An interactive method resolution for Linear programming with fuzzy random variables

This paper proposes a method for solving linear programming where all the coefficients are, in general, fuzzy random variables. We use a fuzzy random ranking method to rank the fuzzy random objective values and to deal with the inequality relation on constraints. It allows us to work with the concept of satisfaction degree of constraints. The bigger the feasibility degree is, the worst the objective value. We suggest the decision-maker (DM)the optimal solution for several different degree of feasibility. With this information the DM is able to establish an optimistic (pessimistic) optimal solution, and a fuzzy goal. By using Belmman-Zadeh min operator, we build fuzzy set in the decision space whose membership function represents the balance between feasibility degree of constraints and satisfaction degree of the goal. The best solution is obtained by this fuzzy set. Finally, a numerical example is solved to clarify our method

Keywords:

Linear programming , Fuzzy stochastic theory , Ranking fuzzy random variables