Coherent conditional probability as a measure of uncertainty of the relevant conditioning events

Abstract

In previous papers, by resorting to the most effective concept of conditional probability, we have been able not only to define fuzzy subsets, but also to introduce in a very natural way the basic continuous T-norms and the relevant dual T-conorms, bound to the former by coherence. Moreover, we have given, as an interesting and fundamental by-product of our approach, a natural interpretation of possibility functions, both from a semantic and a syntactic point of view. In this paper we study the properties of a coherent conditional probability looked on as a general non-additive uncertainty measure of the conditioning events, and we prove that this measure is a capacity if and only if it is a possibility.