Multivariable TS fuzzy model identification based on mixture of Gaussians

Identification of fuzzy models with multidimensional membership functions is considered. Many proposed fuzzy models use one-dimensional fuzzy sets and partition multidimensional input-spaces by Cartesian products of these univariate membership functions. The drawback of this approach is the complexity of the model in terms of the number of rules, which grows exponentially with the number of inputs (curse of dimensionality). Furthermore, decomposition errors which are detrimental to the performance of the model can be occurred. In order to avoid such drawbacks, it is desirable to work with multidimensional membership functions directly for the modeling of multidimensional and highly nonlinear systems. This paper proposes a clustering based identification of Takagi-Sugeno (TS) fuzzy models. The clusters are obtained by the expectation-maximization (EM) identification of a mixture of Gaussians. The proposed method is applied to well-known benchmark problems, and the obtained results are compared with results from the existing fuzzy clustering based identification techniques.