线性SISO TS模糊系统万能逼近的一种新的充分条件

借助于最优逼近理论, 证明了线性SISO TS模糊系统可以逼近任意一个多项式, 然后以Weierstrass逼近定理为桥梁, 证明了该模糊系统可以以任意精度逼近一个任意的连续函数, 从而得到了该模糊系统万能逼近性的一个新的充分条件. 并在证明过程中, 得到了要达到所要求的逼近精度所需的输入模糊集的下确界. 然后从理论上将所得的结果与现有文献中的结果进行了比较, 证明了该结果所需的输入模糊集的数目要少得多, 从而可以简化模糊系统的设计. 最后举例证明了该结论的有效性.

New sufficient conditions for general linear SISO Takagi-Sugeno fuzzy systems as universal approximators

By the best approximation theory, it is first proved that the SISO (single-input single-output) linear Takagi-Sugeno (TS) fuzzy systems can approximate an arbitrary polynomial which, according to Weierstrass approximation theorem, can uniformly approximate any continuous functions on the compact domain. Then new sufficient conditions for general linear SISO TS fuzzy systems as universal approximators are obtained. Formulae are derived to calculate the number of input fuzzy sets to satisfy the given approximation accuracy. Then the presented result is compared with the existing literature's results. The comparison shows that the presented result needs less input fuzzy sets, which can simplify the design of the fuzzy system, and examples are given to show its effectiveness.