Fuzzy Liu Regression Modelling Using α-Cut-Based Methods for Solving Multicollinearity Problem
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, cilt.34, sa.4, ss.439-464, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 34 Sayı: 4
- Basım Tarihi: 2026
- Doi Numarası: 10.1142/s0218488526500182
- Dergi Adı: International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, MathSciNet, zbMATH
- Sayfa Sayıları: ss.439-464
- Anahtar Kelimeler: Bias parameter, Fuzzy logic, Liu regression, Multicollinearity, Ordinary least squares, Ridge regression, α-cut
- Ankara Üniversitesi Adresli: Evet
Özet
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 α-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 α-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 α-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 d=1, 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.