## 4 Examples of Engineering Applications
### Construction Quality Grading
#### 4.4.2 CRITIC Method to Determine the Objective Weight  
According to the assignment results of quality indicators in Table 5, it is standardized through Equation (8) to obtain a standardized matrix. Then, according to Equations (9)-(13), the variability, conflict, information content and weight values of evaluation indicators can be calculated by writing MATLAB code in turn, as shown in Table 7.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Indictors**} & \multicolumn{5}{c}{**Single Weight**} \\ \cline{2-7}  & \(\mathbf{X_{1}}\) & \(\mathbf{X_{2}}\) & \(\mathbf{X_{3}}\) & \(\mathbf{X_{4}}\) & \(\mathbf{X_{5}}\) & \(\mathbf{X_{6}}\) & **Weighted** \\ \cline{2-7}  & **0.2324** & **0.1611** & **0.1279** & **0.0829** & **0.3286** & **0.0671** & **Value** \\ \hline X\({}_{\text{1-1}}\) & 0.2274 & & & & & 0.0528 \\ X\({}_{\text{1-2}}\) & 0.2274 & & & & & 0.0528 \\ X\({}_{\text{1-3}}\) & 0.1222 & & & & & 0.0284 \\ X\({}_{\text{1-4}}\) & 0.4231 & & & & & 0.0983 \\ X\({}_{\text{2-1}}\) & 0.1867 & & & & & 0.0301 \\ X\({}_{\text{2-2}}\) & & 0.2922 & & & & 0.0471 \\ X\({}_{\text{2-3}}\) & & 0.1078 & & & & 0.0174 \\ X\({}_{\text{2-4}}\) & & 0.4133 & & & & 0.0666 \\ X\({}_{\text{3-1}}\) & & & 0.2500 & & & 0.0320 \\ X\({}_{\text{3-2}}\) & & & 0.5000 & & & 0.0639 \\ X\({}_{\text{3-3}}\) & & & 0.2500 & & & 0.0320 \\ X\({}_{\text{4-1}}\) & & & 0.1634 & & & 0.0135 \\ X\({}_{\text{4-2}}\) & & & 0.2970 & & & 0.0246 \\ X\({}_{\text{4-3}}\) & & & 0.5396 & & & 0.0447 \\ X\({}_{\text{5-1}}\) & & & & 0.4133 & & 0.1358 \\ X\({}_{\text{5-2}}\) & & & & 0.1078 & & 0.0354 \\ X\({}_{\text{5-3}}\) & & & & 0.1867 & & 0.0614 \\ X\({}_{\text{5-4}}\) & & & & 0.2922 & & 0.0960 \\ X\({}_{\text{6-1}}\) & & & & & 0.1958 & 0.0131 \\ X\({}_{\text{6-2}}\) & & & & & 0.3108 & 0.0209 \\ X\({}_{\text{6-3}}\) & & & & & 0.4934 & 0.0331 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Subjective weighting values of evaluation indicators.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Indictors**} & \multirow{2}{*}{**Variability**} & \multirow{2}{*}{**Conflict**} & \multicolumn{2}{c}{**Information**} & \multirow{2}{*}{**Weight Values**} \\ \cline{1-1} \cline{5-5}  & & & & **Content** & \\ \hline X\({}_{\text{1-1}}\) & 0.7565 & 21.3548 & 16.1546 & 0.0506 \\ X\({}_{\text{1-2}}\) & 0.7160 & 16.8724 & 12.0807 & 0.0378 \\ X\({}_{\text{1-3}}\) & 0.6359 & 16.6904 & 10.6140 & 0.0332 \\ X\({}_{\text{1-4}}\) & 0.8131 & 19.8678 & 16.1548 & 0.0506 \\ X\({}_{\text{2-1}}\) & 0.8363 & 18.7835 & 15.7090 & 0.0492 \\ X\({}_{\text{2-2}}\) & 0.6790 & 21.3728 & 14.5115 & 0.0455 \\ X\({}_{\text{2-3}}\) & 0.7373 & 17.0894 & 12.6003 & 0.0395 \\ X\({}_{\text{2-4}}\) & 0.8611 & 20.3544 & 17.5273 & 0.0549 \\ X\({}_{\text{3-1}}\) & 0.9158 & 24.7301 & 22.6473 & 0.0709 \\ X\({}_{\text{3-2}}\) & 0.8070 & 23.7479 & 19.1654 & 0.0600 \\ X\({}_{\text{3-3}}\) & 0.7348 & 22.0673 & 16.2151 & 0.0508 \\ X\({}_{\text{4-1}}\) & 0.8643 & 17.6678 & 15.2698 & 0.0478 \\ X\({}_{\text{4-2}}\) & 0.6964 & 17.9953 & 12.5323 & 0.0393 \\ X\({}_{\text{4-3}}\) & 0.6481 & 24.9121 & 16.1455 & 0.0506 \\ X\({}_{\text{5-1}}\) & 0.8982 & 17.3025 & 15.5411 & 0.0487 \\ X\({}_{\text{5-2}}\) & 0.7381 & 20.1038 & 14.8379 & 0.0465 \\ X\({}_{\text{5-3}}\) & 0.9526 & 21.7187 & 20.6888 & 0.0648 \\ X\({}_{\text{5-4}}\) & 0.7477 & 18.9209 & 14.1463 & 0.0443 \\ X\({}_{\text{6-1}}\) & 0.6223 & 16.8129 & 10.4625 & 0.0328 \\ X\({}_{\text{6-2}}\) & 0.7974 & 16.4305 & 13.1012 & 0.0410 \\ X\({}_{\text{6-3}}\) & 0.7294 & 18.0165 & 13.1412 & 0.0412 \\ \hline \hline \end{tabular}
\end{table}
Table 7: The calculated result of the CRITIC method.