Uncertain Elastic Net Regression for Multicollinear Data and Its Applications

Practical socioeconomic systems commonly contain imprecise and subjective data, while existing uncertain regression methods perform poorly for highly multicollinear variables. Uncertain least squares is susceptible to multicollinearity and outliers, and uncertain LASSO fails to stably select correlated variables. To address these issues, this paper proposes an uncertain elastic net regression model targeting multicollinear uncertain data. Based on the minimum uncertain expectation framework, the model adopts combined regularization to realize sparse variable screening and grouping effect, which mitigates multicollinearity and enhances estimation stability. We verify the model via numerical examples and an empirical study on Shandong’s domestic tourism data, taking two classic uncertain regression methods as benchmarks. The results show that our model outperforms competitors in fitting accuracy, coefficient stability and variable selection. This method provides a reliable, interpretable tool for regression modeling under uncertainty and multicollinearity, and can be applied to tourism and socioeconomic research.