TOPSIS——AISM联合求解过程
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原始数据如下
$$ \begin{array}{c|c|c|c|c|c|c}{M_{8 \times19}} &+P1 &+P2 &+P3 &+P4 &+T1 &+T2 &+T3 &+F1 &-F2 &+F3 &+F4 &-S1 &+S2 &+S3 &+C1 &-C2 &+A1 &+A2 &+A3\\ \hline 大连港 &4.67 &0.008 &965.3 &392.03 &129 &104 &44.98 &67.54 &1.99 &0.057 &6819 &16 &86.6 &0.205 &0.95 &15.53537249 &0.174 &0.566 &0.106\\ \hline 青岛港 &4.86 &0.06 &1932 &17 &162 &84 &29.94 &117.41 &1.31 &0.064 &8611 &8 &78 &0.165 &0.9188 &2.239640999 &0.338 &0.64 &0.292\\ \hline 天津港 &4.28 &0.0956 &1601 &75.73 &120 &122 &37.63 &130.6 &1.27 &0.036 &7919 &9 &77 &0.113 &0.9887 &6.230568559 &0.887 &0.61 &0.257\\ \hline 上海港 &5.61 &0.001 &4201 &315.04 &260 &181 &106.08 &380.42 &3.7 &0.066 &16366 &1 &81 &0.194 &0.94 &1.664414737 &0.136 &0.801 &0.327\\ \hline 宁波舟山港 &7.76 &0.078 &2794 &164.12 &247 &171 &94.45 &218.8 &2 &0.071 &16229 &3 &76.1 &0.21 &0.9555 &10.17129633 &0.128 &0.801 &0.451\\ \hline 深圳港 &2.51 &0.041 &2574 &697.5 &239 &73 &32.8 &22.24 &0.83 &0.068 &12775 &4 &88.2 &0.32 &0.7472 &0.354246332 &0.76 &0.485 &0.504\\ \hline 广州港 &6.15 &0.065 &2187 &95.2 &209 &76 &54.51 &86.43 &1.43 &0.068 &9240 &5 &78.3 &0.27 &0.8166 &1.402957241 &0.211 &0.603 &0.159\\ \hline 厦门港 &2.17 &0.0286 &1070 &789 &146 &76 &30.68 &133.41 &0.65 &0.083 &4971 &14 &80.2 &0.22 &0.9102 &1.188728109 &0 &0.647 &0.319\\ \hline \end{array} $$
采用的归一方法如下
极差法
正向指标公式：$$ n_{ij} = \frac{{o_{ij}-min(o_{j})}}{{max(o_{j})-min(o_{j})}} $$
负向指标公式：$$ n_{ij} = \frac{max(o_{j})-{o_{ij}}}{{max(o_{j})-min(o_{j})}} $$
计算后的归一化矩阵如下
$$ \begin{array}{c|c|c|c|c|c|c}{M_{8 \times19}} &+P1 &+P2 &+P3 &+P4 &+T1 &+T2 &+T3 &+F1 &-F2 &+F3 &+F4 &-S1 &+S2 &+S3 &+C1 &-C2 &+A1 &+A2 &+A3\\ \hline 大连港 &0.447 &0.074 &0 &0.486 &0.064 &0.287 &0.198 &0.126 &0.561 &0.447 &0.162 &0 &0.868 &0.444 &0.84 &0 &0.196 &0.256 &0\\ \hline 青岛港 &0.481 &0.624 &0.299 &0 &0.3 &0.102 &0 &0.266 &0.784 &0.596 &0.319 &0.533 &0.157 &0.251 &0.711 &0.876 &0.381 &0.491 &0.467\\ \hline 天津港 &0.377 &1 &0.196 &0.076 &0 &0.454 &0.101 &0.303 &0.797 &0 &0.259 &0.467 &0.074 &0 &1 &0.613 &1 &0.396 &0.379\\ \hline 上海港 &0.615 &0 &1 &0.386 &1 &1 &1 &1 &0 &0.638 &1 &1 &0.405 &0.391 &0.798 &0.914 &0.153 &1 &0.555\\ \hline 宁波舟山港 &1 &0.814 &0.565 &0.191 &0.907 &0.907 &0.847 &0.549 &0.557 &0.745 &0.988 &0.867 &0 &0.469 &0.863 &0.353 &0.144 &1 &0.867\\ \hline 深圳港 &0.061 &0.423 &0.497 &0.881 &0.85 &0 &0.038 &0 &0.941 &0.681 &0.685 &0.8 &1 &1 &0 &1 &0.857 &0 &1\\ \hline 广州港 &0.712 &0.677 &0.378 &0.101 &0.636 &0.028 &0.323 &0.179 &0.744 &0.681 &0.375 &0.733 &0.182 &0.758 &0.287 &0.931 &0.238 &0.373 &0.133\\ \hline 厦门港 &0 &0.292 &0.032 &1 &0.186 &0.028 &0.01 &0.31 &1 &1 &0 &0.133 &0.339 &0.517 &0.675 &0.945 &0 &0.513 &0.535\\ \hline \end{array} $$
正极值点构成
$$ \begin{array}{c|c|c|c|c|c|c}{M_{1 \times19}} &+P1 &+P2 &+P3 &+P4 &+T1 &+T2 &+T3 &+F1 &-F2 &+F3 &+F4 &-S1 &+S2 &+S3 &+C1 &-C2 &+A1 &+A2 &+A3\\ \hline \mathbf{Max} &1 &1 &1 &1 &1 &1 &1 &1 &1 &1 &1 &1 &1 &1 &1 &1 &1 &1 &1\\ \hline \end{array} $$负极值点构成
$$ \begin{array}{c|c|c|c|c|c|c}{M_{1 \times19}} &+P1 &+P2 &+P3 &+P4 &+T1 &+T2 &+T3 &+F1 &-F2 &+F3 &+F4 &-S1 &+S2 &+S3 &+C1 &-C2 &+A1 &+A2 &+A3\\ \hline \mathbf{Min} &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline \end{array} $$带权重的距离公式中权重的计算方法——此处处理的为客观权重方法所得权重
采用的是熵权法（EWM）求权重
$$ \begin{array}{c|c|c|c|c|c|c}{M_{2 \times19}} &+P1 &+P2 &+P3 &+P4 &+T1 &+T2 &+T3 &+F1 &-F2 &+F3 &+F4 &-S1 &+S2 &+S3 &+C1 &-C2 &+A1 &+A2 &+A3\\ \hline EWM所得权重 &0.0467 &0.0481 &0.0608 &0.0709 &0.0586 &0.0984 &0.1086 &0.0569 &0.0251 &0.0257 &0.0507 &0.0388 &0.0693 &0.0356 &0.0293 &0.0285 &0.0663 &0.0398 &0.0418\\ \hline 权重大小顺序 &11 &10 &6 &3 &7 &2 &1 &8 &19 &18 &9 &14 &4 &15 &16 &17 &5 &13 &12\\ \hline \end{array} $$距离公式的选择
欧几里得距离、欧式距离公式
$$d=\sqrt{\sum_{i=1}^N|P_i-Q_i|^2}$$
计算代入权值后得到分维矩阵$K^+, K^- $
$$K^+ =\begin{array}{c|c|c|c|c|c|c}{M_{8 \times19}} &-P1 &-P2 &-P3 &-P4 &-T1 &-T2 &-T3 &-F1 &-F2 &-F3 &-F4 &-S1 &-S2 &-S3 &-C1 &-C2 &-A1 &-A2 &-A3\\ \hline 大连港 &0.0258 &0.0446 &0.0608 &0.0365 &0.0548 &0.0702 &0.0871 &0.0497 &0.011 &0.0142 &0.0425 &0.0388 &0.0092 &0.0198 &0.0047 &0.0285 &0.0533 &0.0296 &0.0418\\ \hline 青岛港 &0.0242 &0.0181 &0.0427 &0.0709 &0.041 &0.0884 &0.1086 &0.0418 &0.0054 &0.0104 &0.0345 &0.0181 &0.0584 &0.0266 &0.0085 &0.0035 &0.0411 &0.0203 &0.0223\\ \hline 天津港 &0.0291 &0 &0.0489 &0.0655 &0.0586 &0.0538 &0.0976 &0.0397 &0.0051 &0.0257 &0.0376 &0.0207 &0.0641 &0.0356 &0 &0.011 &0 &0.024 &0.0259\\ \hline 上海港 &0.018 &0.0481 &0 &0.0435 &0 &0 &0 &0 &0.0251 &0.0093 &0 &0 &0.0412 &0.0216 &0.0059 &0.0025 &0.0562 &0 &0.0186\\ \hline 宁波舟山港 &0 &0.009 &0.0265 &0.0574 &0.0054 &0.0091 &0.0166 &0.0257 &0.0111 &0.0066 &0.0006 &0.0052 &0.0693 &0.0189 &0.004 &0.0184 &0.0568 &0 &0.0056\\ \hline 深圳港 &0.0439 &0.0278 &0.0306 &0.0084 &0.0088 &0.0984 &0.1045 &0.0569 &0.0015 &0.0082 &0.016 &0.0078 &0 &0 &0.0293 &0 &0.0095 &0.0398 &0\\ \hline 广州港 &0.0135 &0.0156 &0.0379 &0.0637 &0.0213 &0.0957 &0.0735 &0.0467 &0.0064 &0.0082 &0.0317 &0.0104 &0.0567 &0.0086 &0.0209 &0.002 &0.0506 &0.0249 &0.0362\\ \hline 厦门港 &0.0467 &0.0341 &0.0589 &0 &0.0477 &0.0957 &0.1075 &0.0393 &0 &0 &0.0507 &0.0336 &0.0458 &0.0172 &0.0095 &0.0016 &0.0663 &0.0194 &0.0194\\ \hline \end{array} $$$$K^- =\begin{array}{c|c|c|c|c|c|c}{M_{8 \times19}} &+P1 &+P2 &+P3 &+P4 &+T1 &+T2 &+T3 &+F1 &+F2 &+F3 &+F4 &+S1 &+S2 &+S3 &+C1 &+C2 &+A1 &+A2 &+A3\\ \hline 大连港 &0.0209 &0.0036 &0 &0.0344 &0.0038 &0.0283 &0.0214 &0.0072 &0.0141 &0.0115 &0.0082 &0 &0.0601 &0.0158 &0.0246 &0 &0.013 &0.0102 &0\\ \hline 青岛港 &0.0225 &0.03 &0.0182 &0 &0.0176 &0.01 &0 &0.0151 &0.0197 &0.0153 &0.0162 &0.0207 &0.0109 &0.0089 &0.0208 &0.025 &0.0253 &0.0195 &0.0195\\ \hline 天津港 &0.0176 &0.0481 &0.012 &0.0054 &0 &0.0447 &0.011 &0.0172 &0.02 &0 &0.0131 &0.0181 &0.0052 &0 &0.0293 &0.0175 &0.0663 &0.0157 &0.0159\\ \hline 上海港 &0.0287 &0 &0.0608 &0.0274 &0.0586 &0.0984 &0.1086 &0.0569 &0 &0.0164 &0.0507 &0.0388 &0.0281 &0.0139 &0.0234 &0.0261 &0.0102 &0.0398 &0.0232\\ \hline 宁波舟山港 &0.0467 &0.0392 &0.0344 &0.0135 &0.0532 &0.0893 &0.092 &0.0312 &0.014 &0.0192 &0.0501 &0.0336 &0 &0.0167 &0.0253 &0.0101 &0.0096 &0.0398 &0.0362\\ \hline 深圳港 &0.0028 &0.0204 &0.0303 &0.0625 &0.0498 &0 &0.0041 &0 &0.0236 &0.0175 &0.0347 &0.0311 &0.0693 &0.0356 &0 &0.0285 &0.0568 &0 &0.0418\\ \hline 广州港 &0.0332 &0.0326 &0.023 &0.0072 &0.0373 &0.0027 &0.035 &0.0102 &0.0187 &0.0175 &0.019 &0.0285 &0.0126 &0.027 &0.0084 &0.0266 &0.0158 &0.0149 &0.0056\\ \hline 厦门港 &0 &0.014 &0.002 &0.0709 &0.0109 &0.0027 &0.0011 &0.0177 &0.0251 &0.0257 &0 &0.0052 &0.0235 &0.0184 &0.0198 &0.027 &0 &0.0204 &0.0224\\ \hline \end{array} $$
上述两者合并后矩阵如下
$$K=\begin{array}{c|c|c|c|c|c|c}{M_{8 \times38}} &-P1 &-P2 &-P3 &-P4 &-T1 &-T2 &-T3 &-F1 &-F2 &-F3 &-F4 &-S1 &-S2 &-S3 &-C1 &-C2 &-A1 &-A2 &-A3 &+P1 &+P2 &+P3 &+P4 &+T1 &+T2 &+T3 &+F1 &+F2 &+F3 &+F4 &+S1 &+S2 &+S3 &+C1 &+C2 &+A1 &+A2 &+A3\\ \hline 大连港 &0.0258 &0.0446 &0.0608 &0.0365 &0.0548 &0.0702 &0.0871 &0.0497 &0.011 &0.0142 &0.0425 &0.0388 &0.0092 &0.0198 &0.0047 &0.0285 &0.0533 &0.0296 &0.0418 &0.0258 &0.0446 &0.0608 &0.0365 &0.0548 &0.0702 &0.0871 &0.0497 &0.011 &0.0142 &0.0425 &0.0388 &0.0092 &0.0198 &0.0047 &0.0285 &0.0533 &0.0296 &0.0418\\ \hline 青岛港 &0.0242 &0.0181 &0.0427 &0.0709 &0.041 &0.0884 &0.1086 &0.0418 &0.0054 &0.0104 &0.0345 &0.0181 &0.0584 &0.0266 &0.0085 &0.0035 &0.0411 &0.0203 &0.0223 &0.0242 &0.0181 &0.0427 &0.0709 &0.041 &0.0884 &0.1086 &0.0418 &0.0054 &0.0104 &0.0345 &0.0181 &0.0584 &0.0266 &0.0085 &0.0035 &0.0411 &0.0203 &0.0223\\ \hline 天津港 &0.0291 &0 &0.0489 &0.0655 &0.0586 &0.0538 &0.0976 &0.0397 &0.0051 &0.0257 &0.0376 &0.0207 &0.0641 &0.0356 &0 &0.011 &0 &0.024 &0.0259 &0.0291 &0 &0.0489 &0.0655 &0.0586 &0.0538 &0.0976 &0.0397 &0.0051 &0.0257 &0.0376 &0.0207 &0.0641 &0.0356 &0 &0.011 &0 &0.024 &0.0259\\ \hline 上海港 &0.018 &0.0481 &0 &0.0435 &0 &0 &0 &0 &0.0251 &0.0093 &0 &0 &0.0412 &0.0216 &0.0059 &0.0025 &0.0562 &0 &0.0186 &0.018 &0.0481 &0 &0.0435 &0 &0 &0 &0 &0.0251 &0.0093 &0 &0 &0.0412 &0.0216 &0.0059 &0.0025 &0.0562 &0 &0.0186\\ \hline 宁波舟山港 &0 &0.009 &0.0265 &0.0574 &0.0054 &0.0091 &0.0166 &0.0257 &0.0111 &0.0066 &0.0006 &0.0052 &0.0693 &0.0189 &0.004 &0.0184 &0.0568 &0 &0.0056 &0 &0.009 &0.0265 &0.0574 &0.0054 &0.0091 &0.0166 &0.0257 &0.0111 &0.0066 &0.0006 &0.0052 &0.0693 &0.0189 &0.004 &0.0184 &0.0568 &0 &0.0056\\ \hline 深圳港 &0.0439 &0.0278 &0.0306 &0.0084 &0.0088 &0.0984 &0.1045 &0.0569 &0.0015 &0.0082 &0.016 &0.0078 &0 &0 &0.0293 &0 &0.0095 &0.0398 &0 &0.0439 &0.0278 &0.0306 &0.0084 &0.0088 &0.0984 &0.1045 &0.0569 &0.0015 &0.0082 &0.016 &0.0078 &0 &0 &0.0293 &0 &0.0095 &0.0398 &0\\ \hline 广州港 &0.0135 &0.0156 &0.0379 &0.0637 &0.0213 &0.0957 &0.0735 &0.0467 &0.0064 &0.0082 &0.0317 &0.0104 &0.0567 &0.0086 &0.0209 &0.002 &0.0506 &0.0249 &0.0362 &0.0135 &0.0156 &0.0379 &0.0637 &0.0213 &0.0957 &0.0735 &0.0467 &0.0064 &0.0082 &0.0317 &0.0104 &0.0567 &0.0086 &0.0209 &0.002 &0.0506 &0.0249 &0.0362\\ \hline 厦门港 &0.0467 &0.0341 &0.0589 &0 &0.0477 &0.0957 &0.1075 &0.0393 &0 &0 &0.0507 &0.0336 &0.0458 &0.0172 &0.0095 &0.0016 &0.0663 &0.0194 &0.0194 &0.0467 &0.0341 &0.0589 &0 &0.0477 &0.0957 &0.1075 &0.0393 &0 &0 &0.0507 &0.0336 &0.0458 &0.0172 &0.0095 &0.0016 &0.0663 &0.0194 &0.0194\\ \hline \end{array} $$对距离矩阵$K^+,K^-$依据权重大小方向进行列变换得到$(K_a^+,K_a^-),(K_d^+,K_d^-)$
按照权重由小到大升序方向得到的变换矩阵$K_{a}^+ $ 如下：
$$K_a^+=\begin{array}{c|c|c|c|c|c|c}{M_{8 \times19}} &-F2 &-F3 &-C2 &-C1 &-S3 &-S1 &-A2 &-A3 &-P1 &-P2 &-F4 &-F1 &-T1 &-P3 &-A1 &-S2 &-P4 &-T2 &-T3\\ \hline 大连港 &0.011 &0.0142 &0.0285 &0.0047 &0.0198 &0.0388 &0.0296 &0.0418 &0.0258 &0.0446 &0.0425 &0.0497 &0.0548 &0.0608 &0.0533 &0.0092 &0.0365 &0.0702 &0.0871\\ \hline 青岛港 &0.0054 &0.0104 &0.0035 &0.0085 &0.0266 &0.0181 &0.0203 &0.0223 &0.0242 &0.0181 &0.0345 &0.0418 &0.041 &0.0427 &0.0411 &0.0584 &0.0709 &0.0884 &0.1086\\ \hline 天津港 &0.0051 &0.0257 &0.011 &0 &0.0356 &0.0207 &0.024 &0.0259 &0.0291 &0 &0.0376 &0.0397 &0.0586 &0.0489 &0 &0.0641 &0.0655 &0.0538 &0.0976\\ \hline 上海港 &0.0251 &0.0093 &0.0025 &0.0059 &0.0216 &0 &0 &0.0186 &0.018 &0.0481 &0 &0 &0 &0 &0.0562 &0.0412 &0.0435 &0 &0\\ \hline 宁波舟山港 &0.0111 &0.0066 &0.0184 &0.004 &0.0189 &0.0052 &0 &0.0056 &0 &0.009 &0.0006 &0.0257 &0.0054 &0.0265 &0.0568 &0.0693 &0.0574 &0.0091 &0.0166\\ \hline 深圳港 &0.0015 &0.0082 &0 &0.0293 &0 &0.0078 &0.0398 &0 &0.0439 &0.0278 &0.016 &0.0569 &0.0088 &0.0306 &0.0095 &0 &0.0084 &0.0984 &0.1045\\ \hline 广州港 &0.0064 &0.0082 &0.002 &0.0209 &0.0086 &0.0104 &0.0249 &0.0362 &0.0135 &0.0156 &0.0317 &0.0467 &0.0213 &0.0379 &0.0506 &0.0567 &0.0637 &0.0957 &0.0735\\ \hline 厦门港 &0 &0 &0.0016 &0.0095 &0.0172 &0.0336 &0.0194 &0.0194 &0.0467 &0.0341 &0.0507 &0.0393 &0.0477 &0.0589 &0.0663 &0.0458 &0 &0.0957 &0.1075\\ \hline \end{array} $$按照权重由小到大升序方向得到的变换矩阵$K_{a}^- $ 如下：
$$K_a^-=\begin{array}{c|c|c|c|c|c|c}{M_{8 \times19}} &+F2 &+F3 &+C2 &+C1 &+S3 &+S1 &+A2 &+A3 &+P1 &+P2 &+F4 &+F1 &+T1 &+P3 &+A1 &+S2 &+P4 &+T2 &+T3\\ \hline 大连港 &0.0141 &0.0115 &0 &0.0246 &0.0158 &0 &0.0102 &0 &0.0209 &0.0036 &0.0082 &0.0072 &0.0038 &0 &0.013 &0.0601 &0.0344 &0.0283 &0.0214\\ \hline 青岛港 &0.0197 &0.0153 &0.025 &0.0208 &0.0089 &0.0207 &0.0195 &0.0195 &0.0225 &0.03 &0.0162 &0.0151 &0.0176 &0.0182 &0.0253 &0.0109 &0 &0.01 &0\\ \hline 天津港 &0.02 &0 &0.0175 &0.0293 &0 &0.0181 &0.0157 &0.0159 &0.0176 &0.0481 &0.0131 &0.0172 &0 &0.012 &0.0663 &0.0052 &0.0054 &0.0447 &0.011\\ \hline 上海港 &0 &0.0164 &0.0261 &0.0234 &0.0139 &0.0388 &0.0398 &0.0232 &0.0287 &0 &0.0507 &0.0569 &0.0586 &0.0608 &0.0102 &0.0281 &0.0274 &0.0984 &0.1086\\ \hline 宁波舟山港 &0.014 &0.0192 &0.0101 &0.0253 &0.0167 &0.0336 &0.0398 &0.0362 &0.0467 &0.0392 &0.0501 &0.0312 &0.0532 &0.0344 &0.0096 &0 &0.0135 &0.0893 &0.092\\ \hline 深圳港 &0.0236 &0.0175 &0.0285 &0 &0.0356 &0.0311 &0 &0.0418 &0.0028 &0.0204 &0.0347 &0 &0.0498 &0.0303 &0.0568 &0.0693 &0.0625 &0 &0.0041\\ \hline 广州港 &0.0187 &0.0175 &0.0266 &0.0084 &0.027 &0.0285 &0.0149 &0.0056 &0.0332 &0.0326 &0.019 &0.0102 &0.0373 &0.023 &0.0158 &0.0126 &0.0072 &0.0027 &0.035\\ \hline 厦门港 &0.0251 &0.0257 &0.027 &0.0198 &0.0184 &0.0052 &0.0204 &0.0224 &0 &0.014 &0 &0.0177 &0.0109 &0.002 &0 &0.0235 &0.0709 &0.0027 &0.0011\\ \hline \end{array} $$按照权重由大到小降序方向得到的变换矩阵$K_{d}^+ $ 如下：
$$K_d^+=\begin{array}{c|c|c|c|c|c|c}{M_{8 \times19}} &-T3 &-T2 &-P4 &-S2 &-A1 &-P3 &-T1 &-F1 &-F4 &-P2 &-P1 &-A3 &-A2 &-S1 &-S3 &-C1 &-C2 &-F3 &-F2\\ \hline 大连港 &0.0871 &0.0702 &0.0365 &0.0092 &0.0533 &0.0608 &0.0548 &0.0497 &0.0425 &0.0446 &0.0258 &0.0418 &0.0296 &0.0388 &0.0198 &0.0047 &0.0285 &0.0142 &0.011\\ \hline 青岛港 &0.1086 &0.0884 &0.0709 &0.0584 &0.0411 &0.0427 &0.041 &0.0418 &0.0345 &0.0181 &0.0242 &0.0223 &0.0203 &0.0181 &0.0266 &0.0085 &0.0035 &0.0104 &0.0054\\ \hline 天津港 &0.0976 &0.0538 &0.0655 &0.0641 &0 &0.0489 &0.0586 &0.0397 &0.0376 &0 &0.0291 &0.0259 &0.024 &0.0207 &0.0356 &0 &0.011 &0.0257 &0.0051\\ \hline 上海港 &0 &0 &0.0435 &0.0412 &0.0562 &0 &0 &0 &0 &0.0481 &0.018 &0.0186 &0 &0 &0.0216 &0.0059 &0.0025 &0.0093 &0.0251\\ \hline 宁波舟山港 &0.0166 &0.0091 &0.0574 &0.0693 &0.0568 &0.0265 &0.0054 &0.0257 &0.0006 &0.009 &0 &0.0056 &0 &0.0052 &0.0189 &0.004 &0.0184 &0.0066 &0.0111\\ \hline 深圳港 &0.1045 &0.0984 &0.0084 &0 &0.0095 &0.0306 &0.0088 &0.0569 &0.016 &0.0278 &0.0439 &0 &0.0398 &0.0078 &0 &0.0293 &0 &0.0082 &0.0015\\ \hline 广州港 &0.0735 &0.0957 &0.0637 &0.0567 &0.0506 &0.0379 &0.0213 &0.0467 &0.0317 &0.0156 &0.0135 &0.0362 &0.0249 &0.0104 &0.0086 &0.0209 &0.002 &0.0082 &0.0064\\ \hline 厦门港 &0.1075 &0.0957 &0 &0.0458 &0.0663 &0.0589 &0.0477 &0.0393 &0.0507 &0.0341 &0.0467 &0.0194 &0.0194 &0.0336 &0.0172 &0.0095 &0.0016 &0 &0\\ \hline \end{array} $$按照权重由大到小降序方向得到的变换矩阵$K_{d}^- $ 如下：
$$K_d^-=\begin{array}{c|c|c|c|c|c|c}{M_{8 \times19}} &-T3 &-T2 &-P4 &-S2 &-A1 &-P3 &-T1 &-F1 &-F4 &-P2 &-P1 &-A3 &-A2 &-S1 &-S3 &-C1 &-C2 &-F3 &-F2\\ \hline 大连港 &0.0214 &0.0283 &0.0344 &0.0601 &0.013 &0 &0.0038 &0.0072 &0.0082 &0.0036 &0.0209 &0 &0.0102 &0 &0.0158 &0.0246 &0 &0.0115 &0.0141\\ \hline 青岛港 &0 &0.01 &0 &0.0109 &0.0253 &0.0182 &0.0176 &0.0151 &0.0162 &0.03 &0.0225 &0.0195 &0.0195 &0.0207 &0.0089 &0.0208 &0.025 &0.0153 &0.0197\\ \hline 天津港 &0.011 &0.0447 &0.0054 &0.0052 &0.0663 &0.012 &0 &0.0172 &0.0131 &0.0481 &0.0176 &0.0159 &0.0157 &0.0181 &0 &0.0293 &0.0175 &0 &0.02\\ \hline 上海港 &0.1086 &0.0984 &0.0274 &0.0281 &0.0102 &0.0608 &0.0586 &0.0569 &0.0507 &0 &0.0287 &0.0232 &0.0398 &0.0388 &0.0139 &0.0234 &0.0261 &0.0164 &0\\ \hline 宁波舟山港 &0.092 &0.0893 &0.0135 &0 &0.0096 &0.0344 &0.0532 &0.0312 &0.0501 &0.0392 &0.0467 &0.0362 &0.0398 &0.0336 &0.0167 &0.0253 &0.0101 &0.0192 &0.014\\ \hline 深圳港 &0.0041 &0 &0.0625 &0.0693 &0.0568 &0.0303 &0.0498 &0 &0.0347 &0.0204 &0.0028 &0.0418 &0 &0.0311 &0.0356 &0 &0.0285 &0.0175 &0.0236\\ \hline 广州港 &0.035 &0.0027 &0.0072 &0.0126 &0.0158 &0.023 &0.0373 &0.0102 &0.019 &0.0326 &0.0332 &0.0056 &0.0149 &0.0285 &0.027 &0.0084 &0.0266 &0.0175 &0.0187\\ \hline 厦门港 &0.0011 &0.0027 &0.0709 &0.0235 &0 &0.002 &0.0109 &0.0177 &0 &0.014 &0 &0.0224 &0.0204 &0.0052 &0.0184 &0.0198 &0.027 &0.0257 &0.0251\\ \hline \end{array} $$上述四个矩阵只是简单的根据权重大小的方向，每一列的位置进行了变换。
对变换后的矩阵从左到右进行累加，获得两对累加矩阵
$K_{a}^+ , K_{a}^-$ 分别累加得到一组对抗矩阵$P_{a} , Q_{a}$
其中$K_{a}^+ \longrightarrow P_{a} $
$$P_a=\begin{array}{c|c|c|c|c|c|c}{M_{8 \times19}} &-P_{a}1 &-P_{a}2 &-P_{a}3 &-P_{a}4 &-P_{a}5 &-P_{a}6 &-P_{a}7 &-P_{a}8 &-P_{a}9 &-P_{a}10 &-P_{a}11 &-P_{a}12 &-P_{a}13 &-P_{a}14 &-P_{a}15 &-P_{a}16 &-P_{a}17 &-P_{a}18 &-P_{a}19\\ \hline 大连港 &0.011 &0.0253 &0.0538 &0.0585 &0.0782 &0.1171 &0.1466 &0.1884 &0.2142 &0.2588 &0.3013 &0.351 &0.4058 &0.4667 &0.52 &0.5292 &0.5656 &0.6358 &0.7229\\ \hline 青岛港 &0.0054 &0.0158 &0.0194 &0.0279 &0.0545 &0.0726 &0.0929 &0.1151 &0.1394 &0.1575 &0.192 &0.2338 &0.2748 &0.3174 &0.3585 &0.4169 &0.4878 &0.5762 &0.6848\\ \hline 天津港 &0.0051 &0.0308 &0.0419 &0.0419 &0.0775 &0.0982 &0.1222 &0.1481 &0.1772 &0.1772 &0.2148 &0.2545 &0.3131 &0.362 &0.362 &0.4261 &0.4916 &0.5453 &0.643\\ \hline 上海港 &0.0251 &0.0344 &0.0369 &0.0428 &0.0644 &0.0644 &0.0644 &0.083 &0.101 &0.1491 &0.1491 &0.1491 &0.1491 &0.1491 &0.2053 &0.2465 &0.29 &0.29 &0.29\\ \hline 宁波舟山港 &0.0111 &0.0177 &0.0361 &0.0401 &0.059 &0.0642 &0.0642 &0.0698 &0.0698 &0.0787 &0.0794 &0.105 &0.1105 &0.1369 &0.1937 &0.263 &0.3204 &0.3295 &0.3461\\ \hline 深圳港 &0.0015 &0.0097 &0.0097 &0.039 &0.039 &0.0468 &0.0865 &0.0865 &0.1304 &0.1582 &0.1741 &0.2311 &0.2399 &0.2705 &0.28 &0.28 &0.2884 &0.3868 &0.4913\\ \hline 广州港 &0.0064 &0.0146 &0.0166 &0.0375 &0.0461 &0.0564 &0.0813 &0.1176 &0.131 &0.1466 &0.1783 &0.225 &0.2463 &0.2842 &0.3348 &0.3915 &0.4552 &0.5509 &0.6244\\ \hline 厦门港 &0 &0 &0.0016 &0.0111 &0.0283 &0.0619 &0.0813 &0.1007 &0.1474 &0.1815 &0.2322 &0.2714 &0.3192 &0.378 &0.4444 &0.4902 &0.4902 &0.5859 &0.6934\\ \hline \end{array} $$其中$K_{a}^- \longrightarrow Q_{a} $
$$Q_a=\begin{array}{c|c|c|c|c|c|c}{M_{8 \times19}} &+Q_{a}1 &+Q_{a}2 &+Q_{a}3 &+Q_{a}4 &+Q_{a}5 &+Q_{a}6 &+Q_{a}7 &+Q_{a}8 &+Q_{a}9 &+Q_{a}10 &+Q_{a}11 &+Q_{a}12 &+Q_{a}13 &+Q_{a}14 &+Q_{a}15 &+Q_{a}16 &+Q_{a}17 &+Q_{a}18 &+Q_{a}19\\ \hline 大连港 &0.0141 &0.0256 &0.0256 &0.0502 &0.066 &0.066 &0.0762 &0.0762 &0.0971 &0.1006 &0.1088 &0.116 &0.1198 &0.1198 &0.1328 &0.1929 &0.2274 &0.2556 &0.2771\\ \hline 青岛港 &0.0197 &0.035 &0.06 &0.0808 &0.0897 &0.1104 &0.1299 &0.1495 &0.1719 &0.202 &0.2182 &0.2333 &0.2509 &0.269 &0.2943 &0.3052 &0.3052 &0.3152 &0.3152\\ \hline 天津港 &0.02 &0.02 &0.0375 &0.0668 &0.0668 &0.0849 &0.1006 &0.1165 &0.1341 &0.1822 &0.1953 &0.2126 &0.2126 &0.2245 &0.2909 &0.296 &0.3014 &0.3461 &0.357\\ \hline 上海港 &0 &0.0164 &0.0425 &0.0659 &0.0798 &0.1186 &0.1584 &0.1816 &0.2103 &0.2103 &0.261 &0.3179 &0.3765 &0.4374 &0.4475 &0.4756 &0.503 &0.6014 &0.71\\ \hline 宁波舟山港 &0.014 &0.0332 &0.0432 &0.0685 &0.0852 &0.1188 &0.1586 &0.1948 &0.2415 &0.2807 &0.3308 &0.362 &0.4152 &0.4495 &0.4591 &0.4591 &0.4726 &0.5619 &0.6539\\ \hline 深圳港 &0.0236 &0.0411 &0.0697 &0.0697 &0.1052 &0.1363 &0.1363 &0.1781 &0.1809 &0.2013 &0.236 &0.236 &0.2858 &0.316 &0.3729 &0.4421 &0.5046 &0.5046 &0.5087\\ \hline 广州港 &0.0187 &0.0362 &0.0628 &0.0712 &0.0981 &0.1266 &0.1415 &0.147 &0.1803 &0.2129 &0.2318 &0.242 &0.2793 &0.3023 &0.318 &0.3306 &0.3378 &0.3406 &0.3756\\ \hline 厦门港 &0.0251 &0.0508 &0.0778 &0.0976 &0.1159 &0.1211 &0.1415 &0.1639 &0.1639 &0.1779 &0.1779 &0.1956 &0.2065 &0.2084 &0.2084 &0.2319 &0.3028 &0.3055 &0.3066\\ \hline \end{array} $$上述两者合并后矩阵如下
$$PaQa=\begin{array}{c|c|c|c|c|c|c}{M_{8 \times38}} &-P_{a}1 &-P_{a}2 &-P_{a}3 &-P_{a}4 &-P_{a}5 &-P_{a}6 &-P_{a}7 &-P_{a}8 &-P_{a}9 &-P_{a}10 &-P_{a}11 &-P_{a}12 &-P_{a}13 &-P_{a}14 &-P_{a}15 &-P_{a}16 &-P_{a}17 &-P_{a}18 &-P_{a}19 &+Q_{a}1 &+Q_{a}2 &+Q_{a}3 &+Q_{a}4 &+Q_{a}5 &+Q_{a}6 &+Q_{a}7 &+Q_{a}8 &+Q_{a}9 &+Q_{a}10 &+Q_{a}11 &+Q_{a}12 &+Q_{a}13 &+Q_{a}14 &+Q_{a}15 &+Q_{a}16 &+Q_{a}17 &+Q_{a}18 &+Q_{a}19\\ \hline 大连港 &0.011 &0.0253 &0.0538 &0.0585 &0.0782 &0.1171 &0.1466 &0.1884 &0.2142 &0.2588 &0.3013 &0.351 &0.4058 &0.4667 &0.52 &0.5292 &0.5656 &0.6358 &0.7229 &0.0141 &0.0256 &0.0256 &0.0502 &0.066 &0.066 &0.0762 &0.0762 &0.0971 &0.1006 &0.1088 &0.116 &0.1198 &0.1198 &0.1328 &0.1929 &0.2274 &0.2556 &0.2771\\ \hline 青岛港 &0.0054 &0.0158 &0.0194 &0.0279 &0.0545 &0.0726 &0.0929 &0.1151 &0.1394 &0.1575 &0.192 &0.2338 &0.2748 &0.3174 &0.3585 &0.4169 &0.4878 &0.5762 &0.6848 &0.0197 &0.035 &0.06 &0.0808 &0.0897 &0.1104 &0.1299 &0.1495 &0.1719 &0.202 &0.2182 &0.2333 &0.2509 &0.269 &0.2943 &0.3052 &0.3052 &0.3152 &0.3152\\ \hline 天津港 &0.0051 &0.0308 &0.0419 &0.0419 &0.0775 &0.0982 &0.1222 &0.1481 &0.1772 &0.1772 &0.2148 &0.2545 &0.3131 &0.362 &0.362 &0.4261 &0.4916 &0.5453 &0.643 &0.02 &0.02 &0.0375 &0.0668 &0.0668 &0.0849 &0.1006 &0.1165 &0.1341 &0.1822 &0.1953 &0.2126 &0.2126 &0.2245 &0.2909 &0.296 &0.3014 &0.3461 &0.357\\ \hline 上海港 &0.0251 &0.0344 &0.0369 &0.0428 &0.0644 &0.0644 &0.0644 &0.083 &0.101 &0.1491 &0.1491 &0.1491 &0.1491 &0.1491 &0.2053 &0.2465 &0.29 &0.29 &0.29 &0 &0.0164 &0.0425 &0.0659 &0.0798 &0.1186 &0.1584 &0.1816 &0.2103 &0.2103 &0.261 &0.3179 &0.3765 &0.4374 &0.4475 &0.4756 &0.503 &0.6014 &0.71\\ \hline 宁波舟山港 &0.0111 &0.0177 &0.0361 &0.0401 &0.059 &0.0642 &0.0642 &0.0698 &0.0698 &0.0787 &0.0794 &0.105 &0.1105 &0.1369 &0.1937 &0.263 &0.3204 &0.3295 &0.3461 &0.014 &0.0332 &0.0432 &0.0685 &0.0852 &0.1188 &0.1586 &0.1948 &0.2415 &0.2807 &0.3308 &0.362 &0.4152 &0.4495 &0.4591 &0.4591 &0.4726 &0.5619 &0.6539\\ \hline 深圳港 &0.0015 &0.0097 &0.0097 &0.039 &0.039 &0.0468 &0.0865 &0.0865 &0.1304 &0.1582 &0.1741 &0.2311 &0.2399 &0.2705 &0.28 &0.28 &0.2884 &0.3868 &0.4913 &0.0236 &0.0411 &0.0697 &0.0697 &0.1052 &0.1363 &0.1363 &0.1781 &0.1809 &0.2013 &0.236 &0.236 &0.2858 &0.316 &0.3729 &0.4421 &0.5046 &0.5046 &0.5087\\ \hline 广州港 &0.0064 &0.0146 &0.0166 &0.0375 &0.0461 &0.0564 &0.0813 &0.1176 &0.131 &0.1466 &0.1783 &0.225 &0.2463 &0.2842 &0.3348 &0.3915 &0.4552 &0.5509 &0.6244 &0.0187 &0.0362 &0.0628 &0.0712 &0.0981 &0.1266 &0.1415 &0.147 &0.1803 &0.2129 &0.2318 &0.242 &0.2793 &0.3023 &0.318 &0.3306 &0.3378 &0.3406 &0.3756\\ \hline 厦门港 &0 &0 &0.0016 &0.0111 &0.0283 &0.0619 &0.0813 &0.1007 &0.1474 &0.1815 &0.2322 &0.2714 &0.3192 &0.378 &0.4444 &0.4902 &0.4902 &0.5859 &0.6934 &0.0251 &0.0508 &0.0778 &0.0976 &0.1159 &0.1211 &0.1415 &0.1639 &0.1639 &0.1779 &0.1779 &0.1956 &0.2065 &0.2084 &0.2084 &0.2319 &0.3028 &0.3055 &0.3066\\ \hline \end{array} $$$K_{d}^+ , K_{d}^-$ 分别累加得到一组对抗矩阵$P_{d} , Q_{d}$
其中$K_{d}^+ \longrightarrow P_{d} $
$$P_d=\begin{array}{c|c|c|c|c|c|c}{M_{8 \times19}} &-P_{d}1 &-P_{d}2 &-P_{d}3 &-P_{d}4 &-P_{d}5 &-P_{d}6 &-P_{d}7 &-P_{d}8 &-P_{d}9 &-P_{d}10 &-P_{d}11 &-P_{d}12 &-P_{d}13 &-P_{d}14 &-P_{d}15 &-P_{d}16 &-P_{d}17 &-P_{d}18 &-P_{d}19\\ \hline 大连港 &0.0871 &0.1573 &0.1938 &0.2029 &0.2563 &0.3171 &0.3719 &0.4217 &0.4641 &0.5087 &0.5345 &0.5763 &0.6059 &0.6447 &0.6645 &0.6691 &0.6977 &0.7119 &0.7229\\ \hline 青岛港 &0.1086 &0.197 &0.2679 &0.3263 &0.3673 &0.41 &0.451 &0.4928 &0.5273 &0.5454 &0.5697 &0.5919 &0.6122 &0.6303 &0.6569 &0.6654 &0.6689 &0.6794 &0.6848\\ \hline 天津港 &0.0976 &0.1514 &0.2169 &0.281 &0.281 &0.3299 &0.3885 &0.4282 &0.4658 &0.4658 &0.4948 &0.5208 &0.5448 &0.5655 &0.6011 &0.6011 &0.6121 &0.6379 &0.643\\ \hline 上海港 &0 &0 &0.0435 &0.0847 &0.1409 &0.1409 &0.1409 &0.1409 &0.1409 &0.1891 &0.207 &0.2256 &0.2256 &0.2256 &0.2472 &0.2532 &0.2556 &0.2649 &0.29\\ \hline 宁波舟山港 &0.0166 &0.0257 &0.0831 &0.1523 &0.2091 &0.2356 &0.241 &0.2667 &0.2673 &0.2763 &0.2763 &0.2818 &0.2818 &0.287 &0.3059 &0.3099 &0.3284 &0.335 &0.3461\\ \hline 深圳港 &0.1045 &0.2029 &0.2113 &0.2113 &0.2208 &0.2514 &0.2602 &0.3172 &0.3331 &0.3609 &0.4048 &0.4048 &0.4445 &0.4523 &0.4523 &0.4816 &0.4816 &0.4898 &0.4913\\ \hline 广州港 &0.0735 &0.1692 &0.233 &0.2896 &0.3402 &0.3781 &0.3994 &0.4461 &0.4778 &0.4934 &0.5068 &0.5431 &0.568 &0.5783 &0.5869 &0.6078 &0.6098 &0.618 &0.6244\\ \hline 厦门港 &0.1075 &0.2032 &0.2032 &0.249 &0.3154 &0.3742 &0.422 &0.4612 &0.5119 &0.546 &0.5927 &0.6121 &0.6315 &0.6651 &0.6823 &0.6918 &0.6934 &0.6934 &0.6934\\ \hline \end{array} $$其中$K_{d}^- \longrightarrow Q_{d} $
$$Q_d=\begin{array}{c|c|c|c|c|c|c}{M_{8 \times19}} &Q_{d}1 &Q_{d}2 &Q_{d}3 &Q_{d}4 &Q_{d}5 &Q_{d}6 &Q_{d}7 &Q_{d}8 &Q_{d}9 &Q_{d}10 &Q_{d}11 &Q_{d}12 &Q_{d}13 &Q_{d}14 &Q_{d}15 &Q_{d}16 &Q_{d}17 &Q_{d}18 &Q_{d}19\\ \hline 大连港 &0.0214 &0.0497 &0.0841 &0.1442 &0.1573 &0.1573 &0.161 &0.1682 &0.1764 &0.18 &0.2009 &0.2009 &0.2111 &0.2111 &0.2269 &0.2515 &0.2515 &0.263 &0.2771\\ \hline 青岛港 &0 &0.01 &0.01 &0.0209 &0.0462 &0.0644 &0.0819 &0.0971 &0.1133 &0.1433 &0.1658 &0.1853 &0.2048 &0.2255 &0.2344 &0.2552 &0.2802 &0.2956 &0.3152\\ \hline 天津港 &0.011 &0.0556 &0.061 &0.0662 &0.1325 &0.1445 &0.1445 &0.1617 &0.1748 &0.2229 &0.2406 &0.2564 &0.2722 &0.2903 &0.2903 &0.3196 &0.337 &0.337 &0.357\\ \hline 上海港 &0.1086 &0.207 &0.2344 &0.2624 &0.2726 &0.3335 &0.3921 &0.449 &0.4997 &0.4997 &0.5284 &0.5516 &0.5914 &0.6302 &0.6441 &0.6675 &0.6936 &0.71 &0.71\\ \hline 宁波舟山港 &0.092 &0.1813 &0.1948 &0.1948 &0.2044 &0.2388 &0.292 &0.3232 &0.3732 &0.4124 &0.4591 &0.4954 &0.5351 &0.5688 &0.5854 &0.6107 &0.6208 &0.64 &0.6539\\ \hline 深圳港 &0.0041 &0.0041 &0.0666 &0.1358 &0.1927 &0.2229 &0.2727 &0.2727 &0.3074 &0.3278 &0.3306 &0.3724 &0.3724 &0.4035 &0.439 &0.439 &0.4676 &0.4851 &0.5087\\ \hline 广州港 &0.035 &0.0378 &0.045 &0.0576 &0.0733 &0.0963 &0.1336 &0.1438 &0.1627 &0.1953 &0.2286 &0.2341 &0.249 &0.2775 &0.3044 &0.3128 &0.3394 &0.3569 &0.3756\\ \hline 厦门港 &0.0011 &0.0038 &0.0747 &0.0981 &0.0981 &0.1001 &0.111 &0.1287 &0.1287 &0.1427 &0.1427 &0.1651 &0.1855 &0.1906 &0.209 &0.2288 &0.2558 &0.2815 &0.3066\\ \hline \end{array} $$上述两者合并后矩阵如下
$$PdQd=\begin{array}{c|c|c|c|c|c|c}{M_{8 \times38}} &-P_{d}1 &-P_{d}2 &-P_{d}3 &-P_{d}4 &-P_{d}5 &-P_{d}6 &-P_{d}7 &-P_{d}8 &-P_{d}9 &-P_{d}10 &-P_{d}11 &-P_{d}12 &-P_{d}13 &-P_{d}14 &-P_{d}15 &-P_{d}16 &-P_{d}17 &-P_{d}18 &-P_{d}19 &Q_{d}1 &Q_{d}2 &Q_{d}3 &Q_{d}4 &Q_{d}5 &Q_{d}6 &Q_{d}7 &Q_{d}8 &Q_{d}9 &Q_{d}10 &Q_{d}11 &Q_{d}12 &Q_{d}13 &Q_{d}14 &Q_{d}15 &Q_{d}16 &Q_{d}17 &Q_{d}18 &Q_{d}19\\ \hline 大连港 &0.0871 &0.1573 &0.1938 &0.2029 &0.2563 &0.3171 &0.3719 &0.4217 &0.4641 &0.5087 &0.5345 &0.5763 &0.6059 &0.6447 &0.6645 &0.6691 &0.6977 &0.7119 &0.7229 &0.0214 &0.0497 &0.0841 &0.1442 &0.1573 &0.1573 &0.161 &0.1682 &0.1764 &0.18 &0.2009 &0.2009 &0.2111 &0.2111 &0.2269 &0.2515 &0.2515 &0.263 &0.2771\\ \hline 青岛港 &0.1086 &0.197 &0.2679 &0.3263 &0.3673 &0.41 &0.451 &0.4928 &0.5273 &0.5454 &0.5697 &0.5919 &0.6122 &0.6303 &0.6569 &0.6654 &0.6689 &0.6794 &0.6848 &0 &0.01 &0.01 &0.0209 &0.0462 &0.0644 &0.0819 &0.0971 &0.1133 &0.1433 &0.1658 &0.1853 &0.2048 &0.2255 &0.2344 &0.2552 &0.2802 &0.2956 &0.3152\\ \hline 天津港 &0.0976 &0.1514 &0.2169 &0.281 &0.281 &0.3299 &0.3885 &0.4282 &0.4658 &0.4658 &0.4948 &0.5208 &0.5448 &0.5655 &0.6011 &0.6011 &0.6121 &0.6379 &0.643 &0.011 &0.0556 &0.061 &0.0662 &0.1325 &0.1445 &0.1445 &0.1617 &0.1748 &0.2229 &0.2406 &0.2564 &0.2722 &0.2903 &0.2903 &0.3196 &0.337 &0.337 &0.357\\ \hline 上海港 &0 &0 &0.0435 &0.0847 &0.1409 &0.1409 &0.1409 &0.1409 &0.1409 &0.1891 &0.207 &0.2256 &0.2256 &0.2256 &0.2472 &0.2532 &0.2556 &0.2649 &0.29 &0.1086 &0.207 &0.2344 &0.2624 &0.2726 &0.3335 &0.3921 &0.449 &0.4997 &0.4997 &0.5284 &0.5516 &0.5914 &0.6302 &0.6441 &0.6675 &0.6936 &0.71 &0.71\\ \hline 宁波舟山港 &0.0166 &0.0257 &0.0831 &0.1523 &0.2091 &0.2356 &0.241 &0.2667 &0.2673 &0.2763 &0.2763 &0.2818 &0.2818 &0.287 &0.3059 &0.3099 &0.3284 &0.335 &0.3461 &0.092 &0.1813 &0.1948 &0.1948 &0.2044 &0.2388 &0.292 &0.3232 &0.3732 &0.4124 &0.4591 &0.4954 &0.5351 &0.5688 &0.5854 &0.6107 &0.6208 &0.64 &0.6539\\ \hline 深圳港 &0.1045 &0.2029 &0.2113 &0.2113 &0.2208 &0.2514 &0.2602 &0.3172 &0.3331 &0.3609 &0.4048 &0.4048 &0.4445 &0.4523 &0.4523 &0.4816 &0.4816 &0.4898 &0.4913 &0.0041 &0.0041 &0.0666 &0.1358 &0.1927 &0.2229 &0.2727 &0.2727 &0.3074 &0.3278 &0.3306 &0.3724 &0.3724 &0.4035 &0.439 &0.439 &0.4676 &0.4851 &0.5087\\ \hline 广州港 &0.0735 &0.1692 &0.233 &0.2896 &0.3402 &0.3781 &0.3994 &0.4461 &0.4778 &0.4934 &0.5068 &0.5431 &0.568 &0.5783 &0.5869 &0.6078 &0.6098 &0.618 &0.6244 &0.035 &0.0378 &0.045 &0.0576 &0.0733 &0.0963 &0.1336 &0.1438 &0.1627 &0.1953 &0.2286 &0.2341 &0.249 &0.2775 &0.3044 &0.3128 &0.3394 &0.3569 &0.3756\\ \hline 厦门港 &0.1075 &0.2032 &0.2032 &0.249 &0.3154 &0.3742 &0.422 &0.4612 &0.5119 &0.546 &0.5927 &0.6121 &0.6315 &0.6651 &0.6823 &0.6918 &0.6934 &0.6934 &0.6934 &0.0011 &0.0038 &0.0747 &0.0981 &0.0981 &0.1001 &0.111 &0.1287 &0.1287 &0.1427 &0.1427 &0.1651 &0.1855 &0.1906 &0.209 &0.2288 &0.2558 &0.2815 &0.3066\\ \hline \end{array} $$根据带权值的距离公式，得到距离矩阵$ \{-d^+, d^- \}$如下
$$Dist=\begin{array}{c|c|c|c|c|c|c}{M_{8 \times2}} &-d^+ &d^-\\ \hline 大连港 &0.19 &0.09\\ \hline 青岛港 &0.1981 &0.0797\\ \hline 天津港 &0.185 &0.1105\\ \hline 上海港 &0.1047 &0.2054\\ \hline 宁波舟山港 &0.1187 &0.1831\\ \hline 深圳港 &0.1748 &0.1504\\ \hline 广州港 &0.1804 &0.0973\\ \hline 厦门港 &0.2066 &0.0995\\ \hline \end{array} $$
设定的贴近度公式
类似曼哈顿距离公式,最常用的贴近度公式$$ 对正理想点的贴近度 \quad \quad C_i^+ ＝ \frac{ d_i^-} { d_i^- + d_i^+} $$$$ 对负理想点的贴近度 \quad \quad C_i^- ＝ \frac{ d_i^+} { d_i^- + d_i^+} $$
计算后的贴近度矩阵如下
$$Similar=\begin{array}{c|c|c|c|c|c|c}{M_{8 \times2}} &C^+ &-C^-\\ \hline 大连港 &0.3214 &0.6786\\ \hline 青岛港 &0.2868 &0.7132\\ \hline 天津港 &0.3738 &0.6262\\ \hline 上海港 &0.6624 &0.3376\\ \hline 宁波舟山港 &0.6068 &0.3932\\ \hline 深圳港 &0.4626 &0.5374\\ \hline 广州港 &0.3503 &0.6497\\ \hline 厦门港 &0.3251 &0.6749\\ \hline \end{array} $$
TOPSIS——AISM联合求解夹逼过程的理解
