On equivalence between Takagi-Sugeno-Kang fuzzy systems with triangular membership functions and Neural Networks with ReLU activation in two or more dimensions
Barnabás Bede, Владик Крейнович, Peter Toth · International Journal of Computers Communications & Control · 2025
We prove the equivalence between Takagi-Sugeno-Kang (TSK) fuzzy systems and neural networks with ReLU activation function in two or more dimensions. The TSK fuzzy systems considered will have tetrahedral membership functions for their antecedents and singleton outputs. We show an example of a fuzzy system that is locally equivalent to a neural network based on the proposed method, and we discuss the potential to provide a local analysis to explain the decision process of neural networks.