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

Document Type : Research Paper


1 Lecturer, Semnan University, Semnan, Iran

2 Department of Applied Mathematics, School of Mathematics and Computer Science, University of Damghan, Damghan, Iran

3 Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran

4 Faculty of Mathematics, Statistics and Computer Science, University of Houston, Houston, Texas, USA


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.