Two Possibilistic Mean-Variance Models for Portfolio Selection

In this paper, we discuss the portfolio selection problem in a fuzzy uncertain environment. Based on the two different definitions of crisp possibilistic variances of a fuzzy number A, Var(A) and \(\overline{Var}(A)\), introduced by Carlsson and Zhang respectively, the fuzzy portfolio selection problem is studied in this paper. Firstly, some properties as in probability theory based on the Carlsson’s and Zhang’s notations are discussed. Secondly, two possibilistc mean-variance models for portfolio selection are proposed, in which the possibilistic mean value of the return is termed measure of investment return, the possibilistic variance of the return is termed measure of investment risk. At last, a numerical example is given to illustrate our proposed approaches.