A hierarchical fuzzy-clustering approach to fuzzy modeling

This paper introduces a new method for fuzzy modeling based on a hierarchical fuzzy-clustering scheme. The method consists of a sequence of steps aiming towards developing a Takagi-Sugeno (TS) fuzzy model of optimal structure, where the fuzzy sets in the premise part are of Gaussian type. Starting from an initial ordinary fuzzy partition of the input space, the algorithm performs a nearest-neighbor search and groups the original input training data into a number of clusters. The centers of these clusters are further processed using an optimal fuzzy clustering technique, which is based on the weighted fuzzy c-means algorithm. The resulted optimal fuzzy partition defines the number of fuzzy rules and provides an initial estimation for the system parameters, which in a next step are fine tuned using the well-known gradient-descend algorithm. The proposed method is successfully applied to three test examples, where the produced fuzzy models prove to be very accurate, as well as compact in size.