Fuzzy portfolio selection problem

Considers an application of a fuzzy random variable to a single index model of a portfolio selection problem. A single index model decomposes the risk on investment into the risk common to all investments caused by a market and the risk individual to each investment caused by other factors. The paper investigates the case where the rate of return on each investment can be represented with a fuzzy random variable. We propose a decision making method based both on possibility theory and on a chance constrained program in stochastic programming, and show that this problem is transformed into a deterministic equivalent problem, which is a nonlinear non-convex programming problem. Further we introduce a subsidiary problem the optimal solution of which has a close relation to that of the original problem and construct an efficient algorithm