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Fuzzy Interval Matrices, Neutrosophic Interval Matrices and Their Applications

By Smarandache, Florentin

Book Id: WPLBN0002828312
Format Type: PDF (eBook)
File Size: 1.04 mb
Reproduction Date: 7/23/2013

Title:	Fuzzy Interval Matrices, Neutrosophic Interval Matrices and Their Applications
Author:	Smarandache, Florentin
Volume:
Language:	English
Subject:	Non Fiction, Education, Neutrosophic Systems
Collections:	Math, Authors Community, Geography, Fine Arts, Sociology, Medicine, Literature, Most Popular Books in China
Historic Publication Date:	2013
Publisher:	World Public Library

Member Page:	Florentin Smarandache
Citation APA MLA Chicago Smarandache, F., & Vasantha Kandasamy, W. B. (2013). Fuzzy Interval Matrices, Neutrosophic Interval Matrices and Their Applications. Retrieved from http://www.self.gutenberg.org/

Description
The new concept of fuzzy interval matrices has been introduced in this book for the first time. The authors have not only introduced the notion of fuzzy interval matrices, interval neutrosophic matrices and fuzzy neutrosophic interval matrices but have also demonstrated some of its applications when the data under study is an unsupervised one and when several experts analyze the problem.

Summary
This book has three chapters. The first chapter is introductory in nature and makes the book a self-contained one. Chapter two introduces the concept of fuzzy interval matrices. Also the notion of fuzzy interval matrices, neutrosophic interval matrices and fuzzy neutrosophic interval matrices, can find applications to Markov chains and Leontief economic models. Chapter three gives the application of fuzzy interval matrices and neutrosophic interval matrices to real-world problems by constructing the models already mentioned. Further these models are mainly useful when the data is an unsupervised one and when one needs a multi-expert model. The new concept of fuzzy interval matrices and neutrosophic interval matrices will find their applications in engineering, medical, industrial, social and psychological problems.

Excerpt
1.2 Definition of Fuzzy Cognitive Maps In this section we recall the notion of Fuzzy Cognitive Maps (FCMs), which was introduced by Bart Kosko in the year 1986. We also give several of its interrelated definitions. FCMs have a major role to play mainly when the data concerned is an unsupervised one. Further this method is most simple and an effective one as it can analyse the data by directed graphs and connection matrices. DEFINITION 1.2.1: An FCM is a directed graph with concepts like policies, events etc. as nodes and causalities as edges. It represents causal relationship between concepts. Example 1.2.1: In Tamil Nadu (a southern state in India) in the last decade several new engineering colleges have been approved and started. The resultant increase in the production of engineering graduates in these years is disproportionate with the need of engineering graduates.

Table of Contents
Dedication 5 Preface 6 Chapter One BASIC CONCEPTS 1.1 Definition of Interval Matrices and Examples 8 1.2 Definition of Fuzzy Cognitive Maps 9 1.3 An Introduction to Neutrosophy 13 1.4 Some Basic Neutrosophic Structures 16 1.5 Some Basic Notions about Neutrosophic Graphs 22 1.6 On Neutrosophic Cognitive Maps with Examples 28 1.7 Definition and Illustration of Fuzzy Relational Maps (FRMs) 33 1.8 Introduction to Fuzzy Associative Memories 40 1.9 Some Basic Concepts of BAM 43 1.10 Properties of Fuzzy Relations and FREs 49 1.11 Binary Neutrosophic Relations and their Properties 56 Chapter Two INTRODUCTION TO FUZZY INTERVAL MATRICES AND NEUTROSOPHIC INTERVAL MATRICES AND THEIR GENERALIZATIONS 2.1 Fuzzy Interval Matrices 68 2.2 Interval Bimatrices and their Generalizations 76 2.3 Neutrosophic Interval Matrices and their Generalizations 92 Chapter Three FUZZY MODELS AND NEUTROSOPHIC MODELS USING FUZZY INTERVAL MATRICES AND NEUTROSOPHIC INTERVAL MATRICES 3.1 Description of FCIMs Model 118 3.2 Description and Illustration of FRIM Model 129 3.3 Description of FCIBM model and its Generalization 139 3.4 FRIBM model and its Application in the Fuzzy Interval Mixed Rectangular Bimatrices 144 3.5 Description of FAIM model and its Generalization 147 3.6 Use of Fuzzy Interval Matrices in Fuzzy Relational Equations Model 167 3.7 IBAM model and its Generalizations 194 3.8 Introduction to Interval Neutrosophic Matrices and use of these Matrices in Neutrosophic Models 243 3.9 Application of Interval of Neutrosophic Matrices to Neutrosophic Models 254 REFERENCE 269 INDEX 297 ABOUT THE AUTHORS 304