A comparison of fuzzy and nonparametric linear regression

Nonparametric linear regression and fuzzy linear regression have been developed based on different perspectives and assumptions, and thus there exist conceptual and methodological differences between the two approaches. This article describes their comparative characteristics such as basic assumptions, parameter estimation, and applications, and then compares their predictive and descriptive performances by a simulation experiment to identify the conditions under which one method performs better than the other. The experimental results indicate that nonparametric linear regression is superior to fuzzy linear regression in predictive capability, whereas their descriptive capabilities depend on various factors. When the size of the data set is small, error terms have small variability, or when the relationships among variables are not well specified, fuzzy linear regression outperforms nonparametric linear regression with respect to descriptive capability. The conditions under which each method can be used as a viable alternative to the conventional least squares regression are also identified. The findings of this article would be useful in selecting the proper regression methodology to employ under specific conditions for descriptive and predictive purposes.