Linear Uniform Estimator-Based Improvements to Fuzzy Regression Models

In regression modeling, collinearity among input variables, unevenness in the output observations, and outlier points can affect parameter estimation and reduce the optimality of the models. Several approaches exist to address these problems, including penalized and nonparametric models. However, each has its challenges and performs well only for a specific purpose, leaving the other problems unaddressed. In this paper, with a primary focus on fuzzy regression models, we propose a method based on a new linear uniform model that covers the functions of all these methods, such as reducing and controlling collinearity, coping with unevenness in a dataset, and outlier effects, as well as addressing the problems in their structures, such as the lack of closed form, the nonlinearity of the model parameter formula relation, and the single-purpose nature of the obtained models. Furthermore, when the normal distribution is assumed, it performs better than the best method for model fit, i.e., the least-squares method. In this paper, we demonstrate the optimal performance of the proposed method in addressing the aforementioned problems through various numerical and practical examples and compare it with other existing methods.