Abstract

In recent years, fuzzy nonparametric regression models have attracted considerable attention due to their flexibility and effectiveness in capturing complex functional relationships between variables without assuming any predefined model structure. This study investigates fuzzy kernel regression models that accommodate crisp input variables and fuzzy output responses within a smooth nonparametric regression framework. Specifically, Gaussian and Epanechnikov kernel functions are employed in three estimation approaches: k-Nadaraya–Watson (k-NW), k-nearest neighbor (k-NN), and local linear smoothing (LLS). The performance of these methods is evaluated through experimental analysis in a fuzzy regression setting. The results indicate that all three approaches are effective and appropriate within the framework of fuzzy theory. Among them, the LLS method demonstrates superior performance, as it effectively mitigates the bias–variance trade-off by adapting to the local structure of the data, thereby providing more accurate and stable estimates.

Keywords

Fuzzy regression, Nonparametric regression, Kernel smoothing, Nadaraya–watson estimator, k-nearest neighbor, Local linear smoothing.

Cite this article

Radhy ZH. Fuzzy kernel regression models for nonparametric function estimation. International Journal of Advanced Technology and Engineering Exploration. 2026;13(135):245-262. DOI : 10.19101/IJATEE.2024.111101551

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