On cluster-wise fuzzy regression analysis

Abstract
Since Tanaka et al. (1982) proposed a study of linear regression analysis with a fuzzy model, fuzzy regression analysis has been widely studied and applied in a variety of substantive areas. Regression analysis in the case of heterogeneity of observations is commonly presented in practice. The authors' main goal is to apply fuzzy clustering techniques to fuzzy regression analysis. Fuzzy clustering is used to overcome the heterogeneous problem in the fuzzy regression model. They present the cluster-wise fuzzy regression analysis in two approaches: the two-stage weighted fuzzy regression and the one-stage generalized fuzzy regression. The two-stage procedure extends the results of Jajuga (1986) and Diamond (1988). The one-stage approach is created by embedding fuzzy clusterings into the fuzzy regression model fitting at each step of procedure. This kind of embedding in the one-stage procedure is more effective since the structure of regression line shape encountered in the data set is taken into account at each iteration of the algorithm. Numerical results give evidence that the one-stage procedure can be highly recommended in cluster-wise fuzzy regression analysis.