Fuzzy Edmundson-Madansky Inequality and Its Application to Portfolio Selection Problems

Within the framework of credibility theory, fuzzy portfolio selection models have been well investigated on the assumption that all security returns have known membership functions for calculating the investment risk. However, this assumption is difficult to achieve in real problems. hi this paper, a fuzzy Edmundson-Madansky inequality is proved to estimate the investment risk by the expected values and ranges of security returns. Then the portfolio selection models are extended by replacing the risk measures with their estimation values, which are formulated to be crisp programming models. Finally, a numerical example is presented to show the effectiveness of the extended models.