A Novel Learning Approach to Remove Oscillations in First‐Order Takagi–Sugeno Fuzzy System: Gradient Descent‐Based Neuro‐Fuzzy Algorithm Using Smoothing Group Lasso Regularization

Abstract As a universal approximator, the first order Takagi–Sugeno fuzzy system possesses the capability to approximate widespread nonlinear systems through a group of IF THEN fuzzy rules. Although group lasso regularization has the advantage of inducing group sparsity and handling variable selection issues, it can lead to numerical oscillations and theoretical challenges in calculating the gradient at the origin when employed directly during training. The paper addresses the aforementioned obstacle by invoking a smoothing function to approximate group lasso regularization. On this basis, a gradient‐based neuro fuzzy learning algorithm with smoothing group lasso regularization for the first order Takagi–Sugeno fuzzy system is proposed. The convergence of the proposed algorithm is rigorously proved under gentle conditions. In addition, experimental outcomes acquired on two approximations and two classification simulations demonstrate that the proposed algorithm outperforms the algorithm with original group lasso regularization and L 2 regularization in terms of error, pruned neurons, and accuracy. This is particularly evident in significant advancements in pruned neurons due to group sparsity. In comparison to the algorithm with L 2 regularization, the proposed algorithm exhibits improvements of 6.3, 5.3, and 142.6 in pruned neurons during sin function, Gabor function, and Sonar benchmark dataset simulations, respectively.