New distances between bodies of evidence based on Dempsterian specialization matrices and their consistency with the conjunctive combination rule

Abstract

Distances in evidence theory are useful tools for belief function approximation or clustering. Efficient approaches are found in the literature, especially full metrics taking focal element interactions into account. In this paper, another aspect is investigated: the ability to detect common evidence pertaining to two different states of belief. This requirement, as well as the previously mentioned ones, are formalized through mathematical properties. To find a belief function distance satisfying the desired properties, matrix norms based distances between Dempsterian specialization matrices are investigated. It is proved that the L1 Dempsterian matrix distance succeeds to fulfill all requirements. Interesting and unprecedented ties between the conjunctive combination rule and this distance are demonstrated. Several basic belief assignment distance experiments are proposed and interpreted thereby allowing to understand advantages and limitations of the newly introduced distances as compared to the existing ones.