Dominances on fuzzy variables based on credibility measure

This paper studies three notions of fuzzy dominance based on credibility measure, namely, the fuzzy mean-risk dominance, the first credibilistic dominance and the second credibilistic dominance. More precisely, we introduce and examine some properties of the Fuzzy Lower Partial Moments (FLPM) of a fuzzy variable and, we deduce the Fuzzy Kappa index (FK) of a fuzzy variable, that is, a riskadjusted performance measure of an asset or a portfolio with fuzzy return. Based on the aforementioned notion, we introduce the fuzzy mean-risk dominance of two fuzzy variables and we characterize it in three specific and interesting cases. We recall the first credibilistic dominance and the second credibilistic dominance for fuzzy variables ∗Corresponding author: Email: [email protected] 1 ha l-0 07 96 21 5, v er si on 1 4 M ar 2 01 3 introduced earlier by Peng et al. [20]. We characterize the first credibilistic dominance and determine some of its properties. We introduce and characterize the notion of crossing points of distributions of two fuzzy numbers and use them to characterize the second credibilistic dominance for fuzzy numbers. We justify that the first credibilistic dominance is stronger than the fuzzy mean-risk dominance and the second credibilistic dominance, and neither of these two later implies the other.