A New High-order Takagi-Sugeno Fuzzy Model Based on Deformed Linear Models

Amongst possible choices for identifying complicated processes for prediction, simulation, and approximation applications, high-order Takagi-Sugeno (TS) fuzzy models are fitting tools. Although they can construct models with rather high complexity, they are not as interpretable as first-order TS fuzzy models. In this paper, we first propose to use Deformed Linear Models (DLMs) in consequence parts of a TS fuzzy model, which provides both complexity and interpretability. We then prove that in order to minimize considered error indices, linear and nonlinear parts of DLMs can be optimized independently. A localization of DLMs in input-space of the TS fuzzy model is done using an appropriate sigmoid-based membership function, which can represent a fuzzy subspace with enough smoothness and flat top. An incremental algorithm is also proposed to identify the suggested fuzzy model. Then, through an illustrative example, the formation of DLMs to approximate a nonlinear function is demonstrated. The applicability and effectiveness of the introduced fuzzy modeling approach is examined in three case studies: prediction of a chaotic time series, identification of a steam generator model, and approximation of a nonlinear function for a sun sensor. The obtained results demonstrate the higher accuracy and better generalization of our modeling approach as compared with those of some other well-known state-of-the-art approaches.