Abstract
By discussing both linear and nonlinear fuzzy situations, we give the relevant model and the solution method. First of all, regarding the target level of investment return and investment risk as the half trapezoidal fuzzy number, we give the fuzzy portfolio selection model of linear satisfaction degree. Then, to describe the investor satisfaction degree of investment return and investment risk better, a logarithmic membership function has been imported. Following, we give the fuzzy portfolio selection model of nonlinear satisfaction degree. Nonlinear optimize model can be transferred to linear programming model, so that model calculation has been simplified significantly. Finally, according to the actual data of Chinese securities market, both of models have been compared by using genetic algorithm. Result indicates that portfolio selection model based on linear and nonlinear membership function includes not only historical data, but also investors' expectation. That accords with human psychology and fact. However, by adopting the nonlinear membership function and adjusting its parameter, it can furthest get portfolio that accords with investor's expectation. Therefore, nonlinear membership function is better than linear membership function.
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