it cannot be easily changed and forms over a long time through multiple steps [12]. An attitude is a phenomenon that continues during a certain period of an individual’s life, establishes the order between the individual and their environment and enables the individual to act in a certain way towards events. In this regard, the social attitudes of the individual towards the values, groups and objects in the society come to the fore. Family (parent influence), environment (friend, relative, teacher influence etc.) and life experiences play an important role in the formation of attitudes [13, 14]. With all these factors, the attitudes at the individual and social level are shaped by interacting with the self-esteem of the individuals. Self-esteem. Self-esteem, which can direct people’s behaviour, attitudes, beliefs, and thoughts, is defined as a positive or negative attitude. The fact that a person assesses themselves positively shows that they have high self-esteem, and the fact that they evaluate themselves negatively indicates that they have low self-esteem [15]. It is seen that individuals with high self-esteem are secure, successful, optimistic, assertive, consider themselves respectable, important, useful and tend to engage in environmentally-sensitive activities. In contrast, individuals with low self-esteem do not show effort, are weak when faced with difficulties in life, are pessimistic, and have a lack self-confidence. They are people who feel insecure, worthless and helpless, and their motivation for life is decreased. Individuals with high self-esteem have self-respect and perceive themselves as valuable people in society. In contrast, individuals with low self-esteem generally consistently evaluate themselves negatively [16]. Individuals with high self-esteem have a positive attitude towards participating in important life duties such as military service that is socially compulsory and conducting beneficial activities as part of these duties. Military service is seen as the most effective service that includes serving the country and loving society.
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2 Set of Problem The military is an organization with different motivation sources, rituals, and elements such as discipline, military activity, team spirit, morale, and leadership. It is important to predict the effects of various stressors on mental health arising from individuals’ selfperceptions and the hierarchical organization of the army and take suitable precautions. Thus, the study aimed to investigate the impact of the attitude of young toward military activities, discipline, social relations, and readiness on their self-esteem. The conceptual model of the problem is given in Fig. 1.
Fig. 1. Conceptual model of the problem
3 Methodology A mixed research method, in which statistical and fuzzy logic inference methods are used in this research. The statistical inference was used to develop an attitude measurement scale and analysis correlations between attitude variables and self-esteem. Then fuzzy inference was used instead of statistical modelling in the data processing stage. Rosenberg’s self-esteem scale [17] was used to measure the self-esteem of the soldiers. The authors developed the attitude scale used in the study (no other research on this topic has been found). 3.1 Design the Attitude Scale The attitude scale consists of 25 questions, and each one of five agreement levels (Strongly disagree (SD), 2-Disagree (D), 3-Neutral (N), 4-Agree (A) and 5-Strongly agree (SA)) (Table 1).
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Table 1. Likert scale for measuring attitude to the military services of the post-military young Questions 1
I think that preparing myself for difficult conditions will make military service easier
2
I imagine that I will complete my military service without punishment
3
I assume that I will mature in the military
4
I assume that my duty in the military will be related to my civilian
5
I believe that the military makes a man
6
I believe that I will be punished for the faults I committed in the military
7
It will be difficult for me to be disciplined in the military
8
I believe that military service will contribute to patience
9
It will be difficult for me to receive orders in the military
10
I think that military service will make me physically stronger
11
I think I will not have adequate sleep in the military
12
I think I will do my military service like in movies of wars
13
I think I can’t stand sleeplessness in the military
14
I believe that I will have a similar lifestyle to which I live before military service in the military
15
I believe that playing sports before military service will be beneficial in the military
16
I think that it is better to be enlisted as early as possible
17
I think I am ready for military service
18
I think that my family is preparing me for military service
19
It is better to do military service as late as possible
20
I want to do my military service more than my family
21
You can distinguish friends from hostile when you are in the military
22
It will be difficult for me to be in the same environment all time with people I do not know
23
I believe that military service is entertaining
24
I believe that my girlfriend / my fiancé will be waiting for me during my military service
25
I think that there is more sharing in the military services
The questionnaire covers four dimensions: Discipline (items 1–9), military activities (items 10–15), readiness (items 16–20), and social relationships (items 21–25). The number of items and the scale’s validity was tested using the explanatory factor analysis (EFA). The Load of items is between 0.6–0.87, and the confirmatory factor analysis CFA index is 0.92. The survey reliability was evaluated by the Gronbach alfa (for discipline α = 0.992, military activities - α = 0.86, readiness- α = 0.83. Table 2 shows the number of survey participants mean (M), standard deviation (SD), minimum (Min) and maximum (Max) values for different variables.
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Table 2. Soldiers’ Rosenberg Self-Esteem and Attitudes Towards Military Service Scale scores Variables
M
Rosenberg’s Self Esteem
SD
Min
Max 3.42
0.84
0.79
0
Discipline
29.01
5.51
15
44
Military Activity
18.65
3.79
10
28
Readiness
14.82
4.12
5
25
Social relationship
14.74
3.33
5
24
Attitude Scale
77.21
11.50
43
117
The results of the Pearson test conducted to examine the correlations between the Rosenberg self-esteem scale and the attitudes towards military service scale scores of the soldiers included in the study are given in Table 3. When Table 3 was examined, it was determined that there were statistically significant and negative correlations between the Rosenberg Self-Esteem Scale scores of the soldiers and the scores they received from the discipline and readiness sub-dimensions in the Attitude Towards Military Service Scale (p < 0.05). As the soldiers’ scores obtained from the discipline and readiness sub-dimensions of the Attitude Towards Military Service Scale increase, the discipline and readiness sub-dimension Rosenberg Self Esteem Scale scores according to the Attitude towards Military Service Scale are reduced. Table 3. Correlations between soldiers’ Rosenberg self-esteem scale and attitudes Variables
Rosenberg Self Esteem
Discipline
Military activity
Readiness
Social relationship
Attitude Scale Towards Military Service
Self Esteem
1
−0.230
0.175
−0.222
−0.003
−0.133
1
0.130
0.500
0.297
0.787
1
0.097
0.124
0.462
1
0.525
0.781
1
0.660
Discipline Military activity Readiness Social relationships Attitude Scale
1
It has been observed that there is a positive and statistically significant correlation between the scores of the soldiers on the Rosenberg Self-Esteem Scale and the military activity sub-dimension in the Attitude Towards Military Service Scale. (p < 0.05). As
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the soldiers’ scores from the military activity sub-dimension increased, their Rosenberg Self Esteem Scores also increased.
4 Fuzzy Logic Modelling the Impact of ATMS on the Self-esteem of Soldiers The fuzzy system based on Mamdani inference is shown in Fig. 2.
Fig. 2. Fuzzy system
The attitude factors – discipline, military activities, readiness and social relationshipdefuzzified using trapezoidal and triangular membership functions. Figure 3 presents the fuzzification of ‘discipline’ using linguistic variables. Strongly disagree (SD), 2Disagree (D), 3-Neutral (N), 4-Agree (A) and 5-Strongly agree (SA).
Fig. 3. Fuzzification of linguistic variable ‘discipline’ with membership function
Fuzzy inference selects appropriate rules from the Rule base using the fuzzified inputs. The fuzzy output part of the rule is defuzzified to obtain a crisp output - ‘selfesteem.‘ If-Then rules are created using the opinion of expert psychologist and the results of correlation analysis between attitude and self-esteem. The fragment of IF-Then rules is given in Table 4. For example, rule 3 can be stated as follows: If ‘Discipline’ is A and, Military activity’ is N and ‘Readiness’ is DA and ‘Social activity’ is A, then. ‘Self-esteem’ is Medium.
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Table 4. Fragment of IF-Then rules Rules N0
IF Discipline
Military activity
Readiness
Social relationship
Self-esteem
Then
1
N
DA
A
N
L
2
DA
A
DA
N
H
3
A
M
DA
A
M
4
VH
DA
N
A
L
5
DA
A
N
N
M
6
A
N
A
A
M
7
A
N
A
L
M
…
…
…
…
…
…
Figure 4 shows the fuzzification of the input variables and Inference flow for the rule 3:
a)
Discipline
c) Readiness
b) Military activity
d) Social relationship
Fig. 4. Fuzzification of input variables using trapezoidal membership function
The small green arrows under the horizontal axis of the associated membership functions denote of the input values (Discipline = 36.86 units, Military activity = 19.36 units, Readiness = 10.62 units and Social relationship = 19.1 units). Table 5 shows how numerical values are translated into membership degrees.
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Variables
Linguistic values
Discipline
μSD (x) = 0.0, μD (x) = 0.0, μN (x) = 0.0, μA (x) = 0.62 μSA (x) = 0.38
Military Activity
μSD (x) = 0.0, μD (x) = 0.2, μN (x) = 0.8, μA (x) = 0.0 μSA (x) = 0.0
Readiness
μSD (x) = 0.3, μD (x) = 0.7, μN (x) = 0.0, μA (x) = 0.0 μSA (x) = 0.0
Social relationship μSD (x) = 0.0, μD (x) = 0.0, μN (x) = 0.0, μA (x) = 0.78 μSA (x) = 0.22
Figure 5 presents the output variable Self-esteem and its defuzzification using the MOM method. Self esteem = { μN (x) = 0.6} and its MOM defuzzification numerical value is 1.75 that corresponds to medium.
Fig. 5. Defuzzification of fuzzy output Self-esteem.
5 Conclusion In the study is proposed the Fuzzy system to establish the relationship between the attitude of young toward military service and self-esteem. The author developed the measurement scale to measure the attitude of young to military service. The attitude scale consists of 25 questions and each one of five agreement levels. The survey reliability was evaluated by the Gronbach alfa (for Discipline α = 0.992, military activities - α = 0.86, readiness- α = 0.83. It has been observed that there is a positive and statistically significant correlation between self-esteem and military activities. Mamdani fuzzy inference system was used to handle imprecision and uncertainty in the data processing stage. If-Then rules are created using the opinion of the expert psychologists and the results of correlation analysis between the attitude and self-esteem. Implementing a fuzzy inference system using FuzzyTEch software shows the applicability of the suggested study for modelling real-world problems.
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References 1. Kroger, J.: Identity development during adolescence. In: Adams, G.R., Berzonsky, M.D., (eds.) Blackwell Handbook of Sdolescence, pp. 205–226. Blackwell Publishing (2003) 2. Lilley, D.L.: Applying positive leadership principles to an investigation of organizational stress in military units and the benefits associated with providing leaders with emotional intelligence social awareness. PhD Thesis, Lindenwood University (2012) 3. Campbell, D.C., Nobel, O.B.: Occupational stressors in military service: A review and framework. Mil. Psychol. 21(2), 47–67 (2009). https://doi.org/10.1080/08995600903249149 4. Rohall, D.E., Prokopenko, O., Ender, M.G., Matthews, M.D.: The role of collective and personal self-esteem in a military context. Current Res. Soc. Psychol. 22, Article 2 (2014). Corpus ID: 23285588 5. Ebrinc, S., et al.: Investigation of the relationship between sociodemographic characteristics, traits, anxiety, anger. expression, self-esteem with personality disorder in criminals arriving for forensic observation (in Turkish). A thinking man I5(2), 97–103 (2002) 6. Boe, O., Säfvenbom, R., Johansen, R.B., Buch, R.: The relationships between self-concept, self-efficacy, and military skills and abilities. Int. J. Learn. Teach. Educ. Res. 17(10), 18–42 (2018). https://doi.org/10.26803/ijlter.17.10.2 7. Girsh, Y.: Negotiating the uniform: Youth attitudes towards military service in Israel. Young 27(3), 304–320 (2019). https://doi.org/10.1177/1103308818787647 8. Orr, E., Liran, E., Meyer, J.: Compulsory military service as a challenge and a threat: Attitudes of Israeli twelfth graders towards conscription. Israel Soc. Sci. Res. 4(2), 5–20 (1986) 9. Yoyen, E.: Investigation of self-esteem and loneliness levels of university students. Kastamonu Educ. J. 25(6), 2185–2198 (2017) 10. Jonathon, D.B., Keith, A.D., Kathleen, E.C.: From the top down: Self-esteem and self evaluation. Cogn. Emot. 15(5), 615–631 (2001). https://doi.org/10.1080/026999301430 00004 11. Tezba¸saran, A.A.: Likert type scale preparation guide. Turkish Psychological Association (in Turkish), Ankara (1997) 12. Türkmen, L.: The influences of elementary science teaching method courses on a Turkish teachers college elementary education major students’ attitudes towards science and science teaching. J. Baltic Sci. Educ. 6(1), 66–77 (2007). Corpus ID: 140768852 13. Güllü, M.: Investigation of secondary education students’ attitudes towards physical education lesson. Gazi Universityi, Ankara (2007) 14. Çetin, N.: The place of military service in turkish culture and the incoming changes of perspective of military service in Turkey (in Turkish) Halic University. J. Educ. Sci. 1, 161–175 (2018) 15. Tanrıverdi, D., et al.: Examination of high school students’ eating attitudes, eating behaviors and self-esteem. Gaziantep Med J. 17 , 33–39 (2011) 16. Fennell, M.: Low self-esteem: A cognitive perspective. Behav. Cognitive Psychother. 25, 1–25 (1997). https://doi.org/10.1017/S1352465800015368 17. Rosenberg, M., Schooler, C., Schoenbach, C., Rosenberg, F.: Global self-esteem and specific self-esteem: different concepts, different outcomes. Am. Sociol. Rev. 60(1), 141–156 (1995). https://doi.org/10.2307/2096350
Applying Type-2 Fuzzy TOPSIS Method to Selection of Facility Location K. R. Aliyeva(B) Department of Instrument-Making Engineering, Azerbaijan State Oil and Industry University, 20 Azadlig Avenue, AZ1010 Baku, Azerbaijan [email protected]
Abstract. Determining location for facility is one of the largest and very extended problem that managers face both when firms are being initially set up and tolerate an extension for different causes. The decision to place a facility contains firms that want to place, replace, or increase their operations. This decision contains the process of determining, analyzing, estimate, and choosing alternatives. Plants, storages, markets, terminals and warehouses are typical locations. Place selection usually begins with determining the need for additional capacity. Then it is decided to begin choosing for the best site. This paper proposes the integration of spectrum selection optimization algorithms based on the evaluation of the characteristics of various locations using the TOPSIS fuzzy method. Proposed technique with type2 fuzzy numbers is used to solve the problem of choosing the location of an object. Major advantages of this technique are simplicity, rationality, ability to measure comparative performance in a simple mathematical form for each alternative. Keywords: Type-2 fuzzy numbers · Multi attribute decision making · Facility location · TOPSIS method
1 Introduction The location of the facility is the most appropriate place where firms can perform their logistics, production, supply functions, store their inventory and support their economic goals [1]. The choice of the location of the object is an integral part of the organizational strategy. The decision concerns organizations seeking to find, relocate or expand their operations. The decision-making process includes identification, analysis and evaluation, and selection among alternatives. Thus, the problem of site location usually begins with the recognition of the need for additional capacity or changes [2]. Object location is very popular investigation theme in decision making. Over the years, much attention has been given to these problems, and different qualitative and quantitative approaches have been proposed to solve these problems. The location of the object has a well-developed theoretical base [3]. In general, research in this sphere has focused on optimization the site selection technique [4]. Therefore, in this context, it is essential for companies to find the most appropriate location for their own goals, policies, objectives, plans and strategies.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 662–668, 2023. https://doi.org/10.1007/978-3-031-25252-5_87
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A poorly chosen location can cause an increase in production and logistics costs, as well as difficulty in finding or accessing key resources such as raw materials, human resources, other resources used for processes, government support and infrastructure, for example. Perhaps more importantly, this choice is not easy to refuse. Thus, it is extremely important for companies to exercise the necessary due diligence [5]. Since site selection is a long-term decision and it is very difficult and expensive to return to it, as mentioned above, it is also important for the development of company goals and objectives. Many of the variable costs, such as rent, logistics and transport, are fixed at a certain level by choosing the location of the object [6]. In addition to the costs of these factors, poor site location can also lead to difficulty in accessing raw materials, markets and labor. The inability to access these critical resources will ultimately lead to a decrease in the competitiveness of companies [7]. While the optimal location of facilities enables companies to effectively fulfill their economic goals and missions, it also contributes to increased efficiency and productivity, even strategic advantages in the long term. Therefore, company managers often strive to select the best location for their facilities, and in doing so they also evaluate many subjective factors, such as growth opportunities, long-term revaluation, prestige, for example, and they also evaluate more objective factors, such as various operating costs [8]. Location choice is important not only for cost and profit or resource availability, but also plays a strategic role in the competitive positioning of companies. For example, in a company that uses just in time systems for production, it is very important to have raw materials or semi-finished products just in time and of high quality. A company in such a situation, if it manages to locate its enterprise near key suppliers, will receive a key strategic advantage in return [9]. This paper is constructed as follows. Section 2 introduces the basic definitions of type-2 fuzzy numbers and the TOPSIS methodology steps that are used in this problem. In Sect. 3, the proposed technique with fuzzy numbers of the type-2 is used to solve the problem of choosing the location of an object. Conclusion represents the main results developed in this paper.
2 Preliminaries Definition. A type-2 fuzzy set A can be represented by a type-2 membership function μA˜ (x, u) where x ∈ X and u ∈ JX , JX ⊆ [0, 1] as follows [10–12]: A˜ =
(x, u), μA˜ (x, u) /∀x ∈ X ∀u ∈ JX ⊆ [0, 1], 0 ≤ μA˜ (x, u) ≤ 1
(1)
An Algorithm of Type-2 Fuzzy TOPSIS Method. The detailed steps of the Type-2 fuzzy TOPSIS modification are shown below [10]: 1. Constructing the normalized decision matrix X = xij n×m by using next formula: xij rij = n
2 k=1 xkj
, i = 1, · · · , n; j = 1, · · · , m
(2)
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K. R. Aliyeva
2. Constructing the weighted normalized decision matrix V = vij n×m by using next formula: vij = wj rij ; i = 1, · · · , n; j = 1, · · · , m 3. Determining the optimal and negative-optimal solution: ∗ A∗ = v1∗ , · · · , vm = max vij∗ |j ∈ b , min vij∗ |j ∈ b − A− = v1− , · · · , vm = max vij− |j ∈ b , min vij− |j ∈ b
(3)
(4) (5)
4. Calculating the separation measure and nearness to the optimal solution, by using Euclidean distance as shown below [13–17]:
2 m ∗ vij − vj∗ ; i = 1, · · · , n D = (6) i=1
D− =
2 m vij − vj− ; i = 1, · · · , n i=1
(7)
5. Ranking the alternatives by determining the relative closeness of each alternative to the optimal solution. The relative closeness (RC) of the alternative Ai is calculated using formula shown below: RCi =
Di−
Di∗ + Di−
; i = 1, · · · , n
(8)
3 Statement of Problem and Solution Procedures Suppose that there are four possible locations-A1 , A2 , A3 , A4 for selection with four criteria’s: C1 - proximity to customers, C2 - cost, C3 - infrastructure, C4 - capacity. Weights of this criteria are shown in below: w1
w2
w3
w4
(0.2, 0.3, 0.4, 0.4; (0.4, 0.5, 0.6, 0.6; 0.55 (0.3, 0.4, 0.5, 0.5; (0.5, 0.6, 0.7, 0.7; 0.25, 35, 0.45; 0.45) ,0.65, 0.75; 0.75) 0.55, 0.65, 0.75; 0.75) 0.55, 0.65, 0.75, 0.75)
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Linguistic values of type-2 fuzzy sets of linguistic terms are presented in the next form: Linguistic terms
Linguistic values of type-2 fuzzy sets
Extremely Poor
(0, 0, 0; 0)
(0, 0, 0; 0)
Very Poor
(0.1, 0.2, 0.3; 0.3)
(0.1, 0.2, 0.3; 0.3)
Poor
(0.2 ,0.3, 0.4; 0.4)
(0.2, 0.3, 0.4; 0.4)
Slightly Poor
(0.25, 35, 0.45; 0.45)
(0.25, 35, 0.45; 0.45)
Fair
(0.3, 0.4, 0.5; 0.5)
(0.3, 0.4, 0.5; 0)
Slightly Good
(0.4, 0.5, 0.6; 0.6)
(0.45, 0.55, 0.65; 0.65)
Good
(0.5, 0.6, 0.7; 0.7)
(0.55, 0.65, 0.75; 0.75)
Very Good
(0.6, 0.7, 0.8; 0.8)
(0.65, 0.75, 0.85; 0.85)
Extremely Good
(0.7, 0.8, 0.9; 0.9)
(0.7, 0.8, 0.9; 0.9)
Steps of type-2 fuzzy TOPSIS method is represented as follows: Step 1: Constructing the decision matrix by using linguistic terms and corresponding type-2 fuzzy numbers based on the decision maker given in Table 1. Table 1. The values of alternatives and criteria weights based on the decision maker C˜ 1 C˜ 2 (0.2, 0.3, 0.4; 0.4) (0.4, 0.5, 0.6; 0.6) (0.25, 35, 0.45; 0.45) (0.55, 0.65, 0.75; 0.75)
C˜ 3 (0.3, 0.4, 0.5; 0.5) (0.55, 0.65, 0.75; 0.75)
C˜ 4 (0.5, 0.6, 0.7; 0.7) (0.55, 0.65, 0.75; 0.75)
A˜ 1
(0.4, 0.5, 0.6; 0.6), (0.55, 0.65, 0.75; 0.75)
(0.6, 0.7, 0.8; 0.8), (0.7, 0.8, 0.9; 0.9)
(0.6, 0.7, 0.8; 0.8) (0.7, 0.8, 0.9; 0.9)
(0.5, 0.6, 0.7; 0.7) (0.55, 0.65, 0.75; 0.75)
A˜ 2
(0.6, 0.7, 0.8; 0.8), (0.7, 0.8, 0.9; 0.9)
(0.2, 0.3, 0.4; 0.4), (0.25, 0.35, 0.45; 0.45)
(0.5, 0.6, 0.7; 0.7), (0.55, 0.65, 0.75; 0.75)
(0.3, 0.4, 0.5; 0.5) (0.55, 0.65, 0.75; 0.75)
A˜ 3
(0.3, 0.4, 0.5; 0.5), (0.55, 0.65, 0.75; 0.75)
(0.4, 0.5, 0.6; 0.6) 0.55, 0.65, 0.75; 0.75)
(0.6, 0.7, 0.8; 0.8), (0.7, 0.8, 0.9; 0.9)
(0.5, 0.6, 0.7; 0.7) (0.55, 0.65, 0.75; 0.75)
A˜ 4
(0.5, 0.6, 0.7 ;0.7), (0.55, 0.65, 0.75; 0.75)
(0.6, 0.7, 0.8; 0.8) (0.7, 0.8, 0.9; 0.9)
(0.3, 0.4, 0.5; 0.5), (0.55, 0.65, 0.75; 0.75)
(0.3, 0.4, 0.5; 0.5) (0.55, 0.65, 0.75; 0.75)
Step-2. Constructing the weighted decision matrix (Table 2).
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K. R. Aliyeva Table 2. The weighted decision matrix C˜ 1
C˜ 2
C˜ 3
C˜ 4
A˜ 1
(0.08, 0.15, 0.24; 0.24), (0.14, 0.23, 0.34; 0.34)
(0.24, 0.35, 0.48; 0.48), (0.39, 0.52, 0.67; 0.67)
(0.18, 0.28, 0.4; 0.4), (0.25, 0.36, 0.49; (0.38, 0.52, 0.67; 0.67) 0.49), (0.27, 0.42, 0.56; 0.56)
A˜ 2
(0.12, 0.21, 0.32; 0.32), (0.18, 0.28, 0.4; 0.4)
(0.08, 0.15, 0.24; 0.24), (0.14, 0.23, 0.34; 0.34)
(0.15, 0.24, 0.35; 0.35), (0.3, 0.42, 0.56; 0.56)
A˜ 3
(0.06, 0.12, 0.2; 0.2), (0.14, 0.23, 0.34; 0.34)
(0.16, 0.25, 0.36; 0.36) 0.3, 0.42, 0.56; 0.56)
(0.18, 0.28, 0.4; 0.4), (0.25 ,0.36, 0.49 ; (0.38, 0.52, 0.67; 0.67) 0.49), (0.27, 0.42, 0.56; 0.56)
A˜ 4
(0.1, 0.18, 0.28; 0.28), (0.14, 0.23, 0.34; 0.34)
(0.24, 0.35, 0.48; 0.48), (0.39, 0.52, 0.67; 0.67)
(0.09, 0.16, 0.25; 0.25), (0.3, 0.42, 0.56; 0.56)
(0.15, 0.24, 0.35; 0.35), (0.27, 0.42, 0.56; 0.56)
(0.15, 0.24, 0.35; 0.35), (0.27, 0.42, 0.56; 0.56)
Step 3. Determining the ideal and negative-ideal solutions: A∗ = { 0.12,0 .21, 0.32;0.32), (0.18,0.28, 0.4;0.4); (0.24,0.35, 0.48;0.48), (0.39,0.52, 0.67;0.67); (0.18,0.28, 0.4;0.4), (0.38,0.52, 0.67;0.67); (0.25,0.36, 0.49;0.49), (0.27,0.42, 0.56;0.56) } A− = { (0.06,0.12, 0.2;0.2), (0.14,0.23, 0.34;0.34); (0.08,0.15, 0.24;0.24), (0.14,0.23, 0.34;0.34); (0.09,0.16, 0.25;0.25), (0.3,0.42, 0.56;0.56); (0.15,0.24, 0.35;0.35), (0.27,0.42, 0.56;0.56) }
Step 4. Calculating separation measure for each alternative: For example, separation measure for first alternative can be calculated by using formulas (6), (7) as SA∗1 = (0.03, 0.05, 0.06; 0.04, 0.06, 0.08), SA−1 = (0.02, 0.03, 0.04; 0.03, 0.05, 0.07) Similarly, for other alternatives: SA∗2 = (0.16, 0.2, 0.24; 0.1, 0.12, 0.14), SA−2 = (0.06, 0.10, 0.12; 0.16, 0, 19, 0.22) SA∗3 = (0.08, 0.11, 0.12; 0.09, 0.1, 0.11), SA−3 = (0.03, 0.04, 0.05; 0.08, 0, 1, 0.11) SA∗4 = (0.09, 0.12, 0.15; 0.08, 0.1, 0.11), SA−4 = (0.04, 0.06, 0.08; 0.05, 0.07, 0.09) Step 5. Determining relative closeness to the ideal solutions by using formula (8): (0.02,0.03,0.04;0.03,0.05,0.07) CA∗1 = (0.03,0.05,0.06;0.04,0.06,0.08)+(0.02,0.03,0.04;0.03,0.05,0.07) = (0.2, 0.37, 0.8; 0.2, 0.45, 1)
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(0.06,0.10,0.12;0.16,0,19,0.22) CA∗2 = (0.16,0.2,0.24;0.1,0.12,0.14)+(0.06,0.10,0.12;0.16,0,19,0.22) = (0.16, 0.33, 0.54; 0.47, 0.65, 1) (0.03,0.04,0.05;0.08,0,1,0.11) CA∗3 = (0.08,0.11,0.12;0.09,0.1,0.11)+(0.03,0.04,0.05;0.08,0,1,0.11) = (0.17, 0.26, 0.45; 0.36, 0.5, 0.64) (0.04,0.06,0.08;0.05,0.07,0.09) CA∗4 = (0.09,0.12,0.15;0.08,0.1,0.11)+(0.04,0.06,0.08;0.05,0.07,0.09) = (0.17, 0.33, 0.61; 0.25, 0.41, 0.63)
Relative closeness to the ideal solutions for each alternative represents that A1 is best alternative.
4 Conclusion Facility location problem can be described with various attributes such as, proximity to customers, cost, infrastructure, capacity. To make decision on facility location in this paper is used fuzzy TOPSIS methodology with type-2 fuzzy numbers to take high uncertainty appropriate the considered problem. In this paper four possible locations- A1 , A2 , A3 , A4 with four criteria’s: C1 - proximity to customers, C2 - cost, C3 - infrastructure, C4 - capacity is used for selection of facility location. By using proposed method was determined that A1 is best location for selection.
References 1. Ko, J.: Solving a distribution facility location problem using an analytic hierarchyprocess approach. In: ISAHP Proceedings, Honolulu, Hawaii, pp. 1991–1996 (2005) 2. Rao, R.V.: Facility location selection. decision making in the manufacturing environment: using graph theory and fuzzy multiple attribute decision making methods, pp. 305–314 (2007) 3. Brandeau, M.L., Chiu, S.S.: An overview of representative problems in location research. Manag. Sci. 35(6), 645–674 (1989) 4. Brown, P.A., Gibson, D.F.: A quantified model for facility site selection-applicationto a multiplant location problem. AIIE Trans. 4(1), 1–10 (1972) 5. Drezner, Z., Wesolowsky, G.O.: Network design: selection and design of links and facility location. Transp. Res. Part A: Policy Pract. 37(3), 241–256 (2003) 6. Hamacher, H. W., Drezner, Z.: Facility location: Applications and Theory, p. 108. Springer, Heidelberg (2002) 7. 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(7–8), 783–795 (2008) 8. Kostas, N.: DERViTSiOTiS Operations Management, p. 382. NewYork, McGraw-Hill Book Co (2005) 9. Yang, J., Lee, H.: An AHP decision model for facility location selection. Facilities 15(9/10), 241–254 (1997) 10. Ilieva, G.: TOPSIS modification with interval type-2 fuzzy numbers. Cybern. Inf. Technol. 16(2), 51–64 (2016) 11. Zadeh, L.A., Aliev, R.A.: Fuzzy logic Theory and Applications. Part I and Part II, p. 610. World Scientific, Singapore (2019)
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12. Aliev, R. A.: Uncertain Computation-Based Decision Theory, p. 521. World Scientific, Singapore (2017) 13. Mehdiyev, N.: Application of fuzzy AHP-TOPSIS method for software package selection. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M.B., Sadikoglu, F.M. (eds.) ICSCCW 2019. AISC, vol. 1095, pp. 827–834. Springer, Cham (2020). https://doi.org/10. 1007/978-3-030-35249-3_109 14. Aliyeva, K.R.: Multi-criteria house buying decision making based on type-2 fuzzy sets. Procedia Comput. Sci. 120, 515–520 (2017). https://doi.org/10.1016/j.procs.2017.11.273 15. Gardashova, L.A.: Z-number based TOPSIS method in multi-criteria decision making. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Sadikoglu, F.M. (eds.) ICAFS 2018. AISC, vol. 896, pp. 42–50. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-041649_10 16. Aliyeva, K.R.: Facility location problem by using fuzzy TOPSIS method. In: B-Quadrat Verlags, Uzbekistan, pp. 55–59 (2018). https://doi.org/10.34920/2018.4-5.55-59 17. Huseynov, O.H., Adilova, N.E.: Multi-criterial optimization problem for fuzzy if-then rules. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 80–88. Springer, Cham (2021). https://doi.org/10.1007/ 978-3-030-64058-3_10
Applying a Fuzzy-Set Approach to Assessing Capital Flight Management: Empirical Research from Azerbaijan Ulviyya Rzayeva1
and Rena Mikayilova1,2(B)
1 Azerbaijan State University of Economics, Baku AZ1001, Azerbaijan
{ulviyya.rzayeva,rana.mikayilova}@unec.edu.az 2 Azerbaijan State Oil and Industry University, 34 Azadlyg Avenue, Baku AZ1010, Azerbaijan
Abstract. The article discusses certain aspects of capital flight as an economic process, formulates methodological techniques for its analysis using the apparatus of fuzzy sets, and substantiates methods for evaluating the scale of this phenomenon based on data on macroeconomic indicators. In the article, this process is assessed as a priority task of national security. The solution of these problems is difficult on the basis of traditionally established approaches. The work explores and analyzes possible organizational schemes, and considers international experience in studying the problem of capital flight and issues of its prevention. The interpretation of the dependence of the capital flight indicator on other macroeconomic indicators based on the provisions of the theory of fuzzy sets makes it possible to reduce the critical dependence on the accuracy of determining their threshold value. Setting parameters and fuzzy rules makes it possible to use the proposed mathematical model to support managerial decision-making. Keywords: Capital flight · Evaluation of alternatives · Fuzzy set approach · Macroeconomic indicators · Mamdani rules
1 Introduction Capital flight is a steady outflow on a huge scale of financial resources in legal and illegal forms, reducing the investment opportunities of the national economy [1]. At the same time, capital of both criminal and legal origin can “fly away”. As practice shows, capital runs from a bad investment climate to a good one, indeed, in a period of permanent political and macroeconomic instability, prohibitively high taxation, insufficient development of the banking system and financial markets, companies and firms are forced to purchase foreign currency to save their capital. At present, the international movement of financial resources has increased significantly. This is largely due to such a phenomenon as the globalization of the world economy, which implies the erasure of boundaries for the free movement of capital. The strengthening of capital flows between countries is an objective process that allows capital to be directed to those countries and those areas that are most in need of capital. However, along with the movement of legal capital, in the context of globalization, © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 669–676, 2023. https://doi.org/10.1007/978-3-031-25252-5_88
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the movement of capital through illegal and semi-legal channels is increasing and is expressed in such a phenomenon as “capital flight”. The presented article is devoted to the development of methods for assessing financial resources moved from the country based on a fuzzy-set approach. The article deals with applying the method of fuzzy logic to assess the indicators of the development of the country’s economy. A methodological substantiation of the expediency of applying the concept of the apparatus of fuzzy sets to improve the tools for analyzing capital flows is given.
2 Methodology While most macroeconomic indicators are presented with specific numerical values (most often within the framework of official statistics), it is not possible to directly calculate the amount of “runaway” capital, primarily due to the lack of a single definition of the phenomenon and the impossibility of establishing the totality of financial flows that formally constitute the flight capital. Accordingly, all numerical data characterizing the scale and dynamics of the phenomenon are estimates built using certain algorithms. The development of such algorithms, and methods for constructing estimates of the amount of capital flight is devoted to a significant amount of work by foreign scientists [2–4]. In this paper, the flow of initial data of a mathematical model is studied on the basis of fuzzy models, while taking into account the existing uncertainty using fuzzy formalisms as follows: the state of the financial system is recognized using fuzzy classifiers, where the model formalism is the membership function of a fuzzy subset of a linguistic variable specified on the corresponding real carrier. At the same time, the need to refine the obtained fuzzy formalisms in time implies the following: - scaling (linguistic classification) is always performed with respect to a number of parameter values measured approximately in the same period of time (vertical principle); - the linguistic interpretation of the results obtained at a one-time interval may undergo correction in the future. This correction may be due, for example, to a change in the macroeconomic paradigm in the country where the observation is made. In the study, the experimental calculation was performed using the FUZZY LOGIC TOOLBOX FOR MATLAB package in interactive mode.
3 Validity of the Use of the Fuzzy Set Approach The use of a fuzzy approach can help in deciding how to prevent capital flight. In addition, many indicators traditionally used in models are represented by qualitative variables, which also complicates the application of classical econometric methods. From the point of view of fuzzy logic, justification of a decision is a way of convincing oneself of its truth (correctness), i.e. giving those convincing arguments or arguments, by virtue of which a decision should be made. This justification is closely related to logic, so the rationale for the decision is the logical proof of the truth of all its conditions. A decision is considered justified when each of its conditions and/or control parameters is confirmed by objective facts of the real world and/or laws of the controlled process.
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The term validity is “fuzzy” in nature, so it can be “reasonably” considered as a fuzzy variable with a domain of definition [0, 1]. Note that, theoretically, the validity value can never reach unity. Since, with any volume and depth of justification, there is always the opportunity to take into account additional data and thereby improve the quality of the decision. To set fuzzy validity, we will proceed from the following considerations. The validity of the decision is the truth of its conditions, therefore, to set the fuzzy validity, we can use the known membership functions for the fuzzy variable “true”. When assessing the validity of a decision as to the probability of its truth, we should proceed from the fact that this assessment does not have a statistical meaning, but the meaning of psychological confidence. According to Polya, in such cases, the numerical expression of validity is not applicable, and modal categories such as medium validity, high validity, etc. should be used [5]. To assess various indicators of a qualitative nature, Harrington’s verbal-numerical scale has become widespread [6]. The scale is universal, but when assessing the validity of management decisions, especially those related to the management of critical infrastructure facilities, it is obviously not accurate enough. Therefore, to assess the validity of management decisions, it is advisable to develop and use special modifications of the scale that reflect the specifics of a particular management decision. The validity of any decision depends on three main factors: the reliability of the initial data, their completeness, and the quality of the decision-making model, which reflects the depth of scientific knowledge of the laws of the controlled process and the degree of use of this knowledge in substantiating a particular decision [7]. Let r is the information decision, D is the degree of reliability of the initial data used ˜ in making this decision, and M is the model for making decision r. Further, let A(D), ˜P(D), K(M ˜ ) are the fuzzy statements denoting, respectively, the reliability D of the initial data, their completeness, and the quality of the model M. Then the relationship of these factors with the validity of the decision r can be represented by the following fuzzy production rule: ˜ ˜ ˜ ˜ (1) A(D) ∧ P(D) ∧ K(M ) → O(r) and reduce the problem of assessing the validity of the decision r to assessing the truth ˜ ˜ ˜ of the antecedent A(D), P(D), K(M ) of this rule.
4 Practical Calculation of a Multicriteria Problem As a practical example of using the proposed method, the problem of assessing the management of capital flight from Azerbaijan as a specific form of cross-border capital movement is considered. It is assumed that the indicator under consideration is influenced by the following macroeconomic factors: • GDP; • Consumer Price Index (CPI); • Political Freedom Index;
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• Economic Freedom Index; • Corruption Perceptions Index. Each input, similarly to the stage of generating alternatives, is divided into seven levels: • • • • • • •
very low; short; below the average; middle; above the average; high; very high.
Similarly, for the case under consideration, we get 57 = 78125 possible strategies. Using (1) and setting the initial values of the concepts according to the current economic situation (Table 1), we calculate their final value (Table 2). Table 1. Current indicators Years
Curr. Acc. (USD Mill.)
Extern. Debt ann. % change
GDP (USD Bill.)
Polit. Stabil. Index (−2.5 weak; 2.5 strong)
Infl., cons. Corr. Ind. Prices. Ann. (a scale of 0 % change (strong) to 100 (no corr.))
2010
3500
59.42
52.91
−0.3
5.727
24
3800
2011
4200
6.02
65.97
−0.39
7.858
24
2750
2012
2500
40.83
69.68
−0.4
1.066
27
550
2013
3050
−2.34
74.16
−0.41
2.416
28
1750
2014
3150
14.42
75.24
−0.56
1.373
29
1500
2015
1100
10.10
53.07
−0.73
4.028
29
4350
2016
−500
9.54
37.87
−0.8
12.443
30
2050
2017
−250
4.87
40.87
−0.75
12.936
31
800
2018
600
5.95
47.11
−0.71
2.269
25
500
2019
1000
−2.29
49.17
−0.69
2.611
30
700
2020
500
–
42.61
−0.73
2.76
30
1350
2021
2000
–
52.65
–
–
700
–
Capit. Flows (USD Mill.)
Thus, we maximize GDP, economic and political stability, current account balance and minimize the level of corruption, CPI. The output is Capital Flight, with a generalized assessment, in which we take 7 levels. The generalized assessment is designed to
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implement the possibility of simultaneously taking into account the influence of all criteria. For convenience, we will give names according to the coordinate of the mathematical expectation of each membership function. The use of fuzzy logic approaches [8–12] allows, at a stage similar, in fact, to assigning criteria weights, to abandon this procedure, which causes difficulties for decision makers due to the need to operate with quantitative data, and translate the problem into natural language. Thus, the decision maker only needs to formulate the dependencies in the form “if A, B, C are high, and E is low, then this is very good”. Statements of this type are proved to be more understandable for decision makers. In most cases, there is no need to formulate the entire set of logical rules, it is enough to draw up a certain number of rules that allow us to clarify the strength of the dependence, the kind of elasticity of the output generalized variable from each of the input criteria. This becomes possible, since the type of extremum is determined for each of the criteria and, in addition, the membership functions are typed according to the input criteria. Thus, automation of the process of generating logical rules can be provided if an elementary algorithm is compiled based on the type of criteria extrema and the elasticity of the generalized output variable for each of them is determined. In addition, it seems obvious to consider only the rules that ensure the maximum value of the output variable, which also significantly reduces the complexity of the task. It should be noted separately that when developing such an algorithm, it is necessary to pay attention to preventing the inclusion of duplicate entries. Table 2. Alternative evaluation matrix by criteria Years
Curr. Acc. (USD Mill.)
Extern. Debt ann. % change
GDP (USD Bill.)
Polit. Stabil. Index (−2.5 weak; 2.5 strong)
Infl., cons. Corr. Ind. Prices. Ann. (a scale of 0 % change (strong) to 100 (no corr.))
Capit. Flows (USD Mill.)
2010
0.0943
0.05726
0.046
0.1673
0.11928
0.0239
0.054
2011
0.0928
0.06736
0.063
0.1782
0.12839
0.0123
0.069
2012
0.1673
0.06251
0.056
0.1729
0.13229
0.0391
0.038
2013
0.1290
0.05364
0.04
0.1673
0.14798
0.0293
0.048
2014
0.0973
0.06253
0.053
0.1562
0.14832
0.0192
0.073
2015
0.9385
0.05827
0.053
0.1782
0.11924
0.0217
0.087
2016
0.9173
0.05463
0.067
0.1672
0.11234
0.0294
0.068
2017
0.1294
0.07289
0.048
0.1548
0.13923
0.0327
0.073
2018
0.1341
0.06537
0.062
0.1473
0.14377
0.0427
0.083
2019
0.0928
0.05672
0.065
0.1798
0.16333
0.0394
0.047
2020
0.0989
–
0.073
0.1678
0.14294
0.0224
0.063
2021
0.1083
–
0.067
–
–
–
–
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Based on logical rules, we alternately substitute alternatives and carry out defuzzification (reduction to clarity). As a result of the defuzzification of all alternatives using the Mamdani algorithm, the quantitative values of the generalized estimates were obtained (Table 3). Table 3. A fragment of the calculation of the alternatives’ generalized assessment The best alternative
Generalized assessment according to Mamdani
41
0.418
43
0.417
47
0.467
52
0.518
58
0518
61
0.629
62
0.629
78
0.667
82
0.630
84
0.635
93
0.612
98
0.543
105
0.479
125
0.417
151
0.418
Alternative 78 has the best score, implying that the values of controlled concepts belong to the following levels: • • • • • •
very low key rate of the CBAR; low required reserve ratio; above-average volume of banking liquidity; above-average rigidity of the tax policy; very high quality of public services; average activity of carrying out reforms aimed at deoffshorization.
This result implies an expansionary monetary policy against the backdrop of fiscal tightening, which should be accompanied by a high quality of public services that will improve the ease of doing business at home. It is interesting to note that the best strategy does not propose increasing the intensity of reforms aimed at deoffshorization while raising the tax burden in the country. This may indicate that the root cause of capital outflow is not the choice of the country with the most relaxed tax conditions, nor the
Applying a Fuzzy-Set Approach to Assessing Capital Flight Management
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search for an economic territory with a high level of stability, but the removal of assets from the country of origin in order to hide and launder them.
5 Conclusion This paper shows the possibilities of applying fuzzy logic to the generated combined alternatives. Azerbaijan, despite the measures taken, cannot solve the problem of capital flight. The author’s vision of a comprehensive solution to the problem is to conduct an expansionary fiscal policy, especially if the country is experiencing depression or is in the stage of an economic crisis. In this case, the government needs to stimulate either aggregate demand, supply, or both. To do this, other things being equal, the government increases its purchases of goods and services, reduces taxes, and increases transfers, if possible. It should be noted that in the last year there has been a certain movement in the leading countries against offshore business, which removes ever more powerful capital flows from national regulation and taxation. Azerbaijan, like other countries as a victim of capital flight, is interested in limiting the possibilities of offshore business. We need an agreed international limitation of the degree of “offshority” of business and greater transparency of flows and so on. True, this may run into problems of national sovereignty. In the situation under consideration, the public sector plays a special role for Azerbaijan, balancing the risks of residents and foreign investors by introducing state guarantees. As the main risks of domestic investment, irrelevant for non-residents, the article highlights an increase in the tax burden, including due to rising inflation and depreciation of the national currency. The simulation results confirm a positive relationship between these factors and capital flight.
References 1. Kant, C.: What is capital flight? World Econ. 25(3), 341–358 (2002). https://doi.org/10.1111/ 1467-9701.00436 2. Brada, J.C., Kutan, A.M., Vukši´c, G.: Capital flight in the presence of domestic borrowing: evidence from eastern european economies. World Dev. 51, 32–46 (2013). https://doi.org/10. 1016/j.worlddev.2013.05.007 3. Brada, J.C., Kutan, A.M., Vukši´c, G.: The Cost of moving money across borders and the volume of capital flight: the case of Russia and other CIS countries. Rev. World Econ. 47(4), 717–744 (2011). https://doi.org/10.1007/S10290-011-0100-3 4. Casella, B.: Looking through conduit FDI in search of a probabilistic approach. Transn. Corp. 26(1), 109–146 (2019) 5. Polya, G.: How to Solve It. A New Aspect of Mathematical Method, Expanded Princeton Science Library Edition, with a new foreword by John H. Conway (2004). ISBN-13: 978– 0691119663 6. Bezhentseva, T. V., Aleksandrova, N.N., Matyus, E.G.: Formation of system of indicators for the evaluation of environmental activities, IOP Conf. Ser.: Mater. Sci. Eng. 451, 012182, (2018). https://doi.org/10.1088/1757-899X/451/1/012182
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7. Shi, Y.: Using fuzzy logic to evaluate and compare state financial condition during and after the great recession of 2008: fuzzy rule-based systems. Public Adm. Q. 44(3), 394–432 (2020). https://doi.org/10.37808/paq.44.3.3 8. Aliyeva, K.R.: Multi-criteria house buying decision making based on type-2 fuzzy sets. Procedia Comput. Sci. 120, 515–520 (2017). https://doi.org/10.1016/j.procs.2017.11.273 9. Aliyeva, K.: Application of interval approximation method of a fuzzy number to the supplier selection. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Sadikoglu, F.M. (eds.) ICAFS 2018. AISC, vol. 896, pp. 472–477. Springer, Cham (2019). https://doi.org/10.1007/ 978-3-030-04164-9_63 10. Eyupoglu, S.Z., Gardashova, L.A., Allahverdiyev, R.A., Saner, T.: Analysis of the job satisfaction index problem by using fuzzy inference. Procedia Comput. Sci. 102, 45–50 (2016). https://doi.org/10.1016/j.procs.2016.09.368 11. Huseynov, O.H., Adilova, N.E.: Multi-criterial optimization problem for fuzzy if-then rules. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 80–88. Springer, Cham (2021). https://doi.org/10.1007/ 978-3-030-64058-3_10 12. Aliev, R.A., Gardashova, L.A.: Z-set based approach to control system design. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 10–21. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-640 58-3_2
Decision Making with Z-Bounded Interval Preference Akif V. Alizadeh1(B)
and Rafig R. Aliyev2
1 Department of Electronics and Automation, Azerbaijan State Oil and Industry University,
20 Azadlig Avenue, 1010 Baku, Azerbaijan [email protected], [email protected] 2 Research Laboratory of Intelligent Control and Decision-Making Systems in Industry and Economics, Azerbaijan State Oil and Industry University, Azadlyg Avenue 20, 1010 Baku, Azerbaijan
Abstract. In many real-world decision problems under uncertainty, information is not exact, and merely lower and upper bounds are available. This leads to dual uncertainties, e.g., both lower and upper bounds are uncertain. In this paper uncertainties in preferences of Decision Makers are expressed as Z-boundary intervals. The lower and upper bounds of an interval can be presented as Z-numbers. Realworld decision making under Z-bounded intervals is provided to demonstrate the effectiveness and feasibility of the proposed approach. Keywords: Uncertainty · Z-bounded interval · Decision making · Z-number · Interval preference
1 Introduction In many real-world decision problems under uncertainty information is not known exactly, and merely lower and upper bounds are available. This leads to dual uncertainties, e.g., both lower and upper bounds are uncertain. In this paper uncertainties in preferences of Decision Makers are expressed as Z-boundary intervals. The lower and upper bounds of an interval can be presented as Z-numbers. The paper [1] proposes a fuzzy interval perturbation approach to temperature field forecasting using interval and fuzzy uncertainties and boundary conditions. In [2] authors consider inexact optimization method which is capable to handle dual uncertainties expressed as fuzzy boundary intervals in constraints and objective function. In [3] a stochastic fuzzy programming method is utilized to handle variables uncertainties expressed as fuzzy boundary intervals. The given approach is applied to optimize water allocation in rivers. In [4] inexact fuzzy chance-constrained programming approach is considered for power system under dual uncertainty. In [5] a new definition of fuzzy bounded set is suggested. Also, properties of such sets are studied.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 677–685, 2023. https://doi.org/10.1007/978-3-031-25252-5_89
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A fuzzy-boundary-interval linear programming tool is developed in [6]. The methodology given in [6] is applied in [7] for optimal water allocation under uncertainty. In [8], by using fuzzy boundary interval variables a model under two fuzzy-interval situation is suggested. In fundamental work [9] the set of fuzzy numbers between two fuzzy numbers bound is considered. Authors extend the concept of real interval to the concept of interval fuzzy segment characterized by two fuzzy bounds. In this paper they also suggest transition mapping procedure that generates the set of fuzzy numbers between fuzzy bounds. Arithmetic operations, inequality and inclusion relationship on fuzzy-interval segments are studied. We have to mention that in general studies on fuzzy-boundary intervals and their applications in decision making in existing literature are very scare. Up to day in existing literature there is no works on Z-bounded interval and especially their application to formulation of decision preference. In this paper Z-bounded interval concept is introduced. On basis of this concept, Zbounded interval decision preference is investigated. Real-world decision making under Z-bounded interval is provided to demonstrate the effectiveness and feasibility of the proposed approach. The rest of paper is organized as follows. In Sect. 2 preliminaries are given. In Sect. 3, Z-boundary interval-based decision preference, decision-making problem and its solution method are given. Experimental studies are given in Sect. 4. Finally, conclusion is presented in Sect. 5.
2 Preliminaries Definition 1. Fuzzy number [10]. A fuzzy number is a fuzzy set A on R which possesses the following properties: a) A is a normal fuzzy set; b) A is a convex fuzzy set; c) α-cut of A, Aα is a closed interval for every α ∈ (0, 1]; d) the support of A, supp(A) is bounded. Definition 2. Z-numbers [10]. A Z-number, Z, has two components, Z = (A, B). The first component, A, is a restriction (constraint) on the values which a real-valued uncertain variable, X, is allowed to take. The second component, B, is a measure of reliability (certainty) of the first component. Typically, A and B are described in a natural language. The concept of a Z-number has a potential for many applications, especially in the realms of economics, decision analysis, risk assessment, prediction, anticipation and rule-based characterization of imprecise functions and relations. Definition 3. Fuzzy bounded interval [9]. Fuzzy bounded interval is set whose elements will be called interval fuzzy segments, as a generalization of a real interval. In the interval fuzzy segments, it is considered fuzzy numbers whose core is a point-wise interval instead of considering real numbers.
Decision Making with Z-Bounded Interval Preference
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Definition 4. Z-numbers S-transformation. Let be a set of all Z-numbers. Let Z1 and Z2 be two Z-numbers, , such that Z1 ≤ Z2 . The Z-number S-transformation is a mapping Tλ (Z1 , Z2 ) = Z12 , that satisfies the following properties: – Tλ=0 (Z1 , Z2 ) = Z1 , where ; ; – Tλ=1 (Z1 , Z2 ) = Z2 , where , such that (λ = 0 = (trimf (0, 0, 0), trimf (1, 1, 1)) ≤ λ ≤ λ = – for any ; 1 = (trimf (1, 1, 1), trimf (1, 1, 1))), Tλ (Z1 , Z2 ) = Z12 is Z-number, if λ1 ≤λ2 , then Tλ1 (Z1 , Z2 ) ≤ Tλ2 (Z1 , Z2 ). – for any λ1 , λ2 Definition. Z-bounded interval. Given Z1 and Z2 Z-numbers, such that Z1 ≤ Z2 and given T , a Z-numbers S-transformation, consider the set of all Z-numbers between Z1 and Z2 obtained by S-transformation T , that is:
. Then, the bounded Z-interval with bounds Z1 , Z2 is represented by defined as the pair:
and is
Definition. Arithmetic operation on Z-bounded interval. Let and be two Z-bounded intervals. Then the arithmetic operations on Z-bounded intervals are defined as follows: Addition.
. Subtraction.
. Multiplication. If Z1 , Z2 , Z3 , Z4 all have definite sign, 1) 0, 2) ≥ 0,
, and.
where Tλ = Tλ1 *Tλ2 if Z1 ≥ 0, Z2 ≥ 0, Z3 ≥ 0, Z4 ≥ 1 *T 2 if Z ≥ 0, Z ≥ 0, Z < 0, Z where Tλ = Tλ=1 1 2 3 4 λ
680
A. V. Alizadeh and R. R. Aliyev 1 *T 2 if Z ≥ 0, Z ≥ 0, Z < 0, Z where Tλ = T1−λ 1 2 3 4 λ
3) < 0,
2 where Tλ = Tλ1 *Tλ=1 if Z1 < 0, Z2 ≥ 0, Z3 ≥ 0, Z4
4) ≥ 0,
1 *T 2 where Tλ = T1−λ λ=0 if Z1 < 0, Z2 ≥ 0, Z3 < 0,
5) Z4 < 0,
2 where Tλ = Tλ1 *T1−λ if Z1 < 0, Z2 < 0, Z3 ≥ 0, Z4
6) ≥ 0,
1 *T 2 where Tλ = Tλ=0 1−λ if Z1 < 0, Z2 < 0, Z3 < 0,
7) Z4 ≥ 0,
1 *T 2 where Tλ = T1−λ 1−λ if Z1 < 0, Z2 < 0, Z3 < 0,
8) Z4 < 0,
Division. / 3 .A, 0 ∈Z / 4 .A, then If Z1 , Z2 , Z3 , Z4 they all have definite sign and 0 ∈Z .
3 Statement of the Problem and Solution Methods Let A = {A1 , A2 , ..., An } be a set of alternatives and Z-bounded interval values of payoff be , i = 1,…,n. Hence, we can represent decision matrix Dn,2 as (Table 1): 0 Table 1. Decision matrix Dn,2
λ1 = 0
λm = 1
A1
Z1,1
Z1,m
A2
Z2,1
Z2,m
.. .
.. .
.. .
An
Zn,1
Zn,m
The problem is to find best alternative Ai [11–14]. , for By using S-transformation T over Z-bounded intervals with λ2 ,..,λm−1 every alternative we define appropriate Zi2 ,…,Zim values. So, we get, Dnm decision matrix (Table 2):
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Table 2. Decision matrix Dn,m λ1 = 0
λ2
λm−1
λm = 1
A1
Z1,1
A2
Z2,1
Z12
Z1,m−1
Z1,m
Z22
Z2,m−1
Z2,m
.. .
.. .
An
Zn,1
…
.. . Zn2
Zn,m−1
Zn,m
In the first step we applied Z-Hurwicz approach, in second step, for comparison alternatives, we applied Fair Price approach. Hurwicz Approach. Alternative Ai is characterized by Ci = αH ∗ max Zi,1 , Zi,2 , ..., Zi,m + (1 − αH ) ∗ min Zi,1 , Zi,2 , ..., Zi,m
(1)
Fair Price Approach. Z-valued fair price is FP(Z(Ci.A, Ci.B)) = +
1
1
K − (α) · Ci.A− (α)d α +
0
L− (α) ln(Ci.B− (α)d α
0
+
1
1
K + (α) · Ci.A+ (α)d α
0
(2)
L+ (α) ln(Ci.B+ (α)d α
0
where K(α) is appropriate fuzzy function. Best alternative is alternative with highest value of fair price.
4 Example Example. Farmer has to make decision on planting a crop given three crops [15]. The payoff depends on state of nature, e.g. weather condition. Here weather condition is characterized as “high rainfall, sure”; “medium rainfall, sure”; and “low rainfall, sure”. Estimated conditional profits under considered states of nature are given in Table 3. Decision maker (farmer) wants to choose decision with maximum profit. Lower and upper bounds of expected conditional profits for every state of nature are given below (D0 matrix). State of nature “very low rainfall” is for λ1 = (trimf (0, 0, 0), trimf (1, 1, 1)) = 0 , state of nature “very high rainfall” is for λ5 = (trimf([1.0,1.0,1.0]), trimf([1.0, , state of nature “low rainfall” is for λ2 = (trimf([0.3,0.4,0.5]), 1.0, 1.0])) = 1 trimf([0.8,0.9,1])); state of nature “medium rainfall” is for λ3 = (trimf([0.4,0.5,0.6]), trimf([0.8,0.9,1])) and state of nature “high rainfall” is for λ4 = (trimf([0.6,0.7,0.8]), trimf([0.8,0.9,1])).
682
A. V. Alizadeh and R. R. Aliyev Table 3. D0 matrix “very low rainfall”
“very high rainfall”
Crop 1
(trimf([1000.0, 2000.0, 3000.0]), trimf([0.8, 0.9, 1.0]));
(trimf([7000.0, 8000.0, 9000.0]), trimf([0.7, 0.8, 0.9]));
Crop 2
(trimf([4500.0, 5000.0, 6000.0]), trimf([0.7, 0.8, 0.9]));
(trimf([3000.0, 3500.0, 4000.0]), trimf([0.8, 0.9, 1.0]));
Crop 3
(trimf([3500.0, 4000.0, 4500.0]), trimf([0.8, 0.9, 1.0]));
(trimf([4500.0, 5000.0, 5500.0]), trimf([0.7, 0.8, 0.9]));
For Crop 1, by using Tλ S-transformation we get Z-bounded interval
For Crop 2
we get
For Crop 3
we get
Then updated D matrix is expressed as shown below (Table 4):
:
(trimf([1000.0, 2000.0, 3000.0]), trimf([0.8, 0.9, 1.0]));
(trimf([4500.0, 5000.0, 6000.0]), trimf([0.7, 0.8, 0.9]));
(trimf([3500.0, 4000.0, 4500.0]), trimf([0.8, 0.9, 1.0]));
Crop 1
Crop 2
Crop 3
“very low rainfall”; λ1 = (trimf([0.0,0.0,0.0]), trimf([1.0, 1.0, 1.0]));
“medium rainfall”; λ3 = (trimf([0.4,0.5,0.6]), trimf([0.8,0.9, 1]));
(trimf([3100,4400,5900]), trimf([0.4596, 0.6372, 0.9008]));
(trimf([3300, 4550,6400]), trimf([0.4555, 0.6272, 0.8858])); (trimf([3200,4500, 6000]), trimf([0.4901, 0.6531, 0.9085]));
(trimf([3000, 4250, 6000]), trimf([0.4698, 0.6376, 0.8903]));
(trimf([2600, 4400, 6600]), (trimf([3200, 5000, trimf([0.4692, 0.6438, 7200]), 0.8974])); trimf([0.4741, 0.6402, 0.8832]));
“low rainfall”; λ2 = (trimf([0.3,0.4,0.5]), trimf([0.8,0.9,1]));
Table 4. D matrix updated
(trimf([7000.0, 8000.0, 9000.0]), trimf([0.7, 0.8, 0.9]));
“very high rainfall”; λ5 = (trimf([1.0,1.0,1.0]), trimf([1.0, 1.0, 1.0]));
(trimf([3400,4700,6200]), trimf([0.4526, 0.6264, 0.0887]));
(trimf([4500.0, 5000.0, 5500.0]), trimf([0.7, 0.8, 0.9]));
(trimf([2850, 4100, 5800]), (trimf([3000.0, 3500.0, trimf([0.4639, 0.6363, 4000.0]), 0.8966])); trimf([0.8, 0.9, 1.0]));
(trimf([4400,6200, 8400]), trimf([0.4676, 0.6367, 0.883]));
“high rainfall λ4 = (trimf([0.6,0.7,0.8]), trimf([0.8,0.9,1]));
Decision Making with Z-Bounded Interval Preference 683
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min Zi,1 , Zi,2 , ..., Zi,5 , and max Zi,1 , Zi,2 , ..., Zi,5 for each alternative are shown in (Table 5). Table 5. Min and max values min(Zi1 , Zi2 , ..., Zi5 )
max(Zi1 , Zi2 , ..., Zi5 )
Crop 1
((1000, 2000, 3000), (0.8001, 0.9003, 0.9967))
((7000, 8000, 9000), (0.6772, 0.7838, 0.8944))
Crop 2
((2850, 3500, 4000), (0.5977, 0.7654, 0.9703))
((4500, 5000, 6400), (0.438, 0.5805, 0.7947))
Crop 3
((3100, 4000, 4500), (0.4279, 0.6031, 0.9026))
((4500, 5000, 6200), (0.5677, 0.6906, 0.8578))
If apply Hurwicz approach with αH = (trimf([0.6,0.7,0.8]), trimf([0.8,0.9,1])), then alternative Ai is characterized by. Ci = αH ∗ max(Zi1 , Zi2 , ..., Zi5 ) + (1 − αH ) ∗ min(Zi1 , Zi2 , ..., Zi5 ) = [((4400, 6200, 8400), (0.4583, 0.6269, 0.8777)); ((3270, 4550, 6720), (0.2694, 0.435, 0.7722)); ((3320, 4700, 6760), (0.2533, 0.4193, 0.7798)); ] Z-valued fair price for Ci calculated as: FP(Z(Ci.A, Ci.B)) =
1
Ci.A− (α)d α +
0
1
Ci.A+ (α)d α
0
1 1 +core(Ci.A) · ( ln(Ci.B− (α)d α + ln(Ci.B+ (α)d α), 0
0
where Ci.A and Ci.B are A and B part of Ci respectively. By using (2) fair price for each alternative Ai is calculated: FairPrice = [6834.98251258984; 1986.31831383195; 1653.56048432834]. So, first alternative is the best alternative.
5 Conclusion Decision making under dual uncertainty is considered, e.g. when both lower and upper bounds of set are uncertain. Studies on decision analysis in such type of uncertain situation in existing literature is very scare. In the paper we have suggested new approach to handle decision making in dual uncertainty environment by using both Hurwicz and fair price approaches. Effectiveness of the suggested approach was demonstrated by real-world decision-making problem, e.g. plant a crops problem.
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References 1. Wang, C., Qiu, Z., He, Y.: Fuzzy interval perturbation method for uncertain heat conduction problem with interval and fuzzy parameters. Int. J. Numer. Meth. Engng 104, 330–346 (2015) 2. Tan, Q., Huang, G.H., Cai, Y.P.: Waste management with recourse: An inexact dynamic programming model containing fuzzy boundary intervals in objectives and constraints. J. Environ. Manag. 91, 1898–1913 (2010) 3. Tavakoli, A., Nikoo, M.R., Kerachian, R., Soltani, M.: River water quality management considering agricultural return flows: application of a nonlinear two-stage stochastic fuzzy programming. Environ. Monit. Assess. 187(4), 1–18 (2015). https://doi.org/10.1007/s10661015-4263-6 4. Zhou, C.Y., Huang, G.H., Chen, J.P., Zhang, X.Y.: Inexact fuzzy chance-constrained fractional programming for sustainable management of electric power systems. Math. Problems Eng. 2018, 1–13 (2018) 5. Jiang, S.Q., Yan, C.-H.: Fuzzy bounded sets and totally fuzzy bounded sets in I-topological vector spaces. Iran. J. Fuzzy Syst. 6(3), 73–90 (2009) 6. Li, Y.P., Huang, G.H., Nie, S.L.: Planning water resources management systems using a fuzzy-boundary interval-stochastic programming method. Adv. Water Res. 33, 1105–1117 (2010) 7. Bekri, E., Disse, M., Yannopoulos, P.: Optimizing water allocation under uncertain system conditions for water and agriculture future scenarios in Alfeios River Basin (Greece)—Part B: fuzzy-boundary intervals combined with multi-stage stochastic programming model. Water 7, 6427–6466 (2015). https://doi.org/10.3390/w7116427 8. Lü, H., Shangguan, W.-B., Yu, D.: Uncertainty quantification of squeal instability under two fuzzy-interval cases. Fuzzy Sets Syst. 328(1), 70–82 (2017) 9. Jorba, L., Adillon, R.: Interval fuzzy segment. Symmetry 10, 309 (2018). https://doi.org/10. 3390/sym10080309 10. Zadeh, L.A., Aliev, R.A.: Fuzzy logic Theory and Applications. Part I and Part II, p. 612. World Scientific, Singapore (2019) 11. Aliev, R.A., Huseynov, O.H., Aliyev, R.R., Alizadeh, A.V.: The Arithmetic of Z-numbers. Theory and Applications. World Scientific, Singapore (2015) 12. Gardashova, L.A., Salmanov, S.: Using Z-number-based information in personnel selection problem. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 302–307. Springer, Cham (2022). https:// doi.org/10.1007/978-3-030-92127-9_42 13. Huseynov, O.H., Adilova, N.E.: Multi-criterial optimization problem for fuzzy if-then rules. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 80–88. Springer, Cham (2021). https://doi.org/10.1007/ 978-3-030-64058-3_10 14. Aliyeva, K.: Fuzzy type-2 decision making method on project selection. In: Aliev, R.A., Yusupbekov, N.R., Kacprzyk, J., Pedrycz, W., Sadikoglu, F.M. (eds.) WCIS 2020. AISC, vol. 1323, pp. 180–185. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-68004-6_23 15. Decision Making under Risk, Certainty and Uncertainty – EconTips. http://ecoptips.com/dec ision-making-under-risk/
Teacher Assessment Model with Basic Uncertain Information Farida Huseynova
and Nigar F. Huseynova(B)
Azerbaijan State Oil and Industry University, 20 Azadlig Ave., Baku AZ1010, Azerbaijan [email protected]
Abstract. The assessment problems of university teachers under extent of uncertainties and ambiguities in education system. This paper explores how to handle and merge those factors in the input information and use the detailed assessment techniques. Here, the basic Information which could be useful in the assessment of an educational institution is proposed to confirm the effectiveness of staff eligibility on the bases of criteria. The flexibility of the proposed model with the involved uncertainties and ambiguities application in educational assessment is proposed to verify by fuzzy systems. Keywords: Assessment · Measurement-based methods · Subjective judgment · Professional growth
1 Introduction It is always needed to focus on problems of satisfying competing demands of instruction and address the sometimes-conflicting concerns of education process. Therefore, there is always a need to provide the comprehensive assessment for a university teacher in a certain period and increase the effectiveness of staff eligibility in the institutions. However, there is no certain evaluation frame capable of collecting, exploring, and interpreting certainty degrees; as a consequence, developing it can be quite helpful in a large number of evaluation problems. It is important to find principles and practicable methods for measuring some quality connected with it. In the paper, a practicable evaluation model is offered to show what steps are necessary to take for the better assessment and practice them in educational system. The real assessment problems consider several kinds of principles by developing the following criteria as: 1. Classroom environment, 2. Language skill, 3. Preparation and Instruction, 4. Professional Responsibility. According to the above-mentioned criteria four performance grades (excellent, good, satisfactory, and bad) were decided. The generalized information was collected and transformed into a more common form which was uncertain Information (UI). Zadeh noted that the rationale for the tradition is that, natural languages are lacking in precision, perceptions are fuzzy in an environment of imprecision, uncertainty and partial truth. Measurement-based methods on perception-based information are needed and CWW can be helpful in it, as one of the © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 686–695, 2023. https://doi.org/10.1007/978-3-031-25252-5_90
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fundamental aims of it is to progress from perceptions to measurements. R. Aliyev suggested logic-driven approach to the development of fuzzy models and stated that, “the networks must refer to as logic-oriented neural networks and constitute an interesting conceptual and computational framework that greatly benefits from the establishment of highly synergistic links between the technology of fuzzy sets [1–4]. Towards an extended Zadeh’s Computing with Words Janusz Kacprzyk added; In fact, except for pure math in which totally abstract concepts and properties, and reasoning [3], may be acceptable, in all other areas even “theoretical” we must resort to concepts and properties which are comprehensible by the humans. Natural language is imprecise (“fuzzy”) but traditional computational linguistics tools have problems with handling imprecision [5–7]. The aim of the paper serving as a guide to teaching effect and result of a professional growth and development of performance expectations for highly effective instructors. The evaluation was provided to get an information and feedback regarding effective practice. A pathway for individual professional growth and a mechanism to nurture professional growth toward common goals supported a learning community to improve and share insights in the teaching process. The aim was to determine if the current instruction or if adjustments needed to be implemented. Certainty degrees with more detailed information could be quite helpful in a large number of evaluation problems. Thereafter, the assessment was provided by a detailed set of observable characteristics of the classes that staff could use to gather ongoing information that contributed to effective performance. Evaluation was provided to get an information and feedback regarding effective practice, a pathway for individual professional growth, a mechanism to nurture professional growth toward common goals and supported a learning community in which people were encouraged to improve and share insights in the profession. The aim was to determine if the current instruction and intervention is positively impacting student achievement or if adjustments need to be implemented. In practice, the collected and involved information contain ever increasingly more uncertainties. Uncertain information has a wide variety of different forms of uncertainties, such as probability information, fuzzy information and its extensions, linguistic information, hesitant information with some existing different types [8]. Hereinafter the more detailed comprehensive assessment by fuzzy set rules have been described.
2 Preliminiaries Definition 1. Fuzzy If-Then rules [9–11]: Fuzzy if-then rule representations are generally used to indicate the conventional statements that fuzzy logic possess. A common fuzzy if-then rule is expressed as follows: If x is A then y is B where A and B denote linguistic values conveyed by fuzzy sets. Multi-input multi-output fuzzy system is formulated in the following form.
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If X 1 is A1 and X 2 is A2 and ... and X n is An Then Y1 is B1 and Y2 is B2 and ... and Ym is Bm where Ai and Bi are data pieces.
Definition 2. Ideal solution methodIdeal solution method [12, 13]. First, all the elements given in xij matrix are normalized by the below mentioned formula ri j : rij =
xij M i=1
(1) xij2
In the second step, assume that normalized ri j matrix and weights W = (w1 , w2 , w3 , ... , wn ) are presented. The final weighted normalized decision matrix Rnorm is below mentioned: ⎤ ⎡ w1 r11 w2 r12 w3 r13 ... wN r1N ⎥ ⎢ w r ⎢ 1 21 w2 r22 w3 r23 ... wN r2N ⎥ ⎥ ⎢ . . ⎥ ⎢ (2) Rnorm = ⎢ ⎥ ⎥ ⎢ . . ⎥ ⎢ ⎦ ⎣ . . w1 rM 1 w2 rM 2 w3 rM 3 ... wN rMN Then Euclidean distance is calculated as a distance of each alternative to the positive ideal solution and negative-ideal solution.
m Si+ = (vi j − vj+ )2 (3) j=1
m − Si = (vi j − vj− )2 , j = 1, 2, 3, ..., m.
(4)
j=1
Finally, the relative closeness to positive and negative ideal solutions is calculated as follows: Ci∗ = Si− /(Si+ + Si− ), 0 ≤ Ci∗ ≤ 1,
i = 1, 2, 3, ..., M .
(5)
3 Statement of the Problem Teacher’s Evaluation Commission consisting of five experts evaluated more than 100 teachers just by gathering information according to the ability of model of desired systems. On the bases of their different subjective judgments and perceptions they made different decisions on the assessments. One commission member was very strict, the
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other might be very lighthearted, therefore the grades on each criterion were accepted from each commission member and the overall grade was divided to number of members of Evaluation Commission. Underneath, we purposely exhibit four samples on each of the grades. Instructor A. All five experts evaluated instructor’s ability in maintaining the classroom environment very highly, because the learning activities were relevant to the curriculum, culture, and instructional goals. The other three experts said that he displayed an extensive content knowledge, with evidence of continuing pursuit of contemporary subject knowledge during the class, goals/objectives, as they were considered according to the varying learning needs of individual students or groups. The other two said that teacher’s preparation and instruction way for maintaining information on student learning and completion of assignments was fully effective, but not all the students participated actively in the maintenance of records. The other experts agreed upon that the teacher’s spoken and written language was perfect and expressive, with well-chosen vocabulary and that was able to enrich the lesson. The experts evaluated instructor’s English language skill as normal. Besides, the experts mentioned that the teacher was persistent in searching effective approaches for students who had difficulties in learning, and he used an extensive repertoire of strategies and solicited additional resources in order to personalize learning. Teacher appealed opportunities for professional development and made a systematic attempt to apply knowledge on the base of research in the classroom and, he displayed continuing search for best practice and anticipated student misconceptions. All five experts noted that his instruction way was the specifically best-example and the professional responsibility was particularly very high. The experts’ opinion about Instructor B. was as follows. They said that he was actively involved in demonstration of a positive attitude towards teaching and selected purposeful activities, strategies and knew in which situations to use them. So, the classroom environment was fine. The other expert’s view was that he had a generally accurate impression of a lesson’s effectiveness and the attainment of goals, but he could also make some general suggestions about improvement for future lessons. Teacher-student interactions were friendly, and it could demonstrate general warmth, caring and respect. Teacher’s system for maintaining information on student learning and completion of assignments was also fully effective. One of the experts said that though there was the lack of experience of teaching at university, the instructor loved to work in a dynamic environment, besides, he had a good background and ability to be a professional teacher. The preparation and instruction were in good quality. And it might not be difficult for him as a teacher to meet students’ needs of learning. He could provide class in English language with a large degree of independence, adapting style and his speech was pleasant. The other expert said that his English is much better than Instructor A’s, but professional responsibility is gracious. Regarding Instructor C. As a teacher, her first objective was to make her students learn the subject in English language and the experts’ assessment on it was good, but one of the experts said the teacher’s language skills was appropriate, vocabulary usage was also correct, but limited. She was a good guide for students during all activities. For two experts she was able to select purposeful activities, strategies and she knew in which
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suitable situations to use them. She could also create enjoyable classroom environment where students felt free to voice their ideas and were not afraid of doing mistakes. For other experts the teacher could not recognize the students’ value of understanding on basic content knowledge in different situations, though she tried to find out tight connections with other parts of the discipline. She also demonstrated general understanding of the different approaches to learning which the students exhibited in learning process. Assessment criteria/descriptors and standards were developed by a teacher. Teacherstudent interactions were generally appropriate, she tried to do her best to fulfill this responsible profession, However, experts pointed out that her Preparation and Instruction, and Professional Responsibility could be improved, as her instruction methods were not so relevant to modern educational technologies. As a result, the experts advised her to develop mutual understanding and respect from her students by teaching them in a better way. About Instructor D. Two of the experts said that his pedagogical background and professionalism was satisfactory, therefore, they accepted the classroom environment as at medium level. But provided speech in English language was not clearly articulated, and the teacher could understand straightforward factual information about common every day or job-related topics in English with difficulty. Consequently, it impacted negatively to the classroom environment. The experts also were dissatisfied that the teacher was unfamiliar with the new different approaches in learning process, therefore the students could not exhibit learning styles, and different “intelligences according to goals/and objectives of the subject. Teacher displayed limited awareness of technology resources and missed the opportunities of being successful at his lessons. The experts advised Instructor D to improve language skill, preparation and instruction, and professional responsibility. After education commissions’ assessment it was needed to provide an indication for decision makers judgments and create a uniform and quantified certainty degree on the base of fuzzy sets for decisions.
4 Solution of the Problem The following rules have been extracted from the text: • If classroom environment is excellent (21), language skill is excellent (20), Preparation and Instruction is good (15), Professional Responsibility is excellent (20) then the overall grade is distinguished (Instructor A) • If classroom environment is good (19), language skill is medium (14), Preparation and Instruction is good (18), Professional Responsibility is good (18) then the overall grade is proficient (Instructor B) • If classroom environment is good (19), language skill is medium (11), Preparation and Instruction is medium (12), Professional Responsibility is bad (7) then the overall grade is basic (Instructor C) • If classroom environment is medium (11), language skill is bad (7), Preparation and Instruction is bad (8), Professional Responsibility is medium (11) then the overall grade is bad (Instructor D)
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2. Codebook for values of criteria and codebook for evaluation grades are presented: Table 1. Codebook for values of criteria Linguistic variables
Triangular fuzzy numbers
Excellent
{20 25 25}
Good
{15 20 25}
Medium
{5 10 15}
Bad
{0 5 10}
Table 2. Codebook for assessment grades Linguistic variables
Triangular fuzzy numbers
Distinguished
{0.75; 1; 1}
Proficient
{0.5; 0.75; 1}
Basic
{0.25; 0.5; 0.75}
Unsatisfactory
{0; 0.25; 0.5}
3. Based on the given data FIS analysis have been presented to calculate the opinions of experts (Fig. 1, 2, 3, 4).
Fig. 1. Fuzzy partition of assessment criteria
To obtain ideal Solution alternatives and attributes are presented (Table 1). Then elements given in the matrix are normalized according to formula X (Table 2). For previous Table 2 the following weighs are categorized: Classroom Environment (0.2), Language (0.3), Preparation and Instruction (0.2), Professional responsibility (0.3).
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Fig. 2. Fuzzy partition of assessment grades
Fig. 3. If Then Rules
Then weighted normalized decision matrix is constructed by multiplying values in Table 2 with corresponding weighs (Tables 3 and 5). The Closeness of each alternative to the positive ideal solution and negative-ideal solution is computed (Tables 4 and 6).
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Fig. 4. Fuzzy inference analysis
Table 3. Decision matrix Classroom environment
Language
Preparation and instruction
Professional responsibility
Teacher A
21
20
15
20
Teacher B
19
14
18
18
Teacher C
19
11
12
7
Teacher D
11
7
8
11
As a result of our calculations in this paper the ranking of teachers has been presented: Teacher A (0,904), Teacher B (0,699), Teacher C (0.289), Teacher D (0.173) which is relevant to experts’ opinions.
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Language
Preparation and instruction
Professional responsibility
Teacher A
0,586
0,723
0,545
0,669
Teacher B
0,53
0,506
0,654
0,602
Teacher C
0,53
0,397
0,436
0,234
Teacher D
0,307
0,253
0,291
0,368
Table 5. Weighed normalized decision matrix Classroom environment Language Preparation and instruction Professional responsibility Teacher A 0,117
0,217
0,109
0,201
Teacher B
0,106
0,152
0,131
0,181
Teacher C
0,106
0,119
0,087
0,07
Teacher D 0,061
0,076
0,058
0,11
Table 6. Closeness to ideal solution S+
S−
Alternative
C
0,022
0,207
Teacher A
0,904
0,069
0,16
Teacher B
0,699
0,17
0,069
Teacher C
0,289
0,191
0,04
Teacher D
0,173
5 Conclusion The proposed model can be helpful for detailed comprehensive evaluation with preferences and uncertainties. Besides this model can be useful to generalize and quantify different types of uncertainty information. Translating expert knowledge to assessment rules can be an effective and flexible comprehensive evaluation model. In practice, decision makers may freely change or modify some steps when necessary, according to different environments and situations.
References 1. Aliev, R.A.: Fundamentals of the Fuzzy Logic-Based Generalized Theory of Decisions. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-34895-2
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2. Bustince, H., et al.: A historical account of types of fuzzy sets and their relationships. IEEE Trans. Fuzzy Syst. 24, 179–194 (2016) 3. Kacprzyk, J.: Studies in Fuzziness and Soft Computing, Bulgaria (2013) 4. Huseynova, F.: Computing with words in natural language processing. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M.B., Sadikoglu, F.M. (eds.) 10th International Conference on Theory and Application of Soft Computing, Computing with Words and Perceptions - ICSCCW-2019. Advances in Intelligent Systems and Computing (AISC), Prague, Czech Republic, vol. 1095, pp. 621–625. Springer, Cham (2020). https://doi.org/10. 1007/978-3-030-35249-3_79 5. Zadeh, L.A.: From computing with numbers to computing with words - from manipulation of measurements to manipulation of perception. In: Wang, P. (eds) Computing with Word, pp 35–67. Wiley Inc. (2001). https://doi.org/10.1109/81.739259 6. Zadeh, L.A.: What computing with words means to me. IEEE Comput. Intell. Mag. (2010). https://doi.org/10.1109/MCI.2009.934561 7. Zadeh L.A.: Computing with Words, Principal Concepts and Ideas. Studies in Fuzziness and Soft Computing, vol. 277, 142 p. (2012). https://doi.org/10.1007/978-3-642-27473-2 8. Jin, L.: Eliciting and measuring hesitance in decision-making. Int. J. Intell. Syst. 34, 1206– 1222 (2019) 9. Zadeh, L.A., Aliev, R.A.: Fuzzy logic Theory and Applications. Part I and Part II, 610 p. World Scientific, Singapore (2019) 10. Adilova, N.E.: Investigation of the quality of fuzzy IF-THEN model for a control system. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, Mo., Babanli, M., Sadikoglu, F.M. (eds.) 11th International Conference on Theory and Application of Soft Computing, Computing with Words and Perceptions and Artificial Intelligence - ICSCCW-2021. LNNS, vol. 362, pp. 28–33. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-92127-9_8 11. Adilova, N.E.: Quality criteria of fuzzy IF-THEN rules and their calculations. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 55–62. Springer, Cham (2021).https://doi.org/10.1007/978-3-030-640 58-3_7 12. Chen, C.-T.: Extension of the TOPSIS for group decision-making under fuzzy environment. Fuzzy Set. Syst. 114(1), 1–9 (2000). https://doi.org/10.1016/S0165-0114(97)00377-1 13. Huseynov, O.H., Adilova, N.E.: Multi-criterial optimization problem for fuzzy if-then rules. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 80–88. Springer, Cham (2021). https://doi.org/10.1007/ 978-3-030-64058-3_10
Design of Receiver in Fuzzy-Chaotic Communication Systems K. M. Babanli(B) Istanbul University, Cerrahpasa, Avcılar, Istanbul 34320, Turkey [email protected]
Abstract. Soft Computing-based communication systems have significant potential to achieve a higher level of security. Suggested before the new approach to the generation of fuzzy-chaotic making signals is developed in this study. The procedure for synchronization of the receiver and transmitter in the fuzzy-chaotic secure system is considered. Time-reversed fuzzy Lorentz system and regular fuzzy Lorentz system are used. The fuzzy time-reversed system is viewed as a receiver system with a fuzzy controller, and the transmitter system is presented as the regular fuzzy Lorentz system. The fuzzy controller provides synchronization of the receiver Lorentz system to transmitter one to get a minimal error. Keywords: Secure system · Fuzzy Lorentz system · Transmitter · Receiver · Time–reversed system
1 Introduction In [1] the possibility of the fractional-order Chen-Lee system (utilizing chain fractance as well as tree fractance circuits) application for building the secure communication purposed electronic circuits is pointed out. The time delay constants and multiple time delays for the control of chaos in the Chen-Lee systems are considered in [2]. Fixed points and chaotic motion are features of the suggested system. In [3–5] the number of works for creating hyperchaotic systems (chaotic systems with more than one positive Lyapunov exponents) is noted. The instability of such systems in more than one direction makes it possible to use them from the perspective of communication security. The fuzzy approach allows building the models for several communication problems. Models based on fuzzy differential equations and IF-THEN rules are developed. Fuzzy DE makes it possible to reflect the system behavior over time under uncertainty in initial conditions and parameters [6–9]. Application of the fuzzy chaotic masking (fuzzy CM) of the transmitted information and relevant synchronization procedures allowing the increase of the security level of the communication system is also examined [10, 11]. This attractive peculiarity of fuzzy chaotic systems (fuzzy CS) causes them very valuable in secure communication systems. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 696–702, 2023. https://doi.org/10.1007/978-3-031-25252-5_91
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In [12], the criterion of synchronization is formulated based on Lyapunov–Krasovskii method. This indicator is used for the synthesis of a quantized state-feedback controller considering transmission-induced delay, data packet dropout, and measurement quantization. Chua’s circuit is utilized for testing the suggested approach. The examined problem is concerned with the application of significant properties of chaos for establishing secure communications. Discovered circumstances necessities the usage of two CS - transmitter/receiver or master/slave. Frequently, the transmitter system appends a message onto a chaotic signal. This type of encoding is named chaotic masking. The decoding of the message is performed by the receiver. Decoding is a process of subtraction between the transmitter signal and its generated copy. Lorenz system (LS) is the best-known nonlinear CS. In the paper, the fuzzy LS is explored as a system with fuzzy both numerical initial conditions and parameters. Trajectories of state variables will be determined by fuzzy functions of time t. There is no information about the design of the receiver in the fuzzy-chaotic secure system in the existing literature. In this study, the solving of this problem is considered. The paper is structured as follows. In Sect. 2 some preliminary information is given. Section 3 describes the methodology of the proposed framework. In Sect. 4 the experimental results are shown. Section 5 presents the conclusion.
2 Preliminaries Definition 1. Fuzzy numberFuzzy number [13–19]. A fuzzy number is a fuzzy set A on real line R which possesses the following properties: a) A is a normal fuzzy set; b) A is a convex fuzzy set; c) α-cut of A, Aα is a closed interval for every α ∈ (0, 1] ; d) the support of A, suppA is bounded. Definition 2. A generalized Hukuhara difference [6, 9]. A generalized Hukuhara difference between fuzzy numbers A, B is a fuzzy number C, if it exists, such that 1) A = B + C A − gH B = C ⇔ , or 2) B = A + (−1)C where addition and scalar multiplication of fuzzy numbers are defined as usual [14]. Definition 3. Lorenz System [20]. Lorenz system is described by the following differential equations: dx2 dx3 dx1 = a(x2 − x1 ), = cx1 − x1 x3 − x2 , = x1 x2 − bx3 , dt dt dt where x1 , x2 , x3 are state variables and a, b, c are parameters. The behavior of this system under some values of a, b and c is chaotic. Definition 4. Time-reversed Lorenz System [21]: Time-reversed Lorentz equations are provided as follows: dx1 (−t) = a(x2 (−t) − x1 (−t)), d (−t)
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dx2 (−t) = cx1 (−t) − x1 (−t) x3 (−t) − x2 (−t), d (−t) dx3 (−t) = x1 (−t) x2 (−t) − bx3 (−t). d (−t)
3 Problem Statement and Solution Receiver system is presented as: dy1 (−t) = −ˆa(y2 (−t) − y1 (−t)) + u1 d (−t) dy2 (−t) = −(ˆcy1 (−t) − y1 (−t)y3 (−t) − y2 (−t)) + u2 d (−t) dy3 (−t) ˆ 3 (−t)) + u3 = −(y1 (−t)y2 (−t) − by d (−t) ˆ and cˆ are where yi (−t) stands for state variable of the receiver system, parameters aˆ , b, estimated parameters. u1 , u2 , and u3 are fuzzy controller to synchronize the receiver Lorenz system to transmitter one; that is, lim e = 0,
t→∞
where the error vector e = [e1 (t) e2 (t) e3 (t)] and e1 (t) = x1 (t) − y1 (−t) e2 (t) = x2 (t) − y2 (−t) e3 (t) = x3 (t) − y3 (−t)
4 Experimental Investigation a = 10.0; b = 8/3; c = 28; x1(i) = x1(j) + (a * (x2(j) − x1(j))) * dt; x2(i) = x2(j) + (c * x1(j) − x1(j) * x3(j) − x2(j)) * dt; x3(i) = x3(j) + (x1(j) * x2(j) − b * x3(j))* dt; y1(i) = y1(j) + ((a_hat(j) * (y2(j) − y1(j))) + u(j,1)) * dt; y2(i) = y2(j) + ((c_hat(j)*y1(j) − y1(j) * y3(j) − y2(j)) + u(j,2)) * dt; y3(i) = y3(j) + ((y1(j) * y2(j) − b_hat(j) * y3(j)) + u(j,3))* dt;
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Initial condition are x1(1) = −0.1;x2(1) = 0.2;x3(1) = 0.3; y1(1) = −0.1; y2(1) = 0.2; y3(1) = 0.3; a_hat(i) = a_hat(j) + ((x2(j) − x1(j)) * e(j,1) − (a − a_hat(j)) * e(j,1)) * dt; c_hat(i) = c_hat(j) + ((x1(j)) * e(j,2) − (c − c_hat(j)) * e(j,2)) * dt; b_hat(i) = b_hat(j) − ((x3(j)) * e(j,3) − (b − b_hat(j)) * e(j,3)) * dt; Controller is described as: u(i,1) = −a_hat(i).* (y2(i) − y1(i)) − a*(x2(i) − x1(i)) − e(i,1) − (a − a_hat(1)).^p; u(i,2) = −c_hat(i).* y1(i) + y1(i).* y3(i) + y2(i) − c.* x1(i) + x1(i).* x3(i) + x2(i) − e(i,2) − (c − c_hat(1)).^p; u(i,3) = −y1(i).* y2(i) + b_hat(i).* y3(i) − x1(i).* x2(1) + b.* x3(i) − e(i,3) − (b − b_hat(1)).^p; Transmitted information is shown in Figs. 1, 2 and 3. 25 20 15 10 5 0 -5 -10 -15 -20
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5 Conclusion In this paper we have suggested a secure communication approach combining fuzzy chaotic masking and synchronization for the receiver Lorentz system to transmitter one by using appropriate control low. Given illustration example shows effectiveness and validity of suggested approach to design high level secure communication system.
References 1. Wang, Sh.-P., Lao, S.-K., Chen, H.-K., Chen, J.-H., Chen, Sh.-Y.: Implementation of the fractional-order Chen-Lee system by electronic circuit. Int. J. Bifurcation Chaos 23(02) (2013). https://doi.org/10.1142/S0218127413500302
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Smart Traffic Monitoring and Control System L. R. Bakirova(B)
and A. R. Bayramov
Azerbaijan State Oil and Industry University, Azadlig Avenue 20, Baku, Azerbaijan [email protected]
Abstract. The article deals with the issues related to digitalization and the development of digital railways in connection with the transition to a high level of technological development. Improving the data-ware and intelligent structure of railways is one of the pressing issues to promote the innovation and development of railways and increase their basic competitiveness. Intelligent transportation systems (ITS) refer to information and communication technologies improving transportation outcomes such as transportation security, transportation productivity, travel reliability, informed travel choices, environmental protection, information exchange, and safety, which are applied to transport infrastructure and vehicles. Perspectives of the smart railway are presented, which allow the railway to be managed on the basis of information security based on the research results, the application of modern sensor and information communication technologies, and big data technology with the aim of efficient use of future smart transport in internal and external connected areas within the trends of creating smart cities and smart villages. An integrated overall structure of the high-level design of intelligent railways and a structural functional model of intelligent monitoring and traffic control systems are proposed to enable the development of high-speed railway construction. Also, the level of big databases, types of big data models, and various big data techniques are reviewed and summarized. The results of this research identify current research gaps and thus directions for future research in BDA in railway transport systems. The ability to use fuzzy logic in control and decision-making under conditions where risks are minimized and eliminated in the railway system by computing known linguistic terms and graphing uncertain knowledge is of great importance. Keywords: Smart monitoring · Big Data · Intelligent transportation systems (ITS) · Machine learning · Internet of Things (IoT) · Digital railway
1 Introduction Currently, there is in-depth research and application examples at a certain level in the fields of smart cities, smart villages, smart homes, smart transportation, and so on. However, the research on smart railways is still in its infancy and in order to make important proposals in this direction, it is required to prepare plans for the development of smart railways without wasting time. In urban areas, the tendency to use metrolike services rather than the railway that is available today with personalized real-time © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 703–711, 2023. https://doi.org/10.1007/978-3-031-25252-5_92
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information for each passenger is interesting. Of course, digital transformation processes have common key components. One of them is formalized ontologies, the development of which is given the most attention in the world today. Big data analytics is increasingly attracting the attention of analysts, researchers, and practitioners of railway transportation and engineering. This makes it necessary to review those research studies. This survey aims to provide a comprehensive review of recent applications of big data in the context of railway engineering and transportation. The application of Big Database (BD), having the ability to directly influence the development tendency of railway transportation, covers three important areas, namely: effective operations, essential maintenance, and security. Each of these areas requires a unique technique and technology as well as a new approach from a modern smart city and digital world view. In that framework, infrastructure requires the transformation of railway transportation into one of the new, higher-level service areas within time and space. It is the demand of time to transform Big Data in this sector into a particularly comfortable, safe, and effective passenger and freight network of the future with many unique features and minimal time loss. Currently, the interaction of this sector both within the sector and with the data and control centers of other transport sectors is not at the required level, and this creates great challenges in control. Due to the challenges of the infrastructure requirements, especially the railway network and railway systems composed of vehicles, the following research is of great importance for the creation of Big Data in the required content and volume.
2 Literature Analysis and Problem Statement Despite the fact that big data has great potential in railways due to the need for analytics and the amount of processed data, challenges arise when predicting the behavior of assets based on physical models and processing experimental data during maintenance [1]. Recent technological advances have caused a revolution in the application of big data cognitive and information tools. There is a lot of data generated by systems using sensors with data acquisition techniques. Data types can have various features, such as structured, semi-structured, and unstructured. Thanks to new achievements in sensor technology, processing and storage of data, and the possibilities of faster computing algorithms, the use of big data is quite dominant in several sectors. This large volume of data collected from various sources provides a basis for a number of opportunities and concepts for future technology that will cover application fields on a new basis and is defined as data that includes data sets with data collection, selection, control, and processing capabilities based on the used software tools [2]. Railway control systems constitute the most productive area for industrial application of formal methods in the development and testing of computer-based equipment, which is related to the ability to precisely define logical rules that guarantee the safe construction of train routes [3]. Data mining (intelligent analysis of data) should not depend on the elements that provide the information. Due to its complexity and sustainable development, it is a key factor for signaling systems. When monitoring of process, equipment, and presentation
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is carried out independently, attempting to “optimize” its functional area regardless of the impact each may have on other functional areas, a low-priority equipment problem can lead to a greater problem in achieving the ability to control a critical process. Cloud computing is able to solve most of the data mining-based problems for railway signaling systems.The processes of configuration and change control management are enhanced by data mining and cloud computing; different types of data from signalling systems are collected, allowing us to control configurations and changes easily and effectively and improve diagnostics of inconsistencies [4]. From the point of view of the digital railway and its development, the anticipation of research in the application of information exchange technology and the role of intelligent network architecture are indicated [5]. Various structural and organizational changes such as fully vertically integrated and distributed architecture should be investigated for more efficient operation of railway stations. Information development of the railway is required to be carried out in real time according to the development of the intelligent railway on the basis of common development prospects, preliminary studies, and research deficiencies of high-speed railway design as a smart railway [6]. The problem of risk assessment with the application of fuzzy logic in the safety of traffic on the railway[7], as well as decision-making based on the numerical data processing of the sensor data reflecting the state of the lines as a measurement result, the traffic situation, the interaction of trains, as well as external effects like meteorological effects, delays and errors in the transmission and reception of information, random situations at intersections and lines, and other situations in the solution of this problem, the problem of integrating consideration of cases such as decision-making and multi-criteria decision-making under conditions of uncertainty [8–12] was considered, and with the transition to a higher level of automatic measurement and control, intelligent monitoring and traffic and movement control issues are considered, making it an important issue to develop a smart railway system that enables safer and more efficient train movement by solving the problems of intelligent monitoring and traffic and movement control issues with the transition to a higher level of automatic measurement and control.
3 Problem Solving and Basic Material In the future, the use of artificial intelligence (AI) in management and decision-making is inevitable. For this, in order to increase the safety of self-driving vehicles by training them to detect obstacles, create and apply a large database for easy solving of processes and problems on the lines, create expert systems that enable the investigation of sources of hazards and the assessment of risks to ensure information security, and general information for each route and train, the possibility of organizing a special database and flexible exchange of information, organizing operative services on the line in real time, selecting an adaptive route and movement schedule based on the identified problems, making optimal decisions for autonomous and other moving and stationary objects in conditions of disconnection from the center and the solution of other issues are in the foreground. Constructing a smart monitoring and control system, assessing the exact position of the train, puts forward the application of remote aero and space technologies, which
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are of particular importance in the development of digital railways. The application of data mining techniques to signalling system maintenance data can help eliminate critical problems and find solutions, and this will significantly improve asset life cycle management. It will also help managers to detect weak points in various procedures. Such discoveries can be used to change maintenance and repair procedures, as a result of which downtime is reduced, uptime increases, and maintenance and repair costs are reduced. DMS is a decision-making system, NB is a knowledge base, CS is a computing system, F/DF is a Fuzzification and Defuzzification executor, and MF is a membership function (Fig. 1). “Smart Railways” big data architecture includes cyber-physical systems, Internet of Things (IoT) and cloud computing, all of which operate together to create. Smart monitoring and management system makes it possible to solve problems such as intermittent and continuous automatic monitoring of the state of the controlled facilities according to the type of parameters, data processing directly in OBCMS, the use of independent energy supply systems, regular receipt of information about the state of lines from LCDS, identifying the location of trains on the line and automatic movement regulation system (AMRS) and interactive visualization unit - control with VT/GIS, risk assessment on the base of BD for mutual control and exchange of information with OBCMS of the interacting facility, etc. At this time, the possibility of approving the decision to transit to an autonomous management system depending on the type of hazard and risk assessment is considered. VT is visualization technologies/geographical information systems, DB is database, LCDS is line control and diagnostics system, ARMS is automatic movement regulation system, OBCMS is on-board control and management system, ACMS is automatic control and management system, and AESCS is alternative energy supply control system. By computing the known linguistic terms and graphing the uncertain knowledge, the possibility of using fuzzy logic in management and decision-making is of great importance, despite the fact that the railway system has certain negative features under conditions where risks are minimal and eliminated (Fig. 2). The algorithm of the created system determines the linguistic variables and the main functions and rules in the base for them under certain conditions, combines their results, creates the required knowledge base, transforms accurate data into fuzzy data using functions (fuzzification), and transforms output data into fuzzy, that is, accurate data (defuzzification) (Table 1). Application Diagram of Fuzzy Set-based Accident Risk Assessment in accordance with the Speed and Position of Two Different Trains A and B is given in Fig. 3. At this time, the selection of membership functions for the modeling of various types of fuzzy data is carried out as follows: The first type of fuzzy set (FS), the membership degree of which is marked as an ordinary number as one of the three membership functions used; the second type is the fuzzy set, the membership function of which is fuzzy; and the third type is accepted as Z-decision making. The probability of an accident is investigated using the measured values of trains A and B on the same line and at different lines and intersections and using the specified rules. A rule table of dependencies between FSs in IF THEN FS relationships, the most common in soft computing technologies.
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Fig. 1. Innovative technology and software for Smart Monitoring and Traffic Control Systems
VT/
AC
DB
AEC
SMTCS
AR
OBCMS
OBC MS
LC
Fig. 2. Integrated systems Smart Monitoring and Traffic Control System.
It is possible to select autonomous or distributed management according to the results of expert systems that allow for the assessment of risks along with the processing of data
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№
Train A Speed
Train B speed
Track lines
Risk assessment
1
Low
Medium
Line is different
Low
2
Low
Medium
Line is same
Medium
3
Low
Medium
Line is same
Medium
4
Low
Low
Line is crossection
Medium
5
Low
Medium
Line is crossection
Medium
6
Low
High
Line is crossection
High
7
Medium
Low
Line is different
Low
8
Medium
Medium
Line is different
Medium
9
Medium
Medium
Line is same
High
10
Medium
Medium
Line is crossection
Very High
11
High
Low
Line is different
Low
12
High
Low
Line is same
Medium
13
High
Low
Line is crossection
High
14
High
Medium
Line is different
Medium
15
High
Medium
Line is same
High
16
High
High
Line is same
Very High
17
High
Medium
Line is same
Very High
18
High
High
Line is crossection
Very High
19
High
Medium
Line is different
Medium
20
High
Medium
Line is same
Very High
21
High
High
Line is same
Very High
Fig. 3. Accident Risk Assessment in accordance with the Speed and Position of Two Different Trains A and B.
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on board in controlled facilities (trains) using modern technologies, including intelligent sensors in intelligent systems and centralized management with the application of IoT. The installation of alternative energy sources and energy regulation management along with measurement control tools in the facility, control points, and stations allows us to supply these facilities with decentralized-autonomous energy and establish the Internet of Things (IoT) within each station. In OBCMS, along with PLC and PLK, special microcontroller-based control, the application of various technological vision systems for risk assessment, detection of fog and obstacles, creation of IoT within train safety and reliability, and improvement of service level are the foundations of the transition to digital railway. Because railway systems have complex technology that includes metro, passenger, and freight train systems, which are directly related to the human factor, the transition to digital technologies, which are the technology of the previous era and the future, along with computerization, automation, and intellectualization, not only being satisfied with autopilot control, but also intelligent monitoring and on the basis of the management system, it is possible to ensure the transitio. The new system allows using modern technologies to improve the quality of services, ensure traffic safety, and increase the efficiency of optimal use of resources. The intelligent monitoring and management system with a big database enables correct forecasts and operational decisions on the basis of processing and analysis, taking into account the visualization of big data, spatial and temporal alignment of data, real-time transmission, and influencing factors in railway operations. Traffic Management Systems (TMS) often consist of subsystems with limited integration capabilities and non-standard interfaces and display rules. Actually, the number and diversity of assets makes the integration of data sources extremely difficult; therefore, network asset status information cannot be widely realized or used to inform TMS decision making. Big data will enable automated, interoperable, interconnected, and advanced traffic management systems; extensible and upgradeable systems using standardized products and interfaces will enable easy migration from legacy systems. Information management systems will have access to a large amount of data about the status of assets and traffic, with the addition of the ability to forecast critical asset status. The positive effects of being able to accurately predict the condition of an asset not only benefit maintenance planning but also benefit other areas, such as traffic management. The development of intelligent monitoring and control systems will enable the further improvement of the following operational areas in railways using big data: development of the information management and controller systems at a new level, which ensures the operability and adaptability of the Integrated Traffic Control and Management System (ITCMS) for trains, taking into account the uncertainties of integration of OBCMS with ACMS for the creation of an advanced asset information system being capable of forecasting, the use of particular and common DB are important conditions to achieve the goal.
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4 Conclusion In smart city and smart village projects, it is appropriate to develop intelligent monitoring and train control systems to ensure high speed of interaction and coordination of multiple trains with high reliability and high operational efficiency in railway networks. At this time, it detects the sources of accidents of various origins, including blind spot warning, collision warning, line and train technical fault warning, intersections on land (cars, etc.), etc. Based on the research findings, the prospects of the intelligent railway are presented, which allows for railway management based on information security, the use of modern sensor and information communication technologies, and the use of big data technology, which should be expanded in order to effectively use smart systems in the future. Within the trend of creating smart cities and smart villages, an integrated overall structure of the high-level design of intelligent railways and a structural functional model of intelligent monitoring and traffic control systems have been developed to enable the development of transport and high-speed railway construction in internal and external connected areas. The developed smart monitoring and train control system (smart monıtorıng and control system) has a large database corresponding to all three systems, as well as expert systems, etc., are decision-making systems capable of assessing the situation to ensure safety and reliability.
References 1. Thaduri, A., Galar, D., Kumar, U.: Railway assets: A potential domain for big data analytics. Procedia Comput. Sci. 53, 457–467 (2015). https://doi.org/10.1016/j.procs.2015.07.323 2. Snijders, C., Matzat, U., Reips, U.-D.: Big data: Big gaps in internet science knowledge. Int. J. Internet Sci. 7(1), 1–5 (2012) 3. Harmattan Hongrie, L.: New results and trends in formal techniques and tools for the development of software for transportation systems: a review. In: Proceedings of the 4th Symposium on Formal Methods for Railway Operation and Control Systems (FORMS03), Budapest (2003) 4. Morant, A., Galar, D., Tamarit, J.: Cloud computing for the maintenance of railway signalling systems (2012) 5. Sneps-Sneppe, M.: On GSM-R prospects of digital railway. Int. J. Open Inf. Technol. 4(12) (2016). ISSN:2307-8162 6. Thompson, L., Bente, H.: What is rail efficiency and how can it be changed? In: Efficiency in Railway Operations and Infrastructure Management (2014) 7. Aliev, R.A., Pedrycz, W., Fazlollahi, B., Alizadeh, A.V., Guirimov, B.G., Huseynov, O.H.: Fuzzy logic-based generalized decision theory with imperfect information. Inf. Sci. 189, 18–42 (2012). https://www.sciencedirect.com/science/article/abs/pii/S0020025511006128 8. Aliev, R.A., Huseynov, O.H.: Decision Theory with Imperfect Information, 444 p. World Scientific, Singapore (2014). https://doi.org/10.1142/9186 9. Aliev, R.A., Gardashova, L.A.: Z-set based approach to control system design. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M.O., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 10–21. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-640 58-3_2
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10. Nuriyev, A.M.: Fuzzy MCDM models for selection of the tourism development site: The case of Azerbaijan. F1000Research 11(310), 1–24 (2022). https://doi.org/10.12688/f1000r esearch.109709.1 11. Aliyeva, K.R.: Multi-criteria house buying decision making based on type-2 fuzzy sets. Procedia Comput. Sci. 120, 515–520 (2017). https://doi.org/10.1016/j.procs.2017.11.273 12. Huseynov, O.H., Adilova, N.E.: Multi-criterial optimization problem for fuzzy if-then rules. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M.O., Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 80–88. Springer, Cham (2021). https://doi.org/10. 1007/978-3-030-64058-3_10
Extension of Delphi Method to Z-Environment Rafig R. Aliyev1
, O. H. Huseynov3(B)
, and E. R. Zeynalov2
1 Azerbaijan State Oil, and Industry University, Azadlyg Avenue, 20, AZ1010 Baku, Azerbaijan 2 Ministry of Agriculture, Baku, Azerbaijan 3 Research Laboratory of Intelligent Control and Decision Making Systems in Industry and
Economics, Azerbaijan State Oil and Industry University, 20 Azadlig, 1010 Baku, Azerbaijan [email protected]
Abstract. Delphi method is very frequently used heuristic methods in forecasting and decision making in complex real-world problems, such as economics, business, engineering etc. Main drawback of existing Delphi methods is that they consider experts knowledge as absolutely reliable. In real-life problems experts’ opinions may be partially reliable. In this paper extension of classical Delphi method to bimodal information environment by using Z-number theory is suggested. Main advantage of proposed Z-Delphi method is fact that is based on direct Z-arithmetic to avoid loss of information. Z-Delphi method is illustrated by numerical example. Keywords: Z-sets · Aggregation of Z-numbers · Delphi method · Distance between Z-numbers
1 Introduction The Delphi method is important representative tool for forecasting and decision making in different areas, such as economics, engineering, medicine, education technology and others. Main characteristics of classical Delphi method are considered in [1–3]. The Delphi tool considered in [3] relies on experts’ opinions in given areas of interest. The opinions of experts are aggregated as statistical measure and return to expert group for updating their knowledge. These classical Delphi methods are widly used in different forecasting problems. The processing of experts’ judgmental knowledge by descriptive statistical methods does not allow to take into account ambiguity and uncertainty inherent in the considered real-world problems. Therefore, a generalization of classical numerical Delphi method to fuzzy environment is considered by different researchers [3–7]. In these approaches experts express their knowledge as linguistic term, which then transform it into fuzzy numbers. [7] considers a combination of “group average” of fuzzy numbers with existing procedures of Delphi tool. Application of fuzzy Delphi methods in realization of innovative product, project management in [5], health research [8], energy market prediction [9] and others [10–12]. The main drawback of both classical and fuzzy Delphi methods is in fact that they don’t take into consideration partial reliability of experts’ opinions. There are a few © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 712–719, 2023. https://doi.org/10.1007/978-3-031-25252-5_93
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works on Z-number valued approach to Delphi method [10–12]. Research in this area is very scarce. In this paper we suggest Z-number-based version of Delphi method using direct Z-arithmetic without transformation of Z-numbers to pure fuzzy numbers. The paper is structured as follows: Sect. 2 includes some preliminaries on existing definition on Z-number theory. The third section is description of suggested Z-valued Delphi method. In Sect. 4, we illustrate the proposed approach on example of predicting oil price.
2 Z-Number Related Some Preliminary Information Definition 1. Continuous Z-Continuous Z-Number [13]. A continuous Z-number is an ordered pair Z = (A, B) where A is a continuous fuzzy number playing a role of a fuzzy constraint on values that a random variable X may take: X is A , B is a continuous fuzzy number with a membership function μB : [0,1] → [0,1], playing a role of a fuzzy constraint on the probability measure of A: P(A) = μA (x)p(x)dx is B. R
Definition 2. A Discrete Z-Number [14]. A discrete Z-number is an ordered pair Z = (A, B) where A is a discrete fuzzy number which describes a fuzzy constraint on values that a random variable X may take – “X is A”, and B is a discrete fuzzy number with a membership function μB : {b1 , ..., bn } → [0, 1], {b1 , ..., bn } ⊂ [0, 1], which describes a fuzzy constraint on the probability measure of A: P(A) is B Definition 3. A Distance Between Z-Numbers [15]. As a Z-number Z = (A, B) is characterized by fuzzy number A, fuzzy number B and underlying set of probability distributions G, the distance between Z-numbers D(Z1 , Z2 ) is defined as follows. Distance between A1 and A2 is computed as D(A1 , A2 ) = sup α∈(0,1] D(Aα1 , Aα2 ) where
α A + Aα12 Aα + Aα22 D(A1 , A2 ) = 11 − 21 2 2
Distance between B1 and B2 is computed analogously. It is needed to find distance between the sets G1 and G2 of probability distributions p1 and p2 underlying Z1 and Z2 . The distance between p1 and p2 can be expressed as 1 1 2 D(G1 , G2 ) = inf p1 ∈G1 ,p2 ∈G2 (1 − (p1 p2 ) 2 dx) R
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Given D(A1 , A2 ), D(B1 , B2 ) and D(G1 , G2 ), the distance for Z-numbers is defined as D(Z1 , Z2 ) = βD(A1 , A2 ) + (1 − β)Dtotal (B1 , B2 ), where DBtotal (B1 , B2 ) is a distance for reliability restriction computed as DBtotal (B1 , B2 ) = wD(B1 , B2 ) + (1 − w)D(G1 , G2 ) β, w ∈ [0, 1] are DM’s assigned importance degrees. Definition 4. Aggregation of Z-Numbers [13–17]. Let a Z-valued vector Z = (Z 1 , Z 2 , …, Z n ) be given. The arithmetic mean operator M() assigns to any vector Z a unique Z-number Z M = M(Z 1 , Z 2 , …, Z n ) = (AM , BM ): 1 Zi n n
M (Z1 , Z2 , . . . , Zn ) =
i=1
3 Z-Valued Delphi Steps The porposed Z-Delphi method consists of following steps: 1. To choose experts in the investigated problem Ei , i = 1,n. 2. To determine the first questionnaire for declaration opinions of experts. 3. To collect opinions of experts, described as linguistic variables, for example as price of oil will be Very high, Sure”. 4. To create Codebook for value of interesting and its reliability. 5. To find average value of experts by using Z-number saggregation procedure given in (Definition 4). 6. To calculate distance between Z-value obtained in Step 5 and experts’ individual opinions. Because of Z-subtraction is used obtained error is not expected crisp zero. It is necessary to formulate a set that would reflect the required accuracy. For example, as ZA0 = (−με, 0; γ + ε), ZB0 here μ is deviation of fuzzy zero, and ε is used for specified accuracy acceptance level. ε is defined considering how close to zero the error should be. If error is more than given accuracy information obtained in Steps 5 and 6 is sent back to experts for second iteration to update their opinion. 7. Experts once again formulate their opinion taking into account information from the first iteration. 8. The whole process is repeated until error between average Z-value opinion and all experts fills into given accuracy.
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4 Numerical Example In this example oil price forecasting problem by using suggested Z-Delphi method is considered. Six experts are chosen for estimation world oil barrel price for the next month. Query was performed by Internet. Opinions of experts as Z-numbers are shown in Table 1. Table 1. Z-valued opinions of experts (first iteration) Expert
Z-number
Expert 1
(115,120,125; very sure)
Expert 2
(114,118,122; likely)
Expert 3
(119,122,125; sure)
Expert 4
(119,125,131; likely)
Expert 5
(110,115,120; sure)
Expert 6
(115,120,125; very sure)
Here likely = {0.6, 0.65, 0.7}; sure = {0.8, 0.85, 0.9}; very sure = {0.9, 0.95, 1}. Average opinion of all experts is calculated as ((115, 120, 125)(0.9, 0.95, 1)) + ((114, 118, 122)(0.6, 0.65, 0.7)) Zaverage = 6 ((119, 122, 125)(0.8, 0.85, 0.9)) + ((119, 125, 131)(0.6, 0.65, 0.7)) 6
((110, 115, 120)(0.8, 0.85, 0.9)) + ((115, 120, 125)(0.9, 0.95, 1)) + 6
+
= (115.3, 120, 124.7)(0.31, 0.39, 0.47) Then in accordance with Step 6 of procedures given in Sect. 3 distances between average Z-value and experts’ individual opinions are calculated as Zdis 1 = (115.3, 120, 124.7)(0.31, 0.39, 0.47) − (115, 120, 125)(0.9, 0.95, 1) = (−9.7, 0, 9.7)(0.29, 0.38, 0.46) Zdis 2 = (115.3, 120, 124.7)(0.31, 0.39, 0.47) − (114, 118, 122)(0.6, 0.65, 0.7) = (−6.7, 2, 10.7)(0.22, 0.3, 0.38) Zdis 3 = (115.3, 120, 124.7)(0.31, 0.39, 0.47) − (119, 122, 125)(0.8, 0.85, 0.9) = (−9.7, 2, 5, 7)(0.27, 0.35, 0.44)
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Zdis 4 = (115.3, 120, 124.7)(0.31, 0.39, 0.47) − (119, 122, 125)(0.9, 0.95, 1) = (−15.7, −5, 5.7)(0.24, 0.31, 0.38) Zdis 5 = (115.3, 120, 124.7)(0.31, 0.39, 0.47) − (110, 115, 120)(0.8, 0.85, 0.9) = (−4.7, 5, 14.7)(0.27, 0.36, 0.44) Zdis 6 = (115.3, 120, 124.7)(0.31, 0.39, 0.47) − (115, 120, 125)(0.9, 0.95, 1) = (−9.7, 0, 9.7)(0.29, 0.38, 0.46) Total error of opinions of experts’ is calculated as 6
(Zaverage − Zdis i ) = (−56.2, 0, 56, 2)(0.05, 0.06, 0.08)
i=1
In this paper the pre-specified acceptance interval was set to [0,8]. It is obvious that error of experts’ opinion is very high, and it is needed to send back obtained in this iteration to experts to update their opinion. Updated opinion of experts in the second iteration is given in Table 2. Table 2. Z-valued opinions of experts (second iteration) Expert
Z-number
Expert 1
(117,120,123; very sure)
Expert 2
(116,120,124; sure)
Expert 3
(118,121,124; very sure)
Expert 4
(115,121,127; sure)
Expert 5
(113,118,123; sure)
Expert 6
(118,120,122; very sure)
Consistance accuracy in the second iteration is 6
(Zaverage − Zdif i ) = (−45.98, 0, 45, 98)(0.03, 0.09, 0.2)
i=1
Again accuracy is not within pre-specified interval. It is needed the next iteration. ˙Information given by experts in the third iteration is given in Table 3.
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Table 3. Z-valued opinions of experts (third iteration) Expert
Z-number
Expert 1
(119.5,120,120.5; very sure)
Expert 2
(119.5,120,120.5; very sure)
Expert 3
(119.5,120,120.5; very sure)
Expert 4
(119.5,120,120.5; very sure)
Expert 5
(119.5,120,120.5; very sure)
Expert 6
(119.5,120,120.5; very sure)
Results of calculation is given below: ((119.5, 120, 120.5)(0.9, 0.95, 1)) + ((119.5, 120, 120.5)(0.9, 0.95, 1)) Zaverage = 6 ((119.5, 120, 120.5)(0.9, 0.95, 1)) + ((119.5, 120, 120.5)(0.9, 0.95, 1)) + 6 ((119.5, 120, 120.5)(0.9, 0.95, 1)) + ((119.5, 120, 120.5)(0.9, 0.95, 1)) + 6 = (119.5, 120, 120.5)(0.7, 0.85, 0.92) Zdis 1 = (119.5, 120, 120.5)(0.7, 0.85, 0.92) − (119.5, 120, 120.5)(0.9, 0.95, 1) = (−1, 0, 1)(0.66, 0.82, 0.9) Zdis 2 = (119.5, 120, 120.5)(0.7, 0.85, 0.92) − (119.5, 120, 120.5)(0.9, 0.95, 1) = (−1, 0, 1)(0.66, 0.82, 0.9) Zdis 3 = (119.5, 120, 120.5)(0.7, 0.85, 0.92) − (119.5, 120, 120.5)(0.9, 0.95, 1) = (−1, 0, 1)(0.66, 0.82, 0.9) Zdis 4 = (119.5, 120, 120.5)(0.7, 0.85, 0.92) − (119.5, 120, 120.5)(0.9, 0.95, 1) = (−1, 0, 1)(0.66, 0.82, 0.9) Zdis 5 = (119.5, 120, 120.5)(0.7, 0.85, 0.92) − (119.5, 120, 120.5)(0.9, 0.95, 1) = (−1, 0, 1)(0.66, 0.82, 0.9) Zdis 6 = (119.5, 120, 120.5)(0.7, 0.85, 0.92) − (119.5, 120, 120.5)(0.9, 0.95, 1) = (−1, 0, 1)(0.66, 0.82, 0.9) Zdis = (−6, 0, 6)(0.32, 0.5, 0.8). Thus, the derived forecasting information on oil price is acceptable. Oil price in the next month will be about 120 $ for barrel with relaibility about 85%.
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5 Conclusion To handle variety and complexity of real-world prediction problems different forecasting methods have been developed. One of widle used among them is Delphi method. Main drawback of classical Delphi tool is that descriptive statistical information processing is used that does not take into account ambiguity and uncertainty of knowledge of experts. Extension of classical Delphi method to fuzzy case does not consider reliability of opinions of experts. In this paper Z-number-based version of Delphi method using direct Z-arithmetic without transformation of Z-numbers to pure fuzzy numbers is proposed. Proposed method is illustrated by example on predicting price of oil.
References 1. Chang, P.-T., Huang, L.-C., Lin, H.-J.: The fuzzy Delphi method via fuzzy statistics and membership function fitting and an application to the human resources. J. Fuzzy Sets Syst. 112, 511–520 (2000) 2. Dalkey, N., Helmer, O.: An experimental application of the Delphi method to the use of experts. Manag. Sci. 9, 458–467 (1963) 3. Aliev, R.A., Fazlollahi, B., Aliev, R.R.: Soft Computing and its Application in Business and Economics. Springer, Heidelberg (2004) 4. Kaufmann, A., Gupta, M.M.: Fuzzy Mathematical Models in Engineering and Management Science. North-Holland, Amsterdam (1988) 5. Bojadziev, G., Bojadziev, M.: Fuzzy logic for business, finance, and management. World Sci. (1997) 6. Ishikawa, A., Amagasa, M., Shiga, T., Tomizawa, G., Tatsuta, R., Mieno, H.: The max-min Delphi method and fuzzy Delphi method via fuzzy integration. J. Fuzzy Sets Syst. 55, 241–253 (1993) 7. Murray, T.J., Pipino, L.L., Gigch, J.P.: A pilot study of fuzzy set modification of Delphi. J. Human Syst. Mgmt. 5, 76–80 (1985) 8. de Meyrick, J.: The Delphi method and health research. Health Educ. 103(1), 7–16 (2002) 9. Czaplicka-Kolarz, K., Stanczyk, K., Kapusta, K.: Technology foresight for a vision of energy sector development in Poland till 2030 Delphi survey as an element of technology foresighting. Tech. Forecast. Soc. Change 76(3), 327–338 (2009) 10. Lawnik, M., Krakowczyk, J., Banasik, A.: Fuzzy Delphi method with Z-numbers. In: Damaševiˇcius, R., Vasiljevien˙e, G. (eds.) ICIST 2019. CCIS, vol. 1078, pp. 24–32. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-30275-7_3 11. Lawnik, M., Banasik, A.: Delphi method supported by forecasting software. Information 11(2), 65 (2020). https://doi.org/10.3390/info11020065 12. Lawnik, M., Banasik, A.: The applications of Z-numbers in the Delphi Method. In: Lopata, A., Gudonien˙e, D., Butkien˙e, R. (eds.) ICIST 2021. CCIS, vol. 1486, pp. 241–250. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-88304-1_19 13. Aliev, R.A., Huseynov, O.H., Zeinalova, L.M.: The arithmetic of continuous Z-numbers. Inf. Sci. 373, 441–460 (2016) 14. Aliev, R.A., Huseynov, O.H., Aliyev, R.R., Alizadeh, A.V.: The Arithmetic of Z-Numbers: Theory and Applications. World Scientific, Singapore (2015) 15. Aliyev, R.R.: Fuzzy logic’s Z-extension-based decision tools and their applications. Dissertation work for the degree of Doctor of Philosophy, 104 p. Baku, Azerbaijan (2021)
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16. Aliev, R.A., Alizadeh, A.V., Huseynov, O.H.: The Arithmetic of Discrete Z-Numbers. Inform. Sci., Elsevier, Netherlands 290, 134–155 (2015). https://doi.org/10.1016/j.ins.2014.08.024 17. Aliev, R.A., Alizadeh, A.V., Jabbarova, K.I., Huseynov, O.H.: Z-number based linear programming. J. Intell. Syst., Wiley, New Jersey, United States 30, 563–589 (2015). https://doi. org/10.1002/int.21709
Analysis of Intelligent Interfaces Based on Fuzzy Logic in Human-Computer Interaction Rahib Imamguluyev(B)
and Aysel Aliyeva
Odlar Yurdu University, Baku 1072, Azerbaijan [email protected]
Abstract. Human-Computer Interaction: It is the ability to use the computer interface (almost all software where we can visually click on buttons or menus and write text) that enables communication with the user and the computer. The human factor plays a big role in this field, as it does in every field. The most basic subject that instructional technologists work on is the design and development of educational products and programs that will support learners effectively, efficiently and satisfied and increase their performance. Compared to the past, significant changes have occurred in this regard, and information technologies have become more involved. Human Computer Interaction (HCI) is one of the most important tools of instructional technologists at this point. They can create more effective and satisfying learning environments by using it in their projects in the most effective way. In this article, Analysis of Intelligent Interfaces Based on Fuzzy Logic in Human-Computer Interaction has been applied. Keywords: Human-Computer Interaction · HCI · Interfaces · Fuzzy logic · Fuzzy set
1 Introduction Human Computer Interaction (HCI) is an interdisciplinary field of design, development, evaluation and application of interactive technologies. Human Computer Interfaces are closely related to various fields of activity, such as ergonomics, graphics and industrial design, sociology, anthropology and education, as well as human behavior, psychology, cognitive sciences, computer technology and software engineering [1]. Theoretical and practical research in the field of Human Computer Interaction (HCI) aims to produce information and communication technology products for human and human needs. In other words, the main goal is to adapt technology to people, not technology [1]. A new interdisciplinary field that emerged in the 1970s and became widespread in the late 1990s, Human Factors and his most popular work, Human Computer Interfaces, are trying to eliminate or minimize these problems. Working people are exploring how to create more user-friendly or, in other words, “user-transparent” information technology systems. As the name suggests, Human Computer Interfaces encompass both technology and people [1, 2]. From a human point of view, it is necessary to get acquainted with © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 720–726, 2023. https://doi.org/10.1007/978-3-031-25252-5_94
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all the sciences of psychology, communication, sociology and organizational sciences., computer science and sociology. It is still debated whether the Human Computer Interfaces are a separate field of science due to the fact that they are influenced by different disciplines and take many basic concepts and theories from these disciplines. In addition to claiming in being a sub-branch of Software Engineering or Psychology, there are those who claim that Human Computer Interfaces are a new field of interdisciplinary work [2]. According to Norman, the first step in the interaction process is perception. The user sitting in front of the screen perceives an error message on the screen, for example, with a visual perception system. This visual information needs to be interpreted in the second step. The error message on the screen goes through a process in the mind in the form of an ordinary or serious message. Therefore, an assessment is carried out. All these steps are called the Evaluation process. At the end of this cognitive evaluation process, what is the goal or expectation is determined, and then the Execution process begins. This process ensures that the reaction is applied in accordance with the set goal. The first step in the realization process is to decide whether or not to do something. According to Norman, it is impossible to create a perfect interface, ie to reset the length between the two ends of the bay. Therefore, it is often inevitable that users will make mistakes when using a program. But the key is to minimize the possibility of error with good design and to give the user the appropriate options to recover from the error, even if it is made. In other words, a life jacket should be immediately available for a swimmer who has difficulty swimming in the bay [2, 3]. Different definitions in the field of human computer interfaces are given by different people. Therefore, the definitions of the field will be clearer if we consider what this field does, what it does, what problems it aims to solve, and its basic dimensions without being bound by a single definition. The dimensions of the irreplaceable definition of Human Computer Interfaces can be summarized as follows [2, 3]: – Interdisciplinary work - Not only the field of science, but many fields of science help to solve existing problems. – Practicality (Usability) - Probably the most important aspect of human computer interfaces. It works on key research topics such as how to make technology easier to use and how to improve the interface. – Design - Looking for an answer to the question of how to design better products in terms of use and functionality. – Impact - Try to understand and answer the question of how technology affects and changes people’s lives. The decision-making and Reaction Selection Center compares and evaluates the information received from the outside world and accepted for processing by the cognitive system with the information stored in short-term and long-term memory. There are two types of decisions made by this center: 1. Automatic decision 2. Willful decision
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If a person has information and experience about the input on the cognitive system, the decision is made very quickly and automatically. For example, a word processor program automatically performs many operations that a user is interested in if it is used for a long time. Operations such as page editing, memorizing, and speaking are performed almost thoughtlessly. However, if the information from the cognitive system is not present in the person’s past experience, then a situation arises that needs to be decided carefully. It takes time to make a decision and choose the appropriate reaction. If we look at the example of a word processor, if a new version of this program is released and the interface is significantly changed according to the old program, the user will lose the old copy. Automatic behavior gives way to voluntary behavior. From the point of view of HCI, this feature of our brain is of great importance. Otherwise, if an interface design does not point to the user and creates uncertainty in decision-making times, decision-making and reaction choice will slow down and even lead to wrong decisions. The decision is made by making the appropriate decisions and selecting the appropriate response. This reaction can be a mouse click, a key press on the keyboard, or a window on the screen [4]. The use of design cannot be judged by a single criterion. In addition, usability is not necessarily a value, but may vary depending on the situation. Therefore, what an HCI expert understands about the use of a product is different from what an ordinary person understands. HCI experts create a utilization rate by evaluating Efficiency, Efficiency and Satisfaction together in the definition of use [1–4]. As you can see, the use of each interface can be different for different people. It is advisable to use a fuzzy logic model to evaluate the suitability of a designed interface.
2 Interface Assessment Methods Suppose you are implementing an information system project. You believe in the importance of the Human-Computer-Interaction concepts and want the system you have developed to be used most easily by your target audience. How would you do that? What method would you use to check system usage or identify usage problems? This section will try to answer these questions [2–5]. Practical tests are one of the most important parts of HCI research. These tests can be applied from the beginning of a software development process or used to test the use of a finished product. As can be easily estimated, there is no single usage test. The most appropriate test or tests should be selected based on the experience of the person or organization performing the test, the size of the project, the size of the resources allocated for the test, and time constraints. This section provides examples of approaches and test types that can be followed when performing tests [4, 5]. Usage tests are divided into two groups as Type and Approach. The approach is related to the source of the data obtained, and this title is divided into four categories: Design Guide-Based, User-Based, Expert-Based, and Model-Based. The type name defines the purpose of the test and is divided into two parts: Formative / Diagnostic and Metrication / Summative. A specific approach and type must be selected for each usage test. For example, a software company may develop a new accounting software project
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(user-based) from the beginning (environment) by regularly testing it with accountants who will use the software. In addition, administrators of an existing virtual shopping site can seek the opinion of an expert to identify problems that exist on the site (End of Process, Expert-Based Approach). 2.1 Expert Appraisals and Heuristics One common approach to interface design and testing is expert evaluation of the interface. The most common of the various expert assessments is the use of heuristics, which provide features with a good interface design. In heuristics, the platform (both hardware and software) is generally independent and aimed at increasing utilization. Numerous heuristic guidelines have been proposed since the 1970s. Recommended by Jacob Nielsen, it is one of the most popular intuitive guides for user interface design today. This guide, Nielsen’s Ten Usability Heuristics, focuses on key points in the design of user interfaces, and usability should be questioned in this context (Nielsen 2010) [1, 2, 5]. Experts make extensive use of heuristics, especially for usage tests during interface assessments. Heuristics is used in expert-based usage tests for reasons such as allowing very fast assessments and requiring no special equipment. Expert-based usage test, as the name implies, is performed by experts. More than one specialist must perform a heuristic assessment. Experts compare their assessments and determine if there is a discrepancy between their interpretations. In my opinion, the best way to compare expert estimates is to use a fuzzy logic model [6].
3 Fuzzy Logic and Expert Systems Fuzzy logic theory is a branch of mathematics that summarizes the concepts of classical logic and set. The concept of fuzzy logic was introduced in 1965 and its founder was the Azerbaijani Lotfi Zade [7–12]. Logic is a science. As you probably know, all sciences originate from the science of logic. That is, this science is related to cognition. Aristotle has this philosophical saying: “What a person says is either true or false.“ Apparently, Aristotle did not accept the intermediate degrees between the categories of false and true. But for the first time in the world, Lotfi Zadeh proved that everything has a degree except God [8, 11]. In other words, there is no such thing as absolute white and absolute black in the world. There are thousands of shades between these two concepts - intermediate nuances. Zadeh softened Aristotle’s sharpness. In other words, it revealed the intermediate categories that actually existed [10] The essence of the theory is tolerance. In the meantime, this theory introduced and restored the rights of shades that were not visible in the open scene. Conflict resolution, truth-finding, and accuracy of calculations cannot be done without paying attention to the intermediate phases. If done, they will have enough flaws [7, 9–12]. Expert systems sometimes use inaccurate knowledge and facts in matters solved by intelligent systems. It is impossible to say whether such knowledge and facts are completely true or completely false (1 or 0); for example, there is knowledge that has an
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accuracy of 0.7. To solve this problem, fuzzy logic is used in expert systems and other software systems of artificial intelligence. In this logic, variables can take any value between 0 (false) and 1 (true). In fuzzy logic, the outcome of an operation is expressed in terms of probability, not in terms of certainty; For example, in addition to the values “true” and “false”, the result may also receive values such as “probably true”, “probably true”, “probably false”, “probably false”. Thus, our suggestion is that after studying the expert opinions on any designed interface, the linguistic variables (eg, very bad, bad, average, good, very good, etc.) are included in the model and the optimal result is obtained. Each linguistic variable has five fuzzy values with triangular membership functions as follows: Input variables - very bad, bad, normal, good, very good (Figs. 1 and 2.) Definition of concepts: ⎧ ⎫ x < 0.5 ⎬ ⎨ 1, µbad (x) = 0.7−x , x ∈ [0.5, 0.7] , ⎩ 0.2 ⎭ x > 0.7 0, ⎧ ⎫ x < 0.5 ⎬ ⎨ 0, µgood (x) = x−0.5 (1) , x ∈ [0.5, 0.7] , ⎩ 0.2 ⎭ x > 0, 7 1, ⎧ ⎫ ⎪ x < 0.5 ⎪ ⎨ 1,
⎬ 0.7−x 2 x ∈ [0.5, 0.7] µverybad (x) = CON µbad (x)2 = , ⎪ ⎪ ⎩ 0.2 x > 0.7 ⎭ 0, ⎫ ⎧ ⎪ x < 0.5 ⎪ ⎬ ⎨ 0, 2 x−0.5 µverygood (x) = CON µgood (x)2 = x ∈ 0.7] [0.5, , ⎪ ⎪ ⎩ 0.2 x > 0.7 ⎭ 1,
Fig. 1. Membership functions of input linguistic variables.
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Fig. 2. Description of the rules of logical derivation.
4 Conclusion The purpose of this work is to use fuzzy logic for optimal evaluation of expert decisions in human computer interfaces. The fuzzy inference system presented in this article can be used both in the process of evaluating site designs and in the optimal evaluation of various software interfaces. The fuzzy inference system of the Sugeno type interprets the input vector values and determines the output vector values based on user-defined rules. The model described provides an analytical framework for planning decisions and is open to easily incorporating new parameters and constraints.
References 1. May, J.: Human-Comput. Interfac. (2015). https://doi.org/10.1016/B978-0-08-097086-8.950 72-4 2. Cagiltay, K.: Human computer interaction and instructional technologies (in Turkish). Fund. Instruct. Technol.: Theor. Res. Trends (2016). https://doi.org/10.14527/9786053644576.18 3. Zhang, E.Y.: Populist human-computer interface. Anal. Curr. Fut. Global Trends Populism (2022). https://doi.org/10.4018/978-1-7998-4679-6.ch007 4. Cagiltay, N., Gurcan, F., Cagiltay, K.: Mapping human–computer interaction research themes and trends from its existence to today: a topic modeling-based review of past 60 years. Int. J. Human-Comput. Interact. 37(4) (2020). https://doi.org/10.1080/10447318.2020.1819668 5. Goswami, L.: Human computer interface using electrooculogram as a substitute. In: International Conference Intelligent. Emerging Methods of Artificial Intelligent Cloud Computer, (2022). https://doi.org/10.1007/978-3-030-92905-3_21 6. Valiyev, A., Imamguluyev, R., Ilkin, G.: Application of fuzzy logic model for daylight evaluation in computer aided interior design areas. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., M., Jamshidi, Babanli, M., Sadikoglu, F.M. (eds.) ICAFS 2020. AISC, vol. 1306, pp. 715–722. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-64058-3_89
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7. Imamguluyev, R.: Application of fuzzy logic model for correct lighting in computer aided interior design areas. In: Kahraman, C., Cevik Onar, S., Oztaysi, B., Sari, I.U., Cebi, S., Tolga, A.C. (eds.) INFUS 2020. AISC, vol. 1197, pp. 1644–1651. Springer, Cham (2021). https:// doi.org/10.1007/978-3-030-51156-2_192 8. Abdullayev, T., Imamguluyev, R., Umarova, N.: Application of fuzzy logic model for optimal solution of light reflection value in lighting calculations. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Mo., Jamshidi, Babanli, M., Sadikoglu, F.M. (eds.) ICSCCW 2021. LNNS, vol. 362, pp. 384–391. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-92127-9_53 9. Imamguluyev, R.: Determination of correct lighting based on fuzzy logic model to reduce electricity in the workplace. In: International Conference on Eurasian Economies, Baku, Azerbaijan (2020). https://doi.org/10.36880/C12.02456 10. Aliev, R., Tserkovny, A.: Fuzzy logic for incidence geometry. In: Kosheleva, O., Shary, S.P., Xiang, G., Zapatrin, R. (eds.) Beyond Traditional Probabilistic Data Processing Techniques: Interval, Fuzzy etc. Methods and Their Applications. SCI, vol. 835, pp. 49–85. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-31041-7_4 11. Zadeh, L.A., Aliev, R.A.: Fuzzy logic Theory and Applications. Part I and Part II, p. 610. World Sci., Singapore (2019) 12. Zadeh, L.A.: Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets Syst. 90, 111–127 (1997)
Determination of the Uncertainty of the Parameters of Oxidative-Reduction Reactions of Titanomagnetites U. N. Sharifova1
, A. N. Mammadov1,2(B) and M. B. Babanly1
, D. B. Tagiev1
,
1 Nagiyev Institute of Catalysis and Inorganic Chemistry of ANAS, Baku, Azerbaijan
[email protected] 2 Azerbaijan Technical University, Baku, Azerbaijan
Abstract. Areas of uncertainty in the thermodynamic parameters of oxidative reduction reactions of titanomagnetite concentrates were identified using the universal genetic algorithm (MGA). The oxidative reduction reactions of titanomagnetite concentrates for the production of iron, titanium dioxide and sodium vnadate in a reactor flow mode, with a change in the composition and pressure of the reaction products, have been investigated. To determine the temperature dependences of the Gibbs free energy of oxidative reduction reactions in the temperature range 900–1400 K, the Temkin-Shvartsman equation was used, modified taking into account the thermodynamic functions of the formation of solid solutions and the value of the vapor pressure of gaseous components. It was revealed that the ranges of temperature and pressure uncertainty for direct reduction of Fe3 O4 to free iron, oxidation of V3+ to V5+ in granules of titanomagnetite concentrates are: P = 0.1 ÷ 1 atm, T = 1000 ÷ 1400K. Keyword: Titanomagnetite concentrates · Redox reactions · Thermodynamics · Multipurpose Genetic Algorithm
1 Introduction Titanomagnetite concentrates are enrichment products of titanomagnetite ores. In particular, the titanomagnetite concentration of Azerbaijan contains: Fetotal - 51–54 mass. %, TiO2 - mass. 5–7% and 1–1.5 mass% V2 O5 and V2 O3 [1]. The growing interest in titanomagnetites is associated with the depletion of magnetite ores and the production of titanium, chromium and vanadium along with iron [2–5]. To determine the optimal conditions of oxidation-reduction reactions thermodynamic calculations are used [6]. In [7], on the basis of the physicochemical theory of granulation in a drum apparatus and on the basis of thermodynamic-kinetic analysis, it was found that the reduction reactions of titanium-magnetite concentrate with natural gas to produce iron powder proceed in the kinetically-diffusion region and are conjugated. In [8], the equilibrium thermodynamic conditions were determined for the direct reduction of magnetite to free iron and the oxidation of vanadium oxide (3) to vanadium oxide (4) and vanadium oxide (5) in granules © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 727–733, 2023. https://doi.org/10.1007/978-3-031-25252-5_95
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of titanomagnetite concentrates. The temperature range of the reduction of magnetite to iron and the oxidation of vanadium using a mixture of natural gas and hydrogen have been determined. Oxidative-reduction reactions of titanomagnetite concentrates take place in a reactor, flow-through mode, changing the composition and pressure of the reaction products. However, to date, the relationship between the temperature, pressure of the gas phase and the productivity of redox reactions has not been sufficiently studied. The aim of this work is to identify the area of uncertainty of the thermodynamic parameters of oxidative-reduction reactions of titanomagnetite concentrates using the multipurpose genetic algorithm (MGA).
2 Thermodynamics of Oxidative Reduction Reactions of Titanomagnetites The total oxidation reaction of vanadium oxide (3) to vanadium (5) and the reduction of magnetite to iron has the following form: 4Fe3 O4 · TiO2 (s) + V2 O3 (s) + CH4 (g) + Na2 CO3 (s, l) = 12FeO(s) + 2NaVO3 (s, l) + 2CO(g) + 2H2 O(g) + TiO2 (s)
(1)
3Fe3 O4 · TiO2 (s) + V2 O3 (s) + 2CH4 (g) + 2H2 (g) + Na2 CO3 (l) = 9Fe(s) + 2NaVO3 (l) + 3CO2 (g) + 6H2 O(g) + TiO2 (s)
(2)
To determine the temperature dependences of the Gibbs free energy of the reactions (1,2) in the temperature range 900–1400K, Temkin-Schwartsman equation [9] was used, modified taking into account the thermodynamic functions of the formation of solid solutions and the vapor pressure values of gaseous components: 298 2 0 − S 0 T − T (a ln T − T − 1 + b T2 + 298 − 298 GT = H298 298 298 2T 2 −2 3 2982 T 298−1 298−2 + c − + + +c∗ T6 + 298 3T 2 2 −T 2 −RT xlnf (x) + (1 − x) ln(1 − x) + RT i lnPi (3) The last term RT νi lnPi of (3) takes into account the deviation from the standard state. Therefore, the following equation represents the temperature dependence of the standard Gibbs free energy in equilibrium: 298 2 0 − S 0 T − T (a ln T − T − 1 + b T2 + 298 − 298 GT = H298 298 298 2T 2 −2 3 2982 T 298−1 298−2 + c +c∗ T6 + 298 − + + 3T 2 2 −T 2 −RT xlnf (x) + (1 − x) ln(1 − x) (4) (3) takes into account the temperature dependence of the specific heat in the form: Cp = a + bT + c∗ T 2 + cT −2
Determination of the Uncertainty of the Parameters
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0 , S 0 - free energies, standard enthalpies and entropies of the reacGT , H298 298 tions (1, 2); νi – stoichiometric coefficients; Pi - partial pressures of components in a non-equilibrium state (the reaction takes place in the reactor under the flow regime of the gas mixture). RT xlnf (x) + (1 − x)ln(1 − x) − is the free energy of formation of solid solutions due to the replacement of ions V3+ in the crystal cell Fe3 O4 of ions Fe3+ with the formation of solid solutions xFe3 O4 + (1 − x)V2 O3 → Fe3x V2(1−x) O3+x , n- the total number of unlike cations in the solid solution; The thermodynamic parameters of simple substances and compounds involved in the reactions taken from [10]. The following values were used in the calculations: 0 0 (V2 O3 ) = −1218.7 ± 2.5 kJ/mol; H298 (NaVO3 ) = −1148.6 ± 2.5; H298 0 0 H298 (Fe3 O4 ) = −1117.7 ± 2.5; H298 (Na2 CO3 ) = −1129.4 ± 2.5; 0 0 H298 (CH4 ) = −74.8 ± 0.5; H298 (CO2 ) = −393.50.5; 0 0 H298 (H2 O, gas) = −241.80.5, S2980 (V2 O3 ) = 98.32 ± 1.5J/(mol.K); 0 (Fe O ) = 146.21 ± 2.5; S 0 (Na CO ) = 134.97 ± 2; S298 ±0 (NaVO3 ) = 99.981.5; S298 3 4 2 3 298 0 (CH ) = 186.19 ± 2.5; S 0 (CO ) = 213.6 ± 0.5; S 0 (H O, gas) = 188.74 ± 2.5, S298 4 2 298 298 2 0 (H ) = 130.61 ± 1.5, S 0 (Fe) = 27.15 ± 0.5, C0 (V O ) = 103.2 ± 0.5J/(mol.K); S298 2 298 298 2 3
C2980 (NaVO3 ) = 97.6 ± 0.5; C2980 (Fe3 O4 ) = 150.8 ± 1.0; C0298 (Na2 CO3 ) = 112.3 ± 1.5;
C0298 (CH4 ) = 35.8 ± 0.5; C0298 (CO2 ) = 37.1 ± 0.5; C0298 (H2 O, gas) = 33.6 ± 0.5, C0298 (H2 ) = 28.8 ± 0.5, C0298 (Fe) = 25.2 ± 0.5. In this temperature range the sodium carbonate and sodium metavanadate melt: Tm (Na2 CO3 ) = 1137K, Tm (NaVO3 ) = 963 K. Therefore, when determining the temperature dependence of the Gibbs free energy of the reaction (1, 2) by (3), the enthalpy and entropy of melting of these compounds were used: Hm (Na2 CO3 ) = 28080 J/mol, Hm (NaVO3 ) = 28310 J/mol, Sm (Na2 CO3 ) = 24.77 J/(mol.K), Sm (Na VO3 ) = 31.38 J/(mol.K). 2.1 Determination of Reaction Conditions by Using MGA Reactions (1) and (2) proceed in a flow mode: methane CH4 is introduced (reaction 1), or a mixture of this gas with hydrogen (reaction 2). At the same time, gaseous reaction products are removed from the reactor: CO2 and H2 O vapors. In the reactor, with a
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continuous supply of methane and hydrogen, gaseous reaction products are removed; for the Gibbs free energy, we can write: GT − GT0 GT∗ = = ln Pini = ln KP (5) RT RT GT∗ in (5) is a measure of the deviation of the system from the equilibrium state. In the equilibrium standard state, the total vapor pressure Pini is equal to 1 atm. In a nonequilibrium state, when gaseous products are removed, this value decreases. It follows from reaction (1, 2) that when used as methane, iron is reduced to state 12. When the second reducing agent, hydrogen, is added to methane, iron is completely reduced to the state of metallic iron. For the conditions of reaction (2), the Multipurpose Genetic Algorithm was used [11]. To carry out the iterative process, the following conditions were used. The main condition for the reaction is GT∗ < 0
(6)
The search is carried out for the temperature range 900–1400 K, for the total pressure of the gas mixture 0 ÷ 1 atm, the ratio of the gas mixture H2 /CH4 = 0 ÷ 1. The MGA then changes the values of the variables depending on how well these values generate the solidus and liquidus curves, which correspond to the present experimental data, taking into account the uncertainties of the for temperature and pressure values based on the condition (6). A fuzzy logic-weighting scheme looks at all the objective values of a particular member and rescales them to a value between 0 and 1. Zero if the value is the worst of the population. One if it falls within the experimental uncertainty.
Fig. 1. 3D model of dependence GT∗ of reactions (2) on temperature and on the total ratio of partial pressures in the flow-through mode of iron reduction and vanadium oxidation with a mixture of methane and hydrogen.
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Figure 1 shows a 3D model of the dependence of the free energies of reactions (2) on temperature and on the total ratio of partial pressures in the flow-through mode of iron reduction and vanadium oxidation with a mixture of methane and hydrogen. The temperature dependences of the Gibbs free energy for reactions (1, 2) are shown in Fig. 2.
Fig. 2. Dependences of the Gibbs free energies of reactions (1 and 2) on temperature in the equilibrium state (lines 2, 4) and in the flow-through mode (lines 1, 3).
3 Results and Discussion It follows from Fig. 1 that in the flow mode, with a decrease in the total vapor pressure, the negative values of the Gibbs free energy increase, indicating the efficiency of redox reactions. In this case, an abrupt increase in the value of GT∗ begins at a total vapor pressure of 0.3 atm. Negative values of the Gibbs energy also increase with increasing temperature. Figure 2 is an uncertainty range of reaction temperatures. Figure 1 and 2, it follows that reactions 1 and 2 proceed at lower temperatures, when the gaseous reaction products are removed and the reactions proceed under nonequilibrium thermodynamic conditions. At the lowest temperature of 950 K, reaction (1) begins. However, in this reaction, FeO is obtained, the reduction of the Fe3 O4 to the production of metallic Fe does not occur. In reaction (2), a complete reduction of iron occurs. This is due to the fact that the redox gas phase contains hydrogen in addition to methane. In order to determine the equilibrium and nonequilibrium thermodynamic conditions of direct reduction of magnetite to free iron and oxidation of V3+ to V5+ in granules fluted with soda vanadist titanomagnetite concentrates with the participation of natural gas, it is necessary to take into account the free energies of formation of solid solutions based on magnetite and the vapor pressure of the components in the flow system when methane is continuously supplied and gaseous reaction products are removed. The 3D model of the free energy of the system deviation from the equilibrium state depending
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on the total ratio of partial pressures in the flow mode of iron reduction and vanadium oxidation shows that the greatest effect of reducing the temperature of redox reactions is observed in the region of low vapor pressure of the reaction products.
4 Conclusions The use of MGA made it possible to determine the ranges of temperature and pressure uncertainty for direct reduction of magnetite to free iron and oxidation of V3+ to V5+ in granules, titanomagnetite concentrates with a mixture of natural gas and hydrogen.For total pressure, the uncertainty interval is: P = 0.1 ÷ 1 atm, for a temperature 1000 ÷ 1400 k. Acknowledgments. This work has been carried out within the framework of the international joint research laboratory “Advanced Materials for Spintronics and Quantum Computing” (AMSQC) established between the Institute of Catalysis and Inorganic Chemistry of ANAS (Azerbaijan) and Donostia International Physics Center (Basque Country, Spain) and partially supported by the Science Development Foundation under the President of the Republic of Azerbaijan, grant number E˙IF/MQM/Elm-Tehsil-1–2016-1(26)-71/01/4-M-33.
References 1. Sharifova, U.N.: Processing of the vanadate fraction in Ajinaur titanium-magnetic concentrates. Azerbaijan Chem. J. 2, 63–68 (2022). https://doi.org/10.32737/0005-2531-2022-263-68 2. Kushnarev, A.V., Mironov, K.Y., Zagainov, S.A., Forshev, A.A.: Improvement in vanadiumcontaining titanomagnetite processing technology. IOP Conf. Series: Materials Sci. Eng. 966, 012062 (2020). https://doi.org/10.1088/1757-899X/966/1/012062 3. Taylor, P.R., Shuey, S.A., Vidal, E.E.: Extractive metallurgy of vanadium-containing titaniferous magnetite ores: a review. Miner. Metall. Proces. 23(2), 80–86 (2006). https://doi.org/ 10.1007/BF03403340 4. Kustov, A.D., Kenova, T.A., Zakirov, R.A., Parfenov, O.G.: Integrated processing of difficultly dressed titanium-containing ores. Mater. Sci. Russ. J. Appl. Chem. 90(8), 1208–1213 (2017). https://doi.org/10.1134/S107042721708002X 5. Mihalev, A.L., Parfenov, O.G.: Waste-free processing of ilmenite and titanomagnetite concentrates. Chem. Sustain. Dev. 16(2), 237–240 (2008). (In Russian). https://elibrary.ru/item. asp?id=11532529 6. Mammadov, A., Pashazade, G., Gasymova, A., Sharifova, U.: Processing of titaniummagnetite concentrates for the production of iron, modifications of titanium dioxide and titanium. Chem. Chem. Technol. 14(2), 227–233 (2020). https://doi.org/10.23939/chcht14.02 7. Mamedov, A.N., Samedzade, G.M., Gasymova, A.M., Gasymov, V.A.: Modelling of the granulation of powder titanium magnetite concentrate and its reduction with natural gas. Cond. Matter Interohases 19(2), 248–255 (2017). https://doi.org/10.17308/kcmf.2017.19/198 8. Sharifova, U.N., Qasimova, A.M., Mammadov, A.N.: Nonequilibrium thermodynamics of oxidative recovery reactions vanadium containing titanomagnetite concentrates. Chem. Prob. 17(4), 551–557 (2019). https://doi.org/10.32737/2221-8688-2019-4-551-557 9. Morachevskij, A.G., Sladkov, I.B. Thermodynamic calculations in metallurgy. Metallurgy (1985) (In Russian). https://search.rsl.ru/ru/record/01001239425
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10. Iorish, V.S., Yungman, V.S.: Database of thermal constants of substances (2006). http://www. chem.msu.ru/cgi-bin/tkv.pl 11. Preuss, M., Wessing, S., Rudolph, G., Sadowski, G.: Solving phase equilibrium problems by means of avoidance-based multiobjectivization. In: Kacprzyk, J., Pedrycz, W. (eds.) Springer Handbook of Computational Intelligence, pp. 1159–1171. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-43505-2_58
Solving Problem of Unit Commitment by Exchange Market Algorithm and Dynamic Planning Method Ebrahim Babaei1
and Sadig Mammadli2(B)
1 Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran
[email protected]
2 Odlar Yurdu University, Koroglu Rahimov Street, 13, 1072 Baku, Azerbaijan
[email protected]
Abstract. This paper solves the unit commitment problem using the exchange market algorithm. Due to the complexity and large size of the unit commitment situation and the existence of multiple constraints and binary variables inside the objective function of this optimization problem, the direct use of intelligent algorithms to find the problem variables may not be desirable. So, the dynamic advance method is used to determine in-circuit power plants by aiming to solve the problem and reducing calculations. After finding the possible modes per hour according to the load for active units, the exchange market algorithm is used for the economic load distribution. In solving the unit commitment problem, the constraints related to the power limit of the generators, the balance of production and consumption, and conditions associated with the power plants’ minimum on/off time are used. Also, to increase the solution speed, the exchange market algorithm is implemented twice. In the first stage, the economic load distribution is done approximately. After determining the optimal path in the second stage, the monetary load distribution in this route is done accurately. A comparison between this method and different methods has been performed to confirm the correctness and speed of combining the exchange market algorithm with the dynamic programming method. Keywords: Unit commitment · Exchange market algorithm · Dynamic planning method · Economic load dispatch
1 Introduction Electricity consumption is intermittent with random changes. Often in the late night or early morning, consumption is low and gradually increases with the opening of industries and consumption centres. In addition to the daily load changes, weekly changes can also be considered, which are usually lower on the weekends than on the weekdays. As a result, there is a need to produce energy in some hours and reduce production in other hours. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 734–746, 2023. https://doi.org/10.1007/978-3-031-25252-5_96
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Since starting up the power plant and unit commitment involves turning on the boiler, synchronizing the generator with the grid, and generating power, it will include a considerable cost. On the other hand, starting up and keeping up multiple power plants to avoid start-up costs is also not economical because of the depreciation of power plant components. In addition, keeping up power plants can cause problems in load dispatch. Therefore, considering the economic and technical aspects, it seems necessary to have a proper plan to turn on or off the power plants. The main difference between economic load dispatch and the unit commitment problem is that in economic load dispatch, the goal is to distribute a certain amount of load between some power plants assuming all of them are keeping up. While unit commitment problem, in addition to the economic load dispatch, considers the commitment of the power plants in such a way that at the end of a certain period (for example, 24 h), the total cost of load supply is minimized. It should be noted that the unit commitment problem is an optimization problem. So the time solution time is crucial because the amount of load predicted may be erroneous, or during operation, other events may lead to changes in the network arrangement that should be identified and notified immediately. The used algorithm in this problem has enough accuracy and speed. It should be noted that the unit commitment problem may be done for a week (168 h), which shows the importance of the mentioned issue, regardless of how the load is forecasted. Indeed, the unit commitment problem is a sub-problem. In this regard, several studies have been conducted to solve the unit commitment problem. In [1], comprehensive research has been conducted on the implemented methods to solve the unit commitment problem considering the effects of renewable resources. In this reference, it is mentioned that the combined methods of meta-heuristic algorithms based on the right-of-way table are used to deal with the large dimensions of this problem and its non-convex and nonlinear properties. Also, some references have used mathematical methods such as MILP to solve the unit commitment problem [2]. This method obtains possible answers. It also determines the amount of optimality of each solution. The problem with this method is that it consumes a high time compared to other methods, such as the priority method. If the dimensions of the problem increase, the solution time also increases exponentially. In this regard, some references, such as [3], by changing the problem’s main formulation’s structure corresponding to the production of each generator in an interval between zero and one, reduce the problem-solving time. Reference [4] has transformed the unit commitment problem into a linear problem in the form of approximation and solved it. The approximation used in this paper based on the dual Lagrange basis is the main problem. In summary, several mathematical and classical methods have been presented to solve this nonlinear and non-convex problem, which are: Lagrangian relaxation (LR), Branch and Bound (BB), Priority list method (PLM), Linear programming (LR), Multiple integer linear programming (MILP), Dynamic programming (DP), Dynamic programming Lagrangian relaxation (DPLR). The common problems with these methods can be named as 1. applying a heavy computational load, 2. getting stuck at local half-points, and 3. poor convergence.
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Many recent advances have been made in intelligent methods and their application in solving complex engineering problems. These methods are based on the laws of nature or physics. The main advantage of these methods is the random selection and movement of points (population), which allows new answers to be generated, which frees up local optimal points. Such approaches are used to solve continuous and discrete problems with little difference in their structure. Examples of these methods are evolutionary programming (EP), evolution strategy (ES), genetic programming (GP), genetic algorithm (GA), and differential evolution (DE). In addition, some methods based on the mass movement of particles have been proposed to solve the unit commitment problem, including particle swarm optimization (PSO), artificial bee colony (ABC), grey wolf optimization (GWO), ant colony optimization (ACO), fireworks algorithm (FWA). In [5], using the developed method of insect search by modifying and creating binary capabilities and creating a meta-innovative algorithm called “Binary coded modified moth flame optimization algorithm” has solved the problem in the placement circuit of power plants. This algorithm is based on the movement of insects looking for points of light. In [6], using a combination of an intelligent method and a mathematical method, the unit commitment problem is solved for energy management in microcircuits despite two-way currents in lines and storage and by considering the voltage constraints and generators’ limitations. This reference uses the genetic method to deal with the problem’s nonlinear constraints that are problematic for the MILP method. The final result of the planning is from the comparison of the answers obtained from the two selected methods. Recently, other approaches to solving the unit commitment problem are presented in the literature [7–9]. The mentioned references show that the unit commitment problem is one of the most critical issues in the operation of power systems, which has attracted a lot of attention. Due to the presence of binary variables to determine power plants’ status and the problem’s large size, complete problem-solving based on intelligent methods will take time. Because intelligent algorithms operate randomly based on the determination of variables, it is difficult to find solutions that can meet all constraints simultaneously. As a result, in this paper, the dynamic programming method will accelerate the problemsolving process.
2 Methods 2.1 Forward Dynamic Programming Approach The dynamic programming optimization method is based on searching for the answer with the least cost for each simple subproblem. This method is commonly used to solve the unit commitment problem because it can control and overcome nonlinear and nonconvex problems in large dimensions and dynamic variables. On the other hand, the main problem of dynamic programming is the dimensional problem that occurs with increasing the size of the system under study. It is necessary to obtain the current cost at any time and add the costs of turning on the power plants (or turning off the power plants) to the cost of that stage to implement this method in a power plant grid. In the end, the route that needs the least cost and meets the problem’s constraints according
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to the priorities table and operational constraints of the power plants will be selected as the best route. The flowchart in Fig. 1 shows how the forward dynamic programming method works. In this figure K represents the current time, L-the state in the previous hour, and I -the status in the present hour. Usually, if there are multiple power plants in the problem during the solution, the number of possible routes also increases too much. Hence, the user sets a limit to determine the maximum number of forwarding routes that should be considered. If the problem becomes impossible with a specific limitation, the problem itself is unsolvable, or the minimum limit is chosen, it can be solved by increasing this limitation. start
K =1 FCOST ( K ,1) = MIN [ PCOST ( K ,1) + SCOST ( K − 1, L : K ,1) ] { L}
K = K +1
X = Do for all states I in Period K
{L} = " N " Feasible States in interval K − 1 FCOST ( K ,1) = MIN [ PCOST ( K ,1) + { L}
SCOST ( K − 1, L : K ,1) + FCOST ( K − 1, L) ] Save N lowest cost
No
X = Do for all states I in Period K
Is K = M last hour ? Yes
Trace optimal schedule
end
Fig. 1. Solving the unit commitment problem using the dynamic programming method [10].
2.2 Formation of the Priority Table Because the load consumed varies over time, turning off a power plant or turning on a new one will sometimes be necessary. Determining which units to turn on or off with each load change will not be easy, especially in a large system. One way to solve this problem is to use a priority table based on the sum of existing power plants’ minimum and maximum production capacity to determine the conditions under which the load can be supplied. The formation of such a table will help reduce the cases under consideration
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of the algorithm by eliminating the instances where the sum of the maximum production capacity of the power plants is less than the load. In this table, the number 2N − 1 to 1 is assigned to each case, respectively. Zero modes are equivalent to shutting down all power plants, which is not considered. Table 1 shows the priority table for a specific example with four power plants. Table 1. Priority table for an example with four power plants [10] State Combination of units Maximum net capacity of the compound 15
1111
690
14
1110
630
13
0111
610
12
0110
550
11
1011
440
10
1101
390
9
1010
380
8
0011
360
7
1100
330
6
0101
310
5
0010
300
4
0100
250
3
1001
140
2
1000
80
1
0001
60
0
0000
0
1234 1 = active unit 0 = inactive unit
2.3 Exchange Market Algorithm The exchange market algorithm is a calculation algorithm inspired by buying and selling exchanges in the cash trading market. This algorithm was introduced in 2014, and solving various power system problems shows this algorithm’s validity and reliability for engineering problems. As mentioned in [11], unlike other intelligent algorithms with only one search operator and one learning operator, this algorithm has two and two learning operators, leading to better answers and higher convergence speed. There is an additional description of exchange markets in the article mentioned. Reference [18] has done economic load distribution using the exchange market algorithm with intelligent search. This algorithm uses a penalty coefficient to reduce the search space and increase the
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convergence speed. In [19], the exchange market algorithm can strategically locate the battery for demand response and mitigate losses. In [20], the exchange market algorithm distributes the economic burden and minimizes pollution as a multi-objective problem. Reference [18] presents locating distributed generation resources in a radial network by the exchange market algorithm. Regarding the operating mechanism of the algorithm, it can be briefly stated that the initial population created (one state) is randomly selected to be within limits set by the constraints. In the next step, each shareholder is arranged according to merit (in this case, the minimum cost of production). The percentage of members in a higher position in this category is selected as smart and successful. According to the number of shares of the first group with a small amount of risk, the second group is those who change their claims to reach the first group. Indeed, if a person in the first group owns a numbers of exchange and another person in the same group owns b numbers of the same exchange, the person in the second group chooses the same exchange between a and b. It will select an exchange between the two values for the value of a particular exchange. The remaining members are in the third category, willing to take a higher risk than the second category to increase their profits. Unlike the second category, they use the difference between their exchange values and the exchange values of the first category and make changes accordingly. It should be noted that the first group members will not change their shares. Also, the mentioned algorithm is implemented for two types of markets with normal states and markets with turbulence. In a normal market situation, unexpected events do not happen, and shareholders aim to maximize their profits without taking non-market risks. The second is the fluctuating market case, which may be due to market policies. In this case, after categorizing the shareholders, each shareholder makes every effort to be ranked higher by taking high risks but intelligently. Each shareholder will pursue different fiscal policies depending on the profits earned at this stage. The categorization is done again, and the shareholders are placed in various categories. Indeed, the goal of a fluctuating market is to escape local optimizations. The steps of the exchange market algorithm are summarized as follows: 1. Determine the number and amount of shares of each member on an initial basis 2. Calculating the objective function and classification of shareholders 3. Apply changes to the exchanges of second-tier individuals in balanced market conditions 4. Apply changes to the exchanges of third parties in balanced market conditions 5. Recalculate the objective function with new exchange values and member rankings 6. Trading in shares of second-tier individuals under fluctuating market conditions (first-tier exchanges remain unchanged) 7. Buying and selling exchanges of third-class individuals under fluctuating market conditions (they make changes in their exchanges regardless of their total exchanges) 8. This loop will be repeated until it reaches the desired goal (go to step 2). Finally, it is noteworthy that a coded binary version of the exchange market algorithm for solving discrete problems has recently been introduced [19].
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3 Problem Formulation The following nomenclature is used in the problem formulation. G
Number of thermal power plants
H
Scheduling time
g
Power plant’s number indicator
h
Time indicator
g FC ψgh
Fuel cost of g th power plant
SUgh
The cost of start-up of the g th power plant at the time of h
Pgh
Obtained optimized generated power for the g th power plant at the time of h
SUghot
The cost of hot start-up of the g th power plant
SUgcold
The cost of cold start-up of the g th power plant
Mdgh.ther.
Minimum downtime of the g th power plant
Mugh.ther.
Minimum uptime of the g th power plant
offgh.ther.
Number of consecutive hours that the g th power plant is down
Ongh−1.ther.
Number of consecutive hours that the g th power plant is up
ther. Pg,min
Minimum thermal power generation by the g th power plant
ther. Pg,max
Maximum thermal power generation by the g th power plant
LDh
System’s load at the time of h
Binary variable to indicate the status of the g th power plant at the time of h
req
SRh
Rotating storage required by the system at the time of h
RDr g RUr g
Ramp down rate of the g th power plant Ramp up rate of the g th power plant
In (1), the fuel cost for the power plant is calculated in terms of each power plant’s production capacity. Note that ag bg and cg are known as production coefficients. g
Fc (Pgh ) = ag + bg (Pgh ) + cg (Pgh )2
(1)
SUgh = SUghot , if Mdgh.ther. ≤ offgh.ther. ≤ Mdgh.ther. + Coldgh SUgh = SUgcold , if offgh.ther. ≥ Mdgh.ther. + Coldgh
(2)
Equation (2) represents the cost of starting a power plant, which is presented in two ways: the cost of cold and hot starting up. With the explanation that if a power plant needs to be shut down for less than a certain amount of time, that power plant will not shut down entirely and will remain on standby. But if the planning time for a unit to shut down is long, the economic mode is to turn the unit off completely and then turn it on again
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if necessary by paying for a cold start-up. With this explanation, the objective function of the problem includes the cost of producing units and starting up the turned-off power plants: g TC = h g Fc (Pgh ) ψgh + SUgh (1 − ψgh )ψgh (3) ∀h ∈ H ; g ∈ G; ψgh ∈ {0, 1} Problem constraints are: ther. ther. ≤ Pgh ψgh ≤ ψgh Pg,max ψgh Pg,min
(4)
The allowable range for the production capacity of each unit is shown in (4). Pgh ψgh = LDh , ∀h ∈ H ; g ∈ G
(5)
Load and production balance are guaranteed at all times using (5). req Pgh ψgh = LDh + SRh
(6)
g
g
If it is necessary to consider the uncertainty of the load (equivalent to considering the reservation), the condition specified in (6) will also be added to the set. ⎧ h−1,ther. ⎪ < Mugh,ther. ⎨ 1, if 1 ≤ Ong ψgh = 0, if 1 ≤ offgh−1,ther. < Mugh,ther. (7) ⎪ ⎩ 0 or 1, otherwise Equation (7) indicates that each turned-on unit will start up again only after a specific time has elapsed (minimum off time). Also, each turned-on unit can be turned off after a particular time (minimum on time) has elapsed. ψgh Pgh,min ≤ Pih ψgh ≤ ψgh Pgh,max
(8)
Equation (8) shows that the production of committed units is in a specific range so the changes in production capacity are limited as follows: ther. , P h−1 − RDr ) Pgh,min = max(Pg,min g g (9) ther. , P h−1 + RUr ) Pgh,max = min(Pg,max g g In principle, the above equations indicate the rate of increase/decrease in power generation of power plants.
4 Applying the Proposed Method to the Unit Commitment Problem As mentioned in the section calculating the active unit production capacity, the exchange market algorithm has been used. In the case of power distribution, the exchange is the same amount of production of each power plant, and each shareholder shows an answer.
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The first step involves creating the initial population (initial values for capabilities). Care must be taken that these values are initially generated to apply to all existing constraints. The algorithm will generate the following populations according to the coefficients introduced in [8]. Note that the user can adjust the number of populations and the number of repetitions. At each stage, 20% of the people formed as the intelligent and first groups. Besides, the remaining 50% was the second group, and 30% was the third group. The penalty method is used to apply the constraints to the algorithm. So that in each iteration, if a person violates one specified constraint, it will be multiplied by a considerable amount to be transferred to the bottom of the shareholders’ table and practically becomes out of competition. First, the possible modes that can supply the load are selected through the priority table to apply the constraints and determine the possible modes for load supply. Also, the unacceptable modes are removed, and economic load distribution is done between the remaining modes. Scheduling is forward, meaning it starts at one o’clock in the morning and continues until 24 h later. The situation of the power plants at zero o’clock is clear because it is related to the previous day. The total possible transfers to the new clock are considered at each hour according to the possible states and paths found for the previous hours. The transfers that violate the minimum on/off time constraints are excluded among these transfers. Also, transfers that the power plants will not be able to provide the desired reservation will be banned. Then, among the remaining transfers, some transfers (in the limit number) that have the lowest cost are saved, and the rest are not considered. According to Fig. 1, the cost of loading in each hour and the cost of starting up the power plants (if a new power plant is turned on) per hour are added to the previous cost. The limit value determines the maximum number of progress paths stored in memory during the algorithm’s execution to accelerate the solution process by reducing the number of paths. This way, the power plants’ composition for n hours will be determined.
5 Simulation and Results The load information and power plants mentioned in [5] were used to test the proposed method’s speed and accuracy. Finally, the problem-solving time and the value of the objective function were compared with other research in this field. The goal is 24-h planning for 10 power plants with start-up and operation costs specified. The proposed algorithm in MATLAB software on a computer with an intel core i5 processor with 6 GB of RAM will get the desired answer in just 14 s. Table 2 shows the results of unit planning for each hour. Table 3 compares the results of other articles with the proposed algorithm. The results indicate the speed and quality of problem solving using the proposed algorithm. By comparing the results, it can be seen that the proposed method performs better than many of the applied methods, and the few mentioned that have a lower total cost have several times more calculation time.
Solving Problem of Unit Commitment by Exchange Market Algorithm
743
Table 2. Power plants scheduling unithour
1
2
3
4
5
6
7
8
1
455
245
0
0
0
0
0
0
0
0
2
455
295
0
0
0
0
0
0
0
0
3
455
370
0
0
25
0
0
0
0
0
4
455
455
0
0
40
0
0
0
0
0
5
455
390
0
130
25
0
0
0
0
0
6
455
360
130
130
25
0
0
0
0
0
7
455
411
129
130
25
0
0
0
0
0
8
455
455
130
130
30
0
0
0
0
0
9
455
455
130
130
85
20
25
0
0
0
10
455
455
130
130
162
26
28
0
14
0
11
455
455
129
130
161
73
25
12
10
0
12
455
455
130
129
160
79
25
47
10
10
13
454
448
128
128
153
53
25
0
11
0
14
455
455
129
130
79
27
25
0
0
0
15
455
455
130
130
30
0
0
0
0
0
16
455
310
130
130
25
0
0
0
0
0
17
455
260
130
130
25
0
0
0
0
0
18
455
360
130
130
25
0
0
0
0
0
19
455
455
130
130
30
0
0
0
0
0
20
455
455
130
130
161
33
26
0
10
0
21
455
452
130
130
74
34
25
0
0
0
22
455
455
0
0
145
20
25
0
0
0
23
455
425
0
0
0
20
0
0
0
0
24
455
345
0
0
0
0
0
0
0
0
Table 3. Comparison of methods Methods
The best total cost in $
Solving time in sec
GAMS (MINLIP) [5]
567022
0.083
MA [17]
566686
61
ICGA [18]
566404
7.4
LRPSO [19]
565869
42 (continued)
9
10
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E. Babaei and S. Mammadli Table 3. (continued) Methods
The best total cost in $
Solving time in sec
SA [20]
565828
3
GRASP [21]
565825
17
GA [22]
565825
221
LRGA [23]
564800
518
Proposed method
564648
14
SFLA [24]
564769
35
EP [25]
564551
100
DPLR [26]
564049
108
6 Conclusion Intelligent methods have received a lot of attention in recent decades due to the complexity of engineering problems, the addition of numerous constraints, and the inability of current mathematical methods to solve such problems. In some cases, combining mathematical and intelligent methods with the benefits of both techniques can yield better results. This paper uses the exchange market intelligent method for power distribution and the dynamic programming method for optimal programming of thermal power plant production units to solve the unit commitment problem. Its speed is essential. The obtained results from the proposed algorithm were compared with the results of the existing methods. Regarding the comparison results, the accuracy and speed of convergence of the proposed algorithm were shown, indicating this method’s effectiveness.
References 1. Abujarad, S.Y., Mustafa, M.W., Jamian, J.J: Recent approaches of unit commitment in the presence of intermittent renewable energy resources: a review. Renew. Sustain. Energy Rev. 70, 215–223 (2017). https://doi.org/10.1016/j.rser.2016.11.246 2. Farhat, A., El-Hawary, M.E.: Optimization methods applied for solving the short-term hydrothermal coordination problem. Electr. Power Syst. Res. 79(9), 1308–1320 (2009). https://doi.org/10.1016/j.epsr.2009.04.001 3. Yang, L., Zhang, C., Jian, J., Meng, K., Xu, Y., Dong, Z.: A novel projected two-binaryvariable formulation for unit commitment in power systems. Appl. Energy 187, 732–745 (2017). https://doi.org/10.1016/j.apenergy.2016.11.096 4. Hua, B., Baldick, R., Wang, J.: Representing operational flexibility in generation expansion planning through convex relaxation of unit commitment. IEEE Trans. Power Syst. 33(2), 2272–2281 (2018). https://doi.org/10.1109/tpwrs.2017.2735026 5. Reddy, K.S., Panwar, L.K., Panigrahi, B.K., Kumar, R.: Solution to unit commitment in power system operation planning using binary coded modified moth flame optimization algorithm (BMMFOA): a flame selection based computational technique. J. Comput. 25, 298–317 (2018). https://doi.org/10.1016/j.jocs.2017.04.011
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6. Nemati, M., Braun, M., Tenbohlen, S.: Optimization of unit commitment and economic dispatch in microgrids based on genetic algorithm and mixed integer linear programming. Appl. Energy 210, 944–963 (2017). https://doi.org/10.1016/j.apenergy 7. Mikami, R., Shiina, T., Tokoro, K.: Unit commitment problem considering market transaction. In: 9th International Congress on Advanced Applied Informatics, pp. 713-718. IEEE Press, Tokyo (2020). https://doi.org/10.1109/IIAI-AAI50415.2020.0014 8. Mohammadi, F., Sharaei-Ardakani, M., Trakas, D.M., Hatziargyriou, N.D.: Machine learning assisted stochastic unit commitment: a feasibility study. In: 52nd North American Power Symposium (NAPS), pp. 1–6. IEEE Press, Tempe (2020). https://doi.org/10.1109/NAPS50 074.2021.9449789 9. Yang, Y., Peng, J. C.-H., Ye, C., Ye, Z., Ding, Y.: A criterion and stochastic unit commitment towards frequency resilience of power systems. IEEE Trans. Power Syst. 37(1), 640–652 (2021). https://doi.org/10.1109/TPWRS.2021.3095180 10. ElAzab, H.A., Swief, R., ElAmary, N., Temarz, H.: Unit commitment towards decarbonized network facing fixed and stochastic resources applying water cycle optimization. Energies 11(5), 1140 (2018). https://doi.org/10.3390/en11051140 11. Ghorbani, N., Babaei, E.: Exchange market algorithm. Appl. Soft Comput. J 19, 177–187 (2014). https://doi.org/10.1016/j.asoc.2014.02.006 12. Ghorbani, N., Babaei, E.: The exchange market algorithm with smart searching for solving economic dispatch problems. Int. J. Manag. Sci. Eng. Manag. 9653, 1–13 (2017). https://doi. org/10.1080/17509653.2017.1365262 13. Khalili, T.: Scheduling and siting of storages considering power peak shaving and loss reduction by exchange market algorithm. In: Smart Grid Conference, pp. 1–7, IEEE Press, Tehran (2017). https://doi.org/10.1109/SGC.2017.8308887 14. Ghorbani, E., Babaei, E., Sadikoglu, F.: Exchange market algorithm for multi-objective economic emission dispatch and reliability. Procedia Comput. Sci. 120, 633–640 (2017). https:// doi.org/10.1016/J.PROCS.2017.11.289 15. Daneshvar, M., Babaei, E.: Exchange market algorithm for multiple DG placement and sizing in a radial distribution system. J. Energy Manag. Technol. 2(1), 54–65 (2018). https://doi.org/ 10.22109/JEMT.2018.116625.1059 16. Ghorbani, N., Babaei, E., Sadikoglu, F.: BEMA: binary exchange market algorithm. Procedia Comput. Sci. 120, 656–663 (2017). https://doi.org/10.1016/j.procs.2017.11.292 17. Saravanan, E., Vasudevan, R., Kothari, D.P.: Unit commitment problem solution using invasive weed optimization algorithm. Int. J. Electr. Power Energy Syst. 55, 21–28 (2014). https://doi. org/10.1016/J.IJEPES.2013.08.020 18. Damousis, I.G., Bakirtzis, A.G., Dokopoulos, A.G.: A solution to the unit-commitment problem using integer-coded genetic algorithm. IEEE Trans. Power Syst. 19(2), 1165–1172 (2004). https://doi.org/10.1109/TPWRS.2003.821625 19. Balci, H.H., Valenzuela, J.F.: Scheduling electric power generators using particle swarm optimization combined with the Lagrangian relaxation method. Int. J. Appl. Math. Comput. Sci. 14, 411–421 (2004). http://eudml.org/doc/207707 20. Simopoulos, D.N., Kavatza, S.D., Vournas, C.D.: Unit commitment by an enhanced simulated annealing algorithm. IEEE Trans. Power Syst. 21(1), 68–76 (2006). https://doi.org/10.1109/ TPWRS.2005.860922 21. Viana, A., De Sousa, J.P., Matos, M.: Using GRASP to solve the unit commitment problem. Ann. Oper. Res. 120, 117–132 (2003). https://doi.org/10.1023/A:1023326413273 22. Kazarliz, S.A., Bakirtzai, A.G., Petridis, V.: A genetic algorithm solution to the unit commitment problem. IEEE Trans. power Syst. 11(1), 83–92 (1996). https://doi.org/10.4236/am. 2015.611165
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23. Cheng, C.P., Liu, C.W., Liu, C.C.: Unit commitment by Lagrangian relaxation and genetic algorithms. Power Syst. IEEE Trans. 15, 707–714 (2000). https://doi.org/10.1016/S0142-061 5(01)00024-2 24. Ebrahimi, J., Hosseinian, S.H., Gharehpetian, G.B.: Unit commitment problem solution using shuffled frog leaping algorithm. IEEE Trans. Power Syst. 26(2), 573–581 (2011). https://doi. org/10.1109/TPWRS.2010.2052639 25. Juste, K.A., Kita, H., Tanaka, E., Hasegawa, J.: An evolutionary programming solution to the unit commitment problem. IEEE Trans. Power Syst. 14(4), 1452–1459 (1999). https://doi. org/10.1109/59.801925 26. Ongsakul, W., Petcharacks, N.: Unit commitment by enhanced adaptive Lagrangian relaxation. IEEE Trans. Power Syst. 19(1), 620–628 (2004). https://doi.org/10.1109/TPWRS.2003. 820707
Regular Identification Algorithms for a Special Class of Neuro-Fuzzy Models ANFIS H. Z. Igamberdiev1(B) , A. N. Yusupbekov1 and Sh. D. Tulyaganov2
, U. F. Mamirov1
,
1 Tashkent State Technical University, Tashkent, Uzbekistan
[email protected] 2 FC “UzLITI Engineering” LLC, Tashkent, Uzbekistan
Abstract. The article proposes computational procedures for the formation and construction of regular identification algorithms for a special class of neuro-fuzzy ANFIS models that take into account the specifics of the learning task, based on algorithms for iterative refinement of the desired solution of the “skeletal” decomposition. The methods of the theory of fuzzy sets and neural network structures in the problems of identification of complex dynamic objects are analyzed. It was found that in the process of fuzzy modeling, the use of a neural or adaptive network improves the fuzzy system. In order to stabilize the desired solution and give greater numerical stability to the pseudo-inversion procedure, various algorithms for stable calculation of an underdetermined matrix pseudo-inverse to a matrix composed of values of basic functions are used, using certain matrix decompositions. The proposed method can be used for training multi-output ANFIS systems, as well as in cases where the basic functions depend nonlinearly on some parameters of the membership function. Keywords: Neuro-fuzzy modeling · Adaptive neuro-fuzzy inference system · Identification · Stable algorithms
1 Introduction The intensity of production processes, as is known, is growing along with the complexity of their control systems. The most important factors of this complication are internal disturbances, in which the initial and current information about the object is incomplete and unclear, changes in the external environment are summarized [1, 2]. The use of high-precision technologies in relation to modern automatic control systems has led to a further increase in their accuracy. When building control systems, an increasingly complete and accurate mathematical representation of technological processes and objects is required. However, the lack of information in the construction of mathematical models of technological processes and objects leads to the fact that the systems that control such objects cannot provide high quality indicators [1, 3]. This is due to the fact that data affecting the object [4], model structure [5], measurement tools (observations) [6], objective uncertainties affect the accuracy of the simulation result © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 747–753, 2023. https://doi.org/10.1007/978-3-031-25252-5_97
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[5]. Methods for constructing mathematical models of dynamic systems based on the observation of their behavior are the subject of identification theory. Methods for identifying the parameters of a mathematical model are widely used in the design of control systems, sometimes they also become an integral part of the controller [7]. In this case, the theory of adaptive control systems is implied, in which a sufficient object model is determined for the existing operating conditions and, taking into account the resulting model, the controller parameters are changed. In most works in identification, adaptive control, and design of control systems in general, linear objects and controllers are traditionally considered. Nevertheless, all systems exhibit non-linear behavior to some extent, which arouses interest in studying methods and approaches to designing non-linear systems. In identification theory, methods containing linguistic information play an important role in building nonlinear models. One of the advanced tools for accounting for linguistic information is fuzzy set theory and fuzzy logic. The main advantage of algorithms based on fuzzy logic is the ability to take into account the opinions and experience of experts developing these decision support systems [8]. However, these systems cannot automatically learn the selection, learning, type, and parameters of membership functions. To eliminate this shortcoming, it is important to use the models and mathematical apparatus of neuro-fuzzy networks (NFNs) [8–11]. In the process of fuzzy modeling, the use of a neural or adaptive network improves the fuzzy system and leads to a hybrid NFNs: the fuzzy system is replaced by a neural network of a special structure, which gives it the properties of adaptability, learning ability, greater flexibility, and accuracy. This system can be implemented as a neural-like structure consisting of five layers, called the Adaptive Neuro-Fuzzy Inference System (ANFIS) [12]. The figure shows the ANFIS network with two input linguistic variables x1 , x2 and four fuzzy rules [13, 14] (Fig. 1).
Fig. 1. Fuzzy neural network ANFIS using the zero-order Sugeno-Takagi algorithm: 1 - Gaussian functions; 2 - antecedents; 3 – signal normalization; 4 - conclusions of the rules
The advantage of an adaptive neuro-fuzzy system over fuzzy inference is the possibility of automatic correction of the parameters of the control device. At the same time, the adaptive neuro-fuzzy system maintains the transparency of the inference.
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The paper [12] explores the possibilities of training a neural network to ensure the stability of fuzzy logic systems in the sense that the concepts of fuzzy logic are built into the network structure. It also provides a natural basis for combining both numeric information in the form of I/O pairs and linguistic information in the form of IF-THEN rules in a single form. The proposed algorithm is achieved through the intelligent ANFIS scheme.
2 Problem Definition The purpose of this work is to construct identification algorithms for a special class of ANFIS neuro-fuzzy models that take into account the specifics of the learning task. The transformation of crisp input values into crisp outputs is also implemented in Takagi-Sugeno fuzzy systems. These systems, in contrast to the considered linguistic models, are a combination of linguistic and analytical models: R1 : if x1 A11 ({a11 }) and . . . and id xn is A1n ({a1n }), then y1 = f1 (x1 , . . . , xn ; {b1 }), R2 : if x2 and . . . and if xn is A2n ({a2n }), then y2 = f2 (x1 , . . . , xn ; {b2 }), ... Rm : if xm is Am1 ({am1 }) and if xn is Amn ({amn }), then ym = fm (x1 , ..., xn ; {bm }), where xj ∈ Rn are the system inputs; yi ∈ Rm - individual rule outputs; Aij are the membership functions depending on the parameters {aij }; fi are functions that depend on system inputs and parameters {bij }. The ANFIS structure models are a combination of linguistic and analytical models. The input and output quantities are real values. Most often, analytic functions in rule conclusions have a structure that is linear in parameters: ym = bm0 + bm1 x1 + bm2 x2 + . . . + bmn xn . The ANFIS system implements a function of the form m n m Aij (xj ) yi αi yi m i=1 j=1 i=1 , y= βi yi = m = m n i=1 αi Aij (xj ) i=1
i=1
j=1
where Aij (xj ) is the value of the membership function Aij at the point xj . The model parameters can be determined based on the training set of input and output data {xi , yi }, i = 1, . . . , k using local optimization methods using the information contained in the error function gradient over the model parameter vector. This takes into account the super positional nature of the models [12].
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Further, we will consider the situation when the functions fi in the conclusions of the rules are linear with respect to their parameters, however, not necessarily linear with respect to the input variables [13, 15, 16]: fi =
n
cij ψij (x1 , . . . ∞, xn ),
j=1
where ψij are the basis functions, cij are the parameters of the membership functions. Then the neuro-fuzzy model ANFIS implements a function of the form y=
m i=1
βi (p)
n
cij ψij (x1 , . . . , xn ) =
j=1
n m
cij βi (p)ψij (x1 , . . . , xn ),
i=1 j=1
where p is a vector consisting of all parameters of the membership functions Aij . The last expression can be rewritten as y = y(x1 , ... , xn ; p, c) =
mn
cq ϕq (x1 , ... , xn ; p),
q=1
where cq and ϕq (x1 , . . . , xn ; p) = βi (p)ψij (x1 , . . . , xn ) are obtained with the corresponding values of the indices i and j; c is a vector that consists of parameters cij , ϕq (x1 , . . . , xn ; p) are basis functions, then the problem of determining the parameters turns out to be a linear least squares problem. From the values of the basis functions ϕq on the training set, a matrix Φ(p) ∈ Rk×(mn) is formed, the rows of which correspond to the data of the set of “input-output” pairs, and the columns correspond to the rules of the fuzzy system, which allows to write the relation c∗ = Φ + (p∗ )˜y,
(1)
where Φ + is the matrix pseudoinverse to Φ; (p∗ , c∗ ) are the optimal values of the parameters of neuro structural models, y˜ ∈ Rk is the teacher’s instructions vector. In this case, only the p parameters that are included in the non-linear model are iteratively optimized. Linear parameters c can be found using a neuro-nonlinear system. The proposed method can be used to train multi-output ANFIS systems, as well as in cases where the functions ψij depend nonlinearly on some parameters c. The proposed training approach can be effectively applied to ANFIS neuro-fuzzy models at the initial stages, when the sample size becomes small. The matrix Φ, as can be seen from the structure of its construction, has a large dimension. To solve such systems of equations, one can, generally speaking, use any of the known methods for solving systems of linear equations [17–21]. However, their application in this case is associated with significant difficulties: the impossibility of solving the problem in one step and reducing the volume of intermediate results, etc. The foregoing explains the practical interest in the use of computational algorithms, to a greater extent adapted to solving systems of equations of the type under consideration. In order to stabilize the desired solution and give greater numerical stability to the pseudo-inversion procedure in (1), it is necessary to use regular methods [17, 18].
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3 Solution Let us consider algorithms for stable computation of Φ + , which use certain decompositions of the matrix Φ [17, 20]. Whereas if rankΦ = k (Φ ∈ Rk×mn with k ≤ mn), then the pseudoinverse to the matrix Φ is the matrix defined by the second Gaussian transformation: Φ + = Φ T (ΦΦ T )−1 .
(2)
The validity of expression (2) is due to the fact that any matrix Φ can be represented as a “skeletal” decomposition [20]: Φ =U ·V with matrices U ∈ Rk×r and V ∈ Rr×mn , where r = rankU ≤ min(k, mn). Let us now put Φ + = V + · U +, where, according to (2) one can arrive at the relations V + = V T (VV T )−1 , U + = (U T U )−1 U T . When inverting a matrix Φ, you can also use a technique based on the calculation Q = ΦΦ T in expression (2). Taking into account that Q is a symmetric non-negative definite matrix of rank l < k, order k × k, then Q+ = T T (TT T )−2 T ,
(3)
where the rank r matrix T(k×l) is determined from the decomposition Q = TTT
(4)
Decomposition (4) is generally not unique [17]. However, the pseudoinverse matrix Q+ = T T (TT T )−2 T is uniquely determined regardless of the decomposition method Q = T T T . Thus, expression (2), taking into account (3), can be written as: Φ + = Φ T Q+ = Φ T T T (TT T )−2 T .
(5)
If the matrix is ill-conditioned, then to increase the stability of the pseudo-inversion procedure in (5), it is advisable to use regular procedures [18, 21] of the form: Φ + = Φ T T T (TT T + αI )−2 T , where α > 0 is the regularization parameter, I is the identity matrix. It is expedient to determine the regularization parameter α here based on the method of model examples [18]. If the matrix Q = ΦΦ T is nonsingular, then expression Q+ = Q−1 (2) also holds.
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Very effective in solving Eq. (1), are also algorithmic procedures associated with the calculation of Z = (ΦΦ T )−1 , rankΦ = p, which is often called the unscaled covariance matrix. We will consider the following decompositions of the matrix [4, 17]: T DΦ = RT 0 ,
(6)
T ˜ DΦS = R˜ T 0 .
(7)
˜ are In expressions (6), (7), Rp×p and R˜ p×p are upper triangular matrices, D, D orthogonal matrices of corresponding dimensions, and S is a permutation matrix. It can be shown [15, 17] that for (6) and (7) for rankΦ = p, respectively, the following relations hold: Z = (ΦΦ T )−1 = (R−1 )T R−1 .
(8)
Then, when inverting the triangular matrix R in (8), one can use the expressions tii = rii−1 , tij = −tjj
j−1
i = 1, . . . , p,
til rlj , j = i + 1, . . . , p, i = 1, . . . , p − 1.
l=i
For case (7), it is also necessary to take into account the operations of left and right multiplication by permutation matrices S and S T , respectively.
4 Conclusion The given expressions allow us to regularize the task of identifying a special class of neuro-fuzzy ANFIS models that take into account the specifics of the learning task when the basic functions depend non-linearly on some parameters of the membership function. The proposed approach to learning can be effectively applied to neuro-fuzzy ANFIS models at the initial stages when the sample size becomes small.
References 1. Apostolakis, G.A.: A commentary on model uncertainty. Presented at Proceedings of Workshop I Advanced Topics Risk Reliability Analysis - Model Uncertainty: Its Character Quantification, Annapolis, MD, pp. 973–980 (1994) 2. Franklin, G., Powell, J., Emami-Naeini, A.: Feedback Control of Dynamical Systems, 6th edn. Addison-Wesley Publishing Co. Inc., Reading (2009) 3. Thunnissen, D.: Uncertainty classification for the design and development of complex systems. In: Proceedings of the 3rd Annual Predictive Methods Conference, pp. 1–16. Veros Software, Santa Ana, CA, (2003). https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1. 1.128.133&rep=rep1&type=pdf
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Author Index
A A. Ahmadov, Shamil 40 Abasova, S. M. 330 Abaszadeh, Rashad G. 608 Abbasov, Ali 147 Abbasova, S. 452 Abbasova, S. V. 493 Abdulla, Kamal 634 Abiyev, Rahib 338 Abizada, Sanan 338 Abulfas, Habibov Ibrahim 485 Adamu, Mustapha Tanimu 218 Adilov, Farukh 579 Adilova, Nigar E. 25, 196 Akda˘g, Sahin ¸ 94 Akhundov, V. J. 549 Akila, Serag Mohamed 435 Alasgarova, F. 382 Algazewe, Wadei 406 Aliev, Rafik A. 634 Alipasha, Agamammadova Sevda 485 Aliyev, A. 188 Aliyev, Elchin 354 Aliyev, Murad 372 Aliyev, Rafig R. 172, 595, 637, 677, 712 Aliyeva, Aysel 720 Aliyeva, K. R. 502, 662 Alizadeh, Akif V. 595, 677 Almezhghwi, Khaled 406, 435 Altınkaynak, Bü¸sra 58 Aparnev, Alexey N. 305 Arsen, I. 579 Averkin, Alexey 4, 180 Axundov, V. J. 476 B Babaei, Ebrahim 31, 734 Babanli, J. M. 67 Babanli, K. M. 696 Babanli, M. B. 6 Babanli, Mustafa 101
Babanly, M. B. 727 Babayev, A. I. 313 Bakhshali, Valeh 265 Bakhtiari, Samsam 31 Bakirova, L. R. 703 Balashirin, Alekperov Ramiz 626 Bayramov, A. R. 703 Bayramov, Imran Y. 493, 608 Bekirova, Aygun 265 Bilgehan, Bülent 77 Birgören, Burak 58 Bozhenyuk, Alexander 16 C Çamur, Hüseyin 50, 218 Chikowero, Takudzwa 218 D Dadasheva, Aygul 113 Damirli, Mehman A. 459 Da¸s, Gülesin Sena 58 Di Caprio, Debora 130 Dimililer, Kamil 274 Dioh, Francis Surfia 247 Dovlatova, Khatira J. 139, 211 Duwa, Basil Bartholomew 289 E Efendiyev, G. 452 Elnure, Shafizade 427 Ertuna, Banu 653 Ewuru, Deborah Amaka F Fariz, Guliev
427
G Gardashova, L. A. 234 Gardashova, Latafat 101 Gasanova, Naila A. 297
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 R. A. Aliev et al. (Eds.): ICAFS 2022, LNNS 610, pp. 755–757, 2023. https://doi.org/10.1007/978-3-031-25252-5
514
756
Gasimzade, T. 382 Gerasimenko, Evgeniya 16 Göçken, Tolunay 58 Godwin, Marilyn Hannah 203, 247 Gojayev, Tural 101 Gökçeku¸s, Hüseyin 203, 247 Guirimov, Babek 637 Guliyev, A. 382 Gulyamov, Shukhrat 346 Gurbanov, A. N. 493 Gurbanov, R. S. 421
H Habibbayli, Tunjay 372 Habibov, I. A. 330 Hasanli, Yadulla 427 Hasanov, G. S. 313 Hasanova, Leyla R. 85 Hasan-zade, D. S. Mamed 313 Huseynov, O. H. 637, 712 Huseynova, Farida 399, 686 Huseynova, Nigar F. 588, 686 Huseynzada, Gunay A. 226
I Ibrahimli, T. H. 421 Igamberdiev, H. Z. 747 Ilgar, Rü¸stü 530 Imamguluyev, Rahib 720 Imanov, Elbrus 435, 564 Imanov, G. 188 Imanova, Gunay E. 164, 522 Imanova, Gunel 164, 469 Imanova, Sevil 154 Imanova, Zarifa 530 Ismayil, Ismayil 265 Ismayilova, Fidan 391 Ismayilova, Hajar 391 Ismayilova, Nigar 282
J Jabbarova, Aynur I. 620 Jabbarova, K. I. 557, 620 Jabiyeva, Aynur J. 256 Jamalova, Zhala 530
Author Index
K Kaba, Serife ¸ 289 Kacprzyk, Janusz 1, 16 Kassem, Youssef 50, 203, 218, 247 Khankishiyeva, Tamilla U. 297 Kibarer, Ay¸seGünay 289 Kirisenko, O. 452 L Lakshitha Liyanagamage, Vidura M Magerramova, T. M. 321 Mahamad, A. N. 539 Malik, Abasova Sevinc 485 Mamirov, U. F. 747 Mammadli, Sadig 734 Mammadov, A. N. 727 Mammadov, Azar G. 608 Mammadova, G. G. 493 Mammadova, K. A. 234 Mardanov, Nail 265 Mason, Momoh Ndorbor 203 Mehdiyev, Nihad 507 Melikov, E. A. 321 Memmedova, Konul 653 Mikayilova, Rena 188, 669 Moldabayeva, G. 452 Mustafayeva, Seving R. 616 N Nkanga, Nkanga Amanam 50 Nuriyev, Aziz 25, 539 Nuriyev, Mahammad 539 Nuru, Mikayilova Rena 122 O Oktay, Serdar 645 Ozsahin, Dilber Uzun
289
P Plesniewicz, Gerald S. 305 Q Quliyev, Agali A. 297 Quoigoah, Marcus Paye
247
564
Author Index
R Rustamov, ˙I. S. 549 Rzayev, Ramin 147 Rzayeva, Ulviyya 669 S Sabuncu, Özlem 77 Sadıko˘glu, Fahreddin 31, 77, 514 Sadıko˘glu, Saide 94 Safarov, Rza S. 608 Safarova, A. A. 321 Salahli, M. A. 382 Salahli, Vugar 382, 530 Saley, James Mulbah 203 Salimov, V. H. 364 Salmanov, Fuad 354 Santos Arteaga, Francisco J. 130 Sardarov, Yagub 530 Sardarova, I. Z. 493 Sekeroglu, Boran 514 Seyfi, Arzu Gul 469 Shahlarli, Mansur 391 Shahmarova, Rafiga S. 297 Sharifova, Aynur V. 297 Sharifova, U. N. 727 Shwehdi, Rabei 406 Sultanova, A. B. 444, 572
757
T Tagiev, D. B. 727 Temizkan, Hasan 413 Tezer, Murat 94 Tulyaganov, Sh. D. 747 U Usmanova, Nargiza Uzun, Berna 289
346
X Xanmammadova, Elmira A.
608
Y Yarushev, Sergey 180 Ye¸silkaya, Murat 58 Yusifov, Salahaddin I. 608 Yusupbekov, A. N. 747 Yusupbekov, Nodirbek 346, 579 Z Zakwan, Ahmed Hamid Mohamed Abdalla 50 Zendah, Husam 274 Zeynalov, E. R. 712