Explainable evolving approach for univariate first-order Takagi-Sugeno fuzzy systems

This paper proposes an evolving strategy for learning the modified neo-fuzzy neuron model NFN-MOD, whose rule consequent incorporates delayed inputs using a first-order Takagi-Sugeno (T-S) fuzzy system. The evolving strategy is based on the recursive Gath-Geva clustering method, which is proposed as a univariate approach in this paper to match the antecedent of the NFN-MOD. The resulting method, the EvNM, is validated using a dataset from a real industrial process, the sulfur recovery unit, and it is compared with state-of-the-art models, namely DENFIS (dynamic evolving neural-fuzzy inference system), EFuNN (evolving fuzzy neural network), eFSLab (evolving fuzzy systems laboratory), ALMMo-1 (autonomous learning of a multimodel system with first-order predictor), and iMU-ZOTS (iterative learning for a model composed of multiple univariate T-S fuzzy systems). Finally, discussions on explainability of the proposed EvNM are presented.