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According to Equation (11), we calculate the weight vector of the two principal components, E = (0.528, 0.472). We use the TOPSIS method, fuzzy optimum method, and fuzzy matter-element method to evaluate reservoir flood control alternatives simultaneously, and compare the evaluation results of the three methods that do not apply the PCA procedures. The results shown in Table 7 indicate that: (1) when PCA procedure is not conducted, i.e., the original decision matrix with criteria correlation (shown in Table 3) serves as the input of the three methods, the optimal alternative, the suboptimal alternative, and the worst alternative obtained by the three methods are consistent with each other, but these methods show a difference in the ranking of other alternatives (alternative one, three, and five); (2) when PCA procedure is conducted, i.e., the new decision matrix without criteria correlation (shown in Table 6) serves as the input of the three methods, the evaluation results of the three methods are consistent. This is because the repeated and interferential information exists in the original criterion system. The PCA eliminates the correlation and improves the consistency of the evaluation results.

Table 7

Ranking order of the six alternatives obtained by different methods

Alternative no.TOPSIS method
Fuzzy optimum method
Fuzzy matter-element method
Without PCA
With PCA
Without PCA
With PCA
Without PCA
With PCA
ciRankciRankuiRankuiRankρHiRankρHiRank
0.299 0.457 0.047 0.423 0.361 0.273 
0.097 0.084 0.022 0.008 0.154 0.059 
0.406 0.509 0.234 0.528 0.453 0.370 
0.740 0.903 0.271 0.989 0.465 0.903 
0.576 0.554 0.140 0.597 0.262 0.390 
0.884 0.993 0.400 1.000 0.486 0.995 
Alternative no.TOPSIS method
Fuzzy optimum method
Fuzzy matter-element method
Without PCA
With PCA
Without PCA
With PCA
Without PCA
With PCA
ciRankciRankuiRankuiRankρHiRankρHiRank
0.299 0.457 0.047 0.423 0.361 0.273 
0.097 0.084 0.022 0.008 0.154 0.059 
0.406 0.509 0.234 0.528 0.453 0.370 
0.740 0.903 0.271 0.989 0.465 0.903 
0.576 0.554 0.140 0.597 0.262 0.390 
0.884 0.993 0.400 1.000 0.486 0.995 

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