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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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...rdered in a paper bound reprint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) 30... ... 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... ...presented by a diagonal bimatrix D = D 1 ∪ D 2 we would gain considerable information about T = T 1 ∪ T 2 . For instance simple number associated... ... SUGGESTED PROBLEMS Now as such this book only views bimatrix as a theory. In fact several more results about bimatrices can also be devel... .... Cambridge Philos. Soc., 31 (1935) 433-435. 6. BURROW, M., Representation Theory of Finite Groups, Dover Publications, 1993. 7. DUBREIL, P., and ... ...lutions to the Student Mathematical Competitions. His latest interest is in information fusion were he works with Dr.Jean Dezert from ONERA (French ...

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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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...rdered in a paper bound reprint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) 30... ...d and recommended for publication by: Dr. Sukanto Bhattacharya, School of Information Technology, Bond University, Queensland, Australia. Dr. Ius... ...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... ...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 ... ...cking of e- mail by students. One of the major problems of today’s world of information technology that is faced by one and all is; How safe are the... ...phic Cognitive State maps of users web behavior is described. Searching for information in general is complex, with lot of indeterminacies and it is... ...ications of intimate technologies, owing to their ability to FIGURE: 3.7.11 INFORMATION CONSTRAINT SUCCESS RELEVANCE FAILURE SEARCH BROWSE TIM...

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...roup and a semigroup simultaneously. This book is a piece of work on Smarandache semigroups and assumes the reader to have a good background on group theory; we give some recollection about groups and some of its properties just for quick reference....

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...an be ordered in a paper bound reprint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) ... ...liminary results 14 2.4 Subgroups 15 3. Some Classical Theorems in Group Theory 3.1 Lagrange's Theorem 21 3.2 Cauchy's Theorems 22 3.3 ... ...marandache semigroups and assumes the reader to have a good background on group theory; we give some recollection about groups and some of its proper... ...e used in this book. Chapters 2 and 3 gives most of the basic concepts on group theory and results in group theory which have been used in this text... ...rch on Smarandache notions. Smarandache notions are revolutionary because group theory does not make one think of the unthinkable that can naturally... ...see that the chapters two and three give most of the relevant concepts in group theory for which we have studied the Smarandache notions. In these t... ... for every b ∈ G, we must have for e ∈ G, e  f = e. Piecing these two bits of information together we get f = e  f = e and so e = f. THEOREM 2.... ... G ( o p , for every a ∈ G where a ∉ Z(G). Look at the class equation with this information. Since p α /o(G) we have that p/o(G), also ∑ ∉Z a )) a (... ...t be divisible by p, so we can write as kp, where k is an integer. Feeding this information back into our equation above, we have . kp 1 )) P ( N ...

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...Number theory is an ancient subject, but we still cannot answer many simplest and most natural questions about the integers. Some old problems have been solved, but more arise. All the research for these ancient or new problems impl...

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...RESEARCH ON SMARANDACHE PROBLEMS IN NUMBER THEORY (Collected papers) Edited by ZHANG WENPENG D... ... Hexis 200 4 RESEARCH ON SMARANDACHE PROBLEMS IN NUMBER THEORY (Collect ed papers) Edited by ZHANG W... ...ordered in a paper bound reprint from: Books on Demand ProQuest Information & Learning (Univers ity of Microfilm International) 300... ...Florentin Smarandache, who listed many new and unsolved problems in number theory. Contents Dedication v Preface xi An arithmetic function and the pr... ...its mean value 49 Gao Nan viii RESEARCH ON SMARANDACHE PROBLEMS IN NUMBER THEORY On the generalized constructive set 53 Gou su On the inferior and su... ...new problems implicated and are still promoting the development of number theory and mathematics. American - Romanian number theorist Florentin Sm...

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...om: Books on Demand ProQuest Information & Learning (University of Microfilm... ...bigraph will prove a major role in the applications of bimodels both in fuzzy theory and neutrosophic theory. Finally we give the matrix represen... ...that gives the hidden pattern of the situation. As we have a very well known theory, which states that the strength of the data 76 depends on, th... ...ps will also be directed neutrosophic graphs. It is no coincidence that graph theory has been independently discovered many times since it may quite... ...bject finds its place in the work of Euler. Subsequent rediscoveries of graph theory were by Kirchhoff and Cayley. Euler (1707-1782) became the fath... ... In Proc. of the 19 th International Conference of the North American Fuzzy Information Processing Society, NAFIPS2000, Atlanta, 2000. http://di... .... In Proc. of the 18 th International Conference of the North American Fuzzy Information Processing Society, by NAFIPS, New York, (1999) 115- 119. ... ...aras, D., and B. Karakostas. The Use of Fuzzy Cognitive maps to Stimulate the Information Systems Strategic Planning Process, Information and Softwa... ...tml 95. Montazemi, A.R., and D. W. Conrath. The Use of Cognitive Mapping for Information Requirements Analysis, MIS Quarterly, 10, 45-55, 1986. 9...

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...ook can be ordered in a paper bound reprint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) 300 N. Zeeb ... ... on the rights was 2k. This is not divisible by 4 if k is odd. Additional information concerning the Concatenated Even Sequence can be gleaned by exa... ...e Fibonacci and Lucas sequences. References 1. Unsolved Problems in Number Theory, edited by Richard K. Guy, Springer, 2004, ISBN 0387208607. 70 Chap... ...hat kind of stereograms can be created by iterating combinations of number theory functions and plotting the number of iterations? 3.2 Altering the Ba...

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... logic and first order interval neutrosophic predicate logic. The interval neutrosophic logic can reason and model fuzzy, incomplete and inconsistent information. In this chapter, we also design an interval neutrosophic inference system based on first order interval neutrosophic predicate logic. The interval neutrosophic inference system can be applied to decision making. ...

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...sophic Propositional Calculus . . . . . . . . . 23 2.2.2 Semantics of Interval Neutrosophic Propositional Calculus . . . . . . . . . 24 2.2.3 Proof Theory of Interval Neutrosophic Propositional Calculus . . . . . . . . 25 2.3 Interval Neutrosophic Predicate Calculus . . . . . . . . . . . . . . . . 27 2.3.1 Syntax of Interval Neutrosophic Predicate Calculus . . . . . . ...

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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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...dered in a paper bound reprint from: Books on Demand ProQuest Information & Learning (University of Microfilm International) 300... ...elds itself to applications to several fields like coding or communication theory, Markov chains, representation of groups and graphs, Leontief econ... ...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-... ...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... ...or the first time we give the results of bimatrices in the field of coding theory. Very recently we have defined the notion of bicodes here we give ... ...utions to the Student Mathematical Competitions. His latest interest is in information fusion were he works with Dr.Jean Dezert from ONERA (French N...

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...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 investigations while, Par...

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...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 . . . . . ...

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...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 info...

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...nality . . . . . . 46 1.6.3 The Generalized Pignistic Transformation . . . 47 1.7 The DSmP transformation . . . . . . . 48 1.7.1 The Probabilistic Information Content (PIC) . . . 49 1.7.2 The DSmP formula . . . . . . . 50 1.7.3 Examples for DSmP and BetP . . . . . . 51 1.8 Fusion of qualitative beliefs . . . . . . . 54 1.8.1 QualitativeOperators . . . . . . . 54 1....

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...ization of Venn Diagram, by Florentin Smarandache.........84 ECONOMICS, BUSINESS, AND POLITICS.................87 10. Introduction to Poly-Emporium Theory in Economics, by V. Christianto, F. Smarandache, in Authors’ book Cultural Advantage for Cities. An Alternative for Developing Countries, InfoLearnQuest, Ann Arbor, 61 p., 2008............88 11. Global Totalitarianism...

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...ization of Venn Diagram, by Florentin Smarandache.........84 ECONOMICS, BUSINESS, AND POLITICS.................87 10. Introduction to Poly-Emporium Theory in Economics, by V. Christianto, F. Smarandache, in Authors’ book Cultural Advantage for Cities. An Alternative for Developing Countries, InfoLearnQuest, Ann Arbor, 61 p., 2008............88 11. Global Totalitarianism...