Hyperellipsoidal Clustering Method for Building Fuzzy Models

Abstract

The basic spirit of fuzzy modeling is to deal with vagueness, but from the aspect of application the emphasis is put on the treatment of nonlinearity. Its feature lies in modeling of an object as a system of understandable substructures. Especially, the model proposed by Takagi and Sugeno consists of a set of linear models with membership functions in which the nonlinearity of the system is embedded. In this paper we consider the fuzzy modeling from the viewpoint of finding local linear substructures of a system from given data. The proposal is a clustering technique called the hyperellipsoidal clustering method which takes account of a balance between continuity and linearity of the data distribution.