Proceedings of the 8th International Conference on the Applications of Science and Mathematics: SCIEMATHIC 2022; 17―19 Oct; Malaysia (Springer Proceedings in Physics, 294) 9819928494, 9789819928491

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Springer Proceedings in Physics 294

Aida Mustapha · Norzuria Ibrahim · Hatijah Basri · Mohd Saifullah Rusiman · Syed Zuhaib Haider Rizvi   Editors

Proceedings of the 8th International Conference on the Applications of Science and Mathematics SCIEMATHIC 2022; 17–19 Oct; Malaysia

Springer Proceedings in Physics Volume 294

Indexed by Scopus The series Springer Proceedings in Physics, founded in 1984, is devoted to timely reports of state-of-the-art developments in physics and related sciences. Typically based on material presented at conferences, workshops and similar scientific meetings, volumes published in this series will constitute a comprehensive up to date source of reference on a field or subfield of relevance in contemporary physics. Proposals must include the following: – – – – –

Name, place and date of the scientific meeting A link to the committees (local organization, international advisors etc.) Scientific description of the meeting List of invited/plenary speakers An estimate of the planned proceedings book parameters (number of pages/ articles, requested number of bulk copies, submission deadline).

Please contact: For Americas and Europe: Dr. Zachary Evenson; [email protected] For Asia, Australia and New Zealand: Dr. Loyola DSilva; loyola.dsilva@springer. com

Aida Mustapha · Norzuria Ibrahim · Hatijah Basri · Mohd Saifullah Rusiman · Syed Zuhaib Haider Rizvi Editors

Proceedings of the 8th International Conference on the Applications of Science and Mathematics SCIEMATHIC 2022; 17–19 Oct; Malaysia

Editors Aida Mustapha Department of Mathematics and Statistics, Faculty of Applied Science and Technology Universiti Tun Hussein Onn Malaysia Johor, Malaysia

Norzuria Ibrahim Department of Mathematics and Statistics, Faculty of Applied Science and Technology Universiti Tun Hussein Onn Malaysia Johor, Malaysia

Hatijah Basri Department of Physics and Chemistry, Faculty of Applied Science and Technology Universiti Tun Hussein Onn Malaysia Johor, Malaysia

Mohd Saifullah Rusiman Department of Mathematics and Statistics, Faculty of Applied Science and Technology Universiti Tun Hussein Onn Malaysia Johor, Malaysia

Syed Zuhaib Haider Rizvi Department of Physics and Chemistry, Faculty of Applied Science and Technology Universiti Tun Hussein Onn Malaysia Johor, Malaysia

ISSN 0930-8989 ISSN 1867-4941 (electronic) Springer Proceedings in Physics ISBN 978-981-99-2849-1 ISBN 978-981-99-2850-7 (eBook) https://doi.org/10.1007/978-981-99-2850-7 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 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 Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Conference Organisation

Patron Ruzairi Abdul Rahim, Vice-Chancellor Universiti, Tun Hussein Onn Malaysia

Advisor Mohamad Zaky Noh, Universiti Tun Hussein Onn Malaysia

Chairman Aida Mustapha, Universiti Tun Hussein Onn Malaysia

Deputy Chairman Sabariah Saharan, Universiti Tun Hussein Onn Malaysia

Secretaries Siti Noor Asyikin Mohd Razali, Universiti Tun Hussein Onn Malaysia Syahirbanun Isa, Universiti Tun Hussein Onn Malaysia

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Conference Organisation

Treasurer Isaudin Ismail, Universiti Tun Hussein Onn Malaysia

Publication and Manuscript Norzuria Ibrahim, Universiti Tun Hussein Onn Malaysia Mohd Saifullah Rusiman, Universiti Tun Hussein Onn Malaysia Hatijah Basri, Universiti Tun Hussein Onn Malaysia Mohd Helmy Abd Wahab, Universiti Tun Hussein Onn Malaysia

Protocol and Inauguration Syahira Mansur, Universiti Tun Hussein Onn Malaysia Siti Suhana Jamaian, Universiti Tun Hussein Onn Malaysia

Promotion, Publicity and Web Norziha Che Him, Universiti Tun Hussein Onn Malaysia Suliadi Firdaus Sufahani, Universiti Tun Hussein Onn Malaysia Faridah Kormin, Universiti Tun Hussein Onn Malaysia Fazleen Izzany Abu Bakar, Universiti Tun Hussein Onn Malaysia Saliza Asman, Universiti Tun Hussein Onn Malaysia

Registration and Certificates Norhaidah Mohd Asrah, Universiti Tun Hussein Onn Malaysia Noor Azliza Abd Latif, Universiti Tun Hussein Onn Malaysia Khuneswari P. Gopal Pillay, Universiti Tun Hussein Onn Malaysia

Souvenir Fazlina Aman, Universiti Tun Hussein Onn Malaysia Maria Elena Nor, Universiti Tun Hussein Onn Malaysia

Conference Organisation

Technical and Logistics Cik Sri Mazzura Muhammad Basri, Universiti Tun Hussein Onn Malaysia Mohd Marhafidz Marjori, Universiti Tun Hussein Onn Malaysia Muhammad Ghazzali Ibrahim, Universiti Tun Hussein Onn Malaysia

Parallel Sessions Rohayu Mohd Salleh, Universiti Tun Hussein Onn Malaysia Noorzehan Fazahiyah Md Shab, Universiti Tun Hussein Onn Malaysia

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Editorial Board

Chief Editor Aida Mustapha, Universiti Tun Hussein Onn Malaysia

Advisory Editorial Board Ishak Hashim, Universiti Kebangsaan Malaysia Sharifah Mohamad, Universiti Malaya Hussein Yousif Eledum, Tabuk University, Saudi Arabia Tom G. Mackay, University of Edinburgh, United Kingdom Hosam Hegazy, Jazan University, Saudi Arabia Darmesah Gabda, Universiti Malaysia Sabah Mohd Helmy Abd Wahab, Universiti Tun Hussein Onn Malaysia

Editorial Board Norzuria Ibrahim, Universiti Tun Hussein Onn Malaysia Hatijah Basri, Universiti Tun Hussein Onn Malaysia Mohd Saifullah Rusiman, Universiti Tun Hussein Onn Malaysia Syed Zuhaib Haider Rizvi, Universiti Tun Hussein Onn Malaysia

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Preface

To sustain a fair, peaceful and a more just world, dealing with the smallest of atoms to the largest of real numbers, Science and Mathematics are profoundly vital in solving many of the major contemporary issues: from ending extreme poverty to reducing maternal and infant mortality, promoting sustainable farming and decent work, and achieving universal literacy. As the synergistic approach of Mathematicians, Scientists and Engineers has undeniable importance in discovering and implementing sustainable solutions, digital advances come to support and accelerate the mean to solution for even the biggest problems. Nevertheless, as changes occur and development takes place, technologies can also threaten privacy, erode security, and fuel inequality. They have implications for human rights and human agency. Like generations before, we—governments, businesses, and individuals—have a choice to make in how we harness and manage new technologies. The responsibility lies not only in the hands of scientists, mathematicians, and engineers but also on the public. With this perspective, the eighth in the series of SCIEMATHIC conferences organised by Faculty of Applied Sciences and Technology (FAST), Universiti Tun Hussein Onn Malaysia every year, SCIEMATHIC 2022 was conceived with a theme of “Realizing Potential with Digital Opportunities.” As COVID-19 precautionary measure, SCIEMATHIC was organised online this year. This book highlights the diverse work of researchers from different parts of the world with a focus on potential applications for future technologies. The quality insight to the reader about the leading trends in sustainable science and technology research was provided in this book. The body of articles covers the research work of Mathematicians, Statisticians, Natural and Data Scientists, as well as Engineers aiming to find sustainable solutions to the major problems in the scientific world. From SCIEMATHIC 2022, we managed to draw 32 papers from 3 countries. In this volume of SPP we present 30 papers, each of these is accepted for oral presentation and publication after blind peer review by at least two independent reviewers. The papers in this proceeding are divided into four parts: Mathematics, Statistics, Engineering and Natural Sciences, as they were presented during the conference.

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Preface

On behalf of SCIEMATHIC 2022 committees, we extend our highest gratitude to our Patron, Prof. Ir. Ts. Dr. Ruzairi Abd Rahim; Advisor, Assoc. Prof. Dr. Mohamad Zaky Noh; Conference Organizer, Faculty of Applied Sciences and Technology, UTHM, Conference Chair, Publication Committee, Manuscript and Review Committee, and all committee members for their treasured efforts in the review process that helped us to pledge the highest quality of the selected papers for the conference. We would like to express our thanks to the Keynote speakers: Prof. Dr. Nazri Mohd Nawi from Universiti Tun Hussein Onn Malaysia, Dr. Vera Hazelwood from Data Science Communities, Cambridge, UK, Prof. Dr. Azami Zaharim from Tamadun Teras Sdn. Bhd., Malaysia and Assoc. Prof. Dr. Sugiyarto Surono from Universitas Ahmad Dahlan, Indonesia. We would also like to acknowledge all the committee members and session chairs for their substantial work in making this event successful. Our special thanks to Dr. Loyoal D’Silva and Ms. Shalini Monica for publishing this proceeding in Springer Proceedings in Physics. Lastly, we cordially thank all the authors for their valuable contributions and other participants of this conference. The conference would not have been possible without them. Johor, Malaysia

Aida Mustapha Norzuria Ibrahim Hatijah Basri Mohd Saifullah Rusiman Syed Zuhaib Haider Rizvi

Contents

Part I 1

2

3

4

5

Mathematics

Solving Lane-Emden Equation by Using Differential Transformation Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Muhammad Aris Izzuddin Razali and Noor Azliza Abd Latif Optimization of Asset Liability Management on Textile and Garment Companies Using Goal Programming Model . . . . . . . . Hagni Wijayanti, Sudradjat Supian, Diah Chaerani, and Adibah Shuib A Two-Stage Fuzzy DEA Approach—Application to Study the Effectiveness of Indian Iron and Steel Industries . . . . . . . . . . . . . . Mariappan Perumal, M. Umaselvi, M. Maragatham, and D. Surjith Jiji

3

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25

An EPQ Model Under Time-Dependent Demand with Single Time Discount Sales and Partial Backlogging . . . . . . . . . . . . . . . . . . . . Mariappan Perumal, Anusuya Baggiyalakshmi, and M. Maragatham

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A Two-Stage Fuzzy DEA Using Triangular Fuzzy Numbers—An Application to Study the Efficiency of Indian Iron and Steel Industries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mariappan Perumal, M. Umaselvi, M. Maragatham, and D. Surjith Jiji

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6

Life Insurance Pricing and Reserving—A Fuzzy Approach . . . . . . . . K. Kapil Raj, S. Srinivasan, Mariappan Perumal, and C. D. Nandakumar

7

Fixed-Point Approach on Eˇ Fuzzy-Metric Space with JCLR Property by Implication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Vijayalakshmi, P. Muruganantham, and A. Nagoor Gani

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8

Contents

Fixed Point Results on Derived Fuzzy Norm Using Fuzzy 2-Normed Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Nagoor Gani, B. Shafina Banu, and P. Muruganantham

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Solving Fuzzy Linear Programming Problems by Using the Limit Existence of the Fuzzy Exponential Penalty Method . . . . . A. Nagoor Gani and R. Yogarani

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10 Robust Optimization of Stock Portfolio Index IDX 30 Using Monte Carlo Simulation in Insurance Company . . . . . . . . . . . . . . . . . . Shofiayumna Felisya Putri and Gunardi

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9

11 Predicting Claim Reserves When the Loss Development Factors are Unstable: A Case Study from Indonesia’s General Insurance Company . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Ruth Cornelia Nugraha and Danang Teguh Qoyyimi 12 Stability Analysis of the Fractional Order Lotka-Volterra System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Soon Hock Gan and Chang Phang Part II

Statistics

13 Gender Comparative Patterns of Online Gaming Among University Students . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Nur Izzah Jamil, Kum Yoke Soo, Noriah Ismail, and Mohammad Abdullah 14 Data Mining Classifier for Predicting India Water Quality Status . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 Nur Atiqah Hamzah, Sabariah Saharan, and Mohd Saifullah Rusiman 15 Improvement of Learning Outcomes on the Limit Chapter Using Kahoot™ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 Isti Kamila, Ani Andriyati, Mulyati, Maya Widyastiti, and Embay Rohaeti 16 Mapping of Fish Consumption in Indonesia Based on Average Linkage Clustering Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 Fitria Virgantari, Yasmin Erika Faridhan, Fajar Delli Wihartiko, and Sonny Koeshendrajana 17 Analysis of Income and Expenditure of Households in Peninsular Malaysia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 Tan Kang May, Sabariah Saharan, and Mohd Saifullah Rusiman 18 A Comparative Analysis of Credit Card Detection Models . . . . . . . . 201 Kimberly Chan Li Kim, Aida Mustapha, Vaashini Palaniappan, Woon Kah Mun, and Vinothini Kasinathan

Contents

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19 Credit Scoring Model for Tenants Using Logistic Regression . . . . . . 213 Kim Sia Ling, Siti Suhana Jamaian, and Syahira Mansur 20 Optimization of Bayesian Structural Time Series (BSTS) Applications in Forecasting Stock Prices Through State Components Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 Benita Katarina and Gunardi 21 Prediction of the Number of BPJS Claims due to COVID-19 Based on Community Mobility and Vaccination in DIY Province Using the Bayesian Structural Time Series . . . . . . . . . . . . . . 249 Maria Stephany Angelina and Gunardi 22 A Study on the New Cases of Influenza A, B, and Covid-19 in Malaysia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275 Norhaidah Mohd Asrah and Nur Faizah Isham 23 An Evaluation of the Forecast Performance of Neural Network . . . . 287 Lok You Li, Maria Elena Nor, Mohd Saifullah Rusiman, and Nur Hidayah Mohd Zulkarnain 24 The Impact of Government Policy Changes on Stock Market Forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301 Low Kian Haw, Maria Elena Nor, and Noorzehan Fazahiyah Md Shab 25 Determining Auto Insurance Pure Premium Based on Mileage (Pay-As-You-Drive Insurance) Using Tree-Based Machine Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317 Dhestar Bagus Wirawan and Gunardi Part III Engineering 26 The Mitigation Model of Greenhouse Gas Emissions Reduction in Coal Mining Company with Surface Mining System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 Doni, Sata Yoshida Srie Rahayu, Rosadi, and Sutanto 27 The Influence of Fibre Feeder Speed and Stacking Layers on Physical Properties of Needle-Punched Nonwovens from Industrial Cotton Waste . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 Siti Nor Hawanis Husain, Azrin Hani Abdul Rashid, Abdussalam Al-Hakimi Mohd Tahir, Muhammad Farid Shaari, Siti Hana Nasir, Siti Aida Ibrahim, Khairani Nasir, Ngoi Pik Kuan, and Mohd Fathullah Ghazli 28 Exploring Cultural Learning with Vertical Chatbot: Korda . . . . . . . 377 Vinothini Kasinathan, Aida Mustapha, Neekita Sewnundun, Diong Jien Bing, Lee Khoon Fang, and Cindy Koh Xin Yi

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Contents

29 Robot Model to Identify the Quality of Air Indoor Area Based on Internet of Things (IoT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 Asep Denih, Irma Anggraeni, and Ema Kurnia Part IV Natural Sciences 30 Onion Peel for Tinted Film Applications . . . . . . . . . . . . . . . . . . . . . . . . . 405 Siti Nursyakirah Idris and Siti Amira Othman 31 Optimization of Spinning Speed for Thin Layers Formation Using Spin Coating Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413 Agus Ismangil and Asep Saepulrohman 32 Effect of Environmental Stress on Biomolecules Production and Cell Wall Degradation in Chlorella vulgaris . . . . . . . . . . . . . . . . . . 421 Syafiqah Md. Nadzir, Norjan Yusof, Azlan Kamari, and Norazela Nordin

Editors and Contributors

About the Editors Aida Mustapha received her Ph.D. in Artificial Intelligence from Universiti Putra Malaysia. At present, she is the Director of Industry and Community Relations Centre, overlooking industrial and community engagements. She has published more than 390 refereed publications in the areas of soft computing, data mining, computational linguistics, and software agents. She is currently the Chief Editor for Journal of Quranic Sciences and Research. Her main passion is pursuing the area of natural language studies and application of natural language processing. Norzuria Ibrahim graduated from Bachelor of Science in Industrial Mathematics from Universiti Teknologi Malaysia, M.Sc. in Mathematics from Universiti Kebangsaan Malaysia, and Ph.D. in Biomechanics from Universiti Malaya. She is currently the Principal Researcher in Fuzzy Mathematics and Applications (FMA) focus group at UTHM. Her research interests are quite wide-ranging under the general umbrella of Mathematics Applications. Her main interest lies in the Mathematical modelling of human movement and analysis in Sports Biomechanics. Hatijah Basri graduated in Bachelor of Science, Master of Chemistry and Ph.D. in Chemical Engineering from Universiti Teknologi Malaysia. Hatijah also received more than MYR100,000.00 research grant since 2011, has been cited more than 700 times and published in more than 40 referred Journal such as Desalination, Chemical Engineering Research and Design, Material Chemistry and Physics, Heliyon, RSC Advances, Surface and Interface Analysis, Desalination and Water Treatment, Food Research. Mohd Saifullah Rusiman received his Ph.D. in Mathematics from Universiti Teknologi Malaysia (UTM) and Dokuz Eylul University (DEU), Turkey. He has 26 years of teaching experience. His area of research interest is focusing on applied statistics specifically statistics modeling, fuzzy statistics and time series. He has

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Editors and Contributors

published more than 90 articles and awarded research grants with valued more than MYR 350,000.00 since 2006 as the main researcher. He is also the Chief Editor of the International Journal of Enhanced Knowledge of Science and Technology (EKST). Syed Zuhaib Haider Rizvi received his Ph.D. in Physics from Universiti Teknologi Malaysia in 2015. At present, he is working with Universiti Tun Hussein Onn Malaysia as a lecturer. He is also a senior researcher at MiNT-Shamsudin Research Center. His research interests are in laser-induced plasma, pulsed laser deposition, plasma spectroscopy and applying machine learning algorithms to spectroscopic data for applied research.

Contributors Azrin Hani Abdul Rashid Faculty of Engineering Technology, Universiti Tun Hussein Onn Malaysia, Pagoh, Muar, Johor, Malaysia Mohammad Abdullah Universiti Teknologi MARA, Masai, Johor, Malaysia Ani Andriyati FMIPA, Universitas Pakuan, Bogor, Indonesia Maria Stephany Angelina Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Yogyakarta, Indonesia Irma Anggraeni Department of Computer Science, University of Pakuan, Bogor City, Indonesia Muhammad Aris Izzuddin Razali Department of Mathematics and Statistics, Faculty of Applied Science and Technology, Universiti Tun Hussein Onn Malaysia, Johor, Malaysia Norhaidah Mohd Asrah Universiti Tun Hussein Onn Malaysia, UTHM Pagoh Campus, Pagoh Higher Education Hub, Panchor, Johor, Malaysia Noor Azliza Abd Latif Department of Mathematics and Statistics, Faculty of Applied Science and Technology, Universiti Tun Hussein Onn Malaysia, Johor, Malaysia Anusuya Baggiyalakshmi Department of Mathematics, Periyar EVR College (Autonomous), Tiruchirappalli, Tamil Nadu, India Diong Jien Bing School of Computing and Technology, Asia Pacific University, Kuala Lumpur, Malaysia Diah Chaerani Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang, Indonesia Asep Denih Department of Computer Science, University of Pakuan, Bogor City, Indonesia

Editors and Contributors

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Doni Postgraduate School of Pakuan University, Pakuan University, Bogor, West Java, Indonesia Lee Khoon Fang School of Computing and Technology, Asia Pacific University, Kuala Lumpur, Malaysia Yasmin Erika Faridhan Pakuan University, Bogor, Indonesia Soon Hock Gan Department of Mathematics and Statistics, Universiti Tun Hussein Onn Malaysia, Pagoh, Malaysia A. Nagoor Gani PG and Research Department of Mathematics, Jamal Mohamed College (Autonomous), Affiliated to Bharathidasan University, Tiruchirappalli, Tamil Nadu, India Mohd Fathullah Ghazli Faculty of Mechanical and Green Technology (FKTM), Centre of Excellence Geopolymer and Green Technology (CEGeoGTech), Arau, Perlis, Malaysia Gunardi Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Yogyakarta, Indonesia Nur Atiqah Hamzah Universiti Tun Hussein Onn Malaysia, Johor, Malaysia Low Kian Haw Department of Mathematics and Statistics, Faculty of Applied Science and Technology, Universiti Tun Hussein Onn Malaysia, Parit Raja, Johor, Malaysia Siti Nor Hawanis Husain Faculty of Engineering Technology, Universiti Tun Hussein Onn Malaysia, Pagoh, Muar, Johor, Malaysia Siti Aida Ibrahim Faculty of Engineering Technology, Universiti Tun Hussein Onn Malaysia, Pagoh, Muar, Johor, Malaysia Siti Nursyakirah Idris Faculty of Applied Sciences and Technology, Universiti Tun Hussein Onn, Parit Raja, Malaysia Nur Faizah Isham Universiti Teknologi Malaysia, Skudai, Johor, Malaysia Noriah Ismail Universiti Teknologi MARA, Segamat, Johor, Malaysia Agus Ismangil Department of Computer Science, Faculty Mathematics and Natural Science, Pakuan University, Bogor, Indonesia Siti Suhana Jamaian Department of Mathematics and Statistics, Faculty of Applied Sciences and Technology, Universiti Tun Hussein Onn Malaysia, Pagoh Educational Hub, Muar, Johor, Malaysia Nur Izzah Jamil Universiti Teknologi MARA, Rembau, Negeri Sembilan, Malaysia Azlan Kamari Department of Chemistry, Faculty of Science and Mathematics, Universiti Pendidikan Sultan Idris, Perak Darul Ridzuan, Malaysia

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Editors and Contributors

Isti Kamila FMIPA, Universitas Pakuan, Bogor, Indonesia K. Kapil Raj Department of Mathematics and Actuarial Science, B.S. Abdur Rahman Crescent Institute of Science and Technology, Chennai, Tamil Nadu, India Vinothini Kasinathan School of Computing and Technology, Asia Pacific University of Technology and Innovation, Kuala Lumpur, Malaysia Benita Katarina Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Yogyakarta, Indonesia Kimberly Chan Li Kim Faculty of Applied Sciences and Technology, Universiti Tun Hussein Onn Malaysia, Pagoh, Johor, Malaysia Sonny Koeshendrajana Center of Research for Behavioural and Circuler Economics, National Research and Innovation Agency Indonesia, Jakarta, Indonesia Ngoi Pik Kuan Chemor, Perak, Malaysia Ema Kurnia Department of Informatics Management, University of Pakuan, Bogor City, Indonesia Lok You Li Department of Mathematics and Statistics, Faculty of Applied Sciences and Technology, Universiti Tun Hussein Onn Malaysia, Parit Raja, Johor, Malaysia Kim Sia Ling Department of Mathematics and Statistics, Faculty of Applied Sciences and Technology, Universiti Tun Hussein Onn Malaysia, Pagoh Educational Hub, Muar, Johor, Malaysia Syahira Mansur Department of Mathematics and Statistics, Faculty of Applied Sciences and Technology, Universiti Tun Hussein Onn Malaysia, Pagoh Educational Hub, Muar, Johor, Malaysia M. Maragatham Department of Mathematics, (Autonomous), Tiruchirappalli, Tamil Nadu, India

Periyar

EVR

College

Mariappan Perumal Department of Management Studies, St. Joseph’s Institute of Management, Tiruchirappalli, Tamil Nadu, India Tan Kang May Department of Mathematics and Statistics, Faculty of Applied Sciences and Technology, Universiti Tun Hussein Onn Malaysia, Johor, Malaysia Abdussalam Al-Hakimi Mohd Tahir Faculty of Engineering Technology, Universiti Tun Hussein Onn Malaysia, Pagoh, Muar, Johor, Malaysia Mulyati FMIPA, Universitas Pakuan, Bogor, Indonesia Woon Kah Mun Faculty of Applied Sciences and Technology, Universiti Tun Hussein Onn Malaysia, Pagoh, Johor, Malaysia P. Muruganantham PG and Research Department of Mathematics, Jamal Mohamed College (Autonomous), Affiliated to Bharathidasan University, Tiruchirappalli, Tamil Nadu, India

Editors and Contributors

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Aida Mustapha Faculty of Applied Sciences and Technology, Universiti Tun Hussein Malaysia, Pagoh, Johor, Malaysia Syafiqah Md. Nadzir Department of Biology, Faculty of Science and Mathematics, Universiti Pendidikan Sultan Idris, Perak Darul Ridzuan, Malaysia A. Nagoor Gani Research Department of Mathematics, Jamal Mohamed College (Autonomous) (Affiliated to Bharathidasan University, Tiruchirappalli-24), Tiruchirappalli, Tamilnadu, India C. D. Nandakumar Department of Mathematics and Actuarial Science, B.S. Abdur Rahman Crescent Institute of Science and Technology, Chennai, Tamil Nadu, India Khairani Nasir Faculty of Engineering Technology, Universiti Tun Hussein Onn Malaysia, Pagoh, Muar, Johor, Malaysia Siti Hana Nasir Faculty of Engineering Technology, Universiti Tun Hussein Onn Malaysia, Pagoh, Muar, Johor, Malaysia Maria Elena Nor Department of Mathematics and Statistics, Faculty of Applied Sciences and Technology, Universiti Tun Hussein Onn Malaysia, Parit Raja, Johor, Malaysia Norazela Nordin Kolej Yayasan UEM Lembah Beringin, Tanjong Malim Perak Darul Ridzuan, Malaysia Ruth Cornelia Nugraha Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Sekip Utara, Yogyakarta, Indonesia Siti Amira Othman Faculty of Applied Sciences and Technology, Universiti Tun Hussein Onn, Parit Raja, Malaysia Vaashini Palaniappan Faculty of Applied Sciences and Technology, Universiti Tun Hussein Onn Malaysia, Pagoh, Johor, Malaysia Chang Phang Department of Mathematics and Statistics, Universiti Tun Hussein Onn Malaysia, Pagoh, Malaysia Shofiayumna Felisya Putri Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Yogyakarta, Indonesia Danang Teguh Qoyyimi Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Sekip Utara, Yogyakarta, Indonesia Sata Yoshida Srie Rahayu Faculty of Mathematics and Natural Science, Pakuan University, Bogor, West Java, Indonesia Embay Rohaeti FMIPA, Universitas Pakuan, Bogor, Indonesia Rosadi Postgraduate School of Pakuan University, Pakuan University, Bogor, West Java, Indonesia

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Editors and Contributors

Mohd Saifullah Rusiman Department of Mathematics and Statistics, Faculty of Applied Sciences and Technology, Universiti Tun Hussein Onn Malaysia, Johor, Malaysia Asep Saepulrohman Department of Computer Science, Faculty Mathematics and Natural Science, Pakuan University, Bogor, Indonesia Sabariah Saharan Department of Mathematics and Statistics, Faculty of Applied Sciences and Technology, Universiti Tun Hussein Onn Malaysia, Johor, Malaysia Neekita Sewnundun School of Computing and Technology, Asia Pacific University, Kuala Lumpur, Malaysia Muhammad Farid Shaari Faculty of Engineering Technology, Universiti Tun Hussein Onn Malaysia, Pagoh, Muar, Johor, Malaysia Noorzehan Fazahiyah Md Shab Department of Mathematics and Statistics, Faculty of Applied Science and Technology, Universiti Tun Hussein Onn Malaysia, Parit Raja, Johor, Malaysia B. Shafina Banu PG and Research Department of Mathematics, Jamal Mohamed College (Autonomous), Affiliated to Bharathidasan University, Tiruchirappalli, Tamil Nadu, India Adibah Shuib Department of Mathematics, Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, Shah Alam, Malaysia Kum Yoke Soo Universiti Teknologi MARA, Rembau, Negeri Sembilan, Malaysia S. Srinivasan Department of Mathematics and Actuarial Science, B.S. Abdur Rahman Crescent Institute of Science and Technology, Chennai, Tamil Nadu, India Sudradjat Supian Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Pakuan, Bogor, Indonesia D. Surjith Jiji Department of Mathematics, Periyar EVR College (Autonomous), Tiruchirappalli, Tamil Nadu, India Sutanto Postgraduate School of Pakuan University, Pakuan University, Bogor, West Java, Indonesia M. Umaselvi Faculty of Business Management, Majan University College, Musat, Oman C. Vijayalakshmi Research Department of Mathematics, Jamal Mohamed College (Autonomous) (Affiliated to Bharathidasan University, Tiruchirappalli-24), Tiruchirappalli, Tamilnadu, India Fitria Virgantari Pakuan University, Bogor, Indonesia Maya Widyastiti FMIPA, Universitas Pakuan, Bogor, Indonesia Fajar Delli Wihartiko Pakuan University, Bogor, Indonesia

Editors and Contributors

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Hagni Wijayanti Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Pakuan, Bogor, Indonesia Dhestar Bagus Wirawan Department of Mathematics, Faculty of Mathematics and Natural sciences, Universitas Gadjah Mada, Yogyakarta, Indonesia Cindy Koh Xin Yi School of Computing and Technology, Asia Pacific University, Kuala Lumpur, Malaysia R. Yogarani Research Department of Mathematics, Jamal Mohamed College (Autonomous), Affiliated to Bharathidasan University, Tiruchirappalli, India Norjan Yusof Department of Biology, Faculty of Science and Mathematics, Universiti Pendidikan Sultan Idris, Perak Darul Ridzuan, Malaysia Nur Hidayah Mohd Zulkarnain Department of Mathematics and Statistics, Faculty of Applied Sciences and Technology, Universiti Tun Hussein Onn Malaysia, Parit Raja, Johor, Malaysia

Part I

Mathematics

Chapter 1

Solving Lane-Emden Equation by Using Differential Transformation Method Muhammad Aris Izzuddin Razali and Noor Azliza Abd Latif

Abstract In this research, a semi-analytical solution called differential transformation method (DTM) was used to solve the Lane-Emden equation. With the help of Maple 2020, the approximate solutions of the Lane-Emden equation were obtained. The numerical result derived by DTM is compared with the result of Adomian decomposition method (ADM), Legendre wavelets and Homotopy perturbation method with Laplace transformation (LT-HPM) which were done by previous research to observe the accuracy of the value with the exact value. After comparing between the methods, the result represents the close approximation of DTM for solving LaneEmden equation depending on the type of Lane-Emden equation and number of terms in DTM. For solving Lane-Emden equation, a few terms of DTM are recommended to obtain the approximate value. DTM has successfully solved three examples. Due to less computational work to obtain an approximation to exact value, DTM is considered to be the simplest method to apply and can solve differential problem.

1.1 Introduction The differential transformation method (DTM) creates an analytical approximation and numerical technique to solve problems regarding differential equations which are used in the form of polynomials based on expansion of the Taylor series. The concept of the DTM was first proposed by Zhou in 1986 [1]. The traditional approach of higher order Taylor series requires symbolic computations of the necessary derivatives of the data functions. Since the Taylor series method took a long time to compute a large order, DTM acts as an alternative process for obtaining Taylor series solutions of differential equations analytically. Compared to the numerical approach, this method is quite good, since its error is rounding off free and requires less computer power [2].

M. Aris Izzuddin Razali · N. Azliza Abd Latif (B) Department of Mathematics and Statistics, Faculty of Applied Science and Technology, Universiti Tun Hussein Onn Malaysia, Johor, Malaysia e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Mustapha et al. (eds.), Proceedings of the 8th International Conference on the Applications of Science and Mathematics, Springer Proceedings in Physics 294, https://doi.org/10.1007/978-981-99-2850-7_1

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M. Aris Izzuddin Razali and N. Azliza Abd Latif

The Lane-Emden equation is a second-order differential equation which is widely used in the field of astrophysics. As the name of the Lame-Emden equation, it takes after two scientists which were Jonathan Homer Lane and Jacob Robert Emden is an American astrophysicist and Swiss astrophysicist as well as meteorology respectively [3]. It is widely used in modeling phenomena in mathematical physics especially in the field of astrophysics such as the thermal behavior of a spherical cloud gas, isothermal spheres and thermionic currents, thermal explosion, and stellar structure [4–7]. The general formula of Lane-Emden equation is y  (x) +

α  y (x) + f (x, y) = g(x) x, α ≥ 0. x

(1.1)

The initial conditions are y (0) = a; y  (0) = b.

(1.2)

where a and b are constant. The existence of f (x, y) makes the equation to be nonlinear or linear and g (x) can be homogeneous and non-homogeneous. The aim of this paper is to obtain the Lane-Emden equation solution using differential transformation method. Three examples are used to demonstrate the accuracy of the DTM. The results obtained are then compared with the exact solution, Adomian decomposition method (ADM) and Homotopy perturbation method with Laplace transformation (LT-HPM).

1.2 Methodology The k-th derivative of the differential transformation for the function y (x) is defined as follows,   1 d k y (x) Y (k) = (1.3) k! dxk x=0 where y (x) and Y (x) are the original function and the transformation function, respectively, and the differential inverse transformation of Y (x) is defined as y (x) =

∞ 

Y (k) (x − x0 )k .

(1.4)

k=0

The fundamental operations performed by differential transformation method are shown in Table 1.1.

1 Solving Lane-Emden Equation by Using Differential …

5

Table 1.1 Fundamental operations performed by differential transformation [8] Original functions Transformed functions y (x) = g (x) ± h (x) y(x) = cg(x) y(x) = y  (x) y(x) = y  (x)

Y (x) = G (x) ± H (x) Y (x) = cG(x), where c is constant Y (k)− = (k + 1)Y (k + 1) Y (k) = (k + 1)(k +  2)Y (k + 1)

y(x) = x m

Y (k) = δ(k − m) =

y (x) = y m (x)

Y (x) =  (k + 1) (k + 2) . . . (k + m) Y (k + m)

y (x) = eay

Y (k) =

eaY (0)  a rk−1 =0

1 if k = m 0 if k = m

r +1 k Y

if k = 0 (r + 1) E (k − r − 1) if k ≥ 1

1.3 Result and Discussion Example 1. Consider the following Lane-Emden equation [9] y  + with initial conditions

  2  y − 2 2x 2 + 3 y = 0 x

(1.5)

y (0) = 1, y  (0) = 0.

(1.6)

y(x) = exp x 2 .

(1.7)

which the exact solution is

From the initial conditions and theorem in Table 1.1, the recurrence relation is Y (0) = 1, Y (1) = 0.

(1.8)

By multiplying equation (1.5) by x and using the theorem in Table 1.1, the recurrence relation obtain is

k k   1 δ(r − 3)Y (k − r ) + 6 δ(r − 1)Y (k − r ) , Y (k + 1) + 4 (k + 1) (k + 2) r =0 r =0 (1.9) Substitute (1.8) into (1.9) at k = 1, we have Y (2) = 1.

(1.10)

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M. Aris Izzuddin Razali and N. Azliza Abd Latif

Fig. 1.1 Exact, DTM and ADM of example 1

Then recurrence relation (1.9) at k = 2, 3, 4, 5, we obtain Y (3) = 0, 1 Y (4) = , 2 Y (5) = 0, 1 Y (6) = . 6 Therefore, combine all the terms above and do the Taylor series up to 7-th term given 1 1 (1.11) Y (x) = 1 + x 2 + x 4 + x 6 . 2 6 Figure 1.1 shows that the DTM are close with the exact solution same goes with Adomian decomposition method (ADM). Table 1.2 shows the result of DTM are very near with the exact solution. Table 1.3 shows that even though DTM solution is very near with exact solution, in term of accuracy, ADM is much better. Example 2. Consider the following Lane-Emden equation as follows [10] y  (x) +

8  y (x) + x y(x) = x 5 − x 4 + 44x 2 − 30X x

(1.12)

1 Solving Lane-Emden Equation by Using Differential … Table 1.2 Numerical solution of DTM for example 1 x Exact solution DTM 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

1.000000000 1.010050167 1.040810774 1.094174284 1.173510871 1.284025417 1.433329415 1.632316220 1.896480879 2.247907987 2.718281828

1.000000000 1.010050167 1.040810667 1.094171500 1.173482667 1.283854167 1.432576000 1.629658167 1.888490667 2.226623500 2.666666667

7

Absolute error 0.0000000E+00 0.0000000E+00 1.0700000E-07 2.7840000E-06 2.8204000E-05 1.7125000E-04 7.5341500E-04 2.6580530E-03 7.9902120E-03 2.1284487E-02 5.1615161E-02

Table 1.3 Absolute error of the method used and minimum absolute error to exact solution for example 1 x DTM ADM Minimum 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.0000000E+00 0.0000000E+00 1.0700000E-07 2.7840000E-06 2.8204000E-05 1.7125000E-04 7.5341500E-04 2.6580530E-03 7.9902120E-03 2.1284487E-02 5.1615161E-02

with initial conditions of

0.000000E+00 0.000000E+00 1.000000E-09 1.000000E-09 2.300000E-08 3.520000E-07 3.187000E-06 2.065700E-05 1.049200E-04 4.426990E-04 1.615161E-03

0.000000E+00 0.000000E+00 1.000000E-09 1.000000E-09 2.300000E-08 3.520000E-07 3.187000E-06 2.065700E-05 1.049200E-04 4.426990E-04 1.615161E-03

y(0) = 0, y  (0) = 0

(1.13)

y(x) = x 4 − x 3 .

(1.14)

and given the exact solution

From the initial conditions and theorem in Table 1.1, we obtain Y (0) = 0, Y (1) = 0.

(1.15)

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M. Aris Izzuddin Razali and N. Azliza Abd Latif

Fig. 1.2 exact, DTM and Legendre wavelets solution of example 2

By multiplying (1.12) by x and using the theorem in Table 1.1, the recurrence relation obtain is Y (k + 1) =

1 (k + 1) (k + 8)

δ (k − 6) − δ (k − 5) + 44δ (k − 3) − 30δ (k − 2) −

k 

δ (r − 2) Y (k − r) .

r=0

(1.16) Substitute (1.15) into (1.16)at k = 1, we obtain Y (2) = 0.

(1.17)

Then recurrence relation (1.16) at k = 2, 3, 4, 5, we obtain Y (3) = −1, Y (4) = 1, Y (5) = 0, Y (6) = 0. Therefore, combine all the term above and do Taylor series up to 7-th terms given Y (x) = x 4 − x 3 .

(1.18)

Figure 1.2 shows that the value from DTM is close with the exact solution. Table 1.4 indicates the absolute error which shows how close between DTM and

1 Solving Lane-Emden Equation by Using Differential … Table 1.4 Numerical solution of DTM for example 2 x Exact solution DTM 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.000E+00 −9.000E-04 −6.400E-03 −1.890E-02 −3.840E-02 −6.250E-02 −8.640E-02 −1.029E-01 −1.024E-01 −7.290E-02 0.000E+00

0.000E+00 −9.000E-04 −6.400E-03 −1.890E-02 −3.840E-02 −6.250E-02 −8.640E-02 −1.029E-01 −1.024E-01 −7.290E-02 0.000E+00

9

Absolute error 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

Table 1.5 Absolute error of the method used and minimum absolute error to exact solution for example 2 x DTM Legendre wavelets Minimum 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

5.81E-12 1.66E-11 1.50E-11 0.00E+00 1.00E-11 4.00E-11 1.00E-11 1.00E-10 2.00E-10 3.30E-10 3.89E-10

0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

exact solution. Table 1.5 depicts that the DTM solution is very near and accurate to the exact solution compare to Legendre wavelets. Example 3, consider the Lane-Emden equation [11]  y 2  y (x) + 4 2e y + e 2 = 0 x

(1.19)

y(0) = 0, y  (0) = 0

(1.20)

y(x) = −2 ln 1 + x 2 .

(1.21)

y  (x) + with the initial conditions of

which the exact functions is

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From the initial conditions and theorem in Table 1.1, we obtain Y (0) = 0, Y (1) = 0.

(1.22)

By multiplying (1.19) by x and using the theorem in Table 1.1, the recurrence relation obtained Y (k + 1) = −

1 (8E 1 (k − 1) + 4E 2 (k − 1)) . (k + 1)(k + 2)

(1.23)

Replacing k − 1 with k, then we get Y (k + 2) = −

1 (8E 1 (k) + 4E 2 (k)) (k + 2) (k + 3)

(1.24)

where E 1 (k) =

k−1  r +1 Y (r + 1) E 1 (k − r − 1), E 2 (k) k r =0

1 r +1 Y (r + 1) E 2 (k − r − 1). 2 r =0 k k−1

=

(1.25)

From the theorem in Table 1.1, we gain E 1 (0) = E 2 (0) = 1. Substituting (1.22) into (1.24) at k = 1, we obtain Y (2) = −2.

(1.26)

Following the above procedure for k = 1, 2, 3, 4 , we obtain E 1 (1) = 0, E 2 (1) = 0, Y (3) = 0, E 1 (2) = −2, E 2 (2) = −1, Y (4) = 1, E 1 (3) = 0, E 2 (3) = 0, Y (5) = 0, 2 E 1 (4) = 0, E 2 (4) = 0, Y (6) = − . 3 Therefore, combine all the terms above and do Taylor series up to 7-th term yield 2 Y (x) = −2x 2 + x 4 − x 6 . 3

(1.27)

1 Solving Lane-Emden Equation by Using Differential …

11

Fig. 1.3 Exact, DTM and LT-HPM solution of example 3 Table 1.6 Numerical solution of DTM for example 3 x Exact solution DTM 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.00000000000 −0.01990066171 −0.07844142630 −0.17235539250 −0.29684001020 −0.44628710260 −0.61496939940 −0.79755224000 −0.98939248360 −1.18665369100 −1.38629436100

0.000000000 −0.019900667 −0.078442667 −0.172386000 −0.297130667 −0.447916667 −0.621504000 −0.818332667 −1.045162667 −1.318194000 −1.666666667

Absolute error 0.00000000E+00 4.96000000E-09 1.24037000E-06 3.06075000E-05 2.90656500E-04 1.62956410E-03 6.53460060E-03 2.07804267E-02 5.57701834E-02 1.31540309E-01 2.80372306E-01

Figure 1.3 depicts that the trend of DTM solution is very near with exact solution at same goes with Homotopy perturbation method with Laplace transformation (LTHPM) solution. It then converges at Table 1.6 shows the numerical result of DTM. In Table 1.7, the absolute error of LT-HPM shows that the method is much closer to the exact solution. This result shows that the LT-HPM is better than DTM.

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Table 1.7 Absolute error of the method used and minimum absolute error to exact solution for example 2 x DTM LT-HPM Minimum 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.00000000E+00 4.96000000E-09 1.24037000E-06 3.06075000E-05 2.90656500E-04 1.62956410E-03 6.53460060E-03 2.07804267E-02 5.57701834E-02 1.31540309E-01 2.80372306E-01

0.00000000E+00 4.00000000E-11 3.96300000E-08 2.19750000E-06 3.70235000E-05 3.23560900E-04 1.86347940E-03 8.04357830E-03 2.81158970E-02 8.36932960E-02 2.19627694E-01

0.00000000E+00 4.00000000E-11 3.96300000E-08 2.19750000E-06 3.70235000E-05 3.23560900E-04 1.86347940E-03 8.04357830E-03 2.81158966E-02 8.36932960E-02 2.19627694E-01

1.4 Conclusion Higher terms of DTM can improve the accuracy to the exact solution. But higher terms required more computational work. For solving Lane-Emden equation, a few terms of DTM are recommended to obtain the approximate value. DTM has successfully solved three examples. Due to less computational work to obtain an approximation to exact value, there are some recommendations that can be made such as make an improvement of the algorithm of DTM to obtain exact solution and using modified DTM with fractional newton [10] or Adomian polynomials or Laplace transform or Padé approximation [11] to improve the result to be close with exact solution.

References 1. J.K. Zhou, Differential Transformation and Its Applications for Electrical Circuits (Huazhong University Press, Wuhan, 1986) 2. I. Hassan, V. Ertürk, Applying differential transformation method to the one-dimensional planar bratu problem, in Contemporary Engineering Sciences (2007) 3. H.J. Lane, On the theoretical temperature of the Sun, under the hypothesis of a gaseous mass maintaining its volume by its internal heat, and depending on the laws of gases as known to terrestrial experiment. Am. J. Sci. 2(148) 57–74 (1870) 4. P. Chambre, On the solution of the Poisson-Boltzmann equation with application to the theory of thermal explosions. J. Chem. Phys. 20, 1795–1797 (1952) 5. S. Chandrasekhar, Introduction to the Study of Stellar Structure (Dover Publications, New York, NY, USA) (1967) 6. P.M. Lima, L. Morgado, Numerical modeling of oxygen diffusion in cells with MichaelisMenten uptake kinetics. J. Math. Chem. 48, 145–158 (2010) 7. O.U. Richardson, The Emission of Electricity From Hot Bodies (Longmans Green and Company, London, UK, 1921)

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8. K. Batiha, B. Batiha, A new algorithm for solving linear ordinary differential equations. World Appl. Sci. J. 15(12), 1774–1779 (2011) 9. A.-M. Wazwaz, A new method for solving singular initial value problems in the second-order ordinary differential equations. Appl. Math. Comput. 128(2002), 45–57 (2002) 10. H. Aminikhah, S. Moradian, Numerical solution of singular Lane-Emden equation. ISRN Math. Phys. 2013, 9 (2013) 11. R. Tripathi, H.K. Mishra, Homotopy Perturbation Method with Laplace Transform (LT HPM) for Solving Lane-Emden Type Differential Equations (LETDEs) (2016). https://doi.org/10. 1186/s40064-016-3487-4

Chapter 2

Optimization of Asset Liability Management on Textile and Garment Companies Using Goal Programming Model Hagni Wijayanti, Sudradjat Supian, Diah Chaerani, and Adibah Shuib

Abstract Asset liability management is an important topic in a company’s financial planning strategy; therefore, quantitative techniques are needed to optimize its management. In the financial statements of a company, there are values of assets, liabilities, equity, income, and financial expenses that can assess the condition of the company. To analyze the optimization of the five elements of the financial statements, a Goal Programming (GP) Model was built. The Goal Programming Model was chosen because it is considered a mathematical model that can be used to obtain optimal solutions to problems that have multiple objectives. Besides, the deviation variables in the Goal Programming Model can produce complete information on the relative achievement of existing goals. The data used are financial statement data on textile and Garment Companies in West Java, Indonesia, namely PANASIA INDO, SUNSON TEXTILE, UNI-CHARM, EVER SHINE, INDO RAMA, INKOBAR, and MANITO. Based on the optimization results of the GP ALM model that was carried out on seven damages, it can be concluded that the asset goal has been achieved for SUNSON TEXTILE, UNI-CHARM, EVER SHINE, INDO RAMA, and INKOBAR companies. Liability has been achieved by the Companies PANASIA SINDO and MANITO. For revenue, no single company has yet achieved its financial goals, but the financial goals for equity and expenses have only been achieved by the SUNSON TEXTIL company. This study also provides recommendations for each company regarding the achievement of assets, liabilities, equity, revenue, and expense targets. H. Wijayanti (B) · S. Supian Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Pakuan, Bogor 16143, Indonesia e-mail: [email protected] D. Chaerani Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia A. Shuib Department of Mathematics, Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, Shah Alam, Malaysia © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Mustapha et al. (eds.), Proceedings of the 8th International Conference on the Applications of Science and Mathematics, Springer Proceedings in Physics 294, https://doi.org/10.1007/978-981-99-2850-7_2

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2.1 Introduction Asset liability management (ALM) is the most important topic in the company’s strategic planning; therefore, quantitative techniques are needed to optimize its management [1]. Assets that are managed effectively and efficiently can achieve the company’s expected goals. Asset management is not just managing and recording a list of assets owned but must optimize assets to prevent company losses and maximize profits. It is important to carry out asset liability revaluation [2] to strengthen business decisions, determine sufficient resources to pay obligations (liability), and after revaluing assets, it may still require more funding, then be ready to meet creditors, so that with asset revaluation, will minimize the risk and doubt about the business decisions that must be taken. A multi-objective model that maximizes assets and minimizes liability will be built to solve the problem of asset liability management [2, 3]. Goal Programming is a mathematical model that is considered suitable for use in solving multi-objective problems that have conflicting objective functions, to minimize deviations from the set targets [4]. The objective programming problem can be solved by assigning weights to the individual deviation parameters of the objective function or by setting a priority for each deviation [5, 6]. Goal Programming as a multi-objective model solution is used in portfolio selection [7], asset liability management [8], financial planning [9], allocation [10], budget, [11] in banking and financial institutions. Tunjo and Zoran [12] also presented the Goal Programming Model on asset liability management for Greek commercial banks. The objectives considered are maximizing profit, reducing risk, maintaining liquidity and solvency at the desired level, and expanding deposits and loans. The Goal Programming Model can be extended and integrated with other methods, [12] using the Taylor formula. Meanwhile, [9] assigns weights to four financial strategies using a linear objective program and then ranks the strategies using the multi-criteria decision-making method. Soheyla et al. [13] developed a mathematical model to find optimal management and equity for Mellat Bank, then determined the priority goals using process hierarchy analysis (AHP) before optimizing them using Goal Programming. An optimization model for liquidity management at Parsian Bank has been completed by [14] by using fuzzy analytical process hierarchy (FAHP) and Goal Programming. From the above background, this study aims to apply the Goal Programming Model to asset and liability management and contribute to analyzing the financial condition of a company and the company’s achievements in meeting asset, liability, equity, revenue, and expense targets for Garment Companies in West Java, Indonesia.

2 Optimization of Asset Liability Management on Textile and Garment …

17

Table 2.1 Financial data of seven companies (in million rupiah) Company

Asset

Liability

Equity

Revenue

Expense

PANASIA INDO

464.949309

389.189

75.7607

− 112.89179

46.1640

SUNSON TEXTILE

519,668.402

319,025

200,644

− 8711.4512

− 19.7739435

UNI-CHARM

7.71338367

3.8354

3.87798

0.29718067

− 0.04772433

EVER SHINE

59.2043813

44.9816

14.2228

− 0.652593

1.959371

INDO RAMA

775.792808

410.006

365.787

36.394815

8.279132667

INKOBAR

90,674.3202

67,427.3

23,247

2358.8175

20,032.21871

MANITO

87,092.2958

50,765

36,327.3

2973.81324

48.799

Average

99,820.3826

62,580.8

37,239.6

− 493.66755

51.91842567

Standard deviation

189,786.814

116,538

73,496.6

3842.85231

11,491.18751

2.2 Research Methods 2.2.1 Data The data used in this study are data from the financial statements of seven Garment Companies in West Java, Indonesia, for the period 2019–2021 which were obtained from publications on the official website of the Indonesia Stock Exchange as given in Table 2.1.

2.2.2 Model Formulation The problem to be researched is the optimization of the financial statements of the PANASIA INDO, SUNSON TEXTILE, UNI-CHARM, EVER SHINE, INDO RAMA, INKOBAR, and MANITO companies to optimize assets, liabilities, equity, revenue, and expenses, which can be seen in Table 2.2. Next, the stages of building a Goal Programming Model are carried out as follows: • Selection of Goal Programming Model without priority is done because each objective function has the same importance in the performance of a company. Table 2.2 Aim is to optimize the financial management of the company

Goal

Description

1

Maximizing assets

2

Minimizing liability

3

Maximizing equity

4

Maximizing revenue

5

Minimize expense

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• Determination of the decision variables to be used in the model is expressed in the form xj with j = 1, 2, 3. xj is the amount of financial statement in year j. • Formulating the constraint functions of the Goal Programming Model on this problem, namely the constraints on assets, liabilities, equity, income, and expenses which are formulated as follows: Maximizing assets: 3 

a1 j x j + d1− − d1+ = b1

(2.1)

a2 j x j + d2− − d2+ = b2

(2.2)

a3 j x j + d3− − d3+ = b3

(2.3)

a4 j x j + d4− − d4+ = b4

(2.4)

a5 j x j + d5− + d5+ = b5 ,

(2.5)

j=1

Minimizing liabilities: 3  j=1

Maximizing equity: 3  j=1

Maximizing revenue: 3  j=1

Minimize expense: 3  j=1

where a1j : The value of asset, in year j = 1, 2, 3. a2j : The value of liability, in year j = 1, 2, 3. a3j : The value of equity, in year j = 1, 2, 3. a4j : The value of revenue, in year j = 1, 2, 3. a5j : The value of expense, in year j = 1, 2, 3. x j : The value of financial statement in year j = 1, 2, 3. bi : Benchmark value when goal i = 1, 2, …, 5. d + : Positive deviation variables when goal i = 1, 2, …, 5. d − : Negative deviation variables when goal i = 1, 2, …, 5. Then the objective function is formulated, as follows:

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19

          Z = d1− − d1+ + d2− − d2+ + = d3− − d3+ + d4− − d4+ + d5− − d5+ . (2.6) • The first constraint function is to maximize assets, then what will be minimized is the deviation below the target (negative deviation) so that the deviation above the target must be zero (d1− ). • The second constraint function is to minimize the liability, then what will be minimized is the deviation above the target (positive deviation) so that the deviation below the target must be zero (d2− ). • The third constraint function is maximizing equity, so what will be minimized is the deviation below the target (negative deviation) so that the deviation above the target must be zero (d3− ). • The fourth constraint function is to maximize revenue, so what will be minimized is the deviation below the target (negative deviation) so that the deviation above the target must be zero (d4− ). • The fifth constraint function is to minimize the expense so that what will be minimized is the deviation below the target (negative deviation) so that the deviation above the target must be zero (d5− ). Since the initial model of the objective function, (2.6) can be simplified to as follows. Min Z = d1− + d2− + d3− + d4− + d5− .

(2.7)

Completion of the Goal Programming Model is using LINGO software. The optimal value obtained in achieving Goal Programming is determined by the deviation value from the benchmark. The greater the deviation, the lower the achievement of the goal is.

2.3 Results and Analysis 2.3.1 Optimization Results From Table 2.3, it can be seen that the Garment Company, PANASIA INDO, has achieved its financial goals for liability to minimize the company’s liabilities which has been achieved but has not yet achieved its financial goals for assets, equity, revenue, and expenses. From Table 2.4, it can be seen that the SUNSON TEXTILE Garment Company has achieved its financial goals for assets, equity, and expenses but has not yet achieved its financial goals for liabilities and revenue. It can be seen from Table 2.5 that UNI-CHARM companies have only achieved their financial goals for assets only, while for liabilities, equity, revenue, and expenses they have not yet reached their financial goals.

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Table 2.3 Model value and goal attainment of PANASIA INDO (million rupiah) Goal

Benchmark value

Negative deviation

Positive deviation

Asset

519,668

Model value 4.5836

519,663

0.00000

Liability

3.83539

3.8367

0.00000

0.00000

Equity

200,643

0.7468

200,642

0.00000

Revenue

2973

2974

0.00000

Expense

− 19.773

0.00000

19,774

− 1.1129 0.4551

Table 2.4 Model value and goal attainment of SUNSON TEXTILE (million rupiah) Goal

Benchmark value

Model value

Negative deviation

Positive deviation

Asset

519,668

519,668

0.000000

0.000000

Liability

3.8353

319,024

0.000000

319,021

Equity

200,643

200,643

0.000000

0.6544401

Revenue

2973

− 8711

11,685

0.000000

Expense

− 19.773

46.1640

0.01522044

0.000001

Table 2.5 Model value and goal attainment of UNI-CHARM (million rupiah) Goal

Benchmark value

Model value

Negative deviation

Positive deviation

Asset

519,668

5,196,683

0.000000

0.000000

Liability

3.8353

2,583,996

0.000000

258,395.8

Equity

200,643

9,582,222

0.000000

60,625

Revenue

2973

24,520,023

0.000000

17,047.89

Expense

− 19.773

− 32,152

0.000000

16,558.65

From Table 2.6, it can be seen that the company EVER SHINE has only achieved financial goals for assets only, while liabilities, equity, revenue, and expenses have not yet achieved financial goals. From Table 2.7, it can be seen that the INDO RAMA company has only achieved financial goals for assets only, while liabilities, equity, revenue, and expenses have not yet achieved financial goals. Table 2.6 Value and goal attainment of EVER SHINE (million rupiah) Goal

Benchmark value

Model value

Negative deviation

Positive deviation

Asset

519,668

519,671

0.000000

0.000000

Liability

3.8353

394,829

0.000000

394,812

Equity

200,643

124,841

75,826

0.6544401

Revenue

2973

− 5728

8701

0.000000

Expense

− 19.773

17,198

0.000000

36,971

2 Optimization of Asset Liability Management on Textile and Garment …

21

Table 2.7 Model value and goal attainment of INDO RAMA (million rupiah) Goal

Benchmark value

Model value

Negative deviation

Positive deviation

Asset

519,668

542,944

0.000000

0.000000

Liability

3.8353

286,945

0.000000

274,637

Equity

200,643

255,998

0.000000

44,376

Revenue

2973

25,471

0.000000

21,342

Expense

− 19.773

5794

0.000000

25,319

Table 2.8 Model value and goal attainment of INKOBAR (million rupiah) Goal

Benchmark value

Model value

Negative deviation

Positive deviation

Asset

519,668

519,668

0.000000

0.000000

Liability

3.8353

386,436

0.000000

386,430

Equity

200,643

133,232

67,411

0.000000

Revenue

2973

13,518

0.000001

10,544

Expense

− 19.773

114,807

0.000000

134,581

Table 2.9 Model value and goal attainment of MANITO (million rupiah) Goal

Benchmark value

Model value

Negative deviation

Positive deviation

Asset

519,668

65.7895

519,667

0.000000

Liability

3.8353

38.3479

0.000000

0.000000

Equity

200,643

27.4416

200,643

0.000000

Revenue

2973

2.24641

2973

0.000001

Expense

− 19.773

0.03686

0.000000

19,773

From Table 2.8, it can be seen that the INKOBAR company has only achieved financial goals for assets only, while liabilities, equity, revenue, and expenses have not yet achieved financial goals. From Table 2.9, it can be seen that the MANITO company has only achieved its financial goals for liability, while for assets, equity, revenue, and expenses, it has not yet achieved its financial goals.

2.3.2 Optimization Analysis In this subsection, we will discuss the optimization analysis of the optimization results from the Goal Programming Model.

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H. Wijayanti et al.

Company

Asset

Liability

Equity

Revenue

Expense

PANASIA INDO

4.583656

3.836776

0.746879

− 1.11293

0.455102

SUNSON TEXTILE

519,668

319,024

200,643

− 8711

46.164

UNI-CHARM

5,196,683

2,583,996

9,582,222

24,520,023

− 32,152

EVER SHINE

519,671

394,829

124,841

− 5728

17,198

INDO RAMA

542,944

286,945

255,998

25,471

5794

INKOBAR

519,668

386,436

133,232

13,518

114,807

MANITO

65.7895

38.3479

27.4416

2.24641

0.03686

Z

7,298,704

3,971,272

10,296,964

24,544,574

105,693

Goal

519,668

3.835399

200,643

2973.8132

− 19,773.94

Sensitivity (b1)

6,779,035

3,971,268

10,096,320

24,541,600

125,467

From the optimization analysis table, it can be concluded that • Assets: Asset value can still be increased by Rp 6,779,035,000, for 3 years. For assets, the range of achievement is between Rp. 519,668,000,000 and Rp. 519,668,000,000 + Rp. 6,779,035,000. If the company’s assets have exceeded the range of achievement, it can be concluded that the company has achieved its financial goals for assets. Companies that have achieved financial goals for assets are SUNSON TEXTILE, UNI-CHARM, EVER SHINE, INDO RAMA, and INKOBAR. • Liability: Liability value can still be reduced by Rp. 3,971,268,349 for 3 years. For liability, the range of achievement is between Rp. 3,971,268,349 and Rp. 38.353.990 − Rp. 3,971,268,349. If the company’s liability is less than the range of achievement, it can be concluded that the company has achieved the financial goals for liability, but if the company exceeds this value, the company does not meet the financial objectives for liability. Companies that have achieved their financial goals for liability are PANASIA SINDO and MANITO. • Equity: Equity value can still be increased by Rp. 10,096,320,000 for 3 years. For equity, the achievement range is between Rp. 10,096,320,000 and Rp. 10,096,320,000 + Rp. 2.00,643,522. If the company’s equity has exceeded the achievement range, it can be concluded that the company has achieved its financial goals for equity. A company that has achieved its financial goals for equity is SUNSON TEXTILE. • Revenue: The value of revenue can still be increased by Rp. 24,541.6 million for 3 years. For revenue, the achievement range is between Rp. 24,541,600,000 and Rp. 24,541.600.000 + Rp. 2,973,000,000. If the company’s income has exceeded the range of achievements, it can be concluded that the company has achieved its financial goals for revenue. All companies have not achieved financial goals for revenue. • Expenses: The value of the expense can still be reduced by Rp. 1.25,467,000 for 3 years. For the load, the range of achievement is between Rp. 1.25.467.000 − Rp. 197,739,400 and Rp. 1.25,467,000. If the company’s expenses are less than the range of achievement, it can be concluded that the company has achieved its

2 Optimization of Asset Liability Management on Textile and Garment …

23

financial goals for expenses, but if the company exceeds this value, the company does not meet the financial objectives for liability. The company that has achieved its financial goals for expenses is SUNSON TEXTILE.

2.4 Conclusions Based on the results of the optimization of the Goal Programming ALM model that was carried out on seven damages, it can be concluded that the asset goal has been achieved for SUNSON TEXTILE, UNI-CHARM, EVER SHINE, INDO RAMA, and INKOBAR companies. Liability has been achieved by the companies PANASIA SINDO and MANITO. For revenue, no single company has yet achieved its financial goals, but the financial goals for equity and expenses have only been achieved by the SUNSON TEXTIL company. This study also provides recommendations for each company regarding the achievement of assets, liabilities, equity, revenue, and expense targets. Acknowledgements This study is supported by The Faculty of Mathematics and Natural Sciences, Universitas Pakuan, Indonesia.

References 1. W.B. Utami, Analysis of current ratio changes effect, asset ratio debt, total asset turnover, return on asset, and price earning ratio in predicting growth income by considering corporate size in the company joined in LQ45 index year 2013–2016. Int. J. Econ. Bus. Account. Res. 1(01), 253 (2017) 2. M. Azizi, A. Neisy, Mathematic modelling and optimization of bank asset and liability by using fractional goal programming approach. Int. J. Model. Optim. 7(2), 85–91 (2017). https://doi. org/10.7763/ijmo.2017.v7.564 3. H. Abdollahi, Multi-objective programming for asset-liability management: the case of Iranian banking industry. Int. J. Ind. Eng. Prod. Res. 31(1), 75–85 (2020) 4. A. Hussain, H. Kim, Goal-programming-based multi-objective optimization in off-grid microgrids. Sustainability 12, 8119 (2020) 5. H. Omrani, M. Valipour, A. Emrouznejad, Using weighted goal programming model for planning regional sustainable development to optimal workforce allocation: an application for provinces of Iran. Soc. Indicat. Res. 141(3), 1007–1035 (2019). https://doi.org/10.1007/s11 205-018-1868-5 6. M. Alluwaici, A.K. Junoh, M.H. Zakaria, A.M. Desa, Weighted linear goal programming approach for solving budgetary manufacturing process. Far East J. Math. Sci. 101(9), 1993– 2021 (2017) 7. N. Hassan, L.W. Siew, S.Y. Shen, Portfolio decision analysis with maximum criterion in the Malaysian stock market. Appl. Math. Sci. 6(109–112), 5483–5486 (2012) 8. K. Kosmidou, G. Baourakis, C. Zopounidis, Credit risk assessment using a multicriteria hierarchical discrimination approach: a comparative analysis. Eur. J. Oper. Res. 138(2), 392–412 (2002). https://doi.org/10.1016/s0377-2217(01)00254-5 9. M. Moradi, H. Janatifar, Performance evaluation of automobile companies based on multicriteria decision-making techniques. Glob. J. Manag. Stud. Res. 1, 77–84 (2014)

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10. N. Hassan, L.W. Siew, S.Y. Shen, Portfolio decision analysis with maximin criterion in the Malaysian stock market. Appl. Math. Sci. 6(109–112), 5483–5486 (2012) 11. M. Mehri, B. Jamshidinavid, Designing a mathematical model of asset and liability management using goal programming (case study: Eghtesad-e-Novin Bank). GMP Rev. 18(3), 186–195 (2015) 12. P. Tunjo, B. Zoran, Financial structure optimization by using a goal programming approach. Croat. Oper. Res. Rev. 3, 150–162 (2012) 13. N. Soheyla, M. Mehizad, P.G. Hadi, Asset and liability optimal management mathematical modeling for banks. J. Basic Appl. Sci. Res. 3(1), 484–493 (2013) 14. R. Mohammadi, M. Sherafati, Optimization of bank liquidity management using goal programming and fuzzy AHP. Res. J. Recent Sci. Malaysia 4(6), 53–61 (2015)

Chapter 3

A Two-Stage Fuzzy DEA Approach—Application to Study the Effectiveness of Indian Iron and Steel Industries Mariappan Perumal, M. Umaselvi, M. Maragatham, and D. Surjith Jiji Abstract The main objective of this research is to use a two-step DEA method to determine the effectiveness of India’s iron and steel industries through Trapezoidal Fuzzy Numbers. The technique provides a structure for analyzing various measures of production and marketability in the chosen industries in order to identify those which are most effective. The proposed fuzzy inference system can build input-output mapping based on fuzzy rules and specified datasets using a hybrid learning process. The results provide the required information regarding the industries those who are doing extremely well in both Productivity and Marketability.

3.1 Introduction DEA is an approach that builds on a new use of LPP. These models were created with the intention of measuring performance. Helps in evaluating the relative performance of a set of firms that use a variety of similar inputs to make a variety of same outputs. Farrel [1] established the DEA Structure. The study by Charnes et al. [2] introduced the latest sequence of discussion on this topic.

M. Perumal (B) Department of Management Studies, St. Joseph’s Institute of Management, Tiruchirappalli, Tamil Nadu 620002, India e-mail: [email protected] M. Umaselvi Faculty of Business Management, Majan University College, Musat, Oman M. Maragatham · D. Surjith Jiji Department of Mathematics, Periyar EVR College (Autonomous), Kajamalai Colony, Tiruchirappalli, Tamil Nadu 620023, India © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Mustapha et al. (eds.), Proceedings of the 8th International Conference on the Applications of Science and Mathematics, Springer Proceedings in Physics 294, https://doi.org/10.1007/978-981-99-2850-7_3

25

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3.1.1 Decision Making Units (DMU) DEA is a linear programming-based approach for assessing the performance efficiency of decision-making units in organizations (DMUs). This approach [2] aims to evaluate how efficiently a DMU utilizes the resources available to create a set of outputs. In DEA, DMU performance is measured in terms of efficiency or productivity, which is defined as the ratio of total outputs to total inputs. Efficiencies calculated using DEA are relative to the best-performing DMU (or DMUs if there are many best-performing DMUs) [3, 4]. The efficiency score for the highest performing DMU is unity (100%), while the performance of other DMUs ranges between 0 and 100 percent in comparison to this best performance [3, 4]. Mariappan et al. evaluated the highly efficient colleges affiliated with Bharathidasan University using Fuzzy DEA [5].

3.1.2 Multi Stage DEA Fare and Grosskopf [6] proposed a DEA network method whereby the DMU is considered a subsystem network. Various strategies could be used in the evaluation of efficiency in the context of the DEA. In recent years, a large amount of research has been undertaken in favor of the DEA in two phases. The Stage 1 and Stage 2 performance measures are produced separately by the two-stage DEA template. The current two-stage DEA model consists of two types: a closed multi stage DEA system and an open multi stage DEA system [6]. DEA System with Two-Stage Closed Type The Stage 1 output measures are considered as the Stage 2 input measures within the DEA two-stage closed system model. Two-Stage Open DEA System Model In the two-stage open DEA system model, the second stage has new inputs in addition to the intermediate variables, therefore the second stage inputs are not identical to the first stage outputs.

3.2 Methods 3.2.1 Collection of Data The essential data were collected from the eleven selected steel industries on their official website for the 2016–2020 fiscal years, based on the availability of reliable data.

3 A Two-Stage Fuzzy DEA Approach—Application to Study …

27

3.2.2 Selecting Input or Output Variables As per the DEA literature, various research has employed various combinations of inputs and outputs. This study takes care of six input and two output variables for Stage: 1 [Productivity] and two input and four output variables for Stage: 2 [Marketability]. The variables under the study are listed below: Tangible Assets: Land, Buildings, Plant and Machinery, and Office Equipment. Intangible Assets: Vehicles, and Computer Software.

3.2.3 Mathematical Modeling Fuzzy Inference System The five functional blocks that make up a fuzzy inference system are: • A set of fuzzy IF-THEN rules included in a rule base. • The membership functions of the fuzzy sets utilized in the fuzzy rules are defined in this database. • The inference operations on the rules are performed by decision-making unit. • A fuzzification inference that converts crisp inputs into linguistic value degrees of match. • A defuzzification interface that converts the inference’s fuzzy findings into a crisp output Fig. 3.1. The knowledge base is a term that refers to both the rule base and the database. The literature has proposed several different forms of FIS. It is due to the differences between the specification of the consequent part and the defuzzification schemes [7, 8].

Fig. 3.1 Fuzzy inference system

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The Fuzzy DEA Principles In real-world challenges, observable values are frequently inaccurate or ambiguous. Unquantifiable, inadequate, and non-accessible data might result in imprecise or vague data. Bounded intervals, ordinal (rank order) data, or fuzzy numbers are commonly used to express imprecise or ambiguous data. Many researchers have developed fuzzy DEA models in previous years to deal with scenarios where part of the input and output data is imprecise or ambiguous [9]. Fuzzy Fractional Type: Fuzzy Constant Returns to Scale Model: Stage 1: The structure of the Output Maximization F-DEA [F-CRS] model can be viewed in the form of a Fractional Programming problem as follows [2, 3, 5]: Maximize the efficiency of the qth DMU: v˜ jq y jq u˜ iq x jq E˜ q

jth fuzzy output value of the qth DMU of stage 1 jth output variable of the qth DMU of stage 1 ith fuzzy input value of the qth DMU of stage 1 ith input variable of the qth DMU of stage 1 Efficiency of the qth DMU of stage 1. m j=1 Max E˜ q = s i=1

subject to the constraints

m j=1

v˜ jq y jq

i=1

u˜ iq x jq

s

v˜ jq y jq u˜ iq x jq

(3.1)

≤1

v jq , y jq , u˜ jq , x˜ jq ≥ 0 for all i = 1, 2, . . . , s; j = 1, 2, . . . , m; q = 1, 2, . . . , n. Stage 2: The overall form of the F-DEA [F-CRS] Second Stage Output Maximization model can be expressed in the following terms: Here, the generic model is constructed to maximize the effectiveness of the output qth variable: w˜ jq y jq v˜iq x jq E˜ q

jth fuzzy output value of the qth DMU of stage 2 jth output variable of the qth DMU of stage 2 ith fuzzy input value of the qth DMU of stage 2 ith input variable of the qth DMU of stage 2 Efficiency of the qth DMU of stage 2. m ˜ jq y jq j=1 w ˜ Max E q = s ˜iq x jq i=1 v

subject to the constraints

m j=1

s

w˜ jq y jq

˜iq x jq i=1 v

≤1

(3.2)

3 A Two-Stage Fuzzy DEA Approach—Application to Study …

29

w˜ jq , y jq , v˜ jq , x jq ≥ 0 for all i = 1, 2, . . . , s; j = 1, 2, . . . , m; q = 1, 2, . . . , n. Fuzzy VRS type: Stage 1: It examines the return to the fuzzy variable scale recommended by Banker et al. [3, 5, 10] is as follows: Min θm Subject to the Constraints Y˜ λ ≥ Y˜m ; X˜ λ ≤ θ X˜ m N 

λn = 1; λ ≥ 0; θm free variable

n=1

Stage 2: The Second Stage F-DEA based on Variable Returns to Scale model can be as follows [3, 5, 10]: Minθm Subject to the Constraints X˜ λ ≤ X˜ m ; Z˜ λ ≥ θ Z˜ m N 

λn = 1; λ ≥ 0; θm free variable

n=1

Fuzzy Number based on Trapezoidal rule: The membership function at A, A = (a1 , a2 , a3 , a4 ), ai ∈ R is defined as: ⎧ x−a1 ⎪ a2 −a1 ⎪ ⎪ ⎨1 μ A = a4 −x ⎪ ⎪ ⎪ ⎩ a4 −a3 0

a1 ≤ x ≤ a2 a2 ≤ x ≤ a3 a3 ≤ x ≤ a4 otherwise

Defuzzification A technique which derives the net values of one or more loose numbers is necessary because the technical procedures require clear control actions. The extraction process of a single number from the output of an aggregated fuzzy set is defined as a defuzzification. It is used to transform findings from fuzzy inference into a net result. Graded Mean Integration Representation For expressing generalized fuzzy numbers, Chen and Hseih suggest graded mean integration representation [8, 11]. Consider the fuzzy number A = (a1 , a2 , a3 , a4 : w), then the h-level graded mean h[L −1 (h)+R −1 (h)] . 2 Then R(A) is defined as [8, 11]

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Table 3.1 Input and output variables considered in this study Productivity stage Time-span under consideration Input variables Output variables Input variables Output variables Property, plant and equipment Inventories and maintenance Raw materials Stores and spares Reserves and surplus Employee salaries

Finished goods

Finished goods

Sales turnover

Stock in trade

Stock in trade

Share holder equity Earnings per share Total revenue

 h L −1 (h)+R −1 (h)

R(A) =

0

w 0

2

dh

hdh

where h ∈ (0, w), and 0 < w ≤ 1. Consider the trapezoidal fuzzy number A. According to Chen and Hsieh the defuzzified value a1 + 2a2 + 2a3 + a4 R(A) = (3.3) 6 The researcher used the Graded Mean Integration representation approach for defuzzification in this study [8, 11].

3.3 Results and Discussion 3.3.1 Stage: 1 F-CCR Model The fuzzy DEA efficiency value is calculated using the F-CCR (Steady Return to Scale) technical efficiency model as indicated in Table 3.2. F-CRS study reveals only five industries achieved a productivity efficiency rating of 1 in fiscal years 2016–2020. For the financial years 2016–2020, based on the F-VRS model, 9 industries seemed to have the highest productivity efficiency score among the selected industries. There are only five Iron and Steel Industries that are highly consistent with an efficiency score of 1 and rank first in productivity among all the Iron and Steel Industries considered. Table 3.2 shows the mean efficiency of the steel industries at stage 1.

3 A Two-Stage Fuzzy DEA Approach—Application to Study …

31

Table 3.2 Efficiency results of stage-1 based on F-CRS, F-VRS and overall Name of the F-CRS F-VRS industry Efficiency score Defuzzified Efficiency Defuzzified score score score ESSAR JSW JINDAL RINL SAIL SURYA TATA TATA BSL TII UGSL VISA

(1,1,1,1) (0.497,0.451,1,1) (0.318,1,1,1) (0.846,1,1,1) (1,1,1,1) (1,1,1,1) (0.929,1,1,1) (1,1,1,1) (1,1,1,1) (1,0.029,0.007,0.045) (0.467,1,1,0.601)

1 0.733167 0.886333 0.974333 1 1 0.988167 1 1 0.186167 0.844667

(1,1,1,1) (1,1,1,1) (0.595,1,1,1) (0.901,1,1,1) (1,1,1,1) (1,1,1,1) (1,1,1,1) (1,1,1,1) (1,1,1,1) (1,1,1,1) (1,1,1,1)

1 1 0.9325 0.9835 1 1 1 1 1 1 1

Mean score

1 (0.866583) 0.909417 0.978917 1 1 0.994083 1 1 0.593083 0.922333

3.3.2 Stage: 2 (Marketability) Fuzzy Variable Return to Scale (F-BCC Model) Table 3.3 indicates that as per F-CRS Model, the maximum efficiency is attained by one industry in marketability. Table 3.3 refers that according to the F-VRS only four industries scored the efficiency score one in marketability.

3.3.3 Tables See Table 3.3.

3.4 Conclusion The current study shows that ESSAR, SAIL, TATA BSL, and TII are highly efficient in Productivity and UGSL thrives in Marketability. The companies which are behind in this study should analyze it carefully and try to improve in the coming years.

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Table 3.3 Efficiency results of stage-II based on F-CRS, F-VRS and overall Name of the industry

F-CRS Efficiency score

F-VRS Defuzzified score

Efficiency score

Mean score Defuzzified score

ESSAR

(0.058,0.012,1,1)

0.513667

(0.898,1,1,1)

0.983

0.748333

JSW

(0.43,0.013,1,1)

0.576

(1,1,1,1)

1

0.788

JINDAL

(1,0.011,0.127,0.341)

0.2695

(1,1,0.99,0.541)

0.920167

0.594833

RINL

(0.16,0.094,0.069,0.049)

0.089167

(1,1,0.517,0.401)

0.739167

0.414167

SAIL

(0.15,0.016,0.011,0.061)

0.044167

(1,1,1,1)

1

0.522083

SURYA

(0.319,0.003,0.114,0.235)

0.131333

(0.529,0.432,1,1)

0.732167

0.43175

TATA

(0.361,0.022,1,1)

0.5675

(1,1,1,1)

1

0.78375 0.74775

TATA BSL

(0.252,0.099,1,1)

0.575

(0.523,1,1,1)

0.9205

TII

(0.496,1,0.092,0.15)

0.471667

(0.498,1,1,0.165)

0.777167

0.624417

UGSL

(1,1,1,1)

1

(1,1,1,1)

1

0.593083

VISA

(0.162,0.009,0.037,0.473)

0.121167

(0.705,0.808,0.672,0.795)

0.743333

0.922333

References 1. M.J. Farrel, The measurement of productivity efficiency. J. Roy. Stat. Soc. (A) 120, 253–281 (1957) 2. A. Charnes, W.W. Cooper, E. Rhodes, Measuring the efficiency of decision making units. Eur. J. Oper. Res. 2, 429–444 (1978) 3. R. Ramanathan, An Introduction to Data Envelopment Analysis: A Tool for Performance Measurement (Sage Publications, New Delhi, 2003) 4. L.M. Seiford, J. Zhu, Profitability and marketability of the top 55 U.S. commercial banks. Manag. Sci. 45(9), 1270–1288 (1999) 5. P. Mariappan et al., Performance efficiency of the colleges affiliated with Bharathidasan University: a fuzzy DEA approach. Int. J. Aquat. Sci. 12(2), 3113–3125 (2021) 6. R. Fare, S. Grosskopf, Productivity and intermediate products: a frontier approach. Econ. Lett. 50(1), 65–70 (1996) 7. S.-H. Chen, C.H. Hseih, Graded mean integration representation of generalized fuzzy number. J. Chin. Fuzzy Syst. Assoc. Taiwan 5(2), 1–7 (2000) 8. F. Sufian, Determinants of bank efficiency during unstable macroeconomic environment: empirical evidence from Malaysia. Res. Int. Bus. Finan. 23, 54–77 (2009) 9. R.D. Banker, A. Charnes, W.W. Cooper, Some models for the estimation of technical and scale inefficiencies in data envelopment analysis. Manag. Sci. 30(9), 1078–1092 (1984) 10. Y. Chen, J. Zhu, Measuring information technology’s indirect impact on firm performance. Inf. Technol. Manag. J. 5(1–2), 9–22 (2004) 11. H.A. Taha, Operations Research—Introduction (Prentice Hall of India (PVT), New Delhi, 2004)

Chapter 4

An EPQ Model Under Time-Dependent Demand with Single Time Discount Sales and Partial Backlogging Mariappan Perumal, Anusuya Baggiyalakshmi, and M. Maragatham

Abstract Considering deterioration as a function of time will make this model more relevant and realistic. In this, the researcher introduced a discount sale at the 3/4 stage of the cycle, and at the end, the inventory is exhausted, but the demand remains. Some regular and reliable customers will wait for the next stock and some of them which would not be considered a loss. This model strives to maximize profits.

4.1 Introduction Many studies have discussed inventory models and inventory models with backlogs in detail; however, in 2016 Kapil Come Bansal and Animesh Kumar Sharma [4] examined an inventory model with time-dependent demand and fractional backlog and proposed a technique to reduce the model’s overall cost. At various times, numerous researchers have discussed the following. In 2013, Mukopadhyay and Goswami [10] developed an inventory model to reduce requests for imperfect time-varying items, which are proponent requests and keep getting worse where there was a small backlog. In 2013, Singh et al. [13] developed two limited storage capabilities for the same training. Singh and Singhal jointly proposed an inventory system with multiple demands for flexible volume and learning in 2015. In 2013, Mukopadhyay and Goswami [10] developed an inventory model for imperfect items when demand followed a time-varying linear pattern. The robustness of the model was recently demonstrated in 2013 by applying the renewal reward theorem to build an economic production quantity model for imperfect items with scarcity and screening restrictions using a time interval as a decision variable.

M. Perumal (B) Department of Management Studies, St. Joseph’s Institute of Management, Tiruchirappalli, Tamil Nadu 620002, India e-mail: [email protected] A. Baggiyalakshmi · M. Maragatham Department of Mathematics, Periyar EVR College (Autonomous), Kajamalai Colony, Tiruchirappalli, Tamil Nadu 620023, India © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Mustapha et al. (eds.), Proceedings of the 8th International Conference on the Applications of Science and Mathematics, Springer Proceedings in Physics 294, https://doi.org/10.1007/978-981-99-2850-7_4

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This paper will help us to maximize the profit by giving discount scales for the imperfect quality items at the time of backlogging, which will satisfy some customers’ needs but not all; this leads to partial backlogging. By giving this discount, we will attract people and our imperfect quality items which remain in inventory will be sold that increase our income and slightly imperfect item with a reasonable cost will make people buy more items.

4.1.1 Assumptions and Notations Assumptions • Assumptions are taken as they are in the base paper, but the demand rate is considered linear. • The deterioration rate is time dependent. • Shortages are permitted through fractional backlogging. • The backlogging rate is an exponentially decreasing function of time. • Replenishment rate is infinite. • A single item is considered over the prescribed interval. • There is no repair or replenishment of deteriorated units and also • A screening process is considered. • The imperfect items/deteriorating items are considered with a percent discount. Notations I (t) = At time ‘t’ the inventory level. θ = Variable rate of defective units out of on-hand inventory, 0 < θ  1. C1 = Holding cost per unit. C3 = Shortage cost per unit. C4 = Lost sales per unit. d = Screening cost per unit. V1 = Selling price of good quality item per unit. V2 = Selling price of imperfect item per unit, Always, V2 < V1 . C0 = Ordering cost per order. K = purchasing cost per unit. Q = ordering size. P = ordering size. d = Screening cost per unit. TC = Total average cost. TR = Total sales volume (good and imperfect) items. T is the total length of the cycle, where at t1 the shortages start 0 ≤ t1 ≤ T. f (t) = a + bt

4 An EPQ Model Under Time-Dependent Demand …

35

a > 0, b > 0 is the variable demand rate. Where ‘a’ is the initial rate of demand and ‘b’ is the demand rate increases exp(−δt) unsatisfied demand is backlogged at a rate; the backlogging parameter δ is a positive constant.

4.2 Methods In the interval (0, t1 ), the inventory decreases due to demand and deterioration, and in the interval (t1 , T ), the demand is fractionally backlogged. I  (t) + θ t I (t) = − f (t), 0 ≤ t ≤ t1 

I (t) − f (t)e

−δt

, t1 ≤ t ≤ T

(4.1) (4.2)

We have the initial conditions that, I (t1 ) = 0 and I (0) = Q

(4.3)

From (4.1) dI + θ t I (t) = −1 − bt dt By solving, we get b aθ 3 bθ 2 I (t) = a(t1 − t) + (t12 − t 2 ) + (t1 + 2t 3 − 3t1 t 2 ) + (t − t 2 )2 2 6 8 1

(4.4)

From (4.2) dI = (−1 − bt)e−δt dt we get I (t) = [aδ + b(δt + 1)]

e−δt1 e−δt − [δa + b(δt + 1)] 1 δ2 δ2

(4.5)

Sub t = 0 in (4.4) we will get the inventory at initial b aθ 3 bθ 4 t + t Q = at1 + t12 + 2 6 1 8 1 Now we can find the holding cost per cycle is

(4.6)

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t1 C H = C1

I (t)dt 0

 C H = C1

at12 bt 3 aθ t14 bθ t15 + 1 + + 2 3 12 15

 (4.7)

Cs Shortage cost per cycle is due to backlog is given by T Cs = −C3  Cs = C3

I (t)dt t1

eδT e−δt1 (aδ 2 + δ 2 b(δT + 2)) − 4 4 δ δ



aδ 2 (1 − δ(T − t1 )) +bδ 2 ((2 − δT )(δt1 + 1) + δ 2 t)



And the opportunity cost (Cl ) per cycle due to lost sales is given by T Cl = C 4

(1 − e−δt )(a + bt)dt

t1

 b e−δT Cl = C4 a(T − t1 ) + (T 2 − T12 ) + (aδ + b(δT + 1)) 2 2 δ −δt1  e −(aδ + b(δt1 + 1)) 2 δ

(4.8)

With this, we are going to find the average total cost TC =

1 [Ordering cost + purchasing cost + screening cost + Holding cost T + Shortage cost + Lost sales]

TC =

1 T



 K + c0 Q + d Q + C1

at12 bt 3 aθ t14 bθ t15 + 1 + + 2 3 12 15



c3 (aδ 2 + bδ[2 + δT ])e−δT δ4

c3 − 4 aδ 2 (1 − δ(T − t1 )) + bδ[(2 − δT )(1 + δt1 ) + δ 2 t12 ] e−δt1 δ  b 1 +c4 a(T − t1 ) + (T 2 − t12 ) + 3 [aδ 2 + bδ(1 + δT )]e−δT 2 δ   1 (4.9) − 3 [aδ 2 + bδ(1 + δt1 )] e−δt1 δ

+

4 An EPQ Model Under Time-Dependent Demand …

37

Total Revenue TR of the cycle is TR = Total sales of (good quality + imperfect quality) item TR = V1 Q(1 − P) + V2 Q P

(4.10)

Our ultimate aim of this model is to find the total profit TP = TR − TC TP = V1 Q(1 − P) + V2 Q P  2   at1 1 bt 3 aθ t14 bθ t15 K + c0 Q + d Q + C1 − + 1 + + T 2 3 12 15  2 aδ (1 − δ(T − t1 )) c3 c3 2 −δT + 4 (aδ + bδ[2 + δT ])e e−δt1 − 4 δ δ +bδ[(2 − δT )(1 + δt1 ) + δ 2 t12 ] ⎧ ⎫ ⎫ b 1 ⎪ ⎪ ⎨a(T − t1 ) + (T 2 − t12 ) + 3 [aδ 2 + bδ(1 + δT )]e−δT ⎪ ⎬ ⎬ 2 δ −δt1 +c4 e 1 ⎪ ⎪ ⎪ ⎩ ⎭ − 3 [aδ 2 + bδ(1 + δt1 )]⎭ δ where bθ t14 b aθ t13 + Q = at1 + t12 + 2 6 8 Sub Q value in (4.12) 

   bθ t14 bθt14 b 2 aθ t13 b 2 aθt13 + + TP = V1 at1 + t1 + (1 − P) + V2 at1 + t1 + P 2 6 8 2 6 8    at12 bt13 aθt14 bθt15 1 + + + K + c0 Q + d Q + C1 − T 2 3 12 15 c3 + 4 (aδ 2 + bδ[2 + δT ])e−δT δ  c3  − 4 aδ 2 (1 − δ(T − t1 )) + bδ[(2 − δT )(1 + δt1 ) + δ 2 t12 ] e−δt1 δ  b +c4 a(T − t1 ) + (T 2 − t12 ) (4.11) 2   1 1 + 3 [aδ 2 + bδ(1 + δT )]e−δT − 3 [aδ 2 + bδ(1 + δt1 )] e−δt1 (4.12) δ δ

The aim of this paper is to maximize the profit where the optimal value of t1 is obtained by ∂TP =0 ∂t1

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Fig. 4.1 Variations of total profit according to the values of t1

and

∂ 2 TP < 0. ∂t12

4.3 Numerical Illustration Let V1 = RS.10, V2 = Rs.5, p = 0.3, a = 100, b = 40, C0 = 2, d = 0.1, c1 = 17, c3 = 20, c4 = 3, δ = 0.8, θ = 0.4, K = 200. In the example above, we discussed maximizing earnings. In tabulation, we found that the total profit and order quantity of various T ’s differs by commodity. In Fig. 4.1, we have the entries of t1 from 0.1 to 2.9. Here, 2.2 is the optimal value because when t1 increases, the profit value also increases. Once it reached 2.2, the next entry of t1 increases further, but profit will begin to fall down. Using these values, Q is also obtained. In tabulation, we have calculated on particular T = 3, and we obtain the optimum value of t1 = 2.2 and Q = 435.

4.4 Conclusions In this article, the researcher discussed an inventory model, according to the application. The ultimate purpose of this model is to maximize benefits. Due to demand and deterioration, we are running out of stock, which is why we will also have a partial decline, which will be seen as a loss of sales. With regard to the above circumstances, in this document, we consider the deteriorated item at a level and giving a discount for the same would decrease the loss, instead of lost sales. This can also minimize the travel cost by considering the inventory which is more feasible.

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References 1. Z.T. Balkhi, L. Benkherouf, On an inventory model for deteriorating items with stock dependent and time varying demand rates. Comput. Oper. Res. 31, 223–240 (2004) 2. K.K. Bansal, A. Navin, Inventory system with stock dependent demand and partial backlogging: a critical analysis. Kushagra Int. Manag. Rev. 2(2), 94–108 (2012) 3. K.K. Bansal, Order level inventory model with decreasing demand and variable deterioration. Int. J. Eng. Sci. Res. 2(9) (2012) 4. K.K. Bansal, A.K. Sharma, Analysis of inventory model with time dependent demand under fractional backlogging. Int. J. Educ. Sci. Res. (2016) 5. T.K. Datta, A.K. Pal, Deterministic inventory systems for deteriorating items with inventory level dependent demand and shortages. J. Oper. Res. Soc. 27, 213–224 (1990) 6. U. Dave, On a heuristic inventory-replenishment rule for items with a linearly increasing demand incorporating shortages. J. Oper. Res. Soc. 38(5), 459–463 (1989) 7. C.Y. Dye, A deteriorating inventory model with stock dependent demand and fractional backlogging under conditions of permissible delay in payments. Opsearch 39(3 & 4), 189–200 (2002) 8. P.N. Gupta, R.N. Aggarwal, An order level inventory model with time dependent deterioration. Opsearch 37(4), 351–359 (2000) 9. A. Kumar, K. K. Bansal, An optimal production model or deteriorating item with stocks and price sensitive demand rate. J. Eng. Comput. Appl. Sci. 2(7), 32–37 (2013) 10. A. Mukhopadhyay, A. Goswami, Application of uncertain programming to an inventory model for imperfect quantity under time varying demand. Adv. Model. Optim. 15(3), 565–582 (2013) 11. M. Nagarajan, S. Rajagopalan, Inventory models for substitutable products: optimal policies and heuristics. Manag. Sci. 54(8), 1453–1466 (2008) 12. B. Sarkar, An EOQ model with delay-in-payments and time-varying deterioration rate. Math. Comput. Model. 55, 367–377 (2012) 13. S. Singh, S. Jain, S. Pareek, An imperfect quality items with learning and inflation under two limited storage capacity. Int. J. Ind. Eng. Comput. 4(4), 479–490 (2013) 14. J.C. Tsou, S.R. Hejazi, M.R. Barzoki, Economic production quantity model for items with continuous quality characteristic, rework and reject. Int. J. Syst. Sci. 43(12), 2261–2267 (2012) 15. Volling, Grunewald, Spengler, An integrated inventory transportation system with periodic pick-ups and leveled replenishment. German Acad. Assoc. Bus. Res. (VHB) 6(2), 173–194 (2013) 16. K.S. Wu, L.Y. Ouyang, C.T. Yang, An optimal replenishment policy for noninstantaneous deteriorating items with stock dependent demand and partial backlogging. Int. J. Prod. Econ. 101, 369–386 (2006)

Chapter 5

A Two-Stage Fuzzy DEA Using Triangular Fuzzy Numbers—An Application to Study the Efficiency of Indian Iron and Steel Industries Mariappan Perumal, M. Umaselvi, M. Maragatham, and D. Surjith Jiji Abstract The researcher uses triangular fuzzy numbers to estimate the effectiveness of the iron and steel industries in India using a two-step analysis of the data envelope. The benchmarking was done with the previous study called “Iron and Steel Industries Efficiency in India: A Two-Stage Fuzzy DEA Approach Using Trapezoidal Fuzzy Numbers”. The main methodology suggests changing the trapezoidal fuzzy numbers from the previous study with triangular fuzzy numbers. The result suggests that the choice of triangular fuzzy numbers looks best.

5.1 Introduction Data Envelope Analysis (DEA) was designed to measure performance. This is used to determine the effectiveness of a group of enterprises, which are using similar type of input and output variables. Reference [3] became the founder of the DEA. The literature in [1] developed a current sequence of discussions on this topic.

5.1.1 DMUs This approach is used to determine the extent to which a DMU uses its resources to optimally [1]. The efficiency gains calculated using the DEA are related to different DMUs (or DMU, the highest performance score is considered Table 5.1). M. Perumal (B) Department of Management Studies, St. Joseph’s Institute of Management, Tiruchirappalli, Tamil Nadu 620002, India e-mail: [email protected] M. Umaselvi Faculty of Business Management, Majan University College, Musat, Oman M. Maragatham · D. Surjith Jiji Department of Mathematics, Periyar EVR College (Autonomous), Kajamalai Colony, Tiruchirappalli, Tamil Nadu 620023, India © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Mustapha et al. (eds.), Proceedings of the 8th International Conference on the Applications of Science and Mathematics, Springer Proceedings in Physics 294, https://doi.org/10.1007/978-981-99-2850-7_5

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Table 5.1 Input and output variables considered in this study Productivity stage Marketability stage Input variables Output variables Input variables Output variables Property, plant and equipment Inventories and maintenance Raw materials Stores and spares Reserves and surplus Employee salaries

FG ST

FG ST

Sales turnover Share holder equity Earnings per share Total revenue

5.1.2 Two State DEA Fare and Grosskopf [2] proposed a model in which each industry under study is treated as a sub-system network. There are a variety of strategies that might be employed in efficiency evaluation within the framework of DEA. In recent years, a considerable amount of research has focused on the DEA in two phases as part of the development of the DEA network. The Stage 1 and Stage 2 performance measures were developed using a special template. The models to be proposed be of two types one is open and the other closed. Two-stage Closed DEA System Model: This model considers the stage one output as the input of the stage two. Open type DEA with 2-stages: In this type, stage 2 has new inputs in addition to the intermediate variables.

5.2 Methodology 5.2.1 Data Collection Data collected from the official websites of the company for the years 2017 to 2020.

5.2.2 Selection of Input and Output Variables Table 5.1 provides the information regarding the input and output variables of different stages. Tangible capital assets include land, buildings, facilities and machines, office equipment and vehicles where intangible capital assets include software.

5 A Two-Stage Fuzzy DEA Using Triangular Fuzzy …

43

Fig. 5.1 Fuzzy inference system

5.2.3 Mathematical Modeling Fuzzy Inference System The combination of the rule base and the database is nothing but the knowledge base. In the literature, several forms of FIS have been proposed. It is due to changes in the subsequent part’s specification and the defuzzification schemes (Fig. 5.1). The Fuzzy DEA Principles In real life it is obvious to see that the values collected through the observation mode won’t be accurate. Utilization of inaccurate data will lead to the otherwise. In the current scenario this models have been created for these kind of data. Fuzzy Fractional DEA Program Fuzzy Constant Returns to Scale Model (F-CRS): Stage 1: The general model is constructed to maximize the efficiency of the qth DMU v˜ jq — jth fuzzy output value of the qth DMU of stage 1 y jq — jth output variable of the qth DMU of stage 1 u˜ iq —ith fuzzy input value of the qth DMU of stage 1 x jq —ith input variable of the qth DMU of stage 1 E˜ q —Efficiency of the qth DMU of stage 1. m j=1 Max E˜ q = s i=1

subject to the constraints

m j=1

v˜ jq y jq

i=1

u˜ iq x jq

s

v˜ jq y jq u˜ iq x jq

(5.1)

≤1

v jq , y jq , u˜ jq , x˜ jq ≥ 0 for all i = 1, 2, . . . , s; j = 1, 2, . . . , m; q = 1, 2, . . . , n.

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Stage 2: F-DEA [F-CRS] model to maximize the efficiency of the qth DMU: w˜ jq — jth fuzzy output value of the qth DMU of stage 2 y jq — jth output variable of the qth DMU of stage 2 v˜iq —ith fuzzy input value of the qth DMU of stage 2 x jq —ith input variable of the qth DMU of stage 2 E˜ q —Efficiency of the qth DMU of stage 2. m j=1 Max E˜ q = s

w˜ jq y jq

˜iq x jq i=1 v

subject to the constraints

m j=1

s

w˜ jq y jq

˜iq x jq i=1 v

(5.2)

≤1

w˜ jq , y jq , v˜iq , xiq ≥ 0 for all i = 1, 2, . . . , s; j = 1, 2, . . . , m; q = 1, 2, . . . , n. Fuzzy-VRS Stage 1: F-DEA [F-CRS] model to maximize the efficiency of the qth DMU: Min θm Subject to the Constraints Y˜ λ ≥ Y˜m ; N 

X˜ λ ≤ θ X˜ m

λn = 1; λ ≥ 0; θm free variable

n=1

Stage 2: Min θm Subject to the Constraints X˜ λ ≤ X˜ m ; N  n=1

Triangular Fuzzy Number

Z˜ λ ≥ θ Z˜ m

λn = 1; λ ≥ 0; θm free variable

5 A Two-Stage Fuzzy DEA Using Triangular Fuzzy …

45

It is represented by A, where A = (a1 , a2 , a3 ), ai ∈ R, ⎧ x−a1 ⎨ a2 −a1 a1 ≤ x ≤ a2 −x a2 ≤ x ≤ a3 μ A = aa33−a 2 ⎩ 0 otherwise

(5.3)

Defuzzification A technique that derives net values from one or more loose numbers is necessary because technical procedures require clear control actions. The procedure of identifying a unique number from the output of an aggregated fuzzy set is known as defuzzification. It helps in transforming the fuzzy to crisp mode. It carried out using a decision-making algorithm that selects the best net worth of an unclear set. GMIR Due to Hseigh the GMIR can be represented as the generalized fuzzy number A = (a1 , a2 , a3 , a4 : w), with level h is given by h[L −1 (h) + R −1 (h)] . 2 Hence R(A) is defined as,  h  L −1 (h)+R −1 (h) R(A) =

0

w 0

2

dh

h dh

where h ∈ (0, w), and 0 < w ≤ 1. If A = (a1 , a2 , a3 ) is a trapezoidal fuzzy number. According to Chen and Hsieh the defuzzified value R(A) =

a1 + 2a2 + a3 4

(5.4)

Here Graded Mean Integration representation approach is used for defuzzification process.

5.3 Results and Discussion 5.3.1 Stage 1: F-CRS Table 5.2 shows the F-DEA’s performance rating with respect to technical effectiveness [return to fuzzy variable scale] in the F-VRS model. For the financial years 2017–2020, all the industries obtained the highest efficiency score among the selected

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Table 5.2 Efficiency results of stage-I based on F-CRS, F-VRS and overall Name of the F-CRS F-VRS industry Efficiency Defuzzified Efficiency Defuzzified score score score score ESSAR JSW JINDAL RINL SAIL SURYA TATA TATA BSL TII UGSL VISA

(1, 1, 1) (0.451, 1, 1) (1, 1, 1) (1, 1, 1) (1, 1, 1) (1, 1, 1) (1, 1, 1) (1, 1, 1) (1, 1, 1) (0.007, 0.045) (1, 1, 0.601)

1 0.86275 1 1 1 1 1 1 1 0.022 0.90025

(1, 1, 1) (1, 1, 1) (1, 1, 1) (1, 1, 1) (1, 1, 1) (1, 1, 1) (1, 1, 1) (1, 1, 1) (1, 1, 1) (1, 1, 1) (1, 1, 1)

1 1 1 1 1 1 1 1 1 1 1

Mean score

1 0.931375 1 1 1 1 1 1 1 0.511 0.950125

industries in productivity. There are eight iron and steel industries that have a reliability rating of 1 and are the most efficient of all the iron and steel industries examined. The iron and steel industries’ mean efficiency in stage 1 is shown in Table 5.1. Table 5.2 shows the F-DEA’s performance rating with respect to technical effectiveness [return to fuzzy variable scale] in the F-VRS model. For the financial years 2017–2020, all the industries obtained the highest efficiency score among the selected industries in productivity. There are eight iron and steel industries that have a reliability rating of 1 and are the most efficient of all the iron and steel industries examined. The iron and steel industries’ mean efficiency in stage 1 is shown in Table 5.1.

5.3.2 Stage 2: F-VRS Model F-VRS model based on Table 5.3 communicates that six industries are doing extremely good in marketability aspect. On the whole only one Iron and Steel Industry signs well.

5.4 Conclusion In addition, the performance of industries was evaluated in terms of productivity and marketability. The results reveal that in terms of production, ESSAR, JINDAL, RINL, SAIL, SURYA, TATA, TATA BSL, and TII are doing extremely good, UGSL

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Table 5.3 Efficiency results of stage-II based on F-CRS, F-VRS and overall Name of the F-CRS F-VRS industry Efficiency Defuzzified Efficiency Defuzzified score score score score ESSAR JSW JINDAL RINL SAIL SURYA TATA TATA BSL TII UGSL VISA

(0.012, 1, 1) (0.013, 1, 1) (0.011, 0.127, 0.341) (0.094, 0.069, 0.049) (0.016, 0.011, 0.061) (0.003, 0.114, 0.235) (0.022, 1, 1) (0.099, 1, 1) (1, 0.092, 0.15) (1, 1, 1) (0.009, 0.037, 0.473)

0.753 0.75325 0.1515

Mean score

1 1 0.88025

0.8765 0.876625 0.515875

0.60875

0.3395

0.02475

(1, 1, 1) (1, 1, 1) (1, 0.99, 0.541) (1, 0.517, 0.401) (1, 1, 1)

1

0.512375

0.1165

(0.432, 1, 1)

0.858

0.48725

0.7555 0.77475 0.3335

(1, 1, 1) (1, 1, 1) (1, 1, 0.165)

1 1 0.79125

0.87775 0.887375 0.562375

1 0.139

(1, 1, 1) 1 (0.808, 0.672, 0.73675 0.795)

1 0.437875

0.07025

doing good in terms of marketability. The comparative result between the previous study and the current study shows that triangular fuzziness improves the efficiency score of the selected industries.

References 1. A. Charnes, W.W. Cooper, E. Rhodes, Measuring the efficiency of decision-making units. Eur. J. Oper. Res. 2, 429–444 (1978) 2. R. Fare, S. Grosskopf, Productivity and intermediate products: a frontier approach. Econ. Lett. 50(1), 65–70 (1996) 3. M.J. Farrel, The measurement of productivity efficiency. J. Roy. Stat. Soc. (A) 120, 253–281 (1957)

Chapter 6

Life Insurance Pricing and Reserving—A Fuzzy Approach K. Kapil Raj, S. Srinivasan, Mariappan Perumal, and C. D. Nandakumar

Abstract In this paper we used a fuzzy technique to estimate the premium and reserve for a term assurance contract which pays benefit contingent on the death of a person provided death must happen in the given time. The deterministic interest rate is assumed as the trapezoidal fuzzy number in the equations of value method to overcome the uncertainty risk associated with it. The resulting fuzzy premiums and reserves are then defoliated using the Graded Mean Integration Representation Method (GMIR). Finally, numerical illustrations are provided to the proposed method and the resulting premiums are compared for different benefits.

6.1 Introduction The premiums are the source of income to any life insurance company that was made by policyholders who is known as insured. The cash outflow of a company is the compensation paid to the subscriber of the policy by sharing their risk. The use of the Equations of Value method is to compute premiums, requires an assumption called basis concerning the anticipated future experiences such as uncertain mortality experiences, investment returns, upcoming expenses, bonus charges. Fuzzy numbers play an imperative role in choice making in optimization and also in forecasting. Normally, the assumptions or basis will not be the best ideas since the basis utilized for the equation of value method for a life insurance contract are uncertain.

K. Kapil Raj · S. Srinivasan · C. D. Nandakumar Department of Mathematics and Actuarial Science, B.S. Abdur Rahman Crescent Institute of Science and Technology, Vandalur, Chennai, Tamil Nadu 600048, India e-mail: [email protected] S. Srinivasan e-mail: [email protected] M. Perumal (B) Department of Management Studies, St. Joseph’s Institute of Management, Tiruchirappalli, Tamil Nadu 620002, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Mustapha et al. (eds.), Proceedings of the 8th International Conference on the Applications of Science and Mathematics, Springer Proceedings in Physics 294, https://doi.org/10.1007/978-981-99-2850-7_6

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The assumptions will only be more thoughtful idea than the best estimates say that if 8% pa is the required rate of restoration on the invested premiums then the computation of premium would be the assumption of 6% pa. As we are assuming that we make less interest than we really supposed to get, then we would need to be presumed if the anticipated rate of 8% were actually earned. Insurance policies whose elements with larger risk of dues are charged with higher rate of premium, i.e. level of risk that governs the insurance premium. The higher premiums are influenced by the lower percentage of interest than that is calculated using the higher rate of interest. Lemaire [9] aims to define the elementary perceptions of fuzzy theory in insurance context by considering a preferred policyholder in the life insurance contract. He also extended the concept of fuzzy numbers to outline insurance premium by illustrating the fuzzy decision making procedures in reinsurance area. Bellman and Zadeh [1] proposed a general theory of decision making in a fuzzy environment. Buckley [15] used to find fuzzy contemporary value and impending value of fuzzy cash amounts using fuzzy interest rates across n years where n may be crisp or a fuzzy number. Young [17] described the effectiveness of using fuzzy logic in insurance pricing decisions. Yahoubov and Haberman [16] reviewed fuzzy concepts and techniques in the actuarial environment for various fields which includes financial mathematics, asset/liability considerations, risk classifications and underwriting in both life and non-life products. Shapiro [13] has overviewed various insurance applications of fuzzy logic which includes categorization, underwriting, expected liabilities, fuzzy future and present values, valuing, asset sharing, cashflows and financings and also verified that fuzzy logic has been positively employed in insurance. Derrig and Ostaszewki [7] presents the purpose of fuzzy sets in areas such as underwriting, peril sorting, interest rates, valuing, assessment of premiums and tariffs. Shapiro [12] reviewed the possible applications of fuzzy logic in insurance and how they are employed in the field of insurance business to tackle the fluctuations of uncertain random variables. de Andrés-Sánchez and González-Vila Puchades [6] modelled fuzzy numbers to quantify insurance interest and discount rates and stochastic approach for mortality behaviour. They conquered not only the expected charge of the policy but also it channels the mortality risk which was useful equally in terms of attaining surplus from mortality deviations. Panjer and Bellhouse [11] studied the stochastic properties of various uncertain insurance components like interest rate, mortality and examined several empirically supported stochastic models to assess the risk associated with the fluctuations of uncertain factors that are useful in setting the reserves and premium margins to the insurance company. Cummins and Derrig [4, 5] analysed Fuzzy Set Theory (FST) as an alternative tool to incorporate vagueness and subjective nature of various parameters that affects the pricing decision. This study revealed that FST can lead into significantly different decisions than conventional approach. In this paper, as said above FST as an alternative approach to the stochastic methods for modelling uncertainty, we used the idea of fuzzy logic assumption to solve the uncertain financial

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mathematics problems in terms of calculating premiums and reserves for a traditional life insurance contract using the traditional deterministic equations of value method with interest rate uncertainty as trapezoidal fuzzy numbers.

6.2 Methods 6.2.1 Fuzzy Approach Let us consider X remains a non-empty set. Then a fuzzy set A in X is depicted by a membership function as µ A : X → [0, 1] (i.e.) ⎧ ⎪ ⎨1, if x ∈ X µ A (x) = 0, if x ∈ X ⎪ ⎩ (0, 1), if x is partly in X various types of membership function distributions, viz. Triangular, Trapezoidal, Pentagonal, Hexagonal, Heptagonal, Gaussian, L − R type fuzzy membership function, S + and S − membership, Intuitionistic membership function. In this paper we used trapezoidal membership as it was most widely used membership function due to its accuracy.

6.2.2 Trapezoidal Fuzzy Membership Function A fuzzy number which is represented by four points such that A = (a1 , a2 , a3 , a4 ) where a1 , a2 , a3 , a4 ∈ R is trapezoidal fuzzy number with its membership function represented as µ A (x) ⎧ 0, x ≤ a1 ⎪ ⎪ ⎪ 1) ⎪ (a(x−a , a 1 < x ≤ a2 ⎨ 2 −a1 ) a2 < x ≤ a3 µ A (x) = 1, ⎪ (a4 −x) ⎪ ⎪ , a < x ≤ a4 ⎪ ⎩ (a4 −a3 ) 3 0, x ≥ a4 If A = (a1 , a2 , a3 , a4 ) is a trapezoidal fuzzy number, then the GMIR method to Defuzzify the number into the crisp values is given by R(A) =

a1 + 2a2 + 2a3 + a4 . 6

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6.2.3 General Form of Fuzzy Premium and Reserve Equations Case I: General Form of Fuzzy Net Premium Equation Let us consider the interest rate for the term assurance contract for next n years whose sum assured is S A with initial expense e and renewable expense g, which is due at the end of year of expiry of an x-year-old life as trapezoidal fuzzy number a1 , a2 , a3 , a4 which is around i% then the fuzzy interest rate has its membership function as, ⎧ 0, y ≤ a1 ⎪ ⎪ ⎪ (y−a1 ) , a < y ≤ a ⎪ 2 ⎨ (a2 −a1 ) 1 a2 < y ≤ a3 µ(1+i) (y) = 1, ⎪ (a4 −y) ⎪ ⎪ , a < y ≤ a4 ⎪ ⎩ (a4 −a3 ) 3 0, y ≥ a4 The inverse function for the above equation is given by,  µ(1+i)−1 =

(a2 − a1 )z + a1 a4 − (a4 − a3 )z

where z ∈ [0, 1]

As we know that by the system of the equations of value, the expected present value of pay-in is equal to the expected present value of outstrip. The present value equation for the income will be given by the product of the anticipated premium and the present value of it and the present value equation of the outgo will be same like the product of the guaranteed benefit and the present value of it. The general premium equation for the n year temporary assurance bond with sum assured S A to be paid at the end of year of demise of a life aged x will be, P ∗ a¨ x:n = S A ∗ A1x:n + e + g

(6.1)

The above equation after using interest rate as fuzzy number will become as P ∗ ( f a¨ x:n ) = S A ∗ ( f A1x:n ) + e + g

l x+1 l x+2 ((a2 − a1 )z + a1 )−1 + ((a2 − a1 )z + a1 )−2 lx lx l x+3 l x+(n−1) + ((a2 − a1 )z + a1 )−3 + · · · + ((a2 − a1 )z + a1 )−(n−1) lx lx l x − l x+1 l x+1 − l x+2 = ((a2 − a1 )z + a1 )−1 + ((a2 − a1 )z + a1 )−2 lx lx l x+2 − l x+3 + ((a2 − a1 )z + a1 )−3 + · · · lx

f a¨ x:n = 1 +

f A1x:n

(6.2)

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l x+(n−1) − l x+(n−1) ((a2 − a1 )z + a1 )−n lx l x+1 l x+2 f a¨ x:n = 1 + (a4 − (a4 − a3 )z)−1 + (a4 − (a4 − a3 )z)−2 lx lx l x+3 l x+(n−1) + (a4 − (a4 − a3 )z)−3 + · · · + (a4 − (a4 − a3 )z)−(n−1) lx lx l x − l x+1 l x+1 − l x+2 f A1x:n = (a4 − (a4 − a3 )z)−1 + (a4 − (a4 − a3 )z)−2 lx lx l x+2 − l x+3 + (a4 − (a4 − a3 )z)−3 + · · · lx l x+(n−1) − l x+(n−1) + (a4 − (a4 − a3 )z)−n lx +

where z ∈ [0, 1], a¨ x:n =

n−1  j=0

Px ∗ v j and A1x:n =

n−1 

v k+1 ∗ k | qx

k=0

e = 0 and g = 0 since net premium contract ignores expenses. Case II: General form of Fuzzy Gross Premium Reserve Equation Let us assume the same set of assumption where the interest rate for the term assurance. Contract for next n years whose sum assured is S A with initial expense e and renewal expense g, which is billed at the year-end of the decease of an x-year-old life as trapezoidal fuzzy number a1 , a2 , a3 , a4 which is around i% then the fuzzy interest rate for the gross premium prospective reserve calculated at the termination of tth year (just in advance to the (t + 1)th premium paid) hence, Gross premium equation for the term assurance contract will be, P ∗ a¨ x:n = S A ∗ A1x:n + e + (g ∗ (a¨ x:n − 1))

(6.3)

The above equation after using interest rate as fuzzy number will become as follows: (6.4) P ∗ f a¨ x:n = S A ∗ f A1x:n + e + (g ∗ ( f a¨ x:n − 1)) Prospective reserve at expiration of tth year = EPV of future benefits + (EPV of future expenses − EPV of future premiums) tV

pro

= S A ∗ A1x+t:n−t + g(a¨ x+t:n−t ) − (P ∗ a¨ x+t:n−t )

(6.5)

The above reserve equation after using interest rate as fuzzy number will become as follows:

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pro

= S A ∗ f A1x+t:n−t + g( f a¨ x+t:n−t ) − (P ∗ f a¨ x+t:n−t )

(6.6)

here e = 0 because initial expenses will not be carried over for tth year, hence: f a¨ x+t:n−t = 1 +

l x+t+1 l x+t+2 ((a2 − a1 )z + a1 )−1 + ((a2 − a1 )z + a1 )−2 l x+t l x+t

l x+t+3 ((a2 − a1 )z + a1 )−3 + · · · l x+t l x+t+(n−t−1) + ((a2 − a1 )z + a1 )−(n−t−1) l x+t l x+t − l x+t+1 l x+t+1 − l x+t+2 = ((a2 − a1 )z + a1 )−1 + l x+t l x+t − l l x+t+2 x+t+3 × ((a2 − a1 )z + a1 )−2 + ((a2 − a1 )z + a1 )−3 l x+t l x+t+(n=t−1) − l x+t+(n−1t−) + ··· + ((a2 − a1 )z + a1 )−(n−t) lx l x+t+1 l x+t+2 =1+ (a4 − (a4 − a3 )z)−1 + (a4 − (a4 − a3 )z)−2 l x+t l x+t l x+t+3 + (a4 − (a4 − a3 )z)−3 + · · · l x+t l x+t+(n−t−1) + (a4 − (a4 − a3 )z)−(n−t−1) l x+t l x+t − l x+t+1 l x+t+1 − l x+t+2 = (a4 − (a4 − a3 )z)−1 + l x+t l x+t − l l x+t+2 x+t+3 × (a4 − (a4 − a3 )z)−2 + (a4 − (a4 − a3 )z)−3 l x+t l x+t+(n−t−1) − l x+t+n−t + ··· + (a4 − (a4 − a3 )z)−(n−t) lx +

f A1x+t:n−t

f a¨ x+t:n−t

f A1x+t:n−t

where z ∈ [0, 1], a¨ x+t:n−t =

n−t−1 

Px+t v j and A1x+t:n−t =

j=0

n−t−1 

v k+1 k | qx+t

k=0

6.3 Results and Discussion We have obtained the comparative deterministic and fuzzy Net premium and fuzzy gross premium rates from Tables 6.1 and 6.2 respectively, which are not similar with

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Table 6.1 Comparison of deterministic and fuzzy net premiums Sl. No. Sum assured Deterministic Fuzzy net Difference net premium premium 1 2 3 4 5

500,000 510,000 520,000 530,000 540,000

330.07 336.68 343.28 349.88 356.48

330.59 337.20 343.81 350.42 357.03

0.51 0.52 0.53 0.54 0.55

Table 6.2 Comparison of deterministic and fuzzy gross premiums Sl. No. Sum assured Deterministic Fuzzy net Difference net premium premium 1 2 3 4 5

20,000 22,000 24,000 26,000 28,000

141.47 144.21 146.95 149.70 152.43

141.66 144.39 147.12 149.86 152.59

0.19 0.18 0.17 0.16 0.16

% difference 0.155 0.154 0.154 0.154 0.154

% difference 0.134 0.125 0.116 0.107 0.105

differences that designates the interest rate uncertainty. In Fig. 6.1, the results of the fuzzy approach of assuming interest for the premium cash flows yield us on average of 0.15% increase in premium than the conventional cashflows that are assumed on the prudent basis for the term assurance net premium contract for five different benefits compensated at the termination of the year of expiry of life. Similarly, from Fig. 6.2, the results of fuzzy office premium (gross premium) cashflows yield us on average of 0.12% increase in premium than the traditional deterministic approach for five different benefits paid out to the policy holders. Similarly, the gross premium reserve equation also holds good on comparing deterministic and fuzzy interest rates.

6.4 Conclusion In this paper we have derived the general fuzzy premium and reserve equations for the term assurance contract whose aids are remunerated by the end of the year of death of life. Numerical illustrations take place based on the assumption to the set of new equations. The use of deterministic basis for the uncertainty is better replaced with fuzzy logic assumption which yield us result with approximately positive increment for different set of benefits. From this we have concluded that the use of fuzzy intervals in estimating the uncertain parameters in financial mathematics of insurance problems are conceptually simple and gives us the greater flexibility in calculation. This study can be further extended by applying the fuzzy logic technique to estimate

56

Fig. 6.1 Comparison of deterministic net premium and fuzzy net premiums

Fig. 6.2 Comparison of deterministic and fuzzy gross premiums

K. Kapil Raj et al.

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the premiums and reserves by considering the interest rate as trapezoidal fuzzy number, fuzzy survival probability for the same or other different kind of contracts and also to the joint life policies which involves two lives.

Appendix 3.1 (a) Traditional method with crisp interest rate for net premium contract (determinist net premium) Here let us assume the 10-year term assurance contract with Sum Assured (S A ) of Rs. 500,000 for a 30-year-old person under the basis of ultimate mortality (AM92) with 4% interest per annum to calculate net premium ignoring expenses. From (6.1) Premium =

500,000 ∗ A130:10 a¨ 30:10

4%pa

Premium = Rs.330.07 3.1 (b) Traditional method with interest rate as fuzzy number for net premium contract (fuzzy net premium) Here let us assume the 10-year term assurance contract with Sum Assured (SA) of Rs. 500,000 for a 30-year-old person under the basis of ultimate mortality (AM92) with interest rate as the trapezoidal fuzzy number which is around 4%, so that the fuzzy interest rate has its membership function as ⎧ ⎪ ⎪ 0, ⎪ ⎪ ⎨ 250y − 258.25, µ(1+i) (y) = 1, ⎪ ⎪ 261.25 − 250y, ⎪ ⎪ ⎩ 0,

y ≤ 1.033 1.033 < y ≤ 1.037 1.037 ≤ y ≤ 1.041 1.041 ≤ y ≤ 1.045 y ≥ 1.045

The inverse function for the above expression is given by,  µ(1+i)−1 =

0.004z + 1.033 1.045 − 0.004z where z ∈ [0, 1]

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From (6.2) l30+1 l30+2 (0.004z + 1033)−1 + (0.004z + 1.033)−2 l30 l30 l30+3 l30+9 + (0.004z + 1.033)−3 + · · · + (0.004z + 1.033)−9 l30 l30 l30 − l30+1 l30+1 − l30+2 = (0.004z + 1.033)−1 + (0.004z + 1.033)−2 l30 l30 l30+2 − l30+3 + (0.004z + 1.033)−3 l30 l30+9 − l30+10 + ··· + (0.004z + 1.033)−10 l3 0 l30+1 l30+2 =1+ (1.045 − 0.004z)−1 + (1.045 − 0.004z)−2 l30 l30 l30+3 l30+9 + (1.045 − 0.004z)−3 + · · · + (1.045 − 0.004z)−9 l30 l30 l30 − l30+1 l30+1 − l30+2 = (1.045 − 0.004z)−1 + (1.045 − 0.004z)−2 l30 l30 l30+2 − l30+3 + (1.045 − 0.004z)−3 l30 l30+9 − l30+10 + ··· + (1.045 − 0.004z)−10 l3 0

f a¨ 30:10 = 1 +

f A130:10

f a¨ 30:10

f A130:10

so therefore, the fuzzy net premium follows 500,000∗ f A1

30:10 at interest rate of (1 + i) = (1.033, 1.037, 1.041, 1.045). P= f a¨ 30:10 Hence the fuzzy net premium for 10-year term contract will be (333.18, 331.44, 329.72, 328.01). By using the GMIR method of defuzzification, the above results are Defuzzified as 333.18 + 2(331.44) + 2(329.72) + 328.01 = Rs.330.59 R(1 + i) = 6

3.1.1 (a) Traditional method with crisp interest rate for gross premium contract (deterministic gross premium) Here we have considered the 10-year term assurance contract with Sum Assured (SA) of Rs. 20,000 for a 40-year-old person with e as Rs. 425 and g as Rs. 72. Gross Premium and the Reserve at termination of (say) 5th year (in advance to the 6th premium) under the basis of ultimate mortality (AM92) with crisp 4% interest rate per annum from (6.3)

6 Life Insurance Pricing and Reserving …

P=

59

20,000 ∗ A140:10 + 425 + (72 ∗ (a¨ 40:10 − 1)) a¨ 40:10

P = Rs.141.47 Office Premium prospective reserve based on (5) is agreed by V pr o = 20,000 ∗ A145:5 + 72 ∗ (a¨ 45:5 ) − P ∗ a¨ 45:5

(6.7)

Reserve at the termination of 5th year is Rs. − 294.36. The negative reserve indicates that the company is operating in such a way that the policyholder who will pay more in the future than the benefit they could expect to receive. 3.1.1 (b) Traditional method with interest rate as fuzzy number for a gross premium and reserve (fuzzy gross premium) Here we have considered the 10-year term assurance contract with Sum Assured (SA) of Rs. 20,000 for a 40-year-old person with e as Rs.425 and g as Rs. 72. Gross Premium and the Reserve at termination of (say) 5th year (in advance to the 6th premium) under the basis of ultimate mortality (AM92) with interest rate as fuzzy number which is around 4% per annum and that follows the trapezoidal fuzzy membership function as follows ⎧ 0, ⎪ ⎪ ⎪ ⎪ ⎨ 250y − 258.75, µ(1+i) (y) = 1, ⎪ ⎪ 262 − 250y, ⎪ ⎪ ⎩ 0,

y ≤ 1.03 1.035 < y ≤ 1.039 1.039 ≤ y ≤ 1.044 1.044 ≤ y ≤ 1.048 y ≥ 1.048

The inverse function for the above expression is given by,  µ(1+i)−1 =

0.004z + 1.035 1.048 − 0.004z

where z ∈ [0, 1]

From (6.4) l40+1 l40+2 (0.004z + 1035)−1 + (0.004z + 1.035)−2 l40 l40 l40+3 l40+9 + (0.004z + 1.035)−3 + · · · + (0.004z + 1.035)−9 l40 l40

f a¨ 40:10 = 1 +

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f A140:10 + 425 + (72 ∗ ( f a¨ 40:10 − 1)) = (0.004z + 1035)−1

l40 − l40+1 l40 l40+2 − l40+3 + ··· l40

l40+1 − l40+2 + (0.004z + 1.035)−3 l40 l40+9 − l40+10 + (0.004z + 1.035)−10 + 425 l40  l40+1 l40+2 + 72 1 + (0.004z + 1035)−1 + (0.004z + 1.035)−2 l40 l40

 l40+3 l40+9 −3 −9 −1 + (0.004z + 1.035) + · · · + (0.004z + 1.035) l40 l40

+ (0.004z + 1.035)−2

l40+1 l40+2 (1.048 − 0.004z)−1 + (1.048 − 0.004z)−2 l40 l40 l40+3 l40+9 + (1.048 − 0.004z)−3 + · · · + (1.048 − 0.004z)−9 l40 l40

f a¨ 40:10 = 1 +

l40 − l40+1 l40 l40+2 − l40+3 l40

f A140:10 + 425 + (72 ∗ ( f a¨ 40:10 − 1)) = (1.048 − 0.004z)−1

l40+1 − l40+2 + (1.048 − 0.004z)−3 l40 l40+9 − l40+10 + · · · + (1.048 − 0.004z)−10 + 425 l40  l40+1 l40+2 + 72 1 + (1.048 − 0.004z)−1 + (1.048 − 0.004z)−2 l40 l40

 l40+3 l40+9 + (1.048 − 0.004z)−3 + · · · + (1.048 − 0.004z)−9 − 1 l40 l40 + (1.048 − 0.004z)−2

so therefore, the Fuzzy gross premium for this contract will be, P=

20,000 ∗ f A140:10 + 425 + (72 ∗ ( f a¨ 40:10 − 1)) f a¨ 40:10

at the interest rate of (1 + i) = (1.035, 1.039, 1.044, 1.048). Hence the fuzzy gross premium for 10-year term contract will be (Rs. 140.87, Rs. 141.35, Rs. 141.96, Rs. 142.45). By using the GMIR method of defuzzification, the above results are Defuzzified as R(1 + i) =

140.87 + 2(141.35) + 2(141.96) + 142.45 = Rs.141.66. 6

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From (6.6) fuzzy Gross Premium prospective reserve equation is given by, l46 l47 (0.004z + 1035)−1 + (0.004z + 1.035)−2 l45 l45 l48 l49 + (0.004z + 1.035)−3 + (0.004z + 1.035)−4 l45 l45

f a¨ 45:5 = 1 +

l − l46 f A145:5 + 72 ∗ ( f a¨ 45:5 ) = (0.004z + 1035)−1 45 + (0.004z + 1.035)−2 l45 l47 − l48 l49 − l50 l46 − l47 × + (0.004z + 1.035)−3 + · · · + (0.004z + 1.035)−10 l45 l45 l45  l46 l 47 + 72 1 + (0.004z + 1035)−1 + (0.004z + 1035)−2 l45 l45  l48 l49 + (0.004z + 1035)−3 + (0.004z + 1035)−4 l45 l45

l46 l47 (1.048 − 0.004z)−1 + (1.048 − 0.004z)−2 l45 l45 l48 l49 + (1.048 − 0.004z)−3 + (1.048 − 0.004z)−4 l45 l45

f a¨ 45:5 = 1 +

l − l46 f A145:5 + 72 ∗ ( f a¨ 45:5 ) = (1.048 − 0.004z)−1 45 + (1.048 − 0.004z)−2 l45 l47 − l48 l49 − l50 l46 − l47 × + (1.048 − 0.004z)−3 + · · · + (1.048 − 0.004z)−10 l45 l45 l45  l46 l 47 + 72 1 + (1.048 − 0.004z)−1 + (1.048 − 0.004z)−2 l45 l45  l48 l49 + (1.048 − 0.004z)−3 + (1.048 − 0.004z)−4 l45 l45

Hence the fuzzy office premium reserve by the finish of 5th time period at the interest rate of (1 + i) = (1.035, 1.039, 1.044, 1.048) is V pro = 20,000 ∗ f A145:5 + (72 ∗ ( f a¨ 45:5 )) − (P ∗ ( f a¨ 45:5 ))

(6.8)

The resulting fuzzy reserves are as follows Rs. − 293.07, Rs. − 294.10, Rs. − 295.41, Rs. − 296.45.

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By using the GMIR method of defuzzification, the above results are Defuzzified as R(1 + i) =

−293.07 + 2(−294.10) + 2(−295.41) + 296.45 = Rs. − 294.7. 6

References 1. R. Bellman, L.A. Zadeh, Decision making in a fuzzy environment. Manag. Sci. 17, BI41–BI64 (1970) 2. S.-H. Chen, C.H. Hsieh, Graded mean integration representation (GMIR) of generalised fuzzy number, in Proceeding of Conference of Taiwan Fuzzy System Association, Taiwan (2000) 3. S.-H. Chen, C.H. Hsieh, Graded mean integration representation (GMIR) of generalised fuzzy number. J. Chunese Fuzzy Syst. Assoc. Taiwan 5(2), 1–7 (2000) 4. J.D. Cummins, R.A. Derrig, Fuzzy financial pricing of property—liability insurance. North Am. Actuar. J. 1, 21–40 (1993) 5. J.D. Cummins, R.A. Derrig, Fuzzy trends in property—liability insurance claim costs. J. Risk Insur. 60, 429–465 (1993) 6. J. de Andrés-Sánchez, L. González-Vila Puchades, Using fuzzy random variables in life annuities. Fuzzy Sets Syst. (2012) 7. R.A. Derrig, K.M. Ostaszewki, Fuzzy Sets Methodologies in Actuarial Science, vol. 2 (Wiley, Chichester, 2004), pp.745–750 8. M.E. Jebaseeli, D.P. Dhayabaran, Optimal solution to fully fuzzy time cost trade off problem. Int. J. Appl. Math. Stat. Sci. 2(2), 27–34 (2013) 9. J. Lemaire, Fuzzy insurance. ASTIN Bull. 20, 33–55 (1990) 10. K.M. Ostaszewski, An Investigation into Possible Applications of Fuzzy Set Methods in Actuarial Science (Society of Actuaries, 1993) 11. H.H. Panjer, D.R. Bellhouse, Stochastic modelling of interest rates with applications to life contingencies. J. Risk Insur. 47, 91–110 (1980) 12. R.A. Shapiro, Fuzzy logic in insurance. Insur.: Math. Econ. 35, 399–424 (2004) 13. A.F. Shapiro, An Overview of Insurance Uses of Fuzzy Logic. ISBN: 978-3-540-72820-7 14. The Actuarial Education Company, IFOA-CM1, Actuarial Mathematics (2019) 15. The fuzzy mathematics of finance. Fuzzy Sets Syst. 21, 257–273 (1987) 16. Y.H. Yahkoubov, S. Haberman, Review of Actuarial Applications of Fuzzy Set Theory (1998) 17. V.R. Young, Insurance rate changing: a fuzzy logic approach. J. Risk Insur. 63, 461–484 (1996) 18. L.A. Zadeh, Fuzzy sets. Inf. Control 8, 338–353 (1965) 19. R. Zhao, R. Govind, Defuzzification of fuzzy intervals. Fuzzy Sets Syst. 43, 45–55 (1991) 20. H.J. Zimmerman, Fuzzy Set Theory and its Applications, 2nd edn. (Kluwer, Academic Publishers, Boston, Massachusetts, 1991)

Chapter 7

Fixed-Point Approach on Eˇ Fuzzy-Metric Space with JCLR Property by Implication C. Vijayalakshmi , P. Muruganantham , and A. Nagoor Gani

Abstract We exhibit a fixed-point approach on  E-Fuzzy-metric Space aimed at weak compatible mappings (wc mapping) providing Joint Common Limit in the Range (JCLR)-property by implication. We also provide some concrete examples of our key findings. We exhibit a fixed-point theorem for six finite families of selfmappings, which can be used to prove other results. Any finite number of mappings can be used to prove common fixed-point theorems. Our outcomes improve and there are numerous existing results in the literature that can be extended.

7.1 Introduction Zadeh [1] hosted the basis of fuzzy-set premise in 1965. The idea of consistent and explicit of the fixed-point hypotheses to illuminate the progression of a mapping and inclusiveness of mentioned field by Mishra et al. [2]. Kramosil and Michalek [5] hosted the model of a fuzzy-metric, then owned generalised over the probabilistic metric to a fuzzy state. George and Veeramani [3] enhanced the fuzzy-metric hosted by Kramosil and Michalek [5]. Popa [8] specified the implication in the hypothesis of fixed-point in metric. Singh and Jain [6] further prolonged the consequence of  c mapping. Also they [8] on fuzzy-metric, also they weakened the estimation of W introduced new structure of implicit relation in 2005. In 2006, [4] gave certain significances of fixed-point in G-Metric. Imdad and Ali [15] gave some significances of Generalised fuzzy-metric with properties. Popa [8] discussed some fixed-point theorems in fuzzy-metric by implicit relation provide work for CLR property in 2015. Sukanya and Jose [11] and Rani and Kumar [12] offered a generalised fuzzymetric and conferred various possessions of generalised fuzzy-metric and moreover gained the fixed-point proposal in generalised fuzzy-metric. In fixed-point theory, the C. Vijayalakshmi (B) · P. Muruganantham · A. Nagoor Gani Research Department of Mathematics, Jamal Mohamed College (Autonomous) (Affiliated to Bharathidasan University, Tiruchirappalli-24), Tiruchirappalli 620020, Tamilnadu, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Mustapha et al. (eds.), Proceedings of the 8th International Conference on the Applications of Science and Mathematics, Springer Proceedings in Physics 294, https://doi.org/10.1007/978-981-99-2850-7_7

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implication covers many contractive situations that one may verify the discrete proposition in all contractive conditions. Singh and Jain [6] prolonged the conception of semi-compatible mappings in fuzzy-metric to gratify an implication. Jain et al. [13] discussed some fixed-point hypothesis with implication. Vijayalakshmi et al. [16] prolonged Generalised fixed-point amusing implication. Chauhan et al. [7] extended fixed-point theorems for Weak Compatible Mappings in Fuzzy-Metric Spaces by (JCLR) Property in Sukanya and Jose [10]. We discussed the fixed-point approach on E-fuzzy-metric space while retaining JCLR-property via implicit relation in this paper.

7.2 Preliminaries Definition 7.1 Consider X is an erratic set and G : X 3 → [0, ∞), it has the subsequent conditions, (a) (b) (c) (d) (e)

G(x, y, t) = 0 iff x = y = z. 0 < G(x, x, y) for all x, y ∈ X with x = y. G(x, y, z) ≥ G(x, x, y), for all x, y, z ∈ X with y = z. G( p{x, y, z}) = G(x, y, z) (Symmetry) p, a permutation function. G(x, y, z) ≤ G(x, a, a) + G(a, y, z), ∀x, y, z, a ∈ X

Therefore, (X, G) is designate as generalised metric on X . Example 7.1 If X = R and the function G : X 3 × [0, ∞) by G(x, y, z) = |x − y| + |y − z| + |z − x|, then (X, G) is G-metric. Definition 7.2 An ordered tuple (X,  E, ∗) named as  E-fuzzy-metric, ∗ is continual t-norm, X is erratic set,  E is Fuzzy-set on X 3 × (0, ∞) which fulfils the following, ∀x, y, z ∈ X , and t, s > 0. (a) (b) (c) (d) (e)

 E(x, y, z, t) ≤  E(x, x, y, t), for all x, y, z ∈ X with z = y;  E(x, x, y, t) > 0.  E(x, y, z, t) = 1 iff x = y = z.  E( p{x, y, z}, t)( Symmetry), p, a permutation function. E(x, y, z, t) =    y, z, s). E(x, y, z, t + s) ≥  E(x, a, z, t) ∗ E(a,  E(x, y, z, ·) : (0, ∞) → [0, 1] is continuous.

Then  E is designate as generalisation of fuzzy-metric. Example 7.2 Consider X as any unpredictable set and G-metric on X . The continualtnorm a ∗ b = min{a, b} for all a, b ∈ [0, 1], t > 0, Ensure that  E(x, y, z, t) = t . t+G(x,y,z)   Formerly X,  E, ∗ designate as  E-fuzzy-metric. ˘ Lemma 7.1 If (X,  E, ∗) be  E-fuzzy-metric. Then E(x, y, z, t) is increasing related as t, ∀x, y, z ∈ X .

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  Definition 7.3 Define A, T are the functions from (X,  E, ∗) into X,  E, ∗ . The couple {A, T } is designate as compatible, if limn→∞  E (AT xn , T Axn , T Axn , t) = 1, whenever {xn } ∈ X such that limn→∞ Axn = limn→∞ T xn = w for some w ∈ X and for all t > 0.     ˘ ∗ into X, E, ˘ ∗ are said as Definition 7.4 Consider A, T are depicts from X, E, weak compatible , if Ax = T x, implies that AT x = T Ax, for some x ∈ X . ˘ ∗) into (X,  Definition 7.5 Consider A, T are depicts from (X, E, E, ∗). A couple {A, T } is designate as non compatible, if limn→∞  E (AT x n , T Ax n , T Ax n , t) = 1, whenever {xn } ∈ X ensure that limn→∞ Axn = limn→∞ T xn = w for some w ∈ X and t > 0. Definition 7.6 The couple {A, T } of metric (X, G) reveals that to persuade a CLR g-property if ∃ {xn } in X ensure that limn→∞ Axn = limn→∞ T xn = T w for some w ∈ X. Example 7.3 Let (X,  E, ∗) be E-fuzzy-metric, where [0, 5] = X with min t-norm t and  E(x, y, z, t) = t+G(x,y,z) , ∀t > 0 and x, y, z ∈ X , define T x = x + 2, Ax = 2x.   Let {xn } = 2 + n1 ∈ X ensure that limn→∞ Axn = limn→∞ T x = T w, where w = {4} ∈ X . Therefore, {A, T } fulfils the CLR g -property. Definition 7.7 Self-mappings (A, T ), (B, S) and (C, U ) on (X, E, ∗ ) fulfils the Joint Common Limit in the Range (JCLR)-property if ∃ sequences {xn } , {yn } and {z n } in X ensure that, limn→∞ Axn = limn→∞ T xn = limn→∞ Byn = limn→∞ Syn = limn→∞ C z n = limn→∞ U z n = T w = Sw = U w. for some w ∈ X . Remark 7.1 If A = B = C, T = S = U, {xn } = {yn } = {z n }, then limn→∞ Axn = limn→∞ T xn = T w for some w ∈ X .

7.3 Implicit Relations  5 Denote (ψ) be the set of all real continuous ψ : R + → R + , takes the sufficient conditions, (i) For u > 0, v ≥ 0, ψ(u, v, u, v, v) ≥ 0 (or) ψ(u, u, v, v, v) ≥ 0 implies v < u. (ii) ψ(u, 1, 1, u, 1) < 0 (or) ψ(u, 1, 1, 1, u) < 0 implies 0 < u < 1.  5 Example 7.4 1. Define ψ : R + → R + by ψ (t1 , t2 , t3 , t4 , t5 ) = t1 − k (min {t2 , t3 , t4 , t5 }), k > 1 then ψ ∈ (ψ).  5 2. Define ψ : R + → R + by ψ (t1 , t2 , t3 , t4 , t5 ) = t1 − kt 2 − min (t3 , t4 , t5 ), k > 0 then ψ ∈ (ψ).

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7.4 Main Results Theorem 7.1 Let (X, E, ∗) be  E-fuzzy-metric, ∗ is a continual t-norm. Self-mappings (A, T ), (B, S) and (C, U ) of X which gratifying, (i) T (X ) ⊃ B(X ), (or U (X ) ⊃ A(X ) or C(X ) ⊂ S(X ), (ii) (B, S), and (C, U) are fulfils JCLR-property (or (C, U) and (A, T) (or) (A, T) and (B, S) satisfies the Joint Common Limit in the Range (JCLR)-property. (iii) For ψ ∈ (ψ) ψ(E(Ax, By, C z, t), E(Ax, T x, T x, t),  E(By, Sy, Sy, t),   E(C z, U z, U z, t), E(T x, Sy, U z, t)) ≥ 0 (iv) A (z n ) converges for every sequence {z n } in X whenever T z n converges (or B (xn ) converges ∀ {xn } in X whenever Sxn converges or C (yn ) converges ∀ {yn } in X whenever U y n converges). (v) T (X ) (or S(X ) or U (X )) is Complete, Then (A, T ), (B, S), (C, U ) revel in the JCLR-property. Proof Suppose (B, S) and (C, U ) consumes JCLR-property, then ∃ {xn } and {yn } in X, ensure that, limn→∞ Bxn = limn→∞ Sxn = limn→∞ C yn = limn→∞ U yn = Sw = U w for some w ∈ X , Since, B(X ) ⊂ T (X ), then ∃ a sequence {z n } in X ensure that, limn→∞ Bxn = limn→∞ T z n = T w, for some w ∈ X . From (iv), A (z n ) converges for every sequence {z n } in X whenever T z n converges. We claim that A (z n ) → T w as n → ∞. On putting x = z n , y = xn , z = yn in (1), we have,  (Az n , Bxn , C yn , t) , E (Az n , T z n , T z n , t) , E (Bxn , Sxn , Sxn , t) , ψ( E   E C yn , U y n , U yn , t ), E (T z n , Sxn , U yn , t) ≥ 0 Limiting as n → ∞ ψ( E( p, T w, T w, t),  E( p, T w, T w, t),  E(T w, T w, T w, t),   E(T w, T w, T w, t), E(T w, T w, T w, t)) ≥ 0, Hence A (z n ) → T w as n → ∞. Therefore the pairs (A, T ), (B, S), (C, U ) revel in the JCLR-property. ˘ Theorem 7.2 Le(X,  E, ∗) t be E-fuzzy-metric , ∗ is a continual t-norm. The Selfmappings (A, T ), (B, S) and (C, U ) of X amusing, for some ψ ∈ (ψ), ∀x, y, z ∈ E(C z, X, t > 0, ψ( E(Ax, By, C z, t),  E(Ax, T x, T x, t),  E(By, Sy, Sy, t),   U z, U z, t), E(T x, Sy, U z, t)) ≥ 0......(4)

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Then A, T, B, S and C, U have eccentric fixed-point which on X , provided (A, T ), (B, S) and (C, U ) are assures the JCLR-property and (A, T ), (B, S) and (C, U ) remain Wc mapping. Proof Suppose (B, S) and (C, U) of a  E-fuzzy-metric space (X,  E, ∗) fulfil the (JCLR) property if ∃ {xn } , {yn } and {z n } in X ensure that, lim Byn = lim Syn = lim C z n = lim U z n = T w = Sw = U w, for w ∈ X.

n→∞

n→∞

n→∞

n→∞

Since B(X ) ⊂ T (X ), ∃ {z n } in X such that limn→∞ Bxn = limn→∞ T z n = T w = Sw = U w. Suppose not, put x = z n , y = xn , z = yn in (4),  (Bx n , Sxn , Sx xn , t) , ψ( E (Az n , Bxn , C yn , t) ,  E (Az n , T z n , T z n , t) , E      T z n , Sxn , U y n , t ≥ 0  C y n , U y n , U y n , t ), E E    (Az n , T w, T w, t) , 1, 1, 1 ≥ 0 ψ E (Az n , T w, T w, t) , E From (ψ) ⇒ E (Az n , T w, T w, t) > 1, which is absurd. Hence Az n = T w. We claim that Ap = T p Suppose not, put x = p, y = xn , z = yn in (4), ψ( E(Ap, T w, T w, t),  E(Ap, T p, T p, t),  E(T w, T w, T w, t),  E(T w, T w, T w, t),  E(T p, T w, T w, t)) ≥ 0 Since T (X ) is complete ∃ p such that T p = T w. From (ψ) Hence Ap = T p. Assume that Ap = T p = Bp = Sp = C p = U p = w. Since (A, T ) is weak compatible. AT p = T Ap ⇒ Aw = T w. Similarly, Bw = Sw and Cw = U w. We claim that Aw = w. Suppose not, put x = w, y = p, z = p in (4),   ψ( E(Aw, w, w, t), E(Aw, w, w, t), 1, 1, 1) ≥ 0 Hence Aw = w. Similarly, Aw = Bw = Cw = Sw = T w = U w = w.

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Therefore W is the common fixed-point of A, B, C, S, T and U . The uniqueness is directly from Theorem 7.1. Hence the theorem. Example 7.5 Let (X,  E, ∗) be  E-fuzzy-metric, where X = [2, 12] with min t-norm t and  E(x, y, z, t) = t+G(x,y,z) , ∀t > 0 and x, y, z ∈ X , ⎧ ⎨ 3, Define U x = 1, ⎩ x,



if x = 3 if x ∈ [0, 3) if x ∈ [3, 12]

Ax =

4, if x ∈ [2, 3) 3, if x ∈ [3, 12]

A(X ) = {4, 3} ⊂ U (X ) = {3} ∪ {1} ∪ (3, 12] Tx =

x, if x ∈ [0, 3) , Bx = 3, if x ∈ [3, 12]



3, if x ∈ [2, 4] 1, if x ∈ [4, 12]

B(X ) = {1, 3} ⊂ T (X ) = {3} ∪ [0, 3] ⎧ ⎨ 3, Sx = 4, ⎩ 0,

if x ∈ [2, 4] if x = 3 if x ∈ (4, 12]

Cx =

3, if x = 3 0, if x ∈ (2, 3) ∪ (3, 12)

C(X ) = {0, 3} ⊂ S(X ) = {0, 3, 14}     Taking {xn } = 3 + n1 , {yn } = 4 − n1 , {z n } = {3} such that lim Axn = lim T x n = lim Byn = lim Syn

n→∞

n→∞

n→∞

n→∞

= lim C z n = lim U z n = 3 = w. n→∞

n→∞

7.5 Conclusion ˘ We reveal a fixed-point approach on E-Fuzzy-metric Space aimed at weak compatible mappings (wc mapping) providing Joint Common Limit in the Range (JCLR) property by implication. We also provide some concrete examples of our key findings. We exhibit a fixed-point theorem for six finite families of self-mappings, which can be used to prove other results. In the Theorem 7.1, we exhibit (A, T ), (B, S), (C, U ) revel in the JCLR-property, provided the conditions (i)–(v). Theorem 7.2 assures A, T, B, S and C, U have eccentric fixed-point which on X , provided (A, T ), (B, S) and (C, U ) are assures the JCLR-property and (A, T ), (B, S) and (C, U ) remain

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W˘ C mapping. In (4.3), we reveal a fixed-point theorem for six finite families of self-mappings have eccentric point on  E-fuzzy-metric.

References 1. L.A. Zadeh, Fuzzy-sets. Inform. Control 8, 338–353 (1965) 2. S.N. Mishra, N. Sharma, S.L. Singh, Common fixed points of maps on fuzzy metric spaces. Int. J. Math. Math Sci. 17, 253–258 (1994) 3. A. George, P. Veeramani, On some results in fuzzy metric space. Fuzzy-Sets Syst. 64, 395–399 (1994) 4. Z. Mustafa, B. Sims, A new approach to generalized metric spaces. J. Nonlinear Convex Math. Soc. 84(4), 329–336 (2006) 5. I. Kramosil, J. Michalek, Fuzzy metric and statistical metric spaces. Kybernetika 11(5), 336– 344 (1975) 6. B. Singh, S. Jain, Semi Compatibility and fixed point theorems in fuzzy metric space using implicit relation. Int. J. Math Sci. 16, 2617–2629 (2005) 7. S. Chauhan, W. Sintunavarat, M. Imdad, Y. Shen, Unified fixed point theorems for mappings in fuzzy metric spaces via implicit relations. J. Egypt. Math. Soc. 23, 334–342 (2015) 8. V. Popa, Some fixed point theorems for compatible mappings satisfying on implicit relation. Demonsratio Math. 32, 157–163 (1999) 9. S. Chauhan, W. Sintunavarat, P. Kumam, Common fixed point theorems for weakly compatible mappings in fuzzy metric spaces using (JCLR) property. Appl. Math. 3, 976–982 (2012) 10. K.P. Sukanya, M. Jose, Generalized fuzzy metric space and its properties. Int. J. Pure Appl. Math. 119(9), 31–39 (2018) 11. K.P. Sukanya, M. Jose, Fixed point theorem in generalized E-fuzzy metric space. Int. J. Pure Appl. Math. 118(10), 317326 (2018) 12. A. Rani, S. Kumar, Common fixed point theorems in fuzzy metric space using implicit relation. Int. J. Comput. Appl. 20(7) (2011). ISSN 0975-8887 13. S. Jain, B. Mundra, S. Aske, Common fixed point theorem in fuzzy metric space using implicit relation. Int. Math. Forum 4(3), 135–141 (2009) 14. G. Sun, K. Yang, Generalized fuzzy metric spaces with properties. Res. J. Appl. Sci. Eng. Tech. 2(7), 673–678 (2010) 15. M. Imdad, J. Ali, General fixed-point theorem in fuzzy metric spaces via an implicit function. J. Appl. Math. Inform. 26, 591–603 (2008) 16. C. Vijayalakshmi, P. Muruganantham, N. Gani, A fixed-point approach on fuzzy-metric space with CLR-property by implication. 43(2) (2020). ISSN 2249-6661 ˜ 17. C. Vijayalakshmi, P. Muruganantham, N. Gani, A fixed-point approach on generalised Efuzzy-metric space by implication, in Advances and Applications in Mathematical Sciences, vol. 20(5) (Mili Publications, 2021), pp. 823–837

Chapter 8

Fixed Point Results on Derived Fuzzy Norm Using Fuzzy 2-Normed Space A. Nagoor Gani, B. Shafina Banu, and P. Muruganantham

Abstract The current effort, a fuzzy 2-normed spaces can be used to form a derived fuzzy normed space and then fixed point results are discussed. AMS subject classification: 54H25; 47H10; 47S40, 54A40. AMS Subject Classifications 54H25 · 47H10 · 47S40 · 54A40

8.1 Introduction The FS developed broadly by lots of writers in various fields. In 1965, Zadeh [7] presented the FSs. The thought of FMS was introduced primarily by Kramosil and Michalek. George and Veeramani [6] give the improved idea of FMS. The notation of FNS was introduced by Katsaras [12, 13], who introduced some general types of fuzzy topological linear spaces. Rumlawang [1] defined a derived norm from 2-NS using the contractive mapping. Bag and Samanta [2] discussed some fp theorems in FNS. Some common fp theorems in fuzzy 2-Banach space are discussed by Stephen John et al. [4]. Mashadi and Sri Gemawati [3] discussed some alternative concepts for FNS and F2NS. The following section discusses basic definitions and properties.

8.2 Preliminaries Notation * Fuzzy set-FS * Fuzzy normed space-FNS * Fuzzy 2-normed space-F2NS A. N. Gani · B. Shafina Banu (B) · P. Muruganantham PG and Research Department of Mathematics, Jamal Mohamed College (Autonomous), Affiliated to Bharathidasan University, Tiruchirappalli 620020, Tamil Nadu, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Mustapha et al. (eds.), Proceedings of the 8th International Conference on the Applications of Science and Mathematics, Springer Proceedings in Physics 294, https://doi.org/10.1007/978-981-99-2850-7_8

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* Fixed point-fp * Vector Space-VS Definition 8.1 [4] Let X be a VS over the field K , ∗ be a continual t-norm and N ¸ be a FS on X × (0, ∞). Then (X, N, ¸ ∗) in FNS if ∀x, y ∈ X and t, s ∈ (0, ∞) as (FN1) N(x, ¸ t) > 0; (FN2) N(x, ¸ t) = 1 iffx = 0;  t for any α = 0; (FN3) N(αx, ¸ t) = N ¸ x, |α| (FN4) N(x, ¸ t) ∗ N(y, ¸ s) ≤ N(x ¸ + y, t + s); (FN5) N(x, ¸ .) : (0, ∞) → [0, 1] is continuous; (FN6) limt→∞ N(x, ¸ t) = 1 and limt→∞ N(x, ¸ t) = 0. Definition 8.2 [6] ∗ : [0, 1] × [0, 1] is continual t-norm if (1) (2) (3) (4)

* is commutative and associative * is continuous a ∗ 1 = a, ∀a ∈ [0, 1] a ∗ b ≤ c ∗ d, ∀a ≤ c, b ≤ d and a, b, c, d ∈ [0, 1].

Example 8.1 See below: (a) a ∗ b = min(a, b), Zadeh’s t-norm (b) a ∗ b = max[0, a + b − 1], Lukasiewicz’s t-norm (c) a ∗ b = a.b, probabilistic t-norm. Definition 8.3 [4] Let X be a VS over the field K , ∗ be a continual t-norm and N ¸ be a FS on X 2 × (0, ∞). Then (X, N, ¸ ∗) is F2NS if ∀x, y, z, u in X and t1 , t2 , t3 ∈ (0, ∞) as (F2N1) N(x, ¸ y, 0) = 0; (F2N2) N(x, ¸ y, t) = 1, ∀t> 0 and atleast two among the three points are equal;  t , ∀t > 0 and α = 0; (F2N3) N(αx, ¸ y, t) = N ¸ x, y, |α| (F2N4) N(x, ¸ y, t) = N(y, ¸ x, t); (F2N5) N(x, ¸ y, t1 ) ∗ N(z, ¸ y, t2 ) ≤ N(x ¸ + z, y, t1 + t2 ), ∀t1 , t2 ≥ 0; (F2N6) N(x, ¸ y, .) : (0, ∞) → [0, 1] is continuous; ¸ y, t) = 1. (F2N7) limn→∞ N(x, (F2N8) N(x, ¸ y, t) ≥ N(x, ¸ z, t) + N(z, ¸ y, t). ¸ ∗) iff limn→∞ Definition 8.4 [4] {xn } is converged to a point x ∈ X in (X, N, N(x ¸ n − x, t) = 1, ∀t > 0. Definition 8.5 [4] {xn } is converged to a point x ∈ X in (X, N, ¸ ∗) iff limn,m→∞ N(x ¸ n − xm , t) = 1, ∀t > 0.

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Definition 8.6 [4] A FNS (X, N, ¸ ∗) is complete if every Cauchy sequence in X is convergent to a point in X . Definition 8.7 [1] Let (X, ., . ) be 2NS and Y = {y1 , y2 } be linearly independent set in X to define a function in X by x = x, y1 + x, y2 . This function . : X → R defines a norm in X . Definition 8.8 [1] Picard sequence is a sequence of successive approximation with initial value x0 if for any x0 ∈ X , the sequence {xk } in X given by xk = f (xk−1 ) = f k (x0 ), k = 1, 2, . . . Definition 8.9 [1] Let (X, ., . ) be a 2NS. Then the mapping f : X → X is said to be a contractive mapping if there exists an element c ∈ (0, 1)  f (x) − f (y) ≤ c x − y, z , ∀x, y, z ∈ X . Definition 8.10 [1] Let (X, ., . ) be a 2NS, Y = {y1 , y2 } be linearly independent set in X and . be a derived norm. Then the mapping f : X → X is said to be a contractive mapping with respect to derived norm if there exists an element c ∈ (0, 1)  f (x) − f (y) ≤ c x − y, z , ∀x, y, z ∈ X .

8.3 Fixed Point Theorem Definition 8.11 Let N(x, ¸ y, t) be a F2NS. Let Y = {y1 , y2 } be a linear independent set in X and cardinality of Y = 2. Now to define a function in X by N(x, ¸ t) =

N (x, y1 , t) + N (x, y2 , t) . 2

(8.1)

(by 8.8) Therefore, N(x, ¸ t) is Derived Fuzzy Norm in X . Theorem 8.1 The derived fuzzy norm N(x, ¸ t) is a FNS which is defined in 8.1. Proof N(x, ¸ 0) = 0 (by F2N1). N(x, ¸ y, t) = 1, ∀t > 0 ⇔ x = y (by F2N2). Suppose if N(x, ¸ y1 , t) = 1, then 1 + N(x, ¸ y2 , t) = 1(by 8.1) 2 ⇔ 1 + N(x, ¸ y2 , t) = 2 ⇔ N(x, ¸ y2 , t) = 1

N(x, ¸ t) = 1 ⇔

x = y2 . ¸ t) = 1 ⇔ x = y1 . Similarly, suppose if N(x, ¸ y2 , t) = 1, then N(x, Thus, N(x, ¸ t) = 1 ⇔ x = y1 and x = y2 .

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x = 0 ⇔ N(0, ¸ t) = 

t N(cx, ¸ y, t) = N ¸ x, y, |c| Therefore,

1+1 ¸ y2 , t) N(0, ¸ y1 , t) + N(0, = =1 2 2

 if c = 0 (by F2N3) N(cx, ¸ y1 , t) + N(cx, ¸ y2 , t) 2    t t N ¸ x, y1 , +N ¸ x, y2 , |c| |c| = 2   t . =N ¸ x, |c|

N(cx, ¸ t) =

N ¸ (x, y, t1 ) ∗ N(z, ¸ y, t2 ) ≤ N ¸ (x + z, y, t1 + t2 ), ∀x, y, z ∈ X and t1 , t2 ≥ 0 (by F2N5). Therefore ¸ + z, y2 , t1 + t2 ) N(x ¸ + z, y1 , t1 + t2 ) + N(x 2 1 ¸ y1 , t1 ) ∗ N(z, ¸ y1 , t2 )] + [N(x, ¸ y2 , t1 ) ∗ N(z, ¸ y2 , t2 )]} ≥ {[N(x, 2 ¸ y1 , t1 ) + N(x, ¸ y2 , t1 )] [N(z, ¸ y2 , t2 )] [N(x, ¸ y1 , t1 ) + N(x, ∗ ≥ 2 2 ≥ N(x, ¸ t1 ) ∗ N(z, ¸ t2 )

N(x ¸ + z, t1 + t2 ) =

N(x, ¸ y, .)(0, ∞) → [0, 1] is continuous (by F2N6). Therefore, N(x, ¸ .) : (0, ∞) → [0, 1] is continuous. ¸ y, t) = 1 (by F2N7).  limt→∞ N(x,  N(x, ¸ y1 , t) + N(x, ¸ y2 , t) = 1. Therefore, limt→∞ N(x, ¸ t) = lim t→∞ 2 Therefore, N(x, ¸ t) is FNS. Theorem 8.2 Let N(x, ¸ y, t) be a F2NS and Y = {y1 , y2 } be a linear independent ¸ t) which is defined set in X . If {xk } → x in X in F2NS, then {xk } → x in X in N(x, in 8.1. Proof W.K. T, limk→∞ N(x ¸ k − x, yi , t) = 1, i = 1, 2 and t > 0. 1 Therefore, limk→∞ N(x limk→ N(x ¸ k − x, t) = ¸ k − x, y1 , t) + limk→ N(x ¸ k − x, y2 , 2  t) = 1 . ¸ t). Therefore, {xk } → x in X in N(x, Definition 8.12 Let (X, N, ¸ ∗) be a F2NS. Then the mapping f : X → X is said to be a contractive mapping in ∃c ∈ (0, 1]  N( ¸ f (x) − f (y), f (z), t) ≥ 1 − c.N(x ¸ − y, z, t), ∀x, y, z in X (by 8.10).

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Definition 8.13 Let (X, N, ¸ ∗) be a F2NS, Y = {y1 , y2 } be linearly independent set in X and N(x, ¸ t) be a derived fuzzy norm. Then the mapping f : X → X is said to be a contractive mapping with respect to derived fuzzy norm if ∃c ∈ (0, 1]  N( ¸ f (x) − f (y), t) ≥ 1 − c.N(x ¸ − y, z, t), ∀x, y, z in X (by 8.11). Theorem 8.3 Let (X, N, ¸ ∗) be a complete F2Ns, K ⊂ X which is a closed and ¸ t) is a derived bounded set, Y = {y1 , y2 } be a linearly independent set in X and N(x, fuzzy norm in X . If f : K → K be a contractive mapping, then K has a fp. Proof For x1 , x2 ∈ K , we have N( ¸ f 3 (x0 ) − f 3 (x1 ), t) = N( ¸ f ( f 2 (x0 )) − f ( f 2 (x1 )), t) ≥ 1 − c.N( ¸ f 2 (x0 ) − f 2 (x1 ), f 2 (z), t)(by 3.5) = 1 − cN( ¸ f ( f (x0 )) − f ( f (x1 )), f ( f (z)), t) ≥ 1 − c(1 − c).N( ¸ f (x0 ) − f (x1 ), f (z), t)(by 3.4) ≥ 1 − c(1 − c)(1 − c)N(x ¸ 0 − x1 , z, t)(by 3.4) = 1 − c(1 − c)2 N(x ¸ 0 − x1 , z, t). By induction hypothesis, we obtain ¸ 0 − x1 , x, t). N( ¸ f k (x0 ) − f k (x1 ), t) ≥ 1 − c(1 − c)k N(x To show that {xk } ∈ X is a Cauchy sequence. Claim: N(x ¸ n , xn+ p , t) = 1, ∀t > 0, p = 1, 2, . . . Let l > k and l = k + p, ∀l, p, k in N . N(x ¸ k − xl , t) = N(x ¸ k − xk+ p , t) ≥ N(x ¸ k − xk+1 , t) + · · · + N(x ¸ k+ p−1 − xk+ p , t)(by F2N8) = N( ¸ f (xk−1 ) − f (xk ), t) + · · · + N( ¸ f (xk+ p−2 ) − f (xk+ p−1 ), t)(by 2.9) = N( ¸ f k (x0 ) − f k (x1 ), t) + · · · + N( ¸ f k+ p−1 (x0 ) − f k+ p−1 (x1 ), t)(by 2.9)   ≥ 1 − c(1 − c)k−1 N(x ¸ 0 − x1 , z, t) + · · · + c(1 − c)k+ p−2 N(x ¸ 0 − x1 , z, t) ≥ 1 − c(1 − c)k−1 {1 + (1 − c) + · · · } N(x ¸ 0 − x1 , z, t) ¸ 0 − x1 , z, tα ) > 1 − Since K ⊂ X is fuzzy bounded if ∀α in (0, 1)∃tα > 0  N(x α, ∀x1 , x2 , z in K [14]. ¸ k − xl , t) = 1. =⇒ lim N(x k,l→∞

=⇒ {xk } is a Cauchy sequence and so its convergent sequence. Let {xk } → x. Now, f (x) = limk→∞ f (xk ) = limk→∞ xk+1 = x (by 2.9) Therefore, f has a fp in K . Hence the theorem.

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Corollary 8.1 Let (X, N, ¸ ∗) be a complete F2NS, K ⊂ X which is a closed and ¸ t) is a bounded set, Y = {y1 , y2 } be a linearly independent set in X , and N(x, derived fuzzy norm in X . If f : X → K is defined as N( ¸ f (x) − f (y), t) ≥ 1 − N(x ¸ − y, z, t), ∀x, y, z ∈ X . Then K has a fp. 1 ∈ X, ∀n in N . n+1 Define x, yi = |s1r2 − s2 r1 |, where x = (s1 , s2 ), yi = (r1 , r2 ) ∈ X, i = 1, 2. t , ∀x, yi ∈ X and t > 0, i = 1, 2. Let N (x, yi , t) = t + x, yi

1 ¸ y1 , t) + N(x, ¸ y2 , t)} . N (x, t) = {N(x, 2 Example 8.2 Let X = R 2 and K ⊂ X . Let xn = 1 −

The contraction mapping f : K → K is defined by f (x) = x if ¸ 0 − x1 , z, t)∀x, y, z in X. ∃c ∈ [0, 1]  N( ¸ f (x0 ) − f (x1 ), t) ≥ 1 − c.N(x Let x0 = (0, 0), x1 = (0.5, 0.5), y1 = (0.5, 0.5), y2 = (0.7, 0.6) and t = 0.8 N( ¸ f (x0 ) − f (x1 ), t) = N( ¸ f (0, 0) − f (0.5, 0.5), 0.8) = N((0.5, ¸ 0.5), 0.8) N((0.5, ¸ 0.5), (0.5, 0.5), 0.8) + N((0.5, ¸ 0.5), (0.7, 0.6), 0.8) = 2 1 + 0.959238 = 0.97619 = 2 Let c = 0.9 and z = (0.6, 0.6). 1 − c.N(x ¸ 0 − x1 , z, t) = 1 − 0.9.N((0.5, ¸ 0.5), (0.6, 0.6), 0.8) = 1 − 0.9.(1) = 0.1. ¸ 1 − x2 , z, t). Therefore, N( ¸ f (x1 ) − f (x2 ), t) ≥ 1 − c.N(x Thus, limn→∞ xn = 1 is the fp of X . Suppose c = 1, then we have the corollary (3.7)

References 1. F.Y. Rumlawang, Fixed point theorem in 2-normed spaces. Tensor Pure Appl. Math. J. 1(1), 41–46 (2020) 2. T. Bag, S.K. Samanta, Some fixed point theorems in fuzzy normed linear spaces. Inform. Sci. 177, 3271–3289 (2007). Science Direct 3. SriGemawati Mashadi, Some alternative concets for fuzzy normed spaces and fuzzy 2-normed space. JP J. Math. Sci. 14, 1–19 (2015)

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4. B. Stephen John, S. Robinson Chellathurai, S.N. Leena Nelson, Some common fixed point theorems in fuzzy 2-banach space. Int. J. Fuzzy Math. Arch. 13, 105–112 (2017) 5. S.A. Mohiuddine, Some new results on approximation in fuzzy 2-normed spaces. Math. Comput. Model. 53, 574–580 (2011) 6. A. George, P. Veeramani, On some results of analysis for fuzzy metric space. Fuzzy Sets Syst. 90, 365–368 (1997) 7. L.A. Zadeh, Fuzzy sets. Inform. Control 8, 338–353 (1965) 8. K. Cho, C. Lee, On convergence in fuzzy normed spaces. FJMS 109, 129–141 (2018) 9. T. Bag, S.K. Samanta, Finite dimensional fuzzy normed linear spaces. Ann. Fuzzy Math. Inform. x(x), 1–xx (2013) 10. J. Xiao, X. Zhu, Fuzzy normed space of operators and its completeness. Fuzzy Sets Syst. 133, 389–399 (2003) 11. G. Rano, T. Bag, Fuzzy normed linear spaces. Int. J. Math. Sci. Comput. 2(2), 16–19 (2012) 12. A.K. Katsaras, Fuzzy topological vector spaces I. Fuzzy Sets Syst. 6, 85–95 (1981) 13. A.K. Katsaras, Fuzzy topological vector spaces II. Fuzzy Sets Syst. 12, 143–154 (1984) 14. A. Szabo, T. Binzar, S. Nadaban, F. Pater, Some properties of fuzzy bounded sets in Fuzzy normed linear spaces. ICNAAM 390009, 1–4 (2017)

Chapter 9

Solving Fuzzy Linear Programming Problems by Using the Limit Existence of the Fuzzy Exponential Penalty Method A. Nagoor Gani

and R. Yogarani

Abstract This article focusses on solving the fuzzy linear programming problem by the fuzzy exponential penalty method. An algorithm is used in this method to solve the fuzzy linear programming problems. Here the objective functions are convex; therefore, fuzzy inequality constraints are established. A specific numerical examples are given.

9.1 Introduction Mathematical modelling and control theory have benefited from fuzzy set theory. There are several methods to apply unresolved decision-making problems in real life. It was introduced in 1965 by Zadeh’s fuzzy set theory. In 1997, Tanaka and Assai [1] introduced fuzzy linear programming, while Dubois and Prade [2] published fuzzy numbers. Hsieh and Chen [3] came up with the idea of a function to deal with fuzzy arithmetical operations, like addition, subtraction, multiplication, and division on fuzzy numbers. There is also a duality to the fuzzy linear programming problem, defined by Mahdavi-Amiri et al. [4], Mahdavi-Amiri and Nasseri [5]. Transforming fuzzy values into crisp ones is known as defuzzification. These strategies have been intensively explored and used in fuzzy systems for some years. According to certain characters, a typical value from a given set was the primary goal of these procedures. From all fuzzy sets to all real numbers, the defuzzification approach creates a relationship. The exponential penalty function approach, which was developed by Wright [6] and Parwadi et al. [7], gives a large cost to infeasible points. The fuzzy exponential penalty approach is an alternate method for answering A. N. Gani · R. Yogarani (B) Research Department of Mathematics, Jamal Mohamed College (Autonomous), Affiliated to Bharathidasan University, Tiruchirappalli 620 020, India e-mail: [email protected] A. N. Gani e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Mustapha et al. (eds.), Proceedings of the 8th International Conference on the Applications of Science and Mathematics, Springer Proceedings in Physics 294, https://doi.org/10.1007/978-981-99-2850-7_9

79

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fuzzy linear programming problems. To approximate fuzzy constraints, the fuzzy exponential penalty technique adds a fuzzy objective function that prescribes a high penalty for breaking the fuzzy requirements. In the context of the fuzzy optimization problem, a fuzzy penalty function whose value increases exponentially with increasing distance from the feasible zone. As part of this procedure, a positive decreasing parameter called the fuzzy exponential penalty parameter determines the fuzzy unconstrained problem’s proximity to the original. In Sect. 9.2, some basic concepts of fuzzy set theory and algebraic operation of triangular fuzzy numbers are given in this paper. In Sect. 9.3, an algorithm is constructed to solve the fuzzy linear programming issue using the fuzzy exponential penalty approach. An example is given in Sect. 9.4.

9.2 Preliminaries 9.2.1 Fuzzy Sets If M˜ = {(x, μ M˜ (x)) : x ∈ M, μ M˜ (x) ∈ [0, 1]} defines a fuzzy set M. The membership function is a pair (x, μ M˜ (x)), where the first element x belongs to the classical set M˜ and the second element μ M˜ (x) belongs to the interval [0, 1].

9.2.2 Fuzzy Number Generalized Fuzzy Number A generalized fuzzy number is a fuzzy subset of the real line R whose μ M˜ (x) membership function satisfies the following requirements. μ M˜ (x) is continuous. A mapping from R to [0, 1], μ M˜ (x) = 0, −∞ < x ≤ m 1 , μ M˜ (x) = L(x) is strictly increasing on [m 1 , m 2 ], μ M˜ (x) = 1, m 2 ≤ x ≤ m 3 , μ M˜ (x) = R(x) is strictly decreasing on [m 3 , m 4 ], μ M˜ (x) = 0, m 4 ≤ x < ∞, where m 1 , m 2 , m 3 , m 4 are real numbers. Triangular Fuzzy Number The fuzzy set M˜ = (m 1 , m 2 , m 3 ), where m 1 ≤ m 2 ≤ m 3 and defined on R, is called the triangular fuzzy number if the membership function of M˜ is given by

9 Solving Fuzzy Linear Programming Problems by Using the Limit …

81

⎧ x−m 1 ⎪ ⎨ m 2 −m 1 , m 1 ≤ x ≤ m 2 −x μ M˜ (x) = mm33−m , m2 ≤ x ≤ m3 ⎪ ⎩ 0, 2 otherwise

Definition The algebraic operation of the exponential triangular fuzzy number properties is as follows. Suppose M˜ = (m 1 , m 2 , m 3 ) and N˜ = (n 1 , n 2 , n 3 ) be two triangular fuzzy numbers. Then: i. The addition of M˜ and N˜ is M˜ + N˜ = (m 1 + n 1 , m 2 + n 2 , m 3 + n 3 ), m 1 , m 2 , m 3 , n 1 , n 2 , n 3 ∈ R. ii. The product of M˜ and N˜ is M˜ × N˜ = (o1 , o2 , o3 )whereT = {m 1 n 1 , m 1 n 3 , m 3 n 1 , m 3 n 3 } o1 = minT, o2 = m 2 n 2 , o3 = maxT. If m 1 , m 2 , m 3 , n 1 , n 2 , n 3 are all nonzero positive real numbers, then M˜ × N˜ = (m 1 n 1 , m 2 n 2 , m 3 n 3 ). iii. − N˜ = (−n 3 , −n 2 , −n 1 ) then the subtraction of N˜ from M˜ is M˜ − N˜ = (m 1 − n 3 , m 2 − n 2 , m 3 − n 1 ). iv. N1˜ = N˜ −1 = 1/n 3 , 1/n 2 , 1/n 1 where n 1 , n 2 , n 3 are all nonzero real numbers, then ˜ N˜ = (m 1 /n 3 , m 2 /n 2 , m 3 /n 1 ). M/ v. Let α ∈ R, then α M˜ = (αm 1 , αm 2 , αm 3 ) if α ≥ 0, α M˜ = (αm 3 , αm 2 , αm 1 )ifα < 0.

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9.3 Fuzzy Exponential Penalty Method Let us assume the primal of the fuzzy linear programming problems. Minimize Z˜ = f˜(x) ˜ ∼

x˜ ≥ Ni , i =1, 2, subject to Mi  ∼ m 11 m 12 ∈ R m×n , f˜, x ∈ R n , Ni ∈ R m , where M1 = m 21 m 22 f˜ = ( f 1 , f 2 , f 3 ), N˜ = (n 1 , n 2 , n 3 ).

(9.1)

Assume that (1) the dual of the fuzzy linear programming problems. Maximize Z˜ = N˜ ( y˜ ) Mi ( y˜ ) ≤ f˜, M2 = M1T = T



m 11 m 21 m 12 m 22



∼T

T ∈ R m×n , N˜ ( y˜ ) = Ni , f˜ = f˜(x) ˜ .

With no loss of generality, we may consider that the rank of the matrix M1 is m. Fuzzy components in the above problem are specified through the triangular fuzzy number. Consider that there is at least one possible solution to a problem in (1). In the fuzzy linear programming problems, we define the fuzzy exponential ˜ x, penalty function E( ˜ δ) : R n → R for every scalar δ > 0 as follows. ˜ x, E( ˜ δ) = f˜(x) ˜ +δ

m 

 Exp(−δ Mi x− ˜

∼ Ni

 .

(9.2)

i=1

It is convex and compact to define the fuzzy exponential penalty function (2). Since the fuzzy exponential penalty parameter δ is increasing in value, the local and ˜ global minimum is E(x, δ) and also that is closed and bounded. n If E˜ : R → (−∞, ∞) is a function defined by ∼

∼

∼

∼

˜ x) E( ˜ = Mi x− ˜ Ni ≤ 0, Mi x− ˜ Ni = 0 for all i, ˜ x) ˜ Ni > 0, Mi x− ˜ Ni = 0 for all i. E( ˜ = Mi x− As a result, the fuzzy exponential penalty equation has been transformed into two weak fuzzy inequalities. A fuzzy exponential penalty function defined the interior of the boundary region ˜ x) ˜ x, so that E( ˜ is continuous. E( ˜ δ) is greater than equivalent to the expression which ˜ x) is zero. The set boundary is reached when E( ˜ approaches ∞. The fuzzy exponential penalty function for fuzzy linear programming problems m ˜ x, Exp(−δ g( ˜ x)), ˜ is represented by E( ˜ δ) = f˜(x) ˜ + δ i=1

9 Solving Fuzzy Linear Programming Problems by Using the Limit …

 where g( ˜ x) ˜ =

83

 ∼ Mi x˜ k − Ni , δ is a positive increasing parameter.

Fuzzy exponential penalty methods are also referred to as fuzzy interior methods.

9.3.1 Fuzzy Exponential Penalty Lemma This lemma focusses on the local and global behaviour of unconstraints minimizer of the fuzzy exponential penalty function. Statement: An exponential parameter δ k is a fuzzy sequence that increases in size. The fuzzy linear programming problems and fuzzy exponential penalty function then for each k condition are below. ˜ x˜ k , δ k ) ≤ E( ˜ x˜ k+1 , δ k+1 ) (i) E( k ˜ ˜ (ii) E(x˜ ) ≥ E(x˜ k+1 ) (iii) f˜(x˜ k ) ≤ f˜ (x˜ k+1 )

 (iv) f˜(x˜ ∗ ) ≥ E˜ x˜ k , δ k ≥ f˜ x˜ k . m Proof:





  i. E˜ x˜ k , δ k = f˜ x˜ k + δ k Exp −δ Mi x˜ k − N˜ i ≥ f˜ x˜ k+1 i=1

+ δ k+1

m 



˜ x˜ k+1 , δ k+1 ). Exp −δ k+1 Mi x˜ k+1 − N˜ i = E(

i=1

˜ x˜ k , δ k ). (x˜ k+1 , δ k+1 ) ≥ E( m



k k 

 ˜ ii. f x˜ +δ Exp −δ k Mi x˜ k − N˜ i ≤ f˜ x˜ k+1

+ δk

i=1 m 



Exp −δ k+1 Mi x˜ k+1 − N˜ i

(9.3)

i=1

m





 f˜ x˜ k+1 +δ k+1 Exp −δ k+1 Mi x˜ k+1 − N˜ i ≤ f˜ x˜ k i=1

+ δ k+1

m 



Exp −δ k Mi x˜ k − N˜ i

i=1

Fuzzy exponential penalty inequalities adding (3) and (4), we get

(9.4)

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A. N. Gani and R. Yogarani m m







  ≤ f˜ x˜ k+1 Exp −δ k Mi x˜ k − N˜ i + f˜ x˜ k+1 + δ k+1 Exp −δ k+1 Mi x˜ k+1 − N˜ i f˜ x˜ k +δ k i=1

+ δk

m 

i=1 m



 Exp −δ k+1 Mi x˜ k+1 − N˜ i + f˜ x˜ k + δ k+1 Exp −δ k Mi x˜ k − N˜ i .

i=1 i=1     m m









  k k+1 k+1 k k k − f˜ x˜ + f˜ x˜ + δ + δ k+1 Exp −δ Mi x˜ k − N˜ i Exp −δ k Mi x˜ k − N˜ i f˜ x˜ + f˜ x˜ i=1

≤δ

k

m 

i=1

m



 Exp −δ k+1 Mi x˜ k+1 − N˜ i + δ k+1 Exp −δ k+1 Mi x˜ k+1 − N˜ i .

i=1

i=1





  f˜ x˜ k + f˜ x˜ k+1 − ( f˜ x˜ k+1 + f˜ x˜ k = 0. m Then (δ k + δ k+1 ) i=1 Exp(−δ k (Mi x˜ k − N˜ i )) ≤ (δ k m k k+1 k+1 k+1 k k+1 ˜ k+1 ˜ ˜ − Ni )), since δ ≤ δ , E(x˜ ) ≤ E(x˜ ). δ ) i=1 Exp(−δ (Mi x˜ However,

+

iii. From the proof of (i), it can be obtained that m





 Exp −δ Mi x˜ k − N˜ i ≥ f˜ x˜ k+1 f˜ x˜ k +δ k+1 i=1

−

m 1 

ηk+1

˜ x˜ k ) ≤ E( ˜ x˜ k+1 ). Exp −δ Mi x˜ k+1 − N˜ i · E(

i=1



 Then f˜ x˜ k+1 ≥ f˜ x˜ k . iv. From the proof of (ii) m 

m



≤ Exp −δ Mi x˜ k − N˜ i Exp −δ Mi x˜ k+1 − N˜ i ,

i=1

i=1



 f˜ x˜ k ≥ f˜ x k+1 · f˜ x˜ ∗ ≥ f˜ x˜ k +

m 



= E˜ x˜ k , δ k ≥ f˜ x˜ k Exp −δ Mi x˜ k − N˜ i

i=1

9.3.2 Fuzzy Exponential Penalty Convergence Theorem This theorem focusses to find the convergence of the fuzzy exponential penalty function. Statement: Assume that the fuzzy linear programming problem and fuzzy exponential penalty functions are a continuous functions. An increasing sequence of positive fuzzy exponential penalty parameter {δ k } is required in a fuzzy linear programming problem

9 Solving Fuzzy Linear Programming Problems by Using the Limit …

85

˜ such that δ k ≥ 1, δ k → ∞, k → ∞. There is an optimal   solution to x˜ of Z . Then limit point x˜ exists inside the bounds of the range of x˜ k .   Proof: Let x˜ be a limit point of x˜ k .    m  ∼



k k k ˜ ˜ ≤ f˜ x˜ ∗ . ˜ +δ E x˜ , δ = f (x) Exp −δ Mi x˜ − Ni

(9.5)

i=1 ∼

From the continuity of f˜(x), ˜ Mi x− ˜ Ni , we get   ∼

k k ˜ ˜ ˜ Lim Exp −δ(Mi x˜ − Ni ) ≤ 0. Lim f x˜ = f (x),

k→∞

k→∞

From the fuzzy exponential penalty lemma (iv), we get 

Lim E˜ x˜ k , δ k = f˜(x ∗ )

k→∞

x˜ is feasible.

9.3.3 Fuzzy Exponential Penalty Function Algorithm 1. Recognize the problem’s fuzzy objective function and restrictions, and restate the problem  in standard forms to reflect these. Write Min Z˜ = f˜(x) ˜ subject to  ∼

Mi x˜ k − Ni

≤ 0.

2. Convert fuzzy exponential penalty function defined ˜ x, E( ˜ δ) = f˜(x) ˜ +δ

m 

   ∼ k Exp −δ Mi x˜ − Ni .

i=1

3. Minimize inequality constraints using fuzzy exponential penalty functions ˜ x, Min E( ˜ δ) = f˜(x) ˜ +δ

m 

   ∼ k Exp −δ Mi x˜ − Ni .

i=1

4. First-order required conditions for optimality, where δ → ∞, are applied to arrive at the optimal solution to this fuzzy linear programming problem that is presented.

 ˜ x, ˜ δ k ), then minimize 5. Compute E˜ x˜ k , δ k = min E( x≥0

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x˜ k andδ = 10, k = 1, 2, . . . , k = I then stop. Alternately, move on to step 5. The fuzzy exponential penalty approach uses the same procedure for the dual fuzzy linear programming problem as the preceding algorithm.

9.4 Numerical Example Assume that the primal fuzzy linear programming problem Min˜z = (3.25, 4, 4.75)x˜1 + (2.25, 3, 3.75)x˜2 2 x˜1 + 3x˜2 ≥ (5.25, 6, 6.75), 4x˜1 + x˜2 ≥ (3.25, 4, 4.75). Solution: In this example, this graph of the given fuzzy linear programming problem can be described in the following (Fig. 9.1). The fuzzy exponential penalty method is given by ˜ x, E( ˜ δ) = (3.25, 4, 4.75)x˜1 + (2.25, 3, 3.75)x˜2 + δ

m 

   ∼ k Exp −δ Mi x˜ − Ni .

i=1

According to this strategy, you can convert fuzzy linear programming issues into a standard form of unconstrained problems. Fig. 9.1 Graphical solution of the primal fuzzy linear programming problem

9 Solving Fuzzy Linear Programming Problems by Using the Limit … Table 9.1 Primal fuzzy linear programming problem solution

87

No

δk

x˜1

x˜2

1

10

(−0.1500, 0.6006, 1.3516)

(−0.3468, 1.6018, 3.5501)

2

102

(−0.1500, 0.6001, 1.3502)

(−0.3500, 1.6002, 3.5500)

3

103

(−0.1500, 0.6000, 1.3500)

(−0.3500, 1.6000, 3.5500)

4

104

(−0.15, 0.60, 1.35)

(−0.35, 1.60, 3.55)

˜ x, Min E( ˜ δ) = (3.25, 4, 4.75)x˜1 + (2.25, 3, 3.75)x˜2 + δ

m 

   ∼ k Exp −δ Mi x˜ − Ni .

i=1

Using the primal–dual fuzzy exponential penalty function algorithm step (iv), we get x˜1 =

0.0407 0.02 + (−0.15, 0.60, 1.35), x˜2 = (−0.35, 1.60, 3.55) + ,& δ δ

y˜1 =

0.1806 0.0018 + (−0.25, 0.80, 1.85), y˜2 = + (−0.3, 0.60, 1.5). δ δ

To get the optimal and feasible solution we need to determine δ k , where δ = 10, k = 1, 2, 3 . . . The fuzzy exponential penalty parameter is selected to be consecutive parameters are increasing by a factor of 10, primal and dual fuzzy linear programming problem solutions are calculated in Tables 9.1, 9.2 for a sequence of parameters given below. The optimal value of problem (1) can be obtained as x˜1 = (−0.15, 0.60, 1.35), x˜2 = (−0.35, 1.60, 3.55), Min˜z = (−1.7, 7.20, 16.1). The corresponding given problem of the optimal values for y˜1 , y˜2 can be obtained as y˜1 = (−0.25, 0.80, 1.85), y˜2 = (−0.3, 0.6, 1.5), Max z˜ = (−3.0, 6.0, 15.0). Table 9.2 Dual fuzzy linear programming problem solution

No

δk

y˜1

y˜2

1

10

(−0.2441, 0.8498, 1.8544)

(−0.2952, 0.6057, 1.5066)

2

102

(−0.2494, 0.8050, 1.8504)

(−0.2995, 0.6006, 1.5007)

3

103

(−0.2500, 0.8005, 1.8500)

(−0.3000, 0.6001, 1.5001)

4

104

(−0.2500, 0.8000, 1.8500)

(−0.3000, 0.6000, 1.5000)

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9.5 Conclusion This paper presents a technique for obtaining a better optimal solution to the primal– dual fuzzy linear programming problem using the fuzzy exponential penalty function with the fuzzy exponential penalty parameter. The table for the primal–dual problems above shows that the primal–dual algorithm created by us when it is the fuzzy exponential penalty parameter provides a convergence rate to the optimal solution.

References 1. H. Tanaka, K. Asai, Fuzzy linear programming problems with fuzzy numbers. Fuzzy Sets Syst. 13(1), 1–10 (1984) 2. D. Dubois, H. Prade, The mean value of a fuzzy number. Fuzzy Sets Syst. 24(3), 279–300 (1987) 3. C.H. Hsieh, S.-H. Chen, Similarity of generalized fuzzy numbers with graded mean integration representation. In Proceedings 8th International Fuzzy Systems Association World Congress, vol. 2 (1999), pp. 551–555 4. A.N. Mahdavi, S.H. Naseri, A.B. Yazdani, Fuzzy Primal Simplex Algorithms for Solving Fuzzy Linear Programming Problems (2009), pp 68–84 5. N. Mahdavi-Amiri, S.H. Nasseri, Duality in fuzzy number linear programming by use of a certain linear ranking function. Appl. Math. Comput. 180(1), 206–216 (2006) 6. S.J. Wright, On the convergence of the Newton/log-barrier method. Math. Program. 90(1), 71–100 (2001) 7. M. Parwadi, I.B. Mohd, N.A. Ibrahim, Solving bounded lp problems using modified logarithmic-exponential functions. In Proceedings of the National Conference on Mathematics and its Applications in UM Malang (2002), pp. 135–141 8. F. Alvarez, R. Cosminetti, Primal and dual convergence of a proximal point exponential penalty method for linear programming. Math. Program. 93(1), 87–96 (2002) 9. J.J. Buckley, Possibilistic linear programming with triangular fuzzy numbers. Fuzzy Sets Syst. 26(1), 135–138 (1988) 10. R. Cominetti, J.P. Dussault, Stable exponential-penalty algorithm with superlinear convergence. J. Optim. Theory Appl. 83(2), 285–309 (1994) 11. A.V. Fiacco, G.P. McCormick, Computational algorithm for the sequential unconstrained minimization technique for nonlinear programming. Manag. Sci. 10(4), 601–617 (1964) 12. A.V. Fiacco, G.P. McCormick, Nonlinear programming sequential unconstrained minimization techniques. SIAM (1990) 13. A. Nagoor Gani, R. Yogarani, Fuzzy linear programming problem using polynomial penalty method. Bull. Pure Appl. Sci. Math. Stat. 38(1), 441–449 (2019) 14. A. Nagoor Gani, R. Yogarani, Solving fuzzy linear programming problem with a fuzzy polynomial barrier method. Int. J. Aquat. Sci. 12, 169–174 (2021) 15. A. Nagoor Gani, R. Yogarani, Solving fuzzy linear programming problem using a fuzzy logarithmic barrier method. Adv. Appl. Math. Sci. 20, 583–595 (2021) 16. A. Nagoor Gani, R. Yogarani, Fuzzy inverse barrier method to find primal and dual optimality solutions of fuzzy linear programming problems. Turk. J. Comput. Math. Educ. 12(9), 957–962 (2021) 17. X. Li, S. Pan, Solving the finite min-max problem via an exponential penalty method 8(2), 3–15 (2003) 18. W. Murray, H. Margaret Wright, Line search procedures for the exponential penalty function. SIAM J. Optim. 4(2), 229–246 (1994)

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19. A. Nagoor Gani, S.N. Assarudeen Mohamed, A new operation on triangular fuzzy number for solving fuzzy linear programming problem. Appl. Math. Sci. 6(11), 25–532 (2012) 20. K. Samia, D. Benterki, A relaxed exponential penalty method for semidefinite programming. RAIRO Oper. Res. 49(3), 555–568 (2015) 21. H.J. Zimmermann, Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst. 1(1), 45 (1978)

Chapter 10

Robust Optimization of Stock Portfolio Index IDX 30 Using Monte Carlo Simulation in Insurance Company Shofiayumna Felisya Putri and Gunardi

Abstract The increase in insurance premiums sold requires insurance company to prepare more reserve funds which will later be used to pay the claims of policyholders. In managing funds to prepare reserve funds, insurance company has to invest the insurance premiums. In investing in stocks, IDX30 is one of the best choices which prepared by Bursa Efek Indonesia (BEI) that used capped free float adjusted market capitalization weighted to define the assets weight. This research would compare Markowitz optimization, robust optimization using Monte Carlo simulation, and capped free float adjusted market capitalization weighted to define which method produces the highest return and Sharpe ratio. Robust optimization is carried out by assuming the worst-case scenario in the uncertainty set for uncertain parameters. This method was chosen because it can overcome the outliers contained in the data and can reduce the error in estimating the mean vector and variance–covariance matrix in the portfolio so that the portfolio can be more robust even though stock prices tend to fluctuate. The Monte Carlo simulation also chosen because this simulation is more realistic conditions related to investment information in optimization. The result is found that robust optimization produces the best portfolio with 5.8332% Sharpe ratio which is extremely high. This happened because robust optimization with Monte Carlo simulation can deal with the circumstances, especially when there are fluctuations in the closing stock price.

10.1 Introduction In the recent years, Indonesian people’s awareness of the importance of having insurance has increased. Of course, with more premiums sold, the insurance company must prepare more and more reserve funds which will later be used to pay the claims of policyholders. In managing funds to prepare reserve funds, there are several ways S. F. Putri · Gunardi (B) Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Yogyakarta, Indonesia e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Mustapha et al. (eds.), Proceedings of the 8th International Conference on the Applications of Science and Mathematics, Springer Proceedings in Physics 294, https://doi.org/10.1007/978-981-99-2850-7_10

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that insurance companies can do, one of which is by investing. The investment that will be made by this insurance company uses funds from insurance premiums that have been paid by the policyholder. There are several financial instruments to choose from to invest in, such as stocks, bonds, mutual funds, options, and others. Among these instruments, stocks have advantages compared to others, namely getting dividends and profitable for long-term investments because stocks are closely related to inflation. Therefore, the longer you invest in stocks, the greater the profit you get. However, before an insurance company decides to invest in stocks, there are several things that need to be considered, namely returns and risks. Return is the return that investors will get on the results of their investments. While risk is the difference between the expected return and the return obtained. Return and risk have a linear relationship, namely the higher the return that can be obtained, the higher the risk, and vice versa. In investing the funds, several strategies are needed to get the maximum return with a certain risk. In investing, it is impossible for an investor to get the maximum return and minimum risk due to the uncertain nature of the investment. Plus, stocks are an investment that has a high risk. Great risk arises when capital is only invested in one stock. To reduce the risks faced, investors usually diversify their investments by forming a portfolio consisting of several stocks. Diversifying losses in one type of investment can be compensated for by investing in other stocks owned by investors [1]. In determining which shares will be used for investment, it is advisable to do an analysis of all the listed shares. Then, choose stocks that tend to be safe and can bring about a large return. The purpose of stocks that tend to be safe can be seen from the company’s performance. Company performance is a measurement of the company’s achievements arising from the management decision-making process because it has a relationship between the effectiveness of capital utilization, efficiency, and profitability of performance activities. Performance that can be achieved by the company in a certain period is a picture of whether a company is healthy or not. Besides being able to provide profits for capital owners or investors, a healthy company can also show the ability to pay debts on time [2]. Thus, it can be concluded that good company performance can produce good returns. Until now, the number of companies listed on the Bursa Efek Indonesia as of February 21, 2022, is 782 companies. These companies are divided into eleven sectors: energy, raw materials, industry, primary consumption, nonprimary consumption, health, finance, property, technology, infrastructure, and transportation. To build a portfolio, the Indonesia Stock Exchange has prepared various types of stock portfolios that investors can choose based on the criteria for the stocks in it, one of which is the IDX30 Index. The IDX30 Index is part of the LQ45 Index which measures the price performance of thirty stocks that have high liquidity and large market capitalization, which are also supported by good company fundamentals. Based on the problems described above, the researcher is interested in conducting research on the analysis of optimizing the stock portfolio owned by an insurance company by diversifying using robust optimization with Monte Carlo simulation.

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Robust optimization is carried out by assuming the worst-case scenario in the uncertainty set for uncertain parameters. Then the set is brought into the worst-case scenario to get the optimal weight [3, 4]. This method was chosen because it can overcome the outliers contained in the data considering the current pandemic can cause stock prices to drop drastically or increase drastically. In a book written by Fabozzi et al. [5], it is stated that the mean–variance model has a high level of sensitivity to parameter changes. In addition to weighting, this method produces quite extreme weights for some assets in the portfolio. To overcome that problem, robust optimization can reduce the error in estimating the mean vector and variance– covariance matrix in the portfolio so that the portfolio can be more robust even though stock prices tend to fluctuate. There are so many other studies about robust optimization with different methods. Rosadi et al. [6] using robust covariance estimators for mean–variance portfolio optimization, such as Minimum Covariance Determinant (MCD), the S, the MM, and the Orthogonalized Gnanadesikan-Kettenring estimator. Min et al. [7] using machine learning-based trade-off parameter that propose the hybrid robust portfolio models under ellipsoidal uncertainty sets design the hybrid portfolios based on variance (HRMV) and value at risk (VaR). Isavnin et al. [8] using Black Litterman Model to reduce the sensitivity of resulting optimal portfolios to uncertain input parameters because the parameter values change every day. Basically, this method shed a light regarding the importance of the estimation error and weights’ stability in the portfolio allocation problem and the potential benefits coming from robust portfolios in comparison to classical techniques [9]. While the Monte Carlo simulation is used for more realistic conditions related to investment information in optimization [10]. The results of this study are expected to be able to provide new knowledge to insurance companies on how to compile an optimal stock portfolio to get the expected return.

10.2 Materials and Methods 10.2.1 Mean–Variance Portfolio Efficient Portfolio and Optimal Portfolio: The choice of a portfolio depends on the investor’s preference for the desired return and the risk that is willing to be borne [11]. In the portfolio discussion, there are two terms that are commonly used, namely efficient portfolio and optimal portfolio. An efficient portfolio is a portfolio that provides a maximum value of expected return with the same risk or a portfolio that provides a minimum risk of the same expected return compared to other portfolios. In an efficient portfolio, the term “efficient frontier” is known, which is a line formed from a number of efficient portfolios. This shows that all portfolios that are on the efficient frontier line are efficient portfolios and cannot be compared which one is better, while all portfolios below that line are declared inefficient. The optimal portfolio can be

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obtained from optimizing a single objective portfolio. Optimization single objective aims to minimize risk by the same expected return or maximizes expected return for the same level of risk. Assuming that short sale is not permitted, and investors ignore risk-free deposits and loans, the single objective portfolio optimization is formulated as follows.  min w T w Minimize risk with the same expected return is wT μ = μ  max w T μ Maximize expected return with the same level of risk is w T w = σ p2 The above optimization problem can be written as 10.1. max μT w − λw T w w

constraint w T e = 1

(10.1)

where e: [1, 1, …, 1]T w: weight of each stocks in portfolio. μ: expected return portfolio. : variance of the portfolio return. p: covariance of the return. λ: risk aversion coefficient or risk index for investors. Mean–Variance Portfolio Weighting: Weighting wm = w1 w2 · · · wN will be calculated in order to minimize risk because in the case of efficient portfolios, there is no limit on the mean portfolio which means that investors do not target a certain level of profit to be achieved so that wT μ is not used as a limitation in this portfolio weight optimization problem. The weighting of wm can be solved by the Lagrange function with two multipliers, namely λ1 and λ2 . Then we get the Lagrange function as follows: L = wT w + λ1(μp − wT μ) + λ2(1 − wT e)

(10.2)

To obtain the optimal value of w, the above equation will be partially derived from w and the result will be equalized to zero and can be obtained that the weighting of −1 the Markowitz portfolio model is w = eT −1e e .

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10.2.2 Optimization Robust Portfolio Optimization robust was developed to solve optimization problems regarding uncertainty in making decisions, so it is often referred to as uncertain optimization [12]. This robust model has been adapted into portfolio optimization to solve problems related to the sensitivity of the mean and variance of the portfolio. This optimization can also overcome the formation of an unstable and not optimal portfolio due to an error in the estimation of the parameters. So, it can be said that the optimization of this robust portfolio is used to represent all available information about the unknown parameter in the form of an uncertainty set containing the values of the most probable parameters. The absolute strategy of robust that minimizes risk is applied by assuming the worst-case scenario for all uncertainties. The main approach considered in the portfolio optimization literature is that the optimal solution can be calculated by assuming the worst realization in the uncertainty set for the uncertain parameter [3]. The optimal portfolio is obtained by solving the following optimization problem, namely:       max min μT w − λ max w T w w

μ∈Uμ

∈U

constraint w T e = 1

10.2.3 Robust Portfolio Allocation Based on Fabozzi et al. [5], another way in which uncertainty in input can be modeled is to consider it directly in optimization process. The robust optimization is an intuitive and efficient way to model this form of uncertainty. First, we discuss the robust version of the mean variance portfolio optimization problem when uncertainty is assumed to exist only in the estimate of expected return. We will show several ways to model uncertainty based on factor models and Bayesian statistics. Then the model will be expanded to include uncertainty into the return covariance matrix. We will therefore present an example of robust from the mean–variance optimization problem. There are many ways to describe uncertainty sets. In the worst-case scenario the optimization of robust assumes that the true parameter lies in the region of uncertainty centered around the estimated value: θU. The uncertainty region can be selected depending on the problem, namely: • Sphere region 

U = {θ |θ − θ 2) ≤ δ}

(10.3)

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• Box region 

U = {θ |θ − θ ∞) ≤ δ}

(10.4)

• Elliptical region 



U = {θ |(θ − θ )TS − 1(θ − θ )) ≤ δ2}

(10.5)

where S  0 is the shape of the ellipse. Uncertainty in Expected Return Estimation: An easy way to combine the uncertainty caused by estimation errors is to require investors to be protected if the estimated expected return μˆi for each asset is around expected return which is actually μi . The error of the estimate can be assumed to be no greater than a few small numbers δ i > 0. Box Set The simplest possible option for the uncertainty set is the method “box”.     Uδ m u = μ||μi − μi ≤ δi , i = 1, ..., N } 



(10.6)

δ i can be determined by assuming some confidence interval around the estimated expected return. For example, when the asset return is assumed to be normally distributed, the 95% confidence interval for μi can be found with λi = 1.96σ i /T, where T is the sample size used in the estimate. The robust formula of the mean–variance problem under the assumption μˆ i is: max

w μˆ T w − δ T |w| − λw T w constraint w T e = 1

(10.7)

Elliptical Set The advantage of the robust optimization approach is that the parameter values in the robust formula can be matched with probabilistic guarantees. For example, if the estimated expected return of assets is assumed to be normally distributed, then there is a ω% probability that the expected return will actually fall in the ellipse around the manager’s estimate of μ. According to Lobo and Boyd [13] and Zymler et al. [14], it is assumed that the uncertainty set in the elliptical region is as follows: 



U μ = {μ = μ + κ1/2u|u2 ≤ 1} This problem can be solved by:

(10.8)

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min μT w μ,μ

obstacles μ = μˆ + κ 1/2 u

97

(10.9)

You can use the Cauchy–Schwartz inequality to find the minimum value, which is as follows:

1 (10.10) μT w = w μT + κ 2 u = μT w + κw 1/2 ≥ μT w − κ|| 1/2 w||2 





1

w so, we get the robust formula as: with u = − ||1/22 w|| 2

  max μT w − κ  1/2 w 2 w

constraint w T e = 1

(10.11)

Uncertainty in Covariance Matrix Return Estimation: Optimizing the mean– variance portfolio is less sensitive to inaccuracies in estimating the covariance matrix than the estimation of errors in expected return. The portfolio optimization mean– variance robust can then be formulated as:       max min μT w − λ max w T w w μ∈Uμ ∈U (10.12) constraint w T e = 1 where U μ and U  is the uncertainty set of expected return and covariance, respectively. Box Set The confidence interval for the entries of the covariance matrix can be used to specify the interval for the individual elements of the covariance matrix: ≤≤ If the assumed interval for expected return estimates like this:     Uδ μ = μ||μi − μi ≤ δi , i = 1, ..., N } 



with short sales not allowed (w ≥ 0 and the  matrix is semi-definite positive, which means that the upper bound of the decreasing matrix is a well-defined covariance matrix. The resulting optimization problem is formulated by replacing μ with μˆ + δ and 4 with  in the formula mean–variance:  T max μ + δ w − λw T w 

w

(10.13)

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where it is equal to: 







max min μ w − λ max w w w

T

μ∈Uμ

T

 

∈U

constraint w T e = 1 In general, the formulation of robust counterpart is a convex problem. The result of this optimization is semi-definite program (SDP). More precisely, assuming as before that the estimate of expected return varies in the interval, then the robust formulation of the mean–variance problem is: 

max μT w − δ T (w+ , w− ) − λ  ,  −  ,  

w,w + ,w− , ,

constraint w T e = 1 w = w+ − w− , w+ ≥ 0, w− ≥ 0

≥



− wT



w 1

≥0  0

(10.14)

where the notation A, B for two symmetric matrices A, B stands for “(Tr( AB)”, the trace matrix for AB. Tr( AB) is equal to the sum of the diagonal elements for the AB matrix or can be expressed as: N (AB)ii = i = 1 N  j = 1 N (A)i j (B)i j Tr(AB) = i=1

(10.15)

Previously explained part of the formulation robust is related to the uncertainty of expected return. In order to reveal the derivative of the strong counterpart of the optimization problem i.e., SDP, it will be shown how to derive terms related to uncertainty in the covariance matrix. As before, start with the worst value for the portfolio variance wT w, which will occur if the estimated covariance matrix  varies within the  ≤  ≤ . For a fixed vector of portfolio weights w, it can be found by solving the optimization problem: maxw T w 

constraint ≤  ≤ 

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0

99

(10.16)

The problem above is a SDP. The dual problem of semidefinite program is:

,  −  ,  min  

w, ,

constraint − Z +

−

= ww

Z  0, ≥ 0, ≥ 0

T

(10.17)

  where and are dual variables associated with the constraint  ≤  ≤  and Z are explicit dual variables slack. The problem can be rewritten as:

,  −  ,  min  

w, ,

constraint



−

T

= ww  0

≥ 0, ≥ 0

(10.18)

  The constraint − = ww T  0 can be converted into the form linear matrix inequality (LMI) and becomes:

,  −  ,  min  

w, ,

 constraint

− wT



w 1

 0

≥ 0, ≥ 0

(10.19)

That way you can use the formula:

,  −  ,  min  

w, ,

(10.20)

instead of using maxw T w in the problem formulation for robust mean–variance. 

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Spherical Set 

Ben-Tal et al. [15] assume  =

1 XT T −1

X where X is the T × N matrix containing 

return data. Next, assume the data matrix is X and the actual matrix can be written as X = X + where is an error matrix constrained in its norm. Thus, the uncertainty set for the data matrix is:   (10.21) u x = X | X − X  F ≤ δ X 



Then the worst scenario is obtained from the robust formulation as follows: 1 X ∈u x T

min max w

XT Xw

constraint w T e = 1

(10.22)

In the inner maximization we can write:

1 T X X w = max  X + w22   F ≤δ X X ∈u x T 

max

(10.23)

We get the following upper bound:

 X + w2 ≤ X w2 + w2 



(10.24)

Next, we will look for the norm inequality:  w2 ≤   F w2 ≤ δ X | w2

(10.25)

with the equation found when is rank-one with the right-hand singular vector parallel to w and when   F = δ X . So, it can be seen that the upper limit is obtained if the error is selected as: 

= δX

X ww T 

w2 X w2

(10.26)

Then, we get:

2 maxw T X T X w = X w2 + δ X | w2 

X ∈u x

(10.27)

So the robust problem becomes: min  Xˆ w2 + δ X w2 w

constraint w T e = 1

(10.28)

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Elliptical Set Lobo and Boyd [13] also Lu [16] say that the uncertainty set of elliptical is as:   T u  = |(vec() − vec( ) S−1 (vec() − vec( ) ≤ δ2 ,   0 



(10.29)

where vec is the vectorization of a matrix,  determines the location, δ determines the size, and S determines the shape, while the worst-case scenario is: max w T w w  T

−1 2 ˆ ˆ constraint vec() − vec  S (vec() − vec  ≤ δ ,  ± 0

(10.30)

With the dual problem gets:   1  

  ˆ ww T + Z + δ  min Tr   S2 vec(ww T + vec(Z ) Z

2

constraint Z ± 0

(10.31)

If we put in the optimization problem robust, we get:   1 1





min max μT w − λ Tr  ww T + Z + δ S 2 vec(ww T + δ S 2 vec(ww T + vec(Z )2 

w,Z μ∈Uμ

constraint w T e = 1, w ∈ W Z 0

(10.32)

Because the above problem still contains complicated provisions, namely     X w T T  0. vec ww and .2 , then we use X  ww which will be written as wT 1 In this way, the optimization problem can be written as:



1 min max μT w − λ Tr  (X + Z ) + δ S 2 (vec(X ) + vec(Z )2 

w,X,Z μ∈Uμ

constraint w T e = 1, w ∈ W 

X w wT 1 Z 0



(10.33)

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10.2.4 Monte Carlo Simulation in Portfolio According to Fabozzi et al. [5], one way in which error estimation can be incorporated into the portfolio allocation process is by Monte Carlo simulation. This technique is based on resampling of the estimated input from the portfolio optimization process, or better known as resampling portfolio. Starting with the initial estimate for expected return, μ, and the covariance matrix,  . First solve for the global minimum variance of the portfolio (GMV) and the maximum portfolio return (MR). It is assumed that the standard deviations of this portfolio are σGMV and σMR where σGMV < σMR . Next, we define an equidistant partition interval [σGMV , σMR ] at point M(m = 1, . . . , M), such that σGMV = σ1 < σ2 < · · · < σ M = σMR . For each of these standard deviations, the corresponding maximum return portfolio is completed. Thus, the representation of efficient frontier with M portfolio is obtained. Denoted the portfolio weight vector corresponding to w1 , . . . , w M . So far we’ve only followed the way to construct the efficient frontier. Next, we will show the process of how to perform a Monte Carlo simulation on a portfolio: 







1. A random sample of T is drawn from a multivariate distribution N (μ,  ) and use this to estimate the new expected return vector, μi , and the covariance matrix, i . 2. Using μ and  , the appropriate global minimum variance and the maximum return portfolio, σGMV and σMR for i can be solved. Then, as before, partition the interval [σGMVi , σMRi ] becomes M equidistant points (m = 1, ..., M). For each standard deviation in the partition, the corresponding maximum return portfolio, w Mi , ..., w M j will be calculated. 3. Repeat steps 1 and 2 I times. 







Usually the parameter I is large, say around 100 or 500. Once the portfolio sampling has been completed for each point in the partition, the weight of the resampled portfolio will be calculated as the average: WM =

I 1 W M,i I i=1

(10.34) 



If efficient frontier is recalculated using the original input μ and  the new weights of the resampled portfolio, the latest resampling efficient frontier will appear under the original efficient frontier. This is because the weights w Mi , ..., w M j are efficient relative to μi and  i , but inefficient relative to the original estimates of μ and  . Therefore, resampling portfolio weights is also inefficient relative to μ and  . With resampling and re-estimation occurring at each step in the portfolio resampling process, the effect of the estimation error is incorporated into the weighting of the resampled portfolio. 











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10.3 Results and Discussion Data that used in this study are 10 stocks which is included in the IDX30 Index made by the Bursa Efek Indonesia (BEI). This index is part of the LQ45 Index which measures the price performance of thirty stocks that have high liquidity and large market capitalization, which are also supported by good company fundamentals. Table 10.1 presents the list of companies. The time series data span was from August 2, 2021 until February 21, 2022. The August 2, 2021 until January 28, 2022 observations were used as the first window to perform the estimation and the uncertainty set. The February 1, 2022 until February 21, 2022 observations referred to the out-of- sample period and were used for the exposé effectiveness analysis. This research uses raise the benchmark interest rate as a risk-free asset. Bank Indonesia Interest Rate (SBI) used is the BI 7 Days Reverse Repo Rate which is valid at the end observation period which is March 2022 at 3.5%. In Fig. 10.1, it can be seen that the daily closing price of each stock for 6 months from August 2, 2021 to January 28, 2022, experienced different fluctuations. The up and down movements of these stocks are caused by many things, one of which is the current state of the market related to the Covid-19 pandemic. From these asset prices, the return and risk will be searched which will later be used to find the weight of each asset. Based on the Fig. 10.2, we can see that the return of each stock has an outlier. Outlier is research data that has an extreme value or a value that differs greatly from most of the other values. The Outlier of the return shares is caused by the stock price fluctuating drastically. Stock with the fewest outliers is BBRI.JK with one outlier. Meanwhile, stock with the most outliers are ASII.JK with nine outliers. A slight outlier means that stock prices or returns did not experience significant fluctuations, while many outliers means that stock prices or returns have a quite significant fluctuate. From the 125 observations, the return and the risk of each stock is shown in Table 10.2. Table 10.1 Asset name for empirical analysis

No

Asset code

Asset name

1

BBRI.JK

Bank Rakyat Indonesia (Persero) Tbk

2

BBCA.JK

Bank Centra Asia Tbk

3

TLKM.JK

Telekomunikasi Indonesia (Persero) Tbk

4

BMRI.JK

Bank Mandiri (Persero) Tbk

5

ASII.JK

Astra International Tbk

6

BBNI.JK

Bank Negara Indonesia (Persero) Tbk

7

MDKA.JK

Merdeka Copper Gold Tbk

8

CPIN.JK

Charoen Pokphand Indonesia Tbk

9

UNTR.JK

United Tractors Tbk

10

ADRO.JK

Adaro Energy Indonesia Tbk

104

Fig. 10.1 Stock price plot

S. F. Putri and Gunardi

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105

Fig. 10.2 Stock return

Table 10.2 Risk and return

Asset code

Return

Risk

ADRO.JK

0.005096

0.000896

ASII.JK

0.001293

0.000428

BBCA.JK

0.002253

0.000198

BBNI.JK

0.003741

0.000402

BBRI.JK

0.000970

0.000314

BMRI.JK

0.002526

0.000271

CPIN.JK

0.000352

0.000296

MDKA.JK

0.002232

0.000849

TLKM.JK

0.002160

0.000285

UNTR.JK

0.001884

0.000593

10.3.1 Robust Optimization The first step is to choose the best set used in GMRP Robust, which is between the box set and the ellipsoid set. The results obtained that the ellipsoid set produces better weights than the box set because the ellipsoid set has a more diverse weight. Then choose the best set for GMVP Robust, the best set among box set, ellipsoid set, and sphere set is sphere set because it produces more stable weight than the other two. So GMVP Robust will use the sphere set. To determine the optimization of the robust portfolio, we will combine GMRP and GMVP where GMRP uses an ellipsoid set and GMVP uses a sphere set. To get the weight with Monte Carlo simulation, it will use I = 100.

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10.3.2 Capped Free Float Adjusted Market Capitalization Method IDX30 Index is using capped free float adjusted market capitalization method to determine the assets weight. This method is used by calculating the weighting on the stock index using the free float market capitalization as the weight and subject to a restriction (capping) usually 5–20%. This restriction is carried out with the hope that the movement of a stock index is not dominated by certain stocks. This free float market capitalization itself is the total scripless shares owned by investors with a share ownership of α2i π . det(diag(λ, λ, . . . , λ) − J = 0

(12.5)



Theorem 2. [4] Suppose that αi s are incommensurate rational numbers in the interval (0, 1) and (1, 2). Let M be the lowest common multiple (LCM) of the denominators vi of αi ’s, where αi = uvii , (u i , vi ) = 1, u i , vi ∈ Z+ , i = 1, 2, . . . , n and η = M1 . Then, the equilibrium point of dynamical system (12.4) with Caputo . derivative is stable if and only if (12.6) satisfies |arg(λ)| > ηπ 2   det(diag λ M×α1 , λ M×α2 , . . . , λ M×αn − J = 0

(12.6)

12.2.2 Stability Analysis of Two-Dimensional Fractional-Order Lotka-Volterra System Before choosing an appropriate stability theorem, we need to find the eigenvalues. There are three general steps to compute the eigenvalues. Firstly, we need to find the equilibrium points. Based on the system (12.2), it has two equilibrium points denoted as (0, 0) and ( γδ , βθ ). Next, we calculate the Jacobian matrices. As a result, the general Jacobian matrices are calculated as: 

−βx2 + θ −βx1 J= δx2 δx1 − γ

 (12.7)

Lastly, we can find eigenvalues and decide the stability for each equilibrium point. At the last step, there is a distinction when finding the eigenvalues. When the fractional-orders of system (12.2) are commensurate, Theorem 1 can be used

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directly whereas Theorem 2 can be utilized for incommensurate fractional-order system (12.2).

12.2.3 Adams–Bashforth–Moulton Method Since time-series plot and phase plane are adopted to verify the stability analysis of fractional-order dynamical system (12.2) and also observe its behaviors, Adams– Bashforth–Moulton method which is also a type of predictor–corrector method will be applied to generate the simulations. Before proceeding to the algorithms of Adams–Bashforth–Moulton method, consider the fractional dynamical system as follows: D αi xi (t) = f i (xi ), x r (0) = x0r

(12.8)

with αi ∈ (0, 1), (1, 2), i = 1, 2, . . . , n, r = 0, 1, 2, . . . , m − 1 and m = [αi ] is the value of αi rounded up to the nearest integer. According to (12.8), we can denote input variables that consist of: fi αi x0 T N

A right-hand side function of the fractional dynamical system (12.8). The order of fractional dynamical system (12.8).  An array of [αi ] that have the initial values x(0), x (0), …, x m−1 The upper bound of the interval. The number of time steps.

Next, some internal variables are needed to introduce. They play important role in the processes of algorithms. Therefore, the internal variables are: h m j, k a, b p

The step size of the algorithm. The number of initial conditions specified. Integer variables used as indices. The weights of corrector and predictor formulae respectively. The predicted value.

For the weights of corrector and predictor formulas, they are: a[k] = (k + 1)α+1 − 2k α+1 + (k − 1)α+1

(12.9)

b[k] = k α − (k − 1)α

(12.10)

Having the related variables, the algorithms of Adams–Bashforth–Moulton method can proceed in two steps. At the initial step, it is the predictor step. It starts from the current value xi in order to calculate an initial guess value p.

12 Stability Analysis of the Fractional Order Lotka-Volterra System

p=

m−1  k=0

 hα ( j h)k x0 [k] + b( j − k) f (kh, x[k]). k! (α + 1) k=0

135

j−1

(12.11)

The next, corrector step refines the initial approximation by using the predicted value (12.9) of the function. It is also the output of the solution of (12.8). The corrector function is defined as: x[ j] =

m−1  k=0

+

hα ( j h)k x0 [k] + ( f ( j h, p) + ( j − 1)α+1 − ( j − 1 − α) j α f (0, x[0]) k! (α + 2)

j−1 

a( j − k) f (kh, x[k]))

k=0

12.3 Results and Discussion In this section, a Maple program is created and implemented in order to generate the simulations of the system (12.2). We will use them to discuss their dynamics and ensure the theorems are valid.

12.3.1 Commensurate Fractional-Order Lotka-Volterra System When α1 and α2 are in the interval (0, 1), we fix the parameter values θ = 0.9, β = 0.5, δ = 0.25, γ = 0.75 with initial conditions x1 (0) = 0.2 and x2 (0) = 0.5. Figure 12.1 shows the simulations of this example with the commensurate α1 = α2 = 0.8 and also 0.9. Based on the stability analysis theorem, it also shows that the equilibrium point (3,1.8) is stable. As we can also see, from Figure 12.1, within the specified time (t=40), (3,1.8) is a stable spiral when commensurate α1 and α2 are 0.8 and 0.9 respectively. Looking at Fig. 12.1 again, it can also be seen that the system with the same fractional-order 0.8 converges to the stable equilibrium faster than that of 0.9. Next, assuming another commensurate fractional-order α1 and α2 in the interval (1,2), that is 1.2. We also let other parameters and also the initial conditions of the system (12.2) as shown in Fig. 12.2. In theory, the system yields both unstable equilibrium points, (0,0) and (50,40). Consequently, as it is expected, the state trajectory of the system moves away from the equilibrium points, which seem to be an unstable node and spiral point for equilibrium (0,0) along with (50,40). To sum up this example, the numerical results are consistent with the theory. Figure 12.3 is showing another example of the system (12.2) with α1 = α2 = 1.15. By using the theory, there are also two unstable equilibrium points, (0,0) and

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Fig. 12.1 Simulations of commensurate (12.2) when θ = 0.9, β = 0.5, δ = 0.25, γ = 0.75 with x1 (0) = 0.2 and x2 (0) = 0.5 (Note: (a), (b) α1 = α2 = 0.8, (c), (d) α1 = α2 = 0.9)

(50,40). In the other words, according to the observation (Fig. 12.3), the system is keeping away from the equilibrium points in the long run. From that, it can be briefly concluded that the numerical outcome proves the outcome of the theory is valid.

12.3.2 Incommensurate Fractional-Order Lotka-Volterra System Similarly, for incommensurate fractional-order of system (12.2) which is in the interval (0,1), as shown in Fig. 12.4, the same parameters will be adopted too

12 Stability Analysis of the Fractional Order Lotka-Volterra System

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Fig. 12.2 Simulations of commensurate (12.2) when θ = 0.1, β = 0.0025, δ = 0.005, γ = 0.25   with x1 (0) = 70, x2 (0) = 30, x1 (0) = 1.75 and x2 (0) = 3 (Note: (a), (b) α1 = α2 = 1.2)

Fig. 12.3 Simulations of commensurate (2) when θ = 0.2, β = 0.005, δ = 0.01, γ = 0.5 with   x1 (0) = 70, x2 (0) = 30, x1 (0) = 3.5 and x2 (0) = 6 (Note: (a), (b) α1 = α2 = 1.15)

that are already set in the case commensurate fractional-order between 0 and 1. From Fig. 12.4, it is clear that the fractional-order Lotka-Volterra system with fixed parameters and the given initial conditions is stable along the time at the stable spiral point (3,1.8). Based on the theorem result, it stated that (3,1.8) is a stable point too. Consequently, it is undoubtedly the same with the outcomes of the related theorem. In a similar fashion, we use the other examples when the incommensurate fractional-order of system (12.2) is in between 1 and 2. According to the example as presented in Fig. 12.5, the related theorem also states that the system (12.2) will

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Fig. 12.4 Simulations of incommensurate (2) when θ = 0.9, β = 0.5, δ = 0.25, γ = 0.75 with x1 (0) = 0.2 and x2 (0) = 0.5 (Note: (a), (b) α1 = 0.8, α2 = 0.9, (c), (d) α1 = 0.9, α2 = 0.8)

be unstable since there are two unstable equilibrium points (0,0) and (50,40). If we look into the plots, the positive equilibrium (50,40) could be a central point, meaning that the number of prey and predator will always orbit or oscillate around 50 (prey population) and 40 (predator population) respectively Thus, we can conclude that the numerical results are satisfied with the conditions of Theorem 2. Before talking about the patterns, we check the stability results by using the theorem. In the same way, the system yields two equilibrium points too: (0,0) and (20,50). Referring to the eigenvalues of both equilibriums, their equilibriums are not in a steady-state so that the system in this example is said to be unstable. Then, we also have sufficient evidence to say that the outcomes from the simulations as well as the theory are consistent. Over and above that, looking at the results of Fig. 12.6,

12 Stability Analysis of the Fractional Order Lotka-Volterra System

139

Fig. 12.5 Simulations of commensurate (2) when θ = 0.2, β = 0.005, δ = 0.01, γ = 0.5 with   x1 (0) = 70, x2 (0) = 30, x1 (0) = 3.5 and x2 (0) = 6 (Note: (a), (b) α1 = 1.2, α2 = 1.1)

we can see that the variation of the prey and predator populations are decreasing when the time, t is around at 10. After that, the simulation becomes periodic. The cycle will continue with the rise and fall of both populations. Moreover, the periodic solution is always passing through the equilibrium point (20,50).

Fig. 12.6 Simulations of commensurate (2) when θ = 1, β = 0.02, δ = 0.02, γ = 0.4 with x1 (0) =   30, x2 (0) = 20, x1 (0) = 18 and x2 (0) = 4 (Note: (a), (b) α1 = 1.1, α2 = 1.4)

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12.4 Conclusion In this paper, we have used two stability analysis theorem for fractional-order dynamical system to compute the stability criterion for the two-dimensional fractional-order Lotka-Volterra system. The stability theorems are also for the fractional-order in the interval (0,1) as well as (1,2). For every stability result, it was verified by the famous predictor–corrector method for fractional-order dynamical systems, Adams–Bashforth–Moulton Method. According to each for a stable fractional-order

example, γ θ Lotka-Volterra system, the equilibrium δ , β could be a stable spiral point. On the other hand, it could be an unstable spiral point or a central point if there is an unstable fractional-order Lotka-Volterra system. For the equilibrium point (0,0), it is always not a stable point without considering the commensurate and incommensurate fractional-order of the system. However, a lot of works can be done by solving the incommensurate fractional order via modification of some existing numerical scheme for solving fractional differential equations such as those operational matrix methods [6, 7]. Besides, ones may need to study other fractional derivative such as Caputo-Hadamard derivative [8]. Analytical solution for incommensurate fractional system also worth be studied [9]. These works will probably be part of our future research work.

References 1. I. Petráš, Chaos in fractional-order population model. Int. J. Bifur. Chaos 22(4), 1–6 (2012) 2. C.P. Li, F.R. Zhang, A survey on the stability of fractional differential equations. Eur. Phys. J. Special Top. 193(1), 27–47 (2011) 3. F. Merrikh-Bayat, More details on analysis of fractional-order Lotka-Volterra equation. arXiv Prepr. arXiv (2013) 4. M.S. Tavazoei, M. Haeri, A note on the stability of fractional order systems. Math. Comput. Simul. 79(5), 1566–1576 (2009) 5. K. Diethelm, N.J. Ford, A.D. Freed, A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dyn. 29(1–4), 3–22 (2002) 6. C. Phang, Y.T. Toh, F.S. Md Nasrudin, An operational matrix method based on poly-Bernoulli polynomials for solving fractional delay differential equations. Computation 8(3), 82 (2020) 7. C. Phang, Y.T. Toh, A. Isah, Poly-Genocchi polynomials and its applications. AIMS Math. 6(8), 8221–8238 (2021) 8. Y.X. Ng, C. Phang, J.R. Loh, A. Isah, Analytical solutions of incommensurate fractional differential equation systems with fractional order 1 < α, β < 2 via bivariate Mittag-Leffler functions. AIMS Math. 7(2), 2281–2317 (2022) 9. Y.T. Toh, C. Phang, Y.X. Ng, Temporal discretization for Caputo-Hadamard fractional derivative with incomplete Gamma function via Whittaker function. Comput. Appl. Math. 40(8), 1–19 (2021)

Part II

Statistics

Chapter 13

Gender Comparative Patterns of Online Gaming Among University Students Nur Izzah Jamil, Kum Yoke Soo, Noriah Ismail, and Mohammad Abdullah

Abstract The COVID-19 pandemic has led to more online learning among students, hence providing greater access to online devices which also intensify their online gaming activities to the point of addiction. This study investigates undergraduate students’ gender differences in online gaming behavior as well as their perception of the positive and negative implications of online gaming on their academic performance. This quantitative study was conducted using online survey approach. The data was primarily collected through online questionnaires using the Google Form platform. After the data was collected in Google Form, it was screened and transferred to SPSS for analysis. Thereafter, descriptive statistics and a comparison of means were used to achieve the objectives of this study. The main objective is to investigate gender differences in online gaming behavior. In contrast to previous studies that showed male students’ tendency to be more addicted to online gaming, this study revealed that male and female students did not show a significant difference in this aspect. This study also sheds some light on their online gaming behavior with both negative and positive implications for online learning.

N. I. Jamil · K. Y. Soo (B) Universiti Teknologi MARA, Cawangan Negeri Sembilan, Kampus Rembau, 71300 Rembau, Negeri Sembilan, Malaysia e-mail: [email protected] N. Ismail Universiti Teknologi MARA, Cawangan Johor, Kampus Segamat, 85000 Segamat, Johor, Malaysia M. Abdullah Universiti Teknologi MARA, Cawangan Johor, Kampus Pasir Gudang, 81750 Masai, Johor, Malaysia © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Mustapha et al. (eds.), Proceedings of the 8th International Conference on the Applications of Science and Mathematics, Springer Proceedings in Physics 294, https://doi.org/10.1007/978-981-99-2850-7_13

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13.1 Introduction Nowadays, many people have found pleasure in playing online games on their computers or mobile devices in their spare time and even more so during the pandemic lockdown. People play online games for various reasons including to relieve stress, as a form of relaxation and as a form of escapism from their daily affairs. Puzzle games have also been found to improve mental alertness. While some games appear harmless, others have been found to promote aggressive and violent behaviors. Moreover, [7] defined online gaming as a form of game played on any device that has an Internet connection. In effect, online gaming is a growing technological culture trending among youngsters in modern society. It has become a part of the global technological civilization that has impacted global citizens including students. There is nothing surprising in students spending a lot of their time playing online games. However, such indulgence may affect them positively and negatively. According to King et al. [13], stay-at-home mandates and quarantines related to the COVID-19 pandemic have greatly increased participation in online gaming. To this effect, students can develop an addiction to online gaming where it is almost impossible to quit playing to the point of replacing all social activities such as social meetings, academic discussions, and outdoor activities [22]. Game developers or creators feed on this to profit from gamers by requiring real money investments for completing missions and buying advantages. In fact, Choo [3] found that university and college students were most vulnerable and at a greater risk of being lured to Internet addiction. Balhara et al. [2] asserted that the uncertainty of the lockdown due to COVID-19 on the future of university students, besides other concerns, has caused them to be particularly vulnerable to stress, and to cope with this, online gaming has been found to be a coping mechanism for them. Since online gaming has become so popular, the objectives of this study will focus on identifying the types of online games university students play and the amount of time and money they spend on online gaming. Furthermore, this study will also focus on the students’ perception on positive and negative implications to online gaming toward their academic performance. In addition, a comparison of means analysis will be used to investigate gender differences in online gaming behavior. To begin with, the study will first review previous literature on this area of research. In recent times, digital activities such as online gaming had significantly increased due to the COVID-19 lockdown [11, 23]. In Italy for example, it was reported that there was an increase of 70% in Fortnite gaming-related Internet traffic [17]. Likewise, US-based telecommunications provider, Verizon, reported a 75% increase in online gaming activities at the initial stay-at-home directives [21]. Online gaming is a popular leisure activity for many people as it can be a stress reliever. Further, the study found that learning takes place unexpectedly where students learn to solve problems, overcome tight situations, be alert and active, and be able to strategize all in the fun of a game. Kuss and Griffiths [16] asserted that youths playing online games find it fun as the games lack seriousness. Li et al. [18] studied the use of digital gaming in the language classroom and found that there

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was progress in vocabulary recall and transfer as well as improvements in writing and listening for game-based language learning. Granic et al. [9] found that online gaming can enrich people’s lives. In the study by Kwon et al. [14], high involvement in gaming was found to be not necessarily problematic and can be adaptive and reduce loneliness. Some researchers have found that online gaming is less harmful than other adverse behaviors to cope with stress such as alcohol and drug abuse as well as overeating [4, 24]. Till date, however, the effects of online gaming have been debated continuously. Numerous past research have shown both positive and negative effects of online gaming on students, especially on their academic performances [6, 8, 20]. The study by Pantling [20] looked at the effect of online games to the academic performance of students in the College of Teacher Education, and the results revealed that there was no significant difference between online gaming and academic performance, thus indicating that students playing online games were still able to perform academically well. Similarly, [5] found that playing online games did not affect students’ grades badly as they were able to discipline and control their online playing behavior. In fact, the study revealed that boys were better players than girls on team games such as League of Legends, Clash of Clans and Crossfire, but both did not show poor academic performance. The study conducted by Garcia et al. [8] on the negative effects of online games on academic performance showed that online game players had an average academic performance, while non-players had a high academic performance. There was also significant correlation between their grades and their playing hours which led to recommendations for parents to monitor student online gaming time. The growth of technology has resulted in societies spending more time online, which has indirectly resulted in Internet addiction among youths [15, 26]. In fact, remote schooling and limited outdoor activities due to the pandemic have led to an unprecedented rise in gaming addiction [13]. As long as an Internet connection is accessible, any online game can be reviewed and played on a variety of platforms, including personal computers, laptops, tablets and smartphones. As a result, today’s youth are seeing significant changes in their Internet usage. The percentage of Malaysians who use the Internet rose by 7.2% from 68.7 to 75.9% in 2016 [19]. This indicates that modern technology has a significant influence on society’s culture especially in terms of student online gaming habits. Previous study by Rosendo-Rios et al. [25] asserted that the current pandemic has provided greater access to online devices among children and young adults, thus intensifying their online gaming activities to the point of addiction. They explained that online gaming addiction is a persistent and recurrent use of the Internet to engage in games that could significantly impair or distress a person’s life. The World Health Organization [28] further elaborates that this persistent behavior is manifested by (i) impaired control over gaming; (ii) increased priority for gaming to the extent that it takes precedence over other activities; and (iii) continual gaming despite negative consequences. The consequences are impairment in the functioning of personal, family, social, educational, and occupational activities.

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In addition, Islam et al. [10] found that academic performance was affected by the time spent by children playing electronic games. In their study of Australian children, addiction to Internet and electronic games was adversely related to academic achievement. The longer they spend on the Internet playing online games, the greater their tendency to become addicted to the games. This reflects a negative development or an impairment that could not only affect academic performance, but lifestyle and culture and as indicated by Rosendo-Rios et al. [25] could lead to impairment and distress. Furthermore, studies have also been done on gender and Internet gaming. Arshad et al. [1] found that male adolescents showed significantly higher scores in Internet gaming disorder compared to female adolescents. Jayalath and Samaranayake [12] compared the computer and Internet using patterns among male and female students, and the findings indicated that there was a significant relationship between gender and formal learning classes. While there was no difference among the genders in terms of time spent and purpose of Internet and computer utilization, females tend to seek more formal learning computer and Internet usage compared to males. Su et al. [27] examined gender-related differences in specific Internet addiction and found that there were specific behavior-related differences in Internet addiction of males and females, whereby male online behavior leaned toward Internet gaming addiction while female online behavior leaned toward social media addiction. Hence, in relation to current literature on online gaming and its implication to academic performance, this study intends to investigate the online gaming behavior of undergraduates of different genders and the relations of online gaming to their academic performance. Thus far, the study has looked at past literature related to online gaming. In the next section, the study will focus on the present study and the methods applied for the study.

13.2 Methodology This study was carried out in 2021 through an online survey approach using fivepoint Likert scale to determine the perception of online gaming behavior among undergraduates. The data was primarily collected through online questionnaires using the Google Form platform. The questionnaires were divided into Part A and Part B. Part A consisted of the demographic profile items formulated using multiple choice type of questions, while Part B consisted of online gaming behavior items using the five-point Likert scale type of questions. The online questionnaire was administered using convenience sampling. Convenience sampling is a type of non-probability sampling in which respondents have an uneven chance of being selected by random selection procedure. The total sample size amounted to 120 respondents based on the online feedback received. As such, the results from this study provided summaries and conclusions about the sample involved, but the results cannot be used to infer to the population.

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To accomplish this, students filled out a gaming habits survey which was analyzed using SPSS version 26. Pilot study of 30 students indicates Cronbach alpha of 0.755 and real fieldwork of 0.747 suggesting that the items have acceptable internal consistency. After the data was collected in Google Form, it was screened and transferred to SPSS for analysis. Thereafter, the descriptive statistics and comparison of means were used to achieve the objectives of this study. Descriptive statistics were used to identify the types of online games university students played and the amount of time and money they spent in online gaming. Besides, this study focused on the students’ perception on positive and negative implications to online gaming toward their academic performance. Furthermore, comparison of means analysis was used to investigate gender differences in online gaming behavior. Thus, the hypothesis for this study if there is any significant difference in online gaming behavior between male and female is as follows: Null hypothesis: The means for the two populations are equal. Alternative hypothesis: The means for the two populations are not equal.

The summation of five items of online gaming behavior was used as the assumptions that the dependent variable must be continuous (online gaming behavior), with categorical independent variable that has two levels, male and female. This categorical independent variable is also called unrelated groups, unpaired groups or independent groups, where the cases in each group are different. Thus, a parametric test of independent t-test was used. The independent t-test requires that the dependent variable be approximately normally distributed within each group. However, since both group’s data are not approximately normally distributed, nonparametric Mann–Whitney U test was used. If the p-value is less than the significance level of 0.05, the null hypothesis is rejected. Also, nonparametric test does not require the assumption of normality which made it a suitable choice for analysis.

13.3 Results and Discussion 13.3.1 Types of Online Games University Students Play Figure 13.1 shows the bar chart of types of online games university students play. Most of the university students played sports games (67.5%) followed by action and adventure games which were 57.5 and 45%, respectively. On the other hand, in the types of games played, horror got the lowest percentage (15%). In fact, based on Fig. 13.2 the popularity of online gaming based on favorite votes among them is Mobile legend (47.5%), Among us (47.5%) and PUBG (42.5%). The other favorite games included Valorant (20%), Minecraft (15%) and Mario Kart Rider (15%) which are still really popular even after over a decade of their launch.

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Fig. 13.1 Types of online games played

Fig. 13.2 Online games played

13.3.2 The Amount of Time and Money Spent in Online Gaming This study revealed the amount of time and money students spent playing online games in a week. Table 13.1 shows that the time spent was mostly only 1 to 2 days in a week (62.5%). Only a few of the students reported playing online games more often (7.5%) and about 10% admitted spending time playing every day. The result also

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Table 13.1 Amount of time and money spent in online gaming Items

Responses

Percent

How often do you play games in a week?

1–2 days

62.5

3–4 days

20.0

Roughly how many hours do you spend playing games each day?

At what time do you usually play games?

5–6 days

7.5

Everyday

10.0

1 h or less

35.0

2–3 h

52.5

4 h or more

12.5

After midnight 30.0 Night

62.5

Noon

7.5

Do you still find the time to play games when you are busy (e.g., having classes)?

No

65.0

Yes

35.0

How much money have you spent on online games (for the past 12 months)

RM 200 and below

87.5

RM 201–RM 500

7.5

RM 501–RM 700

5.0

showed that those who play online games mostly play only for about 2 to 3 h each day (52.5%). Most of the students favored playing during the night with the highest percentage of about 62.5%. Perhaps, students know the need to control themselves to perform well in their academics where about 65% spend more time playing games during their free time or during weekends compared to when they had classes. Majority of these students spent their money moderately on online games (for the past 12 months) which is RM200 and below. This could depend on their money allowance. Students should look at real needs rather than spend money on virtual purchases.

13.3.3 Perception on Positive and Negative Implications to Online Gaming Toward Students’ Academic Performance The study also investigated the gaming behavior of students in relation to positive and negative implications toward their academic performance. A five-point Likert scale was used with the quantifiers: Strongly Disagree, Disagree, Neutral, Agree and Strongly Agree. Table 13.2 shows that the students perceive that online games have both negative and positive impact on their performance. As shown in Table

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13.2, many students were neutral with regard to their perception on online games and its effect to their study time (37.5%) and their priority over performing daily tasks (32.5%). However, due to hours spent playing online games, forty percent of students agreed this may highly affect their sleeping schedule. Understandably, this could influence a student’s academic performance. Moreover, Table 13.2 also shows that there were also positive views. Majority of the students (40%) strongly agreed that playing online games enhanced their memory and their alertness and concentration. Most of them (80%) agreed that playing online games helps them to get away from problems faced in their study. It could be said that self-control is the key for their academic performance. Spending too much time playing online games cuts off students’ learning time, assignment Table 13.2 Perception on positive and negative implications to online gaming toward students’ academic performance Items

Level of agreement

Percent

Online games affect my time to study

SD

10.0

D

17.5

N

37.5

Online games take priority over performing daily task

Online games affect my sleeping schedule

Playing online games enhances my memory, brain’s speed and concentration

Playing online games helps me to get away from my problem in study

A

12.5

SA

22.5

SD

10.0

D

17.5

N

32.5

A

20.0

SA

20.0

SD

5.0

D

7.5

N

20.0

A

40.0

SA

27.5

SD

0.0

D

0.0

N

35.0

A

25.0

SA

40.0

SD

0.0

D

2.5

N

17.5

A

40.0

SA

40.0

13 Gender Comparative Patterns of Online Gaming Among University … Table 13.3 Shapiro–Wilk test

151

Gender

Statistic

Degree of freedom

Male

0.877

42

p-value 0.000

Female

0.877

78

0.000

and social interaction with others. In spite of that, strictly forbidding students from playing online games may prevent them from getting some of the benefits that online games offer.

13.3.4 Gender Differences in Online Gaming Behavior The Shapiro–Wilk test (Table 13.3) was used to test the normality of the dataset as the sample size of 120 was less than 2000. As the p-value is less than 0.05, it was concluded that online gaming behavior is not normally distributed for both male (SW = 0.877, p-value 0.000 < 0.05) and female (SW = 0.877, p-value 0.000 < 0.05) students. This is supported by Fig. 13.3 (normal Q-Q plot) and Fig. 13.4 (histogram) that showed both the departure from normality at 25. Thus, Mann–Whitney U test was used to identify if there was any significant difference in online gaming behavior between the male and female groups. Further result reported on Table 13.4 is that the mean rank for the two groups was tested; male (68.32) and female (56.29). This indicates which group had the higher positive online gaming behavior. In this case, the male respondents had the higher positive online gaming behavior compared to the female respondents by ranks. Table 13.5 shows the Mann–Whitney test as there is no significant difference in the online gaming behavior between the male and female students (U = 1309.500, z = − 1827, p-value = 0.068 > 0.05). Failing to reject the null hypothesis indicates that the sample used in this study did not provide sufficient evidence to conclude that a difference existed in online gaming behavior between male and female students.

Fig. 13.3 Normal Q-Q plot of online gaming behavior (male and female)

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Fig. 13.4 Histogram of online gaming behavior (male and female)

Table 13.4 Mean ranks for the groups

Table 13.5 Test statistics (grouping variable: gender)

Gender

Mean rank

Male

68.32

Female

56.29

Mann–Whitney U Z P-value

1309.500 − 1.827 0.068

13.4 Conclusion This study on gender comparative patterns of online gaming among university students aimed at investigating the online gaming behavior patterns of university students of different genders and the students’ perception of the relations of online gaming to their academic performance. The objectives were to identify the types of online games university students play and the amount of time and money they spent in online gaming, in addition to identifying students’ perception on positive and negative implications to online gaming toward their academic performance and to investigate gender differences in online gaming behavior. Based on the findings, it was found that the most favored type of online games by university students was sports games followed by action and adventure games and the least favored was horror type of games. The most popular online games were Mobile legend, followed by Among us, PUBG, Valorant, Minecraft and Mario Kart Rider. In terms of time spent on online gaming, the analysis of the study thus far has shown that students are able to control themselves when playing online games and only few of them reported playing online games more often than others. Furthermore, it was found for this study that many students prefer to play online games late into the night. It is suggested that students arrange weekends or other free time to spend more time to play games compared to when they have classes during the weekdays.

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In this case, playing online games only during the weekend or during their free time can give them a chance to have a balance between their study and play. This study also looked at the cost of playing online games among university students. The average estimated cost for supporting students’ online gaming is generally low, at RM200 and below. With the amount of time spent in online gaming, this could mean that students may have played online games that are installed for free. On the Internet, many games are free to be installed without cost, but charges are imposed for all kinds of extras. In such a situation, students need to be conscious of the advantages they are paying for to further their online gaming levels. Students therefore are suggested to budget according to their needs and wants when making online virtual purchases. In relation to positive and negative implications of online gaming to students’ academic performance, it was found that gaming late into the night has been associated with higher levels of daytime sleepiness where almost half of the students involved in this study agreed this issue affected their sleeping schedule. As such, this could influence their academic performance since they may not be able to fully concentrate in class. Besides that, the choice of gaming on just weekends or during free time seems a better choice as most of the students can spend more time to play games freely compared to when they have classes during the weekdays. In this case, playing online games only during the weekend or during free time can give them a chance to have a balance between study and play. Previous studies support this [6, 8, 20] with both negative and positive implications to online learning and recommendations for self-control as the key for students’ academic performance. Spending too much time playing online games cuts off students learning time, assignment and to interact socially with people. However, strictly forbidding students from playing online games may prevent them from getting some of the benefits that online games offer. By comparison, male and female students did not show significant difference in their online gaming behavior. However, in the study conducted by [1], it was found that male students showed avid online gaming behavior compared to female students. Similarly, [27] found that there was greater possibility for male students to become addicted to online gaming than female students. This study indicates sample used in this study did not provide sufficient evidence to conclude that the difference existed in online gaming behavior between male and female students. Thus, future research may increase the respondents of the study in which this may point the researcher in different directions in this area of study. Acknowledgements The authors would also like to thank Universiti Teknologi MARA, Malaysia, for the support and keep us motivated throughout the study.

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References 1. S. Arshad, R. Begum, A study of internet gaming disorder among adolescents and its correlation with age and gender. Indian J. Physiotherapy Occup. Ther. 16(1), 131–137 (2021) 2. Y.P.S. Balhara, D. Kattula, S. Singh, S. Chukkali, R. Bhargava, Impact of lockdown following COVID-19 on the gaming behavior of college students. Indian J. Public Health 64(Supplement), S172–S176 (2020) 3. K.K.R. Choo, The cyber threat landscape: challenges and future research directions. Comput. Secur. 30(8), 719–731 (2011) 4. W.R. Corbin, N.M. Farmer, S. Nolen-Hoekesma, Relations among stress, coping strategies, coping motives, alcohol consumption and related problems: a mediated moderation model. Addict. Behav. 38(4), 1912–1919 (2013) 5. D.O. Dumrique, J.G. Castillo, Online gaming: impact on the academic performance and social behavior of the students in polytechnic university of the Philippines laboratory high school. KnE Social Sciences, pp. 1205–1210. Dubai, United Arab Emirates. (2018) 6. Qaisar, S.: Positive and negative effects of online gaming. Retrieved from https://www.tec hbead.com/positive-and-negative-effects-of-online-gaming/#:~:text=Bad%20Academic%20P erformance%20%E2%80%93%20Playing%20online,time%20in%20playing%20online% 20games 7. C.B. Freeman, Internet gaming addiction. J. Nurse Pract. (JNP) 4(1), 42–47 (2008) 8. K. Garcia, N. Jarabe, J. Paragas, Negative effects of online games on academic performance. Southeast Asian J. Sci. Technol. 3(1), 69–72 (2018) 9. I. Granic, A. Lobel, R.C. Engels, The benefits of playing video games. Am. Psychol. 69(1), 66–78 (2014) 10. M.I. Islam, R.K. Biswas, R. Khanam, Effect of internet use and electronic gameplay on academic performance of Australian children. Sci. Rep. 10, 21727 (2020) 11. J. Javad, eSports and gaming industry thriving as video games provide escape from reality during coronavirus pandemic. (2020). Retrieved from https://www.wfaa.com/article/sports/ esports-gaming-industry-thriving-as-video-games-provide-escape-from-reality-during-cor onavirus-pandemic/287-5953d982-d240-4e2b-a2ba-94dd60a8a383 12. L. Jayalath, D. Samaranayake, Does gender role influence the pattern of internet and computer use among physiotherapy undergraduates? South-East Asian J. Med. Educ. 15(1), 50–57 (2021) 13. D.L. King, P.H. Delfabbro, J. Billieux, M.N. Potenza, Problematic online gaming and the COVID-19 pandemic. J. Behav. Addict. 9(2), 184–186 (2020) 14. O. Király, D. Tóth, R. Urbán, Z. Demetrovics, A. Maraz, Intense video gaming is not essentially problematic. Psychol. Addict. Behav. 31, 807–817 (2017) 15. M. Kwon, J.Y. Lee, W.Y. Won, J.W. Park, J.A. Min, C. Hahn, X. Gu, J.H. Choi, D J. Kim, Development and validation of a smartphone addiction scale (SAS). PloS one 8(2), e56936 (2013) 16. D.J. Kuss, M.D. Griffiths, Adolescent online gaming addiction. Educ. Health, 30(1), 15–17. (2012) 17. D. Lepido, N. Rolander, Housebound Italian kids strain network with Fortnite marathon. (2020) 18. K. Li, M. Peterson, J. Wan, Digital gaming in the language classroom: student language performance, engagement, and perception. Int. J. Comput. Assist. Lang. Learn. Teach. (IJCALLT) 12(1), 1–25 (2022) 19. Malaysian Communications and Multimedia Commission, Internet Users Survey 2017. (2017) 20. I. Pajarillo-Aquino, The effect of online games to the academic performance of the students in the college of teacher education. Int. J. Adv. Res. Manage. Soc. Sci. 8(3), 74–86 (2019) 21. A. Pantling, Gaming usage up 75 percent amid coronavirus outbreak, Verizon reports. (2020) Retrieved from https://www.hollywoodreporter.com/news/gaming-usage-up-75-per cent-coronavirus-outbreak-verizon-reports-1285140 22. S. Peracchia, G. Curcio, Exposure to video games: effects on sleep and on post-sleep cognitive abilities. A sistematic review of experimental evidences. Sleep Sci. (Sao Paulo, Brazil), 11(4), 302–314

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23. M. Perez, Video games are being played at record levels as the coronavirus keeps people indoors. (2020). Retrieved from https://www.forbes.com/sites/mattperez/2020/03/16/video-games-arebeing-played-at-record-levels-as-the-coronavirus-keeps-people-indoors/#70eb644e57ba 24. M. Razzoli, C. Pearson, S. Crow, A. Bartolomucci, Stress, overeating, and obesity: insights from human studies and preclinical models. Neurosci. Biobehav. Rev. 6(Pt A), 154–162 (2017) 25. V. Rosendo-Rios, S. Trott, P. Shukla, Systematic literature review online gaming addiction among children and young adults: a framework and research agenda. Addict. Behav. 129. (2022) 26. K.Y. Soo, N. Ismail, Perceived E-learning conditions of Malaysian undergraduates. Int. J. Acad. Res. Progressive Educ. Dev. 10(3), 286–294 (2021) 27. W. Su, X. Han, H. Yu, Y. Wu, M.N. Potenza, Do men become addicted to internet gaming and women to social media? A meta-analysis examining gender-related differences in specific internet addiction. Comput. Hum. Behav. 113, 106480 (2020) 28. World Health Organization. Print Versions for the ICD-11 Beta Draft (Mortality and Morbidity Statistics). Version 05/2021. (2021). Retrieved from https://icd.who.int/browse11/l-m/en/ http:/ /id.who.int/icd/entity/338347362 (15th Dec 2021)

Chapter 14

Data Mining Classifier for Predicting India Water Quality Status Nur Atiqah Hamzah, Sabariah Saharan , and Mohd Saifullah Rusiman

Abstract Classification is one of the methods in data mining that can be used to group the data into class attributes based on similarities shared in the data. In this study, the interest is to find how the classification method can be used on water quality data by identifying water quality index based on the parameters used. This study aims to identify the level of accuracy and effectiveness of each classification method in predicting water quality status based on water quality index. The water quality data used is retrieved from India, with eight water quality parameters: pH, biochemical oxygen demand (BOD), dissolved oxygen (DO), electrical conductivity (EC), nitrate–N + nitrite-N, fecal coliform (FC), total coliform (TC), and temperature. Six different classification algorithms were used in this study to discover which method gave the best result for this data. The J48 (also known as C4.5), REPtree, NBtree, random forest, lazy IBK (also known as KNN), support vector machine (SVM), and artificial neural network (ANN) were the algorithms used for data classification. The percentage of every water class level was discovered, and the water quality index (WQI) for India was identified using weighted arithmetic index. The index was then used as a guideline for water quality status identification. The performance for each algorithm to build classification model was recorded and tabulated. J48 gave the best results in terms of accuracy of classification for this study.

14.1 Introduction Water quality has become a concern to the world, and since last decades’ there were many research focused on water quality (WQ) [1]. Our water sources vary from surface water like river, lake, and coastal areas and groundwater sources. WQ can be divided into biological, hydro-morphological, and physiochemical quality, and the physiochemical WQ variables are widely used for WQ modeling. However, different variables may be applied to assess water quality depending on the water source. To N. A. Hamzah · S. Saharan (B) · M. S. Rusiman Universiti Tun Hussein Onn Malaysia, Johor, Malaysia e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Mustapha et al. (eds.), Proceedings of the 8th International Conference on the Applications of Science and Mathematics, Springer Proceedings in Physics 294, https://doi.org/10.1007/978-981-99-2850-7_14

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discover the quality of water, water quality index (WQI) is used as an indicator that is developed by a complex numerical formula using excess time and may have imprecise values. WQI is an index used to represent the overall water quality status with a single score of subindex [2]. By using the WQI approaches, the WQ can be categorized into a few classes such as good, bad, and worst by presenting the numerical results in simplified form [3]; it depends on the governing bodies that handled the monitoring water quality. Many researchers used artificial intelligence as tools for prediction and classification of WQI as no universal and formal method has been used for these purposes [2, 4]. In this study, the main concern is to identify the accuracy of data mining classifier in predicting the class of water quality. Data mining is the process of gaining useful information from huge data repositories to find unforeseen relationships and to summarize the data in novel ways to make the data comprehensible and useful to the data owner [5]. By using the classification method, the class for a specific dataset can be determined. Classification is one of the recognized approaches in data mining that has been widely used in many sectors, which can be explained as a method with a simple computation technique [6]. As artificial intelligence has been widely used in many industries, this study is going to foresee the effectiveness of some artificial intelligence-based approaches in the classification of water quality data. The result will be beneficial toward improving water quality management. The six classification methods used were J48 (also known as C4.5), REPtree, NBtree, random forest, lazy IBK (also known as KNN), support vector machine (SVM), and artificial neural network (ANN). All necessary measures such as accuracy, F-measure, TP rate, and time taken for building the models were recorded for every technique, as parameters for comparison. Therefore, the main objectives of this study are to predict water quality classification using the six data mining classifier, to identify the accuracy of data mining classifier on water quality data, and to identify the factor that contributes the most to water quality status. This study will become a guideline if there is an improvement that needs to be done toward improving the water quality of the river. Thus, a proper methodology was structured to ensure that the objectives were fulfilled.

14.2 Methodology In this study, the data used was India water quality data which consists of six variables which are pH, biochemical oxygen demand (BOD), chemical oxygen demand (COD), temperature, nitrate–N nitrite-N, fecal coliform, total coliform (TC), and ammonia nitrogen (AN). The water quality index is crucial to be identified for the water quality status to be discovered. Therefore, a formula introduced by National Water Quality Standard (NWQS) is used for index identification. The classification method was used to classify the data, and the percentage of accuracy was identified as a process to justify whether this method is suitable for the India river data.

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14.2.1 Data Preprocessing Data cleaning is the process that takes place after data collection, which includes outlier detection, rule-based data cleaning, data transformation, and data deduplication [7]. Many researchers in various areas conducted data analysis without comprehending the importance of data cleaning as the analysis results can be totally amiss [8]. The India river data had missing values which has been substituted with mean values for each attribute. The data training is a process to train the algorithm or machine learning model in order to predict the outcome of the proposed method. Meanwhile, the testing data is a set of data used to test and validate the performance of the methods used. While data is used directly, this study used both trained and test data which consisted of 70% and 30% of total number of data, respectively. During the preprocessing phase, the missing part is usually omitted by researchers to make the process easier, which can lead to biasness. However, in this study, the missing readings were replaced with the mean value of the existing data available from the dataset. As the data are all in numerical form; thus, a mean data is suitable and easiest method of imputations that can be applied. Therefore, the dataset is completed by replacing the missing part. The mean calculations used by [9] are as follows: x=

n 1 xi , n i=1

(14.1)

where x is the arithmetic mean, n is the number of total instances of the dataset, and x i is the value of the attribute.

14.2.2 Water Quality Index Identification and Calculation The water quality index (WQI) for India water quality data is discovered using the weighted arithmetic WQI. This formulation has been used [10–12]. The WQI can be calculated as follows: n W Q I = i=1

Wi Q i , Wi

(14.2)

where Wi is the relative weight of the ith parameter and Q i is the rating of water quality of the ith parameter. The parameters for calculating WQI must be generated in four steps: 1. Standard value of the eight water quality parameters was selected based on National Water Quality Standard (NWQS).

160 Table 14.1 Class division based on WQI level for India river dataset

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WQI level

Water quality status

Class

0–25

Excellent

I

26–50

Good

II

51–75

Poor

III

76–100

Very poor

IV

> 100

Unsuitable for drinking

V

2. Water quality rating, Qi, was computed using the following formula:   Vi − V0 × 100, Qi = Si − V0

(14.3)

where Q i denoted as the rating of water quality of the ith parameter, Vi denoted as observed value present in the ith parameter, V0 denoted as the ideal value of the parameter which is 0 except for pH and DO are equal to 7 and 14.6, respectively and Si is the standard value of the ith parameter. Notably, if Q i value is equal to 0, it shows that there are no pollutants present, meanwhile if Q i value is between 0 and 100, pollutants are existed but it is within the permissible limit. When Q i value exceeds 100, it shows the pollutants exceed the permissible limit Table 14.1. 3. Relative weight, Wi, was calculated for water quality parameters. The suggested standard values, Si , of the associated parameter are inversely proportional to Wi. 4. The WQI calculations and values can be categorized into five groups as shown in Table 14.1.

14.2.3 Classification Method The classification process of the data was performed using the WEKA software. Six classification methods were used. The accuracy for each model also can be identified. The six selected approaches were J48, REPtree, NBtree, random forest, lazy IBK, SVM, and ANN. In this study, the process of classification for all models was set with split of 70% training and 30% testing from overall dataset. The pruning process was not selected to be included in the classification process as we aim to show how the results vary for each model without any aid of pruning processes or any other technique to improvise the result.

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14.2.3.1

161

Definitions of Classifier Used

In this section, the seven methods of classifier using WEKA software were briefly explained. Every method has different technique to classify the data, and each technique varies in the classification results too. The following were the methods utilized in this study: (i) J48 decision tree J48, also popular by the name C4.5. This decision tree algorithm generates classification decision tree by recursive partitioning of data. Depth-first strategy is used for decision grown. The algorithm ponders all the possible test that can split the dataset and choose the best information gain based on the test that has been done. Discrete and continuous attributes are applicable to this algorithm. For discrete attribute, one test with outcomes as many as the number of distinct values of attribute is considered. For each continuous attribute, binary tests involving all distinct values of the attribute are considered. With the aim of gathering the entropy gain of all these binary tests efficiently, the training dataset belonging to the node in consideration is sorted for the values of the continuous attribute and the entropy gains of the binary cut based on each distinct values are calculated in one scan of the sorted data. This process is repeated for each continuous attribute [13, 14]. (ii) REPtree REPtree is a fast decision tree learner which builds a decision/regression tree using information gain as the splitting criterion and prunes it using reduced error pruning. It only sorts values for numeric attributes once. Missing values are dealt with using C4.5’s method of using fractional instances. (iii) NBTree The naive Bayesian tree learner, NBTree [15], combined naive Bayesian classification and decision tree learning. In an NBTree, a local naive Bayes is deployed on each leaf of a traditional decision tree, and an instance is classified using the local naive Bayes on the leaf into which it falls. The algorithm for learning an NBTree is similar to C4.5. After a tree is grown, a naive Bayes is constructed for each leaf using the data associated with that leaf. An NBTree classifies an example by sorting it to a leaf and applying the naive Bayes in that leaf to assign a class label to it. NBTree frequently achieves higher accuracy than either a naive Bayesian classifier or a decision tree learner. (iv) Random forest This method applies multiple base classifiers, typically decision trees, on a given subset of data independently and makes decisions based on all models [16]. It is a method that calculate the mean of several deep decision trees formed in different parts of the same training set which aims to reduce the variance. It also uses the Bootstrap Aggregating to reduce the variance in the prediction by creating additional data for training from the dataset. RF offers

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the advantages of a decision tree with the improved efficiency of using more than one model [17]. Using RF, best split among all a subset of parameters is randomly chosen and this is done for each node [18]. (v) Lazy IBK/KNN In WEKA software, lazy IBK is the name used for K-nearest neighbors (KNN). This approach classifies samples by determining the closest neighboring points and the class is based on the majority of n neighbors. Nevertheless, this technique is not recommended for a huge dataset as all process involved ensue in testing phase and it iterates through all training datasets and calculate the nearest neighbor each time [19]. (vi) Support Vector Machine (SVM) SVM is a technique that is based on the theory of statistical learning which applies the structural risk minimization principle to discourse the overfitting issue in machine learning by reducing the model’s complexity and fitting the training data successfully. The estimates of the SVM model are formed based on a small subset of training data which is known as support vector. The capability to interpret SVM decisions can be improved by recognizing vectors that are chosen as support vectors [20]. SVM maps the initial data in highdimension feature space in which an optimal separating is created by using a suitable kernel function. For classification, the optimal separating plane in the line that divides the plane into two parts and class is placed in different sides [21]. (vii) Artificial Neural Network (ANN) Artificial neural network works as a human brain’s nervous system, which comprises interconnected neurons that work together in parallel [22]. It is widely used in many fields because of its advantages, such as self-organizing, self-learning, and self-adapting abilities [23]. A neural network comprises four main components, which are inputs, weights, threshold or bias and output. A neural network’s structure is composed of three layers, which are the input, middle, and output layers. Input variables are entered into the algorithm in the input layer. In the middle layer, the input variables are multiplied by weights before they are summed by a constant value. Then, an activation function is added to the sum of the weighted inputs. Activation functions are needed to transform the input signals into output signals. 14.2.3.2

Determining Models Performance

The accuracy of the classification can be calculated using the actual class and predicted class of the data. Thus, based on the tree produced, the confusion matrix was used. The confusion matrix helped compare which dataset has a higher result of correct classification. Table 14.1 shows the confusion matrix for the classification tree. Table 14.2 shows the confusion matrix for the classification tree.

14 Data Mining Classifier for Predicting India Water Quality Status Table 14.2 Confusion matrix

163

Predicted class Actual class

Class = 1

Class = 0

Class = 1

f 11

f 10

Class = 0

f 01

f 00

The accuracy can be calculated from the confusion matrix. The best accuracy score is 1, and the worst score is 0 [24]. Accuracy =

f 11 + f 00 , f 11 + f 00 + f 01 + f 10

(14.4)

where f 11 = actual class and predicted class in Class = 1 f 00 = actual class and predicted class in Class = 0. f 01 = actual class is Class = 0 and predicted class is Class = 1. f 10 = actual class is Class = 1 and predicted class is Class = 0. Classification rules can be obtained from the decision trees that are in the form of if–then statements. Based on the decision rules, the associations between variables can be identified. Another measure that can be obtained from the analysis is sensitivity which calculates the percentage of true-positive outcomes that had been predicted correctly. Sensitivity can be defined as: Sensitivity =

TP , (TP + FN)

(14.5)

where TP is true positive and FN is false negative [25]. For overall measurement of accuracy, F-measure is used which values varying from 0 to 1. The higher the value of F-measure indicates a better accuracy of the analysis done. The F-measure can be calculated as: F − measure =

(2 × Precision × Recall) (Precision + Recall)

(14.6)

To see how effectively each classifier could accurately distinguish between all the positive and negative class, the ROC area is shown how the method works on it. The receiver operator characteristics (ROC) is an evaluation metric for binary classification problems. The higher the ROC area (also known as area under the curve—AUC), the better the performance of the model in differentiating the positive and negative classes. The least value of ROC is 0, and the best value is 1. Therefore, in this study, all the necessary metrics are gathered and compared between all the classifier methods used, to ensure the results are well-explained and the objectives are achieved.

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14.3 Results and Discussion The preprocessing step had been done on the India river dataset for cleaning, and the preprocessing step had been done on the India river dataset for cleaning and imputation. After the data was ready, the water quality index was calculated and classes for every level also had been discovered by using NWQS as guideline. By discovering the WQI status, the number of every status level from the whole data was recorded. The next process which was classification by using seven methods was carried out, and the accuracy in performing the classification process was compared. The results for both processes were explained in Sects. 3.1 and 3.2.

14.3.1 Water Quality Index for India River Dataset WQI for India river dataset that n = 1899 was managed to be calculated using the weighted arithmetic approach that had been discussed in the methodology section earlier. There are five classes which class I for excellent status, class II for good status, class III for very poor status, and class IV for unsuitable for drinking status. The classes are based on the WQI level score. From 1899 data, only 19 were in excellent status. 822 instances were in good category, 744 instances were in poor condition. Meanwhile for very poor and unsuitable status were 167 and 313, respectively. It means that about 64.45% from the dataset were in class III and above. This shows that the pollutants in the river water were high and hazardous to health if it was used as source of drinking water. This dataset was used for classification purposes, and the results were shown in the next section.

14.3.2 Classification Result for India River Datasets Using Seven Classification Methods Table 14.3 presents the comprehensive data on the total number of entries within each water class level, while Table 14.4 showcases the performance of seven classifiers, highlighting their accuracy, error, and other essential parameters, prior to their subsequent comparison. From the table, all methods scored more than 50% of accuracy in classifying the data. The highest accuracy is J48 (89.1129%), followed by random forest (83.304%), REPtree (78.7346%), and NBtree (74.5167%). The other three methods show accuracy more than 60% but less than 70% accuracy are lazy IBK, SVM, and ANN with 62.74175, 60.2812%, 69.7715%, respectively. Meanwhile, by looking into mean absolute error, J48 had the lowest value, which was 0.0495, followed by REPtree, random forest, NBtree, lazy IBK, ANN, and SVM. It shows that in terms of the lowest error, J48 gave the best result compared to other classification methods.

14 Data Mining Classifier for Predicting India Water Quality Status Table 14.3 Water quality index status for India river

165

WQI level

Water quality status

Classes

Total

0–25

Excellent

I

19

26–50

Good

II

822

51–75

Poor

III

744

76–50

Very poor

IV

167

Above 100

Unsuitable for drinking

V

313

Table 14.4 Classification result of seven methods of India river dataset Method

Accuracy

Mean absolute error

Precision

Sensitivity (Tp)

Fp rate

F-measure

Roc area

Time taken (S)

J48

89.1129

0.0495

0.8890

0.8910

0.0560

0.8890

0.923

0.03

REPtree

78.7346

0.0964

0.5800

0.7870

0.1130

0.5623

0.891

0.14

NBtree

74.5167

0.1243

0.5787

0.7450

0.1400

0.5820

0.884

6.30

Random forest

83.304

0.0983

0.8300

0.8330

0.0084

0.8270

0.955

0.64

Lazy IBK

62.7417

0.1249

0.6370

0.6270

0.1660

0.6310

0.731

0.00

SVM

60.2812

0.2369

0.3113

0.6030

0.2440

0.3108

0.702

0.17

ANN

69.7715

0.1410

0.6980

0.6980

0.1880

0.6640

0.865

1.57

Precision is another parameter that can be used in finding the best classification method that suits the utilized data best. Precision is defined as how close measurements of the same item are to each other. Precision is independent of accuracy. That means it is possible to be very precise but not very accurate, and it is also possible to be accurate without being precise. The best-quality scientific observations are both accurate and precise. In this study, J48 has the highest precision score followed by random forest with precision value 0.8890 and 0.8330, respectively. The true-positive rate (TP rate) is also known as sensitivity. From Table 14.3, it showed that the TP rate for all methods is considerably high, which is a good indication. For false positive rate, it should be as low as it can and inversely proportional toward TP rate. The F-measure for all methods has also been discovered. Clearly, the higher the F1 score the better, with 0 being the worst possible and 1 being the best. Out of all the seven methods, SVM had the lowest F-measure. It showed that this method has less predictive power compared to other methods when using the WQI dataset. Meanwhile, the ROC area is also considered for comparison among all these models. All models have high ROC area which were more than 0.5 and some of them approaching to 1. These values indicate that each model is able to distinguish the positive and negative successfully. If the value of ROC area is zero, it means that

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the model fails to differentiate the values and misclassified the data which that is the crucial criteria that has been needed in classification. As dataset may consist of huge number of data; thus, time taken for models to be set up also needed to be considered. Lazy IBK showed a very prompt response in WEKA platform. J48, too, only took 0.03 s to build the model. The longest time taken for a model to be built was using NBtree algorithm. As all methods were performed during the same platform, it shows that for further analysis using huge dataset, time taken in building the model needed to be considered. Figure 14.1 shows the decision tree that can be formed using the J48 classification model. The BOD was put as the first root node showing that it was the most contributing factor in determining the water quality class level. Each split was different to another split, which resulting in various decision rules for classifying the data into the water quality class level.

14.4 Conclusion and Recommendations The WQI for India river dataset was calculated and tabulated into five classes, with each class showing the status for every WQI level. From this calculation, number for every WQI status has also been discovered. It showed that more than half of the data were in categories III, IV, and V, in which the pollutants were high, and the water is unsafe to be consumed. Therefore, the government and responsible authorities in managing the water issue should take actions to control this situation from getting worse. As this study aims to identify the data mining classifier that can give the best results in predicting the class of WQI of India river, it was successfully achieved by conducting seven classification methods using WEKA platform. WEKA software that was used ran on Microsoft 11 64-bit operating system, and all the methods took a very short time to be built. In terms of accuracy, J48 gave the best result with 89.119%. However, when dealing with huge dataset, other parameters should be considered too. Therefore, J48 can also be considered as one of the best methods in classifying the India river dataset with considerably high accuracy (89.119%), low mean absolute error (0.0495), high precision (0.8990), high TP rate (0.8910), low FP rate (0.0560), high F-measure (0.8890), and prompt processing time of 0.03 s to build the model. To conclude, the India river dataset (with the NWQS as guideline) is appropriate to be used to calculate WQI. The WQI serves as a good reference to determine water conditions. The pollutants that exist in water should be controlled to avoid the current situations to worsen. Meanwhile, for classification, in data mining, there were many methods and platforms that can be used for this purpose. Therefore, choosing the right method should always be a priority to give the best result in predicting the class. As this study has successfully carried out seven classification methods, it showed that this WQI data was suitable for classification. In addition, for future work, it is recommended to utilize this data for other data mining technique such as clustering.

Fig. 14.1 Decision tree using J48 (C4.5) using WEKA platform on India river dataset

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Genetic algorithm or fuzzy approach could also be used to improve the results from this work by doing hybridization with optimization method. Acknowledgements The authors would like to thank the Research Management Centre UTHM (RMC) for giving them the chance to carry out this research. This research work is supported by the Ministry of Higher Education, Malaysia, under Fundamental Research Grant Scheme (FRGS) (grant VOT: K297; reference number FRGS/1/2020/STG06/UTHM/02/4). The authors are also extremely thankful to the reviewers for their beautiful remarks.

References 1. T.T.M. Tiyasha, Z.M. Yaseen, A survey on river water quality modelling using artificial intelligence models: 2000–2020. J. Hydrol. 585, 124670 (2020) 2. N.H.A. Malek, W.F.W. Yaacob, S.A.M. Nasir, N. Shaadan, The effect of chemical parameters on water quality index in machine learning studies: a meta-analysis. J. Phys. Conf. Ser. 2084, 12007 (2021) 3. N. Fernandez, A. Ramirez, F. Solano, Physio-chemical water quality indices-a comparative review. Bistua Rev. Ia Fac. Ciencias Basicas. 2, 19–30 (2004) 4. D.T. Bui, K. Khosravi, J. Tiefenbacher, H. Nguyen, N. Kazakis, Improving prediction of water quality indices using novel hybrid machine-learning algorithms. Sci. Total Environ. 721, 137612 (2020) 5. N.A. Hamzah, S. Saharan, K.G. Pillay, Classification tree of breast cancer data with mode value for missing data replacement. Springer Science and Business Media. (2022) 6. I.F. Ilyas, X. Chu, Trends in cleaning relational data: consistency and decuplication. Found. Trends Data Bases 5(4), 281–293 (2015) 7. T. Abbasi, S.A. Abbasi, Water Quality Indices (Elsevier, Amsterdam, The Netherlands, 2012) 8. J.W. Osborne, Best Practices in Data Cleaning (SAGE Publication, USA, 2013) 9. F.B. Hamzah, F.M. Hamzah, S.F. Mohd Razali, O. Jaafar, N.A. Jamil, Imputation methods for recovering streamflow observation: a methodological review. Cogent Environ. Sci. 6(1), 1745133. (2020) 10. S. Tyagi, B. Sharma, P. Singh, R. Dobhal, Water quality assessment in term of water quality index. American J. Water Resour. 2(3), 34–38 (2020) 11. C. Ramakrishna, D.M. Rao, K.S. Rao, N. Srinivas, Studies on groundwater quality in slums of Visakhapatnam Andhra Pradesh. Asian J. Chem. 21(6), 4246–4250 (2009) 12. R.A. Devi, K. Nirmala, Construction of decision tree: attribute selection measures. Int. J. Adv. Res. Technol. 2(4), 343–347 (2013) 13. T. Mitchell, Machine Learning. McGraw Hill. (1997) 14. J.R. Quinlan, Induction of decision trees. Mach. Learn. 1(1), 81–106 (1986) 15. R. Kohavi, Scaling up the accuracy of naïve-bayes classifiers: a decision tree hybrid. In: Proceedings of the Second International Conference on Knowledge Discovery and Data Mining (KDD-96). AAAI Press, 202–207. (1996) 16. U. Ahmed, R. Mumtaz, H. Anwar, A.A. Shah, R. Irfan, J. García-Nieto, Efficient water quality prediction using supervised machine learning. Water 11, 2210 (2019) 17. A. Liaw, M. Wiener, Classification and regression by random forest. R News. 2, 18–22 (2002) 18. L. Breiman, Random forests. Mach. Learn. 45(1), 5–32 (2001) 19. K. Beyer, J. Goldstein, R. Ramakrishnan, U. Shaft, When is “nearest neighbor” meaningful? In: Proceedings of the Database Theory, Berlin/Heidelberg, Germany, 217–235. (1999) 20. J. Nalepa, M. Kawulok, Selecting training sets for support vector machines: a review. Artif. Intell. Rev. 52, 857–900 (2019)

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21. T. Xu, G. Coco, M. Neale, A predictive model of recreational water quality based on adaptive synthetic sampling algorithms and machine learning. Water Res. 177, 115788 (2020) 22. A. Zahiri, A.A. Dehghani, H.M. Azamathulla, Application of gene-expression programming in hydraulic engineering. Springer: Berlin/Heidelberg, Germany, 71–97. 55. (2015) 23. F. Anctil, C. Perrin, V. Andréassian, Impact of the length of observed records on the performance of ANN and of conceptual parsimonious rainfall-runoff forecasting models. Environ. Model. Softw. 19, 357–368 (2004) 24. D.S. Liu, S.J. Fan, A modified decision tree algorithm based on genetic algorithm for mobile user classification problem. Hindawi Publishing Corporation. Sci. World J. (2014) 25. C. Goutte, E. Gaussier, A probabilistic interpretation of precision, recall and F-score, with implication for evaluation. In: Proceedings of the Information Retrieval, New York, NY, USA, 15–19 August 2005, pp. 345–359. (2005)

Chapter 15

Improvement of Learning Outcomes on the Limit Chapter Using Kahoot™ Isti Kamila , Ani Andriyati, Mulyati, Maya Widyastiti, and Embay Rohaeti

Abstract In Bogor, there is a senior high school namely Madrasah Aliyah (MA) AL-Falak. Most MA AL-Falak learners were feeling the effects of the COVID-19 pandemic. During the COVID-19 pandemic, MA AL-Falak students studied virtually. This condition led to loose learning, and based on an interview with mathematics teacher MA AL-Falak, the average student’s mathematics score was relatively low and one of the materials that became a scourge of students was the limit chapter. In this study, treatment was carried out by providing limit chapter using interactive learning media and Kahoot™ in the hope of improving the mathematics learning outcomes of MA AL-Falak students. The method carried out is to provide a pretest to find out the initial ability of students then a limit and Kahoot™ material training treatment is carried out. Furthermore, students are given a posttest and the results of the pretest and posttest will be tested for normality then conduct a t-paired test to find out whether or not there is an increase in learning outcomes of MA AL-Falak students on the limit chapter. There were two basic hypothesis decisions in this study, namely based on the t-paired test and probability values. Both gave the decision that there was an increasing in student learning outcomes through limit chapter training with interactive learning media and Kahoot™.

15.1 Introduction Indonesian students have been impacted by the COVID-19 pandemic. Face-to-face learning changed to virtual learning. That was why Indonesian students having loose learning and made mathematics learning outcomes decrease. This incident happened to the students of MA AL-Falak. The results of an interview with one of the mathematics teachers, the students’ scores during the Even Semester Exam for class XI of the 2019/2020 School Year were relatively low, the average student score was 55 and after analyzing the question items, students could not answer questions about I. Kamila (B) · A. Andriyati · Mulyati · M. Widyastiti · E. Rohaeti FMIPA, Universitas Pakuan, Bogor 16143, Indonesia e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Mustapha et al. (eds.), Proceedings of the 8th International Conference on the Applications of Science and Mathematics, Springer Proceedings in Physics 294, https://doi.org/10.1007/978-981-99-2850-7_15

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the limit chapter mostly, which was around 80%. Whereas the concept of limit is an important part of understanding calculus concepts such as continuity, derivative, and integrals [1]. By understanding the relationship between the concept of limits, continuity, derivatives and integral, students can solve problems related to it [2]. Therefore, this study was interested in improving the learning outcomes of MA AL-Falak students. Learning media can be used as a teaching material that can enrich students’ insights [3]. Furthermore, based on previous study, interactive multimedia improved student motivation in learning [4]. One of the learning media that could increase students’ interest in learning is games. Based on the results of a research, students needed interactive multimedia learning in the form of games that can be accessed via smartphones and computers [5]. Android-based games as a learning plays an important role during the COVID-19 pandemic because it can be accessed by students [6]. Kahoot™ is a game-based web that students can also access at home during online learning. Based on recent studies, Kahoot™ had improved examination score at the college and university level because the students felt positive experience, fun, and engaged their academic environment [7]. In this study, the useful of Kahoot™ media games during online learning is expected to improve the learning outcomes of MA AL-Falak students. Whether or not there is an increasing in learning outcomes, it is necessary to test first with inference statistics. Statistical inference is divided into two large parts, namely estimation and hypothesis testing [8]. The inference statistic used in this study is hypothesis test. One of the inference statistical tests that can be used to determine the presence or absence of improvements before and after treatment is the t-paired test. T-paired tests involve two paired samples; i.e., the treatment is different but applied to the same subject [9]. In the previous studies, paired t-tests were conducted to test whether there was a positive effect of basic computer training for a group of teachers [10]. Therefore, in this study, an increase in student learning outcomes will be tested on limit material using Kahoot™. The test method used in this experiment was a t-pair test.

15.2 Material and Methods 15.2.1 Materials The research subjects in this research were 23 students MA AL-Falak who had chosen by the teacher. Moreover, the materials used in this research were pretest and posttest with 10 questions which would answer by the students. The questions were similar between pretest and posttest. Pretest was used to measure students’ ability in limit chapter. Pretest score data (X1 ) will be used as data that will be inputted as student score data before treatment (X1 ). Besides that, in this research conduct interactive limit learning media training and games in the form of limit chapter questions on the

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Kahoot™ platform. Furthermore, posttest score data will be used as data that will be inputted as student score data after treatment (X2 ).

15.2.2 Methods This study used hypothesis test. The aim of this research was to know whether or not an increasing in the learning outcomes between after giving material through interactive learning media and Kahoot™. This aim will be tested by using t-paired test. The data inputted in this study were pretest and posttest scores. However, before doing t-paired test, conducting normality tests for pretest and posttest data using the Kolmogorov–Smirnov method. Moreover, calculating the average value of pretest and posttest score to know how much the increasing of learning outcomes.

15.3 Result and Discussion Statistical testing is necessary to find out if there is an increasing in test scores between before and after the treatment. T- paired test were used considering the same sample between before and after treatment. The treatment given is the provision of material through interactive learning media and Kahoot™. The first step carried out is to do normality test in two groups of data, namely the pretest scores and the posttest scores to test whether the distribution of data is normal or not. In Table 15.1, it can be seen that the results of the normality test using Kolmogorov–Smirnov showed that the signification rate was more than 0.05, which was 0.074. Based on this significance, it can be concluded that the data on the pretest and posttest scores are normally distributed. Based on the results of descriptive statistical in Table 15.2, the average score of students in the pretest was 34.35. This showed that the average student pretest score was smaller than the KKM score set by the teacher, which was 60. It means that before being given training, the average score of students is still below KKM. KKM is short for Kriteria Ketuntasan Minimal. Kriteria Ketuntasan Minimal (KKM) is minimum student scores that must be achieved to achieve learning competencies. However, after being given material through interactive learning media and KahootTM, the average score of students increased to 78.70. Based on the descriptive value, it can be seen that the implementation of the training has an impact on increasing the test value. Furthermore, statistical testing is carried out using t-paired test so that it can be known whether there is an increase in the value between before and after the provision Table 15.1 Tests of normality (Kolmogorov–Smirnov)

Difference pretest and posttest

Statistic

df

Sig

0.0173

23

0.074

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Table 15.2 Descriptive statistics Mean

N

Std. deviation

Std. error mean

Pretest

34.35

23

11.610

2.421

Posttest

78.70

23

6.944

1.488

Table 15.3 Paired samples test Paired differences Mean

Posttest – pretest

44.348

Std. dev

11.211

t

df

Sig (2-tailed)

18.971

22

0.000

95% confidence interval of the difference Std. error mean

Lower

Upper

2.338

39.500

49.196

of material through interactive learning media and KahootTM . The calculation output of the t-paired test was presented in Table 15.3. The hypotheses used in this study were as follows: H0 : There was no increasing in learning outcomes after giving material through interactive learning media and KahootTM . H1 : There is an increasing in the learning outcomes after giving material through interactive learning media and KahootTM .

15.3.1 Based on the Calculation of t-output and t-table If the calculated statistics (number t-output) > the table statistics (t-table), then H0 is rejected. If the calculated statistics (number t-output) < the table statistics (t-table), then H0 is accepted. The calculated t-value of the output based on Table 15.3 is 18,971. While the table statistics with a significance rate of 5% for one-sided tests with a degree of freedom 23 – 1 = 22 was t(0.05;22) = 1717. Decision: Since t-output = 18.971 > 1.717 then the counting lies in the rejection H0 area.

15.3.2 Based on Probability Values If the probability > 0.05, then H0 is accepted. If the probability of < 0.05, then H0 is rejected.

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Decision: The probability value based on Table 15.3 is 0. For double-sided tests, the probability number is 0. Since the value of the doublesided probability = 0 < 0.05, then H0 is rejected. Therefore, it can be concluded that there was an increase in test scores after giving material through interactive learning media and Kahoot™. In other words, the provision of limit materials through interactive learning media and Kahoot™ is effective in improving students’ mathematics learning competencies, especially in limit chapter.

15.4 Conclusion There was an increasing in test scores after the provision of material through interactive learning media and Kahoot™. In other words, the provision of limit materials through interactive learning media and Kahoot™ was effective in improving students’ mathematics learning competencies, especially in limit chapter. Acknowledgements This research was made possible by funding from research grant provided by Universitas Pakuan, Indonesia. The authors would also like to thank the Fakultas Matematika dan Pengetahuan Alam, Universitas Pakuan for its support.

References 1. P. Sari, GeoGebra as a means for understanding limit concepts. Southeast Asian Math. Educ. J. 7(2), 71–80 (2017) 2. B.E. Susilo, P.S. Darhim, Student’ critical thinking skills toward the relationship of limits, continuity, and derivatives of functions. Int. J. Sci. Technol. Res. 8(9), 2299–2302. (2019) 3. M. Ediyani, U. Hayati, S. Samsul, N.M.B. Fauzi, Study on development of learning media. Bp. Int. Res. Critics Inst. J. (BIRCI-Journal) 3(2), 1336–1342. (2020) 4. A. Ghofur, E. Youhanita, Interactive media development to improve student motivation. Int. J. Educ. Curriculum (IJECA) 3(1), 1–6 (2020) 5. L. Fitrianal, A. Hendriyanto, S. Sahara, F.N. Akbar, Digital literacy: the need for technologybased learning media in the revolutionary era 4.0 for elementary school children. Int. J. Progressive Sci. Technol. (IJPSAT) 26(1), 194–200. (2021) 6. D.U.A. Suliyanah, F.K. Kurniawan, N.A. Lestari, N.A. Yantidewi, M.N.R. Juhatiyah, B.K. Prahani, Literature review on the use of educational physics games in improving learning outcames. In Seminar Nasional Fisika, SNF 2020, pp. 1–11. AIP Publishing, Semarang. (2020) 7. D.H. Iwamoto, J. Hargis, J. Taitano, K. Vuong, Analyzing the efficacy of the testing effect using kahootTM on student performance. Turkish Online J. Distance Educ. (TOJDE) 18(2), 80–93 (2017) 8. R.E. Walpole, R.H. Myers, Ilmu Peluang dan Statistika untuk Insinyur dan Ilmuwan (Translation), 4th edn. (ITB Press, Bandung, 1995) 9. S. Santoso, Menguasai SPSS Versi 25. Gramedia: Jakarta. (2018) 10. C. Montolalu, Y. Langi, Pengaruh Pelatihan Dasar Komputer dan Teknologi Informasi bagi Guru-Guru dengan Uji-T Berpasangan (Paired Sample T-Test). d’Cartesian: Jurnal Matematika dan Aplikasi 7(1), 44–46. (2018)

Chapter 16

Mapping of Fish Consumption in Indonesia Based on Average Linkage Clustering Methods Fitria Virgantari, Yasmin Erika Faridhan, Fajar Delli Wihartiko, and Sonny Koeshendrajana

Abstract This study aimed to conduct grouping the level of fish consumption of 34 provinces in Indonesia and then mapping it. National Socio-economic Survey (SUSENAS) Data of 2019 organized by the Central Bureau of Statistics Indonesia were used in this study. Mapping fish consumption to five number of clusters was carried out based on average linkage clustering method. Results showed that this clustering has a quite good performance indicated by a relatively small variance ratio, i.e., 13.8%. Cluster 1 with the lowest level of fish consumption was Special Region of Yogyakarta and Central Java. Cluster 2 consists of 13 provinces, namely North Sumatera, Jambi, West Kalimantan, Lampung, West Jawa, East Jawa, Bali, East Nusa Tenggara, West Sumatera, South Sumatera, Bengkulu, Banten, and West Nusa Tenggara. Cluster 3 and cluster 4 consist of only one province, namely Jakarta and Papua. Meanwhile, cluster 5 with the highest level of consumption consists of 17 provinces, namely South Kalimantan, North Sulawesi, South Sulawesi, East West Sulawesi, Maluku, North Maluku, Aceh, Riau and Riau Islands, Bangka Belitung Islands, Central Kalimantan, East Kalimantan, North Kalimantan, West Papua, Central Sulawesi, Gorontalo, and West Sulawesi.

F. Virgantari (B) · Y. E. Faridhan · F. D. Wihartiko Pakuan University, Bogor 16610, Indonesia e-mail: [email protected] S. Koeshendrajana Center of Research for Behavioural and Circuler Economics, National Research and Innovation Agency Indonesia, Jakarta 12710, Indonesia © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Mustapha et al. (eds.), Proceedings of the 8th International Conference on the Applications of Science and Mathematics, Springer Proceedings in Physics 294, https://doi.org/10.1007/978-981-99-2850-7_16

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16.1 Introduction 16.1.1 Background Fish is considered one of the potential animal food products in Indonesia. From year to year, the level of animal food consumption of the Indonesian population is mostly contributed by fish products [1]. Based on data from the Capture Fisheries Research Center, Ministry of Maritime Affairs and Fisheries (KKP) [2], the production of fish caught in the sea in this sector has been the largest contributor to Indonesian fishery production in the last 10 years. However, the level of fish consumption per capita in Indonesia is still relatively low. The data shows that the distribution of national fish consumption based on islands has so far been uneven. The level of fish consumption in Java has the lowest rate among the seven major islands in Indonesia [3]. The high disparity in the level of fish consumption in Java and the Eastern Region of Indonesia causes the national fish consumption rate to be relatively low. One way that can be used to easily monitor the level of adequacy of fish consumption is to cluster and then map it throughout Indonesia. Until now there is no map that describes the level of fish consumption in Indonesia. In general, mapping studies carried out are mapping of potential fishing areas in certain areas, such as those carried out by [4–6]. Mapping the level of resilience of fish consumption has been carried out by [7] with multidimensional scaling and [8] with consensus clustering, but only limited to area grouping. An integrative approach was carried out by [9] and the Food Security Council [10] with the Atlas-FSVA for food as a whole, not specifically for fish products.

16.1.2 Purpose of the Study This paper aims to map the level of fish consumption and formulate policy recommendations to increase fish consumption for the Indonesian population. With the mapping of fish consumption in Indonesia, it is hoped that planning, monitoring, and evaluation for program and policymakers, both at the central and local levels, will prioritize interventions and programs based on needs and potential, so that the problem of fish consumption shortages can be addressed quickly and accurately.

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16.2 Materials and Methods 16.2.1 Data Data used in this study is the National Social Economic Survey in 34 provinces of 2019 conducted by Central Bureau of Statistics Indonesia [11, 12]. Variable used in this study is level of consumption (kg/capita/year), participation rate (percentage of household consume to all household in one province), and expenditure level (IDR/ capita/month). The types of fish analyzed were processed fish, fresh fish including milkfish, catfish, mackerel, tuna, skipjack, goldfish and tilapia, and shrimp.

16.2.2 Method of Analysis The grouping of provinces was carried out using the average linkage method [13]. First step was determining the similarity between objects to be studied. In this case, the Euclidean square distance measure was used following the equation: di2j

=

p  

2 X ik − X jk ,

(16.1)

k=1

where di2j is distance of object i and object j, X ik value of object i in variable-k, X jk value of object j in variable k, p = variable used in the study, and i = j. At this stage, a matrix called the distance matrix is generated. After determining of the closest distance from distance matrix, then calculate the average distance of all objects or provinces using the equation:   d(I J )K =

a b dab , NI J NK

(16.2)

where d(I J )K is distance of cluster IJ and cluster K, dab is distance between object a in cluster IJ and object b in cluster K, N I J number of members in cluster IJ, N K is number of member in cluster K. Repeat the steps for merging similar or adjacent objects until they produce the appropriate number of clusters. The grouping of these stages will produce a dendogram. The dendogram can be used in determining cluster members. The optimal number of clusters in this paper is determined based on previous study, namely k = 5 clusters where it gives the smallest sum square of error based on the elbow method [14]. A good clustering has the minimum Vw2 and maximum Vb2 so as to produce the minimum variance ratio (v) according to the following equation.

180 Table 16.1 Fish consumption level grouping

F. Virgantari et al.

Cluster

Category

Color of map

1

Very low

Red

2

Low

Pink

3

Moderate

Yellow

4

High

Light green

5

Very high

Dark green

Vw2 =

k 1  (n i − 1)Vi2 , N − k i=1

(16.3)

where Vw2 is variance within cluster, N is number of observation, n i is number of observation in cluster I, and Vi is variance of cluster i as follows:  1 n i (x i − x)2 , (k − 1) i=1 k

Vb2 =

(16.4)

where Vb is variance between cluster, x i is the centroid of cluster I, and x is the centroid of all clusters: v=

Vw2 × 100% Vb2

(16.5)

A good cluster is a cluster, which has high homogeneity (similarity) between members in one cluster (within cluster) and high heterogeneity between one cluster and another (between clusters). Mapping of fish consumption was carried out based on the results of clustering using the average linkage method. Because it has been determined that the number of clusters to be formed was 5, the mapping will be carried out according to the colors in Table 16.1.

16.3 Results and Discussion 16.3.1 Data Description A description of the level of fish consumption, participation rate, and fish expenditure level of the Indonesian population is presented in Table 16.2. Table 16.1 shows that the level of fish consumption of the Indonesian population varies greatly, from 8.3 kg/cap/year to 44 kg/cap/year. The lowest consumption participation rate is 56.6% while the highest is 98.1%. The level of fish expenditure

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Table 16.2 Household fish consumption, participation, and expenditure level in Indonesia, 2019 Variable Consumption level (kg/caput/ yr)

Minimum 8.3

Participation rate (%)

56.6

Expenditure level IDR/caput/ month)

19.3495

Maximum 44.0 98.1 102.9003

Average 28.7 0.91 62.5406

Standard Deviation 9.8 0.1 20.0619

Source National Socio-Economic Survey, 2019 (processed)

ranged from IDR 19,349.5 to IDR 102,900.3 per capita per month. This figure has increased from the previous year but is still below of government’s target. The results of standardization of data on consumption levels, participation rates, and household fish expenditure levels in Indonesia can be seen in Fig. 16.1. Zcons represents the standard score of level of consumption, Zpart represents standard score of participation rate, and Zexp represents standard score of expenditure level. Based on Fig. 16.1, it can be seen that the distribution of consumption and expenditure is quite good, while the distribution of the participation rate shows some outliers, which indicates that the fish participation rate is not evenly distributed. In this case, there are regions in Indonesia with a participation rate much lower than the average participation rate of the whole area.

Fig. 16.1 Boxplot of consumption level, participation level, and fish expenditure level of Indonesia in 2019

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16.3.2 Clustering Based on Average Linkage Methods The optimal number of clusters is determined based on the results of the previous study, namely k = 5 clusters because this number gives the least sum square of error. The number of k = 5 clusters is categorized into very low, low, medium, high, and very high. Membership of the five clusters is based on the following dendogram (Fig. 16.2). Based on the dendogram, it can be seen that the grouping with five clusters of fish consumption indicators is based on the average linkage method as presented in Table 16.3. The description of each cluster based on the variables of consumption level, participation level, and fish expenditure level according to the optimal number of clusters is presented in Table 16.4. Table 16.2 shows that Cluster 1 was a cluster consisting of two provinces with the lowest levels of consumption, participation, and expenditure levels of fish among other provinces in Indonesia, namely Central Java and DI Yogyakarta (Table 16.3). According to research on fish consumption in Indonesia conducted by [15, 16, and 17], in general the results of the study state that the level of fish consumption in Java, especially in the Special Region of Yogyakarta and Central Java is still relatively lower than other provinces in Indonesia. Cluster 2 shows slightly higher indicators than cluster 1 consisting of thirteen provinces, namely North Sumatera, Jambi, West Kalimantan, Lampung, West Jawa, East Jawa, Bali, East Nusa Tenggara, West Sumatera, South Sumatera, Bengkulu, Banten, West Nusa Tenggara.

Fig. 16.2 Dendogram of average linkage clustering

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Table 16.3 Average linkage clustering of provinces in Indonesia according to fish consumption level, participation rate, and fish expenditure variables Cluster of

Number of cluster

Member of cluster

1

2

Central Java, special region of Yogyakarta

2

13

North Sumatera, Jambi, West Kalimantan, Lampung, West Jawa, East Jawa, Bali, East Nusa Tenggara, West Sumatera, South Sumatera, Bengkulu, Banten, West Nusa Tenggara

3

1

Jakarta

4

1

Papua

5

17

South Kalimantan, North Sulawesi, South Sulawesi, East West Sulawesi, Maluku, North Maluku, Aceh, Riau and Riau Islands, Bangka Belitung Islands, Central Kalimantan, East Kalimantan, North Kalimantan, West Papua, Central Sulawesi, Gorontalo, and West Sulawesi

Source National Socio-Economic Survey, 2019 (processed)

Table 16.4 Average consumption level, participation level, and fish expenditure level statistics from five clusters Cluster of-

Number of province

Fish consumption level

Participation rate

Expenditure level

1

2

9.6

0.66

21,319

2

13

21.7

0.92

51,545

3

1

23.4

0.78

66,614

4

1

23.8

0.67

71,618

5

17

37.0

0.95

75,025

Source National Socio-Economic Survey, 2019 (processed)

Cluster 3 can be said to be a cluster with a medium consumption level, participation level, and medium level of fish expenditure consisting of one province, namely Jakarta. Cluster 4 with indicators of consumption, participation level, and fish expenditure level which is more than adequate consists of 1 province, namely Papua. The last cluster with the highest level of consumption and expenditure of fish in Indonesia consists of 17 provinces, namely South Kalimantan, North Sulawesi, South Sulawesi, East West Sulawesi, Maluku, North Maluku, Aceh, Riau and Riau Islands, Bangka Belitung Islands, Central Kalimantan, East Kalimantan, North Kalimantan, West Papua, Central Sulawesi, Gorontalo, and West Sulawesi. In addition to a good culture of eating fish, the seventeen provinces also have a wealth of natural resources, including the potential for very large fisheries and marine resources.

184 Table 16.5 Sum of squares within cluster and average distance from centroid of each cluster

F. Virgantari et al.

Cluster of

Number of observation

Within cluster sum of squares

Average distance from centroid

1

2

19,948

09,987

2

13

106,723

085,187

3

1

0

0

4

1

0

0

5

17

202,037

102,086

16.3.3 Validity Cluster A good cluster is a cluster that the members are as similar as possible to one another, but not very similar to other cluster members. Similar in this case is defined as the level of similarity between two data. The smaller standard deviation ratio within and between clusters, the higher the homogeneity [18]. Sum of squares within cluster and average distance from centroid of each cluster are presented in Table 16.5. According to Eqs. (16.3), (16.4), and (16.5), it can be calculated the variance ratio as follows: Vw2 = 0187 Vb2 = 1353 v=

Vw2 × 100% = 13.8% Vb2

(16.6)

Based on the results of these calculations, it can be seen that the ratio of variance within clusters and variance between clusters is relatively small, namely 13.8%, so it can be said that the grouping of 34 provinces in five clusters is quite good.

16.3.4 Mapping Visualization of the five clusters shown in different colors is shown in Fig. 16.3. Based on Fig. 16.3, it can be seen that most of the provinces, especially in the middle-eastern region in Indonesia (more than 50%), show a green color or can be said to be quite high in fish consumption indicators, both consumption levels, participation levels, and fish expenditure levels. This shows that the government’s program to increase the level of fish consumption is quite successful. While the western part of Indonesia is mostly pink and red, which indicates a low level of consumption, participation level and level of fish expenditure. Two provinces that really need the government’s attention are shown in red on the map

16 Mapping of Fish Consumption in Indonesia Based on Average Linkage …

185

Fig. 16.3 Mapping of Indonesia’s provinces based on fish consumption level, participation rate, and fish expenditure level Variables, 2019. Source National Socio-Economic Survey, 2019 (processed)

because of the very low level of consumption, participation rate, and level of fish expenditure, namely the Province of the Special Region of Yogyakarta and Central Java. Both provinces are inhabited by very heterogeneous people with very diverse social statuses. This diversity colors the pattern of economic, social, and cultural life of the community, including in their food consumption.

16.4 Conclusion Based on the results of the analysis, it can be concluded that the provinces in Indonesia can be grouped into five clusters based on indicators of consumption levels, participation levels, and fish expenditure levels. In general, the fish consumption map produced shows that most of the provinces in Indonesia show a green color or can be said to be quite high in consumption levels, participation levels, and fish expenditure levels. However, there are several provinces that need to be considered by the government as indicated by the red color on the map because the level of consumption, participation rate, and level of fish expenditure is still very low, namely the province of the Special Region of Yogyakarta and the province of Central Java; therefore, the proposed policy recommendation is to focus the program to increase fish consumption in areas that are still very low.

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References 1. B.K. Pangan, Laporan Tahunan Badan Ketahanan Pangan. Kementrian Pertanian. Jakarta. (2019) 2. [KKP] Kementerian Kelautan dan Perikanan. Kelautan dan Perikanan Dalam Angka Tahun 2018.: Kementerian Kelautan dan Perikanan. Jakarta. (2018) 3. Kementerian Kelautan dan Perikanan. Peta Kebutuhan Ikan Berdasarkan Preferensi Konsumen Rumah Tangga Tahun 2018.: Direktorat Pemasaran, Direktorat Jenderal Penguatan Daya Saing Produk Kelautan dan Perikanan. Jakarta. (2019) 4. R.K. Insanu, Pemetaan Zona Tangkapan Ikan (Fishing Ground) Menggunakan Citra Satelit Terra Modis dan Parameter Oseanografi di Perairan Delta Mahakam. Jurnal Geoid 12(2), 111–119 (2017) 5. I.R. Suhelmi, A.A. Rizki, H. Prihatno, Pemetaan Spasial Jalur Penangkapan Ikan Dalam Rangka Pengelolaan Sumberdaya Kelautan dan Perikanan, Studi Kasus di WPP 713 dan WPP 716. Jurnal Segara 11(2), 85–92. (2015) 6. A. Rahman, A.R. Syam, Pemetaan Sebaran dan Kelimpahan Ikan Napoleon di Teluk Maumere, Kepulauan Sembilan, dan Takabonerante. Jurnal Akuatika 6(1), 45–68. (2015) 7. S. Fauziah, F. Virgantari, S. Setyaningsih, Pemetaan Tingkat Ketahanan Pangan Hewani di Indonesia Menggunakan Metode Multidimensional Scalling. Jurnal Ekologia 17(2), 39–47 (2017) 8. W. Budiaji, Penerapan Consencus Clusterring pada Pemetaan Ketahan Pangan Kota Serang. Jurnal Ilmu Pertanian dan Perikanan 4(1), 19–27 (2015) 9. S.R. Nurhemi, G.S.R. Soekro, R. Suryani, Pemetaan Ketahanan Pangan di Indonesia: Pendekatan TFP dan Indeks Ketahanan Pangan. Working Paper 4/14. Bank Indonesia. Jakarta. (2014) 10. B.K. Pangan.: Peta Ketahanan dan Kerawanan Pangan. Kementrian Pertanian. Jakarta. (2019) 11. [BPS] B.P. Statistik.: Persentase Pengeluaran Rata-rata per Kapita Sebulan Menurut Kelompok Barang di Indonesia. http:/bps.go.id. Last accessed 21 Sept 2020 12. S. Koeshendrajana, T. Apriliani, F.Y. Arthatianti, B. Wardono, E.S. Luhur, Kajian Permintaan Ikan Rumah Tangga Dengan Pendekatan Multi Stage Budgeting Analisis Data Susenas 2019. (Laporan tidak dipublikasikan). Balai Besar Riset Sosial Ekonopmi Kelautan dan Perikanan. Jakarta. (2020) 13. R.A. Johnson, D.W. Wichern, Applied Multivariate Statistical Analysis, 6th edn. (Prentice-Hall International, New Jersey, 2007) 14. F. Virgantari, S. Koeshendrajana, F.Y. Arthatiani, Y.E. Faridhan, F.D. Wihartiko, Pemetaan Tingkat Konsumsi Ikan Rumah Tangga Indonesia. Jurnal Sosial Ekonomi Kelautan Perikanan 17(1), 97–104 (2022) 15. S. Koeshendrajana, F. Arthatiani, F. Virgantari, Price and income elasticities of selected fish commodities in Indonesia: a multi stage budgeting framework. In: IOP Conference Series: Earth and Environmental Sciences 860 012059, pp. 1–13. (2021) 16. I.S. Djunaidah, Tingkat Konsumsi Ikan di Indonesia Ironi di Negeri Bahari. Jurnal Penyuluhan Perikanan dan Kelautan 11(1), 12–24 (2017) 17. F. Arthatiani, Y.N. Kusnadi, Harianto, Analisis Pola Konsumsi dan Model Permintaan Ikan Menurut Karakteristik Rumahtangga di Indonesia. Jurnal Sosial Ekonomi Kelautan dan Perikanan 13(1), 73–86. (2018) 18. A.R. Barakbah, K. Arai, Determining constraints of moving variance to find global optimum and make automatic clustering. In: Proc. Industrial Electronics Seminar (IES), pp 409–13. (2004)

Chapter 17

Analysis of Income and Expenditure of Households in Peninsular Malaysia Tan Kang May, Sabariah Saharan , and Mohd Saifullah Rusiman

Abstract Income and expenditure issues in Malaysia had been recently discussed by many researchers as these are the basis of every sustainable economy. Malaysians should understand their spending behaviour based on their revenue. The study is conducted to demonstrate the relationship between household income and expenditure as well as demographic characteristics in northern region, central region, southern region and east coast of Peninsular Malaysia by using appropriate statistical techniques. The dataset being employed was extracted from Household Expenditure Survey (HES) 2019 by the Department of Statistics Malaysia (DOSM). The study is focused on the households who lived in Kuala Lumpur, Selangor, Johor, Penang and Kelantan to represent each region in Peninsular Malaysia. The data analysis was conducted using Chi-square test, bivariate analysis, simple linear regression and multiple linear regression. The results showed that household expenditure is directly proportional to household income, and household revenue was significantly influenced by all demographic variables while household spending was affected by particular characteristics, such as gender, ethnicity, educational level and activity status. Kelantan households revealed the lowest average household income whereas Kuala Lumpur families possessed the highest household revenue. The findings of household income and expenditure distribution based on activity status and regions can contribute to all Malaysians especially fresh graduates, individuals who are going to settle down, NGOs and retirees. Future research can be conducted by utilising comprehensive data to study the distribution of household revenue and spending at the district areas in each state, along with data visualisation techniques.

T. K. May · S. Saharan (B) · M. S. Rusiman Department of Mathematics and Statistics, Faculty of Applied Sciences and Technology, Universiti Tun Hussein Onn Malaysia, Pagoh Edu Hub, 86400 Johor, Malaysia e-mail: [email protected] M. S. Rusiman e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Mustapha et al. (eds.), Proceedings of the 8th International Conference on the Applications of Science and Mathematics, Springer Proceedings in Physics 294, https://doi.org/10.1007/978-981-99-2850-7_17

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17.1 Introduction Household income is a valuable economic predictor of quality of life as well as an essential risk factor for loans. The wages earned by the parents will influence their children’s future prospects especially on education and body health [1]. Household spending is also the crucial factor in the development of Malaysia’s economy [2]. Hence, income and expenditures are the basis of every sustainable business. Spending without budgeting will cause the difficulty of dealing with unforeseen costs as well as meet the financial targets. It is vital for Malaysians to understand their expenditure pattern in relation to their income, especially in this developing country. Previous studies [3, 4] stated that regional variables were influential in income inequality. Besides, another study found that income level was also positively associated with the educational level [5]. This outcome was supported by other studies [6–9] which illustrated that household heads with higher formal education recorded greater proportion in higher income groups. Furthermore, the increase in family size will decrease the household income [10, 11]. Moreover, the employment status and occupation of the household head also influence the degree of earnings [12, 13]. The trends for income classes by age in all nations were identical where the revenue increased sharply from twenties, peaking about age 40, and then falling [14]. However, Tuyen [15] stated that there were no significant differences in levels of income based on age. There were differences in the pattern of household expenditure by regions [13]. Shamim and Ahmad [16] also acknowledged that urban households were willing to spend more as their income increased compared to rural households in order to enhance the standard of living. It was found that male household heads spent more money compared to females monthly, while there was a slight but substantial positive impact of age on the household consumption. In factor of ethnicity, non-Bumiputera tended to consume more than Bumiputera [17]. The existence of significant bivariate associations between the demographic characteristics and income levels was demonstrated using a Chi-square test by observing the p-value [18]. This method was similar to the previous studies [5, 8] to determine the association between demographic characteristics and household income. Schroeder et al. [19] utilised linear regression analysis to examine the association between household wages and food expenditure as well as household size. Another research by Talukder [20] employed regression models to examine the determinants of household income. Besides, regression methods were also utilised in the analysis of household characteristics and household income towards poverty [8, 21]. The objective of this study is to demonstrate the association between income groups and demographic characteristics in Peninsular Malaysia by using Chi-square test and bivariate analysis. The second objective is to investigate the relationship between household income and household expenditure by region in Peninsular Malaysia using simple linear regression, and the last purpose is to identify the significant demographic determinants of household expenditure in Peninsular by using multiple linear regression.

17 Analysis of Income and Expenditure of Households in Peninsular Malaysia Table 17.1 List of variables

No. Variables

189

Variable types

1

Total household expenditure Quantitative (Continuous)

2

Household income

Quantitative (Continuous)

3

Household size

Quantitative (Discrete)

4

Age

Quantitative (Discrete)

5

Gender

Qualitative (Binary)

6

Ethnicity

Qualitative (Nominal)

7

State

Qualitative (Nominal)

8

Strata

Qualitative (Binary)

9

Marital status

Qualitative (Nominal)

10

Educational level

Qualitative (Ordinal)

11

Activity status

Qualitative (Nominal)

17.2 Materials and Methods This section explains the data description and statistical methods that were employed in completing the objectives of study. All the models and algorithms that were applied in the analysis will be thoroughly explored.

17.2.1 Data Description In this study, the data was extracted from Household Expenditure Survey (HES) 2019 by the Department of Statistics Malaysia (DOSM). The study is focused on the households who stayed in the northern, central, southern and east coast of Peninsular Malaysia. The selected states are Kuala Lumpur, Selangor, Johor, Penang and Kelantan, respectively, to represent each region. The list of households as well as demographic characteristics is used in analysing the impact on household income and expenditure shown in Table 17.1.

17.2.2 Chi-Square Test and Bivariate Analysis In this study, household income and demographic characteristics are the two variables that are included in bivariate analysis. The existence of significant bivariate associations among these two categorical variables was determined using Chi-square test by observing the p-values. The frequency of each variable was illustrated in the contingency table. The proportion of each demographic characteristic on the three income groups, which are B40, M40 and T20, was evaluated to demonstrate the distribution

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of income groups across the demographic categories. The percentage is calculated by using the formula as follow [22]: Percentage =

n × 100%, T

(17.1)

where n = frequency of the demographic characteristics in the specific income groups and T = total number of the demographic characteristics.

17.2.3 Linear Regression Analysis Ordinary least squares (OLS) regression also known as linear regression is utilised to estimate the relationship between a dependent variable and one or more independent variables [23]. This method comprehends the mean change in a dependent variable when each independent variable is adjusted by one unit. The OLS regression procedure minimises the sum of squares of the residuals and constructs a best fit line that assumes the model has a linear trend [24]. Simple Linear Regression. Simple linear regression is a statistical approach used to investigate the relationships between two quantitative variables [25]. Simple regression model includes only one independent variable and a dependent variable. The degree of correlation between these two variables can be evaluated based on the correlation coefficient. The specific simple regression model to evaluate the relationship between total household expenditure and household income by region in this project is constructed as: EXPa = β0 + β1 INCa + ε,

(17.2)

where EXPa = total monthly household expenditure in the particular state; β0 = y (total monthly household expenditure in the particular state) intercept of regression model; β1 = regression coefficient of corresponding independent variable; INCa = household monthly gross income in the particular state; ε = error term and a = representative states in Peninsular Malaysia. Multiple Linear Regression. Multiple linear regression is a statistical approach to analyse the relationship between single dependent variable and multiple independent variables. Multiple linear regression is implemented to predict the result of a dependent variable by combining multiple independent variables and is widely utilised in econometrics as well as financial analysis [26]. In this research, a multiple regression model is constructed to demonstrate the significant demographic determinants of total monthly household expenditure in Peninsular Malaysia. The specific multiple regression model is stated as follow: EXP = β0 + β1 X 1 + β2 X 2 + · · · + βi X i + ε, i = 1, 2, . . . , p.

(17.3)

17 Analysis of Income and Expenditure of Households in Peninsular Malaysia

191

where EXP = total monthly household expenditure; β0 = y (total monthly household expenditure) intercept of regression model; β1 , β2 , . . . , βi = regression coefficients of corresponding independent variables; X 1 , X 2 , . . . , X i = independent variables to estimate total household expenditure; ε = error term and p = number of significant independent variables.

17.3 Results and Discussion This section presents data and discusses the results of each objective by using the methods proposed. The significance outcomes, contribution and limitation of study are included.

17.3.1 Impact of Demographic Variables in Household Revenue Bivariate analysis was employed to analyse the association between demographic characteristics and household income categories. Table 17.2 revealed that there was a highly significant (0.1% significance level) between all demographic variables and the three household income groups. From the results, the majority of male household heads fell in M40 income group (44.1%) while 46.0% of female household heads contributed to B40 income group. This indicated that male household heads tended to generate higher household revenue compared to females. The findings were supported by Thangiah et al. [18] who explained that male household heads were more likely to be categorised into M40 and T20 household income groups compared to females. Household heads with age below 20 and above 60 were more likely to fall in B40 income group which recorded 76.9% and 52.5%, respectively. However, household heads with 20–39 and 40–59 age groups contribute higher frequency in both M40 and T20 income groups. This finding was partially confirmed by Nta [14] showing that the revenue was increased from twenties and peak at the age of 40 years old but contradicted another research by Tuyen [15], who explained that age was an insignificant variable with respect to income levels in the North-West Mountains, Vietnam. Next, the Chinese household heads recorded the highest percentage in T20 income group among all ethnic groups. Most of the Bumiputera and Indian household heads belonged to M40 income group, while other ethnicities of household heads tended to fall in B40 income group. The finding was similar to the result of a study conducted by Gradín [4] who explained that there were differences in revenue between races. Marital status of household heads affected significantly to household income. The status of widow or widower, divorced and separated household heads is mostly

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Table 17.2 Bivariate analysis between demographic characteristics of the household heads and household income groups Variables

Income groups B40 n

M40 %

n

p-value

126.905

< 0.001

322.453

< 0.001

258.928

< 0.001

231.264

< 0.001

T20 %

n

%

Gender Male

1465 29.0

2228 44.1 1356 26.9

Female

435

375

46.0

χ2

39.7 135

14.3

Age groups Below 20

10

76.9

2

20–39

566

28.1

1011 50.2 436

15.4 1

21.7

7.7

40–59

772

26.5

1257 43.1 887

30.4

60 and above

552

52.5

333

31.7 167

15.9

Ethnicity Bumiputera

1276 37.3

1498 43.8 649

19.0

Chinese

399

21.8

779

42.6 650

35.6

Indian

136

24.8

248

45.2 165

30.1

Others

89

45.9

78

40.2 27

13.9

Never married

334

33.2

473

47.0 199

19.8

Married

1248 28.1

1958 44.1 1230 27.7

Widow/widower

233

60.7

111

28.9 40

10.4

Divorced

67

48.9

50

36.5 20

14.6

Separated

18

58.1

11

35.5 2

6.5

Degree/advance diploma

45

4.2

378

35.2 652

60.7

Diploma/certificate

162

17.0

498

52.3 292

30.7

STPM

48

35.3

66

48.5 22

SPM/SPMV

916

36.2

1221 48.3 393

15.5

Marital status

1462.224 < 0.001

Educational level

16.2

PMR/SRP

268

47.4

215

38.3 79

14.1

No certificate

461

62.4

225

8.6 53

7.2

Activity status

696.183

Employer

8

5.0

51

31.7 102

63.4

Government employee

100

17.8

283

50.4 178

31.7

Private employee

965

26.7

1703 47.0 952

26.3

Own account worker

427

40.4

405

21.4

Unemployed

1

100.0 0

Housewife/looking after home 50

79.4

11

38.3 226 0.0 0

0.0

17.5 2

3.2

< 0.001

(continued)

17 Analysis of Income and Expenditure of Households in Peninsular Malaysia

193

Table 17.2 (continued) Variables

Income groups B40 n

M40 %

n

p-value

449.809

< 0.001

931.532

< 0.001

322.250

< 0.001

T20 %

n

%

Student

9

36.0

14

56.0 2

8.0

Government pensioner

119

53.6

83

37.4 20

9.0

Private pensioner

59

64.8

26

28.6 6

6.6

Elderly

150

83.8

26

14.5 3

1.7

Persons with disabilities

7

100.0 0

0.0 0

0.0

Others

5

83.3

1

16.7 0

0.0

1

276

65.1

115

27.1 33

7.8

2

520

44.5

441

37.8 207

17.7

3

367

29.8

589

47.8 276

22.4

4

296

22.8

614

47.2 390

30.0

5

441

23.6

844

45.1 585

31.3

Johor

506

34.3

695

47.2 273

18.5

Kelantan

584

64.7

240

26.6 78

8.6

Penang

343

35.8

435

45.4 181

18.9

Selangor

404

22.7

831

46.7 546

30.7

Kuala Lumpur

63

7.2

402

45.8 413

47.0

Household size

State

Strata Urban

1412 27.5

2321 45.1 1409 27.4

Rural

488

282

57.3

χ2

33.1 82

9.6

grouped in B40 households. However, the majority of married and single household heads are M40 households. Married couples were more likely to have a better quality of life in terms of income as the households might consist of more than one income recipient to support their family. This finding congruent with the study conducted by Arshad [27] who stated that marriage had positive effects on household revenue as family heads worked hard to ensure a better life for the dependents due to responsibility. Single household heads had a better chance to belong with M40 and T20 family income groups compared to other marital status [18]. Those with degree or advanced diploma certificates accounted for 60.7% in T20 income group, while only 7.2% for those who had no certificate. It was obviously to demonstrate that higher educational levels of household heads tended to receive higher household revenue and vice versa. Many researchers’ works [4–9, 28, 29] proved that educational level was positively correlated with income distribution. This is because education plays an essential role in economic performance, and most of the jobs nowadays require high levels of knowledge and technology skills. As a

194

T. K. May et al.

result, these jobs were highly paid in terms of salary to fulfil the demand of expertise in the industry. The activity status of household heads as an employer recorded 63.4% in T20 income group followed by government employees (31.7%) and private employees (26.3%). Most of the employers were able to earn more from direct revenue of the company, such as the sales of goods or services, compared to other activity status. The previous studies [12, 13] supported the findings, saying that self-employed businessmen tended to generate higher household revenue. Based on the result, the bigger family size may generate higher household income since the household size of five accounted for 31.3% in T20 income group while households with only one member recorded 7.8%. Households with more members were more likely to have higher household income due to a higher number of income recipients. Talukder [20] supported that family wages increased as the number of family members increased in Bangladesh but contradicted some previous studies [8, 10, 11] which found that the household revenue decreased when family size increased. Families who live in Kelantan region contributed 64.7% in B40 income group, while only 7.2% of Kuala Lumpur households were B40. Rural families also tended to have a high proportion in B40 income groups (57.3%), while most of the urban households belonged to M40 income group (45.1%). These prove that families who lived in Kuala Lumpur and urban areas were able to enhance their household revenue since there were more career opportunities in cities as well as industrial areas. However, B40 households in Kelantan demonstrated the highest percentage due to the state having limited access to employment opportunities, education, markets and quality infrastructure. The results were supported by some previous research [3, 4] indicating that regional factors were significant in income inequality.

17.3.2 Relationship of Household Income and Household Expenditure Region The estimated regression models for Kuala Lumpur, Selangor, Johor, Penang and Kelantan were well fitted as they passed the diagnostic tests, and the results are presented in Fig. 17.1. It shows that monthly household income had a linear, direct and statistically significant relationship with monthly household expenditure in all regions. These results proved that the household expenditure increased as their income grew. The findings were supported with Najdi et al. [30] demonstrated that household expenses rose as the total gross income increased. This is because when revenue grows, disposable income rises, and thus, consumers purchase more goods and services for their own demands. Richer families were spending more of their income on purchasing vehicles [31]. By comparing the household expenditure in relation to household income among five states in Peninsular Malaysia, Fig. 17.1 presented that Kuala Lumpur families

17 Analysis of Income and Expenditure of Households in Peninsular Malaysia

195

Fig. 17.1 Comparison of household expenditure with respect to household income by region

tended to spend the most, which was RM1361.10 monthly on the average when their monthly income is equal to zero. Selangor recorded the second highest minimum monthly household spending followed by Johor and Penang. These phenomena were affected by the average income of the states as income was directly proportional to expenditure. It proved that the central region possessed a higher average income as well as higher cost of living that led to the growth of spending. Besides, the land was scarce in cities due to the higher population and hence drove up the price of land, along with the rise of rental or property prices. On the other hand, the minimum monthly expenditure of Kelantan families was the lowest, which recorded 2.16 times lower than Kuala Lumpur households. This might be because Kelantan was an undeveloped state, and the cost of living was correspondingly low. It consists of many rural areas which lack of the services and leisure activities that cities have. In addition, the housing in rural areas was generally more affordable due to plentiful land. The findings were confirmed that rural households spent lower in relation to their income compared to urban families [16, 32]. Next, Kelantan households recorded the largest increment in expenditure for every RM1000 of their monthly household income, on average. This was because of an increase in the consumption of major purchases as well as non-essential goods when Kelantan families generated extra income. Inversely, the households who stayed in Kuala Lumpur had the lowest increment in household spending for every thousand Malaysian Ringgit revenue. These findings indicated that the central region had the highest cost of living, followed by the southern region, northern region, and the last was the east coast of Peninsular Malaysia. Najdi et al. [30] also supported that households who lived in central region such as Selangor and Putrajaya possessed a large proportion in the high expenditure group due to their high household revenue.

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17.3.3 Significant Demographic Determinants of Household Expenditure The estimated multiple regression model passed all the diagnostic tests and was well fitted; the results obtained from the models are demonstrated in Table 17.3. All demographic characteristics were statistically significant at 0.01 significance level. The result of the multiple regression model showed that male household heads spent higher than females. Research conducted by Fatima and Ahmad [33] showed that there were different significant factors that affect household expenditure between both male and female heads. Chinese households recorded the highest monthly household spending on average, followed by Indian and Bumiputera families, while the lowest spending was other ethnicities. These findings were congruent with Ayyash and Sek [17] presenting that male and non-Bumiputera tended to spend higher. This might be because Chinese and Indians were more likely to spend money on higher cost services compared to Bumiputera and other ethnicities, such as private educational institutions and private hospitals. Furthermore, all educational levels dummies were negatively significant compared with degree or advanced diploma as the reference level. The results demonstrated that household heads with higher levels of certification tended to contribute higher household expenditure to satisfy their demands. This finding was acknowledged by the studies [13, 32] stating that the level of education attained was positively significant with family expenditure. This was because they possessed greater purchasing ability due to their higher lifetime wages generated. Yan et al. [34] also explained that household heads who with higher levels of education tended to spend more on education expenses for their children, but Molla et al. [35] found that educated families spent less on health expenditure compared to uneducated counterparts due to the knowledge about availability of health technology. Next, all activity status dummies were statistically significant and had negative signs as compared to employers. This represented that the household heads who as an employer tended to spend the most among other activity status as self-employed businessmen had the greatest purchasing ability due to their high employment levels as well as high average revenue levels, followed by government employee and private employee. Households who lived in the central region and cities were more likely to have higher consumption expenditure, indicating the cost of living in urban areas was correspondingly high since the central region had the most economic activities and infrastructure development. The findings were consistent with the results found by Pew Research Center [36] which explained that city households spent 1.6 times greater than rural families, on average. In addition, households in the central region recorded the highest average monthly household spending compared to other regions [17].

17 Analysis of Income and Expenditure of Households in Peninsular Malaysia Table 17.3 Result of estimated multiple regression model

197

Variables

Coefficient

Standard errors

Gender (Male)

−3.5978 ***

0.3155

Chinese

4.8996 ***

0.2992

Indian

2.3935 ***

0.4385

Others

−4.1086 ***

0.6652

Ethnicity (Bumiputera)

Educational level (Degree/advance diploma) Diploma/certificate

−8.3281 ***

0.4452

STPM

−11.7537 ***

0.8666

SPM/SPMV

−13.4382 ***

0.3842

PMR/SRP

−16.0382 ***

0.5112

No certificate

−17.7428 ***

0.4929

−7.6745 ***

1.3304

Activity status (Employer) Government employee Private employee

−11.7829 ***

1.2793

Own account worker

−10.4529 ***

1.3002

Housewife/looking after home

−16.7632 ***

1.7417

Student

−6.6969 *

2.7136

Government pensioner

−13.8133 ***

1.3957

Private pensioner

−17.0601 ***

1.6405

Elderly

−20.1291 ***

1.4230

Persons with disabilities

−18.6514 ***

5.2338

Others

−26.1058 ***

5.2268

−8.1027 ***

0.3841

Penang

−2.6503 ***

0.3861

Selangor

2.0799 ***

0.3427

Kuala Lumpur

5.8355 ***

0.4449

Rural

−2.2198 ***

0.3582

Constant

83.9951 ***

1.3331

R-squared

0.6142

Adjusted R-squared

0.6136

State (Johor) Kelantan

Strata (Urban)

Significant codes: 0 = ‘***’, 0.001 = ‘**’, 0.01 = ‘*’

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17.4 Conclusion In conclusion, male and Chinese household heads aged between 40 and 59 years, married, degree or advanced diploma educated, self-employed, households with five family members, lived in Kuala Lumpur as well as urban areas tended to belong to T20 household income group. The growth of household income would lead to the increase of household spending. Households who stayed in Kuala Lumpur recorded the highest average of monthly minimum spending among other states while Kelantan families recorded the lowest minimum spending per month. Based on the findings, male and Chinese family heads with higher educational levels and entrepreneurship skills possessed greater purchasing ability which resulted in higher household expenditure due to their high lifetime salaries generated. Households who lived in the central region and urban area had higher consumption expenditure per month. The contribution of the study includes helping fresh graduates in locating jobs that meet their requirements and assist those who are going to settle down in a new location in making the best decision possible. Furthermore, the findings of this study will serve as a guide for Malaysian NGOs that aim to provide relief to low-income Malaysians who need food or shelter. These results will also give a useful reference for retirees with little funds who want to enjoy the rest of their lives in a low-consumption state or area. Another research can be conducted by using the comprehensive data to investigate the distribution of household income and expenditure in the district areas for each state in Malaysia. Future researchers can present the findings in a more interesting way by using data visualisation techniques. Acknowledgements The research work is supported by Ministry of Higher Education, Malaysia. Fundamental Research Grant Scheme (FRGS) grant (Vot K297), reference number FRGS/1/2020/ STG06/UTHM/02/4.

References 1. The Guardian, Household income crucial in children’s life prospects, says LSE report. The Guardian. (2017). Retrieved from https://www.theguardian.com/inequality/2017/jul/12/hou sehold-income-crucial-role-children-life-prospects-lse-report?CMP=share_btn_tw 2. A. Ridzuan, M. Razak, Z. Ibrahim, A. Noor, E. Ahmed, Household consumption, domestic investment, government expenditure and economic growth: new evidence from Malaysia. J. Sci. Res. Rep. 3(17), 2373–2381 (2014) 3. R. Cárdenas-Retamal, J. Dresdner-Cid, A. Ceballos-Concha, Impact assessment of salmon farming on income distribution in remote coastal areas: the Chilean case. Food Policy 101, 102078 (2021) 4. C. Gradín, Race and income distribution: evidence from the USA, Brazil and South Africa. Rev. Dev. Econ. 18(1), 73–92 (2014) 5. N. Jumadi, A.A. Bujang, H.A. Zarin, The relationship between demographic factors and housing affordability. Malays. J. Real Estate 5(1), 49–58 (2010) 6. H. Van Vu, The impact of education on household income in rural Vietnam. Int. J. Financ. Stud. 8(1) (2020)

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7. S.A.A. Saadv, A. Adam, The relationship between household income and educational level. (south Darfur rural areas-Sudan) statistical study. Int. J. Adv. Stat. Probab. 4(1), 27 (2016) 8. F. Nusrat, Impact of household and demographic characteristics on poverty in Bangladesh: a logistic regression analysis. In: 2015 Awards for Excellence in Student Research and Creative Activity (2015) 9. B.N. Lazarus, A study of household income determinants and income inequality in the Tominian and Koutiala zones of Mali (2013) 10. T.Q. Tuyen, The impact of farmland loss on income distribution of households in Hanoi’s peri-urban areas Vietnam. Hitotsubashi J. Econ. 55(2), 189–206 (2014) 11. H.G.P. Jansen, J. Pender, A. Damon, W. Wielemaker, R. Schipper, Policies for sustainable development in the hillside areas of Honduras: a quantitative livelihoods approach. Agric. Econ. 34(2), 141–153 (2006) 12. S. Biwei, H. Almas, Analysis of the determinants of income and income gap between Urban and Rural China. China Econ. Policy Rev. 02(01), 1350002 (2013) 13. A. Nasir, N.H. Nik Mustapha, N.F. Kamil, Analysis of income and expenditure of households in the east coast of peninsular Malaysia. J. Glob. Bus. Econ. 2(1), 59–72 (2011) 14. NTA, Lower-income countries and the demographic dividend. NTA Bull. 5, 1–8 (2012) 15. T.Q. Tuyen, Socio-economic determinants of household income among ethnic minorities in the North-West Mountains Vietnam. Croatian Econ. Surv. 17(1), 139–159 (2015) 16. F. Shamim, E. Ahmad, Understanding household consumption patterns in Pakistan. J. Retail. Consum. Serv. 14(2), 150–164 (2007) 17. M. Ayyash, S.K. Sek, Decomposing inequality in household consumption expenditure in Malaysia. Economies 8(4), (2020) 18. G. Thangiah, M.A. Said, H.A. Majid, D. Reidpath, T.T. Su, Income inequality in quality of life among rural communities in Malaysia: a case for immediate policy consideration. Int. J. Environ. Res. Public Health 17(23), 1–19 (2020) 19. L.D. Schroeder, D.L. Sjoquist, P.E. Stephan, Linear regression. In: Understanding regression analysis: an introductory guide, pp. 1–20. SAGE Publications Inc (2017) 20. D. Taluker, Assessing determinants of income of rural households in Bangladesh: a regression analysis. J. Appl. Econ. Bus. Res. 4(2), 80–106 (2014) 21. A. Strothmann, A. Marsh, S. Brown, Impact of household income on poverty levels 22. W. Lens, M. Lacante, M. Vansteenkiste, D. Herrera, Study persistence and academic achievement as a function of the type of competing tendencies. Eur. J. Psychol. Educ. 20(3), 275–287 (2005) 23. J. Frost, Choosing the correct type of regression analysis. Statistics By Jim (2017) 24. J. Frost, Ordinary least squares. Statistics By Jim (2020) 25. R. Bevans, An introduction to simple linear regression. Scribbr (2020) 26. W. Kenton, Multiple linear regression (MLR) definition. Investopedia (2021) 27. M.N.B.M. Arshad, Return to education by ethnicity: a case of Malaysia. Int. J. Econ. Manage. 10(1), 141–154 (2016) 28. P. Cuadrado, O. Fulmore, E. Phillips, The influence of education levels on income inequality (2019) 29. Q. Talley, T. Wang, G. Zaski, Effect of education on wage earning (2018) 30. N.F.N. Najdi, N.F. Khairul Adlee, A.A. Adnan, N.I. Mustafa Khalid, I. Suzilah, Exploratory data analysis on household expenditure survey 1998 and 2014. J. Hum. Capital Dev. (JHCD) 12(1), 25–48 (2019) 31. N. Valenzuela-Levi, The rich and mobility: a new look into the impacts of income inequality on household transport expenditures. Transp. Policy 100, 161–171 (2021) 32. H.L.S. Heng, A.T.K. Guan, Examining Malaysian household expenditure patterns on foodaway-from-home. Asian J. Agricult. Dev., pp. 11–24 (2007) 33. A. Fatima, Z. Ahmad, Estimation of household expenditures on the basis of household characteristics by gender. Pak. J. Soc. Issues 4, 1–15 (2013) 34. G. Yan, Y. Peng, Y. Hao, M. Irfan, H. Wu, Household head’s educational level and household education expenditure in China: the mediating effect of social class identification. Int. J. Educ. Dev. 83, 102400 (2021)

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35. A.A. Molla, C. Chi, A.L.N. Mondaca, Predictors of high out-of-pocket healthcare expenditure: an analysis using Bangladesh household income and expenditure survey, 2010. BMC Health Serv. Res. 17(1), 1–8 (2017) 36. Pew research center: household expenditures and income. In: The Pew Charitable Trusts (2016)

Chapter 18

A Comparative Analysis of Credit Card Detection Models Kimberly Chan Li Kim, Aida Mustapha, Vaashini Palaniappan, Woon Kah Mun, and Vinothini Kasinathan

Abstract Data mining and machine learning are gaining popularity for fraud detection due to their effective results to cater the exponentially growing card transactions that comes with the fast-growing frauds. The aim of this paper is to explore which of the many techniques are capable to detect fraudulent transactions the best. Methods such as logistic regression, decision tree, support vector machine (SVM), Naive Bayes, and random forest are evaluated on their performance based on factors such as accuracy, precision, recall, and F1-score. The results showed that the random forest performed the best among the five methods investigated for credit card fraud detection.

18.1 Introduction A credit card is issued by a bank that allows card holders to make purchases using borrowed funds. The amount borrowed plus any applied interest and/or charges needs to be credited back by the agreed card holder in full. It is essentially a loan facility subjected to its own terms and conditions (T&C) [13]. With its physical presence, this liability also comes with the risk of identity theft and credit card fraud. This could happen when criminals make purchases, usually luxury goods, large sums, or even the most discreet unnoticeable transactions, out of the card holder’s knowledge and awareness. The crime can be committed through lost or stolen cards, counterfeit, phone or phishing scams and applications using someone else’s personal information [1]. To highlight the severity of the matter, according to statistics, USD32.3 billion K. C. L. Kim · A. Mustapha (B) · V. Palaniappan · W. K. Mun Faculty of Applied Sciences and Technology, Universiti Tun Hussein Onn Malaysia, KM1 Jalan Pagoh, 84600 Pagoh, Johor, Malaysia e-mail: [email protected] V. Kasinathan School of Computing and Technology, Asia Pacific University of Technology and Innovation, Jalan Teknologi 5, Taman Teknologi Malaysia, 57000 Kuala Lumpur, Malaysia e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Mustapha et al. (eds.), Proceedings of the 8th International Conference on the Applications of Science and Mathematics, Springer Proceedings in Physics 294, https://doi.org/10.1007/978-981-99-2850-7_18

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dollars were lost globally for fraud reimbursements in 2020, and it is expected to hit USD40 billion dollars in 2027 [16]. It is also known to be the fastest-growing identity theft. Many security improvements have been integrated into credit cards in order to reduce fraud rates, yet many still fall victim to this day, and some, unfortunately, were victims before. The simplest detection can be done when card holders routinely check their card statements and credit reports to mine out any suspicious transactions and make a report to the bank and to the authorities if any, for further action. In this century, however, millions of bank transactions are made and detecting fraudulent activity can be overwhelming [2]. As smart as security now, as smart as criminals are too. Criminals in this century are craftier and more creative. Credit card frauds detection is getting trickier, and it is why many data mining and machine learning techniques are used to effectively tackle this problem especially for data that comes in large volumes. The objective of these algorithms for that purpose is to correctly classify if transactions are fraudulent or genuine. There are many algorithms ranging from simple to complex that is capable to detect fraudulent transactions from the legitimate transactions. The complexity in some of these algorithms is incomparable to the old, traditional rule-based approach that requires a hefty computational power and an extremely tedious learning process when it comes to new fraud patterns that may overwrite the rules set before it. It was incapable and difficult to keep up with the constant evolvement of fraudsters. On the contrary, it deserves its praise and credit since it was the best available option out there to curb the issue. Data mining and machine learning (ML) are not as intimidating as it seems because a novice can understand some of the simpler algorithms without expert knowledge in artificial intelligence (AI). A combination of different algorithms can potentially build the most accurate model in conjunction with finance experts to keep frauds at bay. The one, if not many, perk of ML compared to the outdated method is its ability to adapt and evolve. ML has the power to discern new patterns that the former one could not, and it saves a lot of manual labor each time criminals pull new tactics day by day. This is the turning point and the time is now, out with the old and in with the new. In this work, the Credit Card Transactions Fraud Detection Dataset retrieved from the Kaggle repository (https://www.kaggle.com/datasets/mlg-ulb/cre ditcardfraud) was used to perform the analysis to determine which algorithms provide the best accuracy in detecting frauds among the thousands of transactions that contain many key features. The remainder of this paper is organized as follows. Section 18.2 reviews related works related to credit card fraud detection. Section 18.3 presents the methodology used to perform the data mining task along with the dataset and the evaluation metrics. Section 18.4 presents the results, and finally, Sect. 18.5 concludes with the direction for future work.

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18.2 Related Work to Credit Card Fraud Detection The literature has provided a landscape of machine learning approaches used in the credit card fraud detection domain. Lakshmi and Kavilla [7] demonstrated the accuracy of logistic regression, decision tree, and random forest classifier in detecting fraud transactions. Sensitivity, specificity, accuracy, and error rate are the variables in measuring accuracy. The results were remarkably accurate, that is at least 90%, but the random forest technique presented the best accuracy out of the three. Borah et al. [5] performed a similar approach, including the support vector machines (SVM) and Naive Bayes algorithms and the comparative analysis showed that random forest outperformed the other methods in all four evaluation measures, which are accuracy, precision, recall, and F1-score. Thirunavukkarasu et al. [15] evaluated random forest only and found a much higher accuracy of 99.93%. A larger training data would further improve the algorithm, but speed would be compromised and requires hardware with stronger specifications. More results have been reported on using data mining and machine learning techniques to detect credit card transactions compared to the traditional rule-based approach that requires large computational power and complex rule building in order to precisely detect fraud patterns such as in [1, 8]. The performance of artificial neural networks (ANNs), support vector machines (SVMs), decision tree (DT), and other algorithms was reviewed and evaluated in various works. It was found that heavycomputational methods were capable of learning and adapting to new fraud patterns to counter the evolving sophisticated criminals such as in [6, 9, 10, 17]. Meanwhile, supervised machine learning methods are effective and require comprehensive retraining for new data. In 2019, Maniraj et al. [10] employed the local outlier factor and isolation forest algorithm to two days’ worth of transaction records and found that a high accuracy does not come with high precision. However, when more data is fed into the algorithm, the precision increased. This indicated that the program would have better potential if larger amounts of data were available. Work by [9] reviewed credit card fraud detection and summarized the authors’ choice of classification approach with other models and techniques. The most frequent methods are found to be the hidden Markov model (HMM), K-mean clustering, and decision trees. Kavipriya and Geetha [6] compared the various credit card fraud detection techniques such as HMM, neural network, Bayesian network, genetic algorithm, KNN, SVM, decision tree and fuzzy logic-based system while [17] focused on only Bayesian network classifiers and found that all classifiers have an accuracy of more than 95% when the credit card transactions are filtered with normalization and principal component analysis (PCA) while the pre-processed data has accuracy at most 84%. In summary, there are advantages and disadvantages among various credit card fraud detection algorithms such as decision tree, random forest, logistic regression, ANN, K-nearest neighbors (KNN), and K-means clustering. Each of these techniques have an advantage over the other in certain circumstances such as its simplicity, adaptability, volume, or efficiency.

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18.3 Methodology In this study, different machine learning methods are used to determine which method works best in detecting fraud based on customer’s data. Since the study is used to determine if a transaction is a fraud, classification method will be is used. Since the number of data is large and all algorithms can be found on Python, the experiments were carried out using “sklearn,” a free open-source Python library [11] with fivefold validation method for training and testing. The coding was carried out using the Jupyter Notebook, a web-based open-source computing platform. The classification methodology is shown in Fig. 18.1. Based on the figure, postdata processing, the credit card fraud detection models are trained by using five classification algorithms, which are logistic regression, decision tree, support vector machine, Naive Bayes, and random forest. To determine the best model, the accuracy, precision, recall, and F1-score are analyzed.

Fig. 18.1 Classification methodology

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Fig. 18.2 Excerpt of dataset

18.3.1 Dataset A dataset was obtained from Kaggle, containing information credit card holders and a target class of whether it is a legit or fraudulent transaction. The dataset contained 23 columns, whereby 21 columns are predictor values while 1 column acts as the predicted and 1 as the count. Besides, there is a total of 1,048,575 rows. Under Is Fraud column, 0 represents a legit transaction, while 1 represents a fraudulent one. The excerpt of the dataset is shown in Fig. 18.2, while the description of attributes is provided in Table 18.1.

18.3.2 Algorithms This paper used five algorithms to build the credit card fraud detection models, which include the logistic regression, decision tree, support vector machine, Naive Bayes, and random forest. • Logistic Regression: One of the classification algorithms is logistic regression, which is used to predict binary values in a set of independent variables (1/0, Yes/ No, True/False). Dummy variables are used to represent binary and categorical data. When the resulting variable is categorical, the log of chances is utilized as the dependent variable in logistic regression. It also fits data to a logistic function to estimate the likelihood of an event occurring [4]. • Decision Tree: The decision tree method is a supervised learning technique that can be used to solve problems in classification and regression. It has a tree like structure, hence, the name. A decision tree’s main goal is to split scenarios into yes or no which splits the tree into subtrees [12].

206 Table 18.1 Attribute details

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Attributes

Details

Attribute type

no

Count number

Numeric

trans.date.trans.time

Transaction date and time

Date

cc-num

Credit card number

Nominal

merchant

Name/company of seller

Nominal

category

Type of item purchased

Nominal

amt

Amount of transaction Numeric

first

Credit card holder’s first name

Nominal

last

Credit card holder’s last name

Nominal

gender

Credit card holder’s gender

Binary

street

Credit card holder’s address

Nominal

city

Credit card holder’s address

Nominal

state

Credit card holder’s address

Nominal

zip

Credit card holder’s address

Nominal

lat

Credit card holder’s coordinates

Nominal

long

Credit card holder’s coordinates

Nominal

city-pop

Registered address’ city population

Nominal

job

Credit card holder’s job

Nominal

dob

Credit card holder’s birthdate

Nominal

trans_num

Transaction number

Nominal

unix_time

Unix time stamp

Nominal

merch lat

Coordinates of where purchases are made

Nominal

merch long

Coordinates of where purchases are made

Nominal

is.fraud

Legibility of the transaction

Binary

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• Support Vector Machine: Similar to decision tree, SVM is also a supervised learning method used for classification and regression, but in addition, it can be also used for outlier detection. SVM can be used on unstructured, structured and semi-structured data. As it uses kernel function, it can ease complexities of the data [18]. • Naive Bayes: Naive Bayes is a classification algorithm that works as a probabilistic classifier. Since it works as an assumption, the independence assumptions often have no impact, therefore known as Naive [14]. • Random Forest: This method constructs multiple individual decision trees. Since it applies the same concept, this algorithm is also a supervised machine learning algorithm that can be used in classification and regression problems. Due to its simplicity, it can be said to be one of the most used algorithms. This method uses the ensemble technique to combine multiple decision trees to be used for prediction. This increases the overall performance. Therefore, this method should work better than decision trees [18].

18.3.3 Evaluation Metrics In utilizing classifications models to solve real-world problems, it is necessary to evaluate their performance. In machine learning classification models, performance measurements are used to evaluate how effectively the algorithms perform in a specific situation. Accuracy, precision, recall, and F1-score are examples of performance metrics. The number of times a model predicts a class properly or erroneously can be divided into four categories as follows that made a confusion matrix [3]: • • • •

True positives (TP): model predicts the positive class properly. True negatives (TN): model predicts the negative class properly. False positives (FP): model predicts the positive class inaccurately. False negatives (FN): model predicts the negative class inaccurately.

Accuracy is the ratio of true positives and true negatives to all positive and negative observations. In other words, accuracy indicates the likelihood that a machine learning model would accurately anticipate an outcome based on the total number of predictions it has made. The formula for calculating accuracy is shown in (18.1) [12]. Accuracy =

TP + TN . TP + FP + TN + FN

(18.1)

Precision is the model’s ability to correctly predict the positives out of all the positive predictions it produced and it is measured by its precision score. This score is a good indicator of prediction success when the classes are extremely imbalanced. It denotes the proportion of true positives to the sum of true positives and false positives. The formula for calculating precision is shown in (18.2) [12].

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Precision =

TP . TP + FP

(18.2)

Recall is the model’s ability to correctly predict positives out of real positives, and it is measured by the model recall score. Recall is different from precision because if the machine learning model is attempting to detect positive reviews, the recall score would be the percentage of positive reviews that the model correctly predicted as positive. In other words, it assesses how well the machine learning model recognizes all true positives among all possible positives in a dataset. The better the machine learning model is in identifying both positive and negative samples, the higher the recall score. The formula for calculating recall score is shown in (18.3) [12]. Recall =

TP . TP + FN

(18.3)

F1-score is the model score as a function of precision and recall. It measures precision and recall equally when evaluating accuracy, making it a viable alternative to accuracy metrics because it does not require prior knowledge on the total number of observations. It is frequently utilized as a single value that conveys high-level information regarding the output quality of the model. This is a valuable model measure in situations where one tries to optimize either precision or recall score and the model performance suffers as a result. The formula for calculating F1-score is shown in (18.4) [12]. F1 - Score =

2 × Precision × Recall . Precision + Recall

(18.4)

18.4 Results and Discussion The main purpose of the analyses is to compare the performance of five algorithms that can accurately predict which transactions are likely to be fraudulent. The complete results from the comparative experiments are shown in Table 18.2. Table 18.2 Results from comparative experiments Algorithm

Accuracy

Precision

Recall

F1-score

Logistic regression

0.989951

0.000000

0.000000

0.000000

Decision tree

0.994500

0.734375

0.701493

0.717557

Support vector machine

0.989951

0.000000

0.000000

0.000000

Naive Bayes

0.987401

0.381395

0.407960

0.394231

Random forest

0.995500

0.958678

0.577114

0.720497

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Fig. 18.3 Correlation matrix of dataset

Based on Table 18.2, the results showed that random forest reached over 95% accuracy and precision, while the recall score is seen to be lacking with only 57% compared to the recall score of decision tress, which is 70%. If analyzed closely, the decision tree algorithm can be considered a good model too as it has a constant score above 70% across all four criteria. Therefore, since random forest is an ensemble of decision trees and it has a slightly higher accuracy, it stands as the best method for the data. Figure 18.3 shows the correlation matrix for the dataset that indicates most of the variables have a 0.25 correlation with each other. A few certain variables have high correlation such as Unix timestamp against row number, and the purchaser’s longitude and latitude against the merchant’s longitude and latitude. To illustrates the results from Table 18.2, Fig. 18.4 shows the confusion matrix for logistic regression. From this figure, it is shown that there are 19,771 true positives, 30 false positives, 178 false negatives, and 22 true negatives. This is the base calculation for the results presented in Table 18.2. In summary, the results showed that random forest classifier is the best algorithm to reflect an accurate degree of fraudulent activity, according to experimental results. Random forest can manage many highly skewed datasets in a short amount of time. When compared to algorithms like decision trees, support vector machines, and logistic regression, which do not perform well in managing imbalanced datasets, it exhibits considerable growth in detecting credit card fraud transactions with an accuracy of 99.5% in the end results.

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Fig. 18.4 Confusion matrix for logistic regression

18.5 Conclusions All methods used in this study are classification methods that work well in detecting credit card fraud transaction with random forest being the best algorithm to detect credit card fraudulent transactions. In this study, no method was able to obtain 100% accuracy in fraud detection; therefore, a lot of studies can still be done such as improving the model by splitting time and date to determine the timeframe of transactions. Besides, there are still many machine learning methods that are yet to be tested. To conclude, improvements can still be made via incorporating more features through feature engineering along with different types of algorithms. Acknowledgements This research is funded by Asia Pacific University of Technology and Innovation.

References 1. R. Almutairi, A. Godavarthi, A.R. Kotha, E. Ceesay, in Analyzing Credit Card Fraud Detection Based on Machine Learning Models. 2022 IEEE International IOT, Electronics and Mechatronics Conference (IEMTRONICS) (IEEE, 2022), pp. 1–8 2. B. Al-Smadi, M. Min, in A Critical Review of Credit Card Fraud Detection Techniques. 2020 11th IEEE Annual Ubiquitous Computing, Electronics & Mobile Communication Conference (UEMCON), pp. 732–736 (2020) 3. A.H. Azizan, S.A. Mostafa, A. Mustapha, C.F.M. Foozy, M.H.A. Wahab, M.A. Mohammed, B.A. Khalaf, A machine learning approach for improving the performance of network intrusion detection systems. Ann. Emerg. Technol. Comput. (AETiC) 5(5), 201–208 (2021)

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4. S. Bahramirad, A. Mustapha, M. Eshraghi, in Classification of Liver Disease Diagnosis: A Comparative Study. 2013 Second International Conference on Informatics & Applications (ICIA), pp. 42–46 (2013) 5. L. Borah, B. Saleena, B. Prakash, Credit card fraud detection using data mining techniques. J. Seybold Rep. 15(9) (2020) 6. T. Kavipriya, N. Geetha, Study on credit card fraud detection using data mining techniques. Int. J. Contemp. Res. Comput. Sci. Technol. 3(3), 33–35 (2017) 7. S. Lakshmi, S.D. Kavilla, Machine learning for credit card fraud detection system. Int. J. Appl. Eng. Res. 13(24), 16819–16824 (2018) 8. K.S. Lim, L.H. Lee, Y.W. Sim, A review of machine learning algorithms for fraud detection in credit card transaction. Int. J. Comput. Sci. Network Secur. 21(9), 31–40 (2021) 9. M. Mahajan, S. Sharma, Detects frauds in credit card using data mining techniques. Int. J. Innov. Technol. Explor. Eng. (IJITEE) 9(2), 4891–4895 (2019) 10. S. Maniraj, A. Saini, S. Ahmed, S. Sarkar, Credit card fraud detection using machine learning and data science. Int. J. Eng. Res. 8(9), 110–115 (2019) 11. F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, Scikit-learn: machine learning in python. J. Mach. Learn. Res. 12, 2825–2830 (2011) 12. N. Razali, S. Ismail, A. Mustapha, Machine learning approach for flood risks prediction. IAES Int. J. Artif. Intell. 9(1), 73 (2020) 13. R. Sailusha, V. Gnaneswar, R. Ramesh, G.R. Rao, in Credit Card Fraud Detection Using Machine Learning. 2020 4th international conference on intelligent computing and control systems (ICICCS), pp. 1264–1270 (2020) 14. Z. Saringat, A. Mustapha, R.R. Saedudin, N.A. Samsudin, Comparative analysis of classification algorithms for chronic kidney disease diagnosis. Bull. Electr. Eng. Inform. 8(4), 1496–1501 (2019) 15. M. Thirunavukkarasu, A. Nimisha, A. Jyothsna, Credit card fraud detection through parenclitic network analysis. Int. J. Comput. Sci. Mob. Comput. 10(4), 71–79 (2021) 16. XGenTech: Everything you need to know about fraud prevention strategies for your shopify store. Retrieved 16 Sept 2022 [online]. https://xgentech.net/blogs/resources/everything-youneed-to-know-about-fraud-prevention-strategies-for-your-shopify-store 17. O.S. Yee, S. Sagadevan, N. Malim, Credit card fraud detection using machine learning as data mining technique. J. Telecommun. Electron. Comput. Eng. (JTEC) 10(1–4), 23–27 (2018) 18. N.A.S. Zaidi, A. Mustapha, S.A. Mostafa, M.N. Razali, in A Classification Approach for Crime Prediction. International Conference on Applied Computing to Support Industry: Innovation and Technology, pp. 68–78 (2019)

Chapter 19

Credit Scoring Model for Tenants Using Logistic Regression Kim Sia Ling, Siti Suhana Jamaian, and Syahira Mansur

Abstract This study applies logistic regression to compute the tenants’ credit scores in Malaysia based on their characteristics without relying on their credit history. In this study, penalized maximum likelihood estimation is utilized to find the parameters of the logistic regression model as existing separation in training data. The initial factors considered affecting tenants’ credit score were their gender, age, marital status, monthly income, household monthly income, expense-to-income ratio, number of dependents, monthly rent and number of months late payments. The marital status factor was removed from the logistic regression model as it is insignificant to the model. Furthermore, k-fold cross-validation with Grid Search was applied to determine the appropriate regularization strength value for maximum likelihood estimation. As result, the logistic regression model with regularization strength of 0.1 is the final model selected. This study found that the significant factors of the tenant’s credit score are the number of months late payment, gender, the expense-to-income ratio, monthly rent and age. A graphical user interface application for the proposed tenant’s credit scoring is developed using HTML and Flask library in Python. The user’s credit score, rating indicator of score and tips to maintain or improve credit score are displayed in the graphical user interface. The application aims to increase the confidence of future property owners and developers to select the low-income group, especially the B40 group, as their potential consumers. Besides, it has the potential to support the tenant’s loan application and is only applicable for the tenant with at least six months of rent payment history.

K. S. Ling (B) · S. S. Jamaian · S. Mansur Department of Mathematics and Statistics, Faculty of Applied Sciences and Technology, Universiti Tun Hussein Onn Malaysia, Pagoh Educational Hub, 84600 Muar, Johor, Malaysia e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Mustapha et al. (eds.), Proceedings of the 8th International Conference on the Applications of Science and Mathematics, Springer Proceedings in Physics 294, https://doi.org/10.1007/978-981-99-2850-7_19

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19.1 Introduction National Housing Department Malaysia [1] stated that the median multiple methodology is implemented as the key indicator to measure housing affordability in Malaysia. According to the median multiple methodology, a house is deemed affordable if its price is not more than three times the annual household income. The median monthly Malaysian household gross income decreased from RM5,873 in 2019 to RM5,209 in 2020 [2]. Therefore, the affordable housing for Malaysians with median household income is priced at RM187,524 and below. Based on the National Property Information Centre [3], the median house price in 2021 is RM310,000, which is 1.65 times the price of affordable housing. Some housing schemes such as Perumahan Rakyat 1 Malaysia (PR1MA), Program Perumahan Rakyat (PPR) and the Rent-to-Own scheme are introduced by the government of Malaysia to assist the low-income groups to own a house [4]. A credit score is a creditworthiness indicator used by banks and financial institutions to determine their potential borrowers’ likelihood to default on a loan. The higher the loan applicant’s credit score, the higher the chance of the loan application being approved. Individuals with limited credit history or thin files are referred to as ‘credit unscored’ and those without any credit history are referred to as ‘credit invisible’ [5]. The income level for the household income decile group in Malaysia is shown in [6]. The bank usually rejects the housing loan applications of the B40 group in rural areas as they are ‘credit unscored’ or ‘credit invisible’. Therefore, they typically rent a property, but their rental payment records are not the key for housing loan applications. In Malaysia, the Central Credit Reference Information System (CCRIS) is a system created by the Central Bank of Malaysia to synthesize the credit information of borrowers. The CCRIS report does not show the credit score of the borrower. The report only includes the outstanding loans, special attention accounts and the number of approved or rejected loan or credit facility applications made in the past 12 months [7]. Credit Tip-Off Service (CTOS) and RAM Credit Information Sdn. Bhd. (RAMCI) are the private agencies in Malaysia that provide credit scores for borrowers. On the other hand, FICO score created by Fair Isaac Corporation (FICO) and VantageScore introduced by US national consumer reporting agencies (‘NCRAs’), i.e., Experian, Equifax and TransUnion are common credit scores used in the USA. The credit scoring model that depends only on credit history cannot be used to gain credit scores for those who are ‘credit unscored’ or ‘credit invisible’. Therefore, some credit bureaus have generated credit scores using additional non-financial data, i.e., use of rental payment records by Experian and use of utility data, evictions and other variables by FICO [8]. The research papers that use non-financial data such as rental payment records, utility data, criminal history and delinquency also are reviewed by Njuguna and Sowon [5]. Besides, some researchers utilized other non-financial data such as individual characteristics, loan characteristics and behavioral variables to compute the probability of default or credit score [9–12]. The

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Table 19.1 Individual characteristics that significantly affect default rate References

Individual characteristics Gender

Age

Marital status

[9]

/

/

/

[10]

/

/

[11]

/

[12]

/

/

Income

Payment-to-income ratio /

/

/ /

individual characteristics included in these papers are gender, ethnicity, age, marital status, residential area, children status, educational level, occupation, income, debtto-income ratio or payment-to-income ratio and others. Presented in Table 19.1 are the individual characteristics that significantly affect the default rate according to these papers. Many research papers applied machine learning techniques such as neural networks, support vector machine, decision trees, logistic regression, fuzzy logic and genetic programming, for developing credit scoring models [13, 14]. Furthermore, some papers that proposed hybrid credit scoring models are reviewed by [15, 16]. In this study, we focus on generating a tenant’s credit scoring model without depending on the credit history of tenant by using logistic regression model. The credit scoring model proposed in this study depends on the tenant’s individual characteristics and rent payment behavior. The maximum likelihood method is utilized to generate the parameters of the logistic regression model, and the predictive performance of the proposed model is also evaluated. Moreover, the graphical user interface of the proposed tenant’s credit scoring also is developed. The methodology applied in this research is explained in Sect. 19.2, and the obtained results are discussed in Sect. 19.3.

19.2 Methodology 19.2.1 Rental Information Data The initial factors considered affecting tenants’ credit scores in this study are their gender, age, marital status, monthly income, household income, expense-to-income ratio, number of dependents, previous monthly rent and number of months late payment. The rent paid after a week is considered a late payment and the tenant is assumed to default on rent if making more than two months late payments. The rental information of 33 tenants are collected from a landlord company in Malaysia, 26 (78.79%) of them are considered not default, as specified in [17]. As presented in [17], 81.82% of the tenants are single and 93.94% of them are B40 group. The collected data were transformed into numerical data by referring to [17]. In this

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study, 70% of the collected data is set as a training data, while the remaining data as a testing data.

19.2.2 Logistic Regression The logistic regression transforms the linear regression to the probability of an event success of zero to one. Therefore, the logistic regression is a popular classifier in various fields including credit scoring. The logit of the simple logistic regression with only one factor is g(x) = β0 + β1 x,

(19.1)

where x is the independent variable and β is the logistic regression parameter. Meanwhile, the logit of the multivariable logistic regression with more than one factor is [18]: g(x) = β0 + β1 x1 + β2 x2 + · · · + β p x p ,

(19.2)

where p is the number of x involved. Let binary outcome dependent variable, y = 0 indicates that the tenant does not default, while y = 1 indicates that the tenant defaults, the logistic regression model is: π(x) =

1 , 1 + e−g(x)

(19.3)

where π(x) is the conditional probability of tenant defaulting. After the data have been collected, it is essential to check the multicollinearity among independent variables, where a lot of independent variables are highly correlated with each other. Overfitting data might occur in logistic regression model if the multicollinearity problem existed in training data [18]. In this study, the absolute Spearman’s correlation coefficient of any two factors was ensured smaller than 0.8 to avoid the multicollinearity problem [19].

19.2.3 Maximum Likelihood Estimation Maximum likelihood estimation is a common method used to estimate the parameters of logistic regression, β, by maximizing the likelihood function. The likelihood function for logistic regression with binary outcome dependent variable, y, can be written as [18],

19 Credit Scoring Model for Tenants Using Logistic Regression

(β) =

n 

π(xi ) yi [1 − π(xi )]1−yi ,

217

(19.4)

i=1

where n is the total number of independent data. Normally, the natural log of the likelihood function is preferred to be maximized for parameter estimation for convenience. The natural log of the likelihood function, L(β), can be defined as L(β) =

n 

{yi ln[π(xi )] + (1 − yi ) ln[1 − π(xi )]}.

(19.5)

i=1

Penalized maximum likelihood estimation for solving separation. The logistic regression data can be classified as complete separation, quasi-complete separation or overlap. Separation is either complete or quasi-complete separation in the data, most frequent under the same conditions that lead to small-sample and sparse-data bias, such as the presence of a rare outcome and multicollinearity among independent variables [20]. According to Albert and Anderson [21], maximum likelihood estimates will not exist when the data are under separation. The linear program proposed by Konis [22] was solved to detect separation in this study. The linear program can be written as: maximize

p+1 

X1 j β −

j=1

p+1 

X0 j β

j=1

subject to X 0 β ≤ 0, X 1 β ≥ 0, β is unrestricted,

(19.6)

⎡

⎤ x11 · · · x p1 x12 · · · x p2 ⎥ ⎥, ··· ··· ··· ⎦ x1n · · · x pn ⎡ ⎤ β0 ⎢ β1 ⎥ ⎢ ⎥ β = ⎢ . ⎥, ⎣ .. ⎦

1 ⎢ 1 D=⎢ ⎣··· 1

(19.7)

(19.8)

βp where X 0 is the submatrix of D when yi = 0, while X 1 is the submatrix of D when yi = 1, whereas X 0 j and X 1 j are the elements in column j of X 0 and X 1 , respectively. The data overlap if the feasible solution for the linear program is a zero vector, while the data are under separation if an unbounded solution is gained.

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In this study, limited-memory Broyden–Fletcher–Goldfarb–Shanno (BFGS) numerical method for maximum likelihood estimation using the Scikit-learn library was utilized to find the parameters of logistic regression model. Furthermore, penalized maximum likelihood estimation with ridge regression as a penalty is used for parameter estimation when separation in training data is detected. The objective function for the penalized maximum likelihood estimation can be defined as minimize F(β) = −L(β) + λ R(β), R(β) =

p 

β 2j ,

(19.9)

j=1

where R(β) is ridge regression and λ is positive regularization strength [23]. Tuning regularization strength. Ridge regression produces a set of coefficient estimates whose values depend on the different values of regularization strength, λ. The k-fold cross-validation is a common statistical method used to find the best value for the tuning parameter λ. The training data are split into k-folds of approximately equal size, and one of the folds becomes the validation data. The remaining k−1 folds are used as training data. This procedure is repeated k times to get the optimal λ such that the expected prediction error is minimized [24]. Besides, λ also is a hyperparameter in machine learning algorithms. Generally, a set of pre-specified values is served as candidates of optimal λ for convenience. Then, k-fold cross-validation is applied to select the optimal λ with the highest average accuracy score through the optimization technique. Elgeldawi et al. [25] discussed and used Grid Search, Random Search, Bayesian Optimization, Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) for hyperparameter tuning. In this study, k-fold cross-validation with Grid Search is implemented to tune λ.

19.2.4 Factor Reduction in Model The closer a logistic coefficient is to zero, the less influence the predictor has in predicting the logit. Hence, the factor with a logistic coefficient that closes to zero was tested whether it is significant to the logistic regression model. The Likelihood Ratio, Wald and Score Tests are statistical methods commonly applied for significance test of the logistic coefficient. The Score Test differs from the Likelihood Ratio Test and Wald Test where it does not involve the computation of the maximum likelihood estimates for the logistic coefficient [26]. According to Agresti [27], the Wald Test is the least reliable test among the three tests if the collected data size is small to moderate. Thus, the Likelihood Ratio Test was used in this study to check the significance of the logistic coefficient to the model since the size of the collected data is small. The Likelihood Ratio Test statistic can be expressed as

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Likelihood Ratio Test Statistic = −2 ln

L0 L1

 ,

(19.10)

where L 0 is the likelihood function of the model without excluded factors, while L 1 is the likelihood function of the model that involved all the factors. The excluded factors are significant to the model if the Likelihood Ratio Test statistic does not follow a Chi-square distribution with a degree of freedom equal to the number of factors excluded [18].

19.2.5 Tenant’s Credit Scoring Model In this study, a tenant’s credit scoring model with a range of zero to 100 is proposed. For this proposed model, the tenant with a higher probability of default will have a lower credit score. The proposed credit scoring model is defined as Credit Score = 100(1 − π(x)).

(19.11)

19.2.6 Performance of Model In this study, the testing data were assumed as not default if the computed probability of default, π(x) < 0.5, otherwise the testing data was assumed as default. In addition, the prediction performance of the logistic regression, i.e., accuracy, precision and recall was calculated for evaluation. If the accuracy of testing data is significantly lower than the accuracy of training data, then overfitting occurs. If the accuracy of both testing and training data is low, then underfitting occurs [28]. The area under the receiver operating characteristic curve (AUC) was also computed to check the ability of the model to distinguish the default and not default classes. AUC was computed using the trapezoidal rule in this research [29]. The risk of overfitting occurs is higher if the AUC of testing data is lower than the AUC of training data [30]. Therefore, the accuracy and AUC of both testing and training data were compared to check whether the logistic regression model is overfitting or underfitting.

19.2.7 Graphical User Interface The graphical user interface for the proposed tenant’s credit scoring in this study is a web application developed using HTML and Flask library in Python. The web application aims to increase the confidence of future property owners and developers to

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accept the low-income group, especially the B40 group, as their potential consumers. In addition, the proposed credit scoring has potential to support the tenant’s loan application. The application is only applicable for the tenant with at least six months of rent payment history. The application required the rental information data of the user to compute user’s credit score. The required data are as follows: 1. 2. 3. 4. 5. 6. 7. 8.

Name (Input Box). Gender (Dropdown List). Age: minimum 18 (Input Box). Monthly income: minimum RM300 (Input Box). Household monthly income: minimum RM300 (Input Box). Monthly expense (Input Box). Number of dependents (Dropdown List). Number of months late payment (Dropdown List).

Furthermore, the rating indicator of score and tips to maintain or improve credit score will be displayed in the credit report of the application. The algorithm for generating the tenant credit report: Step 1: Start Step 2: Ask the user to input all required data Step 3: Check the validity of all input Step 4: Not valid? Warning message displayed and go back to Step 1. Step 5: All input data are transformed into numerical data. Step 6: Substitute all numerical data into g(x) (19.2). Step 7: Substitute g(x) into (19.3) to compute the probability of default, π(x). Step 8: Substitute π(x) into (19.11) to determine the credit score of the user (Round to the nearest whole number). Step 9: Compute angle subtended by the arc at the centre of circle where the user’s credit score displayed. The colour of the arc is based on the rating indicator. Step 10: Display the tips to maintain or improve score for user based on the user’s data. Step 11: End The flowchart of algorithm for generating the tenant credit report in the application is summarized in Fig. 19.1.

19 Credit Scoring Model for Tenants Using Logistic Regression

Fig. 19.1 Flowchart of algorithm for generating tenant credit report

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19.3 Results and Discussion 19.3.1 Multivariable Logistic Regression Results Penalized maximum likelihood estimation with ridge regression is implemented to get the parameters of the logistic regression model since separation was detected in the training data. When regularization strength, λ, is set as one, the marital status factor is the only factor among the nine factors with a logistic coefficient of approximately zero. Thus, the Likelihood Ratio Test is utilized to test the significance of marital status factor. The Likelihood Ratio Test result shows that the marital status factor is not significant to the logistic regression model and it can be removed. The candidates of optimal regularization strength, λ, in this study are 0.01, 0.1, 1, 10 and 100. Twofold cross-validation with Grid Search is applied to find the optimal λ since the size of training data is small and the result is presented in Table 19.2. As shown in Table 19.2, the mean accuracies of the model with λ values of 0.01, 0.1 and 1 are similar and higher compared to the model with λ values of 10 or 100. Thus, 0.01, 0.1 and 1 are good choices for λ value. Therefore, the predictive performance of logistic regression with λ values of 0.01, 0.1 and 1 is compared to select the λ value with the best performance. The comparison performance is visualized in Table 19.3. From Table 19.3, the predictive performance of logistic regression is the best when λ is 0.01 and 0.1. Since the ridge penalty term has small effect when λ is approximately zero, we choose value of 0.1 instead of 0.01 as the best λ. The logit of the logistic regression model with regularization strength, λ, of 0.1 is presented in (19.12). The credit score of the tenant can be computed using (19.3) (probability of the tenant defaulting) and (19.11). The analysis of the logistic coefficient without the marital status factor is presented in Table 19.4. Table 19.4 shows that the main factors affecting the tenant’s credit score are the number of months Table 19.2 Result of twofold cross-validation with Grid Search

Table 19.3 Predictive performance of logistic regression with different regularization strengths

Regularization strength, λ

Mean accuracy

Standard deviation accuracy

0.01

0.9583

0.0417

0.1

0.9583

0.0417

1

0.9583

0.0417

10

0.8712

0.0379

100

0.8712

0.0379

Regularization strength, λ

Accuracy

Precision

Recall

0.01

0.90

1.00

0.75

0.1

0.90

1.00

0.75

1

0.80

1.00

0.50

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late payment, gender, the expense-to-income ratio, previous monthly rent and age. Notice that the negative sign of the logistic coefficient indicates that the higher the xi value, the lower the probability of default and vice versa. Thus, female is less likely to default as compared to male. Besides, the probability of the tenant defaulting increases when the tenant’s number of months late payment, the expense-to-income ratio or age increases. Meanwhile, the credit score of the tenant increases when the tenant’s previous monthly rent, monthly income, number of dependents or household income increase. g(x) = −7.5989 + 1.2831 (Gender) + 0.3265 (Age) − 0.2327 (Monthly Income) − 0.1406 (Household Income Group) + 1.0339 (Expense - to - income Ratio) − 0.2294 (Number of Dependents) − 0.9136 (Previous Monthly Rent) + 2.3615 (Number of Months Late Payment)

(19.12)

The performances of the proposed credit scoring model on the testing and training data are also visualized in Table 19.5. According to Table 19.5, there is neither underfitting nor overfitting in this study since the AUC of both training and testing data is equal and the accuracy of training data is slightly higher than the accuracy of testing data.

Table 19.4 Analysis of logistic coefficient (λ = 0.1) Coefficient, β

Factor, x

Value

Sign

Ranking

Odds ratio (increases by one unit)

Gender

1.2831

+

2

3.6078

Age

0.3265

+

5

1.3861

Monthly income

−0.2327

−

6

0.7924

Household income

−0.1406

−

8

0.8688

1.0339

+

3

2.8120

Number of dependents

−0.2294

−

7

0.7950

Previous monthly rent

−0.9136

−

4

0.4011

2.3615

+

1

10.6068

Expense-to-income ratio

Number of months late payment

Table 19.5 Performance of credit scoring model on testing data and training data (λ = 0.1) Data set

Accuracy

Precision

Recall

AUC

Testing data

0.90

1.00

0.75

1.00

Training data

1.00

1.00

1.00

1.00

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19.3.2 Graphical User Interface for Tenant’s Credit Scoring The home page of the web application for tenant’s credit scoring is shown in Fig. 19.2. The aim of creating the application is stated in the home page. After the user fills the data and clicks ‘Confirm and Calculate’ button, the credit score of the user, rating indicator of score and tips to maintain or improve credit score will display in a new page. The user can click ‘Return Home Page’ button to return to the home page. The examples of the generalized credit report are visualized in Fig. 19.3.

Fig. 19.2 Home page of developed web application

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Fig. 19.3 Examples of the generalized credit report

19.4 Conclusion The initial factors considered affecting tenant’s credit score were gender, age, marital status, monthly income, household monthly income, expense-to-income ratio, number of dependents, monthly rent and number of months late payments. The regularization strength for penalized maximum likelihood estimation is initially set as one and the marital status factor is then excluded from the logistic regression model as it is not significant to the model. Besides, the appropriate regularization strength is determined by using k-fold cross-validation with Grid Search. As result, the logistic regression model with regularization strength of 0.1 is the final model selected. The number of months late payment, gender, the expense-to-income ratio, monthly rent and age are the main factors of the tenant’s credit score in this study. Moreover, a web-based graphical user interface application for the proposed tenant’s credit scoring in Malaysia is developed. The user’s credit score, rating indicator of score and tips to maintain or improve credit score are displayed in the application. Acknowledgements We thank the landlord company for providing the rental information data for this research.

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Chapter 20

Optimization of Bayesian Structural Time Series (BSTS) Applications in Forecasting Stock Prices Through State Components Selection Benita Katarina and Gunardi Abstract In recent years, stock market activities have been sluggish due to the COVID-19 outbreaks. Many stocks have fallen, and it is uncertain when the market will recover from this situation. One of the most powerful tools to deal with uncertainty is using the forecasting method to predict the future prices. There is no perfect forecasting method that has been found, but the better ones surely will help the investors maximize their returns as well as minimize their losses. The Bayesian Structural Time Series (BSTS) has high flexibility and is good at describing time series patterns. The method developed by Scott and Variant can be used as an alternative method for forecasting stock prices. We used the BBNI stock prices as the object of this study. BBNI is one of the most outstanding state-owned banking stocks and has the best prospect among the other banking stocks. Based on the results obtained from this study, BSTS has smaller error values than some commonly used classical forecasting methods, i.e., Holt-Winters and SARIMA. However, to produce a model with high accuracy, the proper selection of state components has to be done.

20.1 Introduction The growing popularity of investing has skyrocketed in recent years through the increase of public awareness toward financial management and investment. Among several popular investment instruments, stocks are the most popular choices because of the high rate of return, although the stocks’ investment activities also carry high risks. Therefore, it is important for investors to always be cautious about price changes. Predicting future prices could be one thing to do to avoid the losses caused by those price changes. Researchers and practitioners have widely carried out the application of forecasting methods in the stocks’ investment world. Various methods have continued to B. Katarina · Gunardi (B) Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Yogyakarta, Indonesia e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Mustapha et al. (eds.), Proceedings of the 8th International Conference on the Applications of Science and Mathematics, Springer Proceedings in Physics 294, https://doi.org/10.1007/978-981-99-2850-7_20

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be developed and refined to provide better future predictions. A well-known classical method that is commonly used by the practitioners is Autoregressive Integrated Moving Average (ARIMA). However, this method often gives poor results on financial data because of its limitations in observing volatility, asymmetries, and sudden outbreak at irregular time intervals [1]. The financial time series are usually more complex than ARMA processes, so sometimes it is necessary to combine ARIMA with another methods to increase its performance. Some literature also shows that ARIMA produces larger error values than the other classical methods. According to Fitria, Alam, and Subchan [2], this method is not better than Double Exponential Smoothing (Holt) because of the larger MAPE value obtained. The research conducted by Susanto, Subanti, and Slamet [3] also shows that ARIMA has larger error values than the Holt method in predicting JCI data. The extension of ARIMA for seasonal data, namely the Seasonal Autoregressive Integrated Moving Average (SARIMA), also has larger error values compared to Triple Exponential Smoothing (Holt-Winters) method, an exponential smoothing method for seasonal data [4]. Scott and Varian [5] introduced a method that used a structural time series model to capture trend, seasonality, and other components called Bayesian Structural Time Series (BSTS). This method is an integrated system formed by a combination of three statistical methods. 1. Basic structural model for trend and seasonality, estimated by Kalman filters; 2. Spike and slab regression for variable selection; and 3. Bayesian model averaging for combining results and forecasting. The application of this method has been widely used for nowcasting, forecasting, and inferring causal impact. It has a good ability in describing time series patterns, making it suitable as an option for forecasting complex data. Research conducted by Almarashi [6] shows that the BSTS model produces smaller MAPE values than ARIMA in predicting the Flying Cement’s stock returns. The difference in MAPE values is quite small for short-term forecasting, but it becomes larger when the forecasting range is enlarged. It shows that the BSTS method is better for long-term forecasting. According to Efrizal [7], the structural time series model obtained from the Kalman filter algorithm has higher accuracy than the Holt model in forecasting the Gross Domestic Product (GDP) of Portugal and Hungary. In addition, the structural time series model in state space representation also does not require stationary assumption. The BSTS model is based on a structural time series model, thus the selection of state components used in the model will greatly affect the model performance. Therefore, the researcher wants to investigate the best combinations of state components to build the best model from the available data. Through this study, the researchers also wanted to see whether the BSTS method will be able to give better results in forecasting stock prices than some classical methods, such as Holt-Winters and SARIMA. The results of the models will be compared with the Holt-Winters’ and SARIMA’s.

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20.2 Bayesian Structural Time Series (BSTS) The Bayesian Structural Time Series (BSTS) model is a stochastic state space model which could investigate the trend, seasonality, and regression component separately [8]. The Bayesian approach in this method allows to develop a model based on prior experience and the original data. By combining the prior information with the data, we would get the updated information which later becomes the final Bayesian model or the posterior distribution. The posterior distribution is simulated by the Markov Chain Monte Carlo (MCMC) algorithm. For this study, the computation process will be done using the bsts package [9]. The package uses Kalman filter to estimate the time series components and spike and slab regression for selecting the predictors where the predictors are weighted automatically based on their inclusion probabilities. The forecasts are least dependent on certain hypotheses [8]. This method has been applied to various fields of study, from industrial engineering to studying the behavior of stocks return. The models are used for selecting predictors, time series forecasting, nowcasting, inferring causal effects, and many more.

20.2.1 Basic Structural Time Series Model The general univariate structural time series model can be written as follows [10]. yt = Z tT αt + t αt+1 = Tt αt + Rt ηt

t ∼ N (0, Ht ), ηt ∼ N (0, Q t ),

(20.1) (20.2)

for t = 1, . . . , n where yt is the observed value at time t, αt is the m-dimensional state vector, Z t is the m-dimensional output vector, Tt is the m × m transition matrix, Rt is the m × q control matrix, t is a scalar observation error, and ηt is the q-dimensional system error vector. Equation (20.1) is called the observation equation, it links the observed data yt with the latent state αt . Equation (20.2) is called the transition equation of αt which defines how the latent state evolves over time [6].

20.2.2 State Components We can include a single component or multiple time series components to the model by setting αt with the corresponding state components. The included state components depend on the patterns that are shown on the graph. Here are some commonly used state components.

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Local Level Component

The local level model is the simplest structural time series model. This model assumes the trend follows a random walk process. We can add the local level components into the model by adding this transition equation μt+1 = μt + ημ,t

ημ,t ∼ N (0, σμ2 ).

(20.3)

and the prior is on σμ2 . Therefore, the local level model can be written as

20.2.2.2

yt = μt + t ,

(20.4)

μt+1 = μt + ημ,t .

(20.5)

Local Linear Trend Component

The local linear trend model assumes that both the mean and the slope of the trend follow random walks. The model is defined by a pair of equations, one for the mean and one for the slope. The equation for the mean is μt+1 = μt + δt + ημ,t

ημ,t ∼ N (0, σμ2 ),

(20.6)

and the equation for the slope is δt+1 = δt + ηδ,t

ηδ,t ∼ N (0, σδ2 ),

(20.7)

where μt is the value of the trend at time t and δt is the expected increase in μ between times t and t + 1 [11]. The prior is on σμ2 and σδ2 . The local linear trend model is good for short-term forecasting because it quickly adapts to local variation. For long-term forecasting, this flexibility may lead to wide intervals.

20.2.2.3

Semi-local Linear Trend Component

Although the local linear trend and semi-local linear trend are quite similar, the semilocal linear trend is more useful for long-term forecasting. The semi-local linear trend model is able to balance short-term information from the distant past. It is assumed that the level component follows a random walk and the slope component moves along the AR(1) process centered at D [9]. The equation for the mean is μt+1 = μt + δt + ημ,t

ημ,t ∼ N (0, σμ2 ),

(20.8)

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and the equation for the slope is δt+1 = D + ρ(δt − D) + ηδ,t

ηδ,t ∼ N (0, σδ2 ).

(20.9)

The prior is on σμ2 , σδ2 , D, and ρ. 20.2.2.4

Student Local Linear Trend Component

The student local linear trend model assumes that both the mean and the slope of the trend follow random walks [9]. The equation for the mean is μt+1 = μt + δt + ημ,t

ημ,t ∼ Tvμ (0, σμ2 ),

(20.10)

and the equation for the slope is δt+1 = δt + ηδ,t

ηδ,t ∼ Tvμ (0, σδ2 ).

(20.11)

The prior is on σμ2 , σδ2 , vμ , and vδ . 20.2.2.5

Seasonal Component

According to Brodersen et al. [11], the most frequently used seasonal model is γt+1 = −

S−2 

γt−s + ηγ ,t

ηγ ,t ∼ N (0, σγ2 ),

(20.12)

s=0

where S denotes the number of seasons and γt denotes their joint contribution to yt . The state in this model consists of the S − 1 most recent seasonal effects and the mean of γt+1 is such that the total seasonal effect is zero when summed over S seasons. The transition matrix for seasonal model is an S − 1 × S − 1 matrix with −1’s along the top row, 1’s along the sub diagonal, and 0’s elsewhere. The prior is on σγ2 . 20.2.2.6

Monthly Annual Cycle Component

Monthly annual cycle component is a seasonal state component for daily data [9]. This component represents the contribution of each month (January, February, . . .) to the annual seasonal cycle. There is a one step change at the beginning of each month and after that the input of that month is constant throughout the period. The state of this model is an 11-dimension vector γt , where the first element is contribution to the mean for the current month and the other elements are the values from the most recent ten months. When t is the first day of the month, we have

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γt+1 = −

11 

γt,i + ηγ ,t

ηγ ,t ∼ N (0, σγ2 ).

(20.13)

i=2

when t is any other day, then we have γt+1 = γt . The prior is on σγ2 . 20.2.2.7

Regression Component

The static regression can be written in state space form by setting Z t = β T xt and αt = 1. The dynamic regression component is as follows [11] xtT βt =

J 

x j,t β j,t ,

(20.14)

j=1

β j,t+1 = β j,t + ηβ, j,t

ηβ, j,t ∼ N (0, σβ2j ),

(20.15)

where β j,t is the coefficient for the jth covariates at the time t. This component can be written in state space form by setting Z t = xt , αt = βt and Tt = Rt = I j× j .

20.2.3 Markov Chain Monte Carlo (MCMC) The Markov Chain Monte Carlo (MCMC) algorithm is used to simulate the posterior distribution of the model parameters σ2 , ση2 , and the regression coefficient β. It is assumed that the prior distribution of each variance parameter is v s  1 , . ∼ Γ σ2 2 2

(20.16)

The prior parameter can be interpreted as a prior of sum squares s and weight v, therefore the prior estimate of σ 2 is s/v [11]. For the predictors, we can use a spike and slab prior to choose an appropriate set of β. Let φ = (θ, β, σ2 , α), where θ denote the set of model parameters other than β and σ2 . By repeating these following steps, we would get a sequence of φ (1) , φ (2) , . . . from a Markov chain with stationary distribution p(φ|y) or the posterior distribution of φ given y. 1. Simulate the latent state α from p(α|y, θ, β, σ2 ) using the simulation smoother from Durbin and Koopman [12]. 2. Simulate θ ∼ p(θ |y, θ, α, σ2 ), the draw of θ depends on which state components are present in the model. 3. Simulate β and σ2 from p(β, σ2 |y, α, θ ) using the stochastic search variable selection (SSVS) from George and McCulloch [13].

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After training the model, we could do the forecast based on the posterior predictive distribution. Let y˜ denote the set of values to be forecast. The posterior predictive distribution of y˜ is  p( y˜ |y) =

p( y˜ |φ) p(φ|y)dφ,

(20.17)

where the samples of y˜ from p( y˜ (g) |φ (g) ) can be drawn by iterating (20.1) and (20.2) (g) (g) forward from αn , using parameters θ (g) , β (g) , and σ . For reports, it is preferable to present the forecasting results using graphical methods than summarize the draws from p( y˜ |y) by the mean, which is a Monte Carlo estimate of E( y˜ |y) [10].

20.3 Other Methods 20.3.1 Holt-Winters Exponential Smoothing The Triple Exponential Smoothing (Holt-Winters) method is an extension of the Double Exponential Smoothing (Holt) method that captures seasonality. This method is based on three smoothing equations—one for the level, one for trend, and one for seasonality [14]. Therefore, there are three smoothing parameters involved, that is α, β, and γ , each for the level, trend, and seasonality. This method has different equations depending on whether seasonality is modeled, in an additive or multiplicative way. The basic equations for Holt-Winters’ multiplicative method are as follows Yt + (1 − α)(L t−1 + bt−1 ), St−s bt = β(L t − L t−1 ) + (1 − β)bt−1 , Yt + (1 − γ )St−s , St = γ Lt Ft+m = (L t + bt m)St−s+m . Lt = α

(20.18) (20.19) (20.20) (20.21)

where s is the length of seasonality (e.g., the number of months in a year), L t is the level of the series, bt is the trend component, St is the seasonal component, Yt is the data value, and Ft+m is the forecast for m periods ahead. To initialize levels, trends, and seasonality, the equations are as follows 1 (Y1 + Y2 + · · · + Ys ), s  Ys+2 − Y2 Ys+s − Ys 1 Ys+1 − Y1 + + ··· + , bs = s s s s Y1 Y2 Ys S1 = , S2 = , . . . , Ss = . Ls Ls Ls

Ls =

(20.22) (20.23) (20.24)

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20.3.2 Seasonal Autoregressive Moving Average (SARIMA) The Autoregressive Integrated Moving Average (ARIMA) or Box-Jenkins is a forecasting method developed by George Box and Gwilym Jenkins [15]. An extended version of ARIMA, the Seasonal Autoregressive Integrated Moving Average (SARIMA), is commonly used to forecast seasonal data. When working with multiplicative seasonality, we need to stabilize the variance of data by using logarithm transformations, followed by differencing to maintain a stationary dataset in the mean [16]. The equation of the multiplicative SARIMA model or ARIMA ( p, d, q) × (P, D, Q)s can be written as φ p (B)Φ P (B s )(1 − B)d (1 − B s ) D Yt = θq (B)Θ Q (B s )εt ,

(20.25)

where s is the length of seasonality, p and P are the order of the non-seasonal and seasonal autoregressive part, q and Q are the order of the non-seasonal and seasonal moving average part, d and D are the degrees of non-seasonal and seasonal differencing, and B represents the backshift operator [17]. The non-seasonal and seasonal operators for the autoregressive and moving average parts are as follows: φ p (B) = 1 − φ1 B − · · · − φ p B p ,

(20.26)

Φ P (B ) = 1 − Φ1 B − · · · − Φ P B ,

(20.27)

θq (B) = 1 − θ1 B − · · · − θq B ,

(20.28)

s

s

Ps

q

Θ Q (B ) = 1 − θ1 B − · · · − θ Q B s

s

Qs

.

(20.29)

where φ p denotes the non-seasonal autoregressive parameters, Φ P denotes the seasonal autoregressive parameters, θq denotes the non-seasonal moving average parameters, and Θ Q denotes the seasonal moving average parameters.

20.4 Comparison Metrics 20.4.1 Root Square Mean Error (RMSE) Root Square Mean Error (RMSE) is used to measure the difference between the actual value of the data and the forecast value. It is a measure of accuracy to compare forecasting errors of different models for the same dataset as it is scale-dependent [18]. The RMSE calculation is as follows  RMSE =

n i=1 (yi

n

− x i )2

,

(20.30)

where yi is the forecast value, xi is the actual value, and n is the number of data.

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20.4.2 Mean Absolute Error (MAE) Mean Square Error (MAE) can be used if the outliers represent the corrupted part of the data [19]. The calculation of MAE is as follows n MAE =

i=1

|yi − xi | , n

(20.31)

where yi is the forecast value, xi is the actual value, and n is the number of data.

20.4.3 Mean Absolute Percentage Error (MAPE) According to De Myttenaere et al. in [19], MAPE is recommended where it is more important being sensitive to relative variations than to absolute variations. MAPE can be calculated by

n

1 

xi − yi

(20.32) MAPE =

x , n i=1

i

where yi is the forecast value, xi is the actual value, and n is the number of data. The following are interpetations of MAPE value according to Kasemset et al. [20] (Table 20.1).

20.5 Data Description The data used in this study is the daily stock data of PT Bank Negara Indonesia (BBNI) from May 4, 2020 to April 8, 2022. The dataset consists of 7 columns: Date, Open Price, High Price, Low Price, Close Price, Adjusted Close Price, and Volume, but only the Date and Close Price columns are used. The data is known to have trends and seasonal patterns as shown in Fig. 20.1, thus the use of Holt-Winters, SARIMA, and BSTS would be appropriate. Therefore, we used those three methods

Table 20.1 MAPE interpretation MAPE value (%) ≤ 10 11–20 21–50 > 50

Forecast accuracy Highly accurate forecast Good forecast Reasonable forecast Inaccurate forecast

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Fig. 20.1 BBNI closing price

and compared them. There are 472 rows in the dataset. We took 75% of the data for training the models and 25% of the data for testing. The are several reasons why we use this stock as the object of our study. First, the banking sector seems to be more promising in the pandemic era compared to the other sectors. In Indonesia, one of the most outstanding banking stocks is BBNI, which is owned by PT Bank Negara Indonesia Tbk. Some state-owned banks, including BNI, are known to have good capital structures, good records of performances, and regularly distribute dividends [21]. Last, this stock has the best prospect compared to the other outstanding banking stocks, i.e., BBRI, BMRI, and BBCA, because its growth of Earning Per Share (EPS) and Margin of Safety (MOS) is the highest among the others [22]. So, we would like to see whether this stock will rise in the near future or not. As shown in Fig. 20.1, the data has both trend and seasonal components. It is assumed that there are a day of week effect and a day of year effect. The average number of trading days in a week is 5, thus to accommodate the day of week effect, the number of seasons to be modeled is 5. For the day of year effect, the number of seasons to be modeled is 245, which is the average number of trading days throughout the year. In addition, the data seems to have similar patterns every month, so it is also likely to have a monthly annual cycle.

20.6 Results Based on the component identification that has been done before, we tested several combinations of state components using the bsts R package to get the best model.

20 Optimization of Bayesian Structural Time Series (BSTS) Applications … Table 20.2 Trend models evaluation metrics RMSE Model 1 Model 2 Model 3 Model 4

6304.1182 456.5548 562.5539 8350.0452

MAE

MAPE

5635.3586 382.7476 455.7577 7373.7008

0.4018 0.0505 0.0632 0.4580

239

Each trend state component was tested first to determine the best trend components for the data. Next, the other components were added gradually, starting from the seasonal components and then the monthly annual cycle component. The number of iterations for each model is 500.

20.6.1 Trend Models First, we did the modeling processes using the four trend state components as previously mentioned. We used local linear trend for Model 1, semi-local linear trend for Model 2, local level for Model 3, and student local linear trend for Model 4. Then, the model testing processes were carried out. The results obtained from the testing processes are summarized in Table 20.2. As shown in Table 20.2, Model 2 and Model 3 both have relatively small error values compared to Model 1 and Model 4. The smaller errors, the better the model. Therefore further analyses were carried out using semi-local linear trend and local level components. We added several state components to these two models to get the best model. The first state component tested is seasonal.

20.6.2 Trend + Seasonal Models We used two types of seasonality in the modeling processes as we mentioned before. To model the day of week cycle, the number of seasons to be modeled is 5, and for the day of year cycle, the number of seasons to be modeled is 245. To make it simple, we named them Model 5, Model 6, Model 7, and Model 8. Model 5 is the semi-local linear trend + seasonal (5) model, Model 6 is the semi-local linear trend + seasonal (245) model, Model 7 is the local level + seasonal (5) model, and Model 8 is the local level + seasonal (245) model. The testing results are shown in Table 20.3. From the table, we know that Model 6 has smaller error values compared to others, therefore this model is the best one so far.

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Table 20.3 Trend + seasonal models evaluation metrics RMSE MAE Model 5 Model 6 Model 7 Model 8

402.7658 328.2224 682.5219 1069.4696

347.0647 275.5878 527.2827 785.3371

Table 20.4 Trend + monthly annual cycle models evaluation metrics RMSE MAE Model 9 Model 10

498.2119 576.8740

417.4772 434.8858

MAPE 0.0462 0.0376 0.0749 0.1227

MAPE 0.0547 0.0610

Table 20.5 Trend + seasonal + monthly annual cycle models evaluation metrics RMSE MAE MAPE Model 11 Model 12

411.8957 684.7445

330.2216 532.3875

0.0454 0.0774

20.6.3 Trend + Monthly Annual Cycle Models The second component to be tested is the monthly annual cycle. We combined semilocal linear trend and local level model with the monthly annual cycle component in the modeling processes. Two models were obtained which are Model 9 and Model 10. The first model mentioned is the semi-local linear trend + monthly annual cycle model and the latter is the local level + monthly annual cycle model. As shown in Table 20.4, both models have relatively small error values. However, neither of them is better than Model 6. The semi-local linear trend + seasonal (245) model is still the best model obtained.

20.6.4 Trend + Seasonal + Monthly Annual Cycle Models Next, we tried to model the trend, seasonal, and monthly annual cycle altogether. Two models were obtained which are Model 9, the semi-local linear trend + seasonal (245) + monthly annual cycle model, and Model 10, the local level + seasonal (245) + monthly annual cycle model. Testing processes were carried out and the results obtained are displayed in Table 20.5. The results shown in Table 20.5 do not change the conclusion, Model 6 remains the best model among all models.

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Fig. 20.2 Posterior distribution of model 6

20.6.5 The Best Model Based on the results obtained, we found that Model 6, i.e., the semi-local linear trend and seasonal model, is the best model among all models that have been formed. Figure 20.2 displays the posterior distribution of the model state or the conditional mean Z tT αt given the full data y = y1 , . . . , yt . By taking a look at the plot, it seems that the model fits well with the data. Then, what about the forecast? Fig. 20.3 shows the posterior predictive distribution of the best model. The black line is the original training data series, and the blue line along with the gray area is the forecast and errors. As shown in Fig. 20.3, we know that the forecast tends to have an ascending pattern, just like the original data. A clearer comparison of the forecast results with the original data can be seen in Fig. 20.4b. The MAPE value of this model is less than 10%, which shows that the forecasts are accurate, referring to Table 20.1. Different iterations will lead to different error values, sometimes they’re better, and sometimes they’re worse. Therefore, we want to analyze whether the different iterations in Model 6 result in better models. We repeated the modeling process using the same state components but with different number of iterations, which are 100, 1000, 2000, and 5000. The plots displayed in Figs. 20.4, 20.5, 20.6, 20.7 and 20.8 are the comparisons of the actual data and the forecast values of each model. It is rather difficult to determine the best model from the graphs. However, if we take a look at the error values, the model with 500 iterations is slightly superior to the four models. As shown in Table 20.6, increasing the number of iterations from 100 to 500 will result in a better model. But, as the number of iterations increased from 500, the error values got bigger. Moreover, some models with a large number of iterations require a long modeling duration. For this case, using 500 iterations seems more appropriate.

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Fig. 20.3 Forecasting results of model 6

Fig. 20.4 100

20.6.6 Comparison Additionally, we modeled the data using Holt-Winters and SARIMA to determine which method is superior among the BSTS, Holt-Winters, and SARIMA. The modeling processes were done using R program. However, the Holt-Winters and SARIMA require at least two seasonal periods to be modeled. Thus, we cannot perform the modeling process for the day of year cycle because there are not enough data points to be modeled. The models we formed are the seasonal models with the number of seasons 5. The best model of Holt-Winters has an alpha value of 0.9082, a beta value of 0.0483, and a gamma value of 0.5744. For the SARIMA method, we got ARIMA (0, 2, 1) × (1, 2, 0)5 as the best model. The evaluation metrics and the modeling

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Fig. 20.5 500

Fig. 20.6 1000

duration of these models are shown in Table 20.7. We also include all of the BSTS models in Table 20.7 for comparison. From the table, we know that the Holt-Winters and SARIMA models produce higher error values than BSTS models with the same seasonal specification, i.e., Model 5 and Model 7. Moreover, most BSTS models also outperform those two models. It seems that the BSTS method has better results compared to the HoltWinters and ARIMA. However, some BSTS models require quite a long duration to be modeled. This problem could be a fatal weakness, if the data is too large and complex, a long modeling duration could be a serious problem.

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Fig. 20.7 2000

Fig. 20.8 5000 Table 20.6 Best model with different iterations RMSE MAE 100 iterations 500 iterations 1000 iterations 2000 iterations 5000 iterations

373.8106 328.2224 382.0240 401.3673 396.2262

305.6101 275.5878 330.1357 346.9779 342.3523

MAPE

Modeling duration

0.0419 0.0376 0.0446 0.0470 0.0464

56 s Approx. 4 min Approx. 9 min Approx. 18 min Approx. 45 min

20 Optimization of Bayesian Structural Time Series (BSTS) Applications … Table 20.7 Models evaluation metrics RMSE MAE Holt-Winters SARIMA Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7 Model 8 Model 9 Model 10 Model 11 Model 12

4632.6923 81220.6168 6304.1182 456.5548 562.5539 8350.0452 402.7658 328.2224 682.5219 1069.4696 498.2119 576.8740 411.8957 684.7445

Table 20.8 BBNI forecasts Period Lower limit t t t t t t t t t t

+1 +2 +3 +4 +5 +6 +7 +8 +9 + 10

8509.3159 8345.6198 8252.1225 8156.4516 7934.4599 7797.0917 7966.5938 7971.8002 8102.8750 7964.1440

4165.1000 54733.0597 5635.3586 382.7476 455.7577 7373.7008 347.0647 275.5878 527.2827 785.3371 417.4772 434.8858 330.2216 532.3875

245

MAPE

Modeling duration

0.3380 0.7103 0.4018 0.0505 0.0632 0.4580 0.0462 0.0376 0.0749 0.1227 0.0547 0.0610 0.0454 0.0774

1s 1s 2s 2s 2 detik 2s 2s Approx. 4 min 2s Approx. 4 min 2s 2s Approx. 4 min Approx. 4 min

Mean

Upper limit

8777.1979 8734.1200 8641.8624 8701.1078 8560.0248 8503.9331 8632.5090 8646.7322 8803.4487 8773.4745

9131.5161 9163.6774 9187.5052 9281.3834 9111.3011 9070.0446 9305.5642 9252.1749 9561.5373 9431.4060

20.6.7 Forecast Lastly, we would like to see the stock movements over the next several periods. With a significance level of 5%, we did the forecast for 10 periods ahead using the best model, i.e., Model 6. The results are shown in Table 20.8 and Fig. 20.9. It seems that the BBNI prices fluctuate throughout the next 10 periods, the mean tends to fall within the next 6 d and then rises afterward.

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Fig. 20.9 Forecasting results

20.7 Conclusions From the results, we can conclude that the Bayesian Structural Time Series (BSTS) is able to produce a model with a higher level of accuracy than the Holt-Winters Exponential Smoothing and the Seasonal Autoregressive Integrated Moving Average (SARIMA). The best model of BSTS, which is also the best model of all the models that have been formed, has lower error values than the best model of the Holt-Winters and SARIMA methods. The MAPE value decreased by 0.3004 compared to HoltWinters and 0.6727 compared to SARIMA. Overall, this method offers better results. This study has some limitations as well. We used a quite short period of data and were limited to the COVID-19 pandemic era. Furthermore, we suggest using more data for future research. It would be better to use a longer period to see whether the presence of the pandemic could affect the results. In addition, the state components selection in this study is only based on the time series components shown on the graph. We repeatedly attempted to put them on the model to get the best model. If there is a more systematic method of selecting state components, we suggest trying it. Acknowledgements This work was fully funded by the project of the Final Task Recognition Program of Gadjah Mada University 2022 (grant number: 3550/UN1.P.III/Dit-Lit/PT.01.05/2022) provided by the research directorate and the reputation improvement team of UGM towards the World Class University of the quality service office. The authors also thank reviewers for their careful reading and helpful suggestions.

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References 1. A.C. Petricˇa, S. Stancu, A. Tindeche, Limitation of ARIMA models in financial and monetary economics. Theor. Appl. Econ. 23(4), 19–42 (2016). https://ideas.repec.org/a/agr/journl/ vxxiiiy2016i4(609)p19-42.html 2. I. Fitria, M.S.K. Alam, Subchan, Perbandingan metode ARIMA dan double exponential smoothing Pada Peramalan Harga Saham LQ45 Tiga Perusahaan dengan Nilai earning per share (EPS) Tertinggi. J. Math. Appl. 14(2), 113–125 (2017). https://doi.org/10.12962/limits. v14i2.3060 3. A.F. Susanto, S. Subanti, I. Slamet, Perbandingan exponential smoothing Holt’s method dan double moving averages terhadap peramalan IHSG, in Prosiding Pendidikan Matematika dan Matematika, vol 2 (2020), http://prosiding.himatikauny.org/index.php/prosidinglsm/article/ view/77/51 4. W. Zayat, B. Sennaro˘glu, Performance comparison of Holt-Winters and SARIMA models for tourism forecasting in Turkey. Do˘gu¸s Üniversitesi Dergisi 21(2), 63–77 (2020). https://doi.org/ 10.31671/dogus.2020.449 5. S.L. Scott, H. Varian, Bayesian Variable Selection for Nowcasting Economic Time Series, NBER Working Paper No. 19567 (2012), http://www.nber.org/papers/w19567 6. A.M. Almarashi, K. Khan, Bayesian structural time series. Nanosci. Nanotechnol. Lett. 12, 56–61 (2020). https://doi.org/10.1166/nnl.2020.3083 7. Efrizal, Peramalan Berdasarkan Algoritma Kalman Filter Model Multivariat Structural Time Series dalam Representasi State Space, Thesis, Universitas Lampung, 2017 8. N. Feroze, Forecasting The Patterns of COVID-19 and Causal Impacts of Lockdown in Top Five Affected Countries using Bayesian Structural Time Series Models (Elsevier, 2020). https:// doi.org/10.1016/j.chaos.2020.110196 9. S.L. Scott, Package ’bsts’, Version 0.9.8 (2022), https://cran.r-project.org/web/packages/bsts/ bsts.pdf 10. S.L. Scott, H. Varian, Predicting the present with Bayesian structural time series. SSRN Electron. J. (2013). https://doi.org/10.1504/IJMMNO.2014.059942 11. K.H. Brodersen et al., Inferring causal impact using Bayesian structural time-series models. Annuals Appl. Stat. 9(1), 247–274 (2015). https://doi.org/10.48550/arXiv.1506.00356 12. J. Durbin, S.J. Koopman, A simple and efficient simulation smoother for state space time series analysis. Biometrika 89(3), 603–616 (2002). https://doi.org/10.1093/biomet/89.3.603 13. E.I. George, R.E. McCulloch, Approaches for Bayesian variable selection. Statistica Sinica 7, 339–374 (1997) 14. S.G. Makridakis, S.C. Wheelwright, R.J. Hyndman, Forecasting: Methods and Applications, 3rd edn. (Wiley, New York, 1997) 15. G.E.P. Box, G.M. Jenkins, Time Series Analysis Forecasting and Control (Holden-Day, San Francisco, 1976) 16. S. Moss, J. Liu, J. Moss, Issues in forecasting international tourist travel. J. Manag. Inf. Decis. Sci. 16(2) (2013) 17. W.W.S. Wei, Time Series Analysis Univariate and Multivariate Methods, 2nd edn. (Addison Wesley, Boston, 2006) 18. L. Chen, Stock Price Prediction using Adaptive Time Series Forecasting and Machine Learning Algorithms, Master’s thesis, University of California, 2020 19. D. Chicco, M.J. Warrens, G. Jurman, The coefficient of determination R-squared is more informative than SMAPE, MAE, MAPE, MSE and RMSE in regression analysis evaluation. Peer J. Comput. Sci. (2021). https://doi.org/10.7717/peerj-cs.623 20. C. Kasemset, N. Sae-Haew, A. Sopadang, Multiple regression model for forecasting quantity of supply of off-season Longan. Chiang Mai Univer. J. Nat. Sci. 13(3), 391–402 (2014). https:// doi.org/10.12982/cmujns.2014.0044

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Chapter 21

Prediction of the Number of BPJS Claims due to COVID-19 Based on Community Mobility and Vaccination in DIY Province Using the Bayesian Structural Time Series Maria Stephany Angelina and Gunardi Abstract In this study, an analysis was carried out on the number of BPJS claims due to COVID-19 by considering the mobility factor of the community and the number of people receiving dose 2 vaccination in the DIY province using the Bayesian Structural Time Series (BSTS) and Autoregressive Integrated Moving Average with Exogenous Variable (ARIMAX) methods as comparisons. The data used has a time span from March 2, 2020 to February 17, 2022. In practice, kernel smoothing will also be used to test the ability of the BSTS and ARIMAX methods in overcoming data with a value of 0. Determining the best BSTS model depends on the state components contained in the model. The performance of the BSTS and ARIMAX models will be compared using the Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE) value indicators. From the results of the research conducted, it is found that the best model is the BSTS model which contains a local level trend component with a MAPE value of 32.7% and an RMSE of 2.629033. Looking at the MAPE and RMSE values, it can be concluded that the best model has a decent forecasting ability. However, despite all that, BSTS is less able to follow the cyclical pattern that exists in the claim data, and can only follow the trend pattern.

21.1 Introduction According to WHO, 2019 was the beginning of the COVID-19 pandemic, which is an infectious disease caused by the SARS-CoV-2 virus and causes respiratory infections [28]. The pandemic that originated in the city of Wuhan in China in a short time caused a global pandemic that has been experienced throughout the world M. S. Angelina · Gunardi (B) Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Yogyakarta, Indonesia e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Mustapha et al. (eds.), Proceedings of the 8th International Conference on the Applications of Science and Mathematics, Springer Proceedings in Physics 294, https://doi.org/10.1007/978-981-99-2850-7_21

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including Indonesia itself since March 2, 2020. This virus spreads easily through direct contact with droplets from the respiratory tract of an infected person. Therefore, the government has implemented various policies to limit people’s mobility and encourage the provision of vaccinations to suppress the spread of COVID-19. The number of positive cases of COVID-19 experienced a very high spike, especially when there was a long holiday. According to data from the Satgas COVID19 post-Eid al-Fitr 2021, the special region of Yogyakarta province experienced a 172.03% increase in COVID-19 cases and was in third position in the province category with the highest increase in COVID-19 cases [6]. The spike in COVID-19 cases occurred due to the high mobility of the population before and after the 2021 Eid al-Fitr holiday. Another effort made by the government to increase community immunity so as not to contract the COVID-19 virus is by making a vaccination program. The provincial government of the Special Region of Yogyakarta itself has implemented a second dose vaccination program en masse since March 1, 2021, which is a continuation of the first dose of vaccination with 19,897 people being the target of the vaccine [30]. But in fact, the vaccination program up to the second dose is less effective in reducing the spread of the COVID-19 virus in the DIY province. This is indicated by the very high spike in positive cases of COVID-19 in mid-2021 in the DIY province. On May 22, 2021, there were 138 people who tested positive for COVID-19 on that day and within 2 months that number increased 14 times to 1978 people on July 22, 2021 [26]. With these conditions, it can be seen that there is a very close relationship between community mobility and the spread of the COVID-19 virus as stated by Iacus [14]. Meanwhile, vaccinations imposed by the government are deemed less able to control the spread of this virus if they are not accompanied by appropriate population mobility restrictions. And the COVID-19 pandemic has also put pressure on the insurance industry. According to the Insurance Media Research Institute, life insurance premium income grew very thin by 1.61% from December 2019 to December 2020. However, this premium growth was followed by claims and benefits expenses that soared by 53.25% from Rp 136.43 Trillion in 2019 to Rp 209.08 Trillion. in 2020 [19]. The risks faced due to the COVID-19 pandemic by insurance companies, especially health insurance, are regarding the number of claims that will appear in the future. One of the most widely used health insurances in Indonesia today is the Social Security Administering Body (BPJS) for Health. This BPJS Health also bears the cost of treating COVID-19 patients which has been regulated in the letter of the Coordinating Minister for Human Development and Culture Number S.22/MENKO/PMK/III/2020 concerning the Special Assignment for the Verification of COVID-19 claims [4]. According to the Director of Referral Health Services at the Ministry of Health, as of January 31, 2022, the total BPJS claims caused by the COVID-19 virus in hospitals amounted to Rp 90.2 trillion [27]. The total claim fee that must be paid by BPJS due to COVID-19 will certainly move in line with the movement of COVID-19 cases in Indonesia. Therefore, during this pandemic, actuaries at BPJS Health, especially in the Special Region of Yogyakarta province, need to review the level of financial health and capital adequacy of BPJS in dealing with claims due to COVID-19 in the future so

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as not to suffer losses, and calculate the estimated claim reserve. Which need to be prepared. In addition, the risk manager also needs to mitigate the risks caused by claims due to COVID-19 which are predicted to occur in the future so that later if necessary, risk transfers can be made to reinsurance companies or other insurance companies. And lastly, this research is expected to help underwriters in determining policy rules related to COVID-19, for example the large costs due to COVID-19 that will be borne by BPJS and calculating the amount of premiums that will later be sufficient to pay claims due to COVID-19 in the future. To help BPJS, especially BPJS Health in DIY province, in making the previously mentioned policies to deal with the movement of COVID-19 cases in the future, this research will focus on establishing a model that can capture the pattern of claims movement due to COVID-19 by considering other factors that affect the spread of COVID-19 such as community mobility and data on DIY people who have received up to the second dose of vaccine. To analyze the relationship between community mobility consisting of retail and recreation areas, grocery stores and pharmacies, parks, public transportation, workplaces and residential areas as well as the second dose of vaccination against the number of BPJS claims due to COVID-19 in DIY province, the researchers used the Bayesian method. Bayesian Structural Time Series (BSTS) and Autoregressive Integrated Moving Average with Exogenous Variable (ARIMAX) which can consider external factors that affect the number of claims into the model. ARIMAX is the development of the ARIMA method that can be used in time series data analysis where the dependent variable is influenced by the independent variable or the so-called exogenous variable. There is an alternative method to ARIMAX, namely BSTS which is a more modern method and can handle uncertainty better than ARIMA which is an important feature for prediction in the future, because the Bayesian approach assumes that the model parameters are random so that they have a certain distribution [10]. Where the uncertainty that exists in the data on the number of BPJS claims due to COVID-19 is because the movement of COVID-19 cases is stochastic all the time, so that in order to forecast more accurately, a method is needed that can handle uncertainty or stochastic behavior from this data well. Through BSTS, parameter estimation can be done and quantify its estimation uncertainty through the posterior distribution by first setting the prior distribution. This BSTS method is also more transparent than ARIMA because the model representation does not depend on differencing, lag, and Moving Average (MA) as in ARIMA [16]. However, so far there has been no research on any topic that discusses the comparison between the BSTS and ARIMAX methods. There are also no studies that model the number of insurance claims with community mobility and vaccination using BSTS or ARIMAX. Most studies model COVID-19 cases without paying attention to external factors that affect the spread of the COVID-19 virus and also do not relate this pandemic condition to those faced by health insurance. Therefore, this research was conducted in addition to assisting the DIY provincial government in determining policies related to the COVID-19 pandemic, as well as to assist BPJS Health DIY in estimating claims reserves that need to be prepared to deal with the

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COVID-19 pandemic in the future and other policies with using the best method between ARIMAX or BSTS. Research conducted by Nugroho and Rakhman [21] discussed the relationship between people’s mobility behavior in 6 types of locations and daily cases of COVID19 in the DIY province from March 21, 2020 to March 3, 2021 using multivariable Pearson correlation. The results of this analysis indicate that the level of correlation between the two is relatively low. This is because during the pandemic, people tend to stay at home and not travel due to the implementation of the Enforcement of Restrictions on Community Activities (PPKM) policy by the government. Meanwhile, if the correlation analysis is carried out in the period. When there is a spike in mobility, such as when there is a holiday, the results show that the spread of the COVID-19 virus is more influenced by clusters in residential areas (with a Pearson correlation value of 0.64) than community mobility. There was also a study in the United States by Xie [29] entitled The analysis and forecasting of COVID-19 cases in the United States using Bayesian structural time series models. This study analyzes and forecasts the total confirmed cases of COVID-19 in the US using the variable day, total confirmed cases of COVID-19 per day, cases of death due to COVID-19 per day, cases recovered from COVID19 per day and death rate from February 29, 2020 to April 6, 2020. This analysis takes advantage of the flexibility of local linear trends, seasonality, and contemporary covariates of dynamic coefficients in the BSTS model. The model formed shows that the total confirmed cases of COVID-19 will most likely continue to increase in a straight line so that the total number infected with COVID-19 in the US will reach 600,000 in the near future and will peak in mid-May 2020. Research by Aji et al. [1] on forecasting the number of COVID-19 cases in Indonesia used the ARIMA and ARIMAX models. Exogenous variables in the form of Google Trends are used from March 1, 2020 to November 25, 2020 on the ARIMAX model. Based on the ARIMA and ARIMAX models that have been formed, the results show that the ARIMAX model can improve the performance of the ARIMA model by reducing the MAPE value by 0.8%.

21.2 Bayesian Structural Time Series Bayesian Structural Time Series or BSTS is one of the methods in time series data analysis that can be used for forecasting, feature selection, causal relationships [23], and knowing aspects that have an impact on current or nowcasting [24]. As the name implies, the BSTS method uses a Bayesian approach in estimating modeling. The advantage of the BSTS model is its ability to use spike and slab priors so that a set of correlated variables can be converted into a parsimony or parameter-efficient model. The parameters of the BSTS model are arranged based on the weight of each parameter or what is called the inclusion probability. In addition, the BSTS method is also able to analyze the trend, seasonal, and regression components of the data separately.

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Parameter estimation using the Bayesian method assumes that the parameter value is not single and is a random variable so that the parameters have a certain distribution, namely the prior distribution. This is different from frequentist estimation which assumes that the parameter is constant even though the value is unknown [11]. With the Bayesian approach, it is possible to combine sample information from the population and use the prior distribution for each parameter so that the posterior distribution of the parameters can be obtained. However, due to analytical calculations or intergal solving of the Bayesian posterior distribution formula this is very difficult. Then numerical calculations using the Markov Chain Monte Carlo (MCMC) method such as Gibbs sampling, namely by taking samples from the posterior distribution so that finally the estimated parameter values of the BSTS model can be found [8]. The nowcasting model used in this study has two components. The first is the time series component or the so-called structural time series which functions to capture trends and seasonal patterns in the data and the second is the regression component which captures the effect of mobility and dose 2 vaccination of the DIY community on the number of BPJS claims due to COVID-19. This regression component is called the Spike and Slab regression. Because these two components are additive, it is easy to estimate the joint model using the Bayesian method [23].

21.2.1 Structural Time Series According to Almarashi [2], the structural time series model is the model that underlies the BSTS model. In this model, data comes from some unobserved process known as state space and observed data is generated from state space with additional noise. These unobserved components which will be responsible for generating data such as trends, seasonality, cycles and effects of independent variables will be identified separately before being used in the state space model. BSTS is a time series structural model generated by the Bayesian approach and formulated in the form of state space for time series data. Structural models are easier to generalize if for example there are covariates and also this model can easily process data containing missing values [13]. This state space has several advantages, namely it is modular because independent components can be combined with observation vectors in the model. According to Scott [23], the state space form for the structural time series model is defined by the following observation (21.1) and transition (21.2): yt = Z t T αt + t , t ∼ N (0, Ht )

(21.1)

αt+1 = Tt αt + Rt ηt , ηt ∼ N (0, Q t )

(21.2)

The above equation assumes that all variables are independent. Equation (21.1) is called the observation equation because it relates the observation data yt to the unobserved latent state αt . Where yt represents the scalar observation data at time t,

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αt is a vector of latent state variables with dimension d. While (21.2) is often called the transition equation or state equation because the equation shows the change from the latent state αt over period t. Z t , Tt , Rt are structural parameters in the form of a matrix with matrix elements consisting of known values (often 0 and 1) and unknown parameters. Z t is usually the d dimensional output vector of the transition matrix. While Ht is a structural parameter in the form of a constant diagonal matrix with the diagonal element containing σ2 [20], but in this case Ht is a positive scalar number of σ2 so it can also be denoted as σ2 [23]. The transition matrix Tt is a square matrix, while Rt is often a rectangular matrix of size d × q because some of its state transitions are deterministic. With Rt , we can use a Q t matrix with full rank variance because every linear dependency in the state vector can be transferred from Q t to Rt . t is considered as a scalar observation error in the form of variance noise Ht . And ηt is the system error with dimension q with state diffusion matrix Q t measuring q × q. It should be noted that the value of q ≤ d. Based on the bsts package in R created by Scott [25], state components can be formed by the following functions: 1. AddLocalLevel This AddLocalLevel function aims to add a local level model to the state component of the BSTS model. Where the local level model assumes that the trend is a random walk which is expressed by the following equation: αt+1 = αt + t , t ∼ N (0, σ )

(21.3)

The prior of this trend component depends on the σ parameter. Based on the above equation, it can be seen that with the AddLocalLevel component, the prediction results obtained will be constant over time. 2. AddLocalLinearTrend The AddLocalLinearTrend function aims to add a local linear trend model to the state component of the BSTS model. The local linear trend model assumes that the mean and slope of the trend follow a random walk. The equation for the mean of the trend is as follows: μt+1 = μt + δt + t , t ∼ N (0, σμ )

(21.4)

And the equation for the slope of the trend is as follows: δt+1 = δt + ηt , ηt ∼ N (0, σδ )

(21.5)

The prior distribution is at the σμ level standard deviation and the σδ slope standard deviation. 3. AddSemiLocalLinearTrend The semi local linear trend model is similar to the local linear trend model but is more useful for long-term forecasting. This model assumes the level component

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moves according to a random walk, while the slope component moves based on the A R(1) process centered on the non-zero potential value of D. The equation for the level or mean is as follows: μt+1 = μt + δt + t , t ∼ N (1, σμ )

(21.6)

While the equation for the slope is: δt+1 = D + φ(δt − D) + ηt , ηt ∼ N (1, σδ )

(21.7)

This model differs from the local linear trend model which assumes that the slope of δt follows a random walk. The stationary process A R(1) requires fewer variables than random walks when making far- future forecasts, so this model provides a more reasonable estimate of uncertainty when making long-term forecasts. The prior distribution for the semi local linear trend model has 4 independent components, including: • • • •

Prior distribution of Inverse Gamma at the σμ level standard deviation. Prior distribution of Inverse Gamma on the standard deviation of the slope σδ . Gaussian prior distribution on the slope parameter D in the long run. And the Gaussian prior distribution that has the potential to be truncated on the A R(1) coefficient is φ. If the prior distribution of φ is truncated at (−1.1), then the slope will show a short-run stationary variation around the slope of D in the long run.

4. AddStudentLocalLinearTrend A local linear trend that uses a student-t distribution can also be called a robust local linear trend. Like the AddLocalLinearTrend function, this local linear trend model also assumes that the mean and slope of the trend follow a random walk. The equation for the mean is as follows: μt+1 = μt + δt + t , t ∼ Tvμ (0, σμ )

(21.8)

And the equation for the slope is: δt+1 = δt + ηt , ηt ∼ Tvδ (0, σδ )

(21.9)

The independent prior distribution is assumed to have a level standard deviation of σμ , the standard deviation of the slope is σδ , the tail thickness of the level is vμ and the tail thickness of the slope is vδ . 5. AddSeasonal This function aims to add a seasonal model to the state component of the BSTS model. This seasonal model can be considered as a regression with a dummy variable of nseasons and the sum of the coefficients must be equal to 1. If there is S season then the state vector γ is of dimension S − 1. The first element of the state vector satisfies:

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γt+1,1 = −

S 

γt,i + t , t ∼ N (0, σ )

(21.10)

i=2

21.2.2 Spike and Slab Regression There are several ways to configure the model matrix so that the β regression component can be added to the model state space. An easy way to use is to add a constant 1 for each αt and add β T xt to Z t in the observation equation. By using this method, the dimensions of the state vector will only increase by 1, regardless of how many predictor variables are used. The computational complexity of the Kalman filer is linear with data length and quadratic in state size. So it is important to avoid significantly increasing the state size. If there is a regression coefficient that is believed to change over time, then the coefficient can be added to the model as an additional state variable. However, this study will use a regression coefficient that is constant over time.

21.2.2.1

Determination and Obtaining Prior Distribution

To see which predictor variables really affect the response variable, it is hoped that there will be sparsity, which means that the coefficients of several predictors will be 0. The way to represent sparsity in the Bayesian concept is through spike and slab prior distribution to the regression coefficient. As for the prior distribution of other time series components in the model, it will be determined during state formation. So for the BSTS model that contains a regression component, the prior spike and slab are used to select the variables included in the model. Spikes are used to set the probabilities of the variables to be included in the model. The variables included in the model are variables with non-zero coefficients. And the slab will shrink the variables with non-zero coefficients to their prior expected values, where this prior expectation value is often 0. It is defined that γ is a parameter in the form of a vector with values 0 and 1 where γk = 1 if βk = 0 means that the variable with a non-zero coefficient is selected to be included in the model and γk = 0 if βk = 0 which means that the variable with a zero coefficient is not included in the model. It is defined that βγ is a subset of a non-zero scalar on β (where βk = 0). Prior spikes and slabs to model the number of BPJS claims due to COVID-19 are stated in (21.11) below [23]: p(β, γ , σ2 ) = p(βγ |γ , σ2 ) p(σ2 |γ ) p(γ )

(21.11)

where σ2 is the error variance and the marginal distribution of p(γ ) is called a spike because the probability mass function at point 0 is positive. p(γ ) represents the probability of choosing a given variable to be included in the model.

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For the slab section, a symmetric matrix Ω −1 is defined where Ωγ−1 as rows and columns is adjusted to γk = 1. βγ is assumed to have a prior Normal distribution so as to produce an Inverse Gamma prior distribution for σ2 . The conditional priors p(1/σ2 |γ ) and p(βγ |σ2 , γ ) can be expressed in the following conditional conjugate prior pairs [23]: βγ |σ2 , γ ∼ N (bγ , σ2 (Ωγ−1 )−1 )  v ss  1 , |γ ∼ Gamma σ2 2 2

(21.12)

where ss is the prior sum of squares and v is the shrinkage parameter or sample size of the priors used to study the variance parameter of each coefficient. Gamma(r, s) represents the Gamma distribution with mean rs and variance sr2 . Equation (21.12) is called a slab because we can choose a slightly informative (close to flat) prior parameter with respect to γ .

21.2.2.2

Conditional Posterior

We define yt∗ = yt − Z t∗T αt where Z t∗ is the observation matrix of (21.1) with ∗ so that y∗ is y which has removed the time β T xt = 0. We also define y∗ = y1:n series component such as trends, seasonality, and others. The joint posterior distribution between β and σ2 conditional λ is written using the standard conjugation formula [7] in the following (21.13): βγ |σ2 , γ , y∗ ∼ N (β˜γ , σ2 (Vγ−1 )−1 ) 1 |γ , y∗ ∼ Gamma σ2



N SSγ , 2 2

 (21.13)

where the sufficient statistics can be written as follows: Vγ−1 = (XT X)γ + Ωγ−1 β˜γ = (Vγ−1 )−1 (XγT y∗ + Ωγ−1 bγ ) SSγ = ss + y∗T y∗ + bγT Ωγ−1 bγ − β˜γT Vγ−1 β˜γ N =v+n SSγ can be expressed or calculated in a number of ways other than those listed above.

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Marginal Posterior

By using the concept of conjugation, we can get rid of βγ and obtain the following equation: |Ωγ−1 | 2 p(γ )

1 σ2

analytically to

1

∗

∗

γ |y ∼ C(y )

1

N

|Vγ−1 | 2 SSγ2

−1

(21.14)

where C(y∗ ) is an unknown normalization constant and depends on y∗ but does not depend on γ . The MCMC algorithm used to fit the model does not require an explicit C(y∗ ) calculation. Equation (21.14) is not difficult to evaluate, because the only matrix that needs to be inverted is Vγ−1 which has a low dimension if the observed model has several coefficients from the predictor with a value of 0, this is opposite to probability mass function. Therefore, sparsity in this model is a full posterior distribution feature, not only on the mode value.

21.2.3 Markov Chain Monte Carlo Markov Chain Monte Carlo (MCMC) is a sampling algorithm for performing simulations of the posterior distribution, which can smooth predictions over a large number of possible models using the Bayesian model mean [12, 18]. First, the MCMC algorithm will use the prior Normal distribution to standardize the data so that it will eventually produce a posterior distribution along with its parameter estimates [23]. 21.2.3.1

Parameter Learning

We define θ as the set of model parameters other than β and σ2 . The posterior distribution of the state space model can be simulated directly using the Markov Chain Monte Carlo algorithm with the following steps [23]: 1. Simulate the latent state α of p(α|y, θ, β, σ2 ) using the smoother simulation method from Durbin and Koopman (2002). 2. Simulate θ ∼ p(θ |y, α, β, σ2 ). 3. And finally, simulate β and σ2 of the Markov chain with a stationary distribution p(β, σ2 |y, α, θ ). Define φ = (θ, β, σ2 , α). Repeat the above 3 steps continuously so as to produce a sequence of values φ (1) , φ (2) , . . . of a Markov chain with a stationary distribution p(φ|y) which is the posterior distribution of φ conditional y. The simulation of θ in step 2 depends on the state components present in the model. The simulation in step 3 can be performed using the Stochastic Search Variable Selection (SSVS) algorithm developed by George and McCulloch [8]. This SSVS algorithm produces sufficient performance for MCMC simulation. SSVS is a Gibbs

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sampling algorithm in which each element of γ is taken from its full conditional distribution and is proportional to (21.14). With a full conditional distribution, the value of γk can be obtained directly because γk has only 2 possible values. Next, βγ and σ2 are taken from their full conditional distribution which is closed form as in (21.13).

21.2.3.2

Forecasting

As in the analysis with other Bayesian approaches, forecasting with the BSTS model is also based on the predictive posterior distribution. A simulation of the predictive posterior distribution is carried out with the given model parameters and state parameters from the posterior distribution. Defined y˜ as the set of values to be predicted. The predictive posterior distribution of y˜ given historical data for y is as follows:  p( y˜ |y) =

p( y˜ |φ) p(φ|y)dφ

(21.15)

Remember that φ (1) , φ (2) , . . . is the set of random simulation results from the posterior distribution p(φ|y). Then, a sample is taken from p( y˜ |y) by sampling p( y˜ (g) |φ (g) ), which is done by iteration of (21.1) and (21.2) which is continued from (g) 2(g) αn with parameters θ (g) , β (g) , and σ . Since the different elements of β will be 0 in different MCMC simulations, simulations of the predictive posterior distribution will automatically take into account the sparsity and uncertainty of the model and benefit from the mean Bayesian models. This forecasting method produces a simulated sample of the predictive posterior distribution p( y˜ |y). The simulation results can be summarized into a certain value, for example by using the mean which is a Monte Carlo estimate of E( y˜ |y). In addition, simulation results can also be displayed in the form of histograms, Kernel density estimates, or dynamic density plots. Multivariate summaries such as a collection of quantiles are also suitable for representing simulation results. With this predictive posterior distribution, forecasting can be carried out for several periods in the future or nowcasting which is forecasting one step ahead (or forecasting current, past or future in a short period of time) which is oriented to determine the relationship between the independent variable and the dependent variable.

21.3 ARIMAX One of the extensions of the ARIMA/SARIMA time series model is the Autoregressive Integrated Moving Average with Exogenous Variable (ARIMAX)/Seasonal ARIMAX (SARIMAX) model which includes exogenous variables. In this model, the factors that affect the dependent variable Y at time t are not only a function of variable Y in time, but are also influenced by other independent variables at time t.

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In general, according to [22] the form of the ARIMAX ( p, d, q) model can be given by the following (21.16): (1 − B)d D(B)Yt = μ + C(B)εt + α1 X 1t + · · · + αk X kt

(21.16)

where B is the backward operator and α1 , . . . , αt is a real number. So it applies (B j X )t = X t− j . Here are the equations for D(B) and C(B): D(B) = 1 − (a1 B + a2 B 2 + · · · + a p B p )

(21.17)

C(B) = 1 + b1 B + b2 B 2 + · · · + bq B q

(21.18)

where μ, a1 , a2 , . . . , a p , b1 , b2 , . . . , bq is a real number. It should be noted that α p , bq = 0 and εt ∼ I I D(0, σε2 ). In this model, Yt and X it , i = 1, 2, . . . , k is the time series data which is assumed to be stationary. If both are stationary, that is, they do not contain trends and do not contain volatility clustering, then there is another alternative model that can be used besides ARIMAX/SARIMAX, namely the Autoregressive Distributed Lag (ADL) model. If only Yt is not stationary because it contains a trend, then the ARIMAX/SARIMAX model can be used by adding integrated or differential components into Yt . Meanwhile, if Yt is stationary but X it is not stationary, then the ARIMAX/SARIMAX model can be used directly without the need to add a difference component to Yt . However, if Yt and X it both are not stationary but cointegrated, can use the Error Correction Model. On the other hand, if Yt and X it are both not stationary but also not cointegrated, it is possible to model the differences between Yt and X it where i = 1, 2, . . . , k. A special case of the ARIMAX model that is widely used is the Autoregressive with Exogen Variable (ARX) model. The steps for modeling ARIMAX/SARIMAX are generally the same as modeling ARIMA/SARIMA, but in the estimation of the model, the components of the independent variables are added [22].

21.4 Analysis and Discussion The data used in this study is secondary data consisting of data on community mobility, vaccine dose 2, and the number of claims for BPJS DIY province caused by COVID-19. The three data are daily time series data starting from the beginning of the pandemic, namely March 2, 2020 to February 17, 2022. The following are the details of the data used. 1. Daily data on the number of people who were hospitalized due to COVID-19 who then submitted a claim to the DIY Provincial Health BPJS. 2. The data for community mobility in the DIY province is obtained from mobility reports issued by Google every day, namely the Google COVID-19 Community

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Mobility Reports based on tracking from cellular phone users in the DIY province who activate the location feature on their Google account [9]. This mobility data is in the form of a percentage (%) of the length of time people spend in a place against the baseline value which represents the normal value on that day of the week, namely the median value for the period January 3, 2020 to February 6, 2020 when there was no COVID-19 pandemic [9]. Where this data consists of 6 categories of places including retail and recreation, grocery and pharmacy, parks, transit stations, workplaces and residential. Retail and recreation includes mobility in the areas of restaurants, cafes, shopping centers, amusement parks, museums, libraries, and cinemas. Meanwhile, grocery and pharmacy covers the area of wholesale markets, food warehouses, traditional markets, specialty food stores, drug stores, and pharmacies. Parks include national park areas, public beaches, marinas, dog parks, squares, and public parks. Transit stations include the area of subway, bus and train stations. Workplaces include various workplace locations such as offices and factories. And lastly, residential includes residential areas such as houses and apartments 3. Data on the number of DIY people who have been vaccinated up to the second dose per day are obtained from the website of the Ministry of Health of the Republic of Indonesia. Thus, this study uses a total of 9 variables consisting of date, 1 dependent variable, namely the number of BPJS claims along with 7 independent variables, which are 6 variables of community mobility from various locations and 1 variable vaccination dose 2. From these data with 718 days of observation, it is obtained that there were a total of 48,650 people who submitted claims to the DIY provincial BPJS due to COVID-19 and 2,874,140 people of the DIY province who had received dose 2 vaccinations.

21.4.1 Data Exploration and Visualization Before entering into the analysis, it is necessary to understand and retrieve the information contained in the data by looking for the pattern of the relationship between each data and the relationship between the data with one another visually.

21.4.1.1

Plot of Claim Movement

The plot of the movement of claims from March 2, 2020 to February 17, 2022 is formed as follows. In Fig. 21.1, it can be seen that the data pattern on the number of BPJS DIY claims caused by COVID-19 is not stationary because it shows a significant up and down trend over time. There are 2 peaks or the most significant extreme points, namely around January 2021 and July 2021. These two peaks are a big wave of the spread

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Fig. 21.1 Plot of claim movement

of the COVID-19 virus experienced by Indonesia and the DIY province due to the New Year and post-Eid holidays in 2021. To see if the number of BPJS claims for the DIY province caused by COVID-19 is directly proportional to the number of new COVID-19 cases in the DIY province, a plot will be formed as shown in Fig. 21.2. Where the data for new cases of COVID-19 in the DIY province during the period from March 2, 2020 to February 17, 2022, was obtained from the Corona Statistics [5] website. It can be seen that the data pattern on the number of new COVID-19 cases in the Special Region of Yogyakarta province is also not stationary due to an up and down trend. In addition, there are also 2 waves that are comparable to Fig. 21.1 namely the first wave in February 2021 and the second wave in August 2021. These two events are called waves because of the presence of peaks that are much more significant than the values in the periods before and thereafter in the near future. This was triggered by the New Year and Eid holidays and because according to BAPPEDA DIY (Yogyakarta Special Region Development Planning Agency), 91.49% of the people of DIY province were BPJS health participants [3]. Because the majority of DIY’s people have BPJS health, the pattern of movement of new COVID-19 cases is in line with the number of daily claims arising from COVID-19, although the two patterns are not very close because not all COVID-19 patients submit claims to BPJS.

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Fig. 21.2 Plot comparison of claims with new cases

21.4.1.2

Plot Comparison of Mobility and Claims

The mobility components referred to here are retail and recreation, grocery and pharmacy, parks, transit stations, workplaces, and residential variables. Because the values for the variables in the mobility component have different scales from the claim variables, standardization will be carried out on these 7 variables using the size of the median center and the size of the distribution, namely the interquartile range. So that the plot of the standardization results from each of the independent variables of community mobility against BPJS claims can be compared to understand the relationship between the two visually as follows. In Fig. 21.3, the comparison plot between the results of the standardization of 6 DIY community mobility locations and the number of BPJS DIY claims can be divided into 3 patterns. The first pattern is that of retail and recreation, grocery and pharmacy, parks, and transit stations. These variables show a similar pattern, where the pattern varies over time. These four variables have a high pattern in normal conditions in the period before the COVID-19 pandemic, and then over time and the increase in BPJS claims due to COVID-19, the movement pattern of these four variables decreases. When the number of BPJS claims tends to be stationary or does not change over time, there is an increase in the mobility plots in these 4 locations. Then when the number of BPJS claims due to COVID-19 has increased, the plot of these four variables has decreased even though it is only for about 1 month. Furthermore, when it has entered July 2021 where the number of cases and the number of claims due to COVID-19 has decreased significantly because many

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Fig. 21.3 Comparison of mobility standardization plots with claims

people have received vaccinations, it is also accompanied by an upward movement similar to conditions before entering the pandemic period. The second pattern is seen in the workplaces variable, which shows a high pattern before entering the COVID-19 pandemic, and when it entered the COVID-19 pandemic the movement pattern was relatively stationary and did not follow the movement pattern of the many BPJS claims due to COVID-19. This is because when entering the beginning of the COVID-19 pandemic, the work from home policy was implemented for a long period of time by the majority of companies in Indonesia because they followed the regulations set by the government. Then after July 2021, the pattern of mobility in the workplace began to show an upward trend, due to COVID-19 cases which had shown a decline so that work from office was allowed. While the third pattern is shown by the residential variable. This variable shows a pattern that varies over time. Contrary to the first pattern, the pattern shown by the mobility of the people of the DIY province in housing areas actually showed a low pattern before entering the COVID-19 pandemic period. And when it started to enter the COVID-19 pandemic, the movement pattern of mobility in housing experienced a significant increase due to government policies that asked people not to travel and stay at home to anticipate the spread of the COVID-19 virus. However, after 3 months of the COVID-19 pandemic, the mobility plot in housing began to decline

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Fig. 21.4 Plot comparison of dose 2 vaccination and claims

and followed the movement pattern of the number of BPJS claims due to COVID-19. When entering post-Eid 2021, when the number of BPJS claims due to COVID-19 is experiencing a very significant increase, the mobility of the community in housing also shows a significant increase because people are becoming more aware of the COVID-19 virus and also to suppress the spread of the virus.

21.4.1.3

Plot Comparison of Dose 2 Vaccination and Claims

Furthermore, it can also be seen the comparison plot between vaccine dose 2 with claims that have been standardized by the size of the median center and the size of the distribution, namely the interquartile range. The plot is obtained as follows. From Fig. 21.4 it can be seen that at the beginning of the COVID-19 pandemic until about 1 year later there were no people who received the 2nd dose of vaccination. When the initial dose 2 vaccination was implemented, there was a significant spike in the number of DIY people receiving dose 2 vaccine. The movement pattern of dose 2 vaccination is comparable to the movement pattern of the number of BPJS claims due to COVID-19, although there is a lag of around 100 days. When there was a very significant increase in the number of BPJS claims due to COVID-19, 100 days later there was also a spike in the number of people receiving dose 2 vaccines, because people were increasingly afraid and on guard so as not to contract the COVID-19 virus.

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21.4.2 BSTS and ARIMAX In this analysis, 4 types of data will be used based on the time period and whether or not kernel smoothing is applied to the data, namely. 1. Full data from March 2, 2020 to February 17, 2022. 2. Full data from March 2, 2020 to February 17, 2022 which has been kernel smoothed. 3. Partial data from August 1, 2021 to February 17, 2022. 4. Partial data from August 1, 2021 to February 17, 2022 which has been kernel smoothed. The time period from August 1, 2021 to February 17, 2022 was chosen because the results obtained from the complete data did not show good MAPE or RMSE values. So it is necessary to try to use partial data when the claim movement plot shows a downtrend. Modeling will be carried out using the BSTS and ARIMAX methods using these 4 data types, then look for the best BSTS model from the model, each of which consists of 1 state component, namely local level, local linear trend, semi local linear trend, student local linear trend, or seasonal and by using 3 different niter values. And for a model with a seasonal component, because it is difficult to determine the number of seasons and the length of the season period in the claim data, a special function is used to find a model with a seasonal component that includes the number of seasons and the length of the season period that can produce the smallest RMSE. From the best BSTS model, its performance is measured with the MAPE and RMSE value indicators, then it will be compared with the best ARIMAX model. So that in the end it can be seen which is the best method that can be used on the data in this study.

21.4.2.1

Full Data

The following is a summary table of MAPE and RMSE values obtained from intact data for the period March 2, 2020 to February 17, 2022 Table 21.1. Because in this full data there are 7 values in the claim data which are worth 0, then the resulting MAPE value is ∞ and the ARIMAX model cannot be formed. Both the seasonal components at niter = 100, 500 or 1000 are both obtained from nseasons = 93 and season.duration = 1 days based on the plot generated by the looping function to find the best seasonal component arrangement that produces the smallest RMSE of model. The plot of the results of the looping function to find the arrangement of seasonal components with the smallest RMSE for niter = 100 was obtained in 27.4 minutes, while for niter = 500 it took 8.5 hours, and for niter = 1000 it took 18 hours. From the full data, the best model with an RMSE value of 123.3897 is obtained, namely the BSTS model with a net of = 500 and the state component is seasonal with 93 seasons, each season consisting of 1 day.

21 Prediction of the Number of BPJS Claims due to COVID-19 … Table 21.1 Summary of MAPE and RMSE values for full data Method MAPE BSTS

Niter = 100

Niter = 500

Niter = 1000

Local level Local linear trend Semi local linear trend Student local linear trend Seasonal Local level Local linear trend Semi local linear trend Student local linear trend Seasonal Local level Local linear trend Semi local linear trend Student local linear trend Seasonal

ARIMAX

21.4.2.2

∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ –

267

RMSE 377.8431 412.3976 474.1538 756.0973 125.0399 360.5896 327.9222 456.4079 443.0968 123.3897 368.6202 254.3123 451.363 464.2992 125.5721 –

Smoothed Full Data

The following is a summary table of MAPE and RMSE values obtained from intact data for the period from March 2, 2020 to February 17, 2022, which has been carried out by kernel smoothing Table 21.2. The following is a summary table of MAPE and RMSE values obtained from intact data for the period from March 2, 2020 to February 17, 2022 which has been performed by kernel smoothing: Both the seasonal component at niter = 100, 500 or 1000 are both obtained from nseasons = 147 and season.duration = 1 days based on the plot generated by the looping function to find the best seasonal component arrangement that produces the smallest RMSE model. The plot of the results of the looping function to find the arrangement of seasonal components with the smallest RMSE for niter = 100 was obtained in 1.26 hours, while for niter = 500 it took 2.59 hours, and for niter = 1000 it took 6.47 hours. From the full data that has been smoothed using the kernel method, the best model is obtained with a MAPE value of 26,17355 and an RMSE of 312,7642, namely the BSTS model with a niter of = 500 and the state component is seasonal with 147 seasons, each season consisting of 1 day.

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Table 21.2 Summary of MAPE and RMSE values for smoothed full data Method MAPE BSTS

Niter = 100

Niter = 500

Niter = 1000

ARIMAX (2,0,0)

21.4.2.3

Local level Local linear trend Semi local linear trend Student local linear trend Seasonal Local level Local linear trend Semi local linear trend Student local linear trend Seasonal Local level Local linear trend Semi local linear trend Student local linear trend Seasonal

30.59385 28.95317 29.67441 72.81316 26.26801 30.6811 60.36767 28.28246 57.37971 26.17355 30.38592 69.06413 27.97733 62.24641 26.39878 2.024∗1080

RMSE 353.292 296.0707 326.016 742.0528 313.0246 353.7378 615.5975 312.8739 585.6635 312.7642 351.104 704.4801 309.4058 635.1441 314.8923 1.167∗1084

Partial Data

The following is a summary table of MAPE and RMSE values obtained from partial data for the period August 1, 2021 to February 17, 2022 Table 21.3. Because in this partial data there is 1 value in the claim data which is 0, then the resulting MAPE value is ∞ and the ARIMAX model cannot be formed. The seasonal component on niter = 100 has nseasons = 59 and season.duration = 1 days, while the seasonal component on niter = 500 or 1000 is both obtained from nseasons = 68 and season.duration = 1 days based on the plot generated by the looping function to find the best seasonal component arrangement that produces the smallest RMSE model. The plot of the results of the looping function to find the arrangement of seasonal components with the smallest RMSE for niter = 100 was obtained in 26.84 minutes, while for niter = 500 it took 40.74 minutes, and for niter = 1000 it took 1.32 hours. From the partial data, the best model with an RMSE value of 4.389364 is obtained, namely the BSTS model with a niter or MCMC iteration of 1000 and the state component in the form of a local level.

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21.4.2.4

269

Smoothed Partial Data

The following is a summary table of MAPE and RMSE values obtained from intact data for the period August 1, 2021 to February 17, 2022 which has been kernel smoothed Table 21.4. The results of the looping function to find the arrangement of seasonal components with the smallest RMSE for niter = 100 are obtained in 24.65 minutes and get nseasons = 57 and season.duration = 1 days, while for niter = 500 it takes 1.3 hours and obtained nseasons = 60 and season.duration = 1 days, and for niter = 1000 it takes 1.39 hours which results in nseasons = 70 with season.duration = 1 days. From partial data that has been done by kernel smoothing, the best model with MAPE value of 0.3273575 and RMSE of 2.629033 is the BSTS model with niter = 1000 and the state component is local level. Compared to the other 3 best models obtained from 3 other types of data, it can be seen that the best model with the smallest MAPE and RMSE values is obtained from partial data modeled with BSTS and its state component is local level with a MAPE value of 32.7% which is according to Lewis [17] it can be interpreted that the ability of the BSTS model in forecasting the test data is quite feasible. While the RMSE value of 2.629033 is quite small when compared to the value in the BPJS claim data due to COVID-19 in the DIY province which is in the range of 0–451. The Fig. 21.5 shows the prediction results in the test data using BSTS model containing local level components with 1000 MCMC iterations.

Table 21.3 Summary of MAPE and RMSE values for partial data Method MAPE BSTS

Niter = 100

Niter = 500

Niter = 1000

ARIMAX(1,0,1)

Local level Local linear trend Semi local linear trend Student local linear trend Seasonal Local level Local linear trend Semi local linear trend Student local linear trend Seasonal Local level Local linear trend Semi local linear trend Student local linear trend Seasonal

∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞

RMSE 4.821662 24.6536 72.70953 29.85354 32.41445 4.60071 14.8048 74.62038 8.702952 33.71251 4.389364 5.493563 73.59517 8.857519 33.57176 8.257244

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Fig. 21.5 Plot forecast in test data

The figure shows the forecasting results in the test data along with the value interval range. It can be seen that there is no rising pattern in the median which is marked with a blue line. In addition, the green dotted line interval shows the interval limit for the forecast value of the claim data formed from the model. The claim data

Table 21.4 Summary of MAPE and RMSE values for smoothed partial data Method MAPE BSTS

Niter = 100

Niter = 500

Niter = 1000

ARIMAX (0,0,0)

Local level Local linear trend Semi local linear trend Student local linear trend Seasonal Local level Local linear trend Semi local linear trend Student local linear trend Seasonal Local level Local linear trend Semi local linear trend Student local linear trend Seasonal

0.4290658 3.326384 10.8086 1.533676 3.379279 0.3417439 2.611013 11.68693 2.774572 3.397813 0.3273575 2.386921 11.64131 1.833105 3.405383 1.494∗1024

RMSE 3.840414 24.02884 78.00298 11.61269 27.58503 2.628374 19.03543 84.27164 19.68235 26.46185 2.629033 17.64504 83.91459 13.38156 26.42044 9.559∗1024

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Fig. 21.6 Plot forecast versus actual value in test data

Fig. 21.7 Plot inclusion probability values

pattern formed from the BSTS model can follow the actual claim data pattern in the test data. This can be seen in the following figure. Although in Fig. 21.6 the results of the BSTS model are close to the claim data in the test data, it can be seen that the green line still cannot follow the cyclical pattern of the blue dotted line. From the BSTS model that was formed, it can also be seen that the inclusion probability values for all the coefficients of the predictor variables in the model as shown by Fig. 21.7 and Table 21.5. The variable that has the highest inclusion probability value is indicated by the vaccine dose 2 variable which is 57.65%, then at the bottom are workplaces, transit stations, residential and parks variables which are both worth 19.08%, grocery and pharmacy, retail and recreation. and the last one is intercept. This shows that the vari-

272 Table 21.5 Inclusion probability values Variable (Intercept) Retail and recreation Grocery and pharmacy Parks Transit stations Workplaces Residential Vaccine dose 2

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Inclusion probability 0 0.1418367 0.1479592 0.1908163 0.2183673 0.2346939 0.1908163 0.5765306

able that plays an important role and most influences the number of BPJS claims due to Covid-19 in the DIY province is the number of people who have been vaccinated with dose 2 every day.

21.5 Conclusions It can be concluded that the BSTS method is better than ARIMAX in overcoming the uncertainty that exists in the data on the number of BPJS claims due to COVID-19. However, the drawback of the BSTS method is its inability to follow the cyclical pattern that exists in the data, because the BSTS model formed is only able to follow the trend pattern from the data and the MAPE value obtained is still not small. Because to be declared as a model that has very good forecasting ability, a MAPE value of less than 10% is required according to Lewis [17]. The best model obtained is the BSTS model with a local level trend component which has a MAPE value of 32.7% and its RMSE value is 2.629033. From the MAPE and RMSE values, it can be said that the model’s ability to forecast is feasible and can be used to predict the number of BPJS claims due to COVID-19 in the DIY province for the coming period. And from this model, the highest inclusion probability value is for the vaccine dose variable 2. Which means that the number of people who are vaccinated with dose 2 every day has the most influence on the number of BPJS claims due to COVID-19 in the DIY province when compared to other external factors, namely DIY community mobility. Acknowledgements This work was fully funded by the project of the Final Task Recognition Program of Universitas Gadjah Mada 2022 (grant number: 3550/UN1.P.III/Dit-Lit/PT.01.05/2022) provided by the research directorate and the reputation improvement team of UGM towards the World Class University of the quality service office. The authors also thank reviewers for their careful reading and helpful suggestions.

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25. S.L. Scott, Package bsts, pp. 8-22, 31-33, 66-68, 77-78 and 92 (2021) 26. Task Force for the Acceleration of Handling Covid-19, Distribution Map (2022), https:// covid19.go.id/peta-sebaran. Accessed on 20 Feb 2022 27. Tempo, Kemenkes Jelaskan Soal Tunggakan Klaim Covid-19 Rumah Sakit Rp 25,1 T (2022), https://nasional.tempo.co/read/1560432/kemenkes-jelaskan-soal-tunggakan-klaimcovid-19-rumah-sakit-rp-251-t/. Accessed on 23 Feb 2022 28. World Health Organization, Coronavirus disease (COVID-19) (2019), https://www.who.int/ health-topics/coronavirus. Accessed on 24 Feb 2022 29. L. Xie, The analysis and forecasting COVID-19 cases in the United States using Bayesian structural time series models, in Biostatistics & Epidemiology (United States of America, 2021), pp. 2–5 30. Yogyakarta special regional government, COVID-19 Vaccination in the Special Region of Yogyakarta Phase Two Ready to be Massively held (2021), https://jogjaprov.go.id/berita/detail/ 9195-vaksinasi-covid-19-diy-tahap-kedua-digelar-massal. Accessed on 23 Feb 2022

Chapter 22

A Study on the New Cases of Influenza A, B, and Covid-19 in Malaysia Norhaidah Mohd Asrah

and Nur Faizah Isham

Abstract Coronavirus 2019 also known as Covid-19, is a contagious virus that attacks the acute respiratory system. The way it attacks is the same as influenza A and B viruses. However, it appears to be dissimilar between the two viruses. The objectives of this study are to understand the behavior, distributions, and correlations of the new cases of Covid-19 and influenza A and B, in Malaysia by using the datasets from World Health Organization (WHO). The descriptive statistics of Covid-19 and influenza A and B are used to study the behavior of the new cases, while the Anderson Darling test and Spearman correlation coefficient are used to studying their new cases’ data distributions and correlations, respectively. Based on the results, the new cases data distribution of Covid-19 and influenza A and B is not normal. The correlation for both new cases of influenza A and B is positively strong. However, the correlation between Covid-19 and influenza A and B is weak. This shows that new cases of Covid-19 and both influenzas in Malaysia are not related to each other, but new cases of influenza A and B are dependent on each other. For future research, more data are needed with more variables to improve the current results.

22.1 Introduction An unknown contagious disease will be considered an outbreak when it unexpectedly happens in a high number of affected people. It will become an epidemic when the disease takes more lives than an outbreak and has a larger area of infection. However, an epidemic can still be controlled and treated, not dangerous for a populated area. A pandemic is a disease or an outbreak of an illness that went out of control and spread widely across the world. Examples of outbreak diseases are the influenza virus and N. M. Asrah (B) Universiti Tun Hussein Onn Malaysia, UTHM Pagoh Campus, Pagoh Higher Education Hub, KM 1, Jalan Panchor, 84600 Panchor, Johor, Malaysia e-mail: [email protected] N. F. Isham Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Mustapha et al. (eds.), Proceedings of the 8th International Conference on the Applications of Science and Mathematics, Springer Proceedings in Physics 294, https://doi.org/10.1007/978-981-99-2850-7_22

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Covid-19 [1]. Pandemic comes from the word “pandemick” or vernacular disease in 1666 [2]. It will become a pandemic when WHO declared it formally because of the unexpected fast infectious, severe illness that harms humans and is prevalent over the whole world. The matter will be taken seriously, as it takes more lives than an epidemic, and the international health expert for the cause and solution for the illness will conduct research. WHO is an organization that was founded in 1948 to help people around the world attain the highest level of healthiness and response to emergency health issues, especially with the highest rate of death [3]. When a pandemic occurs, people need to distance themselves from each other as the disease itself is contagious. One way to prevent it become widely spread is for people need to have social distancing. This led people to seclude themselves, and lack of communication becomes one of the effects of it. It affects people’s mental health and becomes a serious matter in a few years. It has opened our eyes that mental awareness is very important in our life. Furthermore, economic fluctuation occurs because of the closed border, and the tourism industry becomes dead. People are losing their jobs because of the collapse of the economy during the pandemic, or they want to come back to their homeland and stay with their families for those who are working overseas [4]. For the past two years, Covid-19 has been dominating the world. It originates from the Huanan market in Wuhan, China and it was reported that several patients associated with seafood from the market have pneumonia. Huanan market is famous for its exquisite seafood and exotic foods such as bats, snakes, birds, and frogs [5]. On December 31, 2019, China government decided to report this severe disease to WHO, and some samples of the exotic foods in the Huanan market were analyzed to find the cause of this pandemic. Covid-19 was announced by WHO on January 30, 2020, to be a very concerning disease internationally as Covid-19 victims increase by the day, month, and year. The cause of Covid-19 is a dangerous respiratory infection where the common symptoms are fever, cough, shortness of breath, loss of sense, and fatigue. A small population of patients had gastrointestinal infection symptoms was found by [2, 5]. The virus spread through droplets released by the carrier when sneezing, coughing, and talking at a close distance [6–8]. Social distancing at least 1 m apart from each other must be practiced to avoid more Covid-19 infection. This disease has familiar symptom as influenza; however, it is completely different as the Covid-19 virus is far more dangerous as its root is a Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV2) plus it can cause low blood oxygen saturation and continue to fail multiple organs and this is what leads people to their deathbed [9]. Many families could not meet or send their loved ones to the end because Covid-19 is a contagious disease. Meanwhile, influenza disease is a type of virus that attacks the respiratory system such as the throat, nose, and lungs. Other symptoms are fever, cough, shortness of breath, fatigue, headache, and myalgia. In early 2020 together with Covid-19, influenza cases also rose and became higher in 2022. However, since it is a seasonal virus, the rate of cases is not as high as Covid-19 and is less dangerous. The symptoms and transmission of influenza are the same as Covid-19. Nevertheless, the illness itself is not life-threatening. There are four types of influenza which are type A, B, C, and D. All types have different symptoms where types A and B are seasonal,

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while types C and D are for children and not dangerous to others [6, 10]. Seasonal influenza which types A and B is very common and always circulates the population, especially during winter [2, 11]. Influenza A virus carries subtypes H1N1 or H3N2, while influenza B carries virus Victoria and Yamagata strains. Influenza may not be as severe as Covid-19 because the symptoms are mild and limiting diseases. Moreover, it was declared by WHO on 11 June 2009 to increase awareness from phase five to phase six [12]. The first case of Covid-19 in Malaysia was the three cases of Chinese from Singapore who had traveled to Johor on January 25, 2020. After the screening and tracing with cooperation from the Singapore Ministry of Health, it was confirmed that the three cases had eight close contacts with Covid-19 patients [8, 9]. The second wave started on February 27, 2020, when new cases flooded, and the graph of mortality rises each day as people with a history of traveling internationally had close contact with Covid-19 patients [9]. A form of cluster occurred that risks many people and sudden increases in Covid-19 patients. Hospitals are full, and the lack of equipment makes the situation worsen. However, implementation is done by the Malaysian Prime Minister by closing the borders and blocking the society from going out where only one of the family members can go out to buy necessities. However, after two years of fighting with Covid-19, the transition from pandemic to endemic started on April 1, 2022 [13]. Although influenza has always been around people, recently the number of cases increases along with Covid-19 [11]. Thus, a study on new cases of Covid-19 and influenza A and B in Malaysia was conducted by observing the behavior of the data and examining the data distribution to study the relationship between the two viruses.

22.2 Methodology 22.2.1 Dataset The data used in this study were taken from the World Health Organization (WHO) website [3]. There are three types of data collected referring to the new cases of influenza A, B, and Covid-19 in Malaysia. The data on influenza A and B were extracted from influenza FluNet on WHO website, meanwhile Covid-19 data were taken from the WHO Covid-19 dashboard data. The new cases of influenza A and B data were collected by weekly, while the new cases of Covid-19 were collected by daily. The Covid-19 data were transformed to weekly data to make it uniformly with influenza A and B dataset. The data used are from the first week of 2020, which was from December 29, 2019, until July 3, 2022 with a total of 132 weeks.

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22.2.2 Descriptive Statistics Descriptive statistics explain and summarize the information in the data collected in a meaningful way by presenting the knowledge in a graphical or tabulate way [14]. By applying this method, the behavior of the dataset can be observed by looking at the pattern of the three datasets from the time series plot, while the distribution of the dataset can be summarized by using the histogram. The descriptive analysis explains the mean, standard deviation, skewness, kurtosis, and correlation between the three diseases.

22.2.3 Normality Test The normality of the dataset can be studied according to the value of their skewness and kurtosis. It also can be visualized by using the histogram, boxplot, and Q-Q plot. The Anderson Darling test can be used to test the hypothesis that the dataset came from normal distribution [15]. The formula for the Anderson Darling test can be referred to (22.1). AD = −n −

n   1 (2i − 1) In F(xi ) + In (1 − F(X n−i+1 )) , n i=1

(22.1)

where n is the sample size, F(X) is the cumulative distribution function for the specified distribution, and i is the ith sample when the data are sorted in ascending order. The distribution is considered normal if the p-value for the Anderson Darling test is more than 0.05. The normality of data is important as it is needed as one of the assumptions in the parametric analysis.

22.2.4 Correlation Coefficient The correlation among influenza A and B, and Covid-19 new cases can be checked using the Pearson or Spearman correlation coefficient. The formula for the Pearson correlation coefficient can be referred to (22.2).  (xi − x)(yi − y) r =  , (22.2) (xi − x)2 (yi − y)2 where r is the correlation coefficient, xi is the value for the x variable, yi is the value for the y variable, xx¯ is the mean for x variable, and y y is the mean for y variable. The Pearson correlation is used when the dataset is random, continuous,

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and jointly normally distributed [16]. Another correlation measurement can be used is the Spearman correlation. Spearman correlation does not require normally distributed data and can be used to analyze nonlinear monotonic relationships. The formula for Spearman correlation can be referred to (22.3).  6 di2 , ρ =1−  2 n n −1

(22.3)

where ρ is the Spearman’s rank correlation coefficient, di is the difference between the two ranks of each observation, and n is the number of observations. The value for correlation is between −1 (strong negative relationship) and + 1 (strong positive relationship). The correlation is strong when the value is between ± 0.7 to ± 1, moderate when is between ± 0.3 to ± 0.7, weak when is between 0 to ± 0.3, and no correlation when the value is 0 [17].

22.3 Results and Discussions Based on the data collected, the behavior of influenza A and B, and Covid-19 new cases dataset is analyzed. Firstly, the pattern of the new cases is studied using the time series plot as in Fig. 22.1. From Fig. 22.1, Covid-19 new cases has an up-and-down pattern or random fluctuation. It starts having an increasing number of cases from week 39. The first peak is on week 37 and is followed by week 115. The number of new cases starts slowly decreasing by week 123. There was big a difference on new cases between Covid-19 and influenza A and B. The new cases of influenza A and B are lower if compared to Covid-19 new cases. Figure 22.2 shows in detail the new cases for both influenza A and B. The new cases of both influenza A and B have slowed increment over the weeks. In week 100, the new cases started to increase to nearly 100 new cases per week. After week 130, the new cases for both keep increasing until 250 new cases per week. Next, the descriptive statistics for influenza A and B, and Covid-19 new cases can be concluded in Table 22.1. All data are based on 132 weeks. The mean for new cases of influenza A (14.55) and B (15.40) is almost the same but for Covid-19 (34,778) is totally different. This is because the number of new cases of Covid-19 is higher compared to influenza A and B. The standard deviation for new cases of influenza A (36.54) and B (37.44) is almost similar. However, the standard deviation for new cases of Covid-19 (49,223) is much higher. The range shows that the difference between the highest and the lowest value for new cases of influenza A and B is 244 and 245. There is not much difference between influenza A and B. Meanwhile, the range for new cases of Covid-19 (213,020) is extremely large. The dispersion or distribution of influenza A and B, and Covid-19 new cases can be visualized using the histogram. Figures 22.3 and 22.4 show the data distribution

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Fig. 22.1 Time series plot of weekly new cases for influenza A, B, and Covid-19 in Malaysia

Fig. 22.2 Time series plot of weekly new cases for influenza A and B in Malaysia Table 22.1 Descriptive statistics for new cases of influenza A, B, and Covid-19 Variable

Total

Mean

Standard deviation

Range

Skewness

Kurtosis

Influenza A

132

14.55

36.54

244

4.40

22.02

Influenza B

132

15.40

37.44

245

4.22

20.39

Covid-19

132

34,778

49,223

213,020

1.91

2.95

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Fig. 22.3 Data distribution of influenza A

and probability plot for new cases of influenza A, respectively. The distribution of new cases of influenza A is not normal. The value for its skewness (4.40) and kurtosis (22.02) is far from the normal range value. Moreover, the Anderson Darling (p-value = < 0.005) test also shows that the distribution is not normal. Figures 22.5 and 22.6 show the data distribution and probability plot for new cases of influenza B, respectively. The distribution of new cases of influenza B is also not normal. The value for its skewness (4.22) and kurtosis (20.39) is also not in the range of normal value. At the same time, the Anderson Darling (p-value = < 0.005) test shows that the distribution is not normal too. Therefore, both influenza A and B do not have a normal distribution. Meanwhile, Figs. 22.7 and 22.8 show the data distribution and probability plot for new cases of Covid-19. The distribution for new cases of Covid-19 is not normal too. Although the value for its skewness (1.91) and kurtosis (2.95) is in the range of normality, the Anderson Darling hypothesis testing (p-value = < 0.005) test shows that the distribution is not normal. Since the new cases distribution is not normal for all diseases, the parametric statistical test cannot be applied for the next analysis. The correlation between new cases of influenza A and B, and Covid-19 is studied using the Spearman correlation coefficient since the dataset is not normally distributed. The Spearman correlation coefficient values can be referred to Table 22.2. The correlation between new cases of influenza A and B is strongly positive (0.999). Meanwhile, there is a positive weak correlation between new cases of Covid-19 and influenza A (0.072) and influenza B (0.077). It can be concluded that Covid-19 and influenza A and B in Malaysia are not correlated at each other. Figure 22.9 show the matrix correlation for new cases of influenza A and B, and Covid-19. The patterns shown are parallel with the results from the Spearman correlation. The correlation plot between new cases of influenza A and B shows the linear positive pattern that explains the strong positive correlation for both. When

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Fig. 22.4 Probability plot of influenza A

Fig. 22.5 Data distribution of influenza B

the new case of influenza A increases, the new case of influenza B also increases. However, the correlation between new cases of Covid-19 and influenza A and B is weak. The value is near zero indicating that there is no correlation among them. The new case for Covid-19 is not related to the new case of influenza A and B in Malaysia.

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Fig. 22.6 Probability plot of influenza B

Fig. 22.7 Data distribution of Covid-19

22.4 Conclusion and Recommendations This study revealed that the new cases of Covid-19 in Malaysia are not dependent on the new cases of influenza. Furthermore, Covid-19 has new cases in drastic amounts because it is a recently new virus in 2019 while influenza is a seasonal virus that already has its own vaccination. After two years of lockdown, Covid-19 has slowed down the record of new cases and death. Although the new case of influenza A and

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Fig. 22.8 Probability plot of Covid-19 Table 22.2 Spearman correlation coefficient Influenza A Influenza B

0.999

Covid-19

0.072

Fig. 22.9 Matrix correlation for influenza A, B, and Covid-19

Influenza B 0.077

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B is still going on before and during the Covid-19 pandemic, the increase is not as higher as in Covid-19 cases. This is because influenza is a seasonal virus, while Covid-19 is a new type of virus found in 2019. However, the symptom of these diseases is roughly the same and hard to distinguish. The correlation between new cases of influenza A and B is positively strong and it tells us that the new cases of both are dependent on each other. For future research, it is recommended to use more datasets for influenza A and B, and Covid-19. Dataset can be collected for more than 132 weeks. Perhaps, the next research can compare the new cases in Malaysia with other countries. At the same time, more variables can be added to the research such as vaccination status, age, number of recovered from the viruses, and many more. Acknowledgements The authors would like to thank Universiti Tun Hussein Onn Malaysia and Universiti Teknologi Malaysia for their support.

References 1. N. Madhav, B. Oppenheim, M. Gallivan, P. Mulembakani, E. Rubin, N. Wolfe, Pandemics: risks, impacts, and mitigation, in Disease Control Priorities: Improving Health and Reducing Poverty (World Bank, Washington, DC, 2017), pp. 315–345 2. M.M. David, K.F. Gregory, S.F. Anthony, What Is a pandemic? J. Infect. Diseas. 200(7), 1018–1021 (2009) 3. World Health Organization Homepage, https://www.who.int/news/item/27-04-2020-who-tim eline---covid-19. Last accessed 29 Oct 2022 4. A. Haleem, M. Javaid, R. Vaishya, Effects of COVID-19 pandemic in daily life. Curr. Med. Res. Pract. 10(2), 78–79 (2020) 5. Y. Hu, S. Zhuoran, W. Jun, T. Aiguo, H. Min, X. Zhongyuan, Laboratory data analysis of novel coronavirus (COVID-19) screening in 2510 patients. Clin. Chimica Acta 507, 94–97 (2020) 6. K.H.D. Tang, B.L.F. Chin, Correlations between control of COVID-19 transmission and influenza occurrences in Malaysia. Public Health 198, 96–101 (2021) 7. K. Ilma, H. Abid, J. Mohd, Analysing COVID-19 pandemic through cases, deaths, and recoveries. J. Oral Biol. Craniofacial Res. 10(4), 450–469 (2020) 8. M. Menhat, Z.I.M. Mohd, Y. Yusuf, N.H.M. Salleh, M.A. Zamri, J. Jeevan, The impact of Covid-19 pandemic: a review on maritime sectors in Malaysia. Ocean Coast. Manag. 209, 1–8 (2021) 9. A.U.M. Shah, S.N.A. Safri, R. Thevadas, N.K. Noordin, A.A. Rahman, Z. Sekawi, A. Ideris, M.T.H. Sultan, COVID-19 outbreak in Malaysia: actions taken by the Malaysian government. Int. J. Infect. 97, 108–116 (2020) 10. M. Dadashi, S. Khaleghnejad, P. Abedi Elkhichi, M. Goudarzi, H. Goudarzi, A. Taghavi, M. Vaezjalali, B. Hajikhani, COVID-19 and influenza co-infection: a systematic review and meta-analysis. Front Med. (Lausanne) 8, 1–9 (2021) 11. S.J. Olsen, E. Azziz-Baumgartner, A.P. Budd, L. Brammer, S. Sullivan, R.F. Pineda, C. Cohen, A.M. Fry, Decreased influenza activity during the COVID-19 pandemic—United States, Australia, Chile, and South Africa. Am. J. Transplant. 20(12), 3681–3685 (2020) 12. C. Simon, M.F. Neil, W. Claude, T. Anders, S. Guillaume, D. Ben, N. Angus, Closure of schools during an influenza pandemic. Lancet. Infect. Dis. 9(8), 473–481 (2009) 13. Malaysia’s endemic guidelines, effective 1 April 2022: for the general public, https://www. humanresourcesonline.net/malaysia-s-endemic-guidelines-effective-1-april-2022-for-the-gen eral-public. Last accessed 25 Jul 2022

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14. Descriptive analysis in education: a guide for researchers, https://danisreading-notes.substack. com/p/descriptive-analysis-in-education. Last accessed 29 Oct 2022 15. Anderson-Darling Test for Normality, https://www.spcforexcel.com/knowledge/basic-statis tics/anderson-darling-test-for-normality. Last accessed 29 Oct 2022 16. S. Patrick, B. Christa, S.A. Lothar, Correlation coefficients: appropriate use and interpretation. Anesth. Analg. 126(5), 1763–1768 (2018) 17. B. Ratner, The correlation coefficient: its values range between +1/−1, or do they? J. Target Meas. Anal. Mark. 17, 139–142 (2009)

Chapter 23

An Evaluation of the Forecast Performance of Neural Network Lok You Li , Maria Elena Nor , Mohd Saifullah Rusiman , and Nur Hidayah Mohd Zulkarnain

Abstract The stock market is a primary investment platform for the public. Investors are hoping to gain profit from it due to the considerable potential of the stock market. However, the stock market is highly volatile, dynamic, and complex. Therefore, the objectives of this study are to forecast the Malaysian stock price using several forecast methods, evaluate the performances of each forecasting method, and identify the most suitable forecast method to be applied in the emerging stock market. The data used in this study is the stock price of the Kuala Lumpur Composite Index (KLCI). The forecast methods applied include the Naïve method, Box-Jenkins model, and Artificial Neural Network (ANN). The Mean Absolute Percentage Error (MAPE), Mean Forecast Error (MFE), Trend Change Error, Chi-Square Test of Independence, and Fisher’s Exact Test are used to evaluate the forecast performance. The findings showed that the ANN has the best forecast performance than the Naïve method and Box-Jenkins model. Future studies are advised to investigate the disappointing performance of the Box-Jenkins model in the testing part, optimize the performance of ANN in MFE, and not evaluate the Naïve method using directional accuracy.

23.1 Introduction The stock market is a complicated system related to social, political, and psychological elements [1]. Based on the statistics published by [2], the total world stock trading value was USD34.8 trillion in Q4 2020. The huge stock market returns have attracted more investors to invest in the stock market. In recent years, foreign investors have begun to focus on ASEAN’s emerging market due to the potential profit [3]. As an emerging market, the Malaysian stock market has attracted foreign investors for investment [4]. In Q2 2020, there is a total value of RM4.6 billion inflows of foreign portfolios to Malaysia compared to RM2.4 billion in Q2 2019 [4]. The potential of L. Y. Li · M. E. Nor (B) · M. S. Rusiman · N. H. M. Zulkarnain Department of Mathematics and Statistics, Faculty of Applied Sciences and Technology, Universiti Tun Hussein Onn Malaysia, Pagoh Edu Hub, 84600 Parit Raja, Johor, Malaysia e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Mustapha et al. (eds.), Proceedings of the 8th International Conference on the Applications of Science and Mathematics, Springer Proceedings in Physics 294, https://doi.org/10.1007/978-981-99-2850-7_23

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the Malaysian stock market has contributed to the inclining number of local investors even during the COVID-19 outbreak in 2020 [5]. Between March 18, 2020, and June 30, 2020, Rakuten Trade has activated almost 50,000 new accounts [5]. In the study of the stock market, many researchers preferred the integrated model. For instance, [6] applied radial basis function neural network optimized by an artificial fish swarm algorithm to forecast the Shanghai Stock exchange’s stock price. At the same time, [7] integrated the simple recurrent neural network with principal component analysis to forecast Total Maroc’s stock price. As a result, the integrated models perform better in the research. The excellent performance of the integrated forecast model has been proved again by [8], where the researchers used the GARCHMIDAS integrated model to forecast the price of S&P500. Reference [9] stated that a mixture of models outperforms other models in longer forecast horizons. Nonetheless, the performance of the integrated model will be affected by sudden events in the stock market, such as the COVID-19 pandemic has affected the Taiwan stock market [10] and Malaysia stock market [11]. Therefore, the integrated forecast model does not perform better on some occasions than the regular forecast model. A stock price forecast model with high accuracy can benefit the public. However, the stock market has the characteristics of high volatility, dynamism, and complexity. It is commonly known that the stock prices are stationary, and it is impossible to forecast the direction of the price and the changes in magnitude. Nevertheless, some researchers found that suitable technical and fundamental analysis could understand price movements and predict the price directions in the future. Therefore, the objectives in this study are to forecast the Malaysian stock market price using the Naïve method, Box-Jenkins model, and Artificial Neural Network (ANN), to evaluate the forecast performance among the Naïve method, Box-Jenkins model, and ANN using Mean Absolute Percentage Error (MAPE), Mean Forecast Error (MFE), Trend Change Error, Chi-Square Test of Independence and Fisher’s Exact Test, and to identify the most suitable forecast method among the three to be used in forecast emerging stock market like Malaysia.

23.2 Materials and Methods 23.2.1 Kuala Lumpur Composite Index Stock Price Data The data was obtained from an online media, Yahoo Finance, and it had 132 observations from 2010 to 2020. The data was then divided into training and testing parts, whereas the training part was from January 2010 until December 2019 for model training and the testing part was from January 2020 until December 2020 for forecast performance evaluation.

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23.2.2 Preliminary Analysis Differencing is the calculation of variations between successive measurements. Once the variations in time series are removed, the mean of the time series is stabilized, and the seasonality is reduced [12]. It is imperative to differentiate the data to achieve a stationary series. The differenced series is shown as the following. 

yt = yt − yt−1 ,

(23.1)

where t = 2, 3, …, n. A Box-Cox transformation is a necessary data pre-processing step that transforms non-normal data into normal data [13]. Box-Cox transformation is a parametric modification approach for improving homoscedasticity, normality, and additivity of the time series data [14]. Reference [15] proposed the origin of the power transformations in which the transformed values are a monotonic function of the measurements in a reasonable spectrum of values. Afterward, [16] altered the transformation to allow for the discontinuity at λ = 0. The Box-Cox transformation is expressed in the following.  ytλ

=

ytλ −1 ,λ λ

= 0 , log yt , λ = 0

(23.2)

for yt > 0, and λ = transformation parameter. Min–max normalization is a transformation approach that linearly alters the original data. Reference [17] claimed that data normalization could increase the accuracy and improve the performance of mining algorithms like neural networks. In the min– max normalization technique, the values will be rescaled to a new range of values [18]. Min–max normalization is expressed as the following. yt scaled =

yt −min(yt ) , max(yt )−min(yt )

(23.3)

where yt is the variable vector, min(yt ) is the minimum value of the variable vector, and max(yt ) is the maximum value of the variable vector.

23.2.3 Forecast Method The Naïve method assumes all detected values from the previous year are predictions for the current year without making adjustments or identifying causal factors [19]. It assumes that history will repeat itself. References [12, 20] suggested that the Naïve forecasts are suitable for model comparison since they are incredibly accurate and suitable to serve as a benchmark for forecasts performance comparison. The

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expression of Naïve forecasts is shown as follow. yˆt+1 = yt ,

(23.4)

where yˆt+1 is the forecast value at time t + 1, yt is the observed value at time t, and t is the number of periods. The Box-Jenkins model integrates differencing, autoregressive, and moving average models, also known as autoregressive integrated moving average (ARIMA). It is a versatile time series modeling method that has been used to model complex processes in many industries [21]. Reference [22] stated that the ARIMA models are commonly used for forecasting stationary time series. The non-seasonal ARIMA model is expressed as follow. ∅ p (B)∇ d yt = θq (B)at ,

(23.5)

where ∅ p (B) is the polynomialsinBoforder p, ∅q (B) is the polynomials in B of order q, B is the backshift operator, ∇ d is the order of differencing, and at is the unknown random errors. The goal of the model identification is to define the values of p, d, q from the ARIMA (p, d, q). One of the limitations of the ARIMA model is that the data must be stationary [23]. Therefore, d represents the order of differencing to obtain stationary data. The value of p is determined from the PACF plot, while the value of q is determined from the ACF plot [24]. The regulation for selecting the values of p and q is illustrated in Table 23.1. After the model identification step, the process continues with the parameter estimation. The goal of parameter estimation is to estimate the parameters of autoregressive and moving average models. The estimation can be done using maximum likelihood estimation or statistical packages [26]. The diagnostic testing is then performed to determine if the chosen model fits the data. Moreover, an ANN is a human brain simulation where the artificial neurons are linked as the brain network [27]. The input layer receives the input values, hidden layer(s) is a set or a few sets of neurons that process the signals from the input layer, Table 23.1 Identification model [25]

ACFs

PACFs

Model

Decay to zero with exponential pattern

Cuts off after lag p

AR (p)

Cuts off after lag q

Decay to zero with exponential pattern

MA (q)

Decay to zero with exponential pattern

Decay to zero with exponential pattern

ARMA (p, q)

Cuts off after lag q

Cuts off after lag p

AR (p)/MA (q)

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Fig. 23.1 Illustration of ANN [28]

and output layers consist of one or multiple outputs. The illustration of an Artificial Neural Network is shown as the following (Fig. 23.1).

23.2.4 Forecast Performance Evaluation MAPE is the average percentage of the absolute error in each period divided by the actual values for that period [29]. Since the MAPE is unit-free, MAPE comes in handy when the scale or size of a forecast attribute is important in determining the precision of a prediction [30, 31]. The formula of MAPE is expressed in the following.  n  1  yt − yˆt  × 100%, MAPE = n i=1  yt 

(23.6)

where yt is the actual value at time t, yˆt is the forecast value at time t, and n is the number of periods. MFE calculates the average deviation of forecast values from actual values. In MFE, the values should be as close to zero as possible since the positive and negative

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prediction errors appear to cancel each other out, resulting in minimum bias [32]. A strong positive MFE indicates that the forecast underestimates (under-forecast) the actual values and vice versa. However, if the MFE is zero, the predicted values are precisely calculated rather than being without errors. The formula of MFE is shown as the following. n 1 yt − yˆt , n i=1

MFE =

(23.7)

where yt is the actual value at time t, yˆt is the forecast value at time t, n is the number of periods. A Trend Change Error happens when the forecast method wrongly forecasts the trend change in the data set [33]. The Trend Change Error is calculated using the percentage of turning points forecast correctly [34]. The definitions of a downturn and an upturn and their negations based on yt−1 , yt , and z are described in the following [35].  yt−1 < yt and

z < yt ≡ downturn z ≥ yt ≡ no downturn

(23.8)

and  yt−1 > yt and

z > yt ≡ upturn , z ≤ yt ≡ no upturn

(23.9)

where y1 , y2 , . . . , yt are the past observations and Z ≡ yt+1 is the first future value. The Chi-Square Test of Independence is a test that compares two variables to determine whether or not they are connected. According to [36, 37], by using a 2 × 2 contingency table, hypothesis testing can be reduced to a basic Chi-Square Test of Independence. As a result, it can see whether the forecast can provide enough detailed direction. The 2 × 2 contingency table of directional between forecast and actual observation is presented as follow. In addition, the Chi-square test statistic regarding Table 23.2 is described as follow [39]. χ = 2

 1 n f,a −  f,a=0

n f · n ·a  N n f · n ·a N

− 0.5

2 .

(23.10)

However, the Chi-square test statistic in (23.10) can be overly cautious due to incorrect acceptance of the independence assumption. Thus, the Yates’ continuity correction is used as the following.

23 An Evaluation of the Forecast Performance of Neural Network Table 23.2 Contingency table of directional between forecast and actual observation [38]

FT ∗

AT ∗

Total

>0

≤0

n 0,0

n 0,1

n 0,0

yt = No downturn  Z > yt = Upturn . > yt and Z < yt = No Upturn

yt−2 < yt−1 < yt and yt−2 > yt−1

(24.18)

(24.19)

24.3 Results and Discussion 24.3.1 Data Separation The selected periodic and aperiodic events effects on the three sectorial indexes which are consumer product, industrial product and finance indexes were shown in Table 24.1. For each of the index, there were 15 models generated for each forecasting methods. Table 24.1 Table captions should be placed above the tables

Government policy

Training data

Testing data

OPR (24 January 2019)

24 December 2018 to 23 January 2019

24 January 2019 to 30 January 2019

Budget 2020

13 August 2019 to 10 October 2019

11 October 2019 to 24 October 2019

GST

2 December 2014 to 1 April 2015 to 28 31 March 2015 April 2015

SST

4 May 2018 to 30 August 2018

3 September 2018 to 3 October 2018

MCO

22 November 2019 to 17 March 2020

18 March 2020 to 14 April 2020

L. K. Haw et al.

680 670 660 650 5/1/2019 7/1/2019 9/1/2019 11/1/2019 13/1/2019 15/1/2019 17/1/2019 19/1/2019 21/1/2019 23/1/2019 25/1/2019 27/1/2019 29/1/2019

640 24/12/2018 26/12/2018 28/12/2018 30/12/2018 1/1/2019 3/1/2019

Closing Price

308

Actual Closing Price

Forecasted Closing Price

Fig. 24.1 Actual versus forecasted closing price of consumer product index using Naïve model

24.3.2 Naïve Forecast Model Taking an example from the 15 Naïve forecast models, Fig. 24.1 shows the actual versus forecasted closing price of consumer product index during announcement of OPR on 24 January 2019. The data possesses slight upward trend but no seasonality; therefore, seasonal Naïve forecast could not be applied. For training data part, the Naïve model was able to capture the fluctuation of the data from 24 December 2018 to 23 January 2019. For testing data, it did not manage to predict the peak from 25 January 2019. These procedures were repeated for the 14 Naïve forecast models for the three sectorial indexes. The magnitude of trend change error could not be applied in determining OPR effect because the last three training data were not having consecutive increasing or decreasing data. For government policy effects on the three sectorial indexes, Naïve forecast model took the last value of training dataset, and it produced a horizontal forecast which does not have any upward and downward trend hence resulted in 50% of trend change error.

24.3.3 Double-Exponential Smoothing Forecast Model Since all of the data have trends, either upward or downward trend on specified intervals, double-exponential smoothing forecast method was used to determine the five government policies impact on the three sectorial indexes. Similarly, as there were totally 15 double-exponential forecast models created, the result of all the error magnitudes was listed down in Tables 24.2, 24.3 and 24.4. Figure 24.2 showed the actual versus forecasted closing price of consumer product index during announcement of OPR on 24 January 2019. The data showed strong upward trend for the whole period. For training data part, there are lags for actual closing prices from 27 December 2018 to 18 January 2019. For testing data, it also managed to

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predict the upward trend. These procedures were repeated for the remaining 14 double-exponential forecast models.

24.3.4 Box–Jenkins Forecast Model For Box–Jenkins forecast for consumer product index during OPR announcement on 25 January 2019, the squared first differenced dataset obtained ADF t-statistics of −6.1202 which is lower than t critical value of −3.0312 indicating stationarity of dataset. Two significant lags were detected from the ACF and PACF plots which were lag 1 and lag 3. Therefore, the tentative models determined were ARIMA (1,1,1), ARIMA (1,1,3), ARIMA (3,1,1) and ARIMA (3,1,3). ARIMA (1,1,3) was the lowest in term of AIC and BIC values. The diagnostic tests also concluded that ARIMA (1,1,3) has residuals with no significant trend and correlation and zero mean. Therefore, it was used to forecast the consumer product index closing price after the training data. The ARIMA (1,1,3) can be written as  (1 + 0.9998B)(1 − B)yt = 1 − 1.3961B − 0.9186B 2 + 0.0561B 3 εt . (24.20) From Fig. 24.3, ARIMA (1,1,3) shows the actual versus forecasted closing price of consumer product index during announcement of OPR on 24 January 2019 by using ARIMA (1,1,3). The model successfully captured the trend and fluctuation in the training data. For testing data, although the forecasted data show a higher fluctuation compared to the actual closing price, it still shows a relatively flat forecast model. Similarly, as there are totally 15 ARIMA forecast models created, these procedures were repeated for the remaining 14 models. The result of all the error magnitudes was listed down in Tables 24.2, 24.3 and 24.4. The trend change error was not applicable to OPR as there was no consecutive increasing and decreasing data at the last 3 training data. Table 24.2 represents the measurement of errors for consumer product index testing data using three forecast models. Movement control order produced highest MAE, MAPE value among the three forecasting methods. It had been downward trend since year 2018 and slumped more than 25% near before the announcement of MCO due to Covid-19 and consumer tend to not spend. The index rebounded after MCO announcement since market anticipated that MCO could curb the pandemic. Since the forecast took the historical data before the announcement being done, the models forecasted a continual downward trend which was contrary to the actual rebound trend, resulted in high forecast error. Naïve forecast produced lower error than the two other forecasts since it was a sideway forecast. In contrast, OPR announcement resulted in lowest forecast error as OPR announcements are announced six times in a year thus not much volatility occurred after the event since market already anticipated the information prior to Monetary Policy Committee meeting. The trend change could not be calculated as there were no consecutive upwards and downwards trend at the end of training data.

N

4.7780

8.7080

7.0910

9.5595

23.4305

Forecasting methods

OPR (24/1/2019)

Budget 2020

GST

SST

MCO

139.7250

4.2557

2.6024

9.3454

1.4164

DES

BJ

230.1722 ARIMA (2,2,3)

9.5595 ARIMA (0,1,0)

6.2983 ARIMA (1,1,0)

7.5842 ARIMA (0,1,1)

3.1263 ARIMA (1,1,3)

where N = Naïve forecast model DES = Double-exponential smoothing forecast model BJ = Box–Jenkins forecast model N/A = Not applicable

MAE

Policy

4.6477

1.3210

1.1687

1.2465

0.7069

N

27.1991

0.3501

0.3778

1.4421

0.4375

DES

MAPE (%)

Table 24.2 Measurement of errors for consumer product index testing data

44.8586 ARIMA (2,2,3)

1.3210 ARIMA (0,1,0)

1.0380 ARIMA (1,1,0)

1.1702 ARIMA (0,1,1)

0.4624 ARIMA (1,1,3)

BJ

50.0000

50.0000

50.0000

50.0000

N/A

N

57.8900

42.1100

57.8900

60.0000

N/A

DES

Trend change error (%)

57.8900 ARIMA (2,2,3)

50.0000 ARIMA (0,1,0)

50.0000 ARIMA (1,1,0)

50.0000 ARIMA (0,1,1)

N/A ARIMA (1,1,3)

BJ

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Table 24.3 Measurement of errors for industrial product index testing data Policy

MAE

Forecasting N methods

MAPE (%) DES

BJ

N

DES

Trend change error (%) BJ

N

DES

BJ

N/A

N/A ARIMA (0,1,0)

OPR (24/1/ 1.4280 2019)

1.3120 1.4280 0.2923 ARIMA (0,1,0)

0.8054 0.8773 N/A ARIMA (0,1,0)

Budget 2020

2.4060

2.1605 2.4060 1.2465 ARIMA (0,1,0)

1.4169 1.57799 50.0000 11.1100 50.0000 ARIMA ARIMA (0,1,0) (0,1,0)

GST

1.7105

0.6521 1.7427 1.1687 ARIMA (1,1,2)

0.4728 1.2529 50.0000 36.8400 42.1100 ARIMA ARIMA (1,1,2) (1,1,2)

SST

4.1055

5.7376 3.2955 1.3210 ARIMA (0,1,0)

3.2354 1.8591 50.0000 52.6300 50.0000 ARIMA ARIMA (0,1,0) (0,1,0)

MCO

4.8560 23.1495 40.3602 4.6477 21.5852 37.6760 50.0000 63.1600 63.1600 ARIMA ARIMA ARIMA (3,2,1) (3,2,1) (3,2,1)

The sector experienced downward trend and upturned immediately after budget announcement; therefore, the models failed to predict the upward trend, causing significant forecast error. Double-exponential smoothing model depicted highest MAE, MAPE and trend change error as the forecast predicted a downtrend. Announcement of GST showed lower forecast error in terms of MAE and MAPE to SST since GST was announced during 2011; hence, volatility was not high during its real implementation. Double-exponential smoothing model managed to predict the upward trend in GST testing data but not the other two models which predicted sideway trend. Training data before SST announcement was sideway trend but slightly turned downward after SST announcement. Similarly, only double-exponential smoothing model managed to forecast the downturn trend. For industrial product index shown in Table 24.3, MCO announcement also produced highest MAE, MAPE and trend change error among the five government policies for the three forecasting models. The spread of pandemic caused drop of more than 29% of the index as all non-essential industries could not operate and rebounded sharply after MCO. This explains why they possess high forecast errors, and the models predicted a downward trend. Similarly, OPR announcement did not cause a significant forecast error for the three models. After Budget 2020 announcement, the index rose upward as government introduced budget which was beneficial to the industry production but none of the three models captured it. GST announcement also produced lower volatility compared to SST and the SST announcement slightly turned down the trend, but double-exponential forecasting model failed to predict them correctly. Finally, Table 24.4 represents the measurement errors for finance index. Finance index slumped in smaller magnitude (20%) compared to consumer product and

217.5960

137.0380

143.8000

524.423

Budget 2020

GST

SST

MCO

88.5140

Forecasting methods

OPR (24 /1/2019)

MAE

N

Policy

3435.5800

293.0230

122.5660

290.3220

51.4502

DES

4536.9430 ARIMA (0,2,1)

143.8000 ARIMA (0,1,0)

137.0380 ARIMA (0,1,0)

217.5960 ARIMA (0,1,0)

88.5140 ARIMA (0,1,0)

BJ

Table 24.4 Measurement of errors for finance index testing data MAPE (%)

37.0917

0.8088

0.8348

1.4311

0.5025

N

28.0928

1.6468

0.7465

0.4200

0.2900

DES

37.0917 ARIMA (0,2,1)

0.8088 ARIMA (0,1,0)

0.8348 ARIMA (0,1,0)

1.4311 ARIMA (0,1,0)

0.5025 ARIMA (0,1,0)

BJ

50.0000

50.0000

50.0000

50.0000

N/A

52.6300

52.6300

42.1100

77.7800

N/A

DES

Trend change error (%) N

52.6300 ARIMA (0,2,1)

50.0000 ARIMA (0,1,0)

50.0000 ARIMA (0,1,0)

50.0000 ARIMA (0,1,0)

N/A ARIMA (0,1,0)

BJ

312 L. K. Haw et al.

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680 675 670 665 660 655 650 645 640 24/12/2018 26/12/2018 28/12/2018 30/12/2018 1/1/2019 3/1/2019 5/1/2019 7/1/2019 9/1/2019 11/1/2019 13/1/2019 15/1/2019 17/1/2019 19/1/2019 21/1/2019 23/1/2019 25/1/2019 27/1/2019 29/1/2019

Closing Price

Fig. 24.2 Actual versus forecasted closing price of consumer product index using DoubleExponential Smoothing model

Actual Closing Price

Forecasted Closing Price

Fig. 24.3 Actual versus forecasted closing price of consumer product index using Box–Jenkins model

industrial product index since banking sector is considered as essential service and allowed to operate during MCO; therefore, the announcement made rebound in the index but not successfully predicted by the three models, producing the highest measurement errors. OPR announcement did not induce significant change to the

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finance index trend; hence, it has lowest MAPE. For Budget 2020, its announcement caused the downward trend to become sideway trend; therefore, Naïve and ARIMA (0,1,0) able to capture the trend with lower measurement error than doubleexponential smoothing model. SST announcement resulted in sideway trend of the index hence Naïve and ARIMA (0,1,0) having smaller measurement errors than double-exponential smoothing model. GST announcement did not alter the upward trend of the index; hence, double-exponential smoothing model produced smaller measurement errors than Naïve and ARIMA (0,1,0) which forecasted sideway trends.

24.4 Conclusion Generally, it was found that for each of the sectorial index, MCO announcement produced highest MAPE, MAE and trend change error. It being the unprecedented lockdown policy led to huge shock among investors hence all the sectorial indexes slumped considerably during its announcement especially the industrial product index amid the fear of economic disturbance led to least accurate forecast. Contrarily, OPR announcement did not cause significant forecast discrepancy from the testing data since it was announced six times a year and within investors’ expectation, making the sectorial indexes efficient in term of this government policy. The measurement errors after Budget 2020 announcement would depend on the trend before the announcement. Budget 2020 introduced beneficial fiscal policies into the industries and led to bullish trend after the announcement. If the trend before the announcement was bullish, it will cause lower measurement errors. In term of taxes effects on sectorial indexes, GST contributed lower measurement errors compared to SST. GST effect was not as obvious as SST as its implication duration was longer than SST giving investors sufficient time to analyse its economic impact. This research provided an insight for investors in Malaysia to make educated decision by understanding the effects of major government policies announcements on different sectorial indexes. It would be essential to realize the risk and reward for each of the government policies on the sectorial indexes and make appropriate adjustment on own investing portfolio. Future research could be done on the remaining indexes and not only on stock market but other derivatives such as bonds, commodities and currencies. Acknowledgements This research was made possible by funding from FRGS Grant [FRGS/1/ 2019/STG06/UTHM/02/7] provided by the Ministry of Higher Education, Malaysia.

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References 1. A. Chen, L. Onn, Successful Investment in Malaysia: A Practical Lesson (Grandpine Capital Sdn. Bhd, Kuala Lumpur, 2017) 2. The Importance of Stock Markets, https://finance.yahoo.com/news/importance-stock-market s075948914.html?guc counter=1. Last accessed 8 Apr 2021 3. B. Comincioli, Stock market as a leading indicator: an application of granger causality. Univer. Avenue Undergraduate J. Econ. (1996) 4. Z. Zulkarnain, S. Sofian, Empirical evidence on the relationship between stock market volatility and macroeconomics volatility in Malaysia. J. Bus. Stud. Q. 4, 61–71 (2012) 5. Why Volatility Is Important for Investors, https://www.investopedia.com/articles/financialthe ory/08/volatilelity.asp. Last accessed 8 Apr 2021 6. M. Baker, J. Wurgler, Investor sentiment in the stock market. J. Econ. Perspect. 21, 129–151 (2007) 7. G. Segal, Interest rate in the objective function of the central bank and monetary policy design. SSRN Electron. J. (2019) 8. K. Woo, B. Tan, S. Wei, T. Ching, C. Tio, S. Ying,The Effect Of Government Policy On Stock Market Return In Malaysia (2014) 9. R. Haron, S. Ayojimi, The impact of GST implementation on the Malaysian stock market index volatility. J. Asian Bus. Econ. Stud. 26, 17–33 (2018) 10. H. Bekhet, N. Othman, Examining the role of fiscal policy in Malaysian stock market. Int. Bus. Res. 5 (2012) 11. Government policy and stock markets, https://economictimes.indiatimes.com/government-pol icy-and-stock-markets/articleshow/2351702.cms?from=mdr. Last accessed 3 May 2021 12. A Gentle Introduction to the Random Walk for Times Series Forecasting with Python, https://machinelearningastery.com/gentle-introduction-random-walk-times-series-for ecastingpython/. Last accessed 17 May 2021 13. P. Newbold, The principles of the box-jenkins approach. Oper. Res. Q. 26 (1970–1977) 14. M. Din, ARIMA by Box Jenkins methodology for estimation and forecasting models in higher education, in Atiner Conference Paper Series, vol. 7 (Athen, 2016) 15. R. Sakia, The Box-Cox transformation technique: a review. The Statistician 1, 169–178 (1992) 16. J. Osborne, Improving your data transformations: applying the Box-Cox transformation 15 (2010) 17. N. Bokde, A. Feijoo, K. Kulat, Analysis of differencing and decomposition preprocessing methods for wind speed prediction. Appl. Soft Comput. 71, 926–938 (2018) 18. Y. Cheung, K. Lai, Lag order and critical values of the augmented dickey–fuller test. J. Bus. Econ. Stat. 13, 277–280 (2014) 19. Unit Root: Simple Definition, Unit Root Tests, https://www.statisticshowto.com/unit-root/. Last accessed 3 Jul 2021 20. R. Sivasamy, D. Shangodoyin, F. Adebayo, Forecasting stock market series with ARIMA model. J. Stat. Econometric Meth. 3, 65–77 (2014) 21. ARIMA models for time series forecasting. https://people.duke.edu/~rnau/seasarim.htm. Last accessed 3 Jun 2021 22. P. Burns, Robustness of the Ljung-box test and its rank equivalent, Burns Stat. 7, 1–17 (2003) 23. S. Prabhakaran, ARIMA Model – Complete Guide to Time Series Forecasting in Python, https://www.machinelearningplus.com/time-series/arima-model-time-series-foreca sting-python/. Last accessed 3 Jun 2021 24. G. Stephanie, Mean Absolute Percentage Error (MAPE), https://www.statisticshowto.com/ mean-absolute-percentage-error-mape/. Last accessed 22 Jun 2021 25. S. Witt, C. Witt, Tourism forecasting: error magnitude, direction of change error, and trend change error. J. Travel Res. 30, 26–33 (1991)

Chapter 25

Determining Auto Insurance Pure Premium Based on Mileage (Pay-As-You-Drive Insurance) Using Tree-Based Machine Learning Dhestar Bagus Wirawan and Gunardi Abstract The current system for determining auto-insurance premium in Indonesia is still not fair enough for the customer, especially related to mileage. There are cross-subsidized between the low-mileage customers and high-mileage customers. In 2012, Ferreira and Minikel target this problem and used Generalized Linear Models to calculate the pure premium based on mileage or known as pay-as-you-drive insurance. Although Generalized Linear Models is often used when modeling in insurance, the dependence of Generalized Linear Models on assumptions and its inability to capture non-linear pattern is the main weaknesses of Generalized Linear Models. This research would use tree-based machine learning, e.g., Random Forest and Gradient Boosting Machine, in calculating the pure premium of pay-as-youdrive insurance and opening the black box of machine learning so that it has the same interpretation capabilities as the Generalized Linear Models. It is concluded that the Gradient Boosting Machine algorithm is able to produce a model that has the lowest Root Mean Square Error, both for modeling claim-frequency and claimseverity. In addition, it is also concluded that pay-as-you-drive insurance is better than traditional motor vehicle insurance.

25.1 Introduction The premium calculation system in Indonesia is still far behind the calculation of motor vehicle insurance premiums in other countries. Therefore, the current motor vehicle premium calculation system in Indonesia is still not fair and relevant. According to Litman [1], there is a relationship between motorized vehicle mileage and claims related to accidents. Research by Litman [1] shows that the farther and more often a person drives, the higher the risk of accidents that may occur to that person. This is an indication that vehicle mileage can be an important factor in determining fairer motor vehicle insurance premiums. Therefore, the calculation of motor D. B. Wirawan · Gunardi (B) Department of Mathematics, Faculty of Mathematics and Natural sciences, Universitas Gadjah Mada, Yogyakarta, Indonesia e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Mustapha et al. (eds.), Proceedings of the 8th International Conference on the Applications of Science and Mathematics, Springer Proceedings in Physics 294, https://doi.org/10.1007/978-981-99-2850-7_25

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vehicle premiums should be based on the distance traveled by each individual vehicle or commonly known as Pay-as-you-drive Insurance. Pay-as-you-drive Insurance itself has been offered by several insurance companies outside Indonesia, such as Real Insurance in Australia, Bharti AXA Car Insurance in India, and the partnership between Carro and NTUC Income in Singapore. However, no insurance company in Indonesia offers this product. Recent research on the calculation of pure premium pay-as-you-drive insurance still uses Generalized Linear Models (GLM) [2, 3] in its calculations [4]. GLM itself has two main weaknesses, namely that it requires weaker assumptions and predictive capabilities [5]. GLM follows the assumption of error values for all distributions belonging to the exponential family distribution [6]. GLM cannot reflect non-linear relationships without manually adjusting (through assumptions). The problem is, Boucher et al. [7] found that there is a non-linear relationship between mileage and the frequency of four types of claims: property damage or physical injury, and motorist fault or non-cyclist error. On the other hand, tree-based machine learning is a machine learning method that utilizes a tree structure or hierarchical structure to make a decision and does not require any assumptions. This method is best used when the data used is quite large and without prior knowledge of the distribution of the data. Although machine learning is often seen as an uninterpretable black box, there are currently many studies that have focused on the interpretability of machine learning, such as the research conducted by Henckaerts [4]. From the problems above, the researcher will calculate the premium for motorized vehicles based on the distance traveled by each individual vehicle or commonly known as pay-as-you-drive insurance by using various methods of tree-based machine learning, such as Random Forest [8] and Gradient Boosting Machine [9, 10]. The results of the two methods will be compared with the results of the payas-you-drive insurance premium calculation using GLM which has been commonly used in studies related to pay-as-you-drive insurance to obtain the best method for the calculation of premiums. In addition, this research will utilize tree-based machine learning without losing the interpretive ability of GLM.

25.2 Random Forest The decision tree, or regression tree [11] in this study, has a major weakness, namely high variance. This means that if we divide the training data into two and train a decision tree on each of these data, the results obtained can be much different. Random Forest [8] is an ensemble model that uses bagging or bootstrap aggregating techniques [12] which consists of a collection of decision trees. The bagging technique reduces the variance of a single tree by taking the average of the predicted results of various trees trained on a bootstrap sample of the original data. Bootstrap sampling (bootstrap sampling) is a sampling method with repeated returns to estimate population parameters. This technique makes prediction results more stable and improves predictive ability compared to a single decision tree.

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Fig. 25.1 An illustration of Random Forest which is a collection of T decision tree

The idea of this bagging technique itself is if we have a dataset D, by taking a bootstrap sample {Dt }t=1,2,...,T , T decision trees will be formed, one for each Dt independently. The results will be aggregated by: f bagg (x) =

T 1  f tree (x|Dt ) T t=1

(25.1)

where the condition (|Dt ) indicates that the tree was trained on the sample Dt (Fig. 25.1). According to Zochbauer [13], the performance improvement is better when there is a lower correlation between each tree. By taking a bootstrap sample that has a smaller size of δ × n, where n is the number of observations in the dataset D and 0 < δ < 1, a lower correlation will be formed between trees and the time required in the training model will also be reduced. However, most of the variability will remain because the trees constructed from the bootstrap sample are still quite similar. It occurs when several independent variables in the data have a much higher predictive ability than other variables. The more important variables will dominate the first partition. It causes almost all trees to use predictor variables that have the highest correlation with the dependent variable in the first partition. Of course, it will cause all trees to be equal to one another.

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To prevent that, Random Forest will sample the variables. For each partition, m variables will be chosen from the p variables at random as a candidate in the optimal √ splitting variable. Random Forest will select the m = p variables to include in each partition. It is known as decorrelating the trees. Apart from this adaptation, Random Forest will follow the same strategy as the bagging technique and predict new variables based on (25.1). The algorithm of Random Forest is specifically discussed in the Algorithm 1 where T and m are considered as tuning parameters.

Algorithm 1: The procedure of creating a Random Forest model Data: dataset D xv , v ∈ 1, 2, . . . , p; δ ∈ (0, 1); for t = 1, 2, . . . , T do Take a bootstrap data sample Dt with size δ × n from data D; while stopping criterion is still not fulfilled do Take m variables from p variables at random; Find the optimal variable of xv from the selected m variables and also the cut-off value of c; end end T fr f (x) = T1 t=1 f tr ee (x|Dt );

Random Forest increases the accuracy obtained by using a set of decision trees compared to using only one decision tree. However, the trees that were formed in Random Forest were built independently of each other and did not share information with each other during the training process.

25.3 Gradient Boosting Machine The Gradient Boosting method [9, 10] was first introduced by Leo Breiman and developed by Jerome H. Friedman in 1999. Recall that bagging creates bootstrap samples from the original training data and trains various decision trees for each sample, then combines each tree to form a single model. It should be noted that each tree is constructed from each sample and is independent of one another. The boosting technique works in a similar way, but in the boosting technique, the trees are trained in a sequential manner. Each tree is trained based on the information obtained from the previous tree. The boosting technique also does not use bootstrap samples, but each tree is trained with a “modified” version of the original training data (Fig. 25.2). The basic idea of the boosting technique is to learn slowly. For example, given the current model, we will train the decision tree on the temporary residual of the current model (pseudo-residual) instead of training it on the dependent variable Y . The pseudo-residual for the i observation in the t iteration, or commonly written as

25 Determining Auto Insurance Pure Premium Based on Mileage . . .

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Fig. 25.2 The illustration of Gradient Boosting Machine which is a set of T decision trees that are trained sequentially on a pseudo-residual

ρi,t , is calculated as the negative gradient of the loss function evaluated in the current model with the following equation: ρi,t = −

∂L {yi , f (xi )} ∂ f (xi )

(25.2)

The boosting method learns slowly by training a small tree with a depth d (with a squared error loss function) against pseudo-residuals so that it will improve the model in areas where the model does not perform well. For each R j region of the tree, bˆ j is calculated as a constant that must be added to the previous model to minimize the loss function, named b which minimizes L {yi , f (xi + b)} along the R j region. The shrinkage parameter λ controls the learning speed by updating x ∈ R j as follows: f new (x) = f old (x) + λ · bˆ j . The smaller λ, the better the accuracy of the model, but it will increase the computation time because more trees are needed to converge.

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The set of T trees in the last iteration is used to make predictions. The algorithm of the Gradient Boosting Machine is shown in the Algorithm 2 where T and d are considered as tuning parameters.

Algorithm 2: The procedure of creating a Gradient Boosting Machine model Data: dataset D δ ∈ (0, 1); n Initialize model with a constant value f 0 (x) = arg minb i=1 L (yi , b); for t = 1, 2, . . . , T do for i = 1, 2, . . . , n do Calculate the pseudo-residuals; ρi,t = −[ ∂ L ∂{yf i(x, fi )(xi )} ] ; end Train the tree with depth d against pseudo-residuals ρi,t so that it produces a R j,t region for j = 1, . . . , Jt ; for j = 1, . . . , Jt do  bˆ j,t = arg minb i:x∈R j,t L (yi , f t−1 (xi ) + b) ; end t bˆ j,t 1(x ∈ R j,t ) ; Update f t (x) = f t−1 (x) + λ Jj=1 end f gbm (x) = f T (x);

25.4 Loss Function for Insurance Data The methods in tree-based machine learning require a loss function (cost function) which must be minimized at the training stage. In general, the standard loss function in regression problems is the squared error loss: L {yi , f (xi )} ∝ {yi − f (xi )}2

(25.3)

where yi is the response variable (dependent) and f (xi ) is the result of the model’s prediction for the variable xi . The concept of loss function can be connected with the concept of deviance to see the relationship between the distribution of the dependent variable and the loss function. Deviance itself is defined as: D{y, f (x)} = −2 · ln[L{ f (x)}/L(y)]

(25.4)

where L{ f (x)} is the likelihood of the model and L(y) is the likelihood of the saturated model (a model where the number of parameters is as much as the number of observations). The definition of the likelihood function itself is as follows:

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Theorem 25.1 (Subanar [14]) Let X 1 , . . . , X n be i.i.d. sample from the population with density f (x|θ1 , . . . , θk ). The likelihood function is defined as L(θ |x) =

n 

f (xi |θ1 , . . . , θk )

(25.5)

i=1

Since L{ f (x)} ≤ L(y), the likelihood ratio is not greater than one. Venables and Ripley [15] found that the loss function L (., .) was selected so that D{y, f (x)} = n L {yi , f (xi )}. i=1 Assuming constant variance, then deviance for normal distribution can be expressed as follows:  1   n 2 √ 1 i=1 2πσ 2 exp − 2σ 2 (yi − f (xi ))   1 D{y, f (x)} = −2 · ln n 2 √ 1 i=1 2πσ 2 exp − 2σ 2 (yi − yi )  n 

 1 2 = −2 · ln exp − 2 (yi − f (xi )) 2σ i=1 

n 1  2 = −2 · ln exp − 2 (yi − f (xi )) 2σ i=1 =

n 1  (yi − f (xi ))2 σ 2 i=1

which ultimately refers to a weighted sum of squared error. This indicates that the loss function based on squared error is good to use when the assumption of a normal distribution is met or when the data is symmetrical. In general, squared error loss is suitable for various continuous symmetric distributions so that claim-frequency and claim-severity data are not suitable for use. In general, insurance data, such as the frequency of claims and the severity of claims, are not symmetrical around their mean. Therefore, the use of squared error is not appropriate to be used as a loss function. The claim-frequency has a characteristic where the value is a positive integer so it is usually assumed to have a Poisson distribution in the GLM model. By using the (25.4) equation on the Poisson distribution, we get the equation:

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⎡

n i=1

D{y, f (x)} = −2 · ln ⎣

exp{− f (xi )} f (xyii!)

n

yi

y

yi i i=1 exp{−yi } yi !

 n

⎤ ⎦

exp{− f (xi )} f (xi ) yi n yi i=1 exp{−yi }yi n  n y = 2 · ln e− i=1 yi yi i = −2 · ln 

i=1

 − 2 · ln e =2·



i=1

n   i=1

−

n i=1

f (xi )

n 

f (xi )

yi

i=1

yi yi ln − {yi − f (xi )} f (xi )



(25.6) From the description above, it can be seen that for the dependent variable with a distribution following the Poisson form, the appropriate loss function to use is yi − {yi − f (xi )}. Meanwhile, claim-severity the Poisson deviance, namely yi ln f (x i) usually has a right-skewed continuous distribution that follows a Gamma or Lognormal distribution. For Gamma distribution, in the same way obtained the following translation: ⎡  α ⎤  n αyi αyi 1 exp − f (xi ) ⎥ ⎢ i=1 y1 (α) f (xi )  α  ⎦  D{y, f (x)} = −2 · ln ⎣  n αyi αyi 1 exp − i=1 y1 (α) yi yi ⎡  α ⎤  n αyi i exp − fαy (xi ) ⎥ ⎢ i=1 f (xi ) n = −2 · ln ⎣ ⎦ α i=1 (α) exp{−α} ⎡ ⎢ = −2 · ln ⎣

e

−

n

αyi i=1 f (xi )

e−

n



n

i=1 α

i=1

n

i=1

αyi f (xi )

(α)α

α ⎤ ⎥ ⎦

    n  α · f (xi ) yi − 1 + ln α =2 f (xi ) α · yi i=1     n  yi yi − f (xi ) − ln α =2 f (xi ) f (xi ) i=1

(25.7)

where the loss function is obtained in the form of Gamma deviance and α is a scaling factor that can be ignored. For the implementation of the above loss function in Random Forest, Henckaerts [16] has developed a programming package distRforest in R which applies the loss function outside the squared error loss. For programming

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packages h2o In R, there are also several loss function options for gradient boosting machines such as Poisson, Gamma, and so on.

25.5 Interpretations of Machine Learning Basically, machine learning methods follow a non-linear and non-parametric approach that is governed by one or more parameters obtained from cross-validation. The flexibility of this model has an impact on models that have poor interpretation capabilities with good accuracy. Although machine learning algorithms focus on predictive capabilities, research into interpretive capabilities has been around for a long time. The variable importance in the Random Forest is one of the important achievements in the field of machine learning interpretation. Currently there are many methods for interpreting machine learning, Molnar [17] made a book dedicated to the topic of methods for opening black box machine learning. In this section, several interpretation methods that will be used in this study will be described.

25.5.1 Shapley Values Shapley values [18] is one of the interpretation methods to see the contribution of each predictor (independent variable) to the response (dependent variable). Shapley values were created by Shapley [18]. Initially the concept of Shapley values was used in cooperative game theory, where the Shapley value is a method for determining how much the payout is for each player based on the contribution of each player to the total payout. Each player cooperates in a coalition and receives the benefits of this cooperation. In machine learning, the “game” is predicting a row in a dataset. The “gain” is the predicted result of that one row minus the average of the predicted results of the entire data row. The “player” is the predictor values of one such line that collaborate with each other to gain an advantage (predict a certain value). The player (predictor) is defined in the set N = {1, 2, . . . , p}. Coalition play is a function that maps a subset of players to a scalar value. v(S) : Power Set(N ) → R1 To be more concrete, suppose a company prints a profit of v(S) determined from the combination of employees S. Assume v(S) is known for all possible employee teams. Shapley’s score determines the credit (amount of contribution) for employee i by taking the weighted average of the benefits earned when i works with S versus when not working with S. This is repeated for all possible teams formed from the S obtained by Shapley’s value:

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φi (v) =

 |S|!(|N | − |S| − 1)! (v(S ∪ {i} − v(S))) |N |! S⊆N \{i}

(25.8)

where (v(S ∪ {i} − v(S))) shows the profit earned if the employee i goes to work, |S|!(|N |−|S|−1)! is the weight given and added up for all possible sets of S without |N |! including i. All possible coalitions (sets) of predictor values must be evaluated with and without the j-th predictor to calculate the Shapley value. This will be problematic when the number of predictors increases because the probability that the coalition formed will increase exponentially. Strumblej and Kononenko [19] propose an approach with Monte-Carlo sampling [20]: φˆ j =

M 1  ˆ m ( f (x+ j ) − fˆ(x−m j )) M m=1

(25.9)

where fˆ(x+m j ) is the prediction for x, but with a random number of predictor values replaced by the predictor value of the random data row z, except for each value the j-th predictor. The x vector in x−m j is almost the same as x+m j , but the value of x mj is also taken from the sample z. The Algorithm 3 shows the procedure for calculating the Shapley value in the machine learning model f .

Algorithm 3: The Shapley value calculation procedure Data: dataset D Input: The number of iterations M, the data row of concern x, the predictor index j, the machine learning model f for m = 1, 2, . . . , M do Fetch a row of random data z from the dataset D; Choose a random permutation o of the predictor values ; Sort rows of data x: x0 = (x(1) , . . . , x( j) , . . . , x( p) ); Sort rows of data z: z 0 = (z (1) , . . . , z ( j) , . . . , z ( p) ); Create 2 new data rows: with j: x+ j = (x(1) , . . . , x( j−1) , x( j) , z ( j+1) , . . . , z ( p) ) ; without j: x− j = (x(1) , . . . , x( j−1) , z ( j) , z ( j+1) , . . . , z ( p) ) ; m ) − fˆ(x m ) Calculate the marginal contribution: φ mj = fˆ(x+ j −j end M m Calculate Shapley value as an mean: φ j (x) = M1 m=1 φ j

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25.5.2 Partial Dependence Plot Partial Dependence Plot (PDP) shows the marginal effect that one or two predictors have on the prediction results of a machine learning model. PDP can show whether the relationship between the dependent variable and the independent variable is linear, monotonous, or complex. For example, when PDP is applied to linear regression, the resulting plot always shows a linear relationship. The partial dependence function for regression is defined as: fˆS (x S ) = E X C [ fˆS (x S , X C )] =



fˆS (x S , X C )dP[X C ]

(25.10)

where x S is the predictor that will be plotted by the partial dependence function and X C is another predictor used in the machine learning model fˆ which is considered as a random variable. Usually there are only one or two predictors in the S set. The predictor in the set S is a predictor whose effect on the prediction result is wanted to be known. The partial function fˆS is estimated by calculating the mean in the training data as follows: n 1 ˆ (25.11) fˆS (x S ) = f S (x S , xC(i) ) n i=1 The partial function shows what is the mean of the marginal effect on the predicted outcome given the predictor values of S. In the above equation, xC(i) is the actual value of the dataset for the predictors out of concern and n is the number of observations in the data. The assumption of PDP is that there is no correlation between the predictor in C and the predictor in S. If this assumption is violated, the PDP will result in an unreasonable or even impossible value.

25.5.3 Friedman’s H-Statistic The prediction of a model cannot be expressed as the sum of the effects of each independent variable when there is an interaction in it, because the effect of one variable depends on the other variable. Friedman [21] created a statistic called Friedman’s H-statistic which is able to estimate the magnitude of the interaction of a variable. If the two independent variables do not interact with each other, we can construct the partial dependence function as follows (assuming the partial dependence function is transformed with the center at zero): fˆkl (xk , xl ) = fˆk (xk ) + fˆl (xl )

(25.12)

where fˆkl (xk , xl ) is a two-way partial dependence function. fˆk (xk ) and fˆl (xl ) are partial dependence functions with one variable.

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Likewise, when a variable has no interaction with other independent variables, it can be expressed as fˆ(x) which is the sum of the partial dependence functions where the first part is a partial dependence function on the variable x j and the second part is a partial dependence function other than x j . Furthermore, the difference between the observed partial dependence function and the partial dependence function without interaction will be measured, the results of which are used as statistics to measure the magnitude of the interaction. The statistical value will be zero when there is no interaction at all and 1 when the entire variance fˆkl (xk , xl ) can be explained by the sum of the partial dependence functions. Mathematically, the H-statistic between the independent variables k and l is as follows: n 2 H jk

=

ˆ (i) (i) ˆ (i) i=i ( f kl (x k , xl ) − f k (x k ) − n ˆ2 (i) (i) i=i f kl (x k , xl )

fˆl (xl(i) ))2

(25.13)

The H-statistic is very heavy in computation because it iterates for all data rows, partial dependence functions will be calculated for each data row. To speed up the computation, we can do sampling on the data but the disadvantage is that the variance of partial dependence will increase which makes the H-statistic unstable.

25.6 Data Description 25.6.1 Data Source The data used in this study is the same data used by Ferreira and Minikel [22] in 2012 which is motor vehicle policy data released by Commonwealth Automobile Reinsurers (CAR) with an effective policy period of 2006. There are 2 main tables in the data, namely: exposure and claim. The exposure table contains information on earned exposure, age group, city code, and distance traveled per year (in miles). Each row shows changes that occur in insurance policies that change insurance coverage or also known as policy endorsements. The claim table contains data on policyholders’ claims for policies that run in 2006. Each row shows claim transactions that have occurred. The data preprocessing process is the same as that of Ferreira and Minikel in their research. In this study, due to limited computational capabilities, the authors took 40% of the total data using stratified random sampling.

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Table 25.1 The hyperparameters in Random Forest’s claim-frequency model tuning H LL UL The best H minsplit maxdepth cp ntrees subsample

10 1 0.0001 100 0.1

100 10 0.1 1000 0.9

100 10 0.0001 1000 0.1

25.7 Results 25.7.1 Modeling Claim-Frequency Using Random Forest In modeling the frequency of claims using the Random Forest algorithm, because the number of claims has characteristics such as a Poisson distribution, the Loss Function that will be used is Poisson Deviance with the equation that can be seen in (25.6). In addition, to obtain hyperparameters from the Random Forest algorithm that can provide the best performance in modeling claim-frequencies, hyperparameter tuning is performed using Bayesian Optimization [23]. Table 25.1 shows the parameters used in tuning the Random Forest claim-frequency model along with the best hyperparameters. The best hyperparameters were obtained as follows. Furthermore, the claim-frequency will be modeled using the best hyperparameters that have been obtained. In order to see the stability of the model on different datasets, an evaluation will be carried out using K-Fold Cross Validation. Because the dataset used by the authors is very large, the K used by the authors is 6. The mean of the RMSE is 0.2774862.

25.7.2 Modeling Claim-Severity Using Random Forest In modeling the severity of claims using the Random Forest algorithm, because the severity of claims has characteristics such as a Gamma distribution, the Loss Function that will be used is Gamma Deviance with the equation that can be seen in (25.7). In addition, to obtain hyperparameters from the Random Forest algorithm that can provide the best performance in modeling claim-severities, hyperparameter tuning is performed using Bayesian Optimization [23]. Table 25.2 shows the parameters used in tuning the Random Forest claim-severity model along with the best hyperparameters. The best hyperparameters were obtained as follows. Next, the claim-severity modeling will be carried out using the best hyperparameters that have been obtained. In order to see the stability of the model on different datasets, an evaluation will be carried out using K-Fold Cross Validation. Because the dataset used by the authors is very large, the K used by the authors is 10. The mean of the RMSE is 3115,474.

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Table 25.2 The hyperparameters in Random Forest’s claim-severity model tuning H LL UL The best H minsplit maxdepth cp ntrees subsample

10 1 0.0001 100 0.1

100 10 0.1 1000 0.9

30 10 0.0001 100 0.9

Table 25.3 The hyperparameters in Gradient Boosting Machine’s claim-frequency model tuning H LL UL The best H min_obs maxdepth shrinkage ntrees

10 1 0.0001 100

100 10 0.3 1000

23 2 0.0779 247

25.7.3 Modeling Claim-Frequency Using Gradient Boosting Machine In modeling the frequency of claims using the Gradient Boosting Machine algorithm, because the number of claims has characteristics such as a Poisson distribution, the Loss Function that will be used is Poisson Deviance with the equation that can be seen in (25.6). In addition, to obtain hyperparameters from the Gradient Boosting Machine algorithm that can provide the best performance in modeling claim-frequencies, hyperparameter tuning is performed using Bayesian Optimization [23]. Table 25.3 shows the parameters used in tuning the Gradient Boosting Machine claim-frequency model along with the best hyperparameters. The best hyperparameters were obtained as follows. Furthermore, the claim-frequency will be modeled using the best hyperparameters that have been obtained. In order to see the stability of the model on different datasets, an evaluation will be carried out using K-Fold Cross Validation. Because the dataset used by the authors is very large, the K used by the authors is 6. The mean of the RMSE is 0.2774793.

25.7.4 Modeling Claim-Severity Using Gradient Boosting Machine In modeling the severity of claims using the Gradient Boosting Machine algorithm, because the severity of claims has characteristics such as a Gamma distribution,

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Table 25.4 The hyperparameters in Gradient Boosting Machine’s claim-severity model tuning H LL UL The best H min_obs maxdepth shrinkage ntrees

10 1 0.0001 100

100 10 0.3 1000

63 4 0.0709 984

the Loss Function that will be used is Gamma Deviance with the equation that can be seen in (25.7). In addition, to obtain hyperparameters from the Gradient Boosting Machine algorithm that can provide the best performance in modeling claim-severities, hyperparameter tuning is performed using Bayesian Optimization [23]. Table 25.4 shows the parameters used in tuning the Gradient Boosting Machine claim-severity model along with the best hyperparameters. The best hyperparameters were obtained as follows. Next, the claim-severity modeling will be carried out using the best hyperparameters that have been obtained. In order to see the stability of the model on different datasets, an evaluation will be carried out using K-Fold Cross Validation. Because the dataset used by the authors is very large, the K used by the authors is 10. The mean of the RMSE is 3050,54.

25.7.5 Model Evaluation Furthermore, a comparison of the RMSEs for the claim-frequency model and the claim-severity model obtained with the Random Forest algorithm, Gradient Boosting Machine algorithm, and Generalized Linear Models (GLM) will be carried out to obtain the best method. In Fig. 25.3, you can see the RMSEs generated by the three methods of claimfrequency modeling for each fold. It can be seen that the resulting RMSEs are not too different for each method. However, if we look closely, we will see that the blue line representing the Gradient Boosting Machine method is the lowest line compared to the other two methods. This shows that for each fold in claim-frequency modeling, the Gradient Boosting Machine is able to outperform the other two methods because it produces the lowest RMSE. In Fig. 25.4, you can see the RMSEs generated by the three methods of claimseverity modeling for each fold. It can be seen that the resulting RMSEs are significantly different for each method. The blue line representing the Gradient Boosting Machine method is the lowest line compared to the other two methods. This shows that for each fold in claim-severity modeling, the Gradient Boosting Machine is able to outperform the other two methods because it produces the lowest RMSE. We also can see that the green line representing the Random Forest method is the highest line

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Fig. 25.3 The comparison of sixfold Cross Validation’s RMSEs for claim-frequency models

Fig. 25.4 The comparison of sixfold Cross Validation’s RMSEs for claim-severity models Table 25.5 The comparison of the RMSEs’ mean Model GBM RF Frequency Severity

0.27748 3050.54

0.27749 3115.47

GLM

T

0.27752 3066.41

0.27776 3079.12

compared to the other two methods. This shows that for each fold in claim-severity modeling, the Random Forest method still cannot outperform the GLM method yet. Furthermore, the mean of the RMSEs generated using sixfold Cross Validation will be compared for each claim-frequency and claim-severity modeling. From Table 25.5, it can be seen that the Gradient Boosting Machine algorithm is able to produce a model that has the lowest RMSE, both for claim-frequency

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Fig. 25.5 Partial dependence plots for the frequency-claim (left) and the severity-claim (right) against the annual mileage

modeling and claim-severity modeling. Therefore, it can be said that the Gradient Boosting Machine algorithm is more suitable for use in modeling the claim-frequency and the claim-severity than the Random Forest algorithm and the GLM method. Therefore, the Gradient Boosting Machine algorithm will be the main model that will be used in the calculation of pay-as-you-drive insurance’s pure premiums. In addition, both on the claim-frequency model and the claim-severity model, models that include mileage are better than those that do not use mileage.

25.7.6 Interpretations of the Best Model In Fig. 25.5, it can be seen the marginal effect that the mean annual mileage has on the claim-frequency and the claim-severity from the machine learning model. In the blue area in the figure, the top line shows the upper limit of the prediction, the bottom line shows the lower limit of the prediction, and the middle line shows the mean of the predicted results. In both figures, it can be seen that the higher the mean annual mileage, the higher the claim-frequency and the claim-severity. However, in the comparison of the claim-severity and the annual mileage, it can be seen that the relationship between both is not very linear and fluctuates slightly. On the other hand, the histograms in the two figures show how much data there is for each point of mean annual mileage. It can be seen that the larger the mean annual mileage, the fewer data available. This is what makes the upper and lower limits of the prediction of claim-frequency and claim-severity wider as the mean annual mileage increases. In Fig. 25.6, it can be seen the marginal effect of the mean annual mileage and class of drivers on the claim-frequency and the claim-severity from the machine learning model. It can be seen that for all classes of drivers, the higher the mean annual mileage, the higher the claim-frequency and the claim-severity. However, in the comparison to the claim-severity, it can be seen that for all classes of drivers, the relationship between the mean annual mileage and the claim-severity is not very linear and fluctuates slightly. On the other hand, in the claim-frequency modeling,

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Fig. 25.6 Partial dependence plots for the claim-frequency (left) and the claim-severity (right) against the annual mileage and the class of drivers

Fig. 25.7 Partial dependence plots for the claim-frequency (left) and the claim-severity (right) against the mileage and the group of territories

the interaction between the annual mileage and the driver class is not too large. It can be seen that the class of drivers that has the highest claim-frequency for all points of the mean annual mileage is class I, then class N, while the class of drivers that has the lowest claim-frequency is class A. The pattern for each class of drivers is also quite similar, in contrast to the claim-severity modeling. In the claim-severity modeling, it can be seen that the pattern for each class of drivers is quite different, especially for the class of drivers B. Claim-severity for each class of drivers also differ in order for each point of the mean annual mileage. Therefore, it can be said that there is an interaction between the annual mileage and the class of drivers. In Fig. 25.7, it can be seen the marginal effect of the mean annual mileage and group of territories on the claim-frequency and the claim-severity from machine learning models. It can be seen that for all groups of territories, the higher the mean annual mileage, the higher the claim-frequency and the claim-severity. However, in the comparison to the claim-severity, it can be seen that for all groups of territories, the relationship between the mean annual mileage and the claim-severity is not very linear and fluctuates slightly. On the other hand, in the claim-frequency modeling, the interaction between the annual mileage and the group of territories is not too large. It can be seen that the group of territories that has the highest claim-frequency for all points of the mean annual mileage is the group of territories 6, then the group of

25 Determining Auto Insurance Pure Premium Based on Mileage . . . Table 25.6 H-statistic for the claim-frequency and the claim-severity Freq Sev Var H-stat Var (cgr,ann_miles) (tgr,ann_miles)

0.0560 0.1763

(cgr,ann_miles) (tgr,ann_miles)

335

H-stat 0.1260 0.3655

territories 5, while the group of territories that has the lowest claim-frequency is the group of territories 1. The existing pattern for each group of territories is also very similar, in contrast to the claim-severity modeling. In the claim-severity modeling, it can be seen that the pattern for each group of territories is very different. The claim-severity for each group of territories also differ in order for each point of the mean annual mileage. Therefore, it can be said that there is an interaction between the annual mileage and the group of territories. Table 25.6 shows the H-statistic values for each claim-frequency model and claimseverity model. The H-statistic value that is close to 1 indicates that there is high interaction between the two variables, whereas if it is close to 0, there is no interaction between the two variables. From Table 25.6, it can be seen that in both models, the interaction between the class of drivers (cgr) and the mean annual mileage (ann_miles) is lower than the interaction between the group of territories (tgr) and ann_miles. The interaction of the variables in the claim-frequency model is always lower than the variables in the claim-severity model. Besides that, the interaction between cgr and ann_miles in the claim-frequency model is lower than the other variables. Figure 25.8 shows the Partial Dependence Plots (PDP) for the class of drivers and the group of territories in the claim-frequency model (top graph) and the claimseverity model (bottom graph), respectively. The PDP on the group of territories variable has the same pattern in both the claim-frequency model and claim-severity model where group 1 has the lowest risk (low claim-frequency and low claim-severity) and group 6 has the highest risk. In the claim-frequency model’s PDP, the group of territories 3 and the group of territories 4 have a low difference, while in the claim-severity model’s PDP the group of territories 3 and the group of territories 2 have a low difference. This could be an indication that the grouping of territory categories is still unable to separate the risks between the groups. On the other hand, the PDP on the class of drivers variable has a different pattern between the claim-frequency model and the claim-severity model. In the claimfrequency model, the class of drivers with less than 3 years of experience (Inexperienced) has the highest frequency of claims, while the Business class has the highest severity. This explains that the risks that occur in the Business class occur with a rare frequency but once there is a very high claim-severity that must be paid by the company. On the other hand, the inexperienced driver class has a high claim-frequency, but the claims that must be paid each time a claim occurs are not as high as the Business class. This makes sense given that inexperienced drivers prefer to drive on

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Fig. 25.8 Partial dependence plots for the claim-frequency (left) and the claim-severity (right) against the class of drivers and the group of territories

Fig. 25.9 Shapley values variable importance for the claim-frequency model using GBM

roads with low traffic and low driving speeds so that accidents are less severe. That is in contrast to the Business driver class who drive only for business purposes out of town so the frequency of claims is low and usually passes through busy traffic with long distances in one way where being on time is the main thing on the driver’s mind so that big risks can occur when driving.

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Fig. 25.10 Shapley values variable importance for the claim-severity model using GBM

Figure 25.9 shows the Shapley Values used to view the variable importance in the claim-frequency model using GBM. The independent variables in the figure are ordered based on their importance or contribution in making predictions. In other words, they are ordered based on their significance in the model where the top variable is the variable with the highest contribution and the bottom variable is the variable with the lowest contribution. The red and blue colors in the figure show the value of the variable where red is the highest value for that variable and blue is the lowest value for that variable. In the claim-frequency model, the ann_miles variable has the highest influence compared to other variables because its position is at the top. The lower the value of ann_miles will give a negative contribution to the claim-frequency prediction results (the blue color is located on the negative axis of the SHAP contribution) while the higher the value of ann_miles, the greater the claim-frequency value (the red color is located on the positive axis of the SHAP contribution). The claim-frequency will increase in the group of territories 6 (the red color shows number 1 and the blue indicates number 0 which means other groups of territories) as well as for the group of territories 5, the class of drivers with less than 3 years experience and the class of drivers with 3–6 years experience. On the other hand, the claim-frequency will decrease when they are in the group of territories 1, the group of territories 2, and the group of territories 3 as well as the class of drivers Adults. The class of drivers S has a very low contribution, as well as for the group of territories 4 (this corresponds to the group of territories graph in Fig. 25.8). Figure 25.10 shows the Shapley Values used to view variable importance on the claim-severity model using GBM. The ann_miles variable has the largest contribution in predicting claim-severity, the same as in the claim-frequency model. The smaller the mean annual mileage, the smaller the claim-severity. On the other hand, the higher the mean annual mileage, the claim-severity value does not always increase. This

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can be seen from the red color which is around the value 0 of the SHAP contribution and it can also be seen in the Partial Dependence Plots (Picture 25.5). The group of territories 6 is still one of the most influential variables with a positive relationship with the claim-severity. The claim-severity will also increase for the class of drivers inexperienced and the class of drivers Business. On the other hand, the claim-severity will be reduced for the group of territories 1, the group of territories 2, and the group of territories 3 as well as the class of drivers Senior Citizen. The class of driver Adults did not have a large influence on severity nor did the group of territories 4 (which don’t appear on the graph due to very low contribution). From the Variable Importance for the claim-frequency model and the claim-severity model, the group of territories 4 consistently has a low contribution so CAR needs to regroup the group of territories so they have significant differences in risk levels between categories.

25.8 Discussion Based on the results of this study, it was found that the Gradient Boosting Machine (GBM) method was able to produce the lowest RMSE compared to the other two methods. This shows that the GBM method is the best method for predicting claims, both in terms of claim-frequency and claim-severity. Therefore, we can say that the GBM method is able to outperform the GLM method which is commonly used in studies related to the calculation of pay-as-you-drive insurance premiums. Then, is the implementation of pay-as-you-drive insurance using the GBM method really better than the traditional pure premium calculation? We will discuss further the comparison of pure premium schemes between traditional motor vehicle insurance and motor vehicle insurance based on mileage (pay-as-you-drive insurance). To perform this comparison, the authors create two models based on GBM. The first model includes ann_miles or the average mileage per year as an independent variable. The second model only uses the variables cgroup (classes of drivers) and tgroup (groups of territories) as independent variables. Figure 25.11 shows a comparison between PAYD insurance’s pure premiums and traditional motor vehicle insurance’s pure premiums. The class of drivers Adults was chosen because of the moderate risk and high market share, while the group of territories 3 was chosen as an example because of the moderate risk compared to other regions. From the figure, it can be seen that the premiums generated using the GBM model managed to capture the pattern of claims that occurred. When compared with the pure premiums of traditional motor vehicle insurance, it can be seen that the pure premiums of traditional motor vehicle insurance undercharge drivers with a mean annual mileage of fewer than 10,000 miles and overcharge drivers with a mean annual mileage of more than 10,000 miles. From this, it can be seen that the premiums generated by PAYD insurance are much better at capturing the driver’s risk.

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Fig. 25.11 A comparison graph of PAYD insurance’s pure premiums (blue) and traditional motor vehicle insurance’s pure premiums (black) in the class of drivers Adults and the group of territories 3

Table 25.7 A comparison of PAYD insurance’s pure premiums and traditional motor vehicle insurance’s pure premiums Type of insurance Min Max Mean Tradisional PAYD

126.0765 38.6503

126.0765 213.8993

126.0765 144.7398

Table 25.7 shows the minimum of pure premiums, maximum of pure premiums, and the mean of pure premiums for each type of insurance, both traditional insurance and PAYD insurance. In PAYD insurance’s premiums, the lowest premium is $3.5523 and the highest is $21.0286. There are 2 premium schemes that the authors observes. First, the policyholder will provide the data needed by the insurance company then the company will predict the distance traveled by the policyholder during the year. From the predicted mileage, the amount of premium that needs to be paid will be determined. This premium determination scheme will be difficult to do if we rely on the policyholder’s actual mileage in a year because predicting the mileage in a year that the policyholder will do will be very risky for the insurance company, especially when we do not have more specific data about the policyholder as the driver’s customary when driving, the percentage of vehicle use in a year for each rating class (against days), and so on. On the other hand, this scheme is very nontransparent because policyholders do not know why the premiums are so high or the predicted annual mileage. The best option the authors can offer with the limited data available is to let policyholders plan the mileage they will travel in a year wherein the insurance company will provide several mileage options based on historical data. When policyholders have reached the mileage limit that they had planned in advance, then they will not

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get the benefits promised at the beginning. However, policyholders will be given the option to “recharge mileage” so that insurance coverage is active again. This scheme is beneficial for both parties, on the policyholder side, this scheme makes policyholders aware of the driving activities carried out and understands that the more mileage planned, the premium amount will also increase. On the insurance company’s side, this reduces the risk posed by predicting mileage and this simple scheme does not require varying data regarding the driving nature of the policyholder. This option is also carried out by several insurance companies that have implemented pay-asyou-drive in their companies such as Bharti AXA in India and Real Insurance in Australia. We can see the comparison between pure premiums of PAYD insurance with pure premiums of traditional insurance through a case study. Suppose there is a policyholder who belongs to the class of drivers Adults and is in the group of territories 3. According to traditional insurance, the pure premium to be paid is $126.08. If the policyholder determines that in the next year he will drive 10,000 miles, then the pure premium to be paid is $109.42. The pure premium generated is much lower than the pure premium that must be paid from traditional insurance. When compared to the mean of total loss incurred for the policyholder at 10,000 miles, the PAYD insurance will also be closer, where the total loss is $105.85. Based on the results of this research and discussion, the authors strongly recommend collaborating with Indonesian insurance companies to obtain data that represents the condition of motor vehicle insurance in Indonesia. The author also suggests using methods that are able to take into account the excess of zero, both in GLM and machine learning. In addition, the authors also suggest regrouping the regional groups using the clustering method to obtain significantly different territory groups for each category. The use of more varied independent variables to take into account other factors that influence claims can also be done in developing this research further.

25.9 Conclusion Based on the results of research that has been done, the Gradient Boosting Machine algorithm is able to produce a model that has the lowest RMSE, both for modeling claim-frequency and modeling claim-severity. In addition, it is also concluded that the mean annual mileage is the most influential variable, both for modeling claimfrequency and modeling claim-severity, and has a relationship that is not too linear and slightly sloped at high annual mileage. This could be because drivers with a high mean annual mileage are more experienced, or they drive more on low-risk roads. On the other hand, the group of territories 4 is always included as the least influential variable, both for frequency and severity modeling. This indicates that the CAR needs to regroup the territories so that each category is significantly different. For the class of drivers, the class of drivers Business has the highest claim-severity and the class of drivers with less than 3 years of driving experience has the highest claim-frequency.

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Premium calculation schemes that include mileage or PAYD insurance are better than traditional motor vehicle insurance premiums that do not include mileage. With the limited data that the authors have, as well as most general insurances in Indonesia, and by knowing the mean annual mileage variable, the best option for determining premium schemes is to let policyholders plan the mileage they will travel in a year beginning by offering several mileage options. When the planned mileage limit has been reached, the policyholder can “recharge the mileage” to reap the benefits. Acknowledgements This work was fully funded by the project of the Final Task Recognition Program of Gadjah Mada University 2022 (grant number: 3550/UN1.P.III/Dit-Lit/PT.01.05/2022) provided by the research directorate and the reputation improvement team of UGM toward the World Class University of the quality service office. The authors also thank reviewers for their careful reading and helpful suggestions.

References 1. T. Litman, Implementing pay-as-you-drive vehicle insurance. The Institute for Public Policy Research (2001). https://www.ippr.org/files/uploadedFiles/events/ToddLitman.pdf 2. M. Muller, Generalized linear model, in Handbook of Computational Statistics (Springer, Berlin, 2012) 3. J.A. Nelder, R.W.M. Wedderburn, Generalized linear models. J. Royal Stat. Soc. Ser. A (General), 135(3), 370-384 (1972). https://www.jstor.org/stable/2344614?origin=JSTOR-pdf 4. R. Henckaerts, M. Cote, K. Antonio, R. Verbelen, Boosting insights in insurance tariff plans with tree-based machine learning method. North Am. Actuarial J. 25(2), 255–285 (2021). https://doi.org/10.1080/10920277.2020.1745656 5. J. Zhou, D. Deng, GLM vs. machine leaning with case studies in pricing, in Casualty Actuarial Society’s Annual Meeting, Nov. 2019, https://www.casact.org/sites/default/files/presentation/ annual_2019_presentations_c-22_zhou.pdf 6. D.H. Alai, M.V. Wüthrich, Taylor approximations for model uncertainty within the Tweedie exponential dispersion family. ASTIN Bull. J. IAA 39(2), 453–477 (2009). https://doi.org/10. 3929/ethz-b-000020804 7. J.P. Boucher, A.M. Peârez-Marõân, M. Santolino, Pay-as-you-drive insurance: the effect of the kilometers on the risk of accident. Anales del Instituto de Actuarios Españoles, 3a época 19, 135–154 (2013). https://actuarios.org/wp-content/uploads/2017/02/anales2013_6.pdf 8. L. Breiman, Random forests. Mach. Learn. 45(1), 5–32 (2001). https://doi.org/10.1023/A: 1010933404324 9. J.H. Friedman, Greedy function approximation: a gradient boosting machine. Ann. Appl. Stat. 29(5), 1189–1232 (2001). https://www.jstor.org/stable/2699986 10. J.H. Friedman, Stochastic gradient boosting. Comput. Stat. Data Anal. 38, 367–378 (2002). https://doi.org/10.1016/S0167-9473(01)00065-2 11. L. Breiman, J.H. Friedman, C.J. Stone, R.A. Olshen, Classification and Regression Trees (Taylor and Francis, New York, 1984) 12. L. Breiman, Bagging predictors. Mach. Learn. 24(2), 123–140 (1996). https://doi.org/10.1007/ BF00058655 13. P. Zöchbauer, M.V.Wüthrich, C. Buser, Data science in non-life insurance pricing. Ph.D. thesis, ETH Zurich (2017) 14. Statistika Matematika Subanar, Statistics Mathematics (Yogyakarta, Graha Ilmu, 2013) 15. W.N. Venables, B.D. Ripley, Tree-based methods, in Modern Applied Statistics with S (Springer, New York, 2002). https://doi.org/10.1007/978-0-387-21706-2_9

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16. R. Henckaerts, distRforest: distribution-based Random Forest, R package version 1.0 (2019). Online available from https://www.github.com/henckr/distRforest 17. C. Molnar, Interpretable machine learning: a guide for making black box models explainable (2019). ISBN 978-0-244-76852-2 18. L.S. Shapley, A value for n-person games, in Contributions to the Theory of Games II, ed. by H. Kuhn, A. Tucker. (Princeton University Press, Princeton, 1953), pp. 307–317. https://doi. org/10.1515/9781400881970-018 19. E. Štrumblej, I. Kononenko, Explaining prediction models and individual predictions with feature contributions. Knowl. Inform. Syst. 41(3), 647–665 (2013). https://doi.org/10.1007/ s10115-013-0679-x 20. D.P. Kroese, R.Y. Rubinstein, Monte Carlo methods. Wiley Interdisc. Rev. Comput. Stat. 4(1), 48–58 (2012). https://doi.org/10.1002/wics.194 21. J.H. Friedman, B.E. Popescu, Predictive learning via rule ensembles. Ann. Appl. Stat. 2(3), 916–954 (2008). https://www.jstor.org/stable/30245114 22. J.H. Ferreira, E. Minikel, Measuring per mile risk for pay-as-you-drive automobile insurance. Transp. Res. Rec. 2297(1), 97–102 (2012). https://doi.org/10.3141/2297-12 23. P.I. Frazier, A tutorial on Bayesian optimization (2018). arXiv:1807.02811v1 [stat.ML]

Part III

Engineering

Chapter 26

The Mitigation Model of Greenhouse Gas Emissions Reduction in Coal Mining Company with Surface Mining System Doni, Sata Yoshida Srie Rahayu, Rosadi, and Sutanto

Abstract The use of fuel oil is one of the largest sources of greenhouse gas (GHG) emissions in the energy sector for coal mining activities. GHG emissions from the energy sector of PT. Cipta Kridatama Site PT. Kuansing Inti Makmur (CK-KIM) in 2021 was calculated according to IPCC Guidelines 2006 method. The purpose of this study was to calculate the GHG emission reduction mitigation actions that have been carried out and analyze various alternative of reduction policy scenarios of the GHG emissions energy sector using simulation model with a dynamic system approach. The simulation applied from 2021 to 2051. There are four scenarios: BAU scenario, which is the current energy use; scenario A, based on the implementation of the generator replacement program with PLTS; B scenario, the implementation of lighting tower replacement program with solar cell lighting tower; and C scenario which is the implementation of a program to replace generator sets and lighting towers with PLTS. The amount of GHG emissions energy sector in CK-KIM in 2021 is 82,500.13 Tons CO2 /year. The largest amount of emission originated from road transportation and off-road transportation, which is 46,073.86 Tons CO2 /year and 32,062.75 Tons CO2 /year. The reduction of GHG emissions for mitigation actions by using solar panels on the extensometer is 0.18 Ton CO2 /year. GHG emission reduction for the e-Reporting System (e-SIAP) program is 1.14 Ton CO2 /year. In the A scenario, GHG emissions are decreasing by 1.39%. In the B scenario, GHG emissions are decreasing to 0.46%, and the C scenario was successfully decreasing by 1.85%. For decreasing the GHG emissions energy sector, it needs to conduct energy management for the use of fuel in road transportation and off-road transportation equipment.

Doni · Rosadi · Sutanto Postgraduate School of Pakuan University, Pakuan University, Jl. Pakuan, PO. Box 452, Bogor, West Java, Indonesia S. Y. S. Rahayu (B) Faculty of Mathematics and Natural Science, Pakuan University, Jl. Pakuan, PO. Box 452, Bogor, West Java, Indonesia e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Mustapha et al. (eds.), Proceedings of the 8th International Conference on the Applications of Science and Mathematics, Springer Proceedings in Physics 294, https://doi.org/10.1007/978-981-99-2850-7_26

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26.1 Introduction Climate change is believed to be the result of increasing concentrations of greenhouse gases (GHG) on the earth’s surface, causing global warming which in turn makes the climate change from its normal state [16]. Human activities that produce high enough GHG emissions are industrial activities [8]. One of the industries that produces quite large GHG emissions is the coal mining industry [9]. The increasing growth of the mining industry will be in line with the higher energy consumption from the use of fuel oil [1]. Coal production will continue to increase until 2050 [12]. The increase in energy consumption from the use of fuel oil will directly increase the resulting GHG emissions. Coal mining is mostly done by coal mining companies using the open-pit mining method. The Mining Industry Energy Bandwidth Study states that energy consumption in the mining industry is around 1246 trillion Btu (365 billion KWH) per year [2]. Electricity and fuel oil (diesel) are the main energy sources in open-pit coal mining. Diesel technology uses 87% of the total energy consumed in material handling [10]. Around 65% of GHG emissions are caused by the burning of fuel oil [3]. In 2019, the sector that gave the largest contribution to national GHG emissions was the forestry and peat fires sector, followed by the energy, waste, agriculture, and IPPU sectors with percentages of 50%, 34%, 7%, 6%, respectively, and 3% [4]. The amount of fuel consumption in coal mining will be directly proportional to the high GHG emissions produced, thus making it important to carry out energy management with a focus on optimizing the use of fuel as the main energy source. Many mining companies have made efforts to reduce GHG emissions, one of which is energy efficiency. Energy efficiency activities in the mining industry are generally carried out by optimizing mining operations, both main activities and supporting activities. Energy efficiency activities carried out in mining operations are usually carried out by saving fuel oil (BBM) for operational activities of heavy mining equipment and vehicles or supporting equipment. Many studies that have been conducted related to GHG emissions in coal mining currently focus on the amount of GHG emissions produced by these mining activities and have not calculated GHG emissions from GHG emission reduction mitigation efforts that will be or have been carried out by the company. The mine based on this, this study will examine the amount of emissions produced by coal mining companies with open mining systems, in this case PT. Cipta Kridatama Site PT. Kuansing Inti Makmur (CK-KIM) which is the object of research and the results of an inventory of GHG emission reduction efforts that have been carried out or have the potential to be reduced, because currently at the research location, the mitigation efforts that have been carried out have not been comprehensively documented. In addition, an analysis will be carried out using a Dynamic System so that GHG emission predictions can be made until 2051 and an analysis of the most optimal mitigation efforts that can be carried out by coal mining companies with open mining systems. So that the mitigation model created can be used as an example for other coal mining companies in Indonesia when they will carry out GHG emission calculations

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and take GHG emission reduction mitigation actions. In this study, the research problems are formulated as follows: 1. What is the level of GHG emission in the energy sector in open-pit coal mining companies in 2021? 2. What is the dynamic model for reducing GHG emissions in the energy sector in open-pit coal mining companies from 2022 to 2051? 3. What are the scenarios and recommendations for the energy sector GHG emission reduction strategy in open-pit coal mining companies? In addressing the research problems, the following are the research purposes in this study. 1. Determine the level of GHG emission in the energy sector in coal mining companies with open mining systems in 2021. 2. Designing a mitigation model for reducing GHG emissions in the energy sector in open-pit coal mining companies from 2022 to 2051. 3. Formulate scenarios and recommendations for strategies for reducing GHG emissions in the energy sector in open-pit coal mining companies. This research was conducted at PT. Cipta Kridatama Site PT. Kuansing Inti Makmur (CK-KIM) in the energy sector. Greenhouse gas (GHG) parameters calculated for the energy sector in this study are CO2 , CH4, and N2 O.

26.2 Research Method 26.2.1 Time and Location This research was conducted at PT. Cipta Kridatama Site PT. Kuansing Inti Makmur (CK-KIM) which is located in Tanjung Belit Village, Jujuhan District, Bungo Regency, Jambi Province from January to April 2022.

26.2.2 Research Framework In general, this study aims to determine the mitigation model for reducing GHG emissions in open-pit coal mining companies in an effort to mitigate GHG emission reductions in the energy sector as shown in Fig. 26.1.

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Fig. 26.1 Research framework

26.2.3 Calculation of GHG Emissions in the Energy Sector Calculation of GHG emissions for the energy sector GHG emission inventory is based on the general equation 26.1,

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Table 26.1 Emission factors for stationary, road transportation, and off-road transportation Fuel type

EF stationary (kg/TJ)

EF road transportation (kg/TJ)

EF Off-road transportation (kg/TJ)

CO2

CH4

N2 O

CO2

CH4

N2 O

CO2

CH4

N2 O

Diesel oil

74,100

3

0.6

74,100

3.9

3.9

74,100

4.15

28.6

Biodiesel

70,800

3

0.6

–

–

–

–

–

–

Source IPCC Guidelines 2006

Table 26.2 Calorific value of Indonesian fuel

Fuel type

Calorific value

Premium

33 × 10–6 TJ/liter

Solar

36 × 10–6 TJ/liter

Minyak diesel

38 × 10–6 TJ/liter

Source Guidelines for the Implementation of the National GHG Inventory [6]

GHG emissions = activity data (AD) × emission factor (EF),

(26.1)

where activity data (DA) is a quantitative quantity of fuel oil (BBM) that releases GHG emissions in Tera Joules (TJ), while the emission factor (FE) is a factor that shows the intensity of emissions per unit of activity in kg/Tera units. Joules. Table 26.1 shows the emission factor values for diesel fuel and biodiesel. The use of fuel oil used is usually in liters, so it needs to be converted to energy units (Tera Joules). To convert liters to Tera Joules (TJ), it is necessary to data the calorific value of the fuel oil used as shown in Table 26.2. Mining equipment used in mining activities at CK-KIM that produces GHG emissions is divided into three categories of emission sources, namely stationary, road transportation, and off-road transportation, as shown in Table 26.3. Calculation of GHG emissions in the energy sector for diesel fuel or biodiesel practically uses the following equation 26.2.   GHG emissions(kg) = volume(litre) × calorivic value(TJ/liter) × EF(kg/TJ)

(26.2)

26.2.4 Calculation of Mitigation Actions Using Solar Panels Solar panels are included in the category of power plants that use solar power (PLTS) that do not produce GHG emissions. The calculation of the achievement of PLTS mitigation activity emission reduction is calculated from the difference between the baseline GHG emission value and the GHG emission value of mitigation activities. The PLTS GHG emission level is equal to zero so that the emission reduction

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Table 26.3 Types of mining equipment that use fuel No

Equipment type

Emission source type

Fuel type

1

Off-highway truck

Road transportation

Biodiesel B30

2

Dump truck coal

Road transportation

Biodiesel B30

3

Water truck

Road transportation

Biodiesel B30

4

Fuel truck

Road transportation

Biodiesel B30

5

Lube oil truck

Road transportation

Biodiesel B30

6

Crane truck

Road transportation

Biodiesel B30

7

Light vehicle

Road transportation

Biodiesel B30

8

Bus

Road transportation

Biodiesel B30

9

Excavator

Off-road transportation

Biodiesel B30

10

Bulldozer

Off-road transportation

Biodiesel B30

11

Grader

Off-road transportation

Biodiesel B30

12

Compactor

Off-road transportation

Biodiesel B30

13

Wheel loader

Off-road transportation

Biodiesel B30

14

Tire handle

Off-road transportation

Biodiesel B30

15

Drilling machine

Stationary

Biodiesel B30

16

Gen-set

Stationary

Biodiesel B30

17

Lighting tower

Stationary

Biodiesel B30

18

Welding machine

Stationary

Biodiesel B30

19

Dewatering pump

Stationary

Biodiesel B30

20

Compressor

Stationary

Biodiesel B30

achieved is the same as the baseline GHG emission. Baseline GHG emissions are GHG emissions that arise when PLTS is not or has not been built and operating. The current use of solar panels at CK-KIM is found in the use of an Extensometer, which is a tool to detect and measure the movement or shift of the ground surface as an early detection of landslide hazards. Calculation of baseline GHG emissions for the use of an Extensometer that uses solar panels as its power source is calculated from data on the capacity of installed electrical equipment (solar panels) and data on operating hours of solar panels per day. It is then multiplied by the emission factor of the electricity system for the Jambi (Sumatra) area in accordance with the Decree of the Minister of Energy and Mineral Resources Number 163 K of 2021, which is 0.93 Ton CO2 /MWH. Calculation of baseline GHG emissions follows the following equation 26.3.   GHG emissions baseline(Ton) = KWP × opeartion time(Jam) × EF(MWH/Ton) (26.3)

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26.2.5 Calculation of Mitigation Actions with the e-Reporting System (e-SIAP) The calculation of the achievement of GHG emission reduction in the application of the e-Reporting system (e-SIAP) is calculated from the difference between the baseline GHG emission value and the GHG emission value of mitigation activities. The level of GHG emission after the implementation of the e-Reporting system (eSIAP) is equal to zero so that the emission reduction achieved is the same as the baseline GHG emission. In the Hazard Report reporting activity prior to the implementation of the eReporting System (e-SIAP), the source of GHG emissions comes from the fuel consumption of operational vehicles used to collect Hazard Report Cards (paper) every day from temporary collection points in several predetermined places. Thus, baseline emissions are calculated by multiplying the total volume of fuel (liters) consumed for vehicles by calculating the distance traveled by the vehicle to the hazard report card storage area every day multiplied by the fuel consumption ratio of the operational vehicles used, which is then multiplied by the calorific value of the fuel (TJ/liter) and emission factor (kg/TJ). Calculation of baseline GHG emissions follows the following equation 26.4. GHG emissions baseline(kg) = volume(litre) × calorific value(TJ/litre) × EF(kg/TJ) Volume(Litre) = distance(km) × vehicle fuel ratio(kitre/km)

(26.4)

26.2.6 Dynamic Systems Analysis The use of dynamic systems in this study is to design a model for reducing GHG emission reductions in the energy sector (stationary and transportation) in coal mining companies with open mining systems from 2022 to 2051. Next, develop scenarios and recommendations for strategies for reducing GHG emissions in the energy sector (stationary) in the energy sector (stationary) where coal mining company opened mining system from 2022 to 2051. Needs Analysis Based on the results of the GHG emission inventory at CK-KIM in 2021, it is known that the largest emission source in CK-KIM is the energy sector (stationary and transportation). These two sectors are the most influential and most determine the level of GHG emissions in CK-KIM. Problem Formulation The formulation of the problem is an analysis of the activity of using movable and immovable mining equipment to build a model for reducing GHG emissions in the

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energy sector and conducting simulations to obtain the best scenario that can reduce GHG emissions in the energy sector at CK-KIM. System Identification The dynamic system model of GHG emission reduction is composed of activity variables that affect the amount of GHG emissions in the energy sector in CK-KIM. Energy management activities consist of energy-saving programs, use of energyefficient equipment, and use of renewable energy sources. In the case of reducing GHG emissions in mining companies with open-pit mining systems, it is depicted in the form of an input–output diagram as in Fig. 26.2 and a causal loop diagram as in Fig. 26.3. Model Design The design of the model is to develop a system model based on the identification results which are represented in the form of causal loop diagrams (CLD) and stock flow diagrams (SFD). The CLD that has been built is then converted into an SFD model using the Powersim Studio 10 computer software. Model Validation Model validation is the stage of testing the level of confidence in the accuracy of the model structure being built. Model validation is carried out using the absolute Environmental Input : Peraturan Presiden No. 98 tahun 2021 PermenESDM No. 14 tahun 2012 PermenLHK No. P72 tahun 2017 Desired Output: GHG emission reduction Energy use efficiency Utilization of renewable energy

Uncontrolled Input: Mining production target Mining equipment condition

The Model of GHG Emissions Reduction

Controlled Input: Total energy requirement Availability of energy sources Energy management knowledge

Unwanted Output : GHG emissions increase Climate change Climate related diseases

Feed Back

Fig. 26.2 Input output diagram

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Fig. 26.3 Causal loop diagram (CLD)

mean error (AME) value, which is the deviation (difference) between the average value (mean) of the simulation results to the actual value and the absolute variation error (AVE), which is the deviation of the variation value from the simulation to the actual, where the acceptable deviation limit is < 10% [7]. AME statistic test calculation:  AME =

ˆ − Ai ˆ Si

 (26.5)

ˆ Ai

ˆ = Si·N Si Âi = Ai·N Information: S: Model value (simulation). N: Observation time interval. A: Actual value. AVE statistical test calculation:  AVE =

ˆ = (Si ˆ − Si)2 ·N Ss

ˆ − Sˆ A Ss Sˆ A

 (26.6)

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Sˆ A = (Âi − Ai)2 ·N Information: ˆ Deviation of simulation value. Ss: Sˆ A : Actual value deviation. Model Simulation Model simulation is a dynamic process of model behavior whose results are time behavior graphs and time behavior tables. The SFD which already contains the data is then simulated to obtain results based on the specifications of the time period, integration, and time stages that have been set previously. Mitigation Strategy Recommendations Based on the model simulation carried out, scenarios for reducing GHG emissions in the energy sector (stationary) are obtained. From the scenarios obtained, it is possible to determine the most effective and optimal strategy recommendations in the context of reducing GHG emissions in open-pit coal mining companies.

26.3 Results and Discussion 26.3.1 Total CK-KIM GHG Emissions in 2021 Based on the results of the calculation of the amount of GHG emissions using the IPCC 2006 method, as in Table 26.4, it is known that the GHG emissions of the energy sector in CK-KIM in 2021 are 82,500.13 Tons CO2 /year. The largest number of emissions resulted from road transportation and off-road transportation, namely 46,073.86 tons CO2 /year and 32,062.75 tons CO2 /year. These two emission sources require special handling in the future so that GHG emissions can be reduced significantly. Table 26.4 Total energy sector GHG emissions at CK-KIM in 2021 using the 2006 IPCC method

No

GHG emissions source

1

Road transportation

46.07386

2

Off-road transportation

32.06275

3

Stationary Total

GHG emissions (Ton CO2 eq per year)

4.36352 82.50013

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Fig. 26.4 Extensometer with solar cell

26.3.2 Results of GHG Emission Mitigation from the Use of Solar Panels in Extensometers The use of solar panels for the Extensometer as shown in Fig. 26.4 does not produce GHG emissions or zero tons of CO2 eq. GHG emission reduction is the same as baseline GHG emission calculation based on installed electrical equipment capacity data (PLTS) and PLTS operating hours data per day and converted to years. Based on the calculation of the amount of baseline GHG emissions using the 2006 IPCC method, it was found that the baseline GHG emission was 0.18 Ton CO2 /year. Thus, reducing GHG emissions for mitigation actions by using solar panels on the extensometer is 0.18 Ton CO2 /year.

26.3.3 Results of GHG Emission Reduction Mitigation with the Implementation of the e-Reporting System (e-SIAP) The application of the e-Reporting System (e-SIAP) at CK-KIM does not produce GHG emissions or zero tons of CO2 eq. GHG emission reduction is the same as baseline GHG emission calculation. Calculation of baseline GHG emissions is done by calculating the distance from each hazard report card storage place to the office as listed in Table 26.5. Calculation of baseline GHG emissions from the application of the e-Reporting System (e-SIAP) shows that to cover a distance of 1 km it takes 8 l of fuel and in 1-year conventional hazard report card collection activities cover a total distance of 3350.08 km and require fuel consumption of 418.76 l. This consumption will produce GHG emissions of 1.14 Ton CO2 eq per year (Fig. 26.5).

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Table 26.5 Hazard report card collection distance Hazard report box

Total unit

Frequency (PP)

Distance to office (km)

Distance total (km/ Year)

Pondok operator 1

2

2.24

1617.28

Stopping mess

1

2

2.10

1516.20

Workshop and warehouse

1

2

0.30

216.60

Total

3350.08

Fig. 26.5 Display of e-reporting system (e-SIAP) application

26.3.4 Modeling The energy sector GHG emission reduction model at CK-KIM is designed based on the causal loop diagram (CLD) that has been created. The structure of the model was built using the Powersim Version 10 program and is presented in the form of a stock flow diagram (SFD) in Fig. 26.6. The system analysis was carried out for 30 years, namely 2021 to 2051, with the initial year of analysis being 2021. The variable in this model is the number of production volume (coal and overburden rock) and the amount of use of B30 biodiesel fuel. Total production of coal and overburden rock produced by CK-KIM in 2021 is 27,560,291 bank cubic meter (BCM) with a production rate of 15.3% per year based on the comparison of data on the amount of coal and overburden production in 2020 with 2021 (Environmental Report CK-KIM 2020, 2021). Energy consumption is the amount of B30 fuel consumed by mining equipment. The total consumption of B30 fuel in 2021 is 29,405,568 l with B30 fuel intensity for coal and overburden production value of 1.07 (Environmental Report CK-KIM 2021). The current usage of B30 fuel in CK-KIM or in business as usual (BAU) conditions consists of use for road transportation equipment by 58.74%, use for off-road

26 The Mitigation Model of Greenhouse Gas Emissions Reduction in Coal …

FE CH4 RT

357

Laju BBM STR

FE CO2 RT

FE N2O RT

Konsumsi BBM RT Laju BBM RT BBM STR Kenaikan BBM STR

GWP CO2 RT

FE CH4 STR

FE N2O STR GWP CH4 RT

Konsumsi BBM STR

FE CO2 STR

BBM RT Kenaikan BBM RT

GWP CO2 STR Emisi GRK RT

GWP N2O RT GWP CH4 STR

Nilai Kalor BBM RT Laju kenaikan produksi

Laju konsumsi BBM RT

Emisi GRK STR

GWP N2O STR

Nilai Kalor BBM STR Laju konsumsi BBM STR

Emisi GRK Road Transportation Kenaikan Emisi RT

Kenaikan Produksi Produksi Coal & OB

FE CH4 ORT Emisi GRK Stasioner Kenaikan Emisi Str

FE CO2 ORT

FE N2O ORT

Konsumsi BBM ORT GWP CO2 ORT Emisi GRK Total Sektor Energi Laju BBM OTR GWP CH4 ORT

Emisi GRK ORT

GWP N2O ORT

BBM ORT Kenaikan BBM ORT Nilai Kalor BBM ORT Laju konsumsi BBM ORT

Emisi GRK Off-Road Transportation Kenaikan Emisi OTR

Fig. 26.6 Stok flow diagram modeling system

transportation equipment by 37.20%, use for off-road transportation equipment, and use for stationary equipment at 4.07% based on B30 fuel consumption data for 2 years, 2020 and 2021 (Environmental Report CK-KIM 2020, 2021).

26.3.5 Simulation The results of the model simulation are presented in Table 26.6. The current total reserves of coal and overburden rock at PT. KIM based on the calculation results at the end of 2018 was 480,171,095 BCM for overburden and 53,455,493 tons for coal [17]. If converted to BCM units for coal, with a coal density of 1.32, then coal reserves and overburden rocks are 520,667,681 BCM. In 2021, the production of coal and overburden rock amounted to 27,560,291 BCM, in 2051 the end of the simulation reached 1,824,815,702.75 BCM. For 30 years from 2021 to 2051, the addition of coal and overburden rock production is 1,797,255,411.75 BCM with an average production increase of 15.26 percent

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Table 26.6 Achievement of B30 fuel production and consumption at CK-KIM Year

Coal & OB (BCM) production BBM RT (liter)

BBM ORT (liter) BBM STR (liter)

2021

27,560,291.00

16,975,914.00

10,723,665.00

1,705,989.00

2022

31,694,334.65

19,182,782.82

12,117,741.45

1,927,767.57

2023

3,644,8484.85

21,676,544.59

13,693,047.84

2,178,377.35

2024

4,1915,757.57

24,494,495.38

15,473,144.06

2,461,566.41

2025

48,203,121.21

27,678,779.78

17,484,652.78

2,781,570.04

2026

55,433,589.39

31,277,021.15

19,757,657.65

3,143,174.15

2027

63,748,627.80

35,343,033.90

22,326,153.14

3,551,786.79

2028

73,310,921.97

39,937,628.31

25,228,553.05

4,013,519.07

2029

84,307,560.27

45,129,519.99

28,508,264.95

4,535,276.55

2030

96,953,694.31

50,996,357.59

32,214,339.39

5,124,862.50

2031

111,496,748.45

57,625,884.08

36,402,203.51

5,791,094.63

2032

128,221,260.72

65,117,249.01

41,134,489.97

6,543,936.93

2033

147,454,449.83

73,582,491.38

46,481,973.66

7,394,648.73

2034

169,572,617.30

83,148,215.26

52,524,630.24

8,355,953.06

2035

195,008,509.90

93,957,483.24

59,352,832.17

9,442,226.96

2036

224,259,786.38

106,171,956.06

67,068,700.35

10,669,716.47

2037

257,898,754.34

119,974,310.35

75,787,631.40

12,056,779.61

2038

296,583,567.49

135,570,970.70

85,640,023.48

13,624,160.96

2039

341,071,102.62

153,195,196.89

96,773,226.53

15,395,301.88

2040

392,231,768.01

173,110,572.49 109,353,745.98

17,396,691.13

2041

451,066,533.21

195,614,946.91 123,569,732.95

19,658,260.97

2042

518,726,513.19

221,044,890.01 139,633,798.24

22,213,834.90

2043

596,535,490.17

249,780,725.71 157,786,192.01

25,101,633.44

2044

686,015,813.70

282,252,220.05 178,298,396.97

28,364,845.78

2045

788,918,185.75

318,945,008.66 201,477,188.58

32,052,275.73

2046

907,255,913.62

360,407,859.78 227,669,223.09

36,219,071.58

2047

104,334,4300.66

407,260,881.55 257,266,222.09

40,927,550.89

2048 1,199,845,945.76

460,204,796.15 290,710,830.97

46,248,132.50

2049 1,379,822,837.62

520,031,419.65 328,503,238.99

52,260,389.73

2050 1,586,796,263.26

587,635,504.21 371,208,660.06

59,054,240.39

2051 1,824,815,702.75

664,028,119.76 419,465,785.87

66,731,291.64

per year. The increase in production achievement causes B30 fuel consumption to increase. At the end of the analysis, namely in 2051 the total consumption of B30 fuel for road transportation reached 664,028,119.76 l/year, for off-road transportation was 419,465,785.87 l/year, and for stationary was 66,731,291.64 l/year. The increase in the amount of B30 fuel consumption will result in the energy sector’s GHG emissions increasing as well if not controlled. Based on the model

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1.000.000

500.000

0 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034 2035 2036 2037 2038 2039 2040 2041 2042 2043 2044 2045 2046 2047 2048 2049 2050 GHC Emission Road T ransportation

GHG Emission O ff-Road Transportation

GHG Emmission Stationer

year

Fig. 26.7 Graph of total energy sector emissions at CK-KIM

simulation results, it is known that the amount of GHG emissions in the energy sector at CK-KIM in 2051 for stationary will reach 130,730.64 Ton CO2 /year. The largest number of emissions in 2051 will come from road transportation and off-road transportation, namely 1,380,369.25 tons of CO2 /year and 960,597.45 tons of CO2 / year. The graph of the increase in GHG emissions in the energy sector at CK-KIM is shown in Fig. 26.7.

26.3.6 Model Validation Model validation tests were carried out on coal and overburden rock production data from 2010 to 2014 with AVE results of 0.72 and AME 0.31. These results indicate that there is a deviation of 0.71 and 0.31% between the model and the actual data. The results of AVE and AME in Table 26.7 showed that 10 percent indicates that the model built has good performance and is relatively accurate and scientifically acceptable.

26.3.7 Model Scenario The model scenario consists of a business as usual (BAU) scenario, scenario A, and scenario B. The BAU scenario is a scenario based on current conditions, namely 55.85% of GHG emissions from road transportation, 33.86% from off-road transportation, and 5.29% came from stationary. Scenario A follows a government program based on the Regulation of the Minister of Energy and Mineral Resources

360 Table 26.7 AVE and AME production test results at CK-KIM

Doni et al.

Year

Actual production (Mill. Simulation production (Mill. BCM) BCM)

2010

8.70

8.70

2011

21.35

10.01

2012

19.48

11.51

2013

17.02

13.23

2014

17.99

15.22

Mean 16.91

11.73

AME

0.31

AVE

0.72

No. 16/2020 concerning the Strategic Plan of the Ministry of Energy and Mineral Resources for 2020–2024, namely efforts to meet electricity needs for areas that have not been reached by the PLN electricity network and in an effort to mitigate CO2 emission reduction in the sector using new and renewable energy by building PLTS (Solar Power Plant). This means that the current source of electricity generated from generators with B30 fuel will be replaced with PLTS. Scenario B replaces the lighting source for the mining area which has been using a lighting tower that uses B30 fuel with a solar-powered lighting tower. Scenario C is a combination of scenarios A and B, namely replacing the gen-set and lighting tower with B30 fuel with PLTS (Figs. 26.8 and 26.9). The results of the model simulation by applying the BAU scenario, scenario A, scenario B, and scenario C are presented in Table 26.8. The largest GHG emission in the energy sector in CK-KIM in 2051 is if energy management based on current conditions without any emission reduction efforts will reach 2,471,697.34 Tons CO2 / year. The simulation results of scenario A are presented in Fig. 26.10. Based on the simulation results of scenario A, the amount of GHG emissions in the energy sector at CK-KIM in 2051 is projected to be 2,437,298.33 Tons CO2 /year. Emission reduction

Fig. 26.8 Use of PLTS as a power source (left side: before and right side: after)

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Fig. 26.9 Solar panel system lighting tower usage (left) lighting tower Berbahan Bakar Minyak (right) lighting tower panel surya

Table 26.8 Energy sector GHG emissions in 2051 with various scenarios Scenario

Road transportation emission (TonCO2 / year)

Off-road transportation emission (TonCO2 / year)

Stationary emission (TonCO2 /year)

Energy sector emission (TonCO2 /year)

BAU

1,380,369.25

960,597.45

130,730.64

2,471,697.34

A

1,380,369.25

960,597.45

96,331.63

2,437,298.33

B

1,380,369.25

960,597.45

119,297,38

2,460,264.08

C

1,380,369.25

960,597.45

84,898. 37

2,425,865.07

by implementing scenario A decreased by 1.39% compared to the BAU scenario. In this scenario, all the use of generators as a source of electricity in the mess, office, workshop, and warehouse have been replaced with the use of rooftop solar power plants. B Scenario replaces all lighting towers as a source of lighting in the mining area at night with solar panel lighting towers as shown in Fig. 26.9. Based on the simulation results of the implementation of scenario B, it is known that the amount of GHG emissions in the energy sector in CK-KIM in 2051 will come as much as 2,460,264.08 Tons of CO2 /year. The emission reduction with the implementation of B scenario is quite small, namely 0.46% when compared to the BAU condition, but the use of new and renewable energy in this case the use of solar panels can already be implemented (Fig. 26.11). C Scenario is to combine the application of a program to replace electricity sources for mess, office, workshop, and warehouse originating from generators and lighting sources in the mining area from lighting towers that use B30 fuel with rooftop solar panels and solar panel lighting towers. Based on the model simulation, by applying scenario C, it is known that the amount of GHG emissions in the energy sector in CK-KIM in 2051 is 2,425,865.07 Tons CO2 /Ton or decreased by 1.85% compared to the BAU scenario (Fig. 26.12).

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Fig. 26.10 Graph of GHG emission simulation results for A scenario

Fig. 26.11 Graph of scenario B, GHG emission simulation results

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Fig. 26.12 Graph of GHG emission simulation results for C scenario

26.4 Conclusions and Suggestions 26.4.1 Conclusions The results of the calculation of GHG emissions in the energy sector at CK-KIM in 2021 using the 2006 IPCC method produce the same amount as the results of calculations using a simulation model, namely 82,500.13 Tons CO2 /year. The percentage error between these two calculations is 0%. This shows that the model was built according to the 2006 IPCC calculation method. The reduction of GHG emissions for mitigation actions by using solar panels on the extensometer is 0.18 Ton CO2 /year. The reduction of GHG emissions for the e-Reporting System (e-SIAP) program is 1.09 Ton CO2 /year. Planning for the installation of rooftop PLTS to replace electricity sources in the mess, office, workshop, and warehouse areas which have been produced from generators in 2051 is only able to reduce GHG emissions for the energy sector by 1.39%. Planning to replace lighting towers for lighting in mining areas at night using solar panel lighting towers can only reduce 0.46% in 2051. Application of a combination program to replace generators as a source of electricity in mess, office, workshop, and warehouse areas as well as replacement of lighting B30-fueled towers as a source of lighting at night in the mining area can reduce GHG emissions the most among the two other scenarios, which is 1.85%. To reduce GHG emissions in the energy sector in large quantities at CK-KIM, it is necessary to implement energy management for mining equipment that falls into the category of road transportation and off-road transportation.

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26.4.2 Suggestions To complement the results of the research that has been carried out, it is recommended that further research be carried out on the potential for GHG emissions from road transportation and off-road transportation equipment. It is also recommended that research be conducted to analyze the consumption of B30 fuel oil in each type of equipment such as OHT, ADT, excavators, bulldozers, and other equipment related to the age of the equipment. In order to reduce GHG emissions in large numbers, CK-KIM Management is advised to carry out overall energy management for each equipment that has been identified as contributing to a large consumption of fuel oil and involves all departments in accordance with their respective authorities. Acknowledgements This research was made possible by funding from research grant number 023.17.1.690523/2022 provided by the Kemendikbud Ristek Republic of Indonesia. The authors would also like to thank the Faculty of Mathematics and Natural Science, and Postgraduate School, Pakuan University, Indonesia, for its support.

References 1. B. Arifiyanto, R.M. Sindu, in Prosiding Seminar Nasional Lahan Suboptimal ke-8, ed. By Dalam Siti Herlina et al. Pengurangan Emisi Gas Rumah Kaca dengan Penerapan E-Reporting System di Pertambangan PT Bukit Asam. Penerbit & Percetakan Universitas Sriwijaya, Palembang (2020) 2. D. Bogunovic, V. Kecojevic, V. Lund, M. Heger, P. Mongeon, Analysis of energy consumption in surface coal mining. Paper SME Publ. Dept. 326, 79–87 (2009) 3. T. Covert, M. Greenstone, C.R. Knittel Will we ever stop using fossil fuels? J. Econ. Perspect. 30(1), 117–138 (2016) 4. Directorate General of Climate Change Control of the Ministry of Environment and Forestry, Report on Inventory of Greenhouse Gas (GHG) Emissions and Monitoring, Reporting, Verification (MPV) 2020. Director General of Climate Change Control of the Ministry of Environment and Forestry, Jakarta (2021) 5. Kementerian Lingkungan Hidup dan Kehutanan, Pedoman Penyelenggaraan Inventarisasi Gas Rumah Kaca Nasional Buku II-Volume 1 Metodologi Penghitungan Tingkat Emisi Gas Rumah Kaca Kegiatan Pengadaan dan penggunaan Energi. KLH, Jakarta (2012) 6. Ministry of Environment and Forestry, Guidelines for Implementing a National Greenhouse Gas Inventory Book II-Volume 1 Methodology for Calculating Greenhouse Gas Emission Levels for Energy Procurement and Use Activities, pp. 1-152 (2012) 7. E.A. Muhammadi, B. Soesilo, Analisis Sistem Dinamis—Lingkungan Hidup, Sosial, Ekonomi, Manajemen (UMJ Press, Jakarta, 2001) 8. M. Muryani, Produksi Bersih dan Model Kerjasama Sebagai Upaya Mitigasi Emisi Gas Rumah Kaca pada Sektor Industri. Jurnal Sosiologi Dialletika, 13(1), 48–65 (2018) 9. S.M. Noor, S.L. Hafizianoor, Analysis of carbon stocks in plants reclamation of former coal mining land at PT. Indobara Borneo. J. Tropical Forests. 8(1), 99–108 (2020) 10. T. Noorgate, N. Haque, Energy and greenhouse gas impacts of mining and mineral processing operations. J. Clean. Prod. 18(3), 266–274 (2010) 11. Peraturan Menteri Lingkungan Hidup dan kehutanan Nomor P73 tahun 2017 Tentang Pedoman Penyelenggaraan dan Pelaporan Inventarisasi Gas Rumah Kaca Nasional.

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12. Pusat Pengkajian Industri Proses dan Energi (PPIPE), Outlook Energi Indonesia 2021 Perspektif Teknologi Energi Indonesia: Tenaga Surya untuk Penyediaan Energi Charging Station. PPIPE, Tangerang (2021) 13. The Intergovernmental Panel on Climate Change, 2006 IPCC Guidelines for National Greenhouse Gas Inventories Volume 2 Energi. The Institute for Global Environmental Strategies (IGES) on Behalf of the IPCC, Hayama (2006) 14. The Intergovernmental Panel on Climate Change, The Second Assessment Report of the Intergovernmental Panel on Climate Change. IPCC, Geneva (1995) 15. A. Tosiani, Carbon Absorption and Emission Activity Book, pp. 1–41 16. A. Tossiani, Buku Kegiatan Serapan dan Emisi Karbon. Dirjen Planologi Kehutanan dan Tata Lingkungan KLHK, Jakarta (2015) 17. D. Waliyan, Good Mining Practice Dengan Sistem Online Sebagai Support Penerapan Tambang Yang Elegan di Sinarmas Mining Site Kuansing Inti Makmur, Muaro Bungo, Jambi. Dalam Prosiding Temu Profesi Tahuan XXVIII PERHAPI, 1(1), 211–224, PERHAPI, Lombok(2019)

Chapter 27

The Influence of Fibre Feeder Speed and Stacking Layers on Physical Properties of Needle-Punched Nonwovens from Industrial Cotton Waste Siti Nor Hawanis Husain, Azrin Hani Abdul Rashid , Abdussalam Al-Hakimi Mohd Tahir, Muhammad Farid Shaari, Siti Hana Nasir, Siti Aida Ibrahim, Khairani Nasir, Ngoi Pik Kuan, and Mohd Fathullah Ghazli

Abstract Cotton is one of the most used fibres in the world of textile, and due to fast fashion phenomena, lots of waste have been produced by the industries. Hence, with the aim to reduce industrial cotton waste, mechanical recycling method was chosen in order to turn cotton waste into a value-added product. This paper reported an analysis of different machine parameters to control the physical properties of the nonwoven web produced from industrial cotton fabric wastes. The fabric wastes are recycled mechanically and turned into a continuous nonwoven web using the needle punching machine. An experiment with a full factorial design was conducted in this study to understand the interaction between more than one factor, specifically the fibre feeder speed and stacking layer. In this study, the speed of fibre feeders (8, 10 and 12 ft/min) and stacking layers (four, five and six layers) were investigated over three stages. To determine the significant factors that can influence the physical properties of the nonwoven web, the analysis of variance was employed (ANOVA). The nonwoven web produced underwent physical testing such as density, thickness and porosity. The difference in fibre feeder speed and stacking layer significantly affected both web thickness and density. Porosity, however, was only affected by S. N. H. Husain · A. H. Abdul Rashid (B) · A. A.-H. Mohd Tahir · M. F. Shaari · S. H. Nasir · S. A. Ibrahim · K. Nasir Faculty of Engineering Technology, Universiti Tun Hussein Onn Malaysia, Pagoh Higher Education Hub, 84600 Pagoh, Muar, Johor, Malaysia e-mail: [email protected] N. P. Kuan Eadeco Sdn. Bhd., Plot 15, Persiaran Perindustrian Kanthan 1, Kanthan, 31200 Chemor, Perak, Malaysia M. F. Ghazli Faculty of Mechanical and Green Technology (FKTM), Centre of Excellence Geopolymer and Green Technology (CEGeoGTech), Pauh Putra Campus, 02600 Arau, Perlis, Malaysia © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Mustapha et al. (eds.), Proceedings of the 8th International Conference on the Applications of Science and Mathematics, Springer Proceedings in Physics 294, https://doi.org/10.1007/978-981-99-2850-7_27

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fibre feeder speed. Higher fibre feeder speed and higher stacking number produced a thicker and denser web. The less dense and less thick web also had a higher porosity percentage.

27.1 Introduction Fibres and fabrics have always played an essential role in human activity including providing protections against cold or hot weather to being the one of the most important economic sources to countries like India, Pakistan, China and Malaysia. With the ongoing improvement in living standards, global population growth has steadily increased global fibre consumption [1, 2]. Clothing is made of cotton and is worn to cover the body, protect it from adverse weather conditions and keep up with trends and fashions. The fabrics are also used for clothes, pillows, rugs, carpets, tablecloths, armchairs, sofas and curtains in every house [3–5]. In 2019, around 111 million metric tonnes of chemicals and textile fibres were produced, representing a more than twofold increase over the previous 20 years. The situation is deteriorating, with preliminary COVID-19 predictions indicating that the global fibre supply might increase to 146 million metric tonnes by 2030 [6, 7]. It is estimated that around 98% of all future fibres will be synthetic, 95% of which is expected to be polyester [8]. As the demand for fabrics has increased, concerns about the environmental impact of fibre production and subsequent disposal operations have become more prominent. The fabrics waste commonly disposed into landfill, this results in higher amounts of the fabric waste in the landfills and more land reserve need to be used for this purpose. Cotton fibres have historically been the most preferred material for clothing and apparel due to their low cost and availability. Cotton shirts are preferred over other materials in hot and humid countries such as Malaysia. Fabrics made of cotton have a variety of advantages, including biodegradability and ease of design and production textiles [9, 10]. The production of textiles has increased as the demand has grown annually. It was recorded that the global fibre supply has increased from 87 to 240 million tonnes by the year of 2050 [11]. Fibre waste is increasing as a result of increased consumption and industrial production. Textiles used as clothing are discarded rapidly in the developed nations, often before they are even worn out. Clothing is either discarded as municipal waste or repurposed in a second-hand clothing market, resulting in indirect production of post-consumer waste [12, 13]. Textile post-consumer waste sometimes referred to as “dirty waste” is collected along with household items, including both natural and synthetic fibres, such as wool, silk, rayon, woven nylon, cotton, polyester and other materials [14]. As a result of the “fast fashion” phenomenon, which describes the high-volume production of lowcost clothing, it has been enormously influential on the change in fashion trends [15, 16]. Textile manufacturing generates significant amounts of waste in addition to postconsumer waste. The waste includes scraps of fibres, yarns and textile scraps, such as

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yarn, fabric, or cloth made by spinning, weaving, or knitting [12, 17]. The production of textile products creates a lot of waste, which is often disposed of in landfills or recycled for energy recovery purposes [18]. Post-consumer waste is not as diverse as post-industrial waste and can be recycled into similar or different products more easily. Many years have passed since the textile waste was disposed of in landfills without being treated. Even so, landfill dumps remain a popular way to manage solid wastes due to their simplicity and cost-effectiveness over recycling waste [19]. It is evident from landfill dumps that the wastes problem is not going away any time soon. Textile recycling involves converting waste into a valuable raw material that serves the same purpose as the original products, garment or household items such as carpets. The reuse and recycling of discarded textiles have several potential environmental benefits [18]. Recycling textiles is a process that creates employment, eliminates landfill waste and provides clothing for the poor [20]. Primary waste, secondary waste, tertiary waste and quaternary waste are the four main ways to recycle waste [12]. Primary recycling is the direct reuse of scrap materials by recycling plants. Mechanical treatment and melt processing are examples of secondary recycling. Defibrillation occurs when textile products undergo cutting, shredding, carding and other mechanical processes [21–23]. The fibrous material obtained by defibrillation is used to produce yarns, nonwoven and other textiles, insulation and roofing felt, carpet components and lower-quality blankets [24]. Chemical processes such as pyrolysis and hydrolysis are used in tertiary recycling which is only suitable for polymer base fibres due to its recycling method will produce microsize fibre which is not suitable for short staples fibres like cotton. Tertiary recycling is often used for textiles made from synthetic fibres, mainly polyamide 6 and polyethylene terephthalate [25]. Quaternary recycling involves burning fibrous solid waste for energy [15, 26]. Thus, this research aims to investigate the physical properties of the nonwoven cotton waste web subjected to two different varied parameters, namely the fibre feeder speed and stacking layers. The nonwoven cotton waste webs were prepared using the needle punching machine with three different types of fibre feeder speed. After that, the nonwoven webs were manually stacked up to six layers and be fed through the needle bed for the second punching process.

27.2 Materials and Methods 27.2.1 Materials The cotton fabric wastes were sourced from Golden Gate Technologies Sdn. Bhd (Melaka, Malaysia). Fabric wastes had been defibrillated, converting them into fibres ready to be fed into the nonwoven needle punching machine (Model DILO YYKS). This machine consists of an opener, hopper, carding and needle punch unit.

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Fig. 27.1 a Fabric wastes undergo opening process; b hopping and carding process; c needle punching process

27.2.2 Web Processing The nonwoven needle punching machine was used to produce the nonwoven cotton waste web. The method involves the penetration of barbed felting needles through a carded web of fibres to produce nonwovens. By mechanically orienting and interlocking the fibres of the carded web, needle punching is achieved. Thousands of barbed felting needles repeatedly pass through and out of the web to achieve this interlocking. The ply of fibres is entangled with each other to form a continuous layer of the web. The machine consists of four minor parts, including an opening, a hopper, a carding mechanism and a needle punching mechanism. Figure 27.1 illustrates the entire process. Four, five and six layers of webs will undergo the repeated punching process.

27.2.3 Physical Test The thickness and the density of the nonwoven web were evaluated. The thickness of the web is measured by using the height gauge with a sensitivity of 0.01 cm.

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The weight of the web is measured using the weighing balance with a sensitivity of 0.001 g. An average of 10 readings for different speeds and layers were recorded. The web thicknesses were measured in centimetre (cm), and the web density was measured in gram per cubic centimetre (g/cm3). The porosity (E) was taken by measuring the size of the pore. The porosity (E) was calculated using the formula in (27.1). ε=

a1 + a2 + a3 am

(27.1)

where ε, is porosity (%); a1 , the first area of the pore; a2 , the second area of the pore; a3 , the third area of the pore; am , the marked area

27.2.4 Design of Experiment Studies of the effect of multiple factors were carried out using factorial design, which is thought to be one of the most effective methods. An effective and systematic approach is provided by this method, which includes all possible experiments. First, factors or parameters of the study need to be identified, followed by the levels at which they will be examined [27]. In this research, fibre feeder speed and stacking layer were examined. There are three different fibre feeder speeds (8, 10 and 12 ft/ min) and three different stacking layers (four, five and six layers). As a result, a 3 × 2 factorial design was used. Five tests were repeated to ensure that the results were not biased. An analysis of variance (ANOVA) was used to determine the significant effects of each factor and level. A p-value of less than 0.05 is considered significant [28]. In order to reduce the possibility of nuisance factors affecting the experiment, Minitab R.18 software was utilized and randomization was activated. Table 27.1 presents the sample’s coding and formulation. Table 27.1 Samples coding and formulation

Sample’s coding

Formulation

S84L

4 webs layered at 8 ft/min speed

S85L

5 webs layered at 8 ft/min speed

S86L

6 webs layered at 8 ft/min speed

S104L

4 webs layered at 10 ft/min speed

S105L

5 webs layered at 10 ft/min speed

S106L

6 webs layered at 10 ft/min speed

S124L

4 webs layered at 12 ft/min speed

S125L

5 webs layered at 12 ft/min speed

S126L

6 webs layered at 12 ft/min speed

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27.3 Results and Discussion The mean grouping is analysed using the ANOVA. The statistical analysis (ANOVA) results for the physical properties tests are shown in Table 27.2 for the difference between the samples regarding web thickness, web density and porosity (%). The ANOVA results show that the fibre feeder speed does not influence the web thickness (p > 0.05). There were significant effects which are p-value less than 0.05 from the stacking layer on the web thickness and interactions between factors. Six layers of stacking were the most effective, according to the significant results, in producing a thick and compact cotton waste nonwoven web. This implies that due to their significant impact, the fibre feeder speed should also be taken into account when altering the stacking layer of the nonwoven web. The R2 value was 62%, indicating stable data with low levels of variability. The main effects plot of mean data and interaction plot are displayed in Fig. 27.2. The six stacking layers offered a thicker web than four and five layers. This is because of the increase in the number of layers. By increasing the speed of the fibre feeder and the number of stacking layers, the web thickness and mass per unit area also increased along with the number of fibres per unit area [29]. Table 27.2 ANOVA test for; (a) thickness; (b) web density; (c) porosity Source

df

SS

MS

F

p

(a) Thickness Fibre feeder speed

2

0.000164

0.000082

0.48

0.624

Stacking layer

2

0.004984

0.002442

14.18

0.000*

Fibre feeder speed × stacking layer

4

0.005316

0.001329

7.72

0.000*

Error

36

0.0062

0.000172

Total

44

0.016564

2

0.07555

0.037774

5.67

0.007*

(b) Web density Fibre feeder speed Stacking layer

2

0.48428

0.24214

36.32

0.000*

Fibre feeder speed × stacking layer

4

0.10713

0.026783

4.02

0.009*

Error

36

0.23998

0.006666

Total

44

0.90694 0.52

0.608

(c) Porosity (%) Fibre feeder speed

2

14.55

7.277

Stacking layer

2

70.76

35.378

2.46

0.100

Fibre feeder speed × stacking layer

4

88.01

22.003

1.53

0.215

Error

36

518.64

14.407

Total

44

691.96

df degree of freedom, SS sum of squares, MS mean square, F F-test, p p-value

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Fig. 27.2 Main effect plot for a thickness and b density and interaction plot for c thickness and d density

Nonwoven web density was significantly affected by the fibre feeder speed (p = 0.007) and stacking layer (p = 0.000). There was evidence of factor of interaction in the analysis (p = 0.009). The main effects and interaction plots of web density were displayed in Fig. 27.2b and d. High web density was found to be associated with fibre feeder speed of 10 ft/min. Increased in fibre feeder speed and stacking layer means more fibres been transferred to the needle punching process which resulted in more fibres per unit area being punched. Therefore, this condition increased the web thickness and web mass per unit area. The variation of the density was affected by both mass and thickness [30]. However, as the speed increased to 12 ft/min, the web density decreased gradually. This is due to the as the speed increases, more fibres are fed to the needle action area, resulting in a high possibility that more area of nonwoven web remains out of getting punched. Besides that, the overall density of the samples were affected by fibre density and packing density [31]. As the feeder speeds and number of stacking layers increased both mass and thickness were increased. Therefore, the web density value increased. During nonwoven web production, it is reported that machine parameters might have been responsible for excellent web thickness and density [32]. The repeated punching process with number of stacking layers will cause higher fibre entanglement which also resulted in the increment of the thickness and density. The ANOVA results for porosity, however, show that neither factor affected the response. As the mass increases, the fibres present also increase, resulting in smaller

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pores and a lower porosity value [20]. A higher percentage of porosity was found in samples with fewer layers, while higher numbers of layers reduced the size of the pore [33]. Layering will reduce the size of the pores in the web [34, 35]. It has been proven that this claim is correct. Because of the high amount of fibres in the material, the fibre-to-fibre bonding had become tighter, resulting in a smaller pore diameter (low percentage of porosity) [36]. Thus, this explained why the ANOVA results showed that an interaction between both factors still exists. The main effects plot Fig. 27.2a and b and interaction plot Fig. 27.2c and d were only displayed for the significant parameters. Figure 27.2b shows that the optimum speed to produce a thicker was the speed of 10 ft/min. When the speed is low (8 ft/ min), the nonwoven web will undergo a high punching per unit area. Multiple highspeed punches at the same spot caused the interlacing of single fibres to break. High fibre damage in the nonwoven has caused low entanglement between the fibres in the web. When there is higher fibre damage, the bonding between each of the fibres will break. Thus, the web becomes looser, and the distribution rate of fibre will be affected, resulting in a lower density at a higher speed [23]. Whereas, high fibre feeder speed (12 ft/min) has led more fibres to escape from needle punching process causing less consolidation of nonwoven web. In addition, six layers of stacking exhibited a thicker and denser web structure when the number of layers increased. Based on Fig. 27.2c and d, it can be seen that five web layers at fibre feeder speed of 10 ft/min (S105L) produced the highest mean of thickness, whereas six web layers at 10 ft/min (S106L) produced the highest mean of density. The speed of 10 ft/min can be used with the number of stacking layers up to five layers to increase the thickness of the web as the results proved that it was the optimum speed to produce a nonwoven cotton waste web. Further increase in the number of stacking layer using this fibre feeder speed will cause the thickness reduction due to fibre shift during needle punching process. During the needle punching process, fibres move from the unbonded area to the interior of the batt, causing a phenomenon known as “fibre shifts” [37, 38]. Because of this, there are fewer fibres present in the area that has not been bonded, which leads to a thin nonwoven web being produced. Regardless of the speed used, the higher the number of stacking layers, the higher the density of the web structure.

27.4 Conclusions The study examined the effects of processing parameters, fibre feeder speed and stacking layer on the physical properties of the cotton waste nonwoven web. This study successfully prepared the nonwoven web using cotton waste via the nonwoven needle punching method. According to the test results, the processing parameters of fabrics influence their physical properties. Both fibre feeder speed and stacking layer were statistically significant (p < 0.05) on the web density. An increase in stacking layers resulted in a thicker and denser web. The optimum number of layers to get a thicker and denser web was 6, while the optimum speed was 10 ft/min.

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Chapter 28

Exploring Cultural Learning with Vertical Chatbot: Korda Vinothini Kasinathan, Aida Mustapha, Neekita Sewnundun, Diong Jien Bing, Lee Khoon Fang, and Cindy Koh Xin Yi

Abstract Cultural heritage is the tangible and tacit legacy of attributes of society inherited from past generations. Its preservation relies on the memory of communities and individuals, hence limiting it from widespread access. To address this issue, this paper proposes the use of a vertical chatbot that serves as the conversational interface between the general public and the expert knowledge. The chatbot is called Korda that focuses on the lost heritage of a traditional dance in Malaysia; the Kuda Kepang. The prototype of Korda is developed on the Chatfuel framework and published as a Messager bot. User acceptance testing of Korda indicated positive feedback due to lack of prior knowledge in the cultural dance. Korda is hoped to promote access to and enjoyment of cultural diversity in Johor, Malaysia, in particular the Kuda Kepang.

28.1 Introduction Cultural heritage is an important attribute which if preserved and disseminated can encourage the sharing of knowledge, values, history as well as increasing the awareness in respect to different cultures and practices. One particular cultural heritage in Malaysia is Kuda Kepang, which is a dance originated from the Javanese culture in Johor, mostly into the sub-regions of Batu Pahat and Muar [1]. Kuda Kepang is a dance which commemorates the history of when one of the nine saints of Java called “Wali Songo” who rode on his horse by imparting his knowledge on different battles’ stories while gaining the attention of multiple congregations. Hence, the dance depicts the horseman through the visualization of a masked dancer followed V. Kasinathan (B) · N. Sewnundun · D. J. Bing · L. K. Fang · C. K. X. Yi School of Computing and Technology, Asia Pacific University, Jalan Teknologi 5, Taman Teknologi Malaysia, 57000 Kuala Lumpur, Malaysia e-mail: [email protected] A. Mustapha Faculty of Applied Sciences and Technology, Universiti Tun Hussein Malaysia, KM1 Jalan Pagoh, 84600 Pagoh, Johor, Malaysia © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Mustapha et al. (eds.), Proceedings of the 8th International Conference on the Applications of Science and Mathematics, Springer Proceedings in Physics 294, https://doi.org/10.1007/978-981-99-2850-7_28

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by other dancers who portray the tigers and snakes on the stream of rich sounds from the Gamelan instruments such as gong, gendang, and kenong [2]. It is point worthy that although with such a huge cultural aspect down the ages, this form of dance is losing popularity and is rarely being practiced and as such with the coming years, this traditional art form might become obsolete. The sudden declination over the past years might have been pushed by the ban by the Johor Fatwa Committee, which forbid Muslims to engage into arts as the latter contradicts Islamic faith [3]. This statement has since then been counterfeited by multiple researchers such as [4], who emphasizes that the artform dance Kuda Kepang contributes to the religion as a dynamic force. Since then, in many rural areas, the dance is no more considered as illegitimate but rather a cultural heritage which requires to be preserved and practiced before it hits extinction. The importance of having systems that can impart knowledge and educate people about the Kuda Kepang lies in the inability of modern people trying to understand and perceive the dance as a modern art, instead it is more than a song and a dance as it is the medium embedding a whole belief system providing insights on history and diversity. In order to promote Malaysian cultural heritage, this paper describes the development of a cultural chatbot for Kuda Kepang called Korda. It is designed to serve as an educational platform in which users can learn more about the artform and the knowledge can be passed on through an interactive and navigational surface. The remainder of this paper is organized into the related works in cultural chatbots in Sect. 28.2, methodology and prototype in Sect. 28.3, Korda evaluation results in Sect. 28.4, and conclusions as well as future works in Sect. 28.5.

28.2 Related Work The field of artificial intelligence (AI) provides a platform to promote this information sharing or knowledge transfer process to the general public via chatbots or conversational agents. A chatbot (chatting robot) is a computer system that allows human to interact with computers using natural language [5]. There are multiple cultural chatbots and chatbots which have been developed around the world with the goal of sharing cultures such as the storyteller chatbot by [6] that supports touristic experiences. A chatbot by [7] aids cultural education by capitalizing the natural language processing (NLP) and inferential approaches to impart knowledge about archaeological parks of cities such as Herculaneum, Paestum and Pompei in Italy. The importance of culture education has gained much insights which even gave foundation to culture chatbot development platform such as the culture chatbot [8]. This initiative includes the development of multiple cultural chatbots, firstly for the Jewish Historical Museum in Amsterdam for sharing of knowledge based on the museum’s collections and exhibitions as well as a Facebook deployed bot for the Polin Museum that is focused on the cultural education of the history of Polish Jews.

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28.3 Methodology Korda is developed using an online tool called Chatfuel [9]. Chatfuel is an online platform that allows users to build chatbot for Facebook Messenger via an easy-touse visual interface. The interaction between natural language input to the natural language output in Chatfuel works through the design of the message flows and is governed by the conversational rules. Figure 28.1 shows the main menu block for natural language interaction in Chatfuel. The natural language algorithm used in Chatfuel is template-based, where each utterance includes a slot and an intent. For example, based on Fig. 28.1, the intent

Fig. 28.1 Main menu block of Korda in chatfuel

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in the main menu is to get the user to choose a navigation option from Origins, Occasions, and Performance. Note that the greeting has a name slot to it: Sure, {{first name}}. Here you go! Each query must have some parameters. In the greeting example, the system needs to know user’s name. This parameter is called slot. Assuming the user chooses the Performance menu, the answer of “I want to proceed with” is save to the {{performance_selection}} in the Performance block. Similar to the Occasion block, the answers collected from the user will be saved in the {{afterfinish-performance}} block. Next, Fig. 28.2 shows the knowledge base of Korda. Based on this figure, it is shown that the intent Kuda Kepang is connected to other intents such as actors, instruments, dancers, and occasions. Figure 28.3 shows Korda’s interface on the Messenger application. The Facebook Messenger in Chatfuel begins a conversation when the user clicks on the Get Started button. Korda begins by greeting the user and offers options to proceed with the conversation. The option includes choosing topics, which are Malaysia’s cultural dance and history of Kuda Kepang. As shown in Fig. 28.4, the selection buttons allow the user to get the better understanding on the topic selected. Meanwhile, selections buttons avoid the user from getting bored due to the long paragraph of the explanation. It allows the explanation on the selected topics to be

Fig. 28.2 Knowledge base of Korda

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Fig. 28.3 Interface of Korda

separated into small section while reduce the chance of getting confused on the contents of the topics. For example, by clicking explore more button on the topic of Malaysia Cultural Dance, only the content of the Malaysia’s culture Dance will be shown for the reference. In addition, instead of having endless chat messages that might confuse the user, the seven instruments are listed in the form of gallery with the attractive pictures and short explanation on the instruments are provided as shown in Fig. 28.5. The engaging pictures allow the user to stay focused in the conversation, and the short description of the pictures allows the user to have better understanding on the pictures. Finally, the words that are related to ending the conversation are added as the keyword for activate the ending block. Once the keyword is entered by the user, the ending block will be activated and the conversation between the chatbot and user will be ended. This feature facilities user as the user can end the conversation at any time by entering the related keywords.

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Fig. 28.4 Screenshots of choice selection and responses by Korda

Fig. 28.5 Gallery of the instruments in Kuda Kepang

28.4 Evaluations The prototype of Korda is evaluated via questionnaire survey as the user acceptance test. The purpose to conduct this survey is to understand the influences of Korda chatbot on the users. Thirty users aging 18 and above are selected to be involved in the survey for getting the satisfaction level of the users on the chatbot. There are five questions provided in the survey. The first question, fourth question, and fifth question are set with yes–no question. The Likert-scale questionnaire is set for both

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Fig. 28.6 Question 1: Do you have a knowledge of Kuda Kepang?

second and third questions by providing five levels of grades, starting extremely hard and extremely easy. The questions are set as follows: • • • • •

Question 1: Do you have a knowledge of Kuda Kepang? Question 2: Does Korda easy to use? Question 3: Does Korda provide sufficient information? Question 4: Can Korda advocate teaching and understanding of Kuda Kepang? Question 5: Are you interested in learning more of Kuda Kepang?

Figure 28.6 shows the user responses for Question 1. Based on the figure, 60.0% of the responses shows that they have no knowledge on Kuda Kepang. This result shows that most of the users do not have the experience or understand what Kuda Kepang is before until using Korda chatbot. This shows that the Korda chatbot plays the important role of being the introducing the cultural dance of Kuda Kepang to the people while protecting the Kuda Kepang from facing the dangerous of being forgotten. Figure 28.7 shows the responses on Korda’s usability. The figure shows that Korda chatbot receive the highest selection for scale 4. 63.4% of the responses had claimed that Korda chatbot is easy to use, 16.7% of the response stated that Korda chatbot has the moderate score in the field of easy to use while 20% of the response stated that Korda chatbot is difficult to use. Figure 28.8 shows the responses to whether Korda provides sufficient information on Kuda Kepang. The results show that most responses were satisfied with the chatbot on explaining about the history and background of Kuda Kepang. 53.3% of the responses had claimed that Korda chatbot provides the satisfied explanation on the history and background of Kuda Kepang, 23.3% of the response stated that Korda chatbot has the moderate score in explaining the history and background, while 23.4% of the response stated that Korda chatbot does not provide the satisfied answer in explaining the history and background of Kuda Kepang.

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Fig. 28.7 Question 2: Does Korda easy to use?

Fig. 28.8 Question 3: Does Korda provides sufficient information?

Figure 28.9 shows the responses on the possibility of Korda in becoming the advocate of teaching and understanding of Kuda Kepang. Based on the figure, there are 66.7% of the responses claimed that Korda chatbot does advocate the presence of Kuda Kepang. However, 33.3% of the responses were against the others 66.7% of the responses by claiming that Korda chatbot cannot advocate the presence of Kuda Kepang. Finally, Fig. 28.10 shows the responses for user interest in learning Kuda Kepang using Korda. The figure concluded that most of the responses are willing to learn Kuda Kepang dance in a score of 68.3%. Meanwhile, there are some of the responses are not interested on learning Kuda Kepang, which has the score of 36.7%. Overall, the user acceptance testing provides base feedback for Korda. These feedbacks are important in improving the prototype.

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Fig. 28.9 Question 4: Can Korda advocate teaching and understanding of Kuda Kepang?

Fig. 28.10 Question 5: Are you interested in learning more of Kuda Kepang?

28.5 Conclusions This paper reported the development of a domain-specific, vertical chatbot called Korda that is designed to provide information on the Kuda Kepang cultural dance. Conversation structure in Korda is topic-based, which includes the origin of Kuda Kepang, the performance of Kuda Kepang, and the occasions when the Kuda Kepang is performed. However, few improvements can be implemented into the chatbot for providing better user experience in the future. In this attempt, Korda has successfully bridged the benefits of simple investigation of Kuda Kepang but is not suitable for getting deep understanding on Kuda Kepang. More knowledge of Kuda Kepang should be included in Korda along with capability of self-learning through its own interactions with users. Overall, Korda has served its purpose as an alternative platform for understanding and learning cultural heritage.

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References 1. S.I. Ahmad, in Proceedings of the 4th Symposium: The ICTM Study Group on Performing Arts of Southeast Asia. The Practice of “Kejawen” in Kuda Kepang Dance (2017), pp. 160–164 2. Pusaka Homepage, https://www.pusaka.org/communities-kuda-kepang. Accessed 19 Aug 2022 3. A.A. Shuaib, R.I.R. Halid, The Search for the Middle Path: Islam and the Tradisional Malay Performings Arts (2011) 4. M.G. Nasuruddin, in Procedia—Social and Behavioral Sciences, vol. 185. Healing Through Trance: Case Study of a Kuda Kepang Performance in Batu Pahat, Johor (2015), pp. 151–155 5. A.S. Lokman, M.A. Ameedeen, in Proceedings of the Future Technologies Conference. Modern Chatbot Systems: A Technical Review (Springer, Cham, 2018), pp. 1012–1023 6. M. Casillo, F. Clarizia, G. D’Aniello, M. De Santo, M. Lombardi, D. Santaniello, CHAT-bot: a cultural heritage aware teller-bot for supporting touristic experiences. Pattern Recogn. Lett. 131, 234–243 (2020) 7. F. Amato, M. Casillo, F. Colace, M. De Santo, M. Lombardi, D. Santaniello, in 2019 IEEE International Conference on Engineering, Technology and Education (TALE). Chat: A Cultural Heritage Adaptive Tutor (IEEE, 2019), pp. 1–5 8. Multilingual Europeana Chatbot Project, https://culturebot.eu/. Accessed 19 Aug 2022 9. Chatfuel, https://chatfuel.com/. Accessed 19 Aug 2022

Chapter 29

Robot Model to Identify the Quality of Air Indoor Area Based on Internet of Things (IoT) Asep Denih , Irma Anggraeni , and Ema Kurnia

Abstract The air quality is one of the environmental components that need to be maintained in order to provide support for living things optimally. The air can be grouped into outdoor air and indoor air. Indoor air quality plays an important role in human health, and the reason is almost 90% of human life which is indoors. As many as 400–500 million people are facing with the problem of indoor air pollution, especially in developing countries. There are several components of indoor air chemical quality including volatile organic compound (VOC), carbon dioxide (CO2 ), and cigarette smoke. There are six sources of pollution in the room, such as lack of air ventilation, contamination in the room, contamination from outdoors, microbes, building materials. In this case, ventilation disturbance becomes the main problem of indoor air quality. In order to identify the air quality of indoor area, the technology of Internet of things model was used to implement in a robot. Hardware programming and fuzzy logic method are used to enhance the robot capabilities in tracing the rooms, detecting walls or object and also to identify the air quality. The result showed that the air quality output reached 94.44% of the actual air quality.

29.1 Introduction Disruption of air ventilation causes differences in the distribution and pressure of air in the room so that harmful gases can spread with different concentrations depending on the distance from the source. Given the nature of air moving from one point to another by the difference in pressure. In addition, gas particles will move from high concentrations to lower concentrations [1]. From these differences in distribution

A. Denih (B) · I. Anggraeni Department of Computer Science, University of Pakuan, Bogor City 16129, Indonesia e-mail: [email protected] E. Kurnia Department of Informatics Management, University of Pakuan, Bogor City 16129, Indonesia © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Mustapha et al. (eds.), Proceedings of the 8th International Conference on the Applications of Science and Mathematics, Springer Proceedings in Physics 294, https://doi.org/10.1007/978-981-99-2850-7_29

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and concentration, measuring air at one point will reduce the accuracy of information. This study aims to identify the quality of air indoor area based on Internet of things (IoT) implemented by using robot, and this approach leverages the current convergence of IoT technologies and robotic devices to enhance robotic capabilities [2]. The scope of this research includes trace rooms detecting walls and objects. Robot can detect air quality including CO2 , VOCs, and cigarette smoke. The robot can transmit information over an Internet connection. The room to be tested by the robot is a room model of 130 cm × 90 cm with a wall height of 30 cm. In addition, the benefits of research are to map a room and to find out harmful gas points in the room area. The following are the minimum requirements for indoor air chemical quality according to the regulation of the Minister of Health of the Republic of Indonesia number 1077/MENKES/PER/V/2011 concerning guidelines for air health in the space of the house [3] as shown in Table 29.1 as follows. The initial stage of collecting data on air pollution parameters needs to be done in the location mapping. The results of this mapping were the input to determine the point’s collection and air measurement [4]. To facilitate the data collection, robotics technology can be used as a tool for mapping as well as measuring air quality, one of which is robot mapping. Robot mapping is one type of robot that has several integrated modules so that the robot can work effectively as mapping, localization, exploration, path planning, and collision avoidance in an unknown environment [5] (Fig. 29.1). IoT is any device connected to the Internet so that it can communicate with other devices. IoT is also a network of connected devices, and each device has a different Table 29.1 Air health in the space of the house No

Parameter type

1

Carbon dioxide (CO2 )

ppm

1000

8h

2

Volatile organic compound (VOC)

ppb

3

8h

3

Environmental tobacco smoke (ETS)/cigarette smoke

µg/m3

35

24 h

4

Temperature

°C

10–30

–

5

Humidity

%Rh

40–60

–

Fig. 29.1 Result of robot mapping

Unit

Level max

Status

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389

IP address. Internet technology provides convenience, one of which is in the field of air pollution monitoring [6, 7].

29.2 Materials and Methods The research stage applied to this research is to utilize the hardware programming research method as shown in Fig. 29.2. START

A

B

PROJECT PLANNING

SOFTWARE DESIGN

MECHANICAL DESIGN

RESEARCH

SOFTWARE IMPLEMENTATION

MECHANICAL IMPLEMENTATION

ELECTRICAL DESIGN

SOFTWARE TESTING

INTEGRATION

COMPONENT PROCUREMENT

TESTING SUCCESSFUL?

NO

OVERALL TESTING

YES PART TESTING

B

TESTING SUCCESSFUL? YES

TESTING SUCCESSFUL?

NO APPLICATION

YES

ELECTRICAL IMPLEMENTATION

A

Fig. 29.2 Research flowchart

END

NO

390 Fig. 29.3 Project planning

A. Denih et al. Sensor Navigasi Sensor VL530X Sensor MPU6050

Mikrokontroler ESP32

Web Server

Sensor Gas Sensor MQ-2 Sensor SGP30 Sensor DHT11

Aktuator Driver

Motor Stepper

29.2.1 Project Planning The project planning stage is the stage of selecting materials utilized in research both from hardware and software. The hardware components needed are the ESP32 microcontroller [8], MPU6050 sensor [9], vl53l0x distance sensor [10], SGP30 gas sensor [11], MQ-2 smoke sensor, DHT11 temperature sensor, stepper motor actuator, 3 s 1600 mAh lipo battery power supply. In addition, the software components used include Visual Studio Code, Processing IDE, Git, Solidworks, Kicad, Ms. Office, Visio, Chrome Browser, and libraries needed to make it easier to create robots [12], the design can be seen in Fig. 29.3.

29.2.2 Electrical Design Electronic design uses the help of Kicad software to make it easier to connect some cables, in order to reduce errors in the cable connection process. The power supply used by the robot was a 12 V-voltage lipo battery [14, 15] can be seen in Fig. 29.4.

29.2.3 Part Testing At this stage, all components that will be used in this system model are tested. In this test, component function testing is carried out using a multimeter. Then test using the platform IO serial monitor by looking at the output of each component.

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Fig. 29.4 Electrical design

29.2.4 Software Design The software design used in this study used Visual Studio Code, Processing IDE, Git, Visio, Chrome Browser. Software design is divided into two, as the following software on robots and software on web clients. Figure 29.5 shows the flowchart of the entire system [16, 17].

29.2.5 Mechanical Design To make it easier in robot assembling, the mechanical system design utilizes SolidWorks 2019 assisted software. The robot has dimensions of 16.5 cm in height and 16 cm in diameter. The dimensions of the robot must be taken into account with the environmental conditions that the robot will pass through [13] (Fig. 29.6).

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Fig. 29.5 Overall system flowchart

Fig. 29.6 Mechanical design

29.3 Results and Discussion The implementation process is carried out by operating the robot in the room scale model that has been created. The model of the room is made as a square and carpeted as shown in Fig. 29.7. This is the integration of combination between hardware and software of the research.

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Fig. 29.7 Robot implementation

Fig. 29.8 Web user interface implémentation

The results of this study that the robot worked based on commands from the web client; furthermore, the robot also sent data to the web client that can be processed to determine the next commands as shown in Fig. 29.8. The point of the location sent by the robot to the Web site as the system information of geographic.

29.3.1 Overall Testing This test was carried out by trying the multiple paths of the circuit using a multimeter. The following table of system structural testing results can be seen in Table 29.2. Functional testing was carried out to determine the integration between the microcontroller, the sensor, and actuator. From the hardware side, it is ensured that the

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Table 29.2 Structural testing No

ESP32

Components

Ohm ()

Status

1

Pin I2C SCL

MPU6050, VL53L0X, SGP30 SCL

0.55

Good

2

Pin I2C SDA

MPU6050, VL53L0X, SGP30 SDA

0.57

Good

3

Pin 32

Motor 1 Step

0.60

Good

4

Pin 33

Motor 1 Dir

0.73

Good

5

Pin 25

Motor 2 Step

0.32

Good

6

Pin 26

Motor 2 Dir

0.44

Good

7

Pin 16

DHT11 D0

0.57

Good

8

Pin 39

Voltage divider battery

0.82

Good

Table 29.3 Functional testing No

Web UI commands

Robot activity

Status

1

Connect to IP Address 192.168.43.222

Robot connected, ready to execute commands

Appropriate

2

Send commands to robot

Receipt commands, parsing commands, and value

Appropriate

3

Forward command

Come forward

Appropriate

4

Turn command

Turn

Appropriate

5

Sensor calibration command

Sensor in calibration and calculation of sensor offset

Appropriate

6

Sensor read commands and air quality calculations

Wall scan, read gas sensor, send JSON Appropriate format data

actuator can move freely. In addition, from the software side, it is ensured that the program code has no errors. For software testing, CodeIgniter (CI) continuous integration services are used, i.e., Travis CI (TC) and GitHub Build. Some tests for the whole system are shown in Table 29.3 as follows. This stage was carried out with the aim of knowing how it works and functions whether it can run well in accordance with the calibration and calculations that have been applied.

29.3.2 Application of Robot Mapping Mapping robot testing was calculating the error of gas coordinate points, room dimensions, and the precision of the robot to return to the starting point or back home. In this section, the robot will look for the coordinates of the position to determine the condition of the gas in the room. According to the image of Fig. 29.9, on the left side is the actual path mapping for air quality detection in the location and the image

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Fig. 29.9 Mapping robot testing

on the right side is the result of mapping by a robot based on the coordinates for detecting gas. The validation testing found that the average error value for each coordinate position of the robot is around 4% and the average value of the accuracy reached the presentation around 96% of the actual coordinate position.

29.3.3 Wall Dimensions Wall dimension testing was carried out to determine the accuracy of mapping by the robot as shown in Fig. 29.10. The trial was carried out by calculating the difference between measurements in the actual room and the results of reading the robot’s coordinates through the website interface. The output map data on the web interface is still in the form of a 2D point cloud or dots, so a linear regression method is needed to find out which straight lines are assumed to be walls. Based on the data from the validation test, for wall dimension validation perform the accuracy of 94.61%. And for the error found that the average error generated was 5.39%. The error, it predicted caused by the sensor technology used in this research.

29.3.4 Back to the Early Point/Back Home Back home testing was carried out to find out the accuracy of the robot to return to the starting point or back home as shown in Table 29.4. In general, the robot can return to a predetermined starting point without losing its direction.

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Fig. 29.10 Wall dimension testing

Table 29.4 Back home testing

No Difference X (cm) Difference Y (cm) Distance to home (cm) 1

13

8

15.26

2

4.5

5

6.73

3

6

8

10.00

4

7

3

7.62

5

4

4.5

6.02

6

5

3

5.83

7

10

4

10.77

8

5

6

7.81

9

6

9

10.82

10

6

8

10.00

29.3.5 Air Quality Error In determining the air quality, the fuzzy method is an appropriate way to map the real input of space into a model output of space [18]. In this step, testing the application of Mamdani fuzzy logic for each sensor to determine the effect of sensor reading errors on the fuzzy logic process. The test is carried out by comparing the output of air quality which is influenced by each sensor at 12 different points. The following is a test comparison for the parameters of VOC, CO2 , smoke, temperature, and humidity as shown in Fig. 29.11. In addition to determining air quality, the Mamdani fuzzy logic calculation process can also anticipate errors in sensor readings on the robot. This is because in the fuzzification process the sensor reading value is converted into a predetermined membership degree. For more details can be seen in Table 29.5.

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Fig. 29.11 Air quality errors of various attributes Table 29.5 Error comparison No

Sensor

Average error without fuzzy (%)

Average error using fuzzy (%)

1

VOC

10.95

0.21

2

CO2

10.63

1.78

3

Smoke

11.68

2.25

4

Temperature

9.61

1.49

5

Humidity

4.46

3.84

9.47

1.92

Average

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In this study, it appeared that this application used fuzzy logic, it allowed to reduce the overall average error from 9.47 to 1.92 for all sensors. In addition to error testing by each sensor, error testing of all sensors is also carried out. This is done by comparing the air quality output from the robot and comparison sensors at 12 points in the location. The comparison of air quality output can be seen in Table 29.6. The data in Table 29.6 appeared to strengthen the results of the research conducted in detail of the performance validation and error value as previously described. It showed that fuzzy Mamdani decreased significantly of percentage error value as much as 7.55%.

29.4 Conclusion In this study, the indoor gas quality detection robot model can produce output and be presented by the web User Interface. However, the air quality output point still has errors with an average of 5.56% of the actual quality. The difference in error is influenced by sensor readings such as the VOC sensor, CO2 sensor, smoke sensor, temperature sensor, and humidity sensor. It means that the overall performance of the robot model reached into 94.44%. The effect of each sensor error on the Mamdani logic process appears that the application uses fuzzy logic will reduce the average error from 9.5 to 1.9 for all sensors. The mapping implementation on the robot has errors of gas coordinates X and Y average error around 4%, it means that the value of accuracy reached into around 96% of the actual coordinate position correspondingly. The wall dimension validation performs the accuracy of 94.61%, and for the error found that the average error generated was 5.39%. The difference is influenced by the displacement of the robot which has a sensitivity of 1 mm and the rotation/turning has a sensitivity of 1° at each command. In addition, the difference or error was also influenced by several factors including the accuracy of the distance and angle sensor readings so that there was a difference between the actual environment and the data presented. Each mapping performed requires a connection between the web UI and the robot, if the connection is lost then the robot will not receive the command and stop. Each data from the sensor will be encoded by the robot into JSON format and then sent to the web UI, any JSON data received by the web UI will be processed, recorded, and presented in the form of a folder. In addition, the data can be downloaded in the format of a .json file.

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Table 29.6 Validation of all sensors using fuzzy Mamdani Node

1

2

3

4

5

6

7

Sensor reading

Fuzzy output of air quality (%)

Difference (%)

Error (%)

Actual

Robot

Actual

Robot

VOC: 0

VOC: 0

57.95

55.05

2.90

5.00

CO2 : 380.23

CO2 : 400

Smoke: 11.55

Smoke: 11.89

Temp: 30.65

Temp: 32.2

Hum: 61.47

Hum: 58

VOC: 1

VOC: 1

48.25

48.66

0.41

0.85

CO2 : 390.26

CO2 : 439

Smoke: 12.32

Smoke: 13.25

Temp: 31.87

Temp: 33.3

Hum: 63.55

Hum: 62

VOC: 0,

VOC: 0

48.68

48.20

0.48

0.99

38.78

38.18

0.60

1.55

38.43

36.93

1.50

3.90

37.56

34.83

2.73

7.27

36.93

37.24

0.31

0.84

CO2 : 405.28

CO2 : 420

Smoke: 15.67

Smoke: 18.63

Temp: 31.06

Temp: 33.3

Hum: 63.23

Hum: 61

VOC: 12

VOC: 10

CO2 : 411.12

CO2 : 483

Smoke: 16.22

Smoke: 18.33

Temp: 30.44

Temp: 32.4

Hum: 64.22

Hum: 62

VOC: 14

VOC: 12

CO2 : 401.72

CO2 : 523

Smoke: 15.98

Smoke: 19.27

Temp: 28.32

Temp: 30.6

Hum: 62.54

Hum: 58

VOC: 9

VOC: 10

CO2 : 478.32

CO2 : 536

Smoke: 17.59

Smoke: 21.54

Temp: 29.45

Temp: 33.2

Hum: 63.26

Hum: 58

VOC: 7

VOC: 8

CO2 : 523.21

CO2 : 508

Smoke: 26.46

Smoke: 26.45

Temp: 28.56

Temp: 31.8

Hum: 61.59

Hum: 59 (continued)

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Table 29.6 (continued) Node

8

9

10

11

12

Sensor reading

Fuzzy output of air quality (%)

Difference (%)

Error (%)

Actual

Robot

Actual

Robot

VOC: 4

VOC: 3

30.11

31.81

1.70

5.65

CO2 : 719.48

CO2 : 671

Smoke: 24.75

Smoke: 25.77

Temp: 28.22

Temp: 31.7

Hum: 61.26

Hum: 58

VOC: 3

VOC: 3

34.94

37.87

2.93

8.39

CO2 : 578.71

CO2 : 493

Smoke: 28.5

Smoke: 29.45

Temp: 27.49,

Temp: 31.7

Hum: 62.91

Hum: 58

VOC: 2

VOC: 1

45.07

51.54

6.47

14.36

43.16

49.73

6.57

15.22

50.90

49.55

1.35

2.65

2.33

5.56

CO2 : 688.21

CO2 : 600

Smoke: 19.23

Smoke: 20.26

Temp: 26.07

Temp: 28.6

Hum: 62.39

Hum: 61

VOC: 0

VOC: 0

CO2 : 579.55

CO2 : 539

Smoke: 24.8

Smoke: 28.51

Temp: 26.36

Temp: 28.9

Hum: 62.89

Hum: 61

VOC: 0

VOC: 0

CO2 : 721.3

CO2 : 705

Smoke: 22.56

Smoke: 28.76

Temp: 26.45

Temp: 29.9

Hum: 61.22

Hum: 61

Average

References 1. H. Widyantara, M. Rivai, D. Purwanto, Gas source localization using an olfactory mobile robot equipped with wind direction sensor, in International Conference on Computer Enginering, Network and Intelegent Multimedia (CENIM), Surabaya Indonesia (2018) 2. Z. Iklima, T.M. Kadarina, Distributed path planning classification with web-based 3D visualization using deep neural network for internet of robotic things. J. Sci. Technol. 13(2), 47–53 (2021) 3. Departemen Kesehatan Republik Indonesia, Peraturan Menteri Kesehatan Republik Indonesia Nomor 1077/MENKES/PER/V/2011 tentang Pedoman Penyehatan Udara Dalam Ruang Rumah, Jakarta (2011)

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4. L. Vinet, A. Zhedanov, A ‘missing’ family of classical orthogonal polynomials. J. Phys. A Math. Theor. 44(8), 37–72 (2010). https://doi.org/10.1088/1751-8113/44/8/085201 5. X. Liu, X. Luo, X. Zhong, Research on simultaneous localization and mapping of indoor mobile robot. IOP Conf. Ser. J. Phys. Conf. Ser. 1074, 012099 (2018) 6. M.I. Suriansyah, P. Harsani, Air pollution monitoring for Bogor smart city based internet of things and social media (Twitter). IOP Conf. Ser. Mater. Sci. Eng. 621(2019), 012006 (2018) 7. E. Krogh,An Introduction to the Internet of Thinks (Bookboon, 2020) 8. N. Kolban, Kolban’s Book on ESP32 (Texas USA, 2018) 9. InvenSense Inc, MPU-6000 and MPU-6050 Product Specification Revision 3.4. Diakses pada 15 Maret 2021 melalui (2013). https://invensense.com 10. STMicroelectronics, VL53L0X World’s smallest Time-of-Flight ranging and gesture detection sensor Datasheet—production data. Diakses pada 17 Maret 2021 melalui (2018). https://www. st.com 11. Sensirion Gas Platform, Datasheet SGP30 Version 0.9. Diakses pada 20 Maret 2021 melalui (2017). https://sensirion.com 12. A. Najmurrokhman, K. Kusnandar, A. Amrulloh, Prototipe Pengendali Suhu Dan Kelembaban Untuk Cold Storage Menggunakan Mikrokontroler Atmega328 Dan Sensor DHT11. Jurnal Teknologi10(1) (2018). Universitas Muhammadiyah Jakarta 13. Syahrul, Motor Stepper: Teknologi, Metoda Dan Rangkaian Kontrol Majalah Ilmiah Unikom 6(2) (2021). Jurusan Teknik Komputer Universitas Komputer Indonesia Majalah Ilmiah Unikom © Unikom Center 14. A. Faisal, L. Son, Rancang Bangun Prototype Robot Pendeteksi Gas Metana Berbasis Mikrokontroler Arduino Untuk Eksplorasi Pertambangan. METAL: Jurnal Sistem Mekanik dan Termal 1(1), 1–8 (2017) 15. S.W. Zholeha, A.B. Pulungan, H. Hamdani, Sistem Monitoring Realtime Gas CO Pada Asap Rokok Berbasis Mikrokontroler. Program Studi Teknik Elektro Industri Jurusan Teknik Elektro, Universitas Negeri Padang (2019) 16. M. Aria, Real-time 2D mapping and localization algorithms for mobile robot applications. IOP Conf. Ser. Mater. Sci. Eng. (2019) 17. S. Pedduri, K.M. Krishna, Mobile Robots: Perception and Navigation, Multi Robotic Conflict Resolution by Cooperative Velocity and Direction Control (International Institute of Information Technology, Hyderabad, India, 2007) 18. E. Argarini Pratama, S. Fitriani, Penerapan Metode Fuzzy Inference System (Fis) Mamdani Dalam Penentuan Pemberian Reward Karyawan Bagian Produksi Pada Ikm Doctor Speed (2017), pp. 978–602

Part IV

Natural Sciences

Chapter 30

Onion Peel for Tinted Film Applications Siti Nursyakirah Idris and Siti Amira Othman

Abstract Usually, tinted film is made of polyethylene terephthalate (PET) as the main material. PET is excellent for manufacturing plastic films because it has a number of benefits, including the ability to act as an amorphous and semicrystalline material. Therefore, the objective of this study is to produce tinted film from PET and natural dyes. Then, to determine the light penetration rate of tinted film using lux meter as well as to evaluate the characterization of tinted film. Synthetic dyes, which are frequently used in the plastic manufacturing sector, will be substituted with natural colors from onion skin. PET film will be produced manually by melting and thinning without using a machine. It will also get the color from the dye extracted from the onion skin along with the glycerine. Natural dye extracted from onion skin is a good dye because consists of auxochrome groups, which are good for light absorption when shine onto it. Experiments conducted found that onion natural dye is able to reduce the penetration of light that penetrates it. By choosing natural dyes over other options, environmental sustainability can be maintained and reducing human reliance on toxic chemicals.

30.1 Introduction The use of tinted film on car mirrors or helmet visors is very commonly seen in any country. The main purpose of users choosing a tinted film is to filter or control the amount of sunlight especially that enters the vehicle or helmet. This is because the tinted film will give a darkening effect on the windows while providing good privacy for users. The degree of darkness for a tinted film can be measured as visible light transmission (VLT) [1]. The light intensity can rise as the percentage of VLT increases. As a result, visibility will gain.

S. N. Idris · S. A. Othman (B) Faculty of Applied Sciences and Technology, Universiti Tun Hussein Onn, Parit Raja, Malaysia e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Mustapha et al. (eds.), Proceedings of the 8th International Conference on the Applications of Science and Mathematics, Springer Proceedings in Physics 294, https://doi.org/10.1007/978-981-99-2850-7_30

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Regarding the effect of a tinted film that can darken the window, the use must be acceptable and following the road rules established by the respective national authorities. This is to ensure the welfare of all road users as well as to deter any potential criminal activity [2]. The tinted film is mostly made of polyester terephthalate (PET) due to its benefits. PET film, also known as polyester film, is a versatile plastic used in a wide range of applications, including packaging (e.g., food, pharmaceutical, health care, medical, industrial, and chemical packaging), electrical (photosensitive resistors, insulators, cable and wire wrap, capacitors, and circuits), and imaging (X-ray film, instant photographs) [3]. Over than 100,000 commercially accessible dyes are available, with over 7107 tons of dyestuff generated yearly across the world. Textile, food, cosmetics, and paper printing are among the industries that employ these dyes, with textiles being the main user [4]. Consumers are familiar with dye-colored window films since they have been available for a long time. New technologies quickly followed, bringing pigment-tinted films and a variety of other varieties into existence. Each offers its own set of benefits and applicability, allowing customers to pick the one that best suits their needs. Dyes and pigments are agents that give an item or material color. The particle size is the primary distinction between dyes and pigments. Because dyes are considerably finer than pigments, they could be affected by UV, while pigments are more UV resistant. As a result, UV rays are unable to degrade pigments. Environmental challenges linked with dyestuff manufacturing and application have risen dramatically over the last decade and are undeniably among the key driving forces influencing the textile dye business today [5]. Malaysia is located on the equator, with the lowest and highest temperatures of 23.1 °C and 35.7 °C, respectively. The stated temperature is in Peninsular Malaysia, and the reported temperatures are from the Malaysian Meteorological Department (Met Malaysia). Because of the constant recorded temperatures, road and highway users were obliged to install and utilize a covering or cover of the inside of their cars to ensure a smooth and comfortable ride to their destination. As a result, colored glass is an alternative to that inner layer of protection. However, the topic of tinted glass is often addressed at the moment. The usage of tinted glass has several advantages and problems. Taking into account the need for vehicle owners to use tinted film either on vehicle windows or on helmet visors, it is permissible based on established rules. The windscreen of a car can be tinted under Rule 5(1) of the Motor Vehicles (Prohibition of Certain Types of Glass Rules, 1991), although it must allow transmission of at least 70% visible light, while side windows, including rear glass, must enable 50% light transmission [6].

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Fig. 30.1 Onion skin

30.2 Methodology 30.2.1 Materials About 1 kg polyethylene terephthalate (PET) from Emory brand was purchased in the form of granules. The glycerine (300 ml) used is from the HmbG Chemicals brand. Acetic acid is a product of Bendosen and will be used as much as 10 ml. However, 1 kg of onion skins is obtained from household use waste (Fig. 30.1). Preparation of colorless Polyethylene Terephthalate (PET) film. PET granules have a very high melting point. It also dries and becomes hard in a very short time. PET is weight by placing 1.5 g of PET granules on parchment paper and heating it around ± 280 °C on a hotplate to produce colorless PET film (Fig. 30.2). Preparation of Onion as Natural Dye. As shown in Fig. 30.3, onion skin is placed in the beaker and a few drops of acetic acid is used to extract the dye from the onion skin. A magnetic stirrer is used to constantly stir the mixture. Leave for a while until the desired dye color is achieved. If the color produced is darker, more dark onion skins are needed. Then, filter the solution to separate the natural dye from the rest of the onion skin. The same step should be repeated at least twice by adding fresh onion skin into the resulting dye to get a darker color (Fig. 30.4). It is important to filter the dye that has been prepared using filter paper so that no fragments of onion skin are left. It is also at once to ensure the tinted film produced is clean of impurities. Fig. 30.2 a PET granules, b PET undergo melting process on hotplate

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Fig. 30.3 Process of making natural dye from onion skin

Fig. 30.4 Different color of dyes produced

Preparation of tinted PET film. A few amounts of dye from the onion peel were dropped on the PET granules as they begin to melt (Fig. 30.5). The amount of dye involved is 0.2 ml (A), 0.4 ml (B), and 0.6 ml (C). In addition, one sample that does not contain any dye as reference film (D) (Fig. 30.6). Wooden sticks are used to thin out the lump of granules PET. When the plastic thinning process is completed, the parchment paper is removed from the hotplate and make sure it is not rolled or folded to get the better results. Then, the paper will be removed from the plastic slowly and if it is difficult, it can be soaked briefly in water so that the paper can be easily removed. Lux Meter Test. The lux meter test is one of the measures that can be carried out to measure brightness in lux, fc, or cd/m2 (Fig. 30.7). Some lux meters, for the recording and saving of readings, have an inbuilt memory or data logger. The tinted film should be examined using a lux meter in open locations or where sunlight can

30 Onion Peel for Tinted Film Applications

409

Fig. 30.5 Tinted filmmaking process

Fig. 30.6 Resulting tinted film labeled with A, B, C, and D

penetrate the tinted film. This is because to ensure that if the tinted film is installed on the windshield and helmet visor, it has an accurate reading of the lux meter. There are four samples in all, and each sample is tested using a lux meter on a laboratory window that has natural lighting from outside. Lux meter readings were also taken in the absence of tinted film to see the difference in light penetrating the plastic of the film. Lux meter test performed took 30 s per sample to obtain average reading.

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Fig. 30.7 Lux meter test

30.3 Results and Discussion Tinted film samples were tested by being placed on a laboratory window glass that had a maximum light source. The darker a tinted film is, the lesser the number of the lux meter reading due to the less light that can penetrate it. The data obtained are recorded in table before being plotted on graph. Based on a study by Hwang et al. [7] conducted on dye-sensitized solar cells, when the concentration of the adsorbed dye was raised, the intensity of the penetrated light decreased, showing that the adsorbed dye inhibits light scattering and penetration. Light average is the lux meter reading for tinted film sample while background light average is the reading for lux meter test without tinted film sample. This aims to see the difference in the level of light penetration of all samples. Based on the data, it can be seen that the lux meter reading for tinted film A is lower when the mirror uses tinted film with an average reading of 12,604.25 lx. As for the background light reading, an average of 21,429.70 lx was recorded and this also shows that there is a difference of 8825.45 lx on average between mirrors with and without tinted film. Data for the other samples showed a similar trend where they all had lower lux meter readings when there was a tinted film that reduced the penetration of light into the interior of the laboratory. The average reading for tinted film B is 12,300.68 lx while the background light reading is 21,453.05 lx. A total of approximately 9152.37 lx of light can be reduced by penetrating the mirror when using tinted film B. Next, sample C shown the average lux meter reading is 12,205.60 lx while 24,355.05 lx for the background light. Thus, the average difference for the two values is 12,149.45 lx. To see the difference between PET film samples that contain

30 Onion Peel for Tinted Film Applications Table 30.1 Lux meter average readings for all film types

411

Type

Background light average (Lux)

Light average (Lux)

Light amount difference (Lux)

A

21,429.70

12,604.25

8825.45

B

21,453.05

12,300.68

9152.37

C

24,355.05

12,205.60

12,149.45

D

21,383.65

16,198.20

5185.45

natural dye and those that are not mixed with dye, the test on sample D found that there is a total of 5185.45 lx of light can be reduced using the plastic film. Tinted films A, B, and C contained different amounts of natural dye of 0.2 ml, 0.4 ml, and 0.6 ml, respectively. Thus, there is little difference in the amount of light that can penetrate the plastic film. This can be seen in Table 30.1 where the light amount difference in lux meter readings is higher for tinted film C which is 12,149.45 lx. As for tinted film A, the difference in lux meter reading is only 8825.45 lx because it has the lowest dye content during the manufacturing process. As for the D film, even though it does not contain dye, it can still reduce the amount of light penetrating the mirror by 5185.45 lx. Thus, the lux meter reading obtained shows the greater the amount of dye contained in the tinted film, the darker the color it has to reduce the amount of light that penetrates it (Fig. 30.8).

16198.20

Sample Types

D C

12205.60

B

12300.68

21383.65 24355.05 21453.05

12604.25

A

21429.70 0.00

5000.00

10000.00

15000.00

20000.00

25000.00

LUX Light Average (Lux)

Background Light Average (Lux)

Fig. 30.8 Graph of lux meter average readings for all film types

30000.00

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30.4 Conclusion A total of six types of analysis were conducted on tinted film samples for characterization. In line with the objective, tinted films were produced from PET pellets as well as using natural dye from onion skin. The lux meter test on the tinted film found that the tinted film produced can reduce the penetration of light that penetrates the mirror. The light average for all tinted films is 12,604.25 lx, 12,300.68 lx, 12,205.60 lx, and 16,198.20 lx, respectively, for PET film A to D. Acknowledgements The authors would like to thank the Faculty of Applied Sciences and Technology for facilities provided that make the research possible.

References 1. M.H.Md. Isa, M. Musa, M.K. Rahman, A.H. Ariffin, A. Hamzah, S. Solah, N.F. Soid, R. Ilyas, W.S. Voon, A study on automotive tint glazing in Malaysia, vol. 159. Research Report Malaysian Institute of Road Safety Research (2015), pp. 1–23. Retrieved from https://www.miros.gov.my 2. A.A. Mustaffa, H.N. Ahmad, M. Rohani, D. Basil, M.Y. Khairul Nizar, The studies on tinted glass usage factors among vehicle users in Malaysia, in Proceedings of Second International Conference—See 2016 Science, Engineering and Environment Osaka (The GEOMATE International Society, Japan, 2016), pp. 215–220 3. NIIR Board of Consultants and Engineers, Handbook on Pet Film and Sheets, Urethane Foams, Flexible Foams, Rigid Foams, Speciality Plastics, Stretch Blow Moulding, Injection Blow Moulding, Injection and Co-injection Preform Technologies, vol. 672 (Asia Pacific Business Press Inc., India, 2020) 4. S. Benkhaya, S. El Harfi, A. El-Harfi, Classifications, properties and applications of textile dyes: a review. Appl. J. Environ. Eng. Sci. 311–320 (2017). https://doi.org/10.48422/IMIST.PRSM/ ajees-v3i3.9681 5. N. Mathur, P. Bhatnagar, P. Bakre, Assessing mutagenicity of textile dyes from Pali (Rajasthan) using Ames bioassay. Appl. Ecol. Environ. Res. 4(1), 111–118 (2006). https://doi.org/10.15666/ aeer/0401_111118 6. The Star Online, JPJ-approved tinted film recommended. The Star (2012). Retrieved from https:/ /www.thestar.com.my/opinion/letters/2012/04/29/jpjapproved-tinted-film-recommended/ 7. K.-J. Hwang, J.-Y. Park, S. Jin, D.W. Cho, Light-penetration and light-scattering effects in dye-sensitized solar cells. New J. Chem. 12, 1–7 (2014). https://doi.org/10.1039/C4NJ01459F

Chapter 31

Optimization of Spinning Speed for Thin Layers Formation Using Spin Coating Technique Agus Ismangil and Asep Saepulrohman

Abstract Thin layer material is a material that has a thickness in the order of micrometers to nanometers. The spin coating method is a material coating technique by spreading the solution over the substrate and then rotating it at a constant speed to obtain a new, homogeneous layer. The result of the optimal thin layer thickness is that at 3000 rpm rotational speed produces a layer thickness of 4.45 nm, meaning that at 3000 rpm, the nanometer size is generally the size of the thin layer. The value of the viscosity coefficient at the optimal rotational speed is at a rotation speed of 3000 rpm, namely 1.84 × 10–6 Ns/m2 . The greater the rotational speed of the spin coating, the smaller the value of the viscosity coefficient will be and based on the graph obtained when the speed is greater, the thinner the layer that has been deposited through the spin coating will be.

31.1 Introduction The development of technology has an important role in every aspect of human life. Seeing the current human need for technology, it is necessary to develop technology to support human activities. One of the technological developments carried out by many researchers is the development of technology in the material field [1]. With the development of technology, especially in the field of materials, materials with new characteristics will be obtained according to the thickness and characteristics of the crystals. Technological developments in the material sector are closely related to the development of optoelectronic devices and electronic devices. Materials with new characteristics can be obtained using existing or under development methods. There have been many studies in the material field to grow materials, especially thin film materials. Thin film materials have been widely applied in various disciplines, such as in the field of mechanics, thin layer materials are used to increase corrosion resistance A. Ismangil (B) · A. Saepulrohman Department of Computer Science, Faculty Mathematics and Natural Science, Pakuan University, Bogor 16144, Indonesia e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Mustapha et al. (eds.), Proceedings of the 8th International Conference on the Applications of Science and Mathematics, Springer Proceedings in Physics 294, https://doi.org/10.1007/978-981-99-2850-7_31

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[2]. In the field of optics, it is used to make anti-reflection lenses, reflector mirrors, protective glass, camera equipment, and waveguides. In electronics, thin films with range of number, i.e., 2–5 nm, are used to make capacitors, semiconductors, and sensors [3]. In industry, thin films are used for various decorative functions. Thin layer material is a material that has a thickness in the order of micrometers to nanometers [4]. Until now, there are several kinds of methods [5] that can be used to grow thin films; among these methods, the plating method using the spin coating method is a simple and fast process that can be used to grow thin layer materials [5, 6]. The growth of thin layer material with this method is a method that is quite easy in the deposition process, is safe, can be carried out at room temperature and does not require vacuum conditions [7, 8]. In addition, the tools used in this method have simple and inexpensive electrical components [9–11]. Based on this, in this research, the growth of lithium tantalate material will be carried out using a spin coating on the surface of a glass substrate.

31.2 Materials and Methods The spin coating method has been widely used in the formation of thin films on the surface of prepared glass and silicon because the resulting thin films have good transparency. The advantage of this method is that the equipment used is quite simple [12], easy to carry out, and economical. One of the round coating tools with a manual model is shown in Fig. 31.1. Fig. 31.1 Spin coating [13]

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31.2.1 Materials Method of making films by precipitating chemicals solution on the surface of the substrates, then prepared with a spin coater at a speed of 3000 rpm for 30 s for each drop of the solution. The specifications of the materials used in this study are: Lithium acetate, silicon, tantalum, BST-BTO, ZnO/BST, SiO2 , BaTiO3 (BST).

31.2.2 Thin Film Deposition Thin film deposition has several steps in the spin coating process. The first step is the deposition of the coating solution on the surface of the substrate. This can be done using a pipette by dripping the coating solution over the substrate. The second step is the substrate accelerate to the rotational speed that we want and find the optimal one; this step is the thinning step of the coating liquid. In this step, there is usually a coating liquid that comes out of the substrate surface due to the rotational motion which causes the inertia of the top solution layer to be unable to be maintained when the substrate rotates faster. The third step is when the substrate is at a constant speed (as desired), which is characterized by a gradual thinning of the coating solution, so that a homogeneous coating solution thickness is obtained. Sometimes, it is also seen at the edges on the part of the substrate that has been dripped with a thicker coating solution. The fourth step is when the substrate is rotated at a constant speed and solvent evaporation occurs. The coating thickness and other properties depend on the type of liquid (viscosity, drying speed, and molarity) as well as the parameters selected during the spin coating process including rotational speed, acceleration, and spin time. In general, high rotational speed and long spin time result in thinner layers [13]. After the coating process is carried out on a thin layer, we calculate the thickness of the thin layer. The calculation of the thickness of the layer (δ) is done by dividing the difference in mass (W ) and the product of the density (ρ) of the coating by the area of the miner layer (A). The equations used are: δ=

W , ρA

(31.1)

where δ is the thickness of the coating, W is the mass weight before and after coating, ρ is the density of the coating, and A is the cross-sectional area of the layer. After the process of calculating the thickness of the thin layer, we calculate the viscosity value, and the equation used is: n=

F , Av

(31.2)

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where η is the coefficient of viscosity, F is the force before and after coating, l is the layer distance, A is the cross-sectional area of the layer, and v is the linear velocity of the film.

31.3 Result and Discussion Spin coating is a method of making a thin layer by utilizing rotation. The coating process is carried out by depositing the coating on the coated in a chemical solution. The spin coating process can be understood by the behavior of the solution flow on a rotating substrate disk. The volumetric flow of the liquid in a radial direction on the substrate surface is minimized; i.e., there is no vibration, no dry spots, and so on, which then accelerates the disk with a specific rotational speed that causes the liquid to be evenly distributed. The determination of the thickness of the coating material formed above was previously carried out by an indirect measurement technique, namely by measuring the difference between the mass before and after the thin layer. The results of the measurement of layer thickness can be seen in Table 31.1. Displayed equations are centered and set on a separate line. From Table 31.1 below, the thickness value is calculated using the formulation (31.1) where we first determine the size of the substrate length and width so that we get the area to be coated, after that first weight the mass of the substrate that has not been coated with a solution with spin coating and the mass of the substrate. After the thin film is given a solution with a spin coating solution so that we get m1 and m2 , then we determine the density value of the solution, namely the solution we use is lithium tantalate, from the value we get then put into the formula, we get the thickness value of the thin layer above. And the spin coating process is regulated from various rotational speeds starting from 1000, 2000, 3000, 4000, 5000, 6000, and 7000 rpm, and each rotational variation of the spin coating for the time to coat the solution is rotated for 30 s assumptions or based on previous research. The solution was rotated for 30 seconds aiming to get a homogeneous layer and the solution in an even coating, so that it is expected to produce a suitable layer, Speed of spin coater, Thickness layer, thickness of rotating speed. Table 31.1 Results of thin layer thickness values

Spin speed (rpm)

Time (s)

Thickness (nm)

1000

30

3.13

2000

30

1.75

3000

30

4.45

4000

30

3.13

5000

30

2.85

6000

30

1.43

7000

30

1.42

31 Optimization of Spinning Speed for Thin Layers Formation Using Spin …

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Layer Thickness (µm)

The results of the thickness of the thin layer on the rotational speed are shown in Fig. 31.2. For a rotational speed value of 3000 rpm it produces a layer of 4.45 nm, meaning that at a speed of 3000 rpm the nanometer size is generally the size of a thin layer, for the value of the rotational speed of 4000 rpm to produce a layer thickness of 3.13 nm, for the value of the rotational speed of 5000 rpm to produce a layer thickness of 2.85 nm, for a rotational speed value of 6000 rpm produces a layer thickness of 1.43 nm, for a rotational speed value of 7000 rpm produces a layer thickness of 1.42 nm, and based on the graph obtained when the speed is greater the thinner the deposited layer will be. Through spin coating. From the results of Table 31.2 above, the viscosity coefficient value is calculated using equation 31.2 where we first determine the length and width of the substrate so that the area to be coated is obtained, after that we weigh the mass of the substrate that has not been coated with spin coating solution and the mass of the substrate after being coated. solution with spin coating, then we determine the value of the linear velocity of the spin coating rotational speed, from the value we get then put it into the equation, we get a viscosity coefficient value of 3.78 10-3 to 2.5 10-7 . The value of the viscosity coefficient at the rotating speed is shown in Fig. 31.3, for the value of the viscosity coefficient at a speed of 3000 rpm there is a very drastic change in the value of the viscosity coefficient. The greater the rotational speed of the spin coating, the smaller the viscosity coefficient value will be.

0.005 0.004 0.003 0.002 0.001 0

0

1000

2000

3000

4000

5000

6000

7000

8000

Spin Speed (rpm) Fig. 31.2 Graph of the relationship between thin film thickness and rotational speed. Thickness values at a rotating speed of 3000–7000 rpm

Table 31.2 Results of viscosity coefficient values

Spin speed (rpm)

Viscosity coefficient (Ns/m2 )

1000

3.78 10–3

2000

1.204 10–3

3000

1.84 10–6

4000

1.03 10–6

5000

6.55 10–7

6000

2.96 10–7

7000

2.5 10–7

A. Ismangil and A. Saepulrohman Viscosity Coefficient (Ns/m2)

418 0.000002 0.0000018 0.0000016 0.0000014 0.0000012 0.000001 0.0000008 0.0000006 0.0000004 0.0000002 0 0

1000

2000

3000

4000

5000

6000

7000

8000

Spin Speed (rpm)

Fig. 31.3 Graph of the relationship between thin film viscosity and rotational speed. The value of the viscosity coefficient at a rotational speed of 1000–7000 rpm

31.4 Conclusion The thin layer coating using a spin coating with an increasing rotational speed will make the layer thinner, with a rotating speed of 3000 rpm to produce a thin layer with a thickness of 4.45 nm which is the size of the thin layer and matches our target. And the value of the viscosity coefficient at a rotational speed of 3000 rpm decreased by 1.84 × 10–6 Ns/m2 .

References 1. W. Amananti, H. Sutanto, Analisis Sifat Optis Lapisan Tipis ZnO, TiO2 , TiO2 : ZnO, dengan dan Tanpa Lapisan Penyangga yang Dideposisikan Menggunakan Metode Sol-Gel Spray Coating. Jurnal Fisika Indonesia 19, 41–44 (2015) 2. Irzaman, D.S. Prawira, Irmansyah, B. Yuliarto, U.J. Siregar, Characterization of lithium tantalate (LiTaO3 ) film on the concentration variations of ruthenium oxide (RuO2 ) dope. Integr. Ferroelectr. 201, 32–42 (2019) 3. I.Sh. Steinberg, V.V. Atuchin, Two-photon holographic recording in LiTaO3 : Fe crystals with high intensity nanosecond pulses at 532 nm. Mater. Chem. Phys. 253, 122956 (2020) 4. Irzaman, H. Syafutra, A. Arif, H. Alatas, M.N. Hilaludin, M. Dahrul, A. Ismangil, D. Yosman, Formation of solar cells based on Ba0.5 Sr0.5 TiO3 (BST) ferroelectric thick film. AIP Conf. Proc. 1586, 24–34 (2014) 5. J. Wang, J. Gou, W. Li, Preparation of room temperature terahertz detector with lithium tantalate crystal and thin film. AIP Adv. 4, 027106 (2014) 6. L.J. Fernández-Menéndez, L. Javier, M. Lopes, A. Cesar, G. Cristina, B. Neara, Spatio-temporal distribution of atomic and molecular excited species in laser-induced breakdown spectroscopy: potential implications on the determination of halogens. Spectrochimica Acta Part B Atomic Spectrosc. 168, 105848 (2020) 7. K. Yamada, M. Ishida, M. Yamaguchi, High performance laminated thin-film shield with conductors and magnetic material multilayer, in IEEE International Symposium on Electromagnetic Compatibility—EMC, pp. 432–437 (2011)

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8. B. Sun, J. Wang, J. Guo, X. Liu, Y Jiang, Influence of thermal annealing on structural and optical properties of RF-sputtered LiTaO3 thin films. Mater. Res. Exp. 6, 026405 (2018) 9. W.T. Hsu, Z. Bin, C.C. Wu, R.K. Choubey, Materials optical properties of Mg, Fe, Co-doped near-stoichiometric LiTaO3 single crystals. 5, 227–238 (2012) 10. A. Ismangil, Subiyanto, Sudradjat, W. Prakoso, The effect of electrical conductivity of LiTaO3 thin film to temperature variations. Int. J. Adv. Sci. Tecnol. 29, 3234–3240 (2020) 11. I. Bhaumik, S. Kumar, R. Bhatt, Resonant Raman scattering in single crystal of congruent LiTaO3 , effect of excitation energy. Solid State Commun. 151, 1869–1872 (2011) 12. C.R. Kalaiselvi, T.S. Senthil, M.V. Shankar, V. Sasirekha, Solvothermal fusion of Ag- and N-doped LiTaO3 perovskite nanospheres for improved photocatalytic hydrogen production. Appl. Organomet. Chem. 35, 6 (2021) 13. A. Ismangil, P.S. Haddy, Design of power bank mobile using solar panel-based microcontroller atmega 328. IOP Conf. Ser. Mater. Sci. Eng. 621, 012008 (2019)

Chapter 32

Effect of Environmental Stress on Biomolecules Production and Cell Wall Degradation in Chlorella vulgaris Syafiqah Md. Nadzir , Norjan Yusof , Azlan Kamari , and Norazela Nordin

Abstract Cell disruption to extract biomolecules for biofuel production, such as lipid and carbohydrate, is one of the challenging downstream processes from an economic standpoint. Environmental stress, namely salt, nitrogen, and temperature, was explored in this study to investigate their effect on lipid and carbohydrate production and cell wall degradation in Chlorella vulgaris UPSI-JRM01. C. vulgaris was cultivated in blue-green 11 (BG11) media following cultivation in salt concentrations of 0, 5, 10, 20, 40, and 60 g/L; nitrogen concentrations of 0, 250, 500, 750, and 1000 mg/L; and temperatures of 28, 25, 40, and 50 °C. Total lipid and carbohydrate content as a percentage of dry weight was determined. Cell wall degradation was measured by polysaccharides content and cell wall thickness. The highest levels of lipid obtained for each stress factor were 40% at a salt concentration of 5 g/L, 51% at a nitrogen concentration of 250 mg/L, and 51% at a temperature of 35 °C. The highest measured concentrations of carbohydrates were 54% at 10 g/L of salt concentration and 61% in deprived nitrogen condition (0 mg/L). Under fluorescence microscopy, the cell wall thickness of calcofluor white-stained cells revealed that cell wall degradation occurred at a nitrogen concentration of 250 mg/L, where the highest lipid concentration (51%) was detected. Under these conditions, the cell wall thickness was 0.154 µm, which corresponded to the lowest total cell wall polysaccharides measured. This study demonstrates the feasibility of nitrogen stress under conditions

S. Md. Nadzir · N. Yusof (B) Department of Biology, Faculty of Science and Mathematics, Universiti Pendidikan Sultan Idris, 35900 Tanjong Malim, Perak Darul Ridzuan, Malaysia e-mail: [email protected] A. Kamari Department of Chemistry, Faculty of Science and Mathematics, Universiti Pendidikan Sultan Idris, 35900 Tanjong Malim, Perak Darul Ridzuan, Malaysia N. Nordin Kolej Yayasan UEM Lembah Beringin, P.O. Box 62, 35900 Tanjong Malim Perak Darul Ridzuan, Malaysia © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 A. Mustapha et al. (eds.), Proceedings of the 8th International Conference on the Applications of Science and Mathematics, Springer Proceedings in Physics 294, https://doi.org/10.1007/978-981-99-2850-7_32

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of a limited nitrogen supply for inducing cell wall degradation and generating a high lipid content.

32.1 Introduction The depletion of fossil fuel supplies has spawned an unprecedented demand for renewable energy that might not only cut reliance on petroleum but also greenhouse gas emissions. Among the potentially valuable alternatives are microalgaederived biofuels. Currently, microalgae biomolecules such as lipid and carbohydrate have attracted considerable interest as credible, renewable, and sustainable biofuel sources. The potential of microalgae for biofuels production can be linked to the fact that it takes less land, has a high growth rate and large biomass yields, and does not compete with edible food crops [1]. Numerous microalgae species, including Chlorella vulgaris, Scenedesmus sp., Oscillatoria sp., Nannochloroposis sp., and Chlorococcum sp., have been identified as potential biofuels producers [2, 3]. Although the development of microalgal biofuels appears promising, the downstream processing required for harvesting, cell disruption, and the extraction of intracellular lipids and carbohydrates is the key challenges preventing their commercialisation. Cell disruption and biomass drying are two of the most energy-intensive phases in the biofuels feedstock recovery process. To this day, several other approaches to the disruption of microalgal cells, including mechanical, thermal, chemical, and biological approaches, have been investigated [4, 5]. Bead beating, microwave, ultrasonication, chemical hydrolysis, osmotic stress, subcritical water hydrolysis, and enzyme hydrolysis are the most often employed techniques [6, 7]. However, mechanical processes such as bead beating and ultrasonication were shown to consume the most energy. Nonmechanical technique energy consumption was shown to be dependent on treatment time, temperature, and stirring [8]. In comparison with the above-mentioned technologies for microalgae cell disruption, enzymatic disruption is intensively explored because of its unique influence on structural cell components. Nevertheless, enzymatic disruption is a costly procedure, owing mostly to the high cost of enzyme manufacture. In order to minimise the cost of biofuel production, it is necessary to investigate a viable method capable of economically disrupting microalgae cells. The cultivation of microalgae under environmental stress conditions is therefore investigated. Environmental stresses such as salt, nitrogen, and temperature are commonly used to promote the accumulation of lipid and carbohydrate. These stress conditions not only had an effect on biomolecules yield, but they were also demonstrated to affect the cell wall structure of microalgae [9]. Therefore, the purpose of this study is to examine the influence of environmental stress, specifically salt, nitrogen, and temperature stress, on the biomolecules production and cell wall degradation of Chlorella vulgaris UPSI JRM01. This discovery is essential for the development of an economical cell disruption approach for microalgae, namely for the extraction of lipids and carbohydrates for biofuel production.

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32.2 Methodology 32.2.1 Microalgae Culture Chlorella vulgaris UPSI JRM01 culture was cultivated in an Erlenmeyer flask to the logarithmic phase (days 6–7) in blue-green 11 media (BG11). Pre-cultured cells were centrifuged (4000 rpm × 5 min) and resuspended in nitrogen-free BG11. About 5.5 × 106 cells/mL of pre-cultured microalgae were inoculated into a 250 mL Erlenmeyer flask containing 100 mL of BG11. The culture was photoautotopically grown at 28 °C, 500 mg/L NO3 − , 10 500 lx, and pH 8. The cell growth was determined at optical density 680 nm.

32.2.2 Experimental Setup The microalgae culture cultivations were exposed to different environmental stress conditions. For salt stress, the microalgae were cultured in BG11 media supplemented with 5, 10, 20, 40, and 60 g/L of sodium chloride (NaCl). The control of this study was cultured in 0 g/l of NaCl. Meanwhile for nitrogen stress, the microalgae culture cultivations were grown to different concentrations of NaNO3 (0, 250, 500, 750, and 1000 mg/L) while the control of this study was cultured in BG11 media. Lastly, for heat stress, the study was performed at a temperature range of 28, 35, 40, 50, and 60 °C. Other parameters were controlled at optimum growth conditions. The temperature at 28 °C served as a control.

32.2.3 Biochemical Analyses Daily samples of microalgae were collected for analysis of lipid, carbohydrate, and cell wall polysaccharides. Prior to the total lipid and carbohydrate analyses, the microalgae cell was disrupted using an ultrasonicator (Hielscher Ultrasonic, UP100H) at 35 kHz and 100% sonication power for 5 min. Total lipid concentration was determined using a modified Bligh and Dyer method [10]. The total carbohydrate content was evaluated using the phenol–sulfuric acid method. The total lipid and carbohydrate yield were calculated using (32.1). Yield (%) = (lipid or carbohydrate dry weight/biomass dry weight) × 100 (32.1) Cell wall polysaccharides were analysed by hydrolysing the sample with 80% H2 SO4 at 0–4 °C for 20 h before diluting the hydrolysate to 1 mol H2 SO4 , filtering and analysing it using the phenol–sulfuric acid method.

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32.2.4 Measurement of Cell Wall Thickness To stain the microalgae cells, a calcofluor white dye capable of binding to cellulose and linked glucans was utilised. After 5 min of staining with calcofluor white solution, the sample was centrifuged at 10,000 rpm for 1 min and washed with phosphate buffer saline (PBS). The samples were then viewed with a fluorescent microscope (Nikon Eclipse TE 2000-U, UK) using a BV-2A filter with an excitation wavelength of 400– 440 nm. The software NIS-elements was then used to measure the thickness of the cell wall.

32.3 Results and Discussion 32.3.1 Effect of Salt Stress Figure 32.1 shows the total lipid and carbohydrate yield of C. vulgaris during salt stress. Figure 32.1 a clearly shows that the total lipid yield is substantial even at increasing salinity, indicating that lipid accumulation occurs even under salt stress conditions. The overall carbohydrate yield reflected this as well. The maximum lipid yield (40%) was obtained under salt stress conditions (5 g/L NaCl). Meanwhile, under salt stress conditions, the highest carbohydrate yield (54%) was obtained at a salt concentration of 10 g/L. Salt stress triggered a carbon redistribution from starch and protein to lipid in the freshwater microalga Chlorella sorokiniana cultivated on BG11 [11]. Meanwhile, in another study involving salinity stress in Acutodesmus dimorphus cultured in BG11, it was found that carbon was redistributed from protein to lipid and carbohydrate [12]. The total cell wall polysaccharides and fluorescence microscopy analyses produced under salt stress from day 1 to day 9 are shown in Fig. 32.2 and Table 32.1. Under 60 g/L NaCl, the total cell wall polysaccharides was 12% on day 1, but increased to 24% on day 9. This is proportional with the microscopy analysis where the mean cell wall thickness on day 1 was 0.175 µm, increasing to 0.321 µm on day 9. This shows that the cell thickness increased under higher salt stress. The lowest total cell wall polysaccharides (7%) were on day third under 5 g/L NaCl where the mean cell wall thickness was at 0.162 µm. According to [13], the diameter of C. sorokiniana HS1 was at least twice under high-salinity conditions, indicating increased osmotic pressure on algal cells. Cell division inhibition, which is connected with cellular response to salt stress, is another possible explanation of larger cell size [11]. Church et al. [14] found that high-salinity stress increased cell size in C. vulgaris, with an increase in average cell diameter from 2.7 µm (without NaCl) to 4.0 µm for algae cultivated in 30 g/L NaCl [14]. Although the reaction to increase salinity is expected to differ between strains, osmosensing and osmoregulation were predicted to produce metabolic alterations, which changed cell volume and biochemical composition [14].

32 Effect of Environmental Stress on Biomolecules Production and Cell …

Total lipid yield (%)

(a)

45 40 35 30 25 20 15 10 5 0

425

Control SS 5 g/L SS 10 g/L SS 20 g/L SS 40 g/L SS 60 g/L 1

2

3

4

5

6

7

8

9

Culvaon period (day)

Total carbohydrate yield (%)

(b)

60 50 Control SS 5 g/L SS 10 g/L SS 20 g/L SS 40 g/L SS 60 g/L

40 30 20 10 0 1

2

3

4

5

6

7

8

9

Culvaon period (day)

Total cell wall polysaccharide (%)

Fig. 32.1 Total lipid and carbohydrate yield of C. vulgaris under salt stress 30 25 20

Control

15

SS 5 g/L SS 10 g/L

10

SS 20 g/L

5

SS 40 g/L SS 60 g/L

0 1

2

3

4 5 6 Culvaon period (day)

7

8

9

Fig. 32.2 Cell wall polysaccharides of C. vulgaris under salt stress

32.3.2 Effect of Nitrogen Stress Nitrogen is required for microalgae growth. To evaluate the effect of nitrogen stress on C. vulgaris, biochemical and microscopy analyses were performed. The total lipid production (shown in Fig. 3a) demonstrates that the highest lipid yield (51%) was obtained on the fifth day at a nitrogen concentration of 250 mg/L before decreasing. At the same conditions (250 mg/L), the total carbohydrate yield rose on the sixth

426

S. Md. Nadzir et al.

Table 32.1 Cell wall measurement of C. vulgaris under salt stress Salt stress (g/L)

Cultivation period (day) 1

2

3

4

5

6

7

8

9

Mean thickness of the cell wall (µm) Control

0.183

0.192

0.199

0.211

0.254

0.232

0.198

0.203

0.215

5

0.183

0.174

0.162

0.165

0.177

0.182

0.195

0.194

0.182

10

0.188

0.192

0.186

0.194

0.197

0.202

0.205

0.201

0.204

20

0.185

0.193

0.188

0.191

0.192

0.205

0.221

0.243

0.254

40

0.185

0.192

0.194

0.201

0.215

0.218

0.221

0.291

0.312

60

0.187

0.198

0.201

0.224

0.276

0.287

0.299

0.310

0.321

day (58%), indicating that lipid synthesis has moved towards carbohydrate biosynthesis (Fig. 3b). The maximum total carbohydrate production (61%) was obtained at 0 mg/L. Feng et al. [15] discovered a considerable increase in lipid yield under nitrogen stress conditions, with the lipid content of C. zofingiensis reaching up to 65.1%. Zhu et al. [16] validated the rise in carbohydrate content in their investigation, where the greatest carbohydrate yield during nitrogen deprivation was at 66.7%. The protein synthesis required for cellular growth is hindered under nitrogen stress, leaving an excess of carbon from photosynthesis, which is then redirected to the metabolic pathways of lipid storage and starch generation [17]. As a result, the lipid and carbohydrate yield was expected to increase under nitrogen stress conditions. Figure 32.4 and Table 32.2 show the total cell wall polysaccharides and cell wall measurement of C. vulgaris under nitrogen stress condition. The thinnest cell wall width was measured under 250 mg/L NaNO3 (0.154 µm) on day 5, and the total cell wall polysaccharide was 9%. This similar trend was also observed in N. oleoabundans [18]. Rashidi et al. [18] stated that nitrogen-containing biopolymers are one of the key components of the microalgae cell wall, and thus, it is not unusual that a limited quantity of nitrogen in the medium produced a drop in the cell wall fraction in the total cell mass of N. oleoabundans. The lipid yield under 250 mg/L was the highest which is important for economic cell disruption with high lipid recovery. Meanwhile, the total cell wall polysaccharide of C. vulgaris was the highest under 0 mg/L NaNO3 on day 9 (21%). The cell wall was also the thickest under this condition (0.211 µm). This trend was also found in a study conducted by Authors [19, 19] where it was reported that nitrogen at 0 mg/L caused the thickening of Nannochloropsis sp., Chlorella sp., and Chloroccum sp. cell wall. Cells reinforce their cell walls to retain structural strength during fast cellular expansion, as seen by the concurrent rise in cell wall thickness and lipid content during nitrogen shortage [21].

32 Effect of Environmental Stress on Biomolecules Production and Cell …

427

(a) 60 Total lipid yield (%)

50 Control

40

NC 0 mg/L

30

NC 250 mg/L NC 500 mg/L

20

NC 750 mg/L 10

NC 1000 mg/L

0 1

2

3

4 5 6 Culvaon period (day)

7

8

9

Total carbohydrate yield (%)

(b) 80 70 60 50 40 30 20 10 0

Control NC 0 mg/L NC 250 mg/L NC 500 mg/L NC 750 mg/L 1

2

3

4 5 6 Culvaon period (day)

7

8

9

NC 1000 mg/L

Total cell wall polysaccharide (%)

Fig. 32.3 Total lipid and carbohydrate yield of C. vulgaris under different nitrogen concentration

25 Control 20

NC 0 mg/L

15

NC 250 mg/L NC 500 mg/L

10

NC 750 mg/L 5

NC 1000 mg/L

0 1

2

3

4

5

6

7

8

9

Culvaon period (day)

Fig. 32.4 Cell wall polysaccharides of C. vulgaris under different nitrogen concentration

32.3.3 Effect of Temperature Stress Temperature stress on lipid and carbohydrate yield was studied from day 1 to day 9 at temperatures ranging from 28 to 60 °C. The total lipid and carbohydrate yield of C. vulgaris under various temperature stress conditions is presented in Fig. 32.5. On day 2 at 50 °C, the greatest yield of lipids was 52%, after which the yield declined.

428

S. Md. Nadzir et al.

Table 32.2 Cell wall measurement of C. vulgaris under different nitrogen concentration Nitrogen conc. (mg/L) Cultivation period (day) 1

2

3

4

5

6

7

8

9

Mean thickness of the cell wall (µm) Control

0.183 0.192 0.199 0.211 0.254 0.232 0.198 0.203 0.215

0

0.172 0.183 0.189 0.192 0.194 0.198 0.202 0.207 0.211

250

0.189 0.175 0.172 0.169 0.154 0.159 0.161 0.162 0.169

500

0.192 0.197 0.193 0.184 0.181 0.176 0.171 0.165 0.159

750

0.185 0.181 0.193 0.192 0.194 0.186 0.184 0.175 0.172

1000

0.195 0.192 0.184 0.183 0.187 0.191 0.173 0.165 0.168

At 35 °C on day 3, a similar result was obtained with a lipid yield of 51%; however, the yield fluctuated from day 4 to day 6 and subsequently increased again on day 7 (43%). According to [22] when the temperature was increased from 25 to 32 °C, the lipid content of Chlamydomonas reinhardtii increased to 76% (coupled with nitrogen starvation). The lipid yield of the control condition (28 °C) increased from 14% on day 1 to 35% on day 9. Meanwhile, the highest carbohydrate yield under temperature stress was 58% at 35 °C, which thereafter declined after prolonged exposure to high temperatures. The breakdown of stored starch occurs at higher temperatures [23]. According to [24] at

Total lipid yield (%)

(a)

60 50 40

Control T 35 °C T 40 °C T 50 °C T 60 °C

30 20 10 0 1

2

3

4

5

6

7

8

9

Culvaon period (day) Total carbohydrate yield (%)

(b) 70 60 50 40

Control T 35 °C T 40 °C T 50 °C T 60 °C

30 20 10 0 1

2

3

4 5 6 Culvaon period (day)

7

8

9

Fig. 32.5 Total lipid and carbohydrate yield of C. vulgaris under different temperature

32 Effect of Environmental Stress on Biomolecules Production and Cell …

429

Total cell wall polysaccharide (%)

high temperatures, carbon synthesis was shifted away from carbohydrate formation and towards lipid production, which explains why carbohydrate yield was low. The total amount of cell wall polysaccharides and cell wall measurement produced during temperature stress from day 1 to day 9 are shown in Fig. 32.6 and Table 32.3. The thinning of the cell wall in this study was correlated to the polysaccharide content of the cell wall. On day 4, the maximum cell wall polysaccharide (29%) was obtained at a temperature of 50 °C. At this condition, the cell wall width was the thickest (0.211 µm). Meanwhile, the lowest cell polysaccharide achieved was on the fourth day of 60 °C (7%) and no cell wall measurement was taken for this condition because the cell wall had already burst and the cell shape had become irregular for measurement. The thinnest microalgae cell wall examined was at 35 °C, with an average thickness of 0.158 µm from day 1 to day 9. According to [25], acute heat shock (40 °C) induced enlargement, altered plasma membrane, and nuclear swelling in 96% of the cells. Novosel et al. [26] reported that there were no changes in microalgae shape at temperatures ranging from 12 to 30 °C, but it did have an influence on algal species size, with microalgae being smaller at higher temperatures. This is consistent with our findings, in which cell size was reduced at 40, 50, and 60 °C compared to the control and 35 °C. 35 30 25 20

Control

15

T 35 °C

10

T 40 °C T 50 °C

5

T 60 °C

0 1

2

3

4

5

6

7

8

9

Culvaon period (day)

Fig. 32.6 Cell wall polysaccharides of C. vulgaris under different temperature

Table 32.3 Cell wall measurement of C. vulgaris under different temperature Temperature (°C)

Cultivation period (day) 1

2

3

4

5

6

7

8

9

Mean thickness of the cell wall (µm) Control

0.172

0.183

0.189

0.192

0.194

0.198

0.202

0.207

0.211

35

0.165

0.169

0.173

0.181

0.192

0.175

0.187

0.174

0.172

40

0.184

0.192

0.195

0.192

0.195

0.201

0.194

0.182

0.183

50

0.187

0.194

0.198

0.211

0.204

0.191

0.185

0.181

0.172

60

0.179

0.193

0.182

–

–

–

–

–

–

430

S. Md. Nadzir et al.

32.4 Conclusion This study shows that specific environmental stress conditions, such as salt, nitrogen, and temperature stress, promote cell wall thinning, and provide a significant lipid and carbohydrate yield. Under nitrogen-stressed conditions (0 and 250 mg/L), the highest levels of lipids and carbohydrates were recorded. In addition, the thinnest cell wall thickness was observed at 250 mg/L under limited nitrogen conditions. These findings are essential for efficient microalgae cell disruption in order to extract lipids and carbohydrate biomolecules for biofuel feedstock. Acknowledgements The financial assistance provided by The Ministry of Higher Education Malaysia (MOHE) under the Fundamental Research Grant Scheme (FRGS) [Code: FRGS/1/2019/ STG05/UPSI/02/1] is gratefully acknowledged.

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