Belief Functions Induced by Randomized Communication Channels

Abstract

The most often used combinatorial definition of belief function over a finite basic space S can be obtained through a binary compatibility relation ρ between the states s (elements of S) and some empirical data (observations) x from an observational space E, when x is taken as the value of a random variable X. We shall investigate a generalized version of this model supposing that the values ρ(s, x) defined by the compatibility relation in question are observed through a random binary communication channel so that the values ρ(s, x) are subjected to random changes (deformations) before reaching the subject and being accepted. The resulting randomized basic probability assignments and belief functions will be analyzed in more detail, namely, we shall prove under which conditions and in which sense and degree they can approximate the corresponding original numerical characteristics of uncertainty.