Showing papers by "Florentin Smarandache published in 2004"
TL;DR: This book is devoted to an emerging branch of Information Fusion based on new approach for modelling the fusion problematic when the information provided by the sources is both uncertain and (highly) conflicting.
Abstract: This book is devoted to an emerging branch of Information Fusion based on new approach for modelling the fusion problematic when the information provided by the sources is both uncertain and (highly) conflicting. This approach, known in literature as DSmT (standing for Dezert-Smarandache Theory), proposes new useful rules of combinations.
576 citations
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29 Apr 2004TL;DR: In this article, a geometric interpretation of the Neutrosophic set is given using a Neutroophic Cube, and distinctions between NS and IFS are underlined.
Abstract: In this paper we generalize the intuitionistic fuzzy set (IFS), paraconsistent set, and intuitionistic set to the neutrosophic set (NS). Several examples are presented. Also, a geometric interpretation of the Neutrosophic Set is given using a Neutrosophic Cube. Many distinctions between NS and IFS are underlined.
225 citations
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TL;DR: In this article, five versions of a Proportional Conflict Redistribution rule (PCR) are proposed for information fusion together with several examples. But they do not satisfy the neutrality property of vacuous belief assignment.
Abstract: In this paper we propose five versions of a Proportional Conflict Redistribution rule (PCR) for information fusion together with several examples. From PCR1 to PCR2, PCR3, PCR4, PCR5 one increases the complexity of the rules and also the exactitude of the redistribution of conflicting masses. PCR1 restricted from the hyper-power set to the power set and without degenerate cases gives the same result as the Weighted Average Operator (WAO) proposed recently by J{\o}sang, Daniel and Vannoorenberghe but does not satisfy the neutrality property of vacuous belief assignment. That's why improved PCR rules are proposed in this paper. PCR4 is an improvement of minC and Dempster's rules. The PCR rules redistribute the conflicting mass, after the conjunctive rule has been applied, proportionally with some functions depending on the masses assigned to their corresponding columns in the mass matrix. There are infinitely many ways these functions (weighting factors) can be chosen depending on the complexity one wants to deal with in specific applications and fusion systems. Any fusion combination rule is at some degree ad-hoc.
111 citations
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TL;DR: In this article, Neutrosophic Cognitive Maps are used in the study of migrant labourers who have become HIV/AIDS victims in rural areas of Tamil Nadu and the role played by the government in helping these migrants with HIV and factors of migration and their vulnerability in catching HIV.
Abstract: This book has seven chapters. The first chapter is introductory in nature and it speaks about the migrant labourers. In chapter two we use Fuzzy Cognitive Maps to analyze the socio-economic problems of HIV/AIDS infected migrant labourers in rural areas of Tamil Nadu. In chapter three we analyze the role played by the government helping these migrant labourers with HIV/AIDS and factors of migration and their vulnerability in catching HIV/AIDS. For the first time Neutrosophic Cognitive Maps are used in the study of migrant labourers who have become HIV/AIDS victims. This study is done in Chapter IV. In chapter V we use Neutrosophic Relational Maps and we define some new neutrosophic tools like Combined Disjoint Block FRM, Combined Overlap NRM and linked NRM. We adopt these new techniques in the study and analysis of this problem. Chapter VI gives a very brief sketch of the life history of these 60 HIV/AIDS infected migrant labourers so that people from different social and cultural backgrounds follow our analysis. The last chapter gives suggestions and conclusions based on our study.
84 citations
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TL;DR: The interval neutrosophic logics is presented which generalizes the fuzzy logic, paraconsistent logic, intuitionistic fuzzy logic and many other non-classical and non-standard logics.
Abstract: In this paper, we present the interval neutrosophic logics which generalizes the fuzzy logic, paraconsistent logic, intuitionistic fuzzy logic and many other non-classical and non-standard logics. We will give the formal definition of interval neutrosophic propositional calculus and interval neutrosophic predicate calculus. Then we give one application of interval neutrosophic logics to do approximate reasoning.
75 citations
Journal Article•
TL;DR: This paper presents in detail the generalized pignistic transformation succinctly developed in the Dezert-Smarandache Theory (DSmT) framework as a tool for decision process and provides the complete result obtained by the GPT and its validation drawn from the probability theory.
47 citations
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TL;DR: This book develops the new concept of Neutrosophic Relational Equations (NREs) that have the capacity to analyze problems with indeterminacy.
Abstract: The introduction of Fuzzy Relational Equations (FREs) has made problems that were unsolvable using algebraic linear equations into solvable ones. FREs have been applied to problemsin medicine, industry, transportation and all types of social problems where the data is an unsupervised one. Yet, FREs lack the capacity to tackle problems where an element of indeterminacy is involved. This book develops the new concept of Neutrosophic Relational Equations (NREs) that have the capacity to analyze problems with indeterminacy. Here, earlier models on FREs are analyzed and new NRE models, with practical applications, are presented.
45 citations
Journal Article•
TL;DR: In this paper, the existence of at least two solutions of problem (1.1) under some restrictions on h(x), 'lembda' and q was proved using variational methods.
Abstract: In this paper, using variational methods, we prove the existence of at least two solutions of problem (1.1) under some restrictions on h(x), 'lembda' and q.
31 citations
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TL;DR: This paper introduces the degree of union and degree of inclusion with respect to the cardinal of sets not with the fuzzy set point of view, besides that of intersection, many fusion rules can be improved.
Abstract: This paper may look like a glossary of the fusion rules and we also introduce new ones presenting their formulas and examples: Conjunctive, Disjunctive, Exclusive Disjunctive, Mixed Conjunctive-Disjunctive rules, Conditional rule, Dempster's, Yager's, Smets' TBM rule, Dubois-Prade's, Dezert-Smarandache classical and hybrid rules, Murphy's average rule, Inagaki-Lefevre-Colot-Vannoorenberghe Unified Combination rules [and, as particular cases: Iganaki's parameterized rule, Weighting Average Operator, minC (M Daniel), and newly Proportional Conflict Redistribution rules (Smarandache-Dezert) among which PCR5 is the most exact way of redistribution of the conflicting mass to non-empty sets following the path of the conjunctive rule], Zhang's Center Combination rule, Convolutive x-Averaging, Consensus Operator (Josang), Cautious Rule (Smets), ?-junctions rules (Smets), etc and three new T-norm & T-conorm rules adjusted from fuzzy and neutrosophic sets to information fusion (Tchamova-Smarandache) Introducing the degree of union and degree of inclusion with respect to the cardinal of sets not with the fuzzy set point of view, besides that of intersection, many fusion rules can be improved There are corner cases where each rule might have difficulties working or may not get an expected result
28 citations
01 Jan 2004
TL;DR: Five versions of a Proportional Conflict Redistribution rule (PCR) for information fusion together with several examples are proposed and improved PCR rules are proposed in this chapter.
Abstract: In this chapter we propose five versions of a Proportional Conflict Redistribution rule (PCR) for information fusion together with several examples. From PCR1 to PCR2, PCR3, PCR4, PCR5 one increases the complexity of the rules and also the exactitude of the redistribution of conflicting masses. PCR1 restricted from the hyper-power set to the power set and without degenerate cases gives the same result as the Weighted Average Operator (WAO) proposed recently by Jøsang, Daniel and Vannoorenberghe but does not satisfy the neutrality property of vacuous belief assignment (VBA). That’s why improved PCR rules are proposed in this chapter. PCR4 is an improvement of minC and Dempster’s rules. The PCR rules redistribute the conflicting mass, after the conjunctive rule has been applied, proportionally with some functions depending on the masses assigned to their corresponding columns in the mass matrix. There are infinitely many ways these functions (weighting factors) can be chosen depending on the complexity one wants to deal with in specific applications and fusion systems. Any fusion combination rule is at some degree ad-hoc.
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03 Aug 2004
TL;DR: A new simple combination rule, similar to Dempster’s rule, but the normalization is d one for each non-empty set with respect to the non-zero sum of its responding mass matrix; in the case when all sets are empty, conflict is redistributed to the disjunctive form of them all.
Abstract: In this paper one proposes a new simple combination rule, similar to Dempster’s rule, but the normalization is d one for each non-empty set with respect to the non-zero sum of its cor responding mass matrix; in the case when all sets are empty th e conflict is redistributed to the disjunctive form of them all (which in many cases coincides with the total ignorance). A general fo mula is proposed together with several numerical examples a nd comparisons with other rules for combination of evidence pu blished in literature.
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TL;DR: Since no fusion theory neither rule fully satisfy all needed applications, the author proposes a Unification of Fusion Theories and a combination of fusion rules in solving problems/applications.
Abstract: Since no fusion theory neither rule fully satisfy all needed applications, the author proposes a Unification of Fusion Theories and a combination of fusion rules in solving problems/applications. For each particular application, one selects the most appropriate model, rule(s), and algorithm of implementation. We are working in the unification of the fusion theories and rules, which looks like a cooking recipe, better we'd say like a logical chart for a computer programmer, but we don't see another method to comprise/unify all things. The unification scenario presented herein, which is now in an incipient form, should periodically be updated incorporating new discoveries from the fusion and engineering research.
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TL;DR: This first PCR rule, called Proportional Conflict Redistribution rule (denoted PCR1), shows that PCR1 and WAO do not preserve unfortunately the neutrality property of the vacuous belief assignment though the fusion process, but can be easily circumvented by new PCR rules presented in a companion paper.
Abstract: One proposes a first alternative rule of combination to WAO (Weighted Average Operator) proposed recently by Josang, Daniel and Vannoorenberghe, called Proportional Conflict Redistribution rule (denoted PCR1). PCR1 and WAO are particular cases of WO (the Weighted Operator) because the conflicting mass is redistributed with respect to some weighting factors. In this first PCR rule, the proportionalization is done for each non-empty set with respect to the non-zero sum of its corresponding mass matrix - instead of its mass column average as in WAO, but the results are the same as Ph. Smets has pointed out. Also, we extend WAO (which herein gives no solution) for the degenerate case when all column sums of all non-empty sets are zero, and then the conflicting mass is transferred to the non-empty disjunctive form of all non-empty sets together; but if this disjunctive form happens to be empty, then one considers an open world (i.e. the frame of discernment might contain new hypotheses) and thus all conflicting mass is transferred to the empty set. In addition to WAO, we propose a general formula for PCR1 (WAO for non-degenerate cases).
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TL;DR: In this paper, a formula for the unification of a class of fusion rules based on the conjunctive and/or disjunctive rule is given, and afterwards the redistribution of the conflicting and non-conflicting mass to the non-empty sets at the second step.
Abstract: In this short note we give a formula for the unification of a class of fusion rules based on the conjunctive and/or disjunctive rule at the first step, and afterwards the redistribution of the conflicting and/or non-conflicting mass to the non-empty sets at the second step.
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TL;DR: In this article, the authors present a survey of plausible and paradoxical reasoning, known as Dezert-Smarandache Theory (DSmT) in the literature, developed for dealing with imprecise, uncertain, or high conflicting sources of information.
Abstract: The management and combination of uncertain, imprecise, fuzzy and even paradoxical or high conflicting sources of information has always been, and still remains today, of primal importance for the development of reliable modern information systems involving artificial reasoning. In this chapter, we present a survey of our recent theory of plausible and paradoxical reasoning, known as Dezert-Smarandache Theory (DSmT) in the literature, developed for dealing with imprecise, uncertain and paradoxical sources of information. We focus our presentation here rather on the foundations of DSmT, and on the two important new rules of combination, than on browsing specific applications of DSmT available in literature. Several simple examples are given throughout the presentation to show the efficiency and the generality of this new approach. The last part of this chapter concerns the presentation of the neutrosophic logic, the neutro-fuzzy inference and its connection with DSmT. Fuzzy logic and neutrosophic logic are useful tools in decision making after fusioning the information using the DSm hybrid rule of combination of masses.
TL;DR: In this paper, a geometric interpretation of the Neutrosophic set is given using a Neutroophic Cube, and distinctions between NS and IFS are underlined.
Abstract: In this paper we generalize the intuitionistic fuzzy set (IFS), paraconsistent set, and intuitionistic set to the neutrosophic set (NS). Several examples are presented. Also, a geometric interpretation of the Neutrosophic Set is given using a Neutrosophic Cube. Many distinctions between NS and IFS are underlined.
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28 Aug 2004
TL;DR: In this paper, a class of estimators for population correlation coefficient when information about the population mean and population variance of one of the variables is not available but information about these parameters of another variable (auxiliary) is available, in two phase sampling and analyzes its properties.
Abstract: This paper proposes a class of estimators for population correlation coefficient when information about the population mean and population variance of one of the variables is not available but information about these parameters of another variable (auxiliary) is available, in two phase sampling and analyzes its properties. Optimum estimator in the class is identified with its variance formula. The estimators of the class involve unknown constants whose optimum values depend on unknown population parameters. In earlier research it has been shown that when these population parameters are replaced by their consistent estimates the resulting class of estimators has the same asymptotic variance as that of optimum estimator. An empirical study is carried out to demonstrate the performance of the constructed estimators.
Journal Article•
TL;DR: This paper proposes a simple algorithm of combining the fusion rules, those rules which first use the conjunctive rule and then the transfer of conflicting mass to the non-empty sets, in such a way that they gain the property of associativity and fulfill the Markovian requirement for dynamic fusion.
Abstract: In this paper one proposes a simple algorithm of combining the fusion rules, those rules which first use the conjunctive rule and then the transfer of conflicting mass to the non-empty sets, in such a way that they gain the property of associativity and fulfill the Markovian requirement for dynamic fusion. Also, a new fusion rule, SDL-improved, is presented.
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01 Sep 2004
TL;DR: The speed of light relative to what has been referred to as the Lorentz speed has been studied extensively in the literature as discussed by the authors, and it has been called the characteristic speed of space.
Abstract: For most of the 20th century, both relativity and star travel fascinated this writer. The reasons Albert Einstein concluded there is an absolute barrier at the speed of light seemed at first clear, then later not so clear upon closer examination. "The speed of light relative to what?" I often asked anyone who would listen. The common response was, "Light needs no specification of that kind; its speed is the same no matter who measures it." "That's true." I would respond; "That's just the second postulate of special relativity which is not in doubt; but that postulate applies to light, and we're talking about rocketships here." However it seemed that no one understood what I was saying. By referring to the universal constant c= 299.792 458 megameters per second as "the speed of light," we paint ourselves into a logical corner in which light is automatically taken as the subject of discussion even when it is not. The careful reader will know not to immediately think "light" when he hears or reads "the speed of light." But it is better to have a neutral name for that 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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TL;DR: This paper argues in favour of a neutrosophic adaptation of the standard 2x2 zero-sum game theoretic model in order to identify an optimal outcome of the Israel-Palestine problem.
Abstract: In our present paper, we have explored the possibilities and developed arguments for an application of principles of neutrosophic game theory as a generalization of the fuzzy game theory model to a better understanding of the Israel-Palestine problem in terms of the goals and governing strategies of either side. We build on an earlier attempted justification of a game theoretic explanation of this problem by Yakir Plessner (2001) and go on to argue in favour of a neutrosophic adaptation of the standard 2x2 zero-sum game theoretic model in order to identify an optimal outcome
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TL;DR: In this article, the generalized pignistic transformation (GPT) succinctly developed in the Dezert-Smarandache Theory (DSmT) framework is presented as a tool for decision process.
Abstract: This paper presents in detail the generalized pignistic transformation (GPT) succinctly developed in the Dezert-Smarandache Theory (DSmT) framework as a tool for decision process. The GPT allows to provide a subjective probability measure from any generalized basic belief assignment given by any corpus of evidence. We mainly focus our presentation on the 3D case and provide the complete result obtained by the GPT and its validation drawn from the probability theory.
01 Jan 2004
TL;DR: The basis of the DSmT framework with respect to the Dempster-Shafer Theory (DST), a mathematical theory of evidence developed in 1976 by Glenn Shafer, is introduced and justified.
Abstract: This chapter presents a general overview and foundations of the DSmT, i.e. the recent theory of plausible and paradoxical reasoning developed by the authors, specially for the static or dynamic fusion of information arising from several independent but potentially highly conflicting, uncertain and imprecise sources of evidence. We introduce and justify here the basis of the DSmT framework with respect to the Dempster-Shafer Theory (DST), a mathematical theory of evidence developed in 1976 by Glenn Shafer. We present the DSm combination rules and provide some simple illustrative examples and comparisons with other main rules of combination available in the literature for the combination of information for simple fusion problems. Detailed presentations on recent advances and applications of DSmT are presented in the next chapters of this book.
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TL;DR: In this paper, a simple algorithm of combining the fusion rules, those rules which first use the conjunctive rule and then the transfer of conflicting mass to the non-empty sets, in such a way that they gain the property of associativity and fulfill the Markovian requirement for dynamic fusion is proposed.
Abstract: In this paper one proposes a simple algorithm of combining the fusion rules, those rules which first use the conjunctive rule and then the transfer of conflicting mass to the non-empty sets, in such a way that they gain the property of associativity and fulfill the Markovian requirement for dynamic fusion. Also, a new rule, SDL-improved, is presented.
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TL;DR: This work generalizes previous works available in literature which appear limited to IBS (Interval-valued belief structures) in the Transferable Belief Model framework and generalizes the DSm rules of combination from scalar fusion to sub- unitary interval fusion and, more general, to any set of sub-unitary intervals fusion.
Abstract: In this paper one studies, within Dezert-Smarandache Theory (DSmT), the case when the sources of information provide imprecise belief functions/masses, and we generalize the DSm rules of combination (classic or hybrid rules) from scalar fusion to sub-unitary interval fusion and, more general, to any set of sub-unitary interval fusion This work generalizes previous works available in literature which appear limited to IBS (Interval-valued belief structures) in the Transferable Belief Model framework Numerical didactic examples of these new DSm fusion rules for dealing with imprecise information are also presented
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TL;DR: In this paper, the authors studied the famous well-known and challen ging Tweety Penguin Triangle Problem (TPTP or TP2) pointed out by Judea Pearl in one of his books and presented the solution of the TP2 based on the fallacious Bayesian reas oning and prove that reasoning cannot be used to conclude on the abilit y of the penguin-bird Tweety to fly or not to fly.
Abstract: In this paper, one studies the famous well-known and challen ging Tweety Penguin Triangle Problem (TPTP or TP2) pointed out by Judea Pearl in one of his books. We first presentthe solution of the TP2 based on the fallacious Bayesian reas oning and prove that reasoning cannot be used to conclude on the abilit y of the penguin-bird Tweety to fly or not to fly. Then we presentin details the counter-intuitive solution obtained from the Dempster -Shafer Theory (DST). Finally, we show how the solution can b e obtained with our new theory of plausible and paradoxical reasoning ( DSmT).
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TL;DR: Five versions of a Proportional Conflict Redistribution rule (PCR) for information fusion together with several examples are proposed and improved PCR rules are proposed in this paper.
Abstract: In this paper we propose five versions of a Proportional Conflict Redistribution rule (PCR) for information fusion togeth er with several examples. From PCR1 to PCR2, PCR3, PCR4, PCR5 on e increases the complexity of the rules and also the exactitu de of the redistribution of conflicting masses. PCR1 restricte d from the hyper-power set to the power set and without degene rate cases gives the same result as the Weighted Average Operator (WAO) proposed recently by Josang, Daniel and Vannoorenberghe bu t does not satisfy the neutrality property of vacuous belief assig nment. That's why improved PCR rules are proposed in this pap er. PCR4 is an improvement of minC and Dempster's rules. The PCR rules re distribute the conflicting mass, after the conjunctive rulehas been applied, proportionally with some functions depending on t he masses assigned to their corresponding columns in the mas s matrix. There are infinitely many ways these functions (weighting fa ctors) can be chosen depending on the complexity one wants to deal with in specific applications and fusion systems. Any fusion comb ination rule is at some degree ad-hoc.