Fuzzy Liu Regression Modelling Using α-Cut-Based Methods for Solving Multicollinearity Problem

Liu regression, originally developed in the context of classical (crisp) statistics as a biased estimation method to mitigate multicollinearity, has not been previously extended to fuzzy regression frameworks. In this study, we propose a novel fuzzy adaptation of Liu regression, implemented within an [Formula: see text]-cut-based estimation structure. This approach provides a systematic methodology for selecting candidate values of the bias parameter d in fuzzy settings. While prior research has primarily concentrated on fuzzy Ridge regression, our work introduces and investigates fuzzy Liu regression for the first time using [Formula: see text]-cut-based estimation, offering a new strategy for addressing multicollinearity in fuzzy datasets. The proposed methodology evaluates 13 distinct formulas for the bias parameter d, comparing their performance against fuzzy OLS under the [Formula: see text]-cut paradigm. Extensive simulations and real-world data sets are employed to assess performance across varying levels of multicollinearity. Results consistently show that fuzzy Liu regression outperforms fuzzy OLS—even in low multicollinearity cases. Notably, the method converges to fuzzy OLS when [Formula: see text], maintaining theoretical coherence. These findings underscore the effectiveness of formula-driven bias selection and establish fuzzy Liu regression as a valuable tool in fuzzy regression analysis.