This paper proposes the method on dimensional reduction of fuzzy relation represented by the matrix. The main purpose of this method is to save the number of elements of fuzzy relation. This solves the problem of memory shortage which is arisen in multivariable system control. And it is also investigated to decide values of the matrix which represent the desirable system. The search for both solutions is carried out with Genetic Algorithm. Each evaluation function is set appropriately. Finally the proposed method is applied to a simple example and the effect is confirmed.
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