A new distance-based total uncertainty measure in Dempster-Shafer evidence theory

Uncertainty measure in Dempster-Shafer (D-S) evidence theory is crucial to assess the quality of information conveyed by belief structures. Most of the previous studies consider this issue from the perspective of viewing the D-S evidence theory as a generalization of probability theory. However, the inconsistency between D-S evidence theory and probability theory may lead to some limitations to existing measures. Deng et al proposed an improved total uncertainty measure which is directly based on D-S evidence theory. In their measure, the belief structures are transformed to belief interval which is constructed by the belief function and plausibility function of a proposition. Inspired by the previous research, a new total uncertainty measure (NTU) is proposed in this paper. The proposed measure is based on the Euclidean distance between the belief interval of the singleton subset and the most uncertain interval. It not only retains the properties and advantages of the previous measure, but also presents a higher sensitivity and greater extent to the change of evidences. Some numerical examples, practical applications and related analyses are used to verify the rationality and sensitivity of the proposed measure.