Stability evaluation of surrounding rock in deep coal roadways based on game theory-based combined weighting and extension cloud model

To address the complex coupling of multiple factors and the coexistence of fuzziness and randomness in the stability evaluation of surrounding rock in deep coal roadways, an evaluation framework based on game theory and the extension cloud model is first established. An expert consensus model using the random forest algorithm is then introduced: missing data are imputed by mean imputation, and outliers are detected and handled via the interquartile range (IQR) method, thereby resolving inconsistencies in qualitative expert ratings. Subsequently, the DEMATEL method and the entropy weight method are employed to determine subjective and objective weights, which are then reconciled through game theory-based combined weighting optimization to resolve conflicts between the two. Finally, a quantitative assessment model integrating cloud similarity and cloud membership is developed to evaluate rock mass stability. The results show that the fusion of game theory and the extension cloud model effectively overcomes the challenge of multi-source information coupling in quantitative stability assessment, achieving a substantial improvement in the balance of calculation results compared to the conventional cloud models. Taking the No.13101 working face at the Zhujixi Coal Mine in Huainan as a case study, the model's evaluation results agree with field measurements to 92.3%;after support optimization, the cumulative roof-to-floor convergence was limited to 118.5 mm and the rib convergence to 167.0 mm, both meeting design requirements. This study thus provides a theoretical basis and a decision-support framework for the dynamic safety control of surrounding rock in deep roadways.