Fuzzy approaches for multiobjective stochastic linear programming problems considering both probability maximization and fractile optimization

In this paper, we propose two kinds of fuzzy approaches to obtain a satisfactory solution for multiobjective stochastic linear programming problems, in which the criteria of probability maximization and fractile optimization are considered simultaneously. In the first approach, a probability maximization model is applied to multiobjective stochastic linear programming problems, where the decision maker is required to specify not permissible objective levels but the corresponding membership functions which represent fuzzy goals for permissible objective levels. By adopting the fuzzy decision to integrate both the membership functions for permissible objective levels and the ones for the probability functions, a probability maximization model is transformed to the maxmin problem without permissible objective levels as parameters. Similarly, in the second approach, a fractile optimization model is applied to multiobjective stochastic linear programming problems, where the decision maker is required to specify not permissible probability levels but the corresponding membership functions which represent fuzzy goals for permissible probability levels. By adopting the fuzzy decision to integrate both the membership functions for permissible probability levels and the ones for the objective functions, a fractile optimization model is transformed to the maxmin problem without permissible probability levels as parameters. It is shown that such two fuzzy approaches are same.