## 5 Results and Discussion
### Multi-Attribute Decision making Results  
The above Pareto solution sets under different inflow frequencies were used as the alternative scheme sets for multi-attribute decision making. The 100 schemes in the Pareto solution set were numbered as 1-100, respectively. The 4-dimensional decision-making attribute values of 100 schemes in each scheme set were calculated. The variation range and standard deviation were shown in Table 2. It can be seen that the 4-dimensional decision-making attribute values of each scheme set for different typical years were different. Figure 7: Pareto solution sets of different typical years. (**a**) Extraordinarily dry year (\(p\) = 95%), (**b**) Dry year (\(p\) = 75%), (**c**) Normal year (\(p\) = 50%), (**d**) Wet year (\(p\) = 25%), (**e**) Extraordinarily wet year (\(p\) = 5%). Therefore, the approach of SEACODE was used to sort, eliminate and select the scheme set to obtain the final decision-making scheme. The number of 4-order effective schemes, non-dominated superior schemes in 3-order subspaces and 3-order effective schemes of the alternative scheme sets under different inflow frequencies were shown in Table 3. When k = 4, the numbers of 4-order effective schemes in each typical year were 6, 6, 5, 6 and 6 by the first-round sorting of the alternative scheme sets, which reduced the preferred range of schemes by 94%, 94%, 95%, 94% and 94%, and greatly reduced the number of alternative schemes. When k = 3, the 4-order effective scheme sets were sorted in the second-round, that is, the non-dominated superior schemes of each 3-order subspace were obtained from the 4-order effective scheme sets. Then the numbers of 3-order effective schemes obtained by the intersection of all 3-order subspaces were 1, 0, 1, 2 and 2, of which the number of 3-order effective schemes in extraordinarily dry year and normal year was 1. The schemes could be used as the final decision-making schemes of extraordinarily dry year, normal year and wet year, and the scheme numbers were 32 and 63, respectively. The number of 3-order effective schemes in dry year was 0. The scheme that occupied the largest number of subspaces need to be determined as the final decision-making scheme. Table 4 showed the optimization processes of 4-order effective schemes to 3-order effective schemes in dry year. It can be seen that No. 13 scheme, No. 51 scheme and No. 85 scheme occupied three subspaces. The total water diversion and total power generation of No. 13 scheme were 11.01 \(\times\) 10\({}^{8}\) m\({}^{3}\) and 1.814 \(\times\) 10\({}^{8}\) kW\(\cdot\)h, respectively, No. 51 scheme were 11.005 \(\times\) 10\({}^{8}\) m\({}^{3}\) and 1.817 \(\times\) 10\({}^{8}\) kW\(\cdot\)h, and No. 85 scheme were 11.067 \(\times\) 10\({}^{8}\) m\({}^{3}\) and 1.804 \(\times\) 10\({}^{8}\) kW\(\cdot\)h, respectively. As the main task of Huangjinxia Reservoir is water supply and considering power generation and ecology at the same time. Therefore, No. 85 scheme with a large total water diversion was selected as the final decision-making scheme in dry year. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Typical Years** & & \(\alpha\) & \(\gamma\) & \(\
u\) & **WSI** \\ \hline Extraordinarily dry year & Variation range & [0, 0.083] & [0, 0.090] & [0.92, 1.00] & [48.03, 51.38] \\ Standard deviation & 0.008 & 0.009 & 0.03 & 1.084 \\ Dry year & Variation range & [0.50, 0.66] & [0.2, 0.33] & [0.71, 1.00] & [15.78, 30.21] \\ Standard deviation & 0.047 & 0.063 & 0.093 & 3.99 \\ Normalization range & [0.583, 0.75] & [0.2, 0.4] & [0.68, 0.99] & [9.13, 18.53] \\ Standard deviation & 0.038 & 0.064 & 0.064 & 2.66 \\ Water year & Variation range & [0.66, 0.83] & [0.25, 0.50] & [0.24, 0.86] & [0.86, 8.20] \\ Standard deviation & 0.063 & 0.265 & 0.179 & 1.85 \\ Extraordinarily wet year & Variation range & [0.67, 0.91] & [0.25, 1.00] & [0.31, 0.99] & [0.91, 14.00] \\ Standard deviation & 0.049 & 0.087 & 0.259 & 4.06 \\ \hline \hline \end{tabular}
\end{table}