Solving fuzzy stochastic multi-objective programming problems based on a fuzzy inequality

Probabilistic or stochastic programming is a framework for modeling optimization problems that involve uncertainty. In this paper, we focus on multi-objective linear programming problems in which the coefficients of constraints and the right hand side vector are fuzzy random variables. There are several methods in the literature that convert this problem to a stochastic or fuzzy problem. By using a special type of fuzzy inequality, we transform the problem into a convenient stochastic problem. Then some known methods are applied to obtain the optimal solution. Finally, the equivalent multi-objective problem is solved by an interactive approach. A numerical example is provided to illustrate the procedure.