Measures of uncertainty for imprecise probabilities: An axiomatic approach

The aim of this paper is to formalize, within a broad range of theories of imprecise probabilities, the notion of a total, aggregate measure of uncertainty and its various disaggregations into measures of nonspecificity and conflict. As a framework for facilitating this aim, we introduce a system of well-justified axiomatic requirements for such measures. It is shown that these requirements can be equivalently defined for belief functions and credal sets. Some important consequences are then derived within this framework, which clarify the role of various uncertainty measures proposed in the literature. Moreover, some well-defined new open problems for future research also emerge from the introduced framework.