# CVaR Reduced Fuzzy Variables and Their Second Order Moments

Document Type: Research Paper

Authors

1 College of Management, Hebei University, Baoding 071002, Hebei, China and College of Science, Agricultural University of Hebei, Baoding 071001, Hebei, China

2 College of Management, Hebei University, Baoding 071002, Hebei, China

Abstract

Based on credibilistic value-at-risk (CVaR) of regular
fuzzy variable, we introduce a new CVaR reduction method for
type-2 fuzzy variables. The reduced fuzzy variables are
characterized by parametric possibility distributions. We establish
some useful analytical expressions for mean values and second
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
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.

Keywords

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