Idempotent conjunctive and disjunctive combination of belief functions by distance minimization

摘要

Idempotence is a desirable property when cautiousness is wanted in an information fusion process, since in this case combining identical information should not lead to the reinforcement of some hypothesis. Idempotent operators also guarantee that identical information items are not counted twice in the fusion process, a very important property in decentralized applications where the information origin cannot always be tracked (ad-hoc wireless networks are typical examples). In the theory of belief functions, a sound way to combine conjunctively multiple information items is to design a combination rule that selects the least informative element among a subset of belief functions more informative than each of the combined ones. In contrast, disjunctive rules can be retrieved by selecting the most informative element among a subset of belief functions less informative than each of the combined ones. One interest of such approaches is that they provide idempotent rules by construction.