On the Optimization of Fuzzy Relation Equations with Continuous t-Norm and with Linear Objective Function

According to [8,12,13,23], the optimization models with a linear objective function subject to fuzzy relation equations is decidable. Algorithms are developed to solve it. In this paper, a complementary problem for the original problem is defined. Due to the structure of the feasible domain and nature of the objective function, individual variable is restricted to become bi-valued. We propose a procedure for separating the decision variables into basic and non-basic variables. An algorithm is proposed to determine the optimal solution. Two examples are considered to explain the procedure.