Compact TS-Fuzzy Models through Clustering and OLS plus FIS Model Reduction

The construction of interpretable Takagi--Sugeno (TS) fuzzy models by means of clustering is addressed. First, it is shown how the antecedent fuzzy sets and the corresponding consequent parameters of the TS model can be derived from clusters obtained by the Gath--Geva algorithm. To preserve the partitioning of the antecedent space, linearly transformed input variables can be used in the model. This may, however, complicate the interpretation of the rules. To form an easily interpretable model that does not use the transformed input variables, a new clustering algorithm is proposed, based on the Expectation Maximization (EM) identification of Gaussian mixture models. The most relevant consequent variables of the TS model are selected by an orthogonal least squares method based on the obtained clusters. For the selection of the relevant antecedent (scheduling) variables a new method has been developed based on Fisher's interclass separability criteria. This new technique is applied to two well-known benchmark problems: the MPG (miles per gallon) prediction and a simulated second-order nonlinear process. The obtained results are compared with results from the literature.

The antecedent algorithm is described in:
[1]J. Abonyi, R. Babuska, F. Szeifert, Modified gath-geva fuzzy clustering for identification of Takagi-Sugeno fuzzy models, IEEE Trans. on Systems, Man and Cybernetics, Part B,612-621, Oct, 2002

This algorithm is also described in:
[2]J. Abonyi, J.A. Roubos, M. Oosterom, F. Szeifert, Compact TS-Fuzzy models through clustering and OLS plus FIS model reduction, FUZZ-IEEE'01 Conference, Sydney, Australia, 1420-1423, 2001,

More MATLAB implementation on my website:
http://www.abonyilab.com/software-and-data