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

•This paper introduces a new family of evidential distances.•These distances are matrix distances between Dempsterian specialization matrices.•3 properties are formalized: definiteness, structure and conjunctive consistency.•Conjunctive consistency depicts ties between the conjunctive rule and distances.•The distance based on the L1 matrix norm has the three desired properties.

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 L1L1 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.