A class of fuzzy clusterwise regression models
In this paper we introduce a class of fuzzy clusterwise regression models with LR fuzzy response variable and numeric explanatory variables, which embodies fuzzy clustering, into a fuzzy regression framework. The model bypasses the heterogeneity problem that could arise in fuzzy regression by subdividing the dataset into homogeneous clusters and performing separate fuzzy regression on each cluster. The integration of the clustering model into the regression framework allows us to simultaneously estimate the regression parameters and the membership degree of each observation to each cluster by optimizing a single objective function. The class of models proposed here includes, as special cases, the fuzzy clusterwise linear regression model and the fuzzy clusterwise polynomial regression model. We also introduce a set of goodness of fit indices to evaluate the fit of the regression model within each cluster as well as in the whole dataset. Finally, we consider some cluster validity criteria that are useful in identifying the optimal number of clusters. Several applications are provided in order to illustrate the approach.
goodness of fit cluster validity fuzzy clusterwise linear regression analysis fuzzy clusterwise polynomial regression analysis lr fuzzy dependent variable