## 4 Engineering Example Calculation
### CRITIC Method to Calculate Evaluation Index Weights  
The quality control index score values in the above table were standardized to obtain the standardized matrix:  
\[ \begin{bmatrix}0.490&1&0.366&0.106&0\\ 0.380&0.855&1&0.285&0\\ 0.373&1&0.373&0.108&0\\ 0.106&0.307&1&0.265&0\\ 0&0.227&1&0.589&0.065\\ 0.375&1&0.432&0.125&0\\ 0&0.255&1&0.833&0.159\\ 0.380&1&0.501&0.145&0\\ 0.278&0.635&1&0.278&0\\ 0.680&1&0.357&0.103&0\\ 0&0.201&1&0.295&-0.049\\ 0&0.201&1&0.295&0\\ 0&0.210&1&0.420&0\\ 0.133&0.356&1&0.267&0\\ \end{bmatrix} \] \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Indicator** & **Rating** & **Indicator** & **Rating** & **Indicator** & **Rating** & **Indicator** & **Rating** \\ \hline \(B_{1}\) & 86 & \(B_{2}\) & 77 & \(B_{3}\) & 84 & \(B_{4}\) & 70 \\ \(B_{5}\) & 63 & \(B_{6}\) & 83 & \(B_{7}\) & 61 & \(B_{8}\) & 82 \\ \(B_{9}\) & 75 & \(B_{10}\) & 88 & \(B_{11}\) & 67 & \(B_{12}\) & 87 \\ \(B_{13}\) & 84 & \(B_{14}\) & 66 & \(B_{15}\) & 67 & \(B_{16}\) & 64 \\ \(B_{17}\) & 69 & \(B_{18}\) & 65 & \(B_{19}\) & 71 & & \\ \hline \end{tabular}
\end{table} 
Table 6: Construction quality control index score value of the special bridge across the Yellow River (unit: points). Figure 3: The completed mega bridge across the Yellow River. Each column is the same level and each row is the same evaluation index. The comparative intensity, \(V_{j}\), of each evaluation index was obtained according to Equation (5) as shown in Table 7.  
The obtained judgment matrix was brought into the CRITIC method calculation equation to obtain each indicator layer and the total weight value \(ow(i)\):  
Bored pile construction: [0.425, 0.160, 0.416]  
Cofferdam construction: [0.279, 0.364, 0.357]  
Bridge pier construction: [0.452, 0.360, 0.188]  
Superstructure construction: [0.160, 0.139, 0.152, 0.145, 0.135, 0.139, 0.130]  
Ancillary works construction: [0.335, 0.395, 0.270] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Indicator** & **Mean Value \(\overline{\tilde{r}_{j}}\)** & **Standard Deviation \(\sigma_{j}\)** & **Contrast Intensity \(V_{j}\)** \\ \hline \(B_{1}\) & 0.3925 & 0.39 & 0.9976 \\ \(B_{2}\) & 0.4143 & 0.50 & 0.8219 \\ \(B_{3}\) & 0.3881 & 0.37 & 1.0460 \\ \(B_{4}\) & 0.3914 & 0.34 & 1.1668 \\ \(B_{5}\) & 0.4168 & 0.38 & 1.1077 \\ \(B_{6}\) & 0.3861 & 0.39 & 0.9993 \\ \(B_{7}\) & 0.4400 & 0.45 & 0.9794 \\ \(B_{8}\) & 0.3858 & 0.41 & 0.9521 \\ \(B_{9}\) & 0.3866 & 0.44 & 0.8824 \\ \(B_{10}\) & 0.4136 & 0.43 & 0.9660 \\ \(B_{11}\) & 0.4216 & 0.29 & 1.4573 \\ \(B_{12}\) & 0.3998 & 0.41 & 0.9782 \\ \(B_{13}\) & 0.3881 & 0.37 & 1.0460 \\ \(B_{14}\) & 0.4178 & 0.31 & 1.3638 \\ \(B_{15}\) & 0.4216 & 0.29 & 1.4573 \\ \(B_{16}\) & 0.4144 & 0.35 & 1.1872 \\ \(B_{17}\) & 0.3964 & 0.32 & 1.2339 \\ \(B_{18}\) & 0.4151 & 0.33 & 1.2732 \\ \(B_{19}\) & 0.3869 & 0.35 & 1.1016 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Contrast intensity, \(V_{j}\) (dimensionless). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Indicator** & **Quantitative Index Values** & **Contrast Intensity \(V_{j}\)** & **Amount of Information \(C_{j}\)** \\ \hline \(B_{1}\) & 10.8222 & 0.9976 & 10.7962 \\ \(B_{2}\) & 4.9439 & 0.8219 & 4.0634 \\ \(B_{3}\) & 10.1068 & 1.0460 & 10.5717 \\ \(B_{4}\) & 6.3079 & 1.1668 & 7.3602 \\ \(B_{5}\) & 8.6459 & 1.1077 & 9.5769 \\ \(B_{6}\) & 9.4084 & 0.9994 & 9.4023 \\ \(B_{7}\) & 10.5537 & 0.9794 & 10.3361 \\ \(B_{8}\) & 8.6343 & 0.9521 & 8.2208 \\ \(B_{9}\) & 4.8620 & 0.8824 & 4.2904 \\ \(B_{10}\) & 12.1067 & 0.9660 & 11.6946 \\ \(B_{11}\) & 6.9754 & 1.4573 & 10.1654 \\ \(B_{12}\) & 11.3705 & 0.9782 & 11.1222 \\ \(B_{13}\) & 10.1068 & 1.0460 & 10.5717 \\ \(B_{14}\) & 7.2319 & 1.3638 & 9.8627 \\ \(B_{15}\) & 6.9754 & 1.4573 & 10.1654 \\ \(B_{16}\) & 8.0302 & 1.1872 & 9.5331 \\ \(B_{17}\) & 6.6266 & 1.2339 & 8.1769 \\ \(B_{18}\) & 7.5727 & 1.2732 & 9.6417 \\ \(B_{19}\) & 5.9768 & 1.1016 & 6.5842 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Indicator information calculations (dimensionless).