On Two Dominances of Fuzzy Variables based on a Parametric Fuzzy Measure and Application to Portfolio Selection with Fuzzy Return

Abstract : Iwamura [18] introduced a new parametric fuzzy measure as a convex linear combination of possibility and necessity measures. This measure generalizes the credibility measure and the parameter of the possibility measure is considered as the decision making (investors) optimism’s level. In this paper, we introduce by means of that mea-sure two new dominances (binary relations) on fuzzy variables. The first one generalizes the first order dominance introduced recently by Tassak et al. [17] and the second one, based on optimism’s level and called optimisnism dominance, is stronger than the first one. We study properties of these dominances on trapezoidal fuzzy numbers and we characterize them. We implement the optiminism dominance in a nu-merical example to display that its set of efficient portfolios enlarges the set of efficient portfolios obtained by Tassak et al. [17] through their first order dominance.