On two dominances of fuzzy variables based on a parametrized fuzzy measure and application to portfolio selection with fuzzy return
Résumé
Yang and Iwamura (Appl Math Sci 46:2271–2288, 2008) introduced a new fuzzy measure as a convex linear combination of possibility and necessity measures. This measure generalizes the credibility measure and the real parameter associated to the possibility measure is considered as the decision making’s optimism level. In this paper, we introduce by means of that measure, two new dominances as binary relations on fuzzy variables. The first one generalizes the first order dominance based on credibility measure and introduced recently by Tassak et al. (J Oper Res Soc 68:1491–1502, 2017) and the second one, based on the investor’s optimism level, is more stronger than the other. Moreover, we study some properties of those dominances and characterize them on the particular family of trapezoidal fuzzy numbers. We implement the second dominance in a numerical example to illustrate the impact of the investor’s attitude through the set of best portfolios.