Nonlinear Function Approximation Based on Least Wilcoxon Takagi-Sugeno Fuzzy Model

The purpose of this paper is based on radial basis function neural network (RBFN) to develop a self-constructing least Wilcoxon-generalized RBFN fuzzy inference system (LW-GRBFNFIS) and applied to nonlinear function approximation and chaotic time series prediction. As is well known in statistics, the resulting linear function by using the rank-based least Wilcoxon (LW) norm approximate to linear function problems are usually robust against (or insensitive to) outliers. In addition, the Takagi-Sugeno fuzzy model and RBFN techniques have been proved the functional equivalence and successfully applied to modeling nonlinear function approximation problems. This paper introduce proposed method to improve traditional least square GRBFNFIS for nonlinear function approximation and overcome outliers´ problem. Nonlinear function approximation and chaotic time series prediction problems used to verify the proposed method. The experiments results show the proposed method can effectively solve outliers´ problems.