Disaggregated total uncertainty measure for credal sets

Abstract

We present a new approach to measure uncertainty/information applicable to theories based on convex sets of probability distributions, also called credal sets. A definition of a total disaggregated uncertainty measure on credal sets is proposed in this paper motivated by recent outcomes. This definition is based on the upper and lower values of Shannon's entropy for a credal set. We justify the use of the proposed total uncertainty measure and the parts into which it is divided: the maximum difference of entropies, which can be used as a non-specificity measure (imprecision), and the minimum of entropy, which represents a measure of conflict (contradiction).