Takagi-Sugeno Fuzzy Systems with Triangular Membership Functions as Interpretable Neural Networks

Abstract

Equivalence between Neural Networks with ReLU activation and Takagi-Sugeno fuzzy systems with triangular membership functions is studied. We prove an equivalence relation between the above mentioned systems under relaxed conditions. As the above proofs are constructive, this method allows us to transform between the considered Neural Networks and Takagi-Sugeno systems. The interpretability of the proposed system is discussed and future research directions are explored.