Abstract
The uncertainty of a financial market is traditionally dealt with probabilistic approaches. However, there are many non-probabilistic factors that affect the financial markets such that the return rate of risky assets may be regarded as fuzzy number, which is a powerful tool used to describe an uncertain environment with vagueness and ambiguity and some type of fuzziness. In this paper, the conventional probabilistic mean-variance model can be simplified as a bi-objective linear programming model based on possibility theory. Furthermore, the fuzzy two-stage algorithm is applied to solve our proposed bi-objective model. Finally, a numerical example of the portfolio selection problem is given to illustrate our proposed effective means and variances. The results of the example also show that the fuzzy two-stage algorithm solving the model is effective and feasible.
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