Comparative study of focal distance measures in theory of belief functions

The focal distance is used to describe the degree of dissimilarity between focal elements in a basic belief assignment (BBA) by jointly using the focal elements' composition and their corresponding mass assignments. It has already been used in applications such as the design of the uncertainty degree of a BBA, and has been used as a criterion to remove focal elements in BBA approximations. The related works on focal distance are relatively limited when compared with researches on the distance between two BBAs. In this paper, the available definitions of focal distance are analyzed and compared based on experiments. All the existing focal distance measures are compared based on the applications aforementioned. We verify that all the existing focal distance measures are not strict metrics. This paper aims to call attention of the researchers on focal distance, and to provide the support for the selection of the focal distance in belief functions based applications.