Optimization of linear objective function with max-t fuzzy relation equations

An optimization model with a linear objective function subject to max-t fuzzy relation equations as constraints is presented, where t is an Archimedean t-norm. Since the non-empty solution set of the fuzzy relation equations is in general a non-convex set, conventional linear programming methods are not suitable for solving such problems. The concept of covering problem is applied to establish 0–1 integer programming problem equivalent to linear programming problem and a binary coded genetic algorithm is proposed to obtain the optimal solution. An example is given for illustration of the method.