A FUZZY APPROACH FOR FUZZY RANDOM MULTIOBJECTIVE LINEAR PROGRAMMING PROBLEMS

Abstract

In this paper, we propose a fuzzy approach for fuzzy random multiobjective linear programming problems (FRMOLP), in which the criteria of probability maximization and fractile optimization are considered simultaneously. In a probability maximization model for FRMOLP, the decision maker is required to specify permissible objective levels for the objective functions involving fuzzy random variables. However, the less values of permissible objective levels for minimization problems results in the less values of the corresponding distribution function because of the con icts between them. Similarly, in a fractile optimization model for FRMOLP, the decision maker is required to specify permissible probability levels for the distribution function of the objective functions involving fuzzy random variables. However, the larger values of permissible probability levels results in the larger values of the corresponding objective function for minimization problems because of the con icts between them. In this paper, it is assumed that the decision maker has fuzzy goals for not only permissible objective level of a probability maximization model but also permissible stochastic level of a fractile optimization model, and such fuzzy goals are quanti ed by eliciting the corresponding membership functions. According to the fuzzy decision, the satisfactory solution of the decision maker for FRMOLP is obtained on the basis of linear programming technique.