Philippe Smets

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We describe the Transferable Belief Model, a model for representing quantified beliefs based on belief functions. Beliefs can be held at two levels: 1) a credal level where beliefs are entertained and quantified by belief functions, 2) a pignistic level where beliefs can be used to make decisions and are quantified by probability functions. The relation(More)
We generalize the Bayes’ theorem within the transferable belief model framework. The Generalized Bayesian Theorem (GBT) allows us to compute the belief over a space Θ given an observation x ⊆ X when one knows only the beliefs over X for every θi ∈ Ω. We also discuss the Disjunctive Rule of Combination (DRC) for distinct pieces of evidence. This rule allows(More)
We generalize the TBM (transferable belief model) to the case where the frame of discernment is the extended set of real numbersR = [−∞,∞], under the assumptions that ‘masses’ can only be given to intervals. Masses become densities, belief functions, plausibility functions and commonality functions become integrals of these densities and pignistic(More)
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(More)
Any belief function can be decomposed into a confidence and a diffidence components. Each components is uniquely decomposable into simple support functions that represent the impact of the simplest form of evidence, the one that only partially supports a given subset of the frame of discernment. The nature of the inverse of Dempster's rule of combination is(More)
When Shafer introduced his theory of evidence based on the use of belief functions, he proposed a rule to combine belief functions induced by distinct pieces of evidence. Since then, theoretical justifications of this socalled Dempster’s rule of combination have been produced and the meaning of distinctness has been assessed. We will present practical(More)