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Approximation of the smooth functions by using fuzzy systems
문병수(B.S. Moon),이장수(J.S. Lee),이동영(D.Y. Lee),권기춘(K.C. Kwon) 한국지능시스템학회 2005 한국지능시스템학회 학술발표 논문집 Vol.15 No.2
A review of how the functions of two or more independent variables can be approximated by using fuzzy systems is provided in this paper. We start with an exact represention of a linear interpolation function of two independent variables by using a fuzzy system. Next, we describe how this function can be approximated by another fuzzy system wi th a lesser number or wi th a desired number of output fuzzy sets. Thus, a reduction of the storage needed is achieved by storing the fuzzy rules or equivalently the output fuzzy set numbers instead of storing the whole discrete function values. A description on how the cubic spline interpolation function can be represented exactly by using the fuzzy system method is provided, along with a few examples where fuzzy rule tables with a size of 7×7 provide a representation of the functions with relative errors of the order of 10<SUP>-2</SUP> or less.