Efficient estimation of Shrinkage parameters in fuzzy Ridge and fuzzy Liu regression models using α-cut-based methods under multicollinearity

AMMAR HOMAIDA

Efficient estimation of Shrinkage parameters in fuzzy Ridge and fuzzy Liu regression models using α-cut-based methods under multicollinearity

Tezin Türü: Doktora

Tezin Yürütüldüğü Kurum: Gazi Üniversitesi, Fen Bilimleri Enstitüsü, İSTATİSTİK ANABİLİM DALI, Türkiye

Tezin Onay Tarihi: 2025

Tezin Dili: İngilizce

Öğrenci: AMMAR HOMAIDA

Danışman: Meral Ebegil

Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu

Özet:

This study presents a novel hybrid fuzzy regression framework that integrates Ridge and Liu estimation techniques within the α-cut-based approach to effectively handle fuzzy datasets affected by multicollinearity. While previous studies relied on K-fold cross-validation to select the fuzzy Ridge bias parameter k, this research explores a broader range of well-established and newly developed formulas to compute k, offering a more efficient and interpretable alternative. Additionally, this work introduces fuzzy Liu estimation into the α-cut-based fuzzy regression context for the first time, applying 13 distinct methods for selecting the fuzzy Liu bias parameter d. Extensive evaluations were conducted using a wide variety of simulated scenarios and three real-world datasets to assess the robustness and accuracy of each method. The results demonstrate that formula-based approaches not only achieve performance comparable to K-fold cross-validation in fuzzy regression but also do so with significantly reduced computational cost. Moreover, the proposed α-cut-based fuzzy Ridge regression consistently outperformed both fuzzy Liu and fuzzy ordinary least squares methods in most evaluation settings. However, findings also indicate that each of the three estimation techniques—fuzzy Ridge, fuzzy Liu, and fuzzy ordinary least squares —exhibits unique strengths depending on the data characteristics and parameter configurations, highlighting their complementary roles within the proposed hybrid framework. These findings underscore the effectiveness of the hybrid model and emphasize the value of formula-driven bias parameter selection in advancing fuzzy regression techniques for complex, uncertain data environments.