On the properties of relative plausibilities

International audienceIn this paper we investigate the properties of the relative plausibility function, the probability built by normalizing the plausibilities of singletons associated with a belief function. On one side, we stress how this probability is a perfect representative of the original belief function when combined with any arbitrary probability through Dempster's rule. This leads to conjecture that this function should also be the solution of the probabilistic approximation problem, formulated naturally in terms of Dempster's rule. On the other side, the geometric properties of relative plausibilities are studied in the context of the geometric approach to the theory of evidence, yielding a description of the representation property which suggests a sketch for the general proof of our conjecture