Sparse fuzzy c-regression models with application to T-S fuzzy systems identification

In this paper, the objective function of fuzzy c-regression models (FCRM) is modified to develop a novel fuzzy partition method on the basis of block structured sparse representation, namely as sparse fuzzy c-regression model. This method takes advantage of the block structured information in the objective function of FCRM and casts fuzzy partition into an optimization problem by making a tradeoff between traditional FCRM and the number of prototypes of hyper-plane with nonzero parameters. An alternating direction method of multipliers (ADMM) based algorithm is exploited to address the proposed optimization problem. Furthermore, based on sparse fuzzy c-regression models, a novel T-S fuzzy systems identification method is developed for reduction of fuzzy rules. Finally, examples on well-known benchmark data set are carried out to illustrate the effectiveness of the proposed methods.