Relationships between possibility measures and nested random sets

Authors:
Enrique Miranda;Inés Couso;Pedro Gil
Affiliations:
Department of Statistics and Operations Research, University of Oviendo, C/ Calvo Sotelo, s/n 33007 Oviendo, Spain;-;Department of Statistics and Operations Research, University of Oviendo, C/ Calvo Sotelo, s/n 33007 Oviendo, Spain
Venue:
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Year:
2002

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Abstract

Different authors have observed some relationships between consonant random sets and possibility measures, specially for finite universes. In this paper, we go deeply into this matter and propose several possible definitions for the concept of consonant random set. Three of these conditions are equivalent for finite universes. In that case, the random set considered is associated to a possibility measure if and only if any of them is satisfied. However, in a general context, none of the six definitions here proposed is sufficient for a random set to induce a possibility measure. Moreover, only one of them seems to be necessary.