## 4 Empirical Research
### Expert Evaluation System  
Thirty experts were invited to participate in our study. All were civil engineers and project managers in building and construction companies and had over 10 years of experience in this field. This work used the Delphi method research paradigm proposed by [PERSON] [45]. A questionnaire containing information about the Chengdu-Chongqing Central Railway was sent to each expert via email. The experts were asked to suggest 20 risks that the project may face during construction, based on their experience. After questionnaire collection was completed, the 15 most frequently mentioned risks were sent to the experts as a new questionnaire. The experts were asked to select the 10 risks that were most likely to lead to project failure out of the 15. After all the questionnaires were collected again, the five most frequently mentioned risks were selected as the scope. Finally, five risks were selected for meticulous ranking: capital chain rupture, decision failure, economic downturn, policy and legal risks, and stakeholder conflict. These five gray rhino risks in the Chengdu-Chongqing Middle Line High-speed Railway construction project have captured the greatest attention of the experts. In this study, the common project risk response methods proposed in the existing studies will be calculated and divided into the five dimensions. Based on these risk response methods, IF-ANP can calculate the quantitative value of relationships among these risks. The risk prevention methods for these five risks are shown in Table 2.  
Next, the priority of various plans to deal with capital chain rupture risks were obtained. The fuzzy synthetic extent values were first calculated from Equation (5):  
\[ \begin{array}{l}\widetilde{S}_{1}=(11.000,15.000,19.000)\otimes\big{(}51.417^{ -1},38.700^{-1},27.650^{-1})=(0.214,0.388,0.687)\\ \widetilde{S}_{2}=(4.583,6.833,9.500)\otimes\big{(}51.417^{-1},38.700^{-1},27.65 0^{-1})=(0.089,0.177,0.344)\\ \widetilde{S}_{3}=(7.333,10.500,14.000)\otimes\big{(}51.417^{-1},38.700^{-1},27.6 50^{-1})=(0.143,0.271,0.506)\\ \widetilde{S}_{4}=(2.783,4.083,5.833)\otimes\big{(}51.417^{-1},38.700^{-1},27.6 50^{-1})=(0.054,0.106,0.211)\\ \widetilde{S}_{5}=(1.950,2.283,3.083)\otimes\big{(}51.417^{-1},38.700^{-1},27.6 50^{-1})=(0.038,0.059,0.112)\\ \end{array} \]  
The values of \(V(\widetilde{S}_{i}\geq\widetilde{S}_{j})\) were calculated from Equation (7). The results are shown in Table 5.  
Therefore, the fifth expert's priorities for planning to deal with the capital chain rupture risk under a general scenario were calculated using Equation (8). Through the same calculation process, the planning priorities for a decision failure risk scenario were also calculated. The results are shown in Table 6.  
The difference between the two sets of data was calculated using Equation (9). In the end, this study obtained \(l^{(5)}(D{\rightarrow}C)=0.668\), the quantitative value of the fifth expert's evaluation of the influence of the risk of decision failure on the risk of a capital chain rupture. Using the same steps, evaluation results of the other 29 experts were acquired. The expert evaluation results were randomly divided into two groups and the F test was used to verify the validity of the data. F value was 0.62 and the \(p\) value was 0.44. Since the \(p\) value was greater than 0.05, there was no significant difference between the two groups of data. This indicates high consistency among the expert evaluation results for the effect of decision failure risk on the risk of capital chain rupture. Based on Equation (10), the value of \(I(D\to C)=0.733\) was calculated. Through the same calculation steps, quantitative values for the interactions between other risks were also calculated. Combining the results of the quantitative calculation of the interrelationships among all risks, a risk interference relation map was drawn, as shown in Figure 3.