Fuzzy robust regression based on exponential-type kernel functions

Abstract

The least squares method is a frequently used technique in fuzzy regression analysis. However, it is highly sensitive to outliers in the dataset. To address this challenge, we propose a novel robust fuzzy regression model based on exponential-type kernel functions. This approach effectively mitigates the influence of poorly fitted observations on the predicted results by reducing their weights. Furthermore, we use the $gh$-transformation to guarantee the nonnegativity of the spreads of the predicted response variable. In order to evaluate the performance of our method, a simulation study and three real data sets were considered. The experimental results demonstrate that the proposed method outperforms several popular robust methods in almost all cases. Furthermore, a sensitivity analysis of the estimated parameters provides further evidence of the superior efficiency of the proposed method.