Foundations for a new theory of plausible and paradoxical reasoning

Dezert, Jean

doi:10.11610/isij.0901

Cited by 103 publications

(83 citation statements)

References 16 publications

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“…More recently [20,84] develop their so called DezertSmarandache theory (DSmT) of plausible and paradoxical reasoning where they also replace the Boolean algebras by a distributive lattice (these authors called it the hyperpower set). One of their motivations was to resolve Zadeh's counterexample and to provide some 'better' solutions for examples with large conflicts.…”

Section: The Jungle Of Combination Rulesmentioning

confidence: 99%

Analyzing the combination of conflicting belief functions

2007

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We consider uncertain data which uncertainty is represented by belief functions and that must be combined. The result of the combination of the belief functions can be partially conflictual. Initially Shafer proposed Dempster's rule of combination where the conflict is reallocated proportionally among the other masses. Then Zadeh presented an example where Dempster's rule of combination produces unsatisfactory results. Several solutions were proposed: the TBM solution where masses are not renormalized and conflict is stored in the mass given to the empty set, Yager's solution where the conflict is transferred to the universe and Dubois and Prade's solution where the masses resulting from pairs of conflictual focal elements are transferred to the union of these subsets. Many other suggestions have then been made, creating a 'jungle' of combination rules. We discuss the nature of the combinations (conjunctive versus disjunctive, revision versus updating, static versus dynamic data fusion), argue about the need for a normalization, examine the possible origins of the conflicts, determine if a combination is justified and analyze many of the proposed solutions.

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Section: The Jungle Of Combination Rulesmentioning

confidence: 99%

Analyzing the combination of conflicting belief functions

2007

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“…4) Apply the DSmT-based GFM, that is, adopt Euclidean information filter to choose basic consistent sources of evidence according to the formula (8). Then combine the consistent sources with the DSm conjunctive rule [4,5,31] and compute gbbas after combination. Then, redistribute partial conflicting masses to the gbbas of sets involved in the partial conflict only with the PCR5 rule [32].…”

Section: Simulation Resultsmentioning

confidence: 99%

Evidence supporting measure of similarity for reducing the complexity in information fusion☆

Dezert

Smarandache

et al. 2011

Information Sciences

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This paper proposes a new solution for reducing the number of sources of evidence to be combined in order to diminish the complexity of the fusion process required in some applications where the real-time constraint and strong computing resource limitation are of prime importance. The basic idea consists in selecting, among the whole set of sources of evidence, only the biggest subset of sources which are not too contradicting based on a criterion of Evidence Supporting Measure of Similarity (ESMS) in order to process solely the coherent information received. The ESMS criterion serves actually as a generic tool for outlier source identification and rejection. Since the ESMS between several belief functions can be defined using several distance measures, we browse the most common ones in this paper and we describe in detail the principle of our Generalized Fusion Machine (GFM). The last part of the paper shows the improvement of the performances of this new approach with respect to the classical one in a real-data based and real-time experiment for robot perception using sonar sensors.

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“…Dempster-Shafer modified Theory or Dezert-Smarandache Theory (DSmT) by Dezert and Smarandache [7,13] allows mutually overlapping elements of a frame of discernment. Thus, a frame of discernment is a finite exhaustive set of elements Θ = {θ 1 , θ 2 , ..., θ n }, but not necessarily exclusive in DSmT.…”

Section: Dedekind Lattice Basic Dsm Notionsmentioning

confidence: 99%

“…As the classical Shafer's frame of discernment may be considered the special case of a so-called hybrid DSm model, the DSm rule of combination is compared with the classic rules of combination in the publications about DSmT [7,13].…”

Section: Introductionmentioning

confidence: 99%