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RELATIONSHIPS BETWEEN POSSIBILITY MEASURES AND NESTED RANDOM SETS

2002; World Scientific; Volume: 10; Issue: 01 Linguagem: Inglês

10.1142/s0218488502001302

1793-6411

Enrique Miranda, Inés Couso, Pedro Gil,

Rough Sets and Fuzzy Logic

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.