A Robust Fuzzy Clustering Approach and its Application to Function Approximation

Function approximation is to model a desired function or an input-output relation from a set of input-output sample data that unfortunately often suffer from noise and outliers in real systems. To overcome this problem, this paper presents an unsupervised fuzzy model construction approach to extract fuzzy rules directly from numerical input-output data for nonlinear function approximation problems with noise and outliers. There are two core ideas in the proposed method: (1) The robust fuzzy c-means (RFCM) algorithm is proposed to greatly mitigate the influence of data noise and outliers; and (2) A fuzzy-based data sifter (FDS) is proposed to locate good turning-points to partition a given nonlinear data domain into piecewise clusters so that a Takagi and Sugeno fuzzy model (TS fuzzy model) can be constructed with fewer rules. Two experiments are illustrated and their results have shown the proposed approach has good performance in various kinds of data domains with data noise and outliers.