A new scaling kernel-based fuzzy system with low computational complexity

Abstract

The approximation capability of fuzzy systems heavily depends on the shapes of the chosen fuzzy membership functions. When fuzzy systems are applied in adaptive control, computational complexity and generalization capability are another two important indexes we must consider. Inspired by the conclusion drawn by S. Mitaim and B.Kosko and wavelet analysis and SVM, the scaling kernel-based fuzzy system SKFS(Scaling Kernel-based Fuzzy System) is presented as a new simplified fuzzy system in this paper, based on Sine × membership functions. SKFS can approximate any function in L2(R), with much less computational complexity than classical fuzzy systems. Compared with another simplified fuzzy system GKFS(Gaussian Kernel-based Fuzzy System) using Gaussian membership functions, SKFS has a better approximation and generalization capabilities, especially in the coexistence of linearity and nonlinearity. Therefore, SKFS is very suitable for fuzzy control. Finally, several experiment results are used to demonstrate the effectiveness of the new simplified fuzzy system SKFS. © Springer-Verlag Berlin Heidelberg 2006.