Advances and Applications of DSmT for Information Fusion by editors Florentin Smarandache, Jean Dezert

By editors Florentin Smarandache, Jean Dezert

This moment quantity devoted to Dezert-Smarandache concept (DSmT) in info Fusion brings in new fusion quantitative principles (such because the PCR1-6, the place PCR5 for 2 assets does the main mathematically special redistribution of conflicting lots to the non-empty units within the fusion literature), qualitative fusion ideas, and the assumption Conditioning Rule (BCR) that's varied from the classical conditioning rule utilized by the fusion group operating with the Mathematical conception of facts. different fusion principles are developed in keeping with T-norm and T-conorm (hence utilizing fuzzy common sense and fuzzy set in details fusion), or extra basic fusion ideas in response to N-norm and N-conorm (hence utilizing neutrosophic common sense and neutrosophic set in details fusion), and an try and unify the fusion ideas and fusion theories. The recognized fusion ideas are prolonged from the ability set to the hyper-power set and comparability among principles are made on many examples. One defines the measure of intersection of 2 units, measure of union of 2 units, and measure of inclusion of 2 units which all assist in enhancing the all latest fusion ideas in addition to the credibility, plausibility, and communality features. The e-book chapters are written via Frederic Dambreville, Milan Daniel, Jean Dezert, Pascal Djiknavorian, Dominic Grenier, Xinhan Huang, Pavlina Dimitrova Konstantinova, Xinde Li, Arnaud Martin, Christophe Osswald, Andrew Schumann, Tzvetan Atanasov Semerdjiev, Florentin Smarandache, Albena Tchamova, and Min Wang.

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A detailed presentation of MinC can also be found in [18] (Chap. 10). The basic idea of minC is to identify all different types of partial conflicts and then transfer them with some proportional redistribution. Two versions of proportional redistributions have been proposed by Milan Daniel: • The minC (version a) ): the mass coming from a partial conflict (called contradiction by M. Daniel) involving several sets X1 ,X2 ,. . ,Xk is proportionalized among all unions ji=1 , of j ≤ k sets Xi of {X1 , .

26) are equal to zero because here there doesn’t exist positive mass products m1 (X1 )m2 (X2 ) to compute for any X ∈ 2Θ , X1 , X2 ∈ 2Θ \ {X} such that X1 ∩ X2 = ∅ and u(X1 ) ∪ u(X2 ) = X, neither for X1 ∩ X2 = ∅ and u(X1 ) = u(X2 ) = ∅. ) and examine the result of the combination of the 3 sources with PCR3. Θ denotes here for 30 PCR RULES FOR INFORMATION FUSION notation convenience A ∪ B ∪ C. 62, which is a sum of factors. ) has no impact on the conjunctive consensus. 1. 10. 1 Principle of PCR4 PCR4 redistributes the partial conflicting mass to the elements involved in the partial conflict, considering the canonical form of the partial conflict.

1 The PCR2 formula In PCR2, the total conflicting mass k12 is distributed only to the non-empty sets involved in the conflict (not to all non-empty sets) and taken the canonical form of the conflict proportionally with respect to their corresponding non-empty column sum. The redistribution is then more exact (accurate) than in PCR1 and WAO. A nice feature of PCR2 is the preservation of the neutral impact of the VBA and of course its ability to deal with all cases/models. A non-empty set X1 ∈ GΘ is considered involved in the conflict if there exists another set X2 ∈ GΘ which is neither included in X1 nor includes X1 such that X1 ∩ X2 = ∅ and m12 (X1 ∩ X2 ) > 0.

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