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... W. B. VASANTHA KANDASAMY FLORENTIN SMARANDACHE FUZZY RELATIONAL MAPS AND NEUTROSOPHIC RELATIONAL MAPS HEXIS Church R... ...LATIONAL MAPS HEXIS Church Rock 2004 1 FUZZY RELATIONAL MAPS AND NEUTROSOPHIC RELATIONAL MAPS W. B. Vasantha Kandasa... ...ird book in the Neutrosophics Series. The earlier two books are Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps (http://gallup.unm.edu/~smarand... ...t Labourers Living With HIV/AIDS Using Fuzzy Theory and Neutrosophic Cognitive Maps: With Specific Reference to Rural Tamil Nadu in India (http://g... ... conveniently viewed as reflexive undirected graphs contrary to fuzzy cognitive maps that are directed graphs. In this context, reflexivity implies ... ...ments x 1 , x 2 ∈ X belong to the same block of the partition if and only if h maps them to the same element of Y. Let A = {a 1 , a 2 , …, a n } an... ...phism and an endomorphism is called an automorphism. In this case the function maps the set X to itself and the relation R and Q are equal. Each of... ...neral, of course, is to consider Θ as an operator (of some finite parity) which maps fuzzy sets and relations onto fuzzy sets or fuzzy relations – a... ...the map µ : X → {0, 1, I} is called the crisp fuzzy neutrosophic set, that is µ maps elements of X to the set 0, 1 and I. µ(x) = 0; for x ∈ X im...

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...W. B. VASANTHA KANDASAMY FLORENTIN SMARANDACHE FUZZY COGNITIVE MAPS AND NEUTROSOPHIC COGNITIVE MAPS XIQUAN Phoenix ... ... SUCCESSFUL LARGE SCALE OPERATION SOCIAL SERVICE 1 Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps W. B. Vasantha Kandasamy Depa... ...ion 4 Preface 5 Chapter One BASIC CONCEPTS ABOUT FUZZY COGNITIVE MAPS AND FUZZY RELATIONAL MAPS 1.1 Definition of Fuzzy Cognitive Maps ... ...PS 1.1 Definition of Fuzzy Cognitive Maps (FCMs) 7 1.2 Fuzzy Cognitive Maps – Properties and Models 10 1.3 Some more illustrations of FCMs 26 1.... ...plications of FCMs 63 1.5 Definition and Illustration of Fuzzy Relational Maps (FRMs) 93 1.6 Models illustrating FRM and combined FRMs 96 1.7 Linke... ... Models illustrating FRM and combined FRMs 96 1.7 Linked Fuzzy Relational Maps 118 Chapter Two ON NEUTROSOPHIC COGNITIVE MAPS AND NEUTROSOPHIC ... ...Chapter Two ON NEUTROSOPHIC COGNITIVE MAPS AND NEUTROSOPHIC RELATIONAL MAPS – PROPERTIES AND APPLICATIONS 2.1 An introduction to neutrosophy 1... ...basic notions about neutrosophic graphs 129 2.4 On neutrosophic cognitive maps with examples 134 2.5 Some more illustrations of NCMs 143 2.6 Applic... ...ions of NCMs 143 2.6 Applications of NCMs 150 2.7 Neutrosophic Cognitive Maps versus Fuzzy Cognitive Maps 157 2.8 Neutrosophic Relational Maps (NRM...

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...In this book authors for the first time introduce new mathematical models analogous to FCMs and NCMs. They have constructed 12 types of MOD Cognitive Maps models, such as: MOD Cognitive Maps model, MOD dual number Cognitive Maps model, MOD neutrosophic Cognitive Maps model, MOD finite complex number Cognitive Maps model, MOD special dual like number Cognitive Maps model, M...

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... role in mathematics are widely accepted by mathematicians today. On the last century, many works are concentrated on the combinatorial properties of maps. The main trend is the enumeration of maps, particularly the rooted maps, pioneered by W. Tutte, and today, this kind of papers are still appeared on the journals frequently today. All of those is surveyed in Liu’s book ...

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...LINFAN MAO AUTOMORPHISM GROUPS OF MAPS, SURFACES AND SMARANDACHE GEOMETRIES American Research Press Rehoboth,... ...ciences Beijing 100080, P.R.China maolinfan@163.com AUTOMORPHISM GROUPS OF MAPS, SURFACES AND SMARANDACHE GEOMETRIES Partially post-doctoral research ... ... century, many works are concentrated on the combinatorial prop- erties of maps. The main trend is the enumeration of maps, particularly the rooted ma... ...nd White [70], especially the [53] for detail. The construction of regular maps on surfaces, related maps with groups and geometry is a glimmer of the... ...d geometry is a glimmer of the map theory with other mathematics. In fact, maps as a kind of the decomposition of surfaces, should be given more atten... ...ith higher dimension are inspired by the Riemann surfaces. The relation of maps with Riemann surfaces has been known in 80s in the last century. Then ... ...emann surfaces, Riemann geometry and finally, the Smarandache geometries by maps is a very interesting problem. Unless the enumeration of unrooted maps... ...y. We introduce the conceptions of Klein surfaces, Smarandache geometries, maps and the semi-arc automorphism group of a graph. Preface ii A relation... ...and the semi-arc automorphism group of a graph. Preface ii A relation for maps and Smarandache manifolds (abbreviated s-manifolds) and a scheme for t...

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...In this book authors for the first time construct a MOD Relational Maps model analogous to Fuzzy Relational Maps (FRMs) model or Neutrosophic Relational Maps (NRMs) model using the MOD rectangular or relational matrices. The advantage of using these models is that we are sure to get the MOD ...

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... 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 f...

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...RERS LIVING WITH HIV/AIDS USING FUZZY THEORY AND NEUTROSOPHIC COGNITIVE MAPS With Specific Reference To Rural Tamilnadu In India XIQUA... ...URERS LIVING WITH HIV/AIDS USING FUZZY THEORY AND NEUTROSOPHIC COGNITIVE MAPS With Specific Reference To Rural Tamilnadu In India W. B. Vasan... ...bourers 4.1 Basic notion of neutrosophy and Neutrosophic cognitive maps 122 4.2 Use of NCM to analyse the HIV/AIDS affected migrant labou... ...of HIV/AIDS Migrant Labourers 271 5.5 Linked Neutrosophic Relational Maps and its application to Migrant Problems 288 5.6 Combined Disjoi... ...du 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 ... ...speaks about the migrant labourers. In chapter two we use Fuzzy Cognitive Maps to analyze the socio-economic problems of HIV/AIDS infected migrant ... ...erability in catching HIV/AIDS. For the first time Neutrosophic Cognitive Maps are used in the study of migrant labourers who have become HIV/AIDS ... ... study is done in Chapter IV. In chapter V we use Neutrosophic Relational Maps and we define some new neutrosophic tools like Combined Disjoint Bloc... ...than the fuzzy model. This book uses the notion of neutrosophic cognitive maps, combined neutrosophic cognitive maps, neutrosophic relational maps a...

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...ok, the famous explorer and chartmaker, in 1778. Between then and the mid-19th century, visitors to HawaiI produced a rich assortment of charts and maps depicting the shores, harbors, towns, and volcanoes of the various islands. This volume traces the story of the mapping of HawaiI during the pivotal years in which the indigenous society was radically transformed by th...

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...uction of mapmaking in the islands. For well over seventy years, mapping in Hawaii was largely carried out by Europeans or Americans, and the early maps of Hawaii were mostly made to serve the needs of those foreigners....

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...In collecting the names from the primary source, the thirty-three maps and quadrangles of the islands, except those of the re-survey of Oahu, were marked in rectangles, the sides of which were one minute long, and the named geographic features located to the nearíest minute of latitude and ...

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...111 -- Molokai -- 143 -- Niihau -- 159 -- Oahu -- 163 -- Leeward Islands -- 197 -- Other Islands -- 199 -- Sources of Place-Names in the Gazetteer: - Maps of the United States Geological Survey -- 200 -- Maps and Charts of the Territorial, the Royal Hawaiian, and the United States Governments -- 202 -- Miscellaneous maps - Key to Identification Symbols -- 205 -- Hawaiian W...

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...sis and study of several of the real world problems which are based only on unsupervised data. The fuzzy and neutrosophic tools like fuzzy cognitive maps invented by Kosko and neutrosophic cognitive maps introduced by us help in the analysis of such real world problems and they happen to be mathematical tools which can give the hidden pattern of the problem under investig...

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...TION OF BIMATRICES TO NEW FUZZY MODELS 3.1. Definition of Fuzzy Cognitive Maps 71 3.2. Fuzzy Cognitive Bimaps and their Applications 76 3.3.... ... Applications 102 4 3.4. Definition and Illustration of Fuzzy Relational Maps 121 3.5. Fuzzy Relational Bimaps and their Applications 124 3.... ... Neutrosophic Trimaps and their Applications 209 4.5 Neutrosophic Relational Maps 218 4.6 Neutrosophic Relational Bimaps and their Applications 22... ...y on unsupervised data. The fuzzy and neutrosophic tools like fuzzy cognitive maps invented by Kosko and neutrosophic cognitive maps introduced by ... ...w tools are used in the construction of fuzzy cognitive bimaps, trimaps and n-maps and fuzzy relational bimaps, trimaps and n-maps. The neutrosophi... ...neralization of some of the results given in our earlier book Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps (2003). Those who wish to simult... ... we dedicate this book to Prof. Dr. Bart Kosko, the father of Fuzzy Cognitive Maps. W.B.VASANTHA KANDASAMY FLORENTIN SMARANDACHE K.ILANTHEN... ...pplications of bimatrices in the fuzzy models in general and fuzzy cognitive maps in particular. To have such models we have to introduce bigraphs ... ... set disjoint from V i (G) for i = 1, 2 and 1 G I and 2 G Ia r e incidence maps that associates with each element of E i (G) an unordered pair o...

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... their life after are described briefly in this chapter. We provide also the references for these concepts. Bart Kosko introduced the Fuzzy Cognitive Maps (FCMs) in the year 1986. Fuzzy Cognitive Maps are fuzzy structures that strongly resemble neural networks, and they have powerful and far-reaching consequences as a mathematical tool for modeling complex systems. FCM was...

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...OF SCHOOL STUDENTS USING RULE BASED CONTROL SYSTEM 89 Chapter Seven MIGRATION OF PARENTS AND THE SCHOOL DROPOUTS A STUDY USING THE FUZZY RELATIONAL MAPS MODEL 99 Chapter Eight THE IMPACT OF MISSIONARY INTERVENTIONS ON THE EDUCATION AND REHABILITATION OF DEPRIVED CHILDREN – A FUZZY ANALYSIS 117 Chapter Nine CONCLUSIONS AND SUGGESTIONS 129 FURTHER READING 139 INDEX ...

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...uestion 1.1. to determine or find structures or properties of configurations, such as those structure results appeared in graph theory, combinatorial maps and design theory,..., etc.. Question 1.2. to enumerate configurations, such as those appeared in the enumeration of graphs, labeled graphs, rooted maps, unrooted maps and combinatorial designs,...,etc.....

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...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 ...

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...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 Illustrati...

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... . , etc.. Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manif...

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...econd Smarandache Bol Loops BY T.G.JA´IY´E O. L´A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11 Smarandachely Precontinuous maps and Preopen Sets in Topological Vector Spaces BY SAYED ELAGAN. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Path Double Covering Number of Product Graphs BY A. NAGARAJAN, V. MAHESWARI, S. NAVANE...

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...LE FUZZY MODELS AND THEIR APPLICATIONS TO REAL WORLD PROBLEMS 71 2.1 Description of Simple Fuzzy Matrix Model 72 2.2 Definition of Fuzzy Cognitive Maps with real world model representation 146 2.3 Definition and Illustration of Fuzzy Relational Maps 205 2.4 Introduction to Bidirectional Associative Memories (BAM) Model and their Application 238 2.5 Description of F...

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...ed in the USA during the last century - are they real or fake? The author examines this and many other issues, like traces in the Indian culture, old maps and buildings, and of course Medieval documents. Together, all this material gives an overwhelming evidence that an extensive Norse exploration or even permanent settlements may have taken place. Text in Norwegian....

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...hin the 2015–47 period. Although robot systems of one millimeter or smaller are not explicitly specified in current DOD and Air Force technology road maps, the technological aims towards this size can be clearly inferred from official documents. This research assesses the likelihood of, and barriers to, the realization of true microrobots and nanorobots (defined as submill...

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...This long essay is the second part of a series, with the first part being “USA Russia & China in the Middle East: Alliances & Conflicts”. Over 80 maps are used to explain the energy war between Russia and Turkey, two countries that have been fighting for regional dominance for many centuries. Today, the main geographical locations of their conflicts are the regions ...

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...YSIS OF THE COLLECTED DATA OF THE PWDS FROM MELMALAYANUR AND KURINJI PADI BLOCKS IN TAMIL NADU 13 Chapter Three THE NEW FUZZY COGNITIVE RELATIONAL MAPS (FCRMS) BIMODEL 29 Chapter Four ANALYSIS OF THE SOCIO ECONOMIC PROBLEMS FACED BY THE PWDS USING (SFCMS) 47 4.1 Application of FCMs Models to Social and Psychological Problems 48 4.2 Expert Opinion of PWDs using Speci...