Fuzzy set connectives as combinations of belief structures

ksInternational audienceConsonant belief structures provide a representation for fuzzy sets owing to the fact that their plausibility measures are essentially possibility measures. We note that two belief structures are equivalent if their plausibility and belief functions are equal. This observation leads us to provide a multiple number of equivalent representations for any belief structure. Commensurate representations can be induced for two different belief structures by forcing the same number of focal elements with the same weights. We show that if we represent two consonant belief structures in a commensurate manner then their aggregations are closed with respect to consonance, provided that the additional requirement that the underlying probability distributions satisfy a condition of correlation is imposed. The results of this work allow us to use belief structure representations for the manipulation of fuzzy subsets under various logical combinations. All basic fuzzy set connectives can thus be interpreted in the framework of the theory of evidence