An SVD-QR-based approach to fuzzy modeling

An SVD-QR-based approach is proposed to design an appropriate fuzzy system directly from some gathered input-output data. A fuzzy system with fuzzy rule tables is defined to approach the input-output pairs of an identified system. In the rule base of the defined fuzzy system, each fuzzy rule table corresponds to a partition of an input space. In order to extract the most important fuzzy rules from the rule base of the defined fuzzy system, a firing strength matrix determined by the membership functions of the premise fuzzy sets is constructed. According to the firing strength matrix, the number of important fuzzy rules is determined by singular value decomposition (SVD), and the most important fuzzy rules are selected by the SVD-QR-based method. Consequently, a reconstructed fuzzy rule base composed of significant fuzzy rules is determined by the firing strength matrix. Furthermore, the recursive least squares method is applied to determine the consequent part of the reconstructed fuzzy system so that a fine fuzzy system is determined by the proposed method according to the gathered input-output data. Finally, a nonlinear system illustrates the efficiency of the proposed approach to fuzzy modeling