A Novel Takagi–Sugeno Fuzzy System Modeling Method with Joint Feature Selection and Rule Reduction

Abstract

Traditional Takagi–Sugeno (T-S) fuzzy system modeling methods always yield a large number of fuzzy rules. Besides, they also include almost all the original features in the final model. These two factors make the final model sophisticated. In this paper, we propose a novel T-S fuzzy system modeling method called GS-FIS (Group Sparse Fuzzy Inference Systems), which performs fuzzy rule reduction and feature selection simultaneously in a unified framework. Considering the group structure information in the T-S fuzzy system and common features among fuzzy rules, we cast the fuzzy system modeling into a joint group sparse optimization problem and further develop an alternating direction method of multipliers procedure to derive the optimum solution to the problem. Experimental results on the synthetic dataset and several real-world datasets show that the proposed method can not only obtain a satisfactory generalization performance but also reduce the number of fuzzy rules and features effectively.