It has been proven that Takagi–Sugeno systems are universal approximators, and they are applied widely to classification and regression problems. The main challenges of these models are convergence analysis and their computational complexity due to the large number of connections and the pruning of unnecessary parameters. The L1/2 regularizer has a specific sparsity capacity and it is representative of Lq(0 <q<1)regularizations. In this report, we propose a gradient-based neuro-fuzzy learning algorithm with a smoothing L1/2regularization for the first-order Takagi–Sugeno fuzzy infer-ence system. The proposed approach performs better bypruning inactive connections, where the number of the redundant connections for removal is higher than that generated by the original L1/2regularizer, while it is also implemented by simultaneous structure and parameter learning processes; it is possible to demonstrate the theoretical convergence analysis of this learning method, which we focus on explicitly. We also provide a series of simulations to demonstrate that the smoothing L1/2regularization can often obtain more compressive representations than the current L1/2regularization.

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