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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)
Description of the transferable belief model to quantify degrees of belief, based on belief functions. The impact of open-and closed-world assumption on conditioning. Presentation of a set of axioms justifying Dempster's rule for the combination of belief functions induced by 2 distinct evidences.
The transferable belief model is a model to represent quantified beliefs based on the use of belief functions, as initially proposed by Shafer. It is developed independently from any underlying related probability model. We summarize our interpretation of the model and present several recent results that characterize the model. We show how rational decision… (More)
Many new models have been proposed to quantify uncertainty. But usually they don't explain how decisions must be derived. In probability theory, the expected utility model is well established and strongly justified. We show that such expected utility model can be derived in the other models proposed to quantify someone's belief. The justification is based… (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)
In the transferable belief model(TBM), pignistic probabilities are used for decision making. The nature of the pignistic transformation is justified by a linearity requirement. We justify the origin of this requirement showing it is not ad hoc but unavoidable provides one accepts expected utility theory.