Universal Approximation for Takagi-Sugeno Fuzzy Systems Using Dynamically Constructive Method-SISO Cases

Abstract

In this paper, a dynamically constructive method is proposed for proving the universal approximation for single input/single output (SISO) Takagi-Sugeno (T-S) fuzzy systems, which is superior to the existing constructive methods only considering the global property of the function to be approximated and also unrelated to the membership functions of fuzzy sets. The dynamically constructive method proposed not only considers the different property of the nonlinear function in different areas, but also the membership functions of fuzzy sets in fuzzy rules. As a result, the number of rules in the constructed T-S model is greatly reduced. Finally some simulation examples confirm that the T-S fuzzy model constructed by our method with small size rule base can approximate the given nonlinear functions at high accuracy as compared with some typical methods.