In this paper, we describe in mathematical language a problem of reduction of a functional rule from aknowledge representation system(KRS). Then the invert relations between the reduction of functional rule and the re-duction of a family of subsets are discussed in detail. In the big frame, not only a series of new concepts, new prob-lems and new theorems are found out, but also new mathematical descriptions for some original concepts and prob-lems in rough set theory are given. Finally based on the theoretical research, an algorithm about reduction of function-al rule is described.
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