The unnormalized Dempster's rule of combination: a new justification from the Least Commitment Principle and some extensions

Frédéric Pichon (1) , Thierry Denoeux (2)

1 Decision Technologies & Mathematics
2 Heudiasyc - Heuristique et Diagnostic des Systèmes Complexes [Compiègne]

In the Transferable Belief Model, belief functions are usually combined using the unnormalized Dempster's rule (also called the TBM conjunctive rule). This rule is used because of its intuitive appeal and because it has received formal justifications as opposed to the many other rules of combination that have been proposed in the literature. This article confirms the singularity of the TBM conjunctive rule by presenting a new formal justification based on (1) the canonical decomposition of belief functions, (2) the least commitment principle and (3) the requirement of having the vacuous belief function as neutral element of the combination. A similar result is also presented for the TBM disjunctive rule. Eventually, the existence of infinite families of rules having similar properties as those two rules is pointed out.

Mots clés: Transferable Belief Model; Dempster-Shafer theory; Information fusion; Evidence theory; Belief functions; Uncertain reasoning; Combination rules

Domaines: Intelligence artificielle [cs.AI]

Frédéric Pichon, Thierry Denoeux. The unnormalized Dempster's rule of combination: a new justification from the Least Commitment Principle and some extensions. Journal of Automated Reasoning, 2010, 45 (1), pp.61-87. ⟨10.1007/s10817-009-9152-7⟩. ⟨hal-00482006⟩