An improved distance-based total uncertainty measure in belief function theory

Uncertainty quantification of mass functions is a crucial and unsolved issue in belief function theory. Previous studies have mostly considered this problem from the perspective of viewing the belief function theory as an extension of probability theory. Recently, Yang and Han have developed a new distance-based total uncertainty measure directly and totally based on the framework of belief function theory so that there is no switch between the frameworks of belief function theory and probability theory in that measure. However, we have found some obvious deficiencies in Yang and Han's uncertainty measure which could lead to counter-intuitive results in some cases. In this paper, an improved distance-based total uncertainty measure has been proposed to overcome the limitations of Yang and Han's uncertainty measure. The proposed measure not only retains the desired properties of original measure, but also possesses higher sensitivity to the change of evidences. A number of examples and applications have verified the effectiveness and rationality of the proposed uncertainty measure.