On the first moments and semi-moments of fuzzy variables based on a new measure and application for portfolio selection with fuzzy returns

Abstract : Possibility, Necessity and Credibility measures are used in the literature in order to deal with imprecision. Recently, Yang and Iwamura [11] introduced a new measure as convex linear combination of possibility and necessity measures and they determined some of its axioms. In this paper, we introduce characteristics (parameters) of a fuzzy vari-able based on that measure, namely, Expected value, Variance, Semi-Variance, Skewness, Kurtosis and Semi-Kurtosis. We determine some properties of these characteristics and we compute them for trapezoidal and triangular fuzzy variables. We display their application for the determination of optimal portfolios when assets returns are described by triangular or trapezoidal fuzzy variables.