Research Information System
Journal of Computational and Applied Mathematics, vol.472, 2026 (SCI-Expanded)
Selecting an optimal bias parameter k is a critical challenge in Ridge regression, particularly in the context of fuzzy datasets affected by multicollinearity. Traditional approaches, such as K-fold cross-validation, are commonly used for this purpose but can be computationally demanding and may not always provide precise estimates. This study systematically investigates the efficiency of 77 distinct formulas for determining k within the framework of fuzzy Ridge regression, an area that has not been previously explored. Unlike previous studies, this work is the first to evaluate such a large set of candidate formulas across 54 simulated scenarios and three real-world datasets, providing an extensive empirical examination of their effectiveness. Additionally, it introduces an analysis of how different α-level sequences influence the selection process and impact the results, demonstrating that formula-driven methods can achieve comparable accuracy to K-fold cross-validation with significantly reduced computational effort. These findings highlight the advantages of using predefined formulas for bias parameter selection, offering a practical and efficient alternative to traditional techniques. Furthermore, this study demonstrates the robustness of α-level-based fuzzy Ridge regression and its effectiveness in handling fuzzy data with multicollinearity, contributing valuable insights into improving the efficiency and applicability of fuzzy regression models in various fields.