Kandasamy W.B.V, Smarandache F., Ilanthenral K. Elementary Fuzzy Matrix Theory and Fuzzy Models for Social Scientists

Automaton, 2007, -352 p.This book aims to assist social scientists to analyze their problems using fuzzy models. The basic and essential fuzzy matrix theory is given. The book does not promise to give the complete properties of basic fuzzy theory or basic fuzzy matrices. Instead, the authors have only tried to give those essential basically needed to develop the fuzzy model. The authors do not present elaborate mathematical theories to work with fuzzy matrices; instead they have given only the needed properties by way of examples. The authors feel that the book should mainly help social scientists who are interested in finding out ways to emancipate the society. Everything is kept at the simplest level and even difficult definitions have been omitted. Another main feature of this book is the description of each fuzzy model using examples from real-world problems. Further, this book gives lots of references so that the interested reader can make use of them.
This book has two chapters. In Chapter One, basic concepts about fuzzy matrices are introduced. Basic notions of matrices are given in section one in order to make the book self-contained. Section two gives the properties of fuzzy matrices. Since the data need to be transformed into fuzzy models, some elementary properties of graphs are given. Further, this section provides details of how to prepare a linguistic questionnaire to make use of in these fuzzy models when the data related with the problem is unsupervised.
Chapter Two has six sections. Section one deals with basic fuzzy matrix theory and can be used in a simple and effective way for analyzing supervised or unsupervised data. The simple elegant graphs related with this model can be understood even by a layman. The notion of Fuzzy Cognitive Maps (FCMs) model is introduced in the second section. This model is illustrated by a few examples. It can give the hidden pattern of the problem under analysis. The generalization of the FCM models, which are known as Fuzzy Relational Maps (FRMs), come handy when the attributes related with the problem can be divided into two disjoint sets. This model comes handy when the number of attributes under study is large. This is described in section three. This also gives a pair of fixed points or limit cycle which happens to be the hidden pattern of the dynamical system. Bidirectional Associative Memories (BAM) model is described in the fourth section of this chapter. They are time or period dependent and are defined in real intervals. One can make use of them when the change or solution is timedependent. This is also illustrated using real-world problems. The fifth section deals with Fuzzy Associative Memories (FAM) model and the model comes handy when one wants the gradations of each and every attribute under study. This model is also described and its working is shown through examples. The last section of this chapter deals with the Fuzzy Relational Equations (FRE) model. This model is useful when there are a set of predicted results and the best solution can be constructed very close, or at times, even equal to the predicted results. The working of this model is also given. Thus the book describes simple but powerful and accurate models that can be used by social scientists.Basic Matrix Theory and Fuzzy Matrix Theory
Basic Matrix Theory
Basic Concepts on Fuzzy Matrices
Basic Concepts on Graphs
Description of Simple Fuzzy Models and their Applications to Real World Problems
Description of Simple Fuzzy Matrix Model
Definition of Fuzzy Cognitive Maps with real world model representation
Definition and Illustration of Fuzzy Relational Maps
Introduction to Bidirectional Associative Memories (BAM) Model and their Application
Description of Fuzzy Associative Memories (FAM) model and their illustrations
Fuzzy Relational Equations (FRE) and their application