Fuzzy local regression models with fuzzy clustering

The TSK model introduced by Takagi Sugeno and Kang TSK fuzzy reasoning is associated with fuzzy rules that have a special format with a func tional type consequent instead of the fuzzy consequent that normally appears in the MamdamiModel In this way the TSK approach tries to decompose the input space into subspaces and then approximate the system in each subspace by a simple linear regression model This characteristic provides e cient models to deal with complex system although the generation of the corresponding fuzzy rules specially the premise struc ture is technically di cult and may lead to a nonlinear programming problem Several alternative approaches have been proposed to reduce the complexity of this building process In the area of fuzzy modeling the procedure of fuzzy clustering has been utilized in di erent ways In one of them fuzzy clusters give rise to local re gression models this is in fact the essence of the idea