Semantics of the Relative Belief of Singletons

Abstract

Summary. In this paper we introduce the relative belief of singletons as a novel Bayesian approximation of a belief function. We discuss its nature in terms of degrees of belief under several different angles, and its applicability to different classes of belief functions.

Dual Properties of the Relative Belief of Singletons

“…is subject to quite a strong condition (4). However it can be proven that the case in whichb does not exist is indeed pathological, as it excludes a great deal of belief and probability measures [14].…”

“…Another Bayesian approximation based on normalizing the belief (instead of plausibility) values of singletons has been recently introduced [14]:…”

“…The different semantics and limitations of the relative belief of singletons have been studied by F. Cuzzolin [14]. In particular, rel.bel.…”

Game-Theoretical Semantics of Epistemic Probability Transformations

“…Some preliminary analyses of the relative belief transform and its close relationship with the (relative) plausibility transform have been presented in [9,10]. A detailed discussion of the geometrical properties ofb andpl has been given in [11].…”

“…A detailed discussion of the geometrical properties ofb andpl has been given in [11]. In [10], in particular, the author has shown that plausibility and belief transforms both commute with Dempster's rule of combination, and meet a number of dual properties with respect to the orthogonal sum, therefore forming what we call the "epistemic" family of transforms. In opposition, an "affine" family can be defined which groups together those transforms which commute with affine combination, and fit in the probability-bound interpretation of belief functions.…”