Inclusion-exclusion principle for belief functions

Felipe Aguirre (1) , Sébastien Destercke (2, 1) , Didier Dubois (3, 4) , Mohamed Sallak (1, 2) , Christelle Jacob (3)

1 Heudiasyc - Heuristique et Diagnostic des Systèmes Complexes [Compiègne]
2 Labex MS2T - Laboratoire d'Excellence "Maîtrise des Systèmes de Systèmes Technologiques"
3 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage
4 CNRS - Centre National de la Recherche Scientifique

The inclusion-exclusion principle is a well-known property in probability theory, and is instrumental in some computational problems such as the evaluation of system reliability or the calculation of the probability of a Boolean formula in diagnosis. However, in the setting of uncertainty theories more general than probability theory, this principle no longer holds in general. It is therefore useful to know for which families of events it continues to hold. This paper investigates this question in the setting of belief functions. After exhibiting original sufficient and necessary conditions for the principle to hold, we illustrate its use on the uncertainty analysis of Boolean and non-Boolean systems in reliability.

Mots clés: exclusion-inclusion principle; belief functions; reliability analysis; boolean formulas

Domaines: Intelligence artificielle [cs.AI]; Logique en informatique [cs.LO]; Calcul [stat.CO]; Risques

Felipe Aguirre, Sébastien Destercke, Didier Dubois, Mohamed Sallak, Christelle Jacob. Inclusion-exclusion principle for belief functions. International Journal of Approximate Reasoning, 2014, 55 (8), pp.1708-1727. ⟨10.1016/j.ijar.2014.04.018⟩. ⟨hal-01056459⟩