Felipe Aguirre, Christelle Jacob, Sébastien Destercke, Didier Dubois, Mohamed Sallak

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Inclusion/exclusion principle for belief functions

Abstract

The inclusion-exclusion principle is a well-known property of set cardinality and probability measures, that is instrumental to solve some problems such as the evaluation of systems reliability or of uncertainty over Boolean formulas. However, when using sets and probabilities conjointly, this principle no longer holds in general. It is therefore useful to know in which cases it is still valid. This paper investigates this question when uncertainty is modelled by belief functions. After exhibiting necessary and sufficient conditions for the principle to hold, we illustrate its use on some applications, i.e. reliability analysis and uncertainty over Boolean formulas.

Keywords

Reliability, Evidence Theory, Inclusion/exclusion principle, Boolean formulas

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E-mail addresses

Felipe Aguirre		felipe.aguirre@hds.utc.fr
Christelle Jacob		jacob@isae.fr
Sébastien Destercke		sebastien.destercke@utc.fr
Didier Dubois		didier.dubois@irit.fr
Mohamed Sallak		mohamed.sallak@hds.utc.fr