# Fuzzy Comprehensive Evaluation of Collapse Risk in Mountain Tunnels Based on Game Theory
## 7 Conclusions  
1. Based on the actual construction conditions of the project, this paper comprehensively considers four aspects: engineering geology, exploration and design, construction management, and natural environment, and deeply analyzes the subjective and objective factors that may affect the risk of tunnel collapse. On the basis of fully considering the operability, comprehensiveness, and representativeness of the evaluation index, a scientific evaluation system including 16 secondary indexes for tunnel collapse risk assessment is constructed.
2. The subjective weighting by improving the traditional analytic hierarchy process based on the D-number theory can increase the accuracy of the evaluation and reduce the impact of the uncertainty environment on the evaluation result. The objective weighting of the indicators by the CRITIC method can comprehensively consider the correlation and difference between the indicators. Performing the weight combination optimization through the game theory avoids the singleness and absoluteness of the weight calculation method and can also strengthen the rationality of the weight distribution coefficient, making the evaluation result more accurate.
3. By combining with the actual data of the project, the risk indicators are distinguished and calculated by using both qualitative and quantitative methods, and the obtained evaluation results have higher accuracy. Through the analysis based on the process example, it can be known that the risk level of each section of the tunnel is between level 3 and level 4, and the overall risk of the tunnel is between medium and higher risk. The evaluation results are consistent with the actual situation of the tunnel, indicating that this evaluation model can be promoted and applied.
4. The findings presented in this article can contribute to the identification of potential collapse risks during the tunnel design phase. Moreover, the risk assessment framework employed in this study can effectively guide maintenance schedules and procedures, ensuring that areas with higher risks are subjected to more frequent review and reinforcement. By integrating fuzzy logic and game theory with other analytical methods, more comprehensive risk assessment models for diverse engineering challenges can be developed.  
This paper presents novel ideas and methodologies for assessing and predicting the risk of tunnel collapse during construction. However, there is still a significant level of subjectivity and reliance on experience in the selection and grading of collapse risk indicators. Conducting in-depth research on the collapse mechanism of tunnels can enhance our objective understanding of collapses and improve the accuracy of risk assessment. Nevertheless, due to limited available cases for tunnel collapse risk assessment, establishing a comprehensive public database becomes challenging, thereby hindering accurate evaluation by intelligent models that consider various features. Therefore, future research should focus on developing dynamic collapse risk assessments based on intelligent algorithms.  
**Author Contributions:** Writing and editing. W.Z.; methodology, S.X.; editing, Z.W. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the National Natural Science Foundation of China (nos. 52278397 and 52168055), and the Natural Science Foundation of Jiangxi Province (20212 ACB204001). Their support is gratefully acknowledged.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Data is contained within the article.  
**Conflicts of Interest:** The authors declare no conflict of interests.