Linear and Nonlinear Approximation of Fuzzy Random Variables

Since it is difficult to find the optimal solution of the vague data based models [1] in traditional ways, we use linear and nonlinear (hybrid) approximation methods simultaneously. We used the technique of simulation [2] and genetic algorithm [3] based on random fuzzy simulation to help find the optimal solution with hybrid algorithm and linear approximation to evaluate these methods efficiency in hybrid environment. Results showed that the probability of crossover and probability of mutation higher, the linear approximation better (in case of nonlinear integer programming). In this paper, we proposed fuzzy linear method and tested it on a portfolio model. We provided a fuzzy nonlinear integer programming model for portfolio selection. A numerical example demonstrates the application of the proposed method.