A Smoothing Interval Neuro-Fuzzy Learning Algorithm Based on First-Order Takagi-Sugeno-Kang System

In the real world, some important available information often exhibits inaccuracies, uncertainties, or ambiguities. Therefore, real-valued data is insufficient to fully capture these nuances and typically requires interval-valued representation. In this study, a first-order Takagi-Sugeno-Kang(TSK1) smoothed interval(SITSK1) fuzzy neural network is introduced, which is a new method that combines interval arithmetic with a TSK1 fuzzy neural network, and fully assimilates the advantages of both. During the experiments, the original interval TSK1(ITSK1) fuzzy neural network leads to significant oscillations in the gradient paradigm of the objective function, which is mainly due to the non-differentiability of the absolute value function. To solve this issue, we propose a smooth function to alleviate the oscillation phenomenon and obtain a more stable and accurate model. A large number of numerical simulations verify the effectiveness of the SITSK1 and demonstrate its enhanced noise handling ability and robustness, making it a valuable tool for handling uncertain data in complex systems.