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

Abstract

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