Fuzzy Programming Approach for Portfolio Selection Problems with Fuzzy Coefficients

The portfolio selection problem (PSP) uses mathematical approaches to model stock exchange investments. Its aim is to find an optimal set of assets to invest on, as well as the optimal investments for each asset. In this paper, a portfolio selection problem (FPSP) with fuzzy objective function coefficient (FPSP) a multiple objective problem including uncertainties is investigated. The FPSP is considered by incorporating fuzzy numbers into the coefficients of the objective functions. Through the use of the  -level sets of the fuzzy numbers, the FDSP is converted into the corresponding ordinary from ( -PSP). And an extended Pareto optimality concept called the  -Pareto optimality is introduced. A fuzzy programming approach is applied to solve the ( -PSP). Simulated annealing and linear membership function is being used to find the compromise solution. Finally, a numerical example is given for the sake of the paper for illustration.