Interval T-S fuzzy modeling based on minimizing 1-norm on approximation error
X. Liu, S. Zhou, Z. Xiong
As the obtained data in many practical applications tend to be uncertain or inaccurate, the conventional modeling methods characterized by the deterministic model for this type of data
have become undesirable. Taking linear programming, the T-S fuzzy model and some ideas from 1-norm minimization into consideration, a novel method identifying interval fuzzy model (INFUMO) consisted of the upper and lower T-S fuzzy model (referred to as f U and f L) has been studied in this paper. In order to solve the INFUMO, optimization problems based on minimizing 1-norm with respect to the approximation error corresponding to f U and f Lare constructed. Finally, the optimization problems are solved by the linear programming and INFUMO is thus constructed. To demonstrate its effectiveness, the proposed method is applied to identify the interval T-S model of static and dynamic nonlinear model with noise. The proposed method can not only deal with uncertain data to be usually modeled as the deterministic model, but also has better robustness.