文章基本信息

标题：On the Approximation of Fuzzy System
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作者：Shihong Yue ; Wei Chen ; Jin Wang 等
期刊名称：International Journal of Distributed Sensor Networks
印刷版ISSN：1550-1329
电子版ISSN：1550-1477
出版年度：2009
卷号：5
DOI：10.1080/15501320802540710
出版社：Hindawi Publishing Corporation
摘要：The choice of fuzzy set function affects how well the fuzzy systems approximate an unknown function. We first examine several popular fuzzy systems, based on which we generalize the error of the fuzzy system by the mathematical functional. Two classes of extended fuzzy systems with special set function are proposed respectively in one-dimensional and two-dimensional reproducing kernel spaces, and they are in fact the best interpolation operators in the sense of classical mathematical approximation. The extended fuzzy system can be used as easily as any typical fuzzy system but has better characters. Our major contributions are as follows. 1.   We prove that the existing fuzzy system with a triangle-shaped set function is by no means the best choice for an uncertain system. On the contrary, the reproducing kernel-shaped set function can give the best approximation in the sense of mathematical functional. According to the result, overlapped symmetric triangles or trapezoid set functions reduce fuzzy systems to piecewise linear systems. Universal Gaussian bell-curve set functions can work well but its learning cost is too expensive to apply under online condition.2.   We explain what our proposed extended fuzzy system is useful for a given uncertain system. This solution is associated with another problem: Is the reproducing kernel condition too specific to limit its applications? We must stress that the reproducing kernel function is easily found in any continuous function space. Consequently, the extended fuzzy system can approximate any continuous function with arbitrary accuracy.