On the relationships between random sets, possibility distributions, p-boxes and clouds

Sébastien Destercke (1, 2) , Didier Dubois (2, 3) , Eric Chojnacki (1)

1 IRSN - Institut de Radioprotection et de Sûreté Nucléaire
2 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage
3 CNRS - Centre National de la Recherche Scientifique

There are many practical representations of probability families that make them easier to handle in applications. Among them are random sets, possibility distributions, Ferson's p-boxes and Neumaier's clouds. Both for theoretical and practical considerations, it is very useful to know whether one representation can be translated into or approximated by other ones. We first briefly recall formalisms and existing results, before exhibiting relationships between all these representations. In this note, which is a summary of an extended forthcoming paper, we restrict ourselves to representations on a finite set X.

Domaines: Autre [cs.OH]; Probabilités [math.PR]

Sébastien Destercke, Didier Dubois, Eric Chojnacki. On the relationships between random sets, possibility distributions, p-boxes and clouds. 28th Linz Seminar on fuzzy set theory, 2007, Linz, Austria. ⟨irsn-00196689⟩