Using suitable Membership Functions (MFs) has a substantial impact on increasing of the accuracy and reduction of redundancy in a neuro-fuzzy modeling approach. In this paper, we suggest sigmoid-based MFs which can generate flexible convex hyper-polygon validity regions in Takagi–Sugeno (TS) fuzzy models. To this end, the sigmoid-based function is equal to the product of some sigmoid functions whose arguments are hyperplane equations. It is discussed that such function can represent a soft, convex, flat region with arbitrary number of hyperplane borders (edges). Afterwards, we introduce first-order and high-order TS fuzzy models, where, the suggested sigmoid-based functions are utilized in the premise parts of the fuzzy rules and linear models or quadratic functions are used as submodels in consequence parts. It is shown that utilized submodels can be optimized locally and globally. An incremental learning algorithm is then suggested to identify both first-order and high-order TS fuzzy models. The performance of introduced TS fuzzy models are examined and compared with existing models in prediction of a chaotic time series as well as in function approximation of a sun sensor. Obtained results demonstrate high accuracy and low redundancy of the suggested high-order TS fuzzy model. Finally, the learning performance of two introduced first-order and high-order TS fuzzy models are compared with each other in identification of a steam generator model. 
Generating flexible convex hyper-polygon validity regions via sigmoid-based membership functions in TS modeling