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, obscure and hugely conflicting resources of knowledge expressed when it comes to generalized uncomplicated trust features. DSmT works past the bounds of the Dempster-Shafer conception and proposes a brand new normal 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 easily 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 may possibly mix trust features whether the refinement of the body of discernment is inaccessible as a result of the imprecise, relative, and vague intrinsic nature of its parts. half 1 of this publication provides in info the final investigations on DSmT but in addition a few similar theoretical works with different techniques for info fusion. half 2 of the ebook provides fascinating purposes of DSmT for fixing either educational fusion difficulties and real-world fusion difficulties. gathered 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. solar, A. P. Tchamova. The booklet 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 conception of believable, doubtful, and paradoxist info) could be released subsequent 12 months. anyone is invited to give a contribution papers or chapters for this moment collective booklet. closing date: Fall 2005. Contributed papers can be despatched to Dr. Jean Dezert (jean.dezert@onera.fr, jdezert@yahoo.com, ONERA - French nationwide institution for Aerospace examine, BP seventy two F-92322, Chatillon Cedex, France) and Prof. Florentin Smarandache (smarand@unm.edu, collage of latest Mexico, two hundred collage street, Gallup, NM 87301, USA).

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The transferable belief model, Artif. , 66(2), pp. 191-234, 1994. , Data Fusion in the Transferable Belief Model, Proceedings of the 3rd International Conference on Information Fusion, Fusion 2000, Paris, July 10-13, 2000, pp PS21-PS33. , On the justification of Dempster’s rule of combination, Artificial Intelligence, 48, pp. 171-197, 1991. nl/~fransv/#pub). , Vol. 4, No. 1, pp. 73-81, 1983. [45] Yager R. , Hedging in the combination of evidence, Journal of Information and Optimization Science, Vol.

M2 (B2 ) ✲ . . . ❘ m(An ∩ B2 ) = m1 (An )m2 (B2 ) ❅ ❇ ❈✄ ❇ ✄❈✂✍✂✫✪ ✫✪ ❇✄ ✂ ❈ . . ✄❇✂ ❈ . ❈ ✄✂ ❇ ✬✩ ✬✩ ❈ ❲ ✄✂ ❇◆❇ m(A1 ∩ Bk ) = m 1 (A1 )m 2 (Bk ) . m1 (An ) ✄✂ ✲ m2 (Bk ) ✲ ✒. . . . 5 The hybrid DSm rule of combination When the free DSm model Mf (Θ) does not hold due to the true nature of the fusion problem under consideration which requires to take into account some known integrity constraints, one has to work with a proper hybrid DSm model M(Θ) = Mf (Θ). e. φ(A) = 1 if A ∈ / ∅ and φ(A) = 0 otherwise, where ∅ {∅M , ∅}.

M(A1 ∩ Bk ) = m 1 (A1 )m 2 (Bk ) . m1 (An ) ✄✂ ✲ m2 (Bk ) ✲ ✒. . . . 5 The hybrid DSm rule of combination When the free DSm model Mf (Θ) does not hold due to the true nature of the fusion problem under consideration which requires to take into account some known integrity constraints, one has to work with a proper hybrid DSm model M(Θ) = Mf (Θ). e. φ(A) = 1 if A ∈ / ∅ and φ(A) = 0 otherwise, where ∅ {∅M , ∅}. ∅M is the set of all elements of DΘ which have been forced to be empty through the constraints of the model M and ∅ is the classical/universal empty set.

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