Two Fuzzy Approaches for Multiobjective Stochastic Programming and Multiobjective Fuzzy Random Programming Through a Probability Maximization Model

In this paper, two kinds of fuzzy approaches are proposed for not only multiobjective stochastic linear programming problems, but also multiobjective fuzzy random linear programming problems through a probability maximization model. In a probability maximization model, it is necessary for the decision maker to specify permissible values of objective functions in advance, which have a great influence on the corresponding distribution function values. In our proposed methods, the decision maker does not specify permissible values of objective functions, but sets his/her membership functions for permissible values. By assuming that the decision maker adopts the fuzzy decision as an aggregation operator of fuzzy goals for not only the permissible objective levels but also the permissible probability levels, a satisfactory solution of the decision maker is easily obtained based on linear programming technique. Two kinds of numerical examples are illustrated to show the feasibility of the proposed methods.