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

By Florentin Smarandache, Jean Dezert

This booklet offers the new theoretical advances and functions of the Dezert-Smarandache concept (DSmT) of believable and paradoxical reasoning for info fusion. DSmT proposes a brand new mathematical framework to house the combo of doubtful, vague and hugely conflicting resources of knowledge expressed when it comes to generalized simple trust capabilities. DSmT works past the bounds of the Dempster-Shafer conception and proposes a brand new common rule of mix which doesn't require a normalization step and works with any types (free DSm, hybrid DSm and Shafer's version) regardless of the measure of clash among resources is. The DSmT is definitely tailored for static and dynamic fusion problematics and permits to paintings on any finite frames (discrete, non-stop and/or hybrid). for this reason it could actually mix trust capabilities whether the refinement of the body of discernment is inaccessible as a result obscure, relative, and vague intrinsic nature of its components. half 1 of this ebook provides in info the final investigations on DSmT but additionally a few comparable theoretical works with different ways for info fusion. half 2 of the booklet provides attention-grabbing purposes of DSmT for fixing either educational fusion difficulties and real-world fusion difficulties. amassed works are by way of S. Corgne, F. Dambreville, M. Daniel, D. De Brucq, J. Dezert, M. Farooq, L. Hubert-Moy, A.-L. Jousselme, S. Kadambe, M. Khoshnevisan, P. D. Konstantinova, P. Maupin, G. Mercier, T. A. Semerdjiev, F. Smarandache, H. sunlight, A. P. Tchamova. The ebook has been introduced in June on the Fusion 2004 convention in Stockholm, Sweden. A moment quantity approximately new purposes and advancements of DSmT (Dezert-Smarandache idea of believable, doubtful, and paradoxist info) may be released subsequent 12 months. anyone is invited to give a contribution papers or chapters for this moment collective booklet. time limit: Fall 2005. Contributed papers may be despatched to Dr. Jean Dezert (,, ONERA - French nationwide institution for Aerospace study, BP seventy two F-92322, Chatillon Cedex, France) and Prof. Florentin Smarandache (, college of recent Mexico, 2 hundred collage street, Gallup, NM 87301, USA).

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94 < 1. 06 ? 34 and the masses add up to 1. 06 > 0 One gets the same results for m∪ (θ1 ), m∪ (θ2 ) as with Dubois & Prade’s rule and as with the hybrid DSm rule. 06 to θ1 ∪ θ2 in the hybrid DSm rule, while in Dubois & Prade’s and disjunctive rules it is not. 9 We mean here non-normalized masses allowing weight of evidence on the empty set as in the TBM of Smets. 4. COMPARISON OF DIFFERENT RULES OF COMBINATIONS 27 A major difference among the hybrid DSm rule and all other combination rules is that DSmT uses from the beginning a hyper-power set, which includes intersections, while other combination rules need to do a refinement in order to get intersections.

Let Θ = {θ1 , . . , θn } be a finite set (called frame) of n exhaustive elements5 . The Dedekind’s lattice, also called in the DSmT framework hyper-power set DΘ is defined as the set of all composite propositions built from elements of Θ with ∪ and ∩ operators6 such that: 5 We 6Θ do not assume here that elements θi are necessary exclusive. There is no restriction on θi but the exhaustivity. generates D Θ under operators ∪ and ∩ 14 CHAPTER 1. PRESENTATION OF DSMT 1. ∅, θ1 , . . , θn ∈ DΘ . 2. If A, B ∈ DΘ , then A ∩ B ∈ DΘ and A ∪ B ∈ DΘ .

3, pp. 81-83, 1984. , A simple view of the Dempster-Shafer theory of evidence and its implications for the rule of combination, Berkeley Cognitive Science Report No. 33, University of California, Berkeley, CA, 1985. 2, pp. 85-90, 1986. 36 REFERENCES Chapter 2 The generation of hyper-power sets Jean Dezert Florentin Smarandache ONERA Department of Mathematics 29 Av. A. Abstract: The development of DSmT is based on the notion of Dedekind’s lattice, called also hyper-power set in the DSmT framework, on which is defined the general basic belief assignments to be combined.

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