W. B. VASANTHA KANDASAMY FLORENTIN SMARANDACHE ANALYSIS OF SOCIAL ASPECTS OF MIGRANT LABOURERS LIVING WITH HIV/AIDS USING FUZZY THEORY AND NEUTROSOPHIC COGNITIVE MAPS With Specific Reference To Rural Tamilnadu In India XIQUAN Phoenix 2004 ANALYSIS OF SOCIAL ASPECTS OF MIGRANT LABOURERS LIVING WITH HIV/AIDS USING FUZZY THEORY AND NEUTROSOPHIC COGNITIVE MAPS With Specific Reference To Rural Tamilnadu In India W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technology, Madras Chennai – 600036, India e-mail: [email protected] web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup, NM 87301, USA e-mail: [email protected] Translation of the Tamil interviews by Meena Kandasamy XIQUAN Phoenix 2004 The picture on the cover is a poster by Bronwyn Bancroft, an Australian Aboorgine artist illustrating the need for education about AIDS. The picture at the top left on the back cover is the red ribbon, an international symbol of the fight against AIDS. The picture at the bottom of the back-cover is a computer generated image of the human immunodeficiency virus (HIV). Pictures courtesy: The Unesco Courier, June 1995. This book can be ordered in a paper bound reprint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) 300 N. Zeeb Road P.O. Box 1346, Ann Arbor MI 48106-1346, USA Tel.: 1-800-521-0600 (Customer Service) http://wwwlib.umi.com/bod/ and online from: Publishing Online, Co. (Seattle, Washington State) at: http://PublishingOnline.com This book has been peer reviewed and recommended for publication by: Dr.Jean Dezert, ONERA (French National Establishment for Aerospace Research), BP 72 F-92322 Chatillon Cedex, France. Dr.M.Khoshnevisan, School of Accounting and Finance, Griffith Univeristy, Australia. Dr. G. Lakshma Reddy, Department of Mathematics and Computer Science, University of Hyderabad, Andhra Pradesh, India Copyright 2004 by W. B. Vasantha Kandasamy, Florentin Smarandache, and Xiquan, 510 E. Townley Ave., Phoenix, AZ 85020 USA Layout and cover design by Kama Kandasamy. Many books can be downloaded from: http://www.gallup.unm.edu/~smarandache/eBooks-otherformats.htm ISBN: 1-931233-83-7 Standard Address Number: 297-5092 Printed in the United States of America Contents Preface 5 Chapter one Introduction 7 Chapter Two Analysis of the Feelings Of HIV/AIDS Affected Migrant Labourers Using Fuzzy Matrices And FCM 2.1 Estimation of the overall age group of the HIV/AIDS patients from migrant labourers in which they are maximum infected using fuzzy matrices 16 2.2. Analysis of socio economic position of the HIV/AIDS patients using FCM 36 2.3 Combined FCM to study the HIV/AIDS affected migrant labourers’ socio-economic problem 62 2.4 Combined disjoint block FCMs and its application to HIV/AIDS problem 68 Chapter three Use of BAM to Study the Factors For Migration and Vulnerability To HIV/AIDS 3.1 Some basic concepts of BAM 98 3.2 Use of BAM model to study the cause of vulnerability to HIV/AIDS and factors for migration 103 Chapter Four Use of NCM to Study the Socioeconomic Problems Of HIV/AIDS Affected Migrant Labourers 4.1 Basic notion of neutrosophy and Neutrosophic cognitive maps 122 4.2 Use of NCM to analyse the HIV/AIDS affected migrant labourers problem 134 4.3 Combined NCM to study migrant problems 147 4.4 Combined block NCMs and their Application to HIV/AIDS disease 162 Chapter five Use of FRM and NRM to study the HIV/AIDS Affected Migrant Labourers and their Socio-economic Conditions 5.1 Use of FRM in the study of relation between HIV/AIDS migrants and their socio-economic conditions 194 5.2 Definition of Linked FRMs and its applications 231 5.3 Use of CDBFRM to analyse the problem of HIV/AIDS affected migrants 245 5.4. NRMs to Analyze the problem of HIV/AIDS Migrant Labourers 271 5.5 Linked Neutrosophic Relational Maps and its application to Migrant Problems 288 5.6 Combined Disjoint Block NRM and Combined Overlap Block NRM 299 Chapter Six Interview of 60 People Living With HIV/AIDS 327 Chapter Seven Conclusions/Suggestions 377 Appendix 1. Linguistic Questionnaire 403 2. Table of Statistics 427 3. C-program for RTD and CETD Matrix 430 4. C-program for FCM 434 5. C-program for CFCM 437 6. C-program for BAM 440 7. C-program for FRM 443 8. C-program for CFRM 448 9. Neutrosophy 453 Further Reading 456 Index 468 Preface Neutrosophic logic grew as an alternative to the existing topics and it represents a mathematical model of uncertainty, vagueness, ambiguity, imprecision, undefined-ness, unknown, incompleteness, inconsistency, redundancy and contradiction. Despite various attempts to reorient logic, there has remained an essential need for an alternative system that could infuse into itself a representation of the real world. Out of this need arose the system of neutrosophy and its connected logic, neutrosophic logic. This new logic, which allows also the concept of indeterminacy to play a role in any real-world problem, was introduced first by one of the authors Florentin Smarandache. In this book for the first time we have ventured into the total analysis of migrant labourers in rural Tamil Nadu who are victims of HIV/AIDS using FCM, BAM and Neutrosophic Cognitive Maps. As in our study and analysis we felt several of the factors related with the psycho, socio, economic problems of these HIV/AIDS patients from rural Tamil Nadu (a southernmost state in India) remain indeterminate apart from the data being an unsupervised one. At the outset, we first emphasize that the study and analysis (and there by the conclusions and suggestions) pertain only to migrant labourers from rural Tamil Nadu who are poor and uneducated and who are HIV/AIDS infected. So this study cannot be extended to urban people or rich/ sophisticated/ educated populations of Tamil Nadu. We have purposefully chosen this study for we saw majority of the people who come to take treatment for HIV/AIDS as inpatients of the Government Hospital for Thoracic Medicine at Tambaram (called the “Tambaram Sanatorium”) hospital are from rural areas with no education, they are poor or become poor due to this disease and have caught this disease due to migration. Further these people are not empowered with trade unions or welfare associations, for these labourers are used till they serve the purpose and once they are ill there is no one to take care of them. At least 75% of them, when they came to know that they had HIV/AIDS, their first reaction was to think of committing suicide. These men at large are shaken to the core in their hearts with fear of stigma and poverty and they suffer from deep depression when they are just in the prime of life. Thus our sample under analysis is these migrant poor uneducated labourers from rural Tamil Nadu. This book is an extended mathematical analysis of the book Love.Life.Lust.Loss: 101 Real Life Stories of Migration and AIDS—A Fuzzy Analysis. 6 This book has seven chapters. The first chapter is introductory in nature and it speaks about the migrant labourers. In chapter two we use Fuzzy Cognitive Maps to analyze the socio-economic problems of HIV/AIDS infected migrant labourers in rural areas of Tamil Nadu. In chapter three we analyze the role played by the government helping these migrant labourers with HIV/AIDS and factors of migration and their vulnerability in catching HIV/AIDS. For the first time Neutrosophic Cognitive Maps are used in the study of migrant labourers who have become HIV/AIDS victims. This study is done in Chapter IV. In chapter V we use Neutrosophic Relational Maps and we define some new neutrosophic tools like Combined Disjoint Block FRM, Combined Overlap NRM and linked NRM. We adopt these new techniques in the study and analysis of this problem. Chapter VI gives a very brief sketch of the life history of these 60 HIV/AIDS infected migrant labourers so that people from different social and cultural backgrounds follow our analysis. The last chapter gives suggestions and conclusions based on our study. This book has 8 appendices. The Appendix 1 is the questionnaire used in interviewing these migrant labourers. The questionnaire was formatted with the help of Dr. K. Kandasamy. Appendix 2 gives the table of these 60 migrant labourers. Appendix 3 to 8 gives the C programs used in finding the resultant vector for any given state vector using the dynamical system. Appendix 9 deals with Neutrosophic logic. We have included a list of further reading. We deeply acknowledge the TNSACS for its financial support and encouragement. We personally acknowledge the project director Mr. Deenabandu, I.A.S of TNSACS for his constant encouragement. We are indebted to Ms.Kama Kandasamy who had taken all pains to format, verify the equations and design the books. We deeply acknowledge the services of Dr.K.Kandasamy who had done a lot of background work and for formatting such a scientific linguistic questionnaire without which we would not have been in a position to get this data. We thank our research scholars Mr.Ganesan, Mr.Kanagamuthu and Mr.Narayanamurthy for taking the interviews. Our deep thanks are due to Meena Kandasamy who translated the Tamil interviews of these migrant labourers. We dedicate this book to the peoples and nations that are working to rehabilitate and support the poor men and women living with HIV/AIDS in the Third- World countries. W.B. Vasantha Kandasamy Florentin Smarandache Chapter One INTRODUCTION Migration acquires great significance in the study of peoples and populations, for it not only involves the merely mathematical spatial redistribution of people, but also because it has enormous impact on livelihood, life-styles, employment, socioeconomic and political stability; or in other words, it influences the entire society.