Fuzzy linear regression using rank transform method

Abstract

In regression analysis, the rank transform (RT) method is known to be neither dependent on the shape of the error distribution nor sensitive to outliers. In this paper, we construct a so-called α-level fuzzy regression model based on the resolution identity theorem and apply RT method to this model. Fuzzy regression models with crisp input/fuzzy output and fuzzy input/fuzzy output are investigated to show the effectiveness of the proposed method. To compare its effectiveness with existing methods, we introduce a new performance measure. In addition, we propose a method to obtain a predicted output with respect to a specific target value and show that our model is more robust compared with other methods when the data contain some outliers.