Uncertainty measure for interval-valued belief structures

Interval-valued belief structures, as an extension of belief structures in classical evidence theory, are developed for better exploitation of uncertain and imprecise information. From the point of view of information theory, uncertainty measure of an interval-valued belief structure is critically important for information processing. However, it is still an open issue to measure its uncertainty. Besides discord and non-specificity, which hide in a precise belief structure, we claim that fuzziness is also associated with an interval-valued belief structure. In this paper, axiomatic requirements for uncertainty measure of interval-valued belief structure are defined. Then an uncertainty measure is proposed to measure the information conveyed by interval-valued belief structures. Its properties are mathematically proved. Finally, numerical experiments are employed to illustrate the performance of the proposed uncertainty measure. It is illustrated that the proposed uncertainty measure is sensitive to the change of belief structures, which might have beneficial effects on decision making.