Solving a Fully Fuzzy Linear Programming Problem through Compromise Programming

In the current literatures, there are several models of fully fuzzy linear programming (FFLP) problems where all the parameters and variables were fuzzy numbers but the constraints were crisp equality or inequality. In this paper, an FFLP problem with fuzzy equality constraints is discussed, and a method for solving this FFLP problem is also proposed. We first transform the fuzzy equality constraints into the crisp inequality ones using the measure of the similarity, which is interpreted as the feasibility degree of constrains, and then transform the fuzzy objective into two crisp objectives by considering expected value and uncertainty of fuzzy objective. Since the feasibility degree of constrains is in conflict with the optimal value of objective function, we finally construct an auxiliary three-objective linear programming problem, which is solved through a compromise programming approach, to solve the initial FFLP problem. To illustrate the proposed method, two numerical examples are solved.