In this paper we propose a credal representation of the set of interval probabilities associated with a belief function, and show how it relates to several classical Bayesian transformations of belief functions through the notion of ``focus" of a pair of simplices. Starting from the interpretation of the pignistic function as the center of mass of the credal set of consistent probabilities, we prove that relative belief and plausibility of singletons and intersection probability can be described as foci of different pairs of simplices in the simplex of all probability measures. Such simplices are associated with the lower and upper probability constraints, respectively. This paves the way for the formulation of frameworks similar to the transferable belief model for lower, upper, and interval constraints.
Keywords. Belief functions, credal sets, Bayesian transformations, upper and lower simplices, focus
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Department of Computing
Oxford Brookes University
OX33 1HX OXFORD