Generalizations of the Relative Belief Transform

Probability transformation of belief functions can be classified into different families, according to the operator they commute with. In particular, as they commute with Dempster’s rule, relative plausibility and belief transforms form one such “epistemic” family, and possess natural rationales within Shafer’s formulation of the theory of evidence. However, the relative belief transform only exists when some mass is assigned to singletons. We show here that relative belief is only a member of a class of “relative mass” mappings, which can be interpreted as lowcost proxies for both plausibility and pignistic transforms.