A Fuzzy System Constructed by Rule Generation and Iterative Linear SVR for Antecedent and Consequent Parameter Optimization

This paper proposes a new fuzzy regression model, i.e., the fuzzy system constructed by rule generation and iterative linear support vector regression (FS-RGLSVR) for structural risk minimization. The FS-RGLSVR is composed of Takagi-Sugeno (TS)-type fuzzy if-then rules. These rules are automatically constructed by a self-splitting rule generation algorithm that introduces the self-splitting technique to the k-means clustering algorithm. This new algorithm regards a cluster as a fuzzy rule, where no preassignment of the cluster (rule) number is necessary. The cost function for parameter learning is defined based on structural risk instead of empirical risk minimization in order to achieve generalizability. Tuning all of the free parameters in the FS-RGLSVR using linear support vector regression (SVR) is proposed to minimize the cost function. Each of the consequent and antecedent part parameters is expressed as a linear combination coefficient in a transformed input space so that the linear SVR is applicable. This paper introduces iterative linear SVR to tune antecedent and consequent parameters. This paper demonstrates the capabilities of FS-RGLSVR by two simulated and four practical regression examples. Comparisons with fuzzy systems with different types of learning algorithms verify the performance of the FS-RGLSVR.