| A fuzzy relation is a generalization of a Boolean relation. For a system defined by fuzzy relation equations, the input and the output parameters of the system are "somehow" related. A decision maker is expected to set the input parameters at some appropriate levels such that the desired output is obtained while one or several objective functions are "simultaneously optimized." Such a problem can be formulated as a multi-objective optimization problem with fuzzy relation equation constraints.;In this research, multi-objective optimization problems subject to fuzzy relation equations are studied. Since the feasible domain of such a problem is in general nonconvex and the objective functions are not necessarily linear, traditional optimization methods may become ineffective and inefficient.;Taking advantage of the special structure of the feasible domain, the problem can be manipulated such that the computational effort is reduced. A genetic-based solution procedure is proposed to solve the reduced problem in order to find the "Pareto-optimal solutions." The major components of the proposed genetic algorithm and some test results are reported. |
