Multidimensional Membership Functions in T–S Fuzzy Models for Modelling and Identification of Nonlinear Multivariable Systems Using Genetic Algorithms

In this work, a new method for Takagi–Sugeno (T–S) fuzzy modelling based on multidimensional membership functions (MDMFs) is proposed. It is verified that the fuzzy inference method of one-dimensional membership functions (1DMFs) may place the fuzzy rules in inappropriate locations for modelling of nonlinear multivariable systems, while the application of MDMFs allows a better identification through a smaller number of fuzzy rules. The proposed method uses a genetic algorithm (GA) for the adjustment of the MDMFs and the T–S method for modelling and identification of the nonlinear system. As a validation example, a nonlinear multivariable system, a coupled tanks system, is chosen. The results show that the proposed method presents less identification error than the T–S method, with less number of fuzzy rules.