A Modified Learning Method for First-order Takagi-Sugeno Fuzzy System: Gradient-based Neuro-fuzzy Algorithm Employing Smoothing Group Lasso Regularization

The first-order Takagi-Sugeno (TS1) fuzzy system harbors an assemblage of IF-THEN fuzzy rules and is capable of approximating nonlinear systems of arbitrary complexity via discerning suitable affiliation functions and rules. As a natural extension of the lasso, group lasso adeptly trims superfluous connections among neurons and disposes the variable selection issue at the group stratum. Nonetheless, a fundamental shortcomings arises when the group lasso regularizer is directly applied during network training, particularly evident as weights converge towards zero, that is numerical oscillations. In addressing this concern, a smoothing function is introduced to approximate the original group lasso regularization (OGLR). Building upon the aforementioned content, a novel gradient-based neuro-fuzzy learning algorithm with smoothing group lasso regularization (SGLR) for the TS1 fuzzy system is proposed. Ultimately, the efficacy of the proposed algorithm is substantiated through three simulations that validate its sparse performance, approximation capability, and generalization potential.