In this paper the famous neural model, the multilayer perceptron, is extended to a new neural model that is called the additive-Takagi–Sugeno-type multilayer perceptron. The present study proves that this new model can also act as a universal approximator, and thus it can be used in many fields, such as system modeling and identification. The concept of f-duality and the fuzzy operator interactive-or are used to prove that the proposed neural model is functionally equal to a kind of fuzzy inference system. Further, this paper presents another new neuro-fuzzy model that is called the sigmoid-adaptive-network-based fuzzy inference system. Simulation studies show that our proposed models both have stronger approximation capability than multilayer perceptrons.