A Dynamically Constrained Multiobjective Genetic Fuzzy System for Regression Problems

In this paper, a multiobjective genetic fuzzy system (GFS) to learn the granularities of fuzzy partitions, tuning the membership functions (MFs), and learning the fuzzy rules is presented. It uses dynamic constraints, which enable three-parameter MF tuning to improve the accuracy while guaranteeing the transparency of fuzzy partitions. The fuzzy models (FMs) are initialized by a method that combines the benefits of Wang-Mendel (WM) and decision-tree algorithms. Thus, the initial FMs have less rules, rule conditions, and input variables than if WM initialization were to be used. Moreover, the fuzzy partitions of initial FMs are always transparent. Our approach is tested against recent multiobjective and monoobjective GFSs on six benchmark problems. It is concluded that the accuracy and interpretability of our FMs are always comparable or better than those in the comparative studies. Furthermore, on some benchmark problems, our approach clearly outperforms some comparative approaches. Suitability of our approach for higher dimensional problems is shown by studying three benchmark problems that have up to 21 input variables.