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In hydrological forecasting problems, forecasted results are usually compared with the benchmark results (i.e., the measures values) to test the performance of forecasting models (Zhu et al. 2016a). However, such a benchmark alternative in MCDM problems of flood control operation is difficult to determine to examine the effectiveness and rationality of the proposed methodology. Instead, multiple MCDM methods should be simultaneously used to test the sensitivity and rationality of the results (Hajkowicz & Collins 2007). Therefore, we use the TOPSIS model (Hwang & Yoon 1981), fuzzy matter-element model (Cai 1994) and fuzzy optimization model (Fu 2008) to evaluate the 10 flood control operation alternatives (listed in Table 1) simultaneously. These three models differ basically depending on how they: (1) determine marginal evaluation on each criterion; and (2) aggregate marginal evaluations across criteria to achieve a global evaluation (Durbach & Stewart 2012). The TOPSIS model determines the best alternative which is simultaneously closest to the ideal point and farthest from the anti-ideal point. The fuzzy matter-element model is a classical MCDM method based on the theory of matter element analysis. The fuzzy optimization model uses fuzzy ideal and anti-ideal weight distances to calculate fuzzy membership degrees, by which the rank of candidate alternatives are determined directly without a need to compare fuzzy numbers. The original criteria system and the selected criteria system are used as the inputs of the three MCDM models, and each criterion is assigned with equal weight. The MCDM results of the three models before and after criteria selection are compared in Table 4. It can be seen from Table 4 that all these three MCDM models get consistent ranking orders of the 10 alternatives before and after criteria selection. The results demonstrate that deleting T, Wab, Qsd, Sl and ZeZid does not influence the MCDM results because these criteria are inherently unimportant to the MCDM results as well as having a weak sensitivity. Before selection, some criteria may be highly correlated and measure the same underlying factor, this may be another reason for deleting some criteria without changing the MCDM results.

Table 4

Comparison between MCDM results before and after criteria selection using three MCDM models

Alternative no.TOPSIS model
Fuzzy matter-element model
Fuzzy optimization model
Before
After
Before
After
Before
After
ciRankciRankρHiRankρHiRankuiRankuiRank
0.515 0.508 0.215 0.201 0.480 0.488 
0.698 0.698 0.398 0.372 0.584 0.591 
0.784 0.786 0.486 0.492 0.671 0.683 
0.892 0.889 0.628 0.644 0.739 0.742 
0.887 0.884 0.593 0.602 0.734 0.736 
0.880 0.881 0.581 0.571 0.730 0.731 
0.872 0.871 0.561 0.510 0.723 0.726 
0.772 0.772 0.443 0.451 0.643 0.651 
0.658 0.666 0.329 0.318 0.555 0.562 
10 0.499 10 0.492 10 0.183 10 0.162 10 0.398 10 0.412 10 
Alternative no.TOPSIS model
Fuzzy matter-element model
Fuzzy optimization model
Before
After
Before
After
Before
After
ciRankciRankρHiRankρHiRankuiRankuiRank
0.515 0.508 0.215 0.201 0.480 0.488 
0.698 0.698 0.398 0.372 0.584 0.591 
0.784 0.786 0.486 0.492 0.671 0.683 
0.892 0.889 0.628 0.644 0.739 0.742 
0.887 0.884 0.593 0.602 0.734 0.736 
0.880 0.881 0.581 0.571 0.730 0.731 
0.872 0.871 0.561 0.510 0.723 0.726 
0.772 0.772 0.443 0.451 0.643 0.651 
0.658 0.666 0.329 0.318 0.555 0.562 
10 0.499 10 0.492 10 0.183 10 0.162 10 0.398 10 0.412 10 

Note:ci, ρHi and ui represent the comprehensive evaluation index of TOPSIS model, fuzzy matter-element model and fuzzy optimization model, respectively.

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