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...Graphs and matrices play a vital role in the analysis 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 u...

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... 5 Preface Graphs and matrices play a vital role in the analysis and study of several of the real world problems which are ba... ...vented by Kosko and neutrosophic cognitive maps introduced by us help in the analysis of such real world problems and they happen to be mathematica... ... 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 un... ...This book, in order to generalize the two models, has systematically invented mathematical tools like bimatrices, trimatrices, n-matrices, bigraphs,... ...y study several models that are at times time dependent or when a comparative analysis is needed can use these models. On a personal note, we th... ...FCM and overlap FCM when some of the attributes overlap i.e. in the study or analysis of a model when we have some common attributes given by exper... ...t will be easy for an expert to work with. He need not be a person with good mathematical background. For an expert may be a doctor or a lay man wh... ... of the NRM model we will proceed on to describe the concepts of it in a more mathematical way. DESCRIPTION OF A NRM: Neutrosophic Cognitive Ma... .... 58. Jacobson, N. Structure of Rings, Colloquium Publications, 37, American Mathematical Society, 1956. 59. Jang, S.R., C.T. Sun and E. Mizutani. ...

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...lem using FRE 196 2.6 Data compression with FRE 196 2.7 Applying FRE to Threat Analysis 196 2.8 FRE application to medical diagnosis 197 2.9 A fuz... ... Neutrosophic Cognitive Maps (http://gallup.unm.edu/~smarandache/NCMs.pdf) and Analysis of Social Aspects of Migrant Labourers Living With HIV/AIDS... ...their properties It is well known fact that binary relations are generalized mathematical functions. Contrary to functions from X to Y, binary re... ...ominated criterion vectors is called the non-dominated set. In the absence of a mathematical specification of the decision maker’s utility function,... ... we can only provide the decision maker with the Pareto optimal set for further analysis. For a problem with multiple linear objective functions, th... ...he transform function f and the threshold value θ, which is reasonable (see the analysis by [6]) in fact for our fuzzy neural network discussed late... ...ity to determine outputs for a given set of inputs without using conventional, mathematical models. FLC follows the general strategy of control wor... ... with sup-t composition nor adjoint equation. Therefore, simple control is not “mathematically correct”. However, solutions of fuzzy relational equa... ...of the fluid under study their by changing the flow rates while analyzing as a mathematical model. So in the study of flow rates in chemical plants...

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...The basic tools used in the analysis of the problem of school dropout and 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. ...

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...Preface 5 Chapter One INTRODUCTION 7 Chapter Two BASIC CONCEPTS 21 Chapter Three CAUSES OF SCHOOL DROPOUTS – A MATHEMATICAL ANALYSIS 35 Chapter Four SCHOOL DROPOUTS AS CHILD LABOURERS 59 Chapter Five SCHOOL DROPOUTS AS RAG PICKERS USING FUZZY MODELS 79 Chapter Six PERFORMANCE ASPECTS OF SCHOOL STUDENTS USING RULE BASED CONTROL ...

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...e that often the subsutras are not used under the main sutra for which it is the subsutra or the corollary. This is the main deviation from the usual mathematical principles of theorem (sutra) and corollaries (subsutra). (2) It cannot be easily compromised that a single sutra (a Sanskrit word) can be mathematically interpreted in this manner even by a stalwart in Sanskrit...

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...Preface 5 Chapter One INTRODUCTION TO VEDIC MATHEMATICS 9 Chapter Two ANALYSIS OF VEDIC MATHEMATICS BY MATHEMATICIANS AND OTHERS 31 2.1 Views of Prof. S.G.Dani about Vedic Mathematics from Frontline 33 2.2 Neither Vedic Nor Mathematics 50 2.3 Views about the Book in Favour and Against 55 2....

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...Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all a...

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...of FRM models and the attributes taken for the study related with the PWDs and the caretakers, the FRM model formed using these attributes and their analysis. The third section gives the suggestions and conclusions derived from the survey as well as the FRM model. Key Words: FRM model, fixed point, hidden pattern, relational matrix, limit cycle. AMS(2000): 04A72....

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...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 ...

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...c logic grew as an alternative to the existing logics and it represents a mathematical model of uncertainty, vagueness, ambiguity, imprecision, undef... ...eural networks, and they have powerful and far-reaching consequences as a mathematical tool for modeling complex systems. Prof. Bart Kosko, the guru... ...as been used to study real-world situations as varied as stock-investment analysis to supervisory system control, and child labor to community mobil... ...ct us almost as much as the determined factors. It is a major handicap in mathematical modeling that we are only able to give weightages for known c... ... systems; mobile robots and in intimate technology such as office plants; analysis of business performance assessment; formalism debate and legal ru... ...s to be better than that of the FCM model in several ways mainly when the analysis of the data can be treated as two disjoint entities. Thus its appl... ...12, 119]. This example illustrates the strengths and weaknesses of FCM analysis. FCM allows experts to represent factual and evaluative concepts ... ...ng issues are naturally solved, since Time is explicitly expressed in the mathematical equations used to describe the relations between concepts. Ho... ...Only the modifier is used. However, its meaning can be represented in the mathematical expression as (Q i ∪ ~ Q i ) ∩ M i which contains the qua...