Credal Semantics of Bayesian Transformations in Terms of Probability Intervals

In this paper, we propose a credal representation of the interval probability associated with a belief function (b.f.) and show how it relates to several classical Bayesian transformations of b.f.´s through the notion of ??focus?? of a pair of simplices. While a b.f. corresponds to a polytope of probabilities consistent with it, the related interval probability is geometrically represented by a pair of upper and lower simplices. Starting from the interpretation of the pignistic function as the center of mass of the credal set of consistent probabilities, we prove that the relative belief of singletons, the relative plausibility of singletons, and the intersection probability can all be described as the foci of different pairs of simplices in the region of all probability measures. The formulation of frameworks similar to the transferable belief model for such Bayesian transformations appears then at hand.