CVaR Reduced Fuzzy Variables and Their Second Order Moments

Abstract

Based on credibilistic value-at-risk (CVaR) of regular<br />fuzzy variable, we introduce a new CVaR reduction method for<br />type-2 fuzzy variables. The reduced fuzzy variables are<br />characterized by parametric possibility distributions. We establish<br />some useful analytical expressions for mean values and second<br />order moments of common reduced fuzzy variables. The convex properties of second order moments with respect to parameters are also discussed. Finally, we take second order moment as a new risk measure, and develop a mean-moment model to optimize fuzzy portfolio selection problems. According to the analytical formulas of second order moments, the mean-moment optimization model is equivalent to parametric<br />quadratic convex programming problems, which can be solved by general-purpose optimization software. The solution results reported in the numerical experiments demonstrate the credibility of the proposed optimization method.