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Approximating the true domain of fuzzy inference sentence with genetic algorithm

Among the various approaches to determine the true domain of fuzzy inference rules in the designing of fuzzy controller, the important one is to solve a system of fuzzy relation equations corresponding to the fuzzy inference sentence. In our earlier work, we gave a new method to construct the system and presented a method to solve the system when the system is consistent. But when the system is inconsistent, it is impossible to give the exact solution. This paper focuses on the searching for the optimal solution which is an approximate representative of the true domain. In this study, we first give the definition of the optimal solution and verify its existence. And then we present a reasonably and effectively method for finding out the approximate optimal solution based on the fuzzy genetic algorithm. Examples show the good performance of the new method.