Improved learning of fuzzy models by structured optimization

A special procedure for learning the parameters of Takagi-Sugeno (TS) fuzzy models is proposed in this paper. It is a kind of structured optimization where the antecedent and the consequence parameters are divided into two groups and learned by two separate algorithms. A classical optimization algorithm (random walk with a variable step size) is used for learning the antecedent parameters and a special algorithm for local learning by the least squares method (LSM) is used for identifying the consequence parameters. Two different modifications of this structured optimization scheme are proposed and investigated. Experimentally, it has been shown that the procedure of dividing the whole set of parameters into two subsets being optimized in a multiply loop sequence speeds-up the total learning process. Finally a decomposition principle for reducing the dimensionality of the multi-input fuzzy models is also proposed and investigated on test examples. The proposed methods and algorithms lead to a faster learning and/or faster calculation of the fuzzy models which can be further used for different simulation and control purposes.