Axioms for uncertainty measures on belief functions and credal sets

Abstract

In this paper we present a system of axioms for total uncertainty measures, which can be equivalently defined for belief functions and credal sets. This system of axioms provides that a measure of total uncertainty coincides with Shannon entropy on the set of probability measures and it is the Hartley measure on the set of {0,1}-valued belief measures. We check this system of axioms for the well-known candidates for total uncertainty measures; in particular, the upper entropy obeys all the necessary requirements. Some properties of such measures of total uncertainty allow us to propose ways for disaggregation of these measures into two parts, which correspond to measures of conflict and measures of nonspecificity.