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Jean Dezert

Publications and source records attributed to Jean Dezert.

34 records · Page 2Linked to original sources
arXiv2006

DSmT: A new paradigm shift for information fusion

The management and combination of uncertain, imprecise, fuzzy and even paradoxical or high conflicting sources of information has always been and still remains of primal importance for the development of reliable information fusion systems. In this short survey paper, we present the theory of plausible and paradoxical reasoning, known as DSmT (Dezert-Smarandache Theory) in literature, developed for dealing with imprecise, uncertain and potentially highly conflicting sources of information. DSmT is a new paradigm shift for information fusion and recent publications have shown the interest and the potential ability of DSmT to solve fusion problems where Dempster's rule used in Dempster-Shafer Theory (DST) provides counter-intuitive results or fails to provide useful result at all. This paper is focused on the foundations of DSmT and on its main rules of combination (classic, hybrid and Proportional Conflict Redistribution rules). Shafer's model on which is based DST appears as a particular and specific case of DSm hybrid model which can be easily handled by DSmT as well. Several simple but illustrative examples are given throughout this paper to show the interest and the generality of this new theory.

cs.AI↗
arXiv2006

An Introduction to the DSm Theory for the Combination of Paradoxical, Uncertain, and Imprecise Sources of Information

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 introduction, 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.

cs.AI↗
arXiv2006

Target Type Tracking with PCR5 and Dempster's rules: A Comparative Analysis

In this paper we consider and analyze the behavior of two combinational rules for temporal (sequential) attribute data fusion for target type estimation. Our comparative analysis is based on Dempster's fusion rule proposed in Dempster-Shafer Theory (DST) and on the Proportional Conflict Redistribution rule no. 5 (PCR5) recently proposed in Dezert-Smarandache Theory (DSmT). We show through very simple scenario and Monte-Carlo simulation, how PCR5 allows a very efficient Target Type Tracking and reduces drastically the latency delay for correct Target Type decision with respect to Demspter's rule. For cases presenting some short Target Type switches, Demspter's rule is proved to be unable to detect the switches and thus to track correctly the Target Type changes. The approach proposed here is totally new, efficient and promising to be incorporated in real-time Generalized Data Association - Multi Target Tracking systems (GDA-MTT) and provides an important result on the behavior of PCR5 with respect to Dempster's rule. The MatLab source code is provided in

cs.AI↗
arXiv2005

Proportional Conflict Redistribution Rules for Information Fusion

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 Jøsang, 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.

cs.AI↗
arXiv2004

The Combination of Paradoxical, Uncertain, and Imprecise Sources of Information based on DSmT and Neutro-Fuzzy Inference

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.

cs.AI↗
arXiv2004

A Simple Proportional Conflict Redistribution Rule

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).

cs.AI↗
arXiv2004

The Generalized Pignistic Transformation

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.

cs.AI↗
arXiv2004

On the Tweety Penguin Triangle Problem

In this paper, one studies the famous well-known and challenging Tweety Penguin Triangle Problem (TPTP or TP2) pointed out by Judea Pearl in one of his books. We first present the solution of the TP2 based on the fallacious Bayesian reasoning and prove that reasoning cannot be used to conclude on the ability of the penguin-bird Tweety to fly or not to fly. Then we present in details the counter-intuitive solution obtained from the Dempster-Shafer Theory (DST). Finally, we show how the solution can be obtained with our new theory of plausible and paradoxical reasoning (DSmT).

math.GM↗
arXiv2004

Combining Uncertain and Paradoxical Evidences for DSm Hybrid Models

This paper presents a general method for combining uncertain and paradoxical source of evidences for a wide class of fusion problems. From the foundations of the Dezert-Smarandache Theory (DSmT) we show how the DSm rule of combination can be adapted to take into account all possible integrity constraints (if any) of the problem under consideration due to the true nature of elements/concepts involved into it. We show how the Shafer's model can be considered as a specific DSm hybrid model and be easily handled by our approach and a new efficient rule of combination different from the Dempster's rule is obtained. Several simple examples are also provided to show the efficiency and the generality of the approach proposed in this work.

math.DS↗
arXiv2004

Infinite classes of counter-examples to the Dempster's rule of combination

This paper presents several classes of fusion problems which cannot be directly attacked by the classical mathematical theory of evidence, also known as the Dempster-Shafer Theory (DST) either because the Shafer's model for the frame of discernment is impossible to obtain or just because the Dempster's rule of combination fails to provide coherent results (or no result at all). We present and discuss the potentiality of the DSmT combined with its classical (or hybrid) rule of combination to attack these infinite classes of fusion problems.

math.GM↗
arXiv2004

Fusion of imprecise, uncertain, and conflicting beliefs with DSm rules of combination

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.

math.GM↗
arXiv2003

On the Generation of Hyper-powersets for the DSmT

The recent theory of plausible and paradoxical reasoning (DSmT for short, or Dezert-Smarandache Theory), developed by the authors, appears to be a nice promising theoretical tools to solve many information fusion problems (for example in military defense, medicine, etc.), where the Shafer's model cannot be used due to the intrinsic paradoxical nature of the elements of the frame of discernment and where a strong internal conflict between sources arises. The main idea of DSmT is to work on the hyper-powerset of the frame of discernment of the problem under consideration. Although the definition of hyper-powerset is well established, the major difficulty in practice is to generate such hyper-powersets in order to implement DSmT fusion rule on computers. We present in this paper a simple algorithm for generating hyper-powersets and discuss the limitations of our actual computers to generate such hyper-powersets when the dimension of the problem increases.

math.GM↗
arXiv2003

On the Blackman's Association Problem

Modern multitarget-multisensor tracking systems involve the development of reliable methods for the data association and the fusion of multiple sensor information, and more specifically the partioning of observations into tracks. This paper discusses and compares the application of Dempster-Shafer Theory (DST) and the Dezert-Smarandache Theory (DSmT) methods to the fusion of multiple sensor attributes for target identification purpose. We focus our attention on the paradoxical Blackman's association problem and propose several approaches to outperfom Blackman's solution. We clarify some preconceived ideas about the use of degree of conflict between sources as potential criterion for partitioning evidences.

math.GM↗
arXiv2003

Proceedings of the First International Conference on Neutrosophy, Neutrosophic Logic, Neutrosophic Set, Neutrosophic Probability and Statistics

Papers on neutrosophy (a generalization of dialectics), on neutrosophic logic, set, probability and statistics (generalizations of fuzzy logic, fuzzy set, and imprecise probability respectively), by Florentin Smarandache, Jean Dezert, S. Bhattacharya, Andrzej Buller, M. Khoshnevisan, S. Singh, Feng Liu, Gh. C. Dinulescu-Campina, Chris Lucas, and C. Gershenson.

math.GM↗