Risk curve and fuzzy portfolio selection

In stochastic environment, variance, semivariance and probability of a bad outcome are three popular definitions of risk for portfolio selection. In fuzzy environment, variance is carried on as the definition of risk. However, in real life, risk is understood in many different ways. In this paper we propose a new definition of risk for portfolio selection in fuzzy environment. Based on this new definition, a new type of model is provided. To give a general solution to the new model problem, a hybrid intelligent algorithm is designed. One numerical example is also presented to illustrate the optimization idea and the effectiveness of the designed algorithm.