On the mathematical theory of evidence and Dempster's rule of combination

Jean Dezert (1) , Albena Tchamova (2) , Frederic Dambreville (3)

1 ONERA - The French Aerospace Lab [Palaiseau]
2 IICT BAS - Institute for Information and Communication Technologies
3 DGA EORD - DGA Ingénierie de Projet

In this paper we present an analysis of the use of Dempster's rule of combination, its consistency with the probability calculus and its usefulness for combining sources of evidence expressed by belief functions in the framework of the Mathematical Theory of Evidence, known also as Dempster-Shafer Theory (DST), or as the classical theory of belief functions. We show that the direct combination of original basic belief assignments of sources of evidence with Dempster's rule is inconsistent with probability calculus and we explain this from a simple experimental protocol. We also show how Dempster's rule can be reconciled with probability calculus for such examples if the combination of sources is done differently. In that case the notion of conflict between sources of evidence becomes meaningless (it just vanishes) because Dempster's rule coincides with the pure conjunctive operator, and the entire fusion process becomes comparable to simple application of Total Probability Theorem (i.e. the weighted average fusion rule). While a direct application of Dempster's rule becomes questionable in the most general case, then arises the need of a methodoloy for organizing and implementing the combination rules with respect to the applications.

Mots clés: Dempster-Shafer Theory; Mathematical Theory of Evidence; Generalized Bayesian Inference; belief functions

Domaines: Intelligence artificielle [cs.AI]

Jean Dezert, Albena Tchamova, Frederic Dambreville. On the mathematical theory of evidence and Dempster's rule of combination. 2011. ⟨hal-00591633⟩