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...Fuzzy theory is one of the best tools to analyze data, when the data under study is an unsupervised one, involving uncertainty coupled with imprecision. However, fuzzy theory cannot cater to analyzing the data involved with indete...

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...NCES 290 INDEX 312 ABOUT THE AUTHORS 316 5 Preface Fuzzy theory is one of the best tools to analyze data, when the data under s... ...pervised one, involving uncertainty coupled with imprecision. However, fuzzy theory cannot cater to analyzing the data involved with indeterminacy.... ...l women in Tamil Nadu. Chapter 2 is an analysis of the situation using fuzzy theory in general and Fuzzy Relational Maps (FRM) in particular. The F... ... of the nodes/ concepts. In Chapter 4 for the first time we use neutrosophic theory in general and neutrosophic relational maps (NRM) in particular... ...ning replaces old stored patterns with new patterns. Learning forms internal representation of prototypes of sampled patterns learned prototypes de... ...ociety? More so is the status of Sudra women. So the role of Indian women or representation of women society in India is just the high caste social... ...spitals. To be more precise these women have no voice in society or even any representation in society, they live and die like plants that have no ... ...n matrix. In practice we sidestep this large numerical matrix with a virtual representation scheme. In the place of the matrix the user encodes the... ...le. Saunders, Philadelphia. 298 56. Klein, A. L., (1996) Women’s Social Representation of Sex, Sexuality and AIDS in Brazil. in Women’s Experi...

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...The theory of loops (groups without associativity), though researched by several mathematicians has not found a sound expression, for books, be it research level or otherwise, solely dealing with the properties of loops are absen...

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...cial identities in loops 22 2.4 Special types of loops 23 2.5 Representation and isotopes of loops 29 2.6 On a new class of loops a... ...of level II 93 4.2 Properties of S-loop II 98 4.3 Smarandache representation of a finite loop L 99 4.4 Smarandache isotopes of loops ... ... n c e s 113 I n d e x 119 5 PREFACE The theory of loops (groups without associativity), though researched by severa... ...the properties of loops are absent. This is in marked contrast with group theory where books are abundantly available for all levels: as graduate te... ...d as advanced research books. The only three books available where the theory of loops are dealt with are: R. H. Bruck, A Survey of Binary System... ...ein, H. O. Pflugfelder and J.D.H. Smith (editors), Quasigroups and Loops: Theory and Applications, Heldermann Verlag, 1990. But none of them are com... ...a new class of loops of even order. We prove that the number of different representations of right alternative loop of even order (2n), in which squ... ...ry permutation σ of a finite set X is a product of disjoint cycles. The representation of a permutation as a product of disjoint cycles, none of wh... ...led in section 3. In section 4 we define some special types of loops. The representation and isotopes of loops is introduced in section 5. Section 6...

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... and its moral and practical implications. The blurring line between life and its representation in the arts is arguably the main theme of "The Tr... ... responsible because they implicitly contracted with their passengers. They made a representation (which was explicit in their case but is implicit... ... the reasonable and justified expectations of consumers, based on such warrants and representations. The payment should be either in kind (as in mor... ...possible where the laws of nature are different. This is the same tired regularity theory in a more exotic guise. They are all descendants of Hume'... ...rld. It mainly arises when we introduce intentional action and perception into the theory of causation. Let us revert to the much- maligned owner of... ... property, planning, wealth and capital. Mental inequalities lead to innovation and theory. Knowledge differentials are at the heart of educational ... ...the brain's activities? A book, a painting, an invention are the documentation and representation of brain waves. They are mere shadows, symbols of... ...es, unless the manufacturers equip the robots with digital or optical or molecular representations of the human figure (masculine and feminine) in ... ...d logic): computability or recursive functions (later to be developed into Automata Theory). The authors confined themselves to dealing with comput...

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...nstituted where two persons meet. Applying this, x thought to the modem theory of history as a process within an unbroken causal system, where fac... ... IS .... It may be supposed that characterisations and ideas, but also representations of persons and things, have been taken out from representa... ... evil or sweetness of its touch. He does not retain from this the visual representation, say, of the wandering orb of light, or of a demonic being ... ... Of course, this happens in a "primitive" form and not in the form of a " theory of knowledge". But whenever the sentence :' I see the tree" is so ... ... world of It, yet be transfigured inii? what is over against man-into the representation of the Thou. There is no going backwards, but in the very ... ...a person approach and meet God. He longs 'for extension in space, for the representation in which the community of the faithful is united with its G...

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..., 1988. ** On this theme see my book “Teoria dell’inconscio esistenziale” {Theory of the Existential Unconscious} and my interpretation of the film ... ...e fourth, which is the Choral Self and Cosmic SELF. What is the SELF in my theory, in my conception of humanity? You can understand it quickly by l... ...my personalistic metapsychology, outlined in my book Teoria della Persona {Theory of the Person}, I can attribute to both human beings and the univer... ...n constant observations. What does this mean? When Einstein created his theory of relativity, first of all special relativity and then general re... ...s of the individual human being B) all of the individual’s perceptions and representations of reality C) all of the human organism’s biological, cul... ...one day I came up with this answer. I think that the Iliad is a symbolic representation of what happens when an ovum is fertilized by a sperm, and... ... when an ovum is fertilized by a sperm, and that the Odyssey is a symbolic representation of what happens from the moment the ovum is fertilized up ... ...g storms which throw them around the Mediterranean. If this is a poetic representation of the life of a foetus in the amniotic liquid, it is diff... ...ording to the laws of life, it is good and just that Ulysses, the symbolic representation of a human being from intrauterine life up until full matur...

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...s lies in its affirmation of the existence of the Personal SELF (see A.M. “Theory of the Person and Existential Personalistic Anthropology”). This s... ...the Odyssey, the sorceress Circe, the nymph Calypso and the Sirens are all representations of this mother that first seduces her son and then castrat... ...*** It is not easy to embrace Sophia-Art. It does not require learning a theory, it means applying it to daily life. Some ways we can do so are as... ...LOGIA PERSONALISTICA ** Ed. Sophia University of Rome (S.U.R.), Rome 1991 THEORY OF THE PERSON AND EXISTENTIAL PERSONALISTIC ANTHROPOLOGY Publishe... ... Sophia University of Rome, 2010 TEORIA DELL’INCONSCIO ESISTENZIALE {The Theory of the Existential Unconscious} Ed. Costellazione d’Arianna Rome 1... ...scious} Ed. Costellazione d’Arianna Rome 1995 TEORIA DELLA PERSONA {The Theory of the Person} 2° ed. Costellazione di Arianna, Rome 1992 ...

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...h consciousness. Still, numerous anecdotes recounted by eyewitnesses support the theory that consciousness survives in the first 2-6 seconds and ... ...n Vladimirovich Michurin (1855-1935) and his brand of Lamarckism - a pre-Darwinian theory of evolution of the species proposed in the French scient... ...t. A species with long necks was born. The Soviet leadership sought an indigenous theory to counter the "capitalistic" works of Mendel and Charles... ...every 4 years and anyone over 20 years of age could vote. A system of proportional representation gave voice and presence in the Reichstag to even ... ...cific Western University, California, USA. Graduate of numerous courses in Finance Theory and International Trading. Certified E-Commerce Concepts ...

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... He just wasn't going to allow her to be mad at him, huh? But he shot this theory to hell with his next words. "Jury wouldn't appreciate—" "Wouldn't a... ...iratorial wink. "I would gather that our Kane is offended by the miniature representation of the Al Jenadriyah festival." "This rendition is profanati... ...at far. Perhaps a little unorthodo—" "You desecrate the essence behind the theory of Islamic art by having this figural sculpture on display." "Kane, ...

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...n?” Donil contemplated how much to tell his grandparents. If he voiced his theory, his grandma would nag him to death. If he said nothing, and later ... ...satisfied with the handout, waged legal battles to get the same rights and representation as their human counterparts, who dominated the upper levels... ...tiny, the Accords of 2130 was reached. Weres and humans had to have equal representation in the legislative and judicial levels and all key governmen...

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...face would be an imposing twenty feet wide. The monument would be both a larger-than-life representation of the mythical lion Amsara, as well as its... ...’m thinking?” “About the coffee? I doubt it,” he replied. “Very funny, I mean about our theory. What if this was something that could prove we’re ... ...y, we are blessed to have with us both the living embodiment of Amsara and now an eternal representation of your protector that has risen from mere s... ...ore real than the waking world.” Jack started to pace the room, caught up in his emerging theory. “What if these people, the Kierani, were able to c...

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...tongue, we have in THE HOLY SCRIPTURES. It was necessary furthermore, to have a visible representation or unchanging body of that truth, which was to... ... years and a half; or forty and two months, or 1260 days, —which led him into his whole theory of this vision, or as he modestly proposeth it, his c... ...ff. Now this principle established upon so broad a basis, bears hard upon our author’s theory of the apocalyptic prophecy who goes about to deprive ... ...ious life cannot represent it perfectly, and we are forced, in order to find its proper representation to meditate the conscious life of the human s... ...f faith. Of which faith indeed my countrymen and churchmen have matured an intellectual theory, (that it is no more than the bare receiving of the wr... ...ct to the coming of Christ, which at present holds possession of the churches, gives no representation whatever either of Christ’s priestly or kingl... ...certainly alludeth to the return out of Babylon; but regardeth it merely as a figure or representation of the liberation by Christ from the captivity...

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...This book aims to assist social scientists to analyze their problems using fuzzy models. The basic and essential fuzzy matrix theory is given. The book does not promise to give the complete properties of basic fuzzy theory or basic fuzzy matrices. Instead, the authors have only tried to give those essential basically needed to develop the fuzzy mode...

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...Preface 4 Dedication 6 Chapter One BASIC MATRIX THEORY AND FUZZY MATRIX THEORY 7 1.1 Basic Matrix Theory 7 1.2 Basic Concepts on Fuzzy Matrices 33 1.3 Basic Concepts on Graphs 47 Chapter Two DESCRIPTION OF SIMPLE FUZZY MODELS AND THEIR APPLICATIONS TO REAL WORLD PRO...

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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 applicat...

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... INDEX 175 ABOUT THE AUTHORS 181 5 Preface Matrix theory has been one of the most utilised concepts in fuzzy models and ne... ...eral real models. In fact it is not an exaggeration if one says that matrix theory and linear algebra (i.e. vector spaces) form an inseparable compo... ...the study of bimatrices for a while in order to develop some aspects of the theory of determinants which will be needed in our further investigatio... .... If v ∈ V = V 1 ∪ V 2 then v ∈ V 1 or v ∈ V 2 if v ∈ V 1 then v has a representation of the form (x 1 , x 2 , x 3 , x 4 , 0, 0, 0, 0, 0) where... ... 2 then v = (0, 0, …, 0, y 1 , y 2 , …, y n ). Contextually we also accept representation of v ∈ V by v = v 1 ∪ v 2 where v 1 = (x 1 , …, x m ) ... ...imatrix A = A 1 ∪ A 2 = ( ) ( ) 12 ij ij AA ∪ is not a bimatrix but is a representation of a bimatrix. An m × n bimatrix over the field F is a fu... ... ( ) ( ) 121212 AAXXYY ∪∪= ∪ 11 22 1 2 AX AX Y Y ∪=∪ gives the bimatrix representation of the system of linear biequations. Now we can define e... ...eed on to define linear Bitransformation in a different way for this way of representation will use bimatrices and is both time saving and economic ... ... SUGGESTED PROBLEMS Now as such this book only views bimatrix as a theory. In fact several more results about bimatrices can also be devel...

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...sues 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 attac...

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...ion framework with a practical codification for low complexity 217 by A. Martin 7.1 Introduction . . . . . . . . . . 218 7.2 Short background on theory of belief functions . . . . 219 7.3 A general belief function framework . . . . . . 221 7.3.1 A practical codification . . . . . . . 221 7.3.2 Adding constraints . . . . . . . 224 7.3.3 Codification of the focal el...

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...Generalized Partitions and New Ideas On Number Theory and Smarandache Sequences Editor’s Note This book ar... ...OWA 42402 USA GENERALIZED PARTITIONS AND SOME NEW IDEAS ON NUMBER THEORY AND SMARANDACHE SEQUENCES Hexis P... ...e On Maohua Le’s Proof of Murthy’s Conjecture On Reciprocal Partition Theory ………………. 18 1.4 Generalization of Partition Functions, Introducti... ...9 1.5 Open Problems and Conjectures On the Factor/Reciprocal Partition Theory ………………. 28 1.6 A General Result on the Smarandache Star Function... ...nd An Elementary Inequality 176 3.11 Smarandache Maximum Reciprocal Representation Function …………………. 178 3.12 Smarandache Determinant Sequ... ...FP) of N, say F 1 , F 2 , . . ., F r arbitrarily and the F k be the SFP representation of N as the product of its divisors in the following way: ... ..., No. 1-2-3, 2001. 5. Amarnath Murthy, "Smarandache Maximum Reciprocal Representation Function", SNJ , Vol 11, No. 1-2-3 , 2000. 6. Amaranth ... ... Σ S(k) ≤ X n . k=1 Section 11 Smarandache Maximum Reciprocal Representation Function Definition: The Smarandache Maximum Reciprocal R... ...=1 r=1 Definition: The Smarandache Maximum Reciprocal Representation Sequence (SMRRS) is defined as T n = f SMRR (n) f SMRR ...

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...OF SOCIAL ASPECTS OF MIGRANT LABOURERS LIVING WITH HIV/AIDS USING FUZZY THEORY AND NEUTROSOPHIC COGNITIVE MAPS With Specific Reference To Rura... ... OF SOCIAL ASPECTS OF MIGRANT LABOURERS LIVING WITH HIV/AIDS USING FUZZY THEORY AND NEUTROSOPHIC COGNITIVE MAPS With Specific Reference To Rura... ... essential need for an alternative system that could infuse into itself a representation of the real world. Out of this need arose the system of neu... ... are used in the study of the problem. In chapter III yet another fuzzy theory technique namely the bi-directional associative memories is used in... ...em. In Chapter IV we first just recall some basic notions of neutrosophic theory, neutrosophic cognitive maps that are utilized in the analysis of t... ...a drunken state and so on. So we cannot give it any statistical form/data representation for the psychological study for the cause may remain an in... ...ents, is carried out in five stages. In the first stage we get a matrix representation of the raw data. Entries corresponding to the intersection ... ... OFF. ON represents the signal +1, OFF represents 0 or – 1 (– 1 when the representation is bipolar). Additive bivalent models describe asynchronous... ...ained the experts opinion, which is given the neutrosophic directed graph representation. Let the correspo...

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...In The 2nd Conference on Combinatorics and Graph Theory of China (Aug. 16-19, 2006, Tianjing), I formally presented a combinatorial conjecture on mathematical sciences (abbreviated to CC Conjecture), i.e., a mathematical science can be reconstructed from or made by combinat...

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...Lie multi-group . . . . . . . . . . . . . . . . . . . . . . . . 315 6.4.3 Homomorphism on lie multi-group . . . . . . . . . . . . 321 6.4.4 Adjoint representation . . . . . . . . . . . . . . . . . 323 6.4.5 Lie multi-subgroup . . . . . . . . . . . . . . . . . . . . . 323 6.4.6 Exponential mapping. . . . . . . . . . . . . . . . . . .324 6.4.7 Action of Lie multi-group ...

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...ebraic structure, linear algebra happens to be one of the subjects which yields 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 al...

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...nd linear bioperators 62 3.3 Bivector spaces over finite fields 93 3.4 Representation of finite bigroup 95 4 3.5 Applications of bimatrix to... ... 131 4.2 Smarandache neutrosophic linear bialgebra 170 4.3 Smarandache representation of finite Smarandache bisemigroup ... ...elds itself to applications to several fields like coding or communication theory, Markov chains, representation of groups and graphs, Leontief econ... ...ons to several fields like coding or communication theory, Markov chains, representation of groups and graphs, Leontief economic models and so on. ... ...in this direction. 1.3.2 Smarandache Leontief economic models Matrix theory has been very successful in describing the interrelations between ... ...ween the industries in the economy 32 under considerations. Using matrix theory we evaluate certain parameters. The basic equations of the input-... ...∈ V = V 1 ∪ 41 V 2 then v ∈ V 1 or v ∈ V 2 if v ∈ V 1 then v has a representation of the form (x 1 , x 2 , x 3 , x 4 , 0, 0, 0, 0, 0) where ... ... 33101 10112 ⎡ ⎤ ⎢ ⎥ − ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ Thus A = A 1 ∪ A 2 is the bimatrix representation for T for it saves both time and space. When we give the b... ...entation existing between members of a set introduced, we have studied the theory of directed graphs to mathematically model the types of sets and r...

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...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 f...

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...eutrosophic Vector spaces 8 Chapter Two SOME BASIC RESULTS ON GRAPH THEORY AND THEIR APPLICATION TO FUZZY MODELS 2.1 Some basics on Gr... ...ophic algebraic structures is very recent. The introduction of neutrosophic theory has put forth a significant concept by giving representation to i... ...uction of neutrosophic theory has put forth a significant concept by giving representation to indeterminates. Uncertainty or indeterminacy happen to... ...n almost all real-world problems. When uncertainty is modeled we use fuzzy theory and when indeterminacy is involved we use neutrosophic theory. Mo... ... further development of the other chapters. Chapter Two recalls basic graph theory definitions and results which has interested us and for which we ... ...m of the values of the directed lines from each point equal to 2. A similar representation of a directed graph arises in that part of numerical anal... ...oncept of digraphs. The directed graphs or the diagraphs are used in the representation of Binary relations on a single set. Thus one of the form... ...epresentation of Binary relations on a single set. Thus one of the forms of representation of a fuzzy relation R(X, X) is represented by the digraph... ...n fact one can say that the graph theory method was more simple and an easy representation even by a lay man. Thus we can say whenever the data h...

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...e reality. Despite various attempts to reorient logic, there has remained an essential need for an alternative system that could infuse into itself a representation of the real world. Out of this need arose the system of Neutrosophy, and its connected logic, Neutrosophic Logic. Neutrosophy is a new branch of philosophy that studies the origin, nature and scope of neutralit...

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... essential need for an alternative system that could infuse into itself a representation of the real world. Out of this need arose the system of Neu... ...ntion here that the Neutrosophic logic is a further generalization of the theory of Fuzzy Logic. In this book we study the concepts of Fuzzy Cogn... ...Fuzzy Visions of Society and Science in the Digital Age writes that fuzzy theory can offer more choices and blur the hard lines of power that define... ...f our age. We have, in our effort at introducing indeterminacy into Fuzzy theory, and by our construction of neutrosophic structures of modeling, on... ...ting to these concepts. An almost exhaustive bibliography relating to the theory of FCMs completes the book. Some of the varied applications of F... ...cision support in intelligent intrusion detection system; hyper-knowledge representation in strategy formation; female infanticide; depression in te... ...al causal structure and perhaps the global equilibrium. The FCM knowledge representation and inference-ing structure reduces to simple vector- matrix... ...ransfers in the route C 8 - Congestion in the vehicle. The graphical representation of the inter-relationship between the nodes is given in the... ... refer [65]. 1.3.3: Adaptive fuzzy cognitive maps for hyperknowledge representation in strategy formation process Carlsson and Fuller [17] ...