Linear Efficacy Method for a Portfolio Selection with Bounded Assets Based on Possibility Theory

Compared with the conventional probabilistic mean-variance method, fuzzy number can better describe an uncertain environment with vagueness and ambiguity. In this paper, the portfolio selection model with bounded assets is proposed by means of possibilistic mean and possibilistic variance under the assumption that the returns of assets are triangular fuzzy numbers. Moreover, the obtained quadratic bi-objective model can be transformed into a linear bi-objective model by maximizing the future expected return and minimizing the future risk. By using linear efficacy method, a numerical example of the portfolio selection problem is provided to illustrate our proposed effective possibilistic means and possibilistic variances, and the obtained optimal solution can not make some objective function dissatisfactory completely.