Fuzzy versus statistical linear regression

Abstract

Statistical linear regression and fuzzy linear regression have been developed from different perspectives, and thus there exist several conceptual and methodological differences between the two approaches. The characteristics of both methods, in terms of basic assumptions, parameter estimation, and application are described and contrasted. Their descriptive and predictive capabilities are also compared via a simulation experiment to identify the conditions under which one outperforms the other. It turns out that statistical linear regression is superior to fuzzy linear regression in terms of predictive capability, whereas their comparative descriptive performance depends on various factors associated with the data set (size, quality) and proper specificity of the model (aptness of the model, heteroscedasticity, autocorrelation, nonrandomness of error terms). Specifically, fuzzy linear regression performance becomes relatively better, vis-à-vis statistical linear regression, as the size of the data set diminishes and the aptness of the regression model deteriorates. Fuzzy linear regression may thus be used as a viable alternative to statistical linear regression in estimating regression parameters when the data set is insufficient to support statistical regression analysis and/or the aptness of the regression model is poor (e.g., due to vague relationship among variables and poor model specification).