Data-Driven Parameter Optimization and Rule Reduction for Zero-Order T-S Fuzzy Systems
Xuehe Zhao, Long Li · Mathematics · 2026
The Takagi–Sugeno (T-S) fuzzy system is extensively applied in system identification and intelligent control due to its strong nonlinear approximation capability and model interpretability. However, traditional zero-order T-S systems encounter three critical limitations: slow convergence and susceptibility to local optima caused by random initialization, overfitting risks stemming from structural redundancy, and gradient oscillations during rule pruning when using traditional non-smooth regularizers (e.g., L1/2). To overcome these challenges, this study proposes a novel gradient learning algorithm that integrates Fuzzy C-Means (FCM) clustering initialization with a smoothing Group Lasso regularization strategy. First, FCM data-drivenly initializes Gaussian membership centers and determines the rule quantity, optimizing the alignment between the initial network structure and underlying data distribution to accelerate training and reduce local optima traps. Second, a piecewise smoothing function is designed to approximate the Group Lasso penalty, facilitating efficient rule reduction through group sparsity constraints while completely resolving gradient oscillation issues arising from nondifferentiability. The global convergence of the proposed algorithm is rigorously established using Lagrange’s mean value theorem, Taylor expansion, and the differential mean value theorem. Comprehensive numerical experiments on nonlinear regression and classification benchmarks demonstrate substantial improvements in convergence rate, computational efficiency, and structural sparsity. Ultimately, this research delivers a theoretically sound and practically efficient framework for T-S fuzzy system optimization, significantly broadening the applicability of fuzzy neural networks in complex engineering scenarios.