A distance measure between intuitionistic fuzzy belief functions

Intuitionistic fuzzy (IF) evidence theory, as an extension of Dempster-Shafer theory of evidence to the intuitionistic fuzzy environment, is exploited to process imprecise and vague information. Since its inception, much interest has been concentrated on IF evidence theory. Many works on the belief functions in IF information systems have appeared. However, there is little research on the distance measure between IF belief functions despite the fact that distance measure in classical belief functions has received close attention. In this paper we mainly investigated the distance measure between IF belief functions based on the Euclidean distance between two column vectors. The similarity between focal elements is also taken into account. The distance and similarity measures between IF sets are investigated firstly. A new similarity measure between IF sets along with its properties and proofs is proposed. The positive definiteness of similarity matrix is investigated to guarantee the metric properties of the distance measure. Then a distance measure between IF belief functions is proposed. It is proved that the proposed distance measure is a metric distance. As is illustrated by examples, the distance measure is sensitive to the change of focal elements. Moreover, its applicability for classical belief functions is also demonstrated.