Coherence for Fuzzy Measures and Applications to Decision Making

Abstract. Coherence is a central issue in probability (de Finetti, 1970). The studies on non-additive models in decision making, e. g., non-expected utility models (Fishburn, 1988), lead to an extension of the coherence principle in nonadditive settings, such as fuzzy or ambiguous contexts. We consider coherence in a class of measures that are decomposable with respect to Archimedean t-conorms (Weber, 1984), in order to interpret the lack of coherence in probability. Coherent fuzzy measures are utilized for the aggregations of scores in multiperson and multiobjective decision making. Furthermore, a geometrical representation of fuzzy and probabilistic uncertainty is considered here in the framework of join spaces (Prenowitz and Jantosciak, 1979) and, more generally, algebraic hyperstructures (Corsini and Leoreanu, 2003); indeed coherent probability assessments and fuzzy sets are join spaces (Corsini and Leoreanu, 2003; Maturo et al., 2006a, 2006b).