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...This book has five chapters. Chapter one is introductory in nature. Fuzzy linguistic spaces are introduced in chapter two. Fuzzy linguistic vector spaces are introduced in chapter three. Chapter four introduces fuzzy linguistic models. The final chapter suggests over 100 problems and some of them are at res...

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...Preface 5 Chapter One Introduction 7 Chapter Two Fuzzy Linguistic Spaces 9 Chapter Three Fuzzy Linguistic Set Vector Spaces 23 Chapter Four Fuzzy Linguistic Models 129 4.1 Operations on Fuzzy Linguistics Matrices 129 4.2 Fuzzy Linguistic Cognitive Models 139 4.3 Fuzzy Lingu...

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... theory cannot cater to analyzing the data involved with indeterminacy. The only tool that can involve itself with indeterminacy is the neutrosophic model....

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...IENTS 3.1. Introduction to Fuzzy Associative Memories 57 3.2. Use of FAM model to study the socio economic problem of women with HIV/AIDS ... ...blem of women with HIV/AIDS 61 4 Chapter Four USE OF NEUTROSOPHIC MODELS TO ANALYZE HIV/AIDS WOMEN PATIENTS' PROBLEM 4.1 Use of NR... ...TS' PROBLEM 4.1 Use of NRM in the Analysis of the Problem 65 4.2 NAM model to study the Problem 77 Chapter Five INTERVIEWS OF 101 ... ...ne quantized patterns. Neural network models represent prototype patterns as vectors of real numbers. So we can alternatively view learning as a fo... ... of real numbers. So we can alternatively view learning as a form of adaptive vector quantization. Thus adaptive vector quantization embeds learning... ...on. Thus adaptive vector quantization embeds learning in a dynamic geometry, vector quantization may be optimal according to different criteria. Th... ...t for the sake of distinction between the two classes we name them as domain space and range space though in reality there is no difference between... ...re is no difference between them. For the causal relations can be from range space to domain space or from domain space to range space. In some of ... ...domain space to range space. In some of the cases the concepts in the domain space (or range) space need not be mutually exclusive. We build rela...

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...entation 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 grap...

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...ophic Algebraic Structures and Their Application to Fuzzy and Neutrosophic Models W. B. Vasantha Kandasamy Department of Mathematics Indian ... ...SOPHIC ALGEBRAIC STRUCTURES 1.1 Neutrosophic Fields 7 1.2 Neutrosophic Vector spaces 8 Chapter Two SOME BASIC RESULTS ON GRAPH THEORY A... ... ALGEBRAIC STRUCTURES 1.1 Neutrosophic Fields 7 1.2 Neutrosophic Vector spaces 8 Chapter Two SOME BASIC RESULTS ON GRAPH THEORY AND THE... ...er Two SOME BASIC RESULTS ON GRAPH THEORY AND THEIR APPLICATION TO FUZZY MODELS 2.1 Some basics on Graphs 18 2.2. More Properties on Graph... ...nian Graphs 44 2.7 Graph Colorings 52 2.8 Application of Graphs to Fuzzy Models 56 Chapter Three NEUTROSOPHIC GRAPHS AND THEIR APPLICATIO... ...he neutrosophic algebraic structures viz. neutrosophic fields, neutrosophic vector spaces and neutrosophic matrices. So we for the first time intro... ...osophic algebraic structures viz. neutrosophic fields, neutrosophic vector spaces and neutrosophic matrices. So we for the first time introduce and... ...ew neutrosophic algebraic structures like neutrosophic fields, neutrosophic spaces and neutrosophic matrices and illustrate them with examples. For ... ...ne we define neutrosophic fields and in section two we define neutrosophic vector spaces and illustrate them by examples. 1.1 Neutrosophic fie...

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...r is predicted or inferred from axiom-determined conditions in the physical model. d.) predictive paradox: theory-based behavioral expectations in a... ...evidence. e.) comparative paradox: a paradoxical component in a theoretical model is noted in comparison with a second, less-paradoxical, model. f.... ...ary conditions in the axioms of quantum mechanics and the standard particle model. The boundaries define behavioral limits between the visible, dete... ...jection. 3 . G D T R e l a t i v i t y 3.1 Elliptic and 4d Space We begin the parametric definition of G-dimensional theory (GDT), ... ...e begin the parametric definition of G-dimensional theory (GDT), by modeling space-time as a 2d surface with local angle of inclination in projective... ... angle of inclination in projective dimension (G), as determined by kinetic vector v: (v ≡ v/c) The matter-containing body is modeled as a closed cir... ...v ≡ v/c) The matter-containing body is modeled as a closed circle in the non-vector 2d plane and so in non-vector 3d frame (k), as closed sphere (S).... ...d plane and so in non-vector 3d frame (k), as closed sphere (S). 9 The vector determinant projection of S in G is defined as a congruent right c... ...is and therefore the positive elliptic focus in S', (Fig.1b). The length of space-time translated into k' is then proportional to angle (Φ), with res...

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...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-matrices, bigraphs, trigraphs and n-graphs and describe some of its properties. These concepts are also extended neutrosophically in this...

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... APPLICATIONS OF BIMATRICES TO SOME FUZZY AND NEUTROSOPHIC MODELS W. B. Vasantha Kandasamy Department of Mathematics India... ... Bimatrices 23 Chapter Three APPLICATION OF BIMATRICES TO NEW FUZZY MODELS 3.1. Definition of Fuzzy Cognitive Maps 71 3.2. Fuzzy Cognit... ...NEUTROSOPHIC BIGRAPHS THEIR GENERALIZATIONS AND APPLICATIONS TO NEUTROSOPHIC MODELS 4.1 Some Basics of Neutrosophic graphs 151 4.2 Neutrosophi... ... 1 , a 2 , … , a n ) where a i ∈ {0, 1}. A is called the instantaneous state vector and it denotes the on-off position of the node at an instant. ... ...TION 3.1.10: If the equilibrium state of a dynamical system is a unique state vector, then it is called a fixed point. Example 3.1.2: Consider a ... ... Let us assume that the FCM settles down with C 1 and C n on i.e. the state vector remains as (1, 0, 0, 75 …, 0, 1) this state vector (1, 0, ... ...n doctor and patient and so on. Thus for us to define a FRM we need a domain space and a range space which are disjoint in the sense of concepts. W... ...ntermediate relation exists within the domain elements or node and the range spaces elements. The number of elements in the range space need not in... ...e space need not in general be equal to the number of elements in the domain space. Thus throughout this section we assume the elements of the d...

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...Matrix theory has been one of the most utilised concepts in fuzzy models and neutrosophic models. From solving equations to characterising linear transformations or linear operators, matrices are used. Matrices find their applications in several real models. In fact it is not an exaggera...

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...Matrices provide a very powerful tool for dealing with linear models. Bimatrices which we are going to define in this chapter are still a powerful and an advanced tool which can handle over one linear model at a time. Bimatrices will be useful when time bound comparisons are needed in...

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...bimatrix 58 1.7 Special types of Bimatrices 76 Chapter Two BIVECTOR SPACES AND THEIR PROPERTIES 2.1 Introduction to Bivector Spaces 79 ... ...9 2.2. Systems of linear biequations 87 2.3 Bitransformation in bivector spaces 96 2.4 Linear bioperators on Bivector spaces 105 2.5 Bieigen v... ... Linear bioperators on Bivector spaces 105 2.5 Bieigen values and Bieigen vectors 117 2.6 Bidiagonalizable linear bioperator and its properties... ...tructures 139 3.2. Neutrosophic bimatrices 148 3.3. Neutrosophic bivector spaces 157 Chapter Four SUGGESTED PROBLEMS 159 BIBLIOGRAP... ...face Matrix theory has been one of the most utilised concepts in fuzzy models and neutrosophic models. From solving equations to characterising... ...rators, matrices are used. Matrices find their applications in several real models. In fact it is not an exaggeration if one says that matrix theory... ...not an exaggeration if one says that matrix theory and linear algebra (i.e. vector spaces) form an inseparable component of each other. The study ... ...acy we construct neutrosophic bimatrices, which can be used in neutrosophic models. By no means we make any claim that the concept of indeterminac... ...ties. Chapter 2 introduces bivector spaces and defines notions like bieigen vectors, bipolynomials etc. In Chapter 3 neutrosophic bimatrices and fuz...

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...This book has four chapters. The first chapter just introduces n-group which is essential for the definition of n-vector spaces and n-linear algebras of type I. Chapter two gives the notion of n-vector spaces and several related results which are analogues of the classical linear algebra theorems. In case of n-vector spaces we can define...

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...n-VECTOR SPACES OF TYPE I AND THEIR PROPERTIES In this chapter we introduce the notion of n-vector spaces and describe some of their important properties. Here we define the concept of n-vector spaces over a field which will b...

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...Preface 5 Chapter One BASIC CONCEPTS 7 Chapter Two n-VECTOR SPACES OF TYPE I AND THEIR PROPERTIES 13 Chapter Three APPLICATIONS OF n-LINEAR ALGEBRA OF TYPE I 81 Chapter Four SUGGESTED PROBLEMS 103 FURTHER READING 111 INDEX 116 ABOUT THE AUTHORS 120...

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...s itself to applications to several fields like coding or communication theory, Markov chains, representation of groups and graphs, Leontief economic models and so on. This book has for the first time, introduced a new algebraic structure called linear bialgebra, which is also a very powerful algebraic tool that can yield itself to applications. With the recent introduct...

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...TURES AND S-BISTRUCTURES 2.1 Basic concepts of bigroups and bivector spaces 37 2.2 Introduction of S-bigroups and S-bivector spaces 46 ... ... 51 3.2 Linear bitransformation and linear bioperators 62 3.3 Bivector spaces over finite fields 93 3.4 Representation of finite bigroup 95 ... ...raphs 102 3.6 Jordan biform 108 3.7 Application of bivector spaces to bicodes 113 3.8 Best biapproximation and its application 123 ... ...ry, Markov chains, representation of groups and graphs, Leontief economic models and so on. This book has for the first time, introduced a new alge... ...eutrosophic bivector spaces. Their 6 probable applications to real-world models are discussed. We have aimed to make this book engrossing and ill... ...rem and give some properties about linear algebra. DEFINITION 1.1.1: A vector space or a linear space consists of the following: i. a field F... ...f the following: i. a field F of scalars. ii. a set V of objects called vectors. 8 iii. a rule (or operation) called vector addition; which as... ... (or operation) called vector addition; which associates with each pair of vectors α, β ∈ V; α + β in V, called the sum of α and β in such a way tha... ...ng ones. Further we deal with a Smarandache analogue of Leontief economic models. 1.3.1 Smarandache Markov chains Suppose a physical or a mat...

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The securities industry, its markets, instruments (equity, debt, derivatives), trading strategies, underlying economic models, and future.

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...by three cash flows: (i) The firm's future cash flows (incorporated into valuation models, such as the CAPM or FAR) (ii) Future cash flows in secur... ...logy and wherever and whenever humans are involved, answers don't come easy. A few models have been developed and are in wide use but it is difficu... ... say that any of them has real predictive or even explanatory powers. Some of these models are "technical" in nature: they ignore the fundamentals o... ...st level in 40 years. Inflation gyrated from double digits to a single digit in the space of two decades. This uncertainty is, inevitably, incorpora... ...o decelerate. Massive exposure to American debt, both public and private, served a vector of contagion. The weakening of traditional export markets... ...ndently of each other. What the crisis has revealed is that contagion transmission vectors and mechanisms have actually become more potent as barri... ...cts, utilities, natural monopolies, mining operations, defense contractors, and the space industry. They allow their holders to block business move... ...ly. They engage Strategies to obtain their highest ranked outcome. A Strategy is a vector, which details the acts, with which the DA will react in ...

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...As an alternative to the existing logics we propose the Neutrosophic Logic to represent a mathematical model of uncertainty, vagueness, ambiguity, imprecision, undefined, unknown, incompleteness, inconsistency, redundancy, contradiction. It is a non-classical logic. Eksioglu (1999) explains some of them: “Imprecision of the hu...

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... dependant on many parameters, and therefore they can be considered set-valued vector functions or even operators. The parameters can be: time, spac... ...d set-valued vector functions or even operators. The parameters can be: time, space, etc. (some of them are hidden/unknown parameters): T(t, s, …),... ...idden/unknown parameters): T(t, s, …), I(t, s, …), F(t, s, …), where t=time, s=space, etc., that's why the neutrosophic logic can be used in quantum ... ... existing logics we propose the Neutrosophic Logic to represent a mathematical model of uncertainty, vagueness, ambiguity, imprecision, undefined, un... ...to describe computer-based problem solving systems which employ computational models of some of the known mechanisms of evolution as key elements in... ...ructures. The major evolutionary algorithms studied are: genetic algorithm (a model of machine learning based on genetic operators), evolutionary p... ...ally T, I, F are subsets, but dynamically the components T, I, F are set-valued vector functions/operators depending on many parameters, such as: tim... ...valued vector functions/operators depending on many parameters, such as: time, space, etc. (some of them are hidden parameters, i.e. unknown paramet... ...lly T, I, F are subsets, but dynamically the components T, I, F are set- valued vector functions/operators depending on many parameters, such as: time...

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...tity; measurable in terms of the expected information content of a set of alternative choices. The entropic notion of utility is subsequently used to model the financial behavior of individual investors based on their governing risk-return preferences involving financial structured products manufactured out of complex, multi-asset options. Evolutionary superiority of the B...

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... ... 47 4. A Proposed Information Theoretic Model of Utility Applicable to Active Risk Management Engineered by M... ...ternative choices. The entropic notion of utility is subsequently used to model the financial behavior of individual investors based on their govern... ...cenarios is computationally demonstrated using a haploid genetic algorithm model programmed in Borland C. The work explores, both theoretically and ... ...sis of partial information, one should use that utiltiy curve (or utility vector) whose utiltiy density function (or utility increment vector) has m... ...her preference for a particular strategy within a pre-defined probability space. In Appendix (i), we use a Monte Carlo simulation technique to numeri... ...in t + 1 is equi-probable between the two possible states given the market vector in time t. However, if this restriction {m 11 = m 22 , m 12 = m 2... ... M and ρ is a generalized version of p whereby the elements of the market vector are no longer restricted to their efficient equilibrium values. Thou... ...out any insurance. Three alternative market scenarios (probability spaces) have been explored – “Down”, “Neutral” and “Up”, categorized accor... ...g a particular investment strategy under each of the aforementioned event spaces D, N and U and the results are provided in Appendix (i). ...

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.... 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 Generalized belief functions . . . . . . 20 1.2.4 The classic DSm rule of combination . . . . . 21 1.2.5 The hybrid DSm rule of combination . . . . . 22 1.2.6 Examples of combination rules . . . . ...

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...f Fuzzy Cognitive Maps (FCMs) 7 1.2 Fuzzy Cognitive Maps – Properties and Models 10 1.3 Some more illustrations of FCMs 26 1.4 Applications of FCMs... ...3 1.5 Definition and Illustration of Fuzzy Relational Maps (FRMs) 93 1.6 Models illustrating FRM and combined FRMs 96 1.7 Linked Fuzzy Relational M... ...as an alternative to the existing logics and it represents a mathematical model of uncertainty, vagueness, ambiguity, imprecision, undefined, unknow... ...ophic graphs, neutrosophic fields, neutrosophic matrices and neutrosophic vector spaces. We provide many illustrations and applications relating NCM... ...raphs, neutrosophic fields, neutrosophic matrices and neutrosophic vector spaces. We provide many illustrations and applications relating NCMs. In t... ... a 2 , … , a n ) where a i ∈ {0, 1}. A is called the instantaneous state vector and it denotes the on-off position of the node at an instant. a ... ... 1.1.10: If the equilibrium state of a dynamical system is a unique state vector, then it is called a fixed point. Example 1.1.2: Consider a FCM w... ...ion, Park and Kim [78] deal with time lags on not continuous but discrete space. The t ij is a value in a finite set Ω of M-many values Ω = M 1 t }... ...cal concepts that underlie the design of OP#1. These concepts are: E-mail Space, Text Classification, Plant Behavior Architecture, and Sculptural Pr...

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...he name of the man who produced them, and in this way we can compose a parallel onomastic dictionary, in which the work is included in the person’s space, keeping its content. The consecrated proper names evolve through quickly imposed habits, a large range of increments that announce the essential outline of their peak production. No space for ambiguity remains when w...

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...allel onomastic dictionary, in which the work is included in the person’s space, keeping its content. The consecrated proper names evolve through qu... ...crements that announce the essential outline of their peak production. No space for ambiguity remains when we address to readers or listeners who are... ...forward, because the poems constituted only an element of the significant space of the page, the expression tended towards an autonomy in an univers... ... greater length afterward. one arouses a permanent confrontation with the models and, in fact, a self repressing of the temptation of an exhibition o... ...isciplinary crossroads, as an intercultural competence. It offers a social model of equilibrium that accentuates the extremes. The acceleration of th... ... of the Romanian postmodernity”. The poet “has fixed to himself a lyrical model and succeeded in making it accepted, today, as a 23 lyrical model... ...n the doctrinaire requirements of this way of writing and in the specific vectors of movement. His work constitutes the top of the movement that he ... ...nite one, to the neutrosophic probability, defining it as a tridimensional vector whose elements are real subcrowds. While this chapter is written, a...

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...TY PROCEEDINGS OF THE CONFERENCE OF 18 FEB 2005 Cover Montage by Bob Wise Models of X-1 Rocket Plane & San Francisco Cable Car by the Danbury Mint ... ...Sequiturs in Relativity Four in number at this point Dr. Smith of "Lost in Space" had a knack of easing out of binds that he'd gotten himself into.... ...ke this: Since there is no luminiferous ether, there can be no "road" in space upon which to conceptually post a sign like this for rocketships: ... ...he rocketship denotes that a rocket motor, in effect, has traction to empty space. A rocket does not require air to push against as was once thought ... ... will hence have the necessary property. We must also deal not in ordinary vectors, but in tensors, or relativistic 4-vectors. The specific 4-vect... ...c 4-vectors needed are position, velocity and acceleration. The position 4-vector is α x = (t,x,y,z) and it defines a path in space/time called a... ... as, in general, a simple differentiation destroys the tensor quality of 4-vectors. We also need the metric tensor αβ g where 00 g = -1, ij g =... ...e, he had arrived to that “…in homogeneous isotropic cosmological 35 models spatial infinity of the Universe depends on our choice of that re... ...81 E. Irvington Rd./Tucson, AZ 85709-4000 Abstract Space-forms that model material, material interactions, and the structure of metric space...

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...Borissova, D. Rabounski On the Possibility of Instant Displacements in the Space-Time of General Relativity. . . . . . . . . . . . . . . . . . . . . .... .... . . . . . . . . . . . . . . . . . . . . . . . 17 C. Castro On Dual Phase-Space Relativity, the Machian Principle and Mod- ifed Newtonian Dynamics. .... .... . 20 C. Castro, M. Pavˇ siˇ c The Extended Relativity Theory in Clifford Spaces.. . . . .31 K. Dombrowski Rational Numbers Distribution and Resonanc... ...ully defne his real reference space. Thus, chr.inv.-projections of a world-vector Q α are b α Q α = Q 0 √ g 00 andh i α Q α =Q i , while chr.inv.-proj... ...i = ∂ ∂x i + + 1 c 2 v i ∂ ∂t are non-commutative. They are the chr.inv.-vector of gravitational inertial forceF i , the chr.inv.-tensor of angular ... ... of which isF i , so thatF i =h ik F k . The d’Alem- bert equations of the vector feld F α =−2c 2 b β a ∙α β∙ in the absence of sources are F α =0. Th... ...tudies [1], he concluded that “. . . in homogeneous isotropic cosmological models spa- tial infnity of the Universe depends on our choice of that refe... ...chuller [61] related to the effects of maximal acceleration in Born-Infeld models that also maintains Lo- rentz invariance, in contrast to the approac... ... spaces (Clifford spaces); in the physics of D-branes and covariant Matrix models by [137] and within the context of Lie algebra stability by [48]. A ...

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...bility To HIV/AIDS 3.1 Some basic concepts of BAM 98 3.2 Use of BAM model to study the cause of vulnerability to HIV/AIDS and factors for... ...as an alternative to the existing topics and it represents a mathematical model of uncertainty, vagueness, ambiguity, imprecision, undefined-ness, ... ...urers. Appendix 3 to 8 gives the C programs used in finding the resultant vector for any given state vector using the dynamical system. Appendix 9 d... ...eterminate relations is carried out mainly and solely by the neutrosophic models. We in this book have for the first time adopted the neutrosophic m... ...r a self-contained one. The conclusions are based on several of the state vectors and many experts opinions are utilized, to make the book a compre... ...ity increases with expert sample size. We reason with FCMs. We pass state vectors C repeatedly through the FCM connection matrix E, thresholding or ... ...igsberg Bridge Problem. Psychologist Lewin proposed in 1936 that the life space of an individual be represented by a planar map. His view point led ... ...erpretation by Lee and Yang the points stand for small cubes in Euclidean space where each cube may or may not be occupied by a molecule. Then two p... ...not be occupied by a molecule. Then two points are adjacent whenever both spaces are occupied. Feynmann proposed the diagram in which the points r...

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...hwarzschild” solution, r is taken both as a coordinate and a radius in the spacetime manifold of the point-mass. In my previous papers [1, 2] on the g... ... noted. In the context of (M g ,g g )r is a Euclidean parameter in the fat spacetime manifold (M s ,g s ) of Special Relativity. Insofar as the point-... ...itions on the real number line, the radial line in (M s ,g s ), not in the spacetime manifold of the gravitational feld, (M g ,g g ). The gravitationa... ...gravitational tensor. The variations of θ and ϕ displace the proper radius vector, R p (r 0 )≡0, over the spherical surface of fnite area 4πα 2 , as n... ...tion that a material body cannot collapse to a point, and therefore such a model is inadequate. A more realistic model must be sought in terms of a no... ...respect to his real references). Thus, the chr.inv.-projections of a world-vector Q α are b α Q α = Q 0 √ g 00 and h i α Q α =Q i , while chr.inv.-pro... ...ik may not be stationary. The observable characteristics are the chr.inv.- vector of gravitational inertial forceF i , the chr.inv.-tensor of angular ... ...e substantial supposition that the under action of gravitational waves the model will behave like a harmonic oscillator where the forcing power is in ... ...r made calculations and theoretical propositions for the behaviour of this model. This model is known as the quadrupole mass-detector [17]. The Weber ...

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...apter 4 : The Intangible Consciousness. (38.) hapter 5 : Dancing in Higher Space. (46.) hapter 6 : Hitching a Ride on a Reality. (63.) hapter 7 : R... ... hapter 7 : Realities Surfing the Quantum hapter 8 : Parking in Hilbert’s Space. (94.) hapter 9 : The Flow of Entropy. (108.) hapter 10 : The Case... ...ents, we may gaze into the night sky and see the myriads of stars deep in space, catch a glimpse even of other galaxies, perhaps like our own, and ... ...geometrical space-time sweep of general relativity. Now, the standard model of quantum mechanics is based on the idea that the elementary buil... ...nergy? For this, I intend to invoke the idea of the energy/momentum 4-vector. Initially, I will run over the general conventional idea of ... ...n over the general conventional idea of what exactly an energy/momentum 4-vector is, and then I will expand this initial idea to accommodate the mu... ...date the much wider meaning for the concept of the 60 energy/momentum 4-vector which I intend to use for this book. I hope, by the way, that... ...er, the situation with the “Big Bang” was quite different. In the standard models of the “Big Bang”, it is found that any distorting tidal effect d... ... of the Riemann Christoffel Tensor is here zero. The universe progresses, modelled by a vector field in phase space (see Fig.39), to entropic compa...

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...there are situations that allow compensatability among the values of a solution vector. In such cases the min operator is not the best choice for th... ...al concepts and convenient notation. First let ℘ denote the set of all possible vectors. p = {p j | j ∈ J} such that p j ∈ [0, 1] for all j ∈ J, ... ...there are situations that allow compensatability among the values of a solution vector. In this case, the min operator is not the best choice for th... ...study the non-linear optimization problems. They have presented an optimization model with a nonlinear objective function subject to a system of fuz... ... the user’s criterion function, they solve the following non linear programming model with fuzzy relation constrains min f(x) s.t x o A = b (... ...e user based on the objective function f(x). some related applications of this model with different objective functions can be found in [107] for m... ...GAOFRC’s feasibility of individuals limits the search process to a much smaller space. In general, a GA initializes the population randomly. It wor... ... was presented to transform the efficient point in an “interval-valued decision space” into a “constant-valued decision space” with a given level of... ...RE constraints. It is a stochastic searching method which explores the solution space by evaluating the population at hand and evolving the current ...

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...there are situations that allow compensatability among the values of a solution vector. In such cases the min operator is not the best choice for th... ...al concepts and convenient notation. First let ℘ denote the set of all possible vectors. p = {p j | j ∈ J} such that p j ∈ [0, 1] for all j ∈ J, ... ...there are situations that allow compensatability among the values of a solution vector. In this case, the min operator is not the best choice for th... ...study the non-linear optimization problems. They have presented an optimization model with a nonlinear objective function subject to a system of fuz... ... the user’s criterion function, they solve the following non linear programming model with fuzzy relation constrains min f(x) s.t x o A = b (... ...e user based on the objective function f(x). some related applications of this model with different objective functions can be found in [107] for m... ...GAOFRC’s feasibility of individuals limits the search process to a much smaller space. In general, a GA initializes the population randomly. It wor... ... was presented to transform the efficient point in an “interval-valued decision space” into a “constant-valued decision space” with a given level of... ...RE constraints. It is a stochastic searching method which explores the solution space by evaluating the population at hand and evolving the current ...

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...d absolute relative bias indicate that certain of these estimators substantially improve the MMSE estimator in some guessed interval of the parameter space of beta, especially for censored samples with small sizes. Subsequently, a modified class of shrinkage estimators is proposed with its properties. Part2. In this section we have analyzed the two classes of estimators fo...

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...tantially improve the MMSE estimator in some guessed interval of the parameter space of beta, especially for censored samples with small sizes. Subs... ...sing multiauxiliary information. This error minimization is vital in financial modeling whereby the objective function lies upon minimizing over-sho... ...active in the area of estimation and data sampling applied in financial survey modeling and applied statistics. In our future research, we will addr... ...stantially improve the MMSE estimator in some guessed interval of the parameter space of β , especially for censored samples with small sizes. Subseq... ... in describing the ‘wear-out’ or fatigue failures. 6 Kao(1959) used it as a model for vacuum tube failures while Lieblin and Zelen(1956) used it a... ...samples (S n and S m ) chosen, let (u,v) assume values in a closed convex sub- space, P, of the two dimensional real space containing the point (1,1)... ...auxiliary variates X 1 , X 2 , ...,X p . Further, let the population mean row vector ( ) p µ µ µ µ , , , 2 1 ~ = ′ of the vector ( ) p X X X X , ,... ... − + = 1 0 0 ; 1 0 , * , * g e u e u y y θ θ µ θ µ denote the p element column vector of first partial derivatives of g(⋅) and g (2) (⋅) denotes a p×...

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...nition of Fuzzy Cognitive Maps 9 1.2 Fuzzy Cognitive Maps – Properties and Models 13 1.3 Fuzzy Relational Maps 18 1.4 An Introduction to Neutr... ...ected Graphs and Neutrosophic Directed Graphs of these Fuzzy and Neutrosophic models happen to be very dense. We have represented 16 such graphs in ... ... and illustrate them with examples. Section two gives the properties and some models of FCM. Section three describes the notion of Fuzzy Relational ... ... 1 , a 2 , … , a n ) where a i ∈ {0, 1}. A is called the instantaneous state vector and it denotes the ON - OFF position of the node at an instant.... ...TION 1.1.10: If the equilibrium state of a dynamical system is a unique state vector, then it is called a fixed point. Example 1.1.2: Consider a ... ... Let us assume that the FCM settles down with C 1 and C n on i.e. the state vector remains as (1, 0, 0, …, 0, 1) this state vector (1, 0, 0, …,... ...n doctor and patient and so on. Thus for us to define a FRM we need a domain space and a range space which are disjoint in the sense of concepts. W... ...ntermediate relation exists within the domain elements or node and the range spaces elements. The number of elements in the range space need not in... ...e space need not in general be equal to the number of elements in the domain space. Thus throughout this section we assume the elements of the dom...

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...at universal constant. It has been called the Lorentz speed; Ignazio Ciufolini & John Archibald Wheeler (1995) called it the characteristic speed of space, and they were then able to apply it to all "primordial forces" whether electromagnetic or gravitational or other (what other, C&W did not say)....

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.... Tilton, Echo Electronic Press, 1995; ch.4, "The Dynamic Equipotential Model." Top - The pattern of isochrons from a particle moving at the v... ...ini & John Archibald Wheeler (1995) called it the characteristic speed of space, and they were then able to apply it to all "primordial forces" wheth... ...res an analogy wherein a case is made for calling c the resonant speed of space. For the engineer and the radio amateur, the term "resonance" can ... ...n Bussard and others. An eight-year manned mission is planned to place a spacebuoy ¼-way to Alpha Centauri at San Salvador Station and return to Ea... ...a point generating a line. [2] "Speed," the magnitude of the velocity vector, is sometimes used colloquially when the vector nature is not criti... ...cided on to meet the allotted budget and to decrease ship mass. Computer modeling showed two eco modules to be adequate for a full crew of 12. They... ...steady acceleration during the trip has been ¼G, and to return the gravity vector closer to normal, the ship rotation was increased to provide a tota...

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...of these geometries looks the same at any point and in any direction within the space. Most of the study of geometry at the undergraduate level conce... ..., it is now most likely to be associated with a class of differential geometric spaces called Riemannian manifolds. Here, geometry is studied throug... ...metries of Euclid, Gauss, Bolyai, et al, are particular examples of one kind of space, and extending attention to non-uniform spaces brings much gene... ...he gives an example and poses the question, “Now, the problem is to find a nice model (on manifolds) for this Paradoxist Geometry, and study some of... ...es the paper into a kind of saddle shape (see Figure 1). Figure 1. A paper model with seven equilateral triangles around one vertex. We will ... ...igures 2 and 3). The basic concept of an s-manifold is contained in these paper models made of equilateral triangles taped together edge to edge wit... ...arity. The curvature for a smooth curve is a measure of how quickly the tangent vector changes direction with respect to arclength. Integrating this... ... along an arc, therefore, results in the net change in direction of the tangent vector as an angle measured in radians. For example, the curvature f... ...∫ ds = к θ r = ( 1/r) θ r = θ, and θ is exactly the angle between the tangent vector at A and the tangent vector at C. Figure 16. The change ...

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...GH. C. DINULESCU–CÂMPINA MODELLING OF RATIONALITY … … … … AND BEYOND THE PHYSICS sup(T)+... ...n Research Press Rehoboth 2002 2 GH. C. DINULESCU–CÂMPINA MODELLING OF RATIONALITY … … … … AND BEYOND THE PHYSICS ... ...mic edition. 6 “In another life, probably, my name was Thales” I. MODELLING OF RATIONALITY 1. A SPECULATIVE EXISTENTIAL MODEL OF THE RATIONA... ... 3.Any entity, including the rational one, is deemed as an element of the space−time. 4.The fundamental law governing spatio-temporality and its ele... ...ing away of point P from points X and Y is accomplished with such speeds, vectors or intensities, so as to make their sum universally constant for an... ...nclusion was also reached by G.W. Leibniz who thought that the spiritual ″space″ was of a corpuscular-dissociative nature (the theory of monads). It... ...rium between the two categories of activities, they may be represented by vectors of the same length. If, for example, the intellectual activity prev... ...a shorter time interval, this can be graphically represented by a shorter vector; but according to the law of movement within the material reality, t... ...e rational entity, of the divinity and of their scope of definition – the space-time. The MESER concept seeks and finds support in the thinking of t...

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...ng block of life. The origin of life. The development of microbiology and microscopy. The germ theory of diseases, vaccines, and antibiotics. The vector insects and infectious diseases. The virus, viral diseases, and vaccines. The principle of vegetation and the basic requirements of plants. William Harvey, the heart and the circulatory system. Carl Linneaus and th...

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... NATURE’S INTUITIVE CREATIONS IS THE PROCESS OF UNIVERSAL TRANSFORMATION, WHERE PHYSICAL, CHEMICAL AND BIOLOGICAL EVOLUTION TRANSFORM MATTER, ENERGY, SPACE, TIME AND LIFE ITSELF ...

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...st 32 MARIE CURIE (1867 - 1934) French Chemist 32 PIERRE CURIE (1859 - 1906) French Chemist 32 ABSTRACT ON THE GENESIS OF THE QUANTIZED ATOMIC MODEL 33 JOSEPH J. THOMSON (1856 - 1940) English Physicist 46 ERNEST RUTHERFORD (1871 - 1937) British Physicist 47 NIELS H. BOHR (1885 - 1962) Danish Physicist 48 MAX K. PLANCK (1858 - 1947) German Physicist 49 JAMES C...

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...der, either by decaying or by actively spreading disorder onto other systems. Such vectors we call "Entropic Agents". Conversely, some physical sys... ...r or decrease disorder either in themselves or in their environment. We call these vectors "Negentropic Agents". Human Beings are Negentropic Agent... ...ssertions can be easily converted into a formalism. In Quantum Mechanics, the State Vector can be constrained to collapse to the most order-enhancin... ...hancing event. If we had a computer the size of the Universe that could infallibly model it, we would have been able to predict which events will i... ...lex (the same way all particles are contained in all other particles). Still, these models merely reflect choices of descriptive language, with no b... ...of the behaviors of all complex systems on to a tiny sliver of the state (or phase) space (sort of a mega attractor basin). According to this view, ... ... of as attractors. Contexts can be thought of as attractor landscapes in the phase space of language. They can also be described as fitness landsca... ...idely deployed in many branches of the Humanities, the encroachment of mathematical modeling and statistics notwithstanding. Yet, mathematics reigns... ...he universe (theories) tend to be continuous. Newtonian time is equated to a river. Space is a yarn. Einstein was the last classicist (relativity ju...

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...istory shows that the box had competitors—and today they are back. The early models of commercial (as compared to academic) computing assumed that the... ...gram- ming. The PC of the 1980s—the parent of today’s PC—diverged from these models, but the result was by no means a foregone conclusion. Internet us... ...ting a resurgence of The Rise and Stall of the Generative Net 8 the initial model of bundled hardware and software that is created and con- trolled b... ...system makers sometimes tried to expand their offerings into the “application space”—for example, Microsoft and Apple each developed their own versions... ...ut this flexibility and power are not without risks. Whether through a sneaky vector like the one Morris used, or through the front door, when a trusti... ...tion technology can be subverted does not lessen the concern about any given vector of compromise. Both the problem and the likely solutions are cause... ...the home page of the New York Times, he or she will see banner ads and other spaces that are filled on the fly from third-party advertising aggregators ... ...ffective. For example, on camping trips, Swiss Army knives are ideal. Luggage space is often at a premium, and such a tool will be useful in a range of... ...) (“Together these shifts can move the boundaries of liberty along all three vectors of liberal political morality. They enable democratic discourse t...

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...orks; - to create contradictory literary and artistic works in scientific spaces (using scientific: symbols, meta-language, matrices, theorems, lemm... ..., I, F are subsets, but dynamically the components T, I, F are set-valued vector functions/operators depending on many parameters, such as: time, spa... ...d vector functions/operators depending on many parameters, such as: time, space, etc. (some of them are hidden parameters, i.e. unknown parameters):... ... unknown parameters): T(t, s, …), I(t, s, …), F(t, s, …), where t=time, s=space, etc., that's why the neutrosophic logic can be used in quantum phys... ...alize the Hilbert's for/mal/ization of geometry: by constructing an anti-model, which doesn't respect any of his 20 axioms! (F. Smarandache, <Parad... ... essence. What could be a philosophical algebra? But a philosophical vector space? And how should we introduce a philosophical norm on it? ... ...he degradation.) Dante was Florentine (but not Smarandache)! I am a model of unmodeled artist. An anti-Goethe and non-Faust. A sacerdotal si... ... psychological processes in connection with mathematics. D) Mathematical Modeling of Psychological Processes: a) Improvement of Weber's and Fechner... ...> A logic devoted to paradoxes, in which each proposition has the logical vector value (1, I, 1); here I is a real standard or non-standard subset,...

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...hy not extend the woman's ownership of her body and right to it further in time and space to the post-natal period? Contracts to provide goods and ... ...fetus created. The egg and sperm can be compared to the famous wave function (state vector) in quantum mechanics – the represent millions of potenti... ...s the construction of an ad-hoc mini theory. Reality has to be thoroughly surveyed, models constructed, one of them selected (on empirical or aesth... ...instances of the Principal-Agent Problem. Economists would do well to discard their models and go back to basics. They could start by asking: Why d... ...rring well, and hoping for the best. No one, for instance, offered a linear revenue model of how to translate "eyeballs" - i.e., the number of visit... ...der, either by decaying or by actively spreading disorder onto other systems. Such vectors we call "Entropic Agents". Conversely, some physical sys... ...r or decrease disorder either in themselves or in their environment. We call these vectors "Negentropic Agents". Human Beings are Negentropic Agent... ...use" has been raised with every scientific advance - from in vitro fertilization to space travel. Every technology can be potentially abused. Telev... ...s. - Through legislation, bureaucracy, control of the media, cornering advertising space in the media, controlling infrastructure, owning intellec...

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...hy not extend the woman's ownership of her body and right to it further in time and space to the post-natal period? Contracts to provide goods and ... ...fetus created. The egg and sperm can be compared to the famous wave function (state vector) in quantum mechanics – the represent millions of potenti... ...s the construction of an ad-hoc mini theory. Reality has to be thoroughly surveyed, models constructed, one of them selected (on empirical or aesth... ...instances of the Principal-Agent Problem. Economists would do well to discard their models and go back to basics. They could start by asking: Why d... ...rring well, and hoping for the best. No one, for instance, offered a linear revenue model of how to translate "eyeballs" - i.e., the number of visit... ...der, either by decaying or by actively spreading disorder onto other systems. Such vectors we call "Entropic Agents". Conversely, some physical sys... ...r or decrease disorder either in themselves or in their environment. We call these vectors "Negentropic Agents". Human Beings are Negentropic Agent... ...use" has been raised with every scientific advance - from in vitro fertilization to space travel. Every technology can be potentially abused. Telev... ...s. - Through legislation, bureaucracy, control of the media, cornering advertising space in the media, controlling infrastructure, owning intellec...

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...ngs of a graph on a surfaces................10 2.5 Maps as a combinatorial model of Klein surfaces and s-manifolds .......... 12 §3 The semi-arc autom... ...fine a Klein surface. A Klein surface is a Hausdorff, connected, topological space S together with a family = {(U i ,φ i ) |i ∈ I} such that the chart... ...olyai-Gauss and Riemannian geometries may be united altogether in the same space, by some Smarandache geometries. These last geometries can be either ... ...a subspace) and with the Parallel Universes (because they combine separate spaces into one space) too([32]). Chapter 1 Preliminary 3 In [61], Smarand... ...try. He also posed a question on the paradoxist geometry, i.e., find a nice model on manifolds for this paradoxist geometry and study some of its chara... ... ofg onX α,β is an automorphism of the mapM. ♮ 2.5 Maps as a combinatorial model of Klein surfaces and s-manifolds 2.5.1 The model of Klein surfaces G... ... g[Γ](x), g[Γ](x) or G[Γ](x) are known, and vice via. Denote the variable vector (x 1 ,x 2 ,···) by x ¯ , r ¯ (Γ) =(···, r 2 (Γ), r 1 (Γ),r 0 (Γ),r 1... ...P∈S P α 2 (P) ,∈ Div(S), call U 1 ≥ U 2 if α 1 (P)≥α 2 (P). Now we define a vector space L(U) ={f ∈H(S)|(f)≥U,U ∈Div(S)} Ω(U) ={ω|ω is an abelian diffe... ... Problems for Combinatorial Maps 105 Comparing with the divisors and their vector space, there ia also cycle space and cocycle space in graphical spac...

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...nstantly engaged in the rational pursuit of self interest. This is not a realistic model - merely a useful approximation. According to this latter ... ...tures in economics - or something is very flawed with the intellectual pillars and models of this field. Neo-classical economics has failed on sev... ...y be too multi-dimensional and hyper- complex to be usefully captured by econometric models. These either lack predictive powers or lapse into logica... ...st level in 40 years. Inflation gyrated from double digits to a single digit in the space of two decades. This uncertainty is, inevitably, incorpora... ...ly. They engage Strategies to obtain their highest ranked outcome. A Strategy is a vector, which details the acts, with which the DA will react in ... ... to others to the extent that at least one of them is forced to alter at least one vector (Strategy). The Consequence to the agent is the value o... ...orky (1868-1936), Russian novelist, author, and playright Airplanes, missiles, and space shuttles crash due to lack of maintenance, absent-mindedne... ...nded military research. The pharmaceutical, biomedical, information technology and space industries, for instance - though largely private - rely h...

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...UPS: THE NEED FOR GROUPS TO ACT 69 A Case in Point: The WCTU 71 THE COMMUNICATION MODEL 71 The Objective of the Communication 71 Communication Eff... ... In Part II marketing strategy is discussed by following the time-honored four Ps model -- product, price, promotion and place (channels of distrib... ...n with no loss of continuity). The promotion chapter introduces the communication model, treating the objective, the message and the effect of a co... ...who saw ideas in two modes or realms of being: One is the world of phenomena, in space and time, the world of "sights and sounds," as he called it,... ...y recognizing that ideas underlie all tangibles: "Things and qualities in the time-space world are more or less close reflections of the abstract id... ...: private nursing homes, day-care centers and so forth. The service of providing space for which rent is paid is also listed there. In cell (7),... ...en called the approach-avoidance concept. Product attributes comprise an approach vector because they attract the consumer whereas price factors re... ...whereas price factors repel him or her. The latter are components of an avoidance vector. The model thus has an element of pleasure/pain theory bui...

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...ge in attitude towards everything that had previously been known about time, space, mass, motion, and gravity. Einstein’s theory unified time F O ... ...s, motion, and gravity. Einstein’s theory unified time F O R E WO R D 11 and space into a single entity—time-space—revoking the premise that time a... ...e will be able to unveil the existence of every part of reality, beyond time, space and motion. The Wisdom of Kabbalah grants all the above to anyon... ...ole, as a complex machine. I will dem- onstrate this concept using a toy-train model. If we switch on the train, it will ride the rails and little pe... ... train, it will ride the rails and little people will move about in it. This model is only a machine. You will certainly say that in the toy-train m... ...receding events in the universe. They will even insist that there is no other model. Reality is made solely of a universe and a “toy train” within i... ...orces depict the picture of the world within us in much the same way electric vectors cre- ate images on the TV or computer screen. When we look at t...

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.... I‘m still getting used to these earthly beds. When you‘re weightless in space you sleep anywhere and you don‘t have to worry about the weight of y... ... --―Wreck, you think that just because you took one little cruise through space you can tell us what to do. Remember I‘m still the quarterback, so ... ...se my knowledge a bit. And while I gazed from my window into the abyss of space, my mind did play with thoughts on how the illnesses of the human si... ...cessities. We went from bicycles to cars, now people want more and better models. Bigger, flatter TVs, more rooms in their houses, second homes, ple... ...fore there is no God. Then as they proceeded to the last room there was a model of Sputnik hanging from the ceiling. Obviously science, not God, was... ...base it on science as Bacon proposed. We can use the Scandinavian welfare model. But no approach to society has yet been universally acclaimed by th... ...egative for societies. Prostitutes have been shown to be both victims and vectors of sexually transmitted diseases. This is particularly true where ...

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...ndant on many parameters, and therefore they can be considered set-valued vector functions or even operators. The parameters can be: time, space... ...lued vector functions or even operators. The parameters can be: time, space, etc. (some of them are hidden/unknown parameters): T(t, s, …), I(t,... .../unknown parameters): T(t, s, …), I(t, s, …), F(t, s, …), where t=time, s=space, etc., which allows the neutrosophic logic to be used in quantum phy... ... the abbreviations T = (1,0,0) and F = (0,0,1), then it is clear that this model is equivalent to classical logic. 56 Example: If the va... ...ndant on many parameters, and therefore they can be considered set-valued vector functions or even operators. T, I, and F are called neutrosophic ...

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...ontemplate an intercept.They assumed the fighter escort would be discreet,“vectored to a position five miles directly behind the hijacked aircraft,” w... ... show the Otis fighters were airborne at 8:53. Lacking a target, they were vectored toward military-controlled airspace off the Long Island coast.To a... ...craft’s identity or type was unknown. 146 Reagan National controllers then vectored an unarmed National Guard C- 130H cargo aircraft, which had just t... ...n Khartoum in late 1994 or early 1995. Bin Ladin is said to have asked for space to establish training camps, as well as assistance in procuring weapo... ... raised the “remote possibility” of Yemen, which offered vast uncontrolled spaces. In November, the CSG dis- cussed whether the sanctions had rattled ... ...r of the “planes operation.” Khalid Sheikh Mohammed No one exemplifies the model of the terrorist entrepreneur more clearly than Khalid Sheikh Mohamme... ...ld.They used the game software to increase their familiarity with aircraft models and functions, and to highlight gaps in cabin security.While in Kara... ...re, in order to keep long lines of foreigners away from vulnerable embassy spaces. The program permitted visa applications to be made through travel a... ...d because few tolerant or sec- ular Muslim democracies provide alternative models for the future, Bin Ladin’s message finds receptive ears. It has att...