A fuzzy additive regression model with exact predictors and fuzzy responses

Abstract

Fuzzy regression analysis is aimed at modeling the relationship between a set of fuzzy responses and a set of non-fuzzy/fuzzy predictors. However, compared to parametric methods, nonparametric regression often provides a very flexible approach to exploring the relationship between a response and the associated predictors without specifying a parametric model. In this paper, a novel fuzzy additive regression model with non-fuzzy predictors and fuzzy responses was proposed. For this purpose, a back-fitting stepwise regression approach with kernel smoothing was introduced to estimate a fuzzy smooth function corresponding to each predictor. An extended cross-validation criterion was also utilized to evaluate the unknown bandwidths. Some common goodness-of-fit criteria were employed to evaluate the performance of the proposed method. Effectiveness of the developed method was demonstrated through four numerical examples including two simulation studies based on three common kernels. The proposed method was further compared with several conventional fuzzy linear/nonlinear regression models, clearly indicating superior accuracy of the proposed model over other methods. Thus, it can be successfully applied to improve the prediction accuracy and interpretability of the fuzzy regression models for real-life applications in the context of intelligence systems.