A fuzzy varying coefficient model and its estimation

The fuzzy linear regression model has been a useful tool for analyzing relationships between a set of variables in a fuzzy environment and has been extensively studied in the literature. However, this model may fail to reflect the more complicated regression relationships that are usually found in practice because of its simple and predefined linear structure. In order to enhance the feasibility and adaptability of the fuzzy linear models, we propose in this paper a fuzzy varying coefficient model in which the fuzzy coefficients in the fuzzy linear models are allowed to vary with a covariate. A restricted weighted least-squares estimation is suggested for locally fitting the model. Furthermore, some real-world datasets are analyzed in order to evaluate the performance of the proposed method, and the results show that the proposed model with its estimation approach performs satisfactorily in predicting the fuzzy response even in the case where the regression relationship is complicated.