Fractional multivariable grey optimization model with interaction effects and its application

Shuangbing Guo; Huanyu Zhou; Yuzhen Chen; Wenhao Gong; Shuangbing Guo; Huanyu Zhou; Yuzhen Chen; Wenhao Gong

doi:10.3934/math.2025853

AIMS Mathematics

2025, Volume 10, Issue 8: 19079-19105. doi: 10.3934/math.2025853

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Fractional multivariable grey optimization model with interaction effects and its application

School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang 453003, China

Received: 13 June 2025 Revised: 01 August 2025 Accepted: 11 August 2025 Published: 21 August 2025
MSC : 62M10, 93E11, 90C30

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.
- multivariate grey prediction model,
- interaction effect,
- fractional-order accumulation,
- carbon dioxide emissions,
- the genetic algorithm
Citation: Shuangbing Guo, Huanyu Zhou, Yuzhen Chen, Wenhao Gong. Fractional multivariable grey optimization model with interaction effects and its application[J]. AIMS Mathematics, 2025, 10(8): 19079-19105. doi: 10.3934/math.2025853

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Abstract

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.

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