Triangular type-2 fuzzy neural networks version of the Stone-Weierstrass theorem

The universal approximation capability of type-2 fuzzy neural networks plays an important role in the approximation theory of type-2 fuzzy neural networks. In this study, we propose a triangular type-2 fuzzy number by using the interval type-2 triangular fuzzy number as introduced in our previous work. Moreover, we introduce some triangular type-2 fuzzy operations. Then, we use these concepts to construct three layer feedforward triangular type-2 fuzzy neural networks. Furthermore, we establish a main theorem that shows the universal approximation capability of these networks. The main theorem can be regarded as the triangular type-2 fuzzy neural networks version of the Stone-Weierstrass theorem.