Description Details
This book has four chapters. In chapter one the authors introduce the three types of super FRM models. Chapter two uses these three new super fuzzy models to study the role of media which feverishly argued against 27 percent reservation for OBCs in Central Government-run institutions in India. The experts we consulted were divided into 19 groups depending on their profession. These groups of experts gave their opinion and comments on the news-items that appeared about reservations in dailies and weekly magazines, and the gist of these lengthy discussions form the third chapter of this book. The fourth chapter gives the conclusions based on our study....

Table of Contents Details
Dedication 5 Preface 6 Chapter One INTRODUCTION TO NEW SUPER FUZZY MODELS 7 1.1 Supermatrices and Fuzzy Supermatrices 7 1.2 Super Fuzzy Relational Maps 45 Chapter Two ANALYSIS OF THE ROLE OF MEDIA ON RESERVATION FOR OBC USING SUPER FUZZY MODELS 57 2.1 Brief Description of the Attributes Given by the Experts 58 2.2 Super Row FRM Model to Study the Role of Media on OBC Reservation 77 2.3 Super Fuzzy Mixed FRM Model to Study the Role of Media in Falsely Blaming the Government and Supporting Dr. Venugopal 88 2.4 Use of Super Column FRM Model to Study the Interrelation between the Government and Public 102 2.5 Analysis of Role of Media on Reservation for OBC using Fuzzy Cognitive Map 117 2.6 Observations based on this Analysis by Students and Experts through Seminars and Discussions 121 Chapter Three EXCERPT OF NEWS FROM PRINT MEDIA AND SUGGESTIONS AND COMMENTS BY THE EXPERTS 145 Chapter Four ANALYSIS SUGGESTIONS AND CONCLUSIONS BASED ON DISCUSSIONS, QUESTIONNAIRE, INTERVIEWS AND MATHEMATICAL MODELS 357 4.1 A View and Analysis by Group of Educationalists about Role of Media on OBC Reservation 357 4.1.1 Students Pro...

Description Details
This book has seven chapters. Chapter one provides several basic notions to make this book self-contained. Chapter two introduces neutrosophic groups and neutrosophic N-groups and gives several examples. The third chapter deals with neutrosophic semigroups and neutrosophic N-semigroups, giving several interesting results. Chapter four introduces neutrosophic loops and neutrosophic N-loops. Chapter five just introduces the concept of neutrosophic groupoids and neutrosophic Ngroupoids. Sixth chapter innovatively gives mixed neutrosophic structures and their duals. The final chapter gives problems for the interested reader to solve. Our main motivation is to attract more researchers towards algebra and its various applications....

Excerpt Details
1.1 Groups, N-group and their basic Properties It is a well-known fact that groups are the only algebraic structures with a single binary operation that is mathematically so perfect that an introduction of a richer structure within it is impossible. Now we proceed on to define a group. DEFINITION 1.1.1: A non empty set of elements G is said to form a group if in G there is defined a binary operation, called the product and denoted by '•' such that ...

Table of Contents Details
Preface 5 Chapter One INTRODUCTION 1.1 Groups, N-group and their basic Properties 7 1.2 Semigroups and N-semigroups 11 1.3 Loops and N-loops 12 1.4 Groupoids and N-groupoids 25 1.5 Mixed N-algebraic Structures 32 Chapter Two NEUTROSOPHIC GROUPS AND NEUTROSOPHIC N-GROUPS 2.1 Neutrosophic Groups and their Properties 40 2.2 Neutrosophic Bigroups and their Properties 52 2.3 Neutrosophic N-groups and their Properties 68 Chapter Three NEUTROSOPHIC SEMIGROUPS AND THEIR GENERALIZATIONS 3.1 Neutrosophic Semigroups 81 3.2 Neutrosophic Bisemigroups and their Properties 88 3.3 Neutrosophic N-Semigroup 98 Chapter Four NEUTROSOPHIC LOOPS AND THEIR GENERALIZATIONS 4.1 Neutrosophic loops and their Properties 113 4.2 Neutrosophic Biloops 133 4.3 Neutrosophic N-loop 152 Chapter five NEUTROSOPHIC GROUPOIDS AND THEIR GENERALIZATIONS 5.1 Neutrosophic Groupoids 171 5.2 Neutrosophic Bigroupoids and their generalizations 182 Chapter Six MIXED NEUTROSOPHIC STRUCTURES 187 Chapter Seven PROBLEMS 195 REFERENCE 201 INDEX 207 ABOUT THE AUTHORS 219 ...

Description Details
This book has five chapters. Chapter one is introductory in nature. Fuzzy linguistic spaces are introduced in chapter two. Fuzzy linguistic vector spaces are introduced in chapter three. Chapter four introduces fuzzy linguistic models. The final chapter suggests over 100 problems and some of them are at research level....

Table of Contents Details
Preface 5 Chapter One Introduction 7 Chapter Two Fuzzy Linguistic Spaces 9 Chapter Three Fuzzy Linguistic Set Vector Spaces 23 Chapter Four Fuzzy Linguistic Models 129 4.1 Operations on Fuzzy Linguistics Matrices 129 4.2 Fuzzy Linguistic Cognitive Models 139 4.3 Fuzzy Linguistic Relational Map Model 148 Chapter Five Suggested Problems 165 Further Reading 187 Index 189 About the Authors 192...

Description Details
This book is organized into 5 chapters. The first chapter introduces real neutrosophic complex numbers. Chapter two introduces the notion of finite complex numbers; algebraic structures like groups, rings etc are defined using them. Matrices and polynomials are constructed using these finite complex numbers. Chapter three introduces the notion of neutrosophic complex modulo integers. Algebraic structures using neutrosophic complex modulo integers are built and around 90 examples are given. Some probable applications are suggested in chapter four and chapter five suggests around 160 problems some of which are at research level....

Excerpt Details
In this chapter we for the first time we define the notion of integer neutrosophic complex numbers, rational neutrosophic complex numbers and real neutrosophic complex numbers and derive interesting properties related with them....

Table of Contents Details
Preface 5 Chapter One REAL NEUTROSOPHIC COMPLEX NUMBERS 7 Chapter Two FINITE COMPLEX NUMBERS 89 Chapter Three NEUTROSOPHIC COMPLEX MODULO INTEGERS 125 Chapter Four APPLICATIONS OF COMPLEX NEUTROSOPHIC NUMBERS AND ALGEBRAIC STRUCTURES USING THEM 175 Chapter Five SUGGESTED PROBLEMS 177 FURTHER READING 215 INDEX 217 ABOUT THE AUTHORS 220...

Description Details
This book has four chapters. The first chapter just introduces n-group which is essential for the definition of n-vector spaces and n-linear algebras of type I. Chapter two gives the notion of n-vector spaces and several related results which are analogues of the classical linear algebra theorems. In case of n-vector spaces we can define several types of linear transformations. The applications of these algebraic structures are given in Chapter 3. Chapter four gives some problem to make the subject easily understandable....

Excerpt Details
n-VECTOR SPACES OF TYPE I AND THEIR PROPERTIES In this chapter we introduce the notion of n-vector spaces and describe some of their important properties. Here we define the concept of n-vector spaces over a field which will be known as the type I n-vector spaces or n-vector spaces of type I. Several interesting properties about them are derived in this chapter. DEFINITION 2.1: A n-vector space or a n-linear space of type I (n 2)...

Table of Contents Details
Preface 5 Chapter One BASIC CONCEPTS 7 Chapter Two n-VECTOR SPACES OF TYPE I AND THEIR PROPERTIES 13 Chapter Three APPLICATIONS OF n-LINEAR ALGEBRA OF TYPE I 81 Chapter Four SUGGESTED PROBLEMS 103 FURTHER READING 111 INDEX 116 ABOUT THE AUTHORS 120...