Description Details
This book is organized into seven chapters. The first one is introductory in nature. In the second chapter authors give the unique and new way of analyzing the data which is time dependent. In chapter three the authors for the first time define the new concept of matrices with linguistic variables. In chapter four authors have used super matrices in super fuzzy models like super FCMs, super FRMs super FAMs etc. In chapter five we define interval matrix and matrix interval using the natural class of intervals, that is intervals of the form [a, b] where a b or a and b not comparable. In the final chapter we have defined the new notion of bimatrices and n-matrices. Using these new concepts we have constructed linear algebra of type I and linear algebra of type II. Using these matrices we can build n-eigen values and n-eigen vectors....

Table of Contents Details
Preface 5 Chapter One INTRODUCTION 7 Chapter Two AVERAGE TIME DEPENDENT (ATD) DATA MATRIX 9 Chapter Three FUZZY LINGUISTIC MATRICES AND THEIR APPLICATIONS 43 Chapter Four SUPERMATRICES AND THEIR APPLICATIONS 65 Chapter Five INTERVAL MATRICES AND NATURAL CLASS OF INTERVALS 149 Chapter Six DSM MATRIX OF REFINED LABELS 203 Chapter Seven N-MATRICES AND THEIR APPLICATIONS 205 FURTHER READING 217 INDEX 222 ABOUT THE AUTHORS 226...

Description Details
In this book authors study and analyze the problem of school dropouts and their life after. The problems can by no means be analyzed by collecting the numerical data. For such data can only serve as information beyond that the data can be of no use, for the school dropouts suffer an environment change after becoming a school dropout. Thus the emotions of the school dropout; is technically involved....

Excerpt Details
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. 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, bilevel-logic graph....

Table of Contents Details
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 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 143 ABOUT THE AUTHORS 145...

Description Details
In this book the authors study the erasure techniques in concatenated Maximum Rank Distance (MRD) codes. The authors for the first time in this book introduce the new notion of concatenation of MRD codes with binary codes, where we take the outer code as the RD code and the binary code as the inner code....

Excerpt Details
We want to find efficient algebraic methods to improve the realiability of the transmission of messages. In this chapter we give only simple coding and decoding algorithms which can be easily understood by a beginner. Binary symmetric channel is an illustration of a model for a transmission channel. Now we will proceed onto define a linear code algebraically....

Table of Contents Details
Preface 5 Chapter One BASIC CONCEPTS 7 Chapter Two ALGEBRAIC LINEAR CODES AND THEIR PROPERTIES 29 Chapter Three ERASURE DECODING OF MAXIMUM RANK DISTANCE CODES 49 3.1 Introduction 49 3.2 Maximum Rank Distance Codes 51 3.3 Erasure Decoding of MRD Codes 54 Chapter Four MRD CODES –SOME PROPERTIES AND A DECODING TECHNIQUE 63 4.1 Introduction 63 4.2 Error-erasure Decoding Techniques to MRD Codes 64 4.3 Invertible q-Cyclic RD Codes 83 4.4 Rank Distance Codes With Complementary Duals 101 4.4.1 MRD Codes With Complementary Duals 103 4.4.2 The 2-User F-Adder Channel 106 4.4.3 Coding for the 2-user F-Adder Channel 107 Chapter Five EFFECTIVE ERASURE CODES FOR RELIABLE COMPUTER COMMUNICATION PROTOCOLS USING CODES OVER ARBITRARY RINGS 111 5.1 Integer Rank Distance Codes 112 5.2 Maximum Integer Rank Distance Codes 114 Chapter Six CONCATENATION OF ALGEBRAIC CODES 129 6.1 Concatenation of Linear Block Codes 129 6.2 Concatenation of RD Codes With CR-Metric 140 FURTHER READING 153 INDEX 157 ABOUT THE AUTHORS 161...

Description Details
科学面临的难题 _ 中智学为何诞生 中智学(neutrosophy)起源于1995年美国, 它站在东西文化交融的立场上, 从对立统一的角度探索从科学技术到文学艺术的一切宏观及微观结构, 构造超越一切学科、超越自然科学与社会科学界限的统一场, 以解决当今认知科学、信息科学、系统科学、经济学、量子力学等科学技术前沿难题——非确定性问题。中智学努力通过新型开放模式改造当今各自然科 与社会科学, 实现它们的新陈代谢、改革创新和更新换代。中智学在我们中国还属空白, 故借 对学科正式命名并引入中国。...

Excerpt Details
中智学, 新的哲学分支 _(Neutrosophy - A New Branch of Philosophy) 摘要: 本文推出了一个新的哲学分支, 中智学 _(neutrosphy), 研究中性的起源、本质和范畴以及和不同思想观念的作用。它的基本点是: 任何观念具有T%的真实性、I%的不确定性以及 的谬误性, 其中T, I, F为╟-0, 1+╢的标准或非标准子集。 _基本理论:任何观念 _ 趋于被 _ 所中和、削弱和平衡 _(不仅仅是被黑格尔主 的), 达到一种平衡状态。 中智学是中智逻辑学 _(在模糊逻辑的基础上总结出来的多值逻辑)、中智集合论 _(模糊 合论的概括总结)、中智概率论和中智统计学 _(分别是经典及非精确概率论、统计学的概括 结) 的基础。 _ 关键字与短语: 非标准分析, 超实数, 无穷小, 单子, 非标准实数单位区间, 集合运算。 _...

Table of Contents Details
译者序 _Preface by the Translator ........................................5 作者简介 _Author’s Biography ..........................................9 译者简介 _Biography of the Translator.................................12 原书前言 _查尔斯·李 _.....................................................19 Preface by Charles T. Le 0．引言: 非标准实数单位区间 _.......................................24 Introduction: The Non-Standard Real Unit Interval 1．中智学——哲学的崭新分支 _.......................................27 Neutrosophy - a new branch of philosophy 2．中智逻辑——逻辑学的统一 _........................................90 Neutrosophic Logic - a unifying field in logics 3．中智集合论——集合论的统一 _....................................109 Neutrosophic Set - a unifying field in sets 4．中智概率论 _..........................................................113 ——传统概率论和非精确概率论的概括总结 _ ——以及中智统计学 _ Neutrosophic Probability - a generalization of classical and imprecise probabilities - and Neutrosophic Statistics 附录: 中智学产生的定义 _..............................................117 Addenda: Definitions derived from Neutrosophics...

Description Details
1. 科学面临的难题 中智学为何诞生 中智学(neutrosophy)起源于1995年美国, 它站在东西文化交融的立场上, 从对立统一的角度探索从科学技术到文学 艺术的一切宏观及微观结构, 构造超越一切学科、超越自然科学与社会科学界限的统一场, 以 决当今认知科学、信息 科学、系统科学、经济学、量子力学等科学技术前沿难题——非确定性问题。中智学努力通 新型开放模式改造当今 各自然科学与社会科学, 实现它们的新陈代谢、改革创新和更新换代。中智学在我们中国还 空白, 故借此对学科正式 命名并引入中国。...

Excerpt Details
中智学, 新的哲学分支(Neutrosophy - A New Branch of Philosophy) 摘要: 本文推出了一个新的哲学分支, 中智学 (neutrosphy), 研究中性的起源、本质和范畴以及和不同思想观念的 作用。它的基本点是: 任何观念具有T%的真实性、I%的不确定性以及 F%的谬误性, 其中T, I, F 为╟-0, 1+╢的标准或 非标准子集。 基本理论:任何观念 趋于被 所中和、削弱和平衡 (不仅仅是被黑格尔主张的), 达到一种 平衡状态。 中智学是中智逻辑学 (在模糊逻辑的基础上总结出来的多值逻辑)、中智集合论 (模糊集合论的概括总结)、中智概 率论和中智统计学 (分别是经典及非精确概率论、统计学的概括总结) 的基础。 关键字与短语: 非标准分析, 超实数, 无穷小, 单子, 非标准实数单位区间, 集合运算。...

Table of Contents Details
译者序 Preface by the Translator ..................................5 作者简介 Author’s Biography ..............................9 译者简介 Biography of the Translator...........................12 原书前言 查尔斯·李 ............................................18 Preface by Charles T. Le 0．引言: 非标准实数单位区间 ..............................23 Introduction: The Non-Standard Real Unit Interval 1．中智学——哲学的崭新分支 ..............................26 Neutrosophy - a new branch of philosophy 2．中智逻辑——逻辑学的统一 ...............................83 Neutrosophic Logic - a unifying field in logics 3．中智集合论——集合论的统一 ..............................100 Neutrosophic Set - a unifying field in sets 4．中智概率论 ...........................................103 ——传统概率论和非精确概率论的概括总结 ——以及中智统计学 Neutrosophic Probability - a generalization of classical and imprecise probabilities - and Neutrosophic Statistics 附录: 中智学产生的定义 ..................................106 Addenda: Definitions derived from Neutrosophics...

Description Details
In part 1, we have defined a fuzzy utility system, with different financial goals, different levels of risk tolerance and different personal preferences, liquid assets, etc. In part 2, we have defined a computational model for a simple portfolio insurance strategy using a protective put and computationally derive the investor’s governing utility structures underlying such a strategy under alternative market scenarios. In Part 3, it is proposed an artificial classification scheme to isolate truly benign tumors from those that initially start off as benign but subsequently show metastases. In part 4, an alternative methodological approach has been proposed for quantifying utility in terms of expected information content of the decision-maker’s choice set....

Excerpt Details
In this paper we have designed our fuzzy system so that customers are classified to belong to any one of the following three categories: *Conservative and security-oriented (risk shy) *Growth-oriented and dynamic (risk neutral) *Chance-oriented and progressive (risk happy) A neutrosophic system has three components – that’s why it may be considered as just a generalization of a fuzzy system which has only two components. Besides being useful for clients, investor classification has benefits for the professional investment consultants as well. Most brokerage houses would value this information as it gives them a way of targeting clients with a range of financial products more effectively - including insurance, saving schemes, mutual funds, and so forth. Overall, many responsible brokerage houses realize that if they provide an effective service that is tailored to individual needs, in the long-term there is far more chance that they will retain their clients no matter whether the market is up or down....

Description Details
This book has five chapters. In Chapter I, we give a brief description of the sixteen sutras invented by the Swamiji. Chapter II gives the text of select articles about Vedic Mathematics that appeared in the media. Chapter III recalls some basic notions of some Fuzzy and Neutrosophic models used in this book. This chapter also introduces a fuzzy model to study the problem when we have to handle the opinion of multiexperts. Chapter IV analyses the problem using these models. The final chapter gives the observations made from our study....

Excerpt Details
We then remove the common factor if any from each and we find x + 1 staring us in the face i.e. x + 1 is the HCF. Two things are to be noted importantly. (1) We see 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 except the Jagadguru Puri Sankaracharya. We wind up the material from the book of Vedic Mathematics and proceed on to give the opinion/views of great personalities on Vedic Mathematics given by Jagadguru. Since the notion of integral and differential calculus was not in vogue in Vedic times, here we do not discuss about the authenticated inventor, further we have not given the adaptation of certain sutras in these fields. Further as most of the educated experts felt that since the Jagadguru had obtained his degree with mathematics as one of the subjects, most of the results given in book on Ve...

Table of Contents Details
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 2.4 Vedas: Repositories of Ancient Indian Lore 58 2.5 A Rational Approach to Study Ancient Literature 59 2.6 Shanghai Rankings and Indian Universities 60 2.7 Conclusions derived on Vedic Mathematics and the Calculations of Guru Tirthaji - Secrets of Ancient Maths 61 Chapter Three INTRODUCTION TO BASIC CONCEPTS AND A NEW FUZZY MODEL 65 3.1 Introduction to FCM and the Working of this Model 65 3.2 Definition and Illustration of Fuzzy Relational Maps (FRMS) 72 3.3 Definition of the New Fuzzy Dynamical System 77 3.4 Neutrosophic Cognitive Maps with Examples 78 3.5 Description of Neutrosophic Relational Maps 87 3.6 Description of the new Fuzzy Neutrosophic model 92 Chapter Four MATHEMATICAL ANALYSIS OF THE VIEWS ABOUT VEDIC MATHEMATICS USING FUZZY MODELS 95 4.1 Views of students about the use of Vedic Mathematics in their c...

Description Details
This book has four chapters. In chapter one the authors introduce the three types of super FRM models. Chapter two uses these three new super fuzzy models to study the role of media which feverishly argued against 27 percent reservation for OBCs in Central Government-run institutions in India. The experts we consulted were divided into 19 groups depending on their profession. These groups of experts gave their opinion and comments on the news-items that appeared about reservations in dailies and weekly magazines, and the gist of these lengthy discussions form the third chapter of this book. The fourth chapter gives the conclusions based on our study....

Table of Contents Details
Dedication 5 Preface 6 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 Super Fuzzy Mixed FRM Model to Study the Role of Media in Falsely Blaming the Government and Supporting Dr. Venugopal 88 2.4 Use of Super Column FRM Model to Study the Interrelation between the Government and Public 102 2.5 Analysis of Role of Media on Reservation for OBC using Fuzzy Cognitive Map 117 2.6 Observations based on this Analysis by Students and Experts through Seminars and Discussions 121 Chapter Three EXCERPT OF NEWS FROM PRINT MEDIA AND SUGGESTIONS AND COMMENTS BY THE EXPERTS 145 Chapter Four ANALYSIS SUGGESTIONS AND CONCLUSIONS BASED ON DISCUSSIONS, QUESTIONNAIRE, INTERVIEWS AND MATHEMATICAL MODELS 357 4.1 A View and Analysis by Group of Educationalists about Role of Media on OBC Reservation 357 4.1.1 Students Pro...

Description Details
In this book, we consider various many-valued logics: standard, linear, hyperbolic, parabolic, non-Archimedean, p -adic, interval, neutrosophic, etc. We survey also results which show the tree different proof-theoretic frameworks for many-valued logics, e.g. frameworks of the following deductive calculi: Hilbert ’s style, sequent, and hypersequent. Recall that hypersequents are a natural generalization of Gentzen ’s style sequents that was introduced independently by Avron and Pottinger . In particular, we examine Hilbert ’s style, sequent, and hypersequent calculi for infinite-valued logics based on the three fundamental continuous t-norms: Lukasiewicz ’s, Godel ’s, and Product logics....

Excerpt Details
1.1 Neutrality concept in logic Every point of view A tends to be neutralized, diminished, balanced by Non-A. At the same time, in between A and Non-A there are infinitely many points of view Neut-A. Let’s note by A an idea, or proposition, theory, event, concept, entity, by Non-A what is not A, and by Anti-A the opposite of A. Neut-A means what is neither A nor Anti-A, i.e. neutrality is also in between the two extremes. ...

Table of Contents Details
1 Introduction. . . . . . . . . . . . . . . 9 1.1 Neutrality concept in logic . . . . . . . . . . . . . . . . . . . . . . 9 1.2 Neutrality and non-Archimedean logical multiple-validity . . . . 10 1.3 Neutrality and neutrosophic logic . . . . . . . . . . . . . . . . . . 13 2 First-order logical language. . . . . . . . . . . . . . . 17 2.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2 Hilbert’s type calculus for classical logic . . . . . . . . . . . . . . 20 2.3 Sequent calculus for classical logic . . . . . . . . . . . . . . . . . 22 3 n -valued Lukasiewicz’s logics. . . . . . . . . . . . . . . 27 3.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2 Originality of (p + 1)-valued Lukasiewicz’s logics . . . . . . . . . 30 3.3 n-valued Lukasiewicz’s calculi of Hilbert’s type . . . . . . . . . . 32 3.4 Sequent calculi for n-valued Lukasiewicz’s logics . . . . . . . . . . 33 3.5 Hypersequent calculus for 3-valued Lukasiewicz’s propositional logic . . . . . . . . . . . .37 4 Infinite valued Lukasiewicz’s logics. . . . . . . . . . . . . . . 39 4.1 Prelimi...

Description Details
We focus our discussions in this book on cities, because in our opinion a city is the smallest economic entity which has ‘self-organizing’ character, in a sense that a city can grow by itself (with minimum intervention). Nonetheless, this book will not discuss the self-organization character itself, but a new concept called ‘Cultural Economy’ development. Cultural Economic here is part of leisure and tourism industry, and depends on taste, advertisement, history, and the quality of being diverse, distinctive, with a large spectrum of varieties....

Table of Contents Details
Content ................... 3 Prologue ....................... 4 Biography of authors .................. 7 Chapter 1. Historical Precursor ............. 8 Pitfalls of Industrialization Is there alternative to industrialization? A review of economics thinking Box I: Cultural Advantage and Cultural Studies Chapter 2. Cultural Advantage as Alternative ............. 20 De-Industrialization and Emergence of Experience Economy Cultural Advantage, a new proposition Chapter 3. High-Tech/High-Touch and Cultural Advantage ..... 31 To automate or not to automate? How to implement Cultural Advantage in city development Box III: Cultural Advantage and Anthropology Chapter 4. A few examples: Lessons to learn ............. 40 a. Nicosia b. Toronto c. Venice d. Huzhou e. Valencia f. Chicago g. Romanian Lesson h. Eastern Europe Lesson i. Argentina Lesson Chapter 5. Introduction to Poly-Emporium Theory ............. 49 A new proposition: Extended Tobin Tax Bibliography.........60...

Description Details
...c to the General Theory of Relativity to obtain a generalisation of Einstein’s four dimensional pseudo-Riemannian differentiable manifold in terms of Smarandache Geometry (Smarandache manifolds), by which new classes of relativistic particles and non-quantum teleportation are developed....

Excerpt Details
1.2 The basics of neutrosophy Neutrosophy studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. It considers that every idea tends to be neutralized, balanced by ideas; as a state of equilibrium. Neutrosophy is the basis of neutrosophic logic, neutrosophic set which generalizes the fuzzy set, and of neutrosphic probability and neutrosophic statistics, which generalize the classical and imprecise probability and statistics respectively. Neutrosophic Logic is a multiple-valued logic in which each proposition is estimated to have percentages of truth, indeterminacy, and falsity in T, I, and F respectively, where T, I, F are standard or non-standard subsets included in the non-standard unit interval ] −0, 1+[. It is an extension of fuzzy, intuitionistic, paraconsistent logics. ...

Table of Contents Details
Preface of the Editor 4 Chapter 1 PROBLEM STATEMENT . THE BASICS OF NEUTROSOPHY 1.1 Problem statement 5 1.2 The basics of neutrosophy 8 1.3 Neutrosophic subjects 13 1.4 Neutrosophic logic. The origin of neutrosophy 14 1.5 Definitions of neutrosophic 16 Chapter 2 TRAJECTORIES AND PARTICLES 2.1 Einstein’s basic space-time 18 2.2 Standard set of trajectories and particles. A way to expand the set 22 2.3 Introducing trajectories of mixed isotropic/non-isotropic kind 28 2.4 Particles moving along mixed isotropic/non-isotropic trajectories 31 2.5 S-denying the signature conditions. Classification of the expanded spaces 35 2.6 More on an expanded space-time of kind IV 45 2.7 A space-time of kind IV: a home space for virtual photons 52 2.8 A space-time of kind IV: non-quantum teleportation of photons 55 2.9 Conclusions 59 Chapter 3 ENTANGLED STATES AND QUANTUM CAUSALITY THRESHOLD 3.1 Disentangled and entangled particles in General Relativity. Problem statement 61 3.2 Incorporating entangled states into General Relativity 64 3.3 Quantum Causality Threshold in General Relativity 69 3.4 Conclusions 72 Biblio...

Description Details
We have used the 2-adaptive fuzzy model having the two fuzzy models, fuzzy matrices model and BAMs viz. model to analyze the views of public about HIV/ AIDS disease, patient and the awareness program. This book has five chapters and 6 appendices. The first chapter just recalls the definition of four fuzzy models used in this book and gives illustration of some of them. Chapter two introduces the new n-adaptive fuzzy models. Chapter three uses for the first time 2 adaptive fuzzy models to study psychological and sociological problems about HIV/AIDS. Chapter four gives an outline of the interviews. Chapter five gives the suggestions and conclusion based on our study. Of the 6 appendices four of them are C-program made to make the working of the fuzzy model simple....

Excerpt Details
In this chapter for the first time we introduce the new class of n-adaptive fuzzy models (n a positive integer and n ≥ 2) and illustrate it. These n-adaptive fuzzy models can analyze a problem using different models so one can get in one case the hidden pattern, in one case the maximum time period in some case output state vector for a given input vector and so on. So this new model has the capacity to analyze the problem in different angles, which can give multiple suggestions and solutions about the problem. This chapter has two sections. Section one defines the new model gives illustrations and section two defines some special n-adaptive models and proposes some problems....

Table of Contents Details
Chapter One SOME BASIC FUZZY MODELS WITH ILLUSTRATIONS 1.1 Fuzzy matrices and their applications 9 1.2 Definition and illustration of Fuzzy Relational Maps (FRMs) 16 1.3 Some basic concepts of BAM with illustration 20 1.3.1 Some basic concepts of BAM 22 1.3.2 Use of BAM Model to study the cause of vulnerability to HIV/AIDS and factors for migration 28 1.4 Introduction to Fuzzy Associative Memories (FAM) 35 Chapter Two ON A NEW CLASS OF N-ADAPTIVE FUZZY MODELS WITH ILLUSTRATIONS 2.1 On a new class of n-adaptive fuzzy models with illustrations 39 2.2 Some special n-adaptive models 49 Chapter Three USE OF 2-ADAPTIVE FUZZY MODEL TO ANALYZE THE PUBLIC AWARENESS OF HIV/AIDS 3.1 Study of the psychological and social problems the public have about HIV/AIDS patients using CETD matrix 52 3.2 Use of 2 adaptive fuzzy model to analyze the problem 72 Chapter Four PUBLIC ATTITUDE AND AWARENESS ABOUT HIV/AIDS 4.1 Introduction 77 4.2 Interviews 81 Chapter Five CONCLUSIONS 167 Appendix 1. Questionnaire 177 2. Table of Statistics 191 3. C-program for CETD and RTD Matrix 198 4. C-program for FRM 202 5. C-program for CFRM 2...

Description Details
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....

Excerpt Details
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 Details
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 i...

Description Details
This book was intended to discuss some paradoxes in Quantum Mechanics from the viewpoint of Multi-Valued-logic pioneered by Lukasiewicz, and a recent concept Neutrosophic Logic. Essentially, this new concept offers new insights on the idea of ‘identity’, which too often it has been accepted as given....

Excerpt Details
2 Lukasiewicz Multi-Valued-logic: History and Introduction to Multi- Valued Algebra 2.1 Introduction to trivalent logic and plurivalent logic We all have heard of typical binary logic, Yes or No. Or in a famous phrase by Shakespeare: “To be or not to be.” In the same way all computer hardwares from early sixties up to this year are built upon the same binary logic. It is known that the Classical Logic, also called Bivalent Logic for taking only two values {0, 1}, or Boolean Logic from British mathematician George Boole (1815-64), was named by the philosopher Quine (1981) “sweet simplicity.” [57] But this typical binary logic is not without problems. In the light of aforementioned ‘garment analogue’, we can compare this binary logic with a classic black-and-white tuxedo. It is timeless design, but of course you will not wear it for all occasions. Aristotle himself apparently knew this problem; therefore he introduced new terms ‘contingency’ and ‘possibility’ into his modal logic [5]. And then American logician Lewis first formulated these concepts of logical modality. ...

Table of Contents Details
Contents Foreword 6 1 Introduction: Paradoxes, Lukasiewicz, Multi-Valued logic 7 2 Lukasiewicz Multi-Valued Logic: History and Introduction to Multi-Valued Algebra 10 2.1. Introduction to trivalent logic and plurivalent logic 10 2.2. History of Lukasiewicz and Multi-Valued Logic 12 2.3. Introduction to Multi-Valued Algebra, Chang’s Notation 15 2.4. Linkage between Multi-Valued Logic and Quantum Mechanics 15 2.5. Exercise 17 3 Neutrosophy 25 3.1. Introduction to Neutrosophy 25 3.2. Introduction to Non-Standard Analysis 26 3.3. Definition of Neutrosophic Components 27 3.4. Formalization 28 3.5. Evolution of an Idea 30 3.6. Definition of Neutrosophic Logic 31 3.7. Differences between Neutrosophic Logic and IFL 32 3.8. Operations with Sets 33 3.9. Generalizations 34 4 Schrödinger Equation 39 4.1. Introduction 39 4.2. Quantum wave dynamics and classical dynamical system 43 4.3. A new derivation of Schrödinger-type Equation 45 5 Solution to Schrödinger’s Cat Paradox 47 5.1. Standard interpretation 47 5.2. Schrödinger’s Cat Paradox 48 5.3. Hidden-variable hypothesis 50 5.4. Hydrodynamic viewpoint and diffusion i...

Description Details
Applications demonstrate the power of the DSmT framework. In this third Volume, DSmT is applied to the entire spectrum of the Information Fusion that would interest any reader in data, sensor, information, and mathematical fusion topics. Highlighted in Figure 1 are the contemporary issues that include the links between (1) data conditioning and information management, (2) combined situation and impact assessment, and (2) knowledge representation between machine processing and user coordination. Various applications leverage DSmT “Advances” listed above along with DSmH (hybrid), DSmP (Probabilistic), and DSmT theoretical insights. The third volume attacks these application issues of coordination between the “levels” of information fusion....

Table of Contents Details
...Part I Advances on DSmT 1 Chapter 1 An introduction to DSmT 3 by J. Dezert and F. Smarandache 1.1 Introduction . . . . . . . . . . 4 1.2 Foundations of DSmT . . . . . . . . . 4 1.2.1 The power set, hyper-power set and super-power set . . 6 1.2.2 Notion of free and hybrid DSm models . . . . 18 1.2.3 Ge...

Description Details
...This second book devoted on advances and applications of Dezert-Smarandache Theory (DSmT) for information fusion collects recent papers from different researchers working in engineering and mathematics. Part 1 of this book presents the current state-of-the-art on theoretical investigation...

Table of Contents Details
...Preamble iii Prefaces v Part I Advances on DSmT 1 Chapter 1 Proportional Conflict Redistribution Rules for Information Fusion 3 by Florentin Smarandache and Jean Dezert 1.1 Introduction . . . . . . . . . . . 3 1.2 The principal rules of combination . . . . . . . 6 1.2.1 Notion of total and partial conflicting masses . . . . . 6 1.2.2 The conjunctive ...

Description Details
...n the information provided by the sources is both uncertain and (highly) conflicting. This approach, known in literature as DSmT (standing for Dezert-Smarandache Theory), proposes new useful rules of combinations. We gathered in this volume a presentation of DSmT from the beginning to the latest development. Part 1 of this book presents the current state-of-the-art on theo...

Table of Contents Details
...57 8.2.1 Preliminary: about probability . . . 157 8.2.2 Dempster Shafer Theory . . . . 161 8.2.3 Transferable Belief Model . . . . 162 8.3 Dezert Smarandache Theory (DSmT) . . . 163 8.3.1 Dezert Smarandache model . . . . 164 8.3.2 Fusion rule . . . . . 166 8.4 Probability over logical propositions . . . . 167 8.4.1 Definition . . . . . 167 8.4.2 Property . . . . ....

Description Details
In this book authors for the first time introduce the notion of supermatrices of refined labels. Authors prove super row matrix of refined labels form a group under addition. However super row matrix of refined labels do not form a group under product; it only forms a semigroup under multiplication. In this book super column matrix of refined labels and m Å~ n matrix of refined labels are introduced and studied. We mainly study this to introduce to super vector space of refined labels using matrices....

Excerpt Details
THEOREM 1.1.1: Let S = {(a1 a2 a3 | a4 a5 | a6 a7 a8 a9 | … | an-1, an) | ai ∈ R; 1 ≤ i ≤ n} be the collection of all super row vectors with same type of partition, S is a group under addition. Infact S is an abelian group of infinite order under addition. The proof is direct and hence left as an exercise to the reader. If the field of reals R in Theorem 1.1.1 is replaced by Q the field of rationals or Z the integers or by the modulo integers Zn, n < ∞ still the conclusion of the theorem 1.1.1 is true. Further the same conclusion holds good if the partitions are changed. S contains only same type of partition. However in case of Zn, S becomes a finite commutative group....

Description Details
In this book authors for the first time introduce the notion of super interval matrices using the special intervals of the form [0, a], a belongs to Z+ ∪ {0} or Zn or Q+ ∪ {0} or R+ ∪ {0}....

Excerpt Details
SUPER INTERVAL SEMILINEAR ALGEBRAS In this chapter we for the first time introduce the notion of semilinear algebra of super interval matrices over semifields of type I (super semilinear algebra of type I) and semilinear algebra of super interval matrices over interval semifields of type II (super semilinear algebra of type II) and study their properties and illustrate them with examples. DEFINITION 4.1: Let V be a semivector space of super interval matrices defined over the semifield S of type I. If on V we for every pair of elements x, y ∈ V; x . y is in V where ‘.’ is the product defined on V, then we call V a semilinear algebra of super interval matrices over the semifield S of type I. We will illustrate this situation by some examples. Example 4.1: Let V = {([0, a1] [0, a2] | [0, a3] [0, a4] | [0, a5] [0, a6] | [0,a7]) | ai ∪ Z+ ∪ {0}; 1 ≤ i ≤ 7} be a semivector space of super interval matrices defined over the semifield S = Z+ ∪ {0} of type I. Consider x = ([0, 5] [0, 3] | [0, 9] [0, 1] [0, 2] [0, 8] | [0, 6]) and y =([0, 1] [0, 2] | [0, 3] [0, 5] [0, 3] [0, 1] | [0, 5]) in V. We define the product ‘.’ on V as x.y =...

Table of Contents Details
CONTENTS Preface 5 Chapter One INTRODUCTION 7 Chapter Two INTERVAL SUPERMATRICES 9 Chapter Three SEMIRINGS AND SEMIVECTOR SPACES USING SUPER INTERVAL MATRICES 83 Chapter Four SUPER INTERVAL SEMILINEAR ALGEBRAS 137 Chapter Five SUPER FUZZY INTERVAL MATRICES 203 5.1 Super Fuzzy Interval Matrices 203 5.2 Special Fuzzy Linear Algebras Using Super Fuzzy Interval Matrices 246 Chapter Six APPLICATION OF SUPER INTERVAL MATRICES AND SET LINEAR ALGEBRAS BUILT USING SUPER INTERVAL MATRICES 255 Chapter Seven SUGGESTED PROBLEMS 257 FURTHER READING 281 INDEX 285 ABOUT THE AUTHORS 287...

Description Details
introduction of neutrosophic theory has put forth a significant concept by giving representation to indeterminates. Uncertainty or indeterminacy happen to be one of the major factors in almost all real-world problems. When uncertainty is modeled we use fuzzy theory and when indeterminacy is involved we use neutrosophic theory. Most of the fuzzy models which deal with the analysis and study of unsupervised data make use of the directed graphs or bipartite graphs. Thus the use of graphs has become inevitable in fuzzy models. The neutrosophic models are fuzzy models that permit the factor of indeterminacy. It also plays a significant role, and utilizes the concept of neutrosophic graphs. Thus neutrosophic graphs and neutrosophic bipartite graphs plays the role of representing the neutrosophic models. Thus to construct the neutrosophic graphs one needs some of the neutrosophic algebraic structures viz. neutrosophic fields, neutrosophic vector spaces and neutrosophic matrices. So we for the first time introduce and study these concepts. As our analysis in this book is application of neutrosophic algebraic structure we found it deem fit t...

Full Text Search Details
...36, India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexic... ... e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup,... ...re, Karnataka, India. Copyright 2004 by W. B. Vasantha Kandasamy and Florentin Smarandache Layout by Kama Kandasamy. Cover design by Mee... ...aka, India. Copyright 2004 by W. B. Vasantha Kandasamy and Florentin Smarandache Layout by Kama Kandasamy. Cover design by Meena Kandasa... ...Kandasamy. Many books can be downloaded from: http://www.gallup.unm.edu/~smarandache/eBooks-otherformats.htm ISBN: 1-931233-87-X ... ...standing of Periyar's ideology and approach. W.B.VASANTHA KANDASAMY FLORENTIN SMARANDACHE 7 Chapter One Introduction to So... ...f Periyar's ideology and approach. W.B.VASANTHA KANDASAMY FLORENTIN SMARANDACHE 7 Chapter One Introduction to Some Neutr... ...sed the concept of indeterminacy till the year 1995. Only in the year 1995 Florentine Smarandache introduced and studied the notion of indeterminac... ...cept of indeterminacy till the year 1995. Only in the year 1995 Florentine Smarandache introduced and studied the notion of indeterminacy, creating...

Description Details
This book has six chapters. The first one is introductory in nature just giving only the needed concepts to make this book a self contained one. Chapter two introduces the notion of refined plane of labels, the three dimensional space of refined labels DSm vector spaces. Clearly any n-dimensional space of refined labels can be easily studied as a matter of routine....

Table of Contents Details
Preface 5 Chapter One INTRODUCTION 7 Chapter Two DSm VECTOR SPACES 17 Chapter Three SPECIAL DSm VECTOR SPACES 83 Chapter Four DSm SEMIVECTOR SPACE OF REFINED LABELS 133 Chapter Five APPLICATIONS OF DSm SEMIVECTOR SPACES OF ORDINARY LABELS AND REFINED LABELS 173 Chapter Six SUGGESTED PROBLEMS 175 FURTHER READING 207 INDEX 211 ABOUT THE AUTHORS 214...

Description Details
The aim of this book is two fold. At the outset the book gives most of the available literature about Fuzzy Relational Equations (FREs) and its properties for there is no book that solely caters to FREs and its applications. Though we have a comprehensive bibliography, we do not promise to give all the possible available literature about FRE and its applications. We have given only those papers which we could access and which interested us specially. We have taken those papers which in our opinion could be transformed for neutrosophic study....

Full Text Search Details
... W. B. VASANTHA KANDASAMY FLORENTIN SMARANDACHE FUZZY RELATIONAL MAPS AND NEUTROSOPHIC... ... W. B. VASANTHA KANDASAMY FLORENTIN SMARANDACHE FUZZY RELATIONAL MAPS AND NEUTROSOPHIC RELATION... ...600036, India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New M... ...dia e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gal... ...Mysore, Karnataka, India. Copyright 2004 by W. B. Vasantha Kandasamy and Florentin Smarandache Layout by Kama Kandasamy. Cover design by... ...rnataka, India. Copyright 2004 by W. B. Vasantha Kandasamy and Florentin Smarandache Layout by Kama Kandasamy. Cover design by Meena Kan... ...ena Kandasamy. Many books can be downloaded from: http://www.gallup.unm.edu/~smarandache/eBooks-otherformats.htm ISBN: 1-931233-86-1 ... ...re Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps (http://gallup.unm.edu/~smarandache/NCMs.pdf) and Analysis of Social Aspects of Migrant Labo... ...out his help this book would not have been possible. W.B.VASANTHA KANDASAMY FLORENTIN SMARANDACHE 9 Chapter One FUZZY RELATIONAL...

Description Details
K.R.Narayanan was a lauded hero and a distinguished victim of his Dalit background. Even in an international platform when he was on an official visit to Paris, the media headlines blazed, ‘An Untouchable at Elysee’. He was visibly upset and it proved that a Dalit who rose up to such heights was never spared from the pangs of outcaste-ness and untouchability, which is based on birth. Thus, if the erstwhile first citizen of India faces such humiliation, what will be the plight of the last man who is a Dalit? As one of the world’s largest socio-economically oppressed, culturally subjugated and politically marginalized group of people, the 138 million Dalits in India suffer not only from the excesses of the traditional oppressor castes, but also from State Oppression— which includes, but is not limited to, authoritarianism, police brutality, economic embargo, criminalization of activists, electoral violence, repressive laws that aim to curb fundamental rights, and the non-implementation of laws that safeguard Dalit rights. The Dalits were considered untouchable for thousands of years by the Hindu society until the Constitution of India...

Full Text Search Details
...a Kandasamy e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache e-mail: smarand@unm.edu K. Kandasamy e-... ...y e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache e-mail: smarand@unm.edu K. Kandasamy e-mail: dr.... ...Karnataka, India Copyright 2005 by Hexis, W. B. Vasantha Kandasamy, Florentin Smarandache and K. Kandasamy Cover Design and Lay... ...India Copyright 2005 by Hexis, W. B. Vasantha Kandasamy, Florentin Smarandache and K. Kandasamy Cover Design and Layout by Kama... ...wnloaded from the following E-Library of Science: http://www.gallup.unm.edu/~smarandache/eBooks-otherformats.htm ISBN: 1931233-00-4 S... ...to working for the rights of the subjugated people. W.B.VASANTHA KANDASAMY FLORENTIN SMARANDACHE K.KANDASAMY 26-11-2005 9 Chapter On... ... for the rights of the subjugated people. W.B.VASANTHA KANDASAMY FLORENTIN SMARANDACHE K.KANDASAMY 26-11-2005 9 Chapter One BAS... ...s In this section we introduce the notion of neutrosophic logic created by Florentine Smarandache [55-59], which is an extension / combination of... ...s section we introduce the notion of neutrosophic logic created by Florentine Smarandache [55-59], which is an extension / combination of the fuzzy ...

Description Details
The authors use linguistic paradoxes, play against the grain on linguistic clichés, and employ mathematical combinations of words involving contradictions, antitheses, oxymoron, which fully characterize the paradoxism movement in literature and science....

Excerpt Details
A descris ceva de nedescris. ● Unul venea după bani, iar celălalt după amiază. ● Memoria, fiind de genul feminin, mă cam înşeală. ● A avut o tentativă de omor prin imprudenţă. ● El a rămas repetent, iar ea a rămas gravidă. ● A legat un cal putere de un arbore cotit, într-un câmp electromagnetic. ● Unul avea ochi albaştri, iar celălalt avea darul beţiei. ● L-a scos din minţi şi l-a băgat în spital. ● Nevasta generalului în retragere era mereu în atac. ● Este fondatorul unui partid extremist de centru. ● Elevii de la şcoala de marină învăţau lecţiile ca pe apă. ● I-a venit pe chelie să-şi lase plete. ● Era în stare de staţionare interzisă. ● Îi merge vorba că ar fi mut. ● A avut o cădere înălţătoare: din lac în puţ. ● Culmea fericirii: să pleci bou şi să te întorci taur. ● De ce le zice pui de găină, dacă mama lor este o cloşcă? ● A împărţit un măr în trei jumătăţi inegale, în mod echitabil. He described the indescribable. ● One coming after money, and the other in the afternoon. ● Memory, being feminine, I kind of cheating. ● He had attempted manslaughter. ● He retained student, and she got pregnant. ● A tied...

Description Details
...origin, nature and scope of neutralities, as well as their interactions with different ideational spectra. This was introduced by one of the authors, Florentin Smarandache. A few of the mentionable characteristics of this mode of thinking are [90-94]: It proposes new philosophical theses, principles, laws, methods, formulas and movements; it reveals that the world is full ...

Full Text Search Details
...W. B. VASANTHA KANDASAMY FLORENTIN SMARANDACHE FUZZY COGNITIVE MAPS AND NEUTROSOPHIC COGNITIV... ...W. B. VASANTHA KANDASAMY FLORENTIN SMARANDACHE FUZZY COGNITIVE MAPS AND NEUTROSOPHIC COGNITIVE MAPS ... ...ology, Madras Chennai – 600036, India E-mail: vasantha@iitm.ac.in Florentin Smarandache Department of Mathematics University of New Mexico ... ...ras Chennai – 600036, India E-mail: vasantha@iitm.ac.in Florentin Smarandache Department of Mathematics University of New Mexico Gallup, N... ...ersity, Australia. Copyright 2003 by W. B. Vasantha Kandasamy, Florentin Smarandache, and Xiquan, 510 E. Townley Ave., Phoenix, AZ 85020,... ...stralia. Copyright 2003 by W. B. Vasantha Kandasamy, Florentin Smarandache, and Xiquan, 510 E. Townley Ave., Phoenix, AZ 85020, USA ... ...ownloaded from the Digital Library of Science: http://www.gallup.unm.edu/~smarandache/eBooks-otherformats.htm ISBN: 1-931233-76-4 St... ... different ideational spectra. This was introduced by one of the authors, Florentin Smarandache. A few of the mentionable characteristics of this mo... ... ideational spectra. This was introduced by one of the authors, Florentin Smarandache. A few of the mentionable characteristics of this mode of thin...