By Florentin Smarandache, Jean Dezert

This ebook provides the hot theoretical advances and purposes of the Dezert-Smarandache idea (DSmT) of believable and paradoxical reasoning for info fusion. DSmT proposes a brand new mathematical framework to accommodate the mix of doubtful, obscure and hugely conflicting resources of knowledge expressed by way of generalized uncomplicated trust features. DSmT works past the bounds of the Dempster-Shafer conception and proposes a brand new common rule of mixture 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 assets 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). consequently it might probably mix trust services whether the refinement of the body of discernment is inaccessible as a result of the obscure, relative, and obscure intrinsic nature of its components. half 1 of this publication offers in info the final investigations on DSmT but in addition a few comparable theoretical works with different techniques for info fusion. half 2 of the ebook provides fascinating functions of DSmT for fixing either educational fusion difficulties and real-world fusion difficulties.

Collected works are through 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 e-book has been introduced in June on the Fusion 2004 convention in Stockholm, Sweden.

A moment quantity approximately new functions and advancements of DSmT (Dezert-Smarandache thought of believable, doubtful, and paradoxist info) could be released subsequent yr. anyone is invited to give a contribution papers or chapters for this moment collective ebook. closing date: Fall 2005.

Contributed papers could 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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9998. Both Yager’s and Smets’ results are less specific than the result obtained with the hybrid DSm rule. There is a loss of information somehow when using Yager’s or Smets’ rules. 5 Fifth example Suppose one extends Dubois & Prade’s rule from the power set 2Θ to the hyper-power set DΘ . ) term is missing): a) at least one singleton is empty and the element of its column are all non zero b) at least an union of singletons is empty and elements of its column are all non zero c) or at least an intersection is empty and the elements of its column are non zero 28 CHAPTER 1.

1. 1 The generation of DΘ Memory size requirements and complexity Before going further on the generation of DΘ , it is important to estimate the memory size for storing the elements of DΘ for |Θ| = n. 4). 40 CHAPTER 2. THE GENERATION OF HYPER-POWER SETS |Θ| = n size/elem. # of elem. 7 · 1015 Gb This table shows the extreme difficulties for our computers to store all the elements of DΘ when |Θ| > 6. This complexity remains however smaller than the number of all Boolean functions built from the ultimate refinement (if accessible) 2Θref of same initial frame Θ for applying DST.

The second layer of the network consists in all gbba of focal elements Bj , j = 1, . . ). Each node of layer 2 is connected with each node of layer 1. The output layer (on the right) consists in the combined basic belief assignments of all possible intersections Ai ∩ Bj , i = 1, . . , n and j = 1, . . , k. 3. FOUNDATIONS OF THE DSMT 17 of the classic DSm rule (not included on the figure) consists in the compression of the output layer by regrouping (summing up) all the combined belief assignments corresponding to the same focal elements (by example if X = A2 ∩ B3 = A4 ∩ B5 , then m(X) = m(A2 ∩ B3 ) + m(A4 ∩ B5 )).

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