On the properties of relative plausibilities

In 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.