Fractional multivariable grey optimization model with interaction effects and its application

To further enhance the accuracy and stability of multivariate grey prediction models and expand their application scope, a fractional multivariate grey optimization model with interaction effects was proposed. Building upon traditional grey models, we optimized the background value parameters and introduced fractional-order accumulation to improve fitting accuracy. Additionally, the model fully incorporates interaction effects among driving factors and integrates linear and nonlinear correction terms to enhance adaptability. The developed model exhibits high flexibility, as it can degenerate into eight classical grey models through parameter adjustments. The genetic algorithm was employed to solve the optimal parameters for global optimization, and ablation experiments were conducted to verify the effectiveness of each component. Finally, the developed model was utilized in forecasting China's carbon dioxide emissions from energy consumption. It exhibits superior performance compared to existing models, excelling in both simulation accuracy and predictive capability. This confirms its strong adaptability and stability as an effective tool for predicting China's carbon dioxide emissions from energy consumption.