Uncertainty measure in evidence theory with its applications

Uncertainty measure in evidence theory supplies a new criterion to assess the quality and quantity of knowledge conveyed by belief structures. As generalizations of uncertainty measure in the probabilistic framework, several uncertainty measures for belief structures have been developed. Among them, aggregate uncertainty AU and the ambiguity measure AM are well known. However, the inconsistency between evidential and probabilistic frameworks causes limitations to existing measures. They are quite insensitive to the change of belief functions. In this paper, we consider the definition of a novel uncertainty measure for belief structures based on belief intervals. Based on the relation between evidence theory and probability theory, belief structures are transformed to belief intervals on singleton subsets, with the belief function Bel and the plausibility function Pl as its lower and upper bounds, respectively. An uncertainty measure SU for belief structures is then defined based on interval probabilities in the framework of evidence theory, without changing the theoretical frameworks. The center and the span of the interval is used to define the total uncertainty degree of the belief structure. It is proved that SU is identical to Shannon entropy and AM for Bayesian belief structures. Moreover, the proposed uncertainty measure has a wider range determined by the cardinality of discernment frame, which is more practical. Numerical examples, applications and related analyses are provided to verify the rationality of our new measure.