...he end of which there were two little sketches of the arts of rheto ric and logic, the latter finishing with a specimen of a dis pute in the Socrati... ...dvantage of more time for reading and studying, and a won derful genius for mathematical learning, in which he far outstript me. While I liv’d in Bos...

...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...

...NG written by Lao Zi, an ancient philosopher of China. Then how it works to mathematics, not suspended in thought? This paper explains this action by mathematical logic on mathematical systems generalized to Smarandache systems, or such systems with combinatorial structures, i.e., combinatorial systems, and shows how to extend the homomorphism theorem in abstract algebra t...

... 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,... ...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... ...rt was the union leader but the third expert opinion is best for we see much logic when the employee works for less number of hours, poor performan... ...s find their application is real world problems which are modeled using fuzzy logic and neutrosophic logic. C 2 FIGURE 3.6.9 151 Chapter... ...rminacy to play a role. Such study is possible only by using the Neutrosophic logic or the concept of indeterminacy. Example 4.5.1: Female infant... ... 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... ..., E.S., and D.A. Farber. Beyond the Formalism Debate: Expert Reasoning, Fuzzy Logic and Complex Statutes, Vanderbilt Law Review, 52, 1243-1340, 1999... .... 58. Jacobson, N. Structure of Rings, Colloquium Publications, 37, American Mathematical Society, 1956. 59. Jang, S.R., C.T. Sun and E. Mizutani. ...

...nitive 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 investigation. This book, in order to generalize the two models, has systematically invented mathematical tools like bimatrices, trimatrices, n-matric...

...IC DEFINITIONS ON NEUTROSOPHIC THEORY 3.1 Neutrosophic sets and neutrosophic logic 222 3.2 Fuzzy neutrosophic sets 230 5 3.3 On neutrosophi... ...their properties It is well known fact that binary relations are generalized mathematical functions. Contrary to functions from X to Y, binary re... ...ant role in fuzzy relation equations. While the t-norm i may be interpreted as logical conjunction, the corresponding operation w i may be interpr... ... as logical conjunction, the corresponding operation w i may be interpreted as logical implication. The following basic properties 31 of w i ... ...ominated criterion vectors is called the non-dominated set. In the absence of a mathematical specification of the decision maker’s utility function,... ... plausible control and adjoint equation results in simple fuzzy control. Fuzzy logic control is one of the expanding application fields of fuzzy se... ...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...

... OF DISSENT 5 PREFACE In a world of chaotic alignments, traditional logic with its strict boundaries of truth and falsity has not imbued itsel... ...apability of reflecting the reality. Despite various attempts to reorient logic, there has remained an essential need for an alternative system that... ...orld. Out of this need arose the system of Neutrosophy, and its connected logic, Neutrosophic Logic. Neutrosophy is a new branch of philosophy that ... ...spectrum of Neutralities. This philosophy forms the basis of Neutrosophic logic. Neutrosophic logic grew as an alternative to the existing logics... ...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... ...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... ...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...

...In a world of chaotic alignments, traditional logic with its strict boundaries of truth and falsity has not imbued itself with the capability of reflecting the reality. Despite various attempts to reorient logic, there has remained an essential need for an alternative sy...

...osophy 453 Further Reading 456 Index 468 Preface Neutrosophic logic grew as an alternative to the existing topics and it represents a ma... ...c logic grew as an alternative to the existing topics and it represents a mathematical model of uncertainty, vagueness, ambiguity, imprecision, unde... ...tency, redundancy and contradiction. Despite various attempts to reorient logic, there has remained an essential need for an alternative system tha... ...world. Out of this need arose the system of neutrosophy and its connected logic, neutrosophic logic. This new logic, which allows also the concept o... ...oor uneducated labourers from rural Tamil Nadu. This book is an extended mathematical analysis of the book Love.Life.Lust.Loss: 101 Real Life Stori... ...te vector using the dynamical system. Appendix 9 deals with Neutrosophic logic. We have included a list of further reading. We deeply acknowledge... ...the study of peoples and populations, for it not only involves the merely mathematical spatial redistribution of people, but also because it has eno... ...f the literature on the said topic. We like to point out that most of the mathematical research into migration has dealt with it on purely statistic... ...tions simple and easy. 14 It is important to mention that the relevant mathematical notions used in each of these chapters are described in the ...

...Migration acquires great significance in the study of peoples and populations, for it not only involves the merely mathematical spatial redistribution of people, but also because it has enormous impact on livelihood, life-styles, employment, socioeconomic and political stability; or in other words, it influences the entire society. When u...

...ear 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 a fuzzy extension of the cognitive map pioneered in 1976 by political scientist Robert Axelord, who used it to represent knowledge as an interconnected, directed, bileve...

...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 ...

...d with its first systematic exposition. 2 This conception is, of course, a logical correlate of the conceptions of the external relation of stimulus a... ...y stage short of attainment of this goal is merely an unfolding toward it. Logically the 61 John Dewey doctrine is only a variant of the preparation ... ...ng to Froebel, the actuating force is the presentation of symbols, largely mathematical, corresponding to the essential traits of the Absolute. When t... ...to Froebel, the mystic symbolic value of certain objects and acts (largely mathematical) stand for the Absolute Whole which is in process of unfolding... ...with rigid ad- herence to their past customs. On such a basis it is wholly logical to fear intercourse with others, for such contact might dissolve cu... ...upposed) except the acknowledgment of duty or the value of discipline. The logical result is expressed with literal truth in the words of an American ... ... has been led to foresee (infer) a future eclipse. No matter how great the mathematical probability, the inference is hypothetical—a matter of probabi... ...In practice, overemphasis upon formed material leads to an exaggeration of mathematical qualities, since intellect finds its profit in physical things... ...ases, of geographical study which tend to become specialized and separate. Mathematical or astronomical, physiographic, topographic, political, commer...