TOPSIS——AISM联合求解过程
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原始数据如下
$$ \begin{array}{c|c|c|c|c|c|c}{M_{13 \times5}} &DO &COD(Mn) &COD(Cr) &BOD(5) &TP\\ \hline 白沙 &0.105 &0.593 &0.708 &1 &0.655\\ \hline 黄谦 &0.474 &0.593 &0.308 &0 &0.195\\ \hline 望龙门 &0.368 &0.519 &0.083 &0.579 &0\\ \hline 寸滩 &0.316 &0.481 &0 &0.526 &0.164\\ \hline 黄草峡 &0.316 &1 &0.125 &0.105 &0.425\\ \hline 鸭嘴石 &0.158 &0.222 &0.917 &0.368 &0.473\\ \hline 美女啧 &0.474 &0.333 &1 &0.474 &0.451\\ \hline 米市圈 &0.368 &0.593 &0.6 &0.263 &0.447\\ \hline 九条沟 &0.842 &0.111 &0.067 &0.158 &1\\ \hline 沱口 &0.632 &0 &0.683 &0.368 &0.451\\ \hline 红砂啧 &1 &0.111 &0.392 &0.368 &0.465\\ \hline 晒网坝 &0.947 &0.407 &0.333 &0.263 &0.429\\ \hline 盐码头 &0 &0.222 &0.642 &0.895 &0.429\\ \hline \end{array} $$
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
$$ \begin{array}{c|c|c|c|c|c|c}{M_{13 \times5}} &DO &COD(Mn) &COD(Cr) &BOD(5) &TP\\ \hline 白沙 &0.105 &0.593 &0.708 &1 &0.655\\ \hline 黄谦 &0.474 &0.593 &0.308 &0 &0.195\\ \hline 望龙门 &0.368 &0.519 &0.083 &0.579 &0\\ \hline 寸滩 &0.316 &0.481 &0 &0.526 &0.164\\ \hline 黄草峡 &0.316 &1 &0.125 &0.105 &0.425\\ \hline 鸭嘴石 &0.158 &0.222 &0.917 &0.368 &0.473\\ \hline 美女啧 &0.474 &0.333 &1 &0.474 &0.451\\ \hline 米市圈 &0.368 &0.593 &0.6 &0.263 &0.447\\ \hline 九条沟 &0.842 &0.111 &0.067 &0.158 &1\\ \hline 沱口 &0.632 &0 &0.683 &0.368 &0.451\\ \hline 红砂啧 &1 &0.111 &0.392 &0.368 &0.465\\ \hline 晒网坝 &0.947 &0.407 &0.333 &0.263 &0.429\\ \hline 盐码头 &0 &0.222 &0.642 &0.895 &0.429\\ \hline \end{array} $$
正极值点构成
$$ \begin{array}{c|c|c|c|c|c|c}{M_{1 \times5}} &DO &COD(Mn) &COD(Cr) &BOD(5) &TP\\ \hline \mathbf{Max} &1 &1 &1 &1 &1\\ \hline \end{array} $$负极值点构成
$$ \begin{array}{c|c|c|c|c|c|c}{M_{1 \times5}} &DO &COD(Mn) &COD(Cr) &BOD(5) &TP\\ \hline \mathbf{Min} &0 &0 &0 &0 &0\\ \hline \end{array} $$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
$$ \begin{array}{c|c|c|c|c|c|c}{M_{2 \times5}} &DO &COD(Mn) &COD(Cr) &BOD(5) &TP\\ \hline EWM所得权重 &0.2024 &0.2024 &0.2498 &0.2034 &0.1419\\ \hline 权重大小顺序 &3 &4 &1 &2 &5\\ \hline \end{array} $$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^- $
$$K^+ =\begin{array}{c|c|c|c|c|c|c}{M_{13 \times5}} &-DO &-COD(Mn) &-COD(Cr) &-BOD(5) &-TP\\ \hline 白沙 &0.1812 &0.0824 &0.0729 &0 &0.049\\ \hline 黄谦 &0.1065 &0.0824 &0.1729 &0.2034 &0.1143\\ \hline 望龙门 &0.1279 &0.0974 &0.2291 &0.0856 &0.1419\\ \hline 寸滩 &0.1385 &0.1051 &0.2498 &0.0964 &0.1187\\ \hline 黄草峡 &0.1385 &0 &0.2186 &0.1821 &0.0816\\ \hline 鸭嘴石 &0.1704 &0.1575 &0.0207 &0.1286 &0.0748\\ \hline 美女啧 &0.1065 &0.135 &0 &0.107 &0.0779\\ \hline 米市圈 &0.1279 &0.0824 &0.0999 &0.1499 &0.0785\\ \hline 九条沟 &0.032 &0.1799 &0.2331 &0.1713 &0\\ \hline 沱口 &0.0745 &0.2024 &0.0792 &0.1286 &0.0779\\ \hline 红砂啧 &0 &0.1799 &0.1519 &0.1286 &0.0759\\ \hline 晒网坝 &0.0107 &0.12 &0.1666 &0.1499 &0.081\\ \hline 盐码头 &0.2024 &0.1575 &0.0894 &0.0214 &0.081\\ \hline \end{array} $$$$K^- =\begin{array}{c|c|c|c|c|c|c}{M_{13 \times5}} &+DO &+COD(Mn) &+COD(Cr) &+BOD(5) &+TP\\ \hline 白沙 &0.0213 &0.12 &0.1769 &0.2034 &0.093\\ \hline 黄谦 &0.0959 &0.12 &0.0769 &0 &0.0277\\ \hline 望龙门 &0.0745 &0.1051 &0.0207 &0.1178 &0\\ \hline 寸滩 &0.064 &0.0974 &0 &0.107 &0.0233\\ \hline 黄草峡 &0.064 &0.2024 &0.0312 &0.0214 &0.0603\\ \hline 鸭嘴石 &0.032 &0.0449 &0.2291 &0.0749 &0.0671\\ \hline 美女啧 &0.0959 &0.0674 &0.2498 &0.0964 &0.064\\ \hline 米市圈 &0.0745 &0.12 &0.1499 &0.0535 &0.0634\\ \hline 九条沟 &0.1704 &0.0225 &0.0167 &0.0321 &0.1419\\ \hline 沱口 &0.1279 &0 &0.1706 &0.0749 &0.064\\ \hline 红砂啧 &0.2024 &0.0225 &0.0979 &0.0749 &0.066\\ \hline 晒网坝 &0.1917 &0.0824 &0.0832 &0.0535 &0.0609\\ \hline 盐码头 &0 &0.0449 &0.1604 &0.1821 &0.0609\\ \hline \end{array} $$
上述两者合并后矩阵如下
$$K=\begin{array}{c|c|c|c|c|c|c}{M_{13 \times10}} &-DO &-COD(Mn) &-COD(Cr) &-BOD(5) &-TP &+DO &+COD(Mn) &+COD(Cr) &+BOD(5) &+TP\\ \hline 白沙 &0.1812 &0.0824 &0.0729 &0 &0.049 &0.1812 &0.0824 &0.0729 &0 &0.049\\ \hline 黄谦 &0.1065 &0.0824 &0.1729 &0.2034 &0.1143 &0.1065 &0.0824 &0.1729 &0.2034 &0.1143\\ \hline 望龙门 &0.1279 &0.0974 &0.2291 &0.0856 &0.1419 &0.1279 &0.0974 &0.2291 &0.0856 &0.1419\\ \hline 寸滩 &0.1385 &0.1051 &0.2498 &0.0964 &0.1187 &0.1385 &0.1051 &0.2498 &0.0964 &0.1187\\ \hline 黄草峡 &0.1385 &0 &0.2186 &0.1821 &0.0816 &0.1385 &0 &0.2186 &0.1821 &0.0816\\ \hline 鸭嘴石 &0.1704 &0.1575 &0.0207 &0.1286 &0.0748 &0.1704 &0.1575 &0.0207 &0.1286 &0.0748\\ \hline 美女啧 &0.1065 &0.135 &0 &0.107 &0.0779 &0.1065 &0.135 &0 &0.107 &0.0779\\ \hline 米市圈 &0.1279 &0.0824 &0.0999 &0.1499 &0.0785 &0.1279 &0.0824 &0.0999 &0.1499 &0.0785\\ \hline 九条沟 &0.032 &0.1799 &0.2331 &0.1713 &0 &0.032 &0.1799 &0.2331 &0.1713 &0\\ \hline 沱口 &0.0745 &0.2024 &0.0792 &0.1286 &0.0779 &0.0745 &0.2024 &0.0792 &0.1286 &0.0779\\ \hline 红砂啧 &0 &0.1799 &0.1519 &0.1286 &0.0759 &0 &0.1799 &0.1519 &0.1286 &0.0759\\ \hline 晒网坝 &0.0107 &0.12 &0.1666 &0.1499 &0.081 &0.0107 &0.12 &0.1666 &0.1499 &0.081\\ \hline 盐码头 &0.2024 &0.1575 &0.0894 &0.0214 &0.081 &0.2024 &0.1575 &0.0894 &0.0214 &0.081\\ \hline \end{array} $$对距离矩阵$K^+,K^-$依据权重大小方向进行列变换得到$(K_a^+,K_a^-)$
按照权重由小到大升序方向得到的变换矩阵$K_{a}^+ $ 如下：
$$K_a^+=\begin{array}{c|c|c|c|c|c|c}{M_{13 \times5}} &-TP &-COD(Mn) &-DO &-BOD(5) &-COD(Cr)\\ \hline 白沙 &0.049 &0.0824 &0.1812 &0 &0.0729\\ \hline 黄谦 &0.1143 &0.0824 &0.1065 &0.2034 &0.1729\\ \hline 望龙门 &0.1419 &0.0974 &0.1279 &0.0856 &0.2291\\ \hline 寸滩 &0.1187 &0.1051 &0.1385 &0.0964 &0.2498\\ \hline 黄草峡 &0.0816 &0 &0.1385 &0.1821 &0.2186\\ \hline 鸭嘴石 &0.0748 &0.1575 &0.1704 &0.1286 &0.0207\\ \hline 美女啧 &0.0779 &0.135 &0.1065 &0.107 &0\\ \hline 米市圈 &0.0785 &0.0824 &0.1279 &0.1499 &0.0999\\ \hline 九条沟 &0 &0.1799 &0.032 &0.1713 &0.2331\\ \hline 沱口 &0.0779 &0.2024 &0.0745 &0.1286 &0.0792\\ \hline 红砂啧 &0.0759 &0.1799 &0 &0.1286 &0.1519\\ \hline 晒网坝 &0.081 &0.12 &0.0107 &0.1499 &0.1666\\ \hline 盐码头 &0.081 &0.1575 &0.2024 &0.0214 &0.0894\\ \hline \end{array} $$按照权重由小到大升序方向得到的变换矩阵$K_{a}^- $ 如下：
$$K_a^-=\begin{array}{c|c|c|c|c|c|c}{M_{13 \times5}} &+TP &+COD(Mn) &+DO &+BOD(5) &+COD(Cr)\\ \hline 白沙 &0.093 &0.12 &0.0213 &0.2034 &0.1769\\ \hline 黄谦 &0.0277 &0.12 &0.0959 &0 &0.0769\\ \hline 望龙门 &0 &0.1051 &0.0745 &0.1178 &0.0207\\ \hline 寸滩 &0.0233 &0.0974 &0.064 &0.107 &0\\ \hline 黄草峡 &0.0603 &0.2024 &0.064 &0.0214 &0.0312\\ \hline 鸭嘴石 &0.0671 &0.0449 &0.032 &0.0749 &0.2291\\ \hline 美女啧 &0.064 &0.0674 &0.0959 &0.0964 &0.2498\\ \hline 米市圈 &0.0634 &0.12 &0.0745 &0.0535 &0.1499\\ \hline 九条沟 &0.1419 &0.0225 &0.1704 &0.0321 &0.0167\\ \hline 沱口 &0.064 &0 &0.1279 &0.0749 &0.1706\\ \hline 红砂啧 &0.066 &0.0225 &0.2024 &0.0749 &0.0979\\ \hline 晒网坝 &0.0609 &0.0824 &0.1917 &0.0535 &0.0832\\ \hline 盐码头 &0.0609 &0.0449 &0 &0.1821 &0.1604\\ \hline \end{array} $$上述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} $
$$P_a=\begin{array}{c|c|c|c|c|c|c}{M_{13 \times5}} &-P_{a}1 &-P_{a}2 &-P_{a}3 &-P_{a}4 &-P_{a}5\\ \hline 白沙 &0.049 &0.1313 &0.3125 &0.3125 &0.3855\\ \hline 黄谦 &0.1143 &0.1966 &0.3031 &0.5065 &0.6794\\ \hline 望龙门 &0.1419 &0.2393 &0.3672 &0.4529 &0.6819\\ \hline 寸滩 &0.1187 &0.2237 &0.3622 &0.4586 &0.7084\\ \hline 黄草峡 &0.0816 &0.0816 &0.2201 &0.4021 &0.6207\\ \hline 鸭嘴石 &0.0748 &0.2323 &0.4027 &0.5313 &0.552\\ \hline 美女啧 &0.0779 &0.2129 &0.3194 &0.4264 &0.4264\\ \hline 米市圈 &0.0785 &0.1609 &0.2888 &0.4387 &0.5387\\ \hline 九条沟 &0 &0.1799 &0.2119 &0.3832 &0.6163\\ \hline 沱口 &0.0779 &0.2803 &0.3548 &0.4834 &0.5626\\ \hline 红砂啧 &0.0759 &0.2559 &0.2559 &0.3844 &0.5363\\ \hline 晒网坝 &0.081 &0.2011 &0.2118 &0.3617 &0.5284\\ \hline 盐码头 &0.081 &0.2385 &0.4409 &0.4623 &0.5517\\ \hline \end{array} $$其中$K_{a}^- \longrightarrow Q_{a} $
$$Q_a=\begin{array}{c|c|c|c|c|c|c}{M_{13 \times5}} &+Q_{a}1 &+Q_{a}2 &+Q_{a}3 &+Q_{a}4 &+Q_{a}5\\ \hline 白沙 &0.093 &0.213 &0.2342 &0.4377 &0.6145\\ \hline 黄谦 &0.0277 &0.1477 &0.2437 &0.2437 &0.3206\\ \hline 望龙门 &0 &0.1051 &0.1795 &0.2973 &0.3181\\ \hline 寸滩 &0.0233 &0.1206 &0.1846 &0.2916 &0.2916\\ \hline 黄草峡 &0.0603 &0.2627 &0.3267 &0.3481 &0.3793\\ \hline 鸭嘴石 &0.0671 &0.1121 &0.1441 &0.2189 &0.448\\ \hline 美女啧 &0.064 &0.1314 &0.2274 &0.3238 &0.5736\\ \hline 米市圈 &0.0634 &0.1835 &0.258 &0.3115 &0.4613\\ \hline 九条沟 &0.1419 &0.1644 &0.3348 &0.367 &0.3837\\ \hline 沱口 &0.064 &0.064 &0.1919 &0.2668 &0.4374\\ \hline 红砂啧 &0.066 &0.0885 &0.2909 &0.3658 &0.4637\\ \hline 晒网坝 &0.0609 &0.1433 &0.335 &0.3885 &0.4716\\ \hline 盐码头 &0.0609 &0.1058 &0.1058 &0.2879 &0.4483\\ \hline \end{array} $$上述两者合并后矩阵如下
$$PaQa=\begin{array}{c|c|c|c|c|c|c}{M_{13 \times10}} &-P_{a}1 &-P_{a}2 &-P_{a}3 &-P_{a}4 &-P_{a}5 &+Q_{a}1 &+Q_{a}2 &+Q_{a}3 &+Q_{a}4 &+Q_{a}5\\ \hline 白沙 &0.049 &0.1313 &0.3125 &0.3125 &0.3855 &0.093 &0.213 &0.2342 &0.4377 &0.6145\\ \hline 黄谦 &0.1143 &0.1966 &0.3031 &0.5065 &0.6794 &0.0277 &0.1477 &0.2437 &0.2437 &0.3206\\ \hline 望龙门 &0.1419 &0.2393 &0.3672 &0.4529 &0.6819 &0 &0.1051 &0.1795 &0.2973 &0.3181\\ \hline 寸滩 &0.1187 &0.2237 &0.3622 &0.4586 &0.7084 &0.0233 &0.1206 &0.1846 &0.2916 &0.2916\\ \hline 黄草峡 &0.0816 &0.0816 &0.2201 &0.4021 &0.6207 &0.0603 &0.2627 &0.3267 &0.3481 &0.3793\\ \hline 鸭嘴石 &0.0748 &0.2323 &0.4027 &0.5313 &0.552 &0.0671 &0.1121 &0.1441 &0.2189 &0.448\\ \hline 美女啧 &0.0779 &0.2129 &0.3194 &0.4264 &0.4264 &0.064 &0.1314 &0.2274 &0.3238 &0.5736\\ \hline 米市圈 &0.0785 &0.1609 &0.2888 &0.4387 &0.5387 &0.0634 &0.1835 &0.258 &0.3115 &0.4613\\ \hline 九条沟 &0 &0.1799 &0.2119 &0.3832 &0.6163 &0.1419 &0.1644 &0.3348 &0.367 &0.3837\\ \hline 沱口 &0.0779 &0.2803 &0.3548 &0.4834 &0.5626 &0.064 &0.064 &0.1919 &0.2668 &0.4374\\ \hline 红砂啧 &0.0759 &0.2559 &0.2559 &0.3844 &0.5363 &0.066 &0.0885 &0.2909 &0.3658 &0.4637\\ \hline 晒网坝 &0.081 &0.2011 &0.2118 &0.3617 &0.5284 &0.0609 &0.1433 &0.335 &0.3885 &0.4716\\ \hline 盐码头 &0.081 &0.2385 &0.4409 &0.4623 &0.5517 &0.0609 &0.1058 &0.1058 &0.2879 &0.4483\\ \hline \end{array} $$降维过程的理解
矩阵的数目为5
$$10列矩阵=\begin{array}{c|c|c|c|c|c|c}{M_{13 \times10}} &-P_{a}1 &-P_{a}2 &-P_{a}3 &-P_{a}4 &-P_{a}5 &+Q_{a}1 &+Q_{a}2 &+Q_{a}3 &+Q_{a}4 &+Q_{a}5\\ \hline 白沙 &0.049 &0.1313 &0.3125 &0.3125 &0.3855 &0.093 &0.213 &0.2342 &0.4377 &0.6145\\ \hline 黄谦 &0.1143 &0.1966 &0.3031 &0.5065 &0.6794 &0.0277 &0.1477 &0.2437 &0.2437 &0.3206\\ \hline 望龙门 &0.1419 &0.2393 &0.3672 &0.4529 &0.6819 &0 &0.1051 &0.1795 &0.2973 &0.3181\\ \hline 寸滩 &0.1187 &0.2237 &0.3622 &0.4586 &0.7084 &0.0233 &0.1206 &0.1846 &0.2916 &0.2916\\ \hline 黄草峡 &0.0816 &0.0816 &0.2201 &0.4021 &0.6207 &0.0603 &0.2627 &0.3267 &0.3481 &0.3793\\ \hline 鸭嘴石 &0.0748 &0.2323 &0.4027 &0.5313 &0.552 &0.0671 &0.1121 &0.1441 &0.2189 &0.448\\ \hline 美女啧 &0.0779 &0.2129 &0.3194 &0.4264 &0.4264 &0.064 &0.1314 &0.2274 &0.3238 &0.5736\\ \hline 米市圈 &0.0785 &0.1609 &0.2888 &0.4387 &0.5387 &0.0634 &0.1835 &0.258 &0.3115 &0.4613\\ \hline 九条沟 &0 &0.1799 &0.2119 &0.3832 &0.6163 &0.1419 &0.1644 &0.3348 &0.367 &0.3837\\ \hline 沱口 &0.0779 &0.2803 &0.3548 &0.4834 &0.5626 &0.064 &0.064 &0.1919 &0.2668 &0.4374\\ \hline 红砂啧 &0.0759 &0.2559 &0.2559 &0.3844 &0.5363 &0.066 &0.0885 &0.2909 &0.3658 &0.4637\\ \hline 晒网坝 &0.081 &0.2011 &0.2118 &0.3617 &0.5284 &0.0609 &0.1433 &0.335 &0.3885 &0.4716\\ \hline 盐码头 &0.081 &0.2385 &0.4409 &0.4623 &0.5517 &0.0609 &0.1058 &0.1058 &0.2879 &0.4483\\ \hline \end{array} $$$$8列矩阵=\begin{array}{c|c|c|c|c|c|c}{M_{13 \times8}} &-P_{a}2 &-P_{a}3 &-P_{a}4 &-P_{a}5 &+Q_{a}2 &+Q_{a}3 &+Q_{a}4 &+Q_{a}5\\ \hline 白沙 &0.1313 &0.3125 &0.3125 &0.3855 &0.213 &0.2342 &0.4377 &0.6145\\ \hline 黄谦 &0.1966 &0.3031 &0.5065 &0.6794 &0.1477 &0.2437 &0.2437 &0.3206\\ \hline 望龙门 &0.2393 &0.3672 &0.4529 &0.6819 &0.1051 &0.1795 &0.2973 &0.3181\\ \hline 寸滩 &0.2237 &0.3622 &0.4586 &0.7084 &0.1206 &0.1846 &0.2916 &0.2916\\ \hline 黄草峡 &0.0816 &0.2201 &0.4021 &0.6207 &0.2627 &0.3267 &0.3481 &0.3793\\ \hline 鸭嘴石 &0.2323 &0.4027 &0.5313 &0.552 &0.1121 &0.1441 &0.2189 &0.448\\ \hline 美女啧 &0.2129 &0.3194 &0.4264 &0.4264 &0.1314 &0.2274 &0.3238 &0.5736\\ \hline 米市圈 &0.1609 &0.2888 &0.4387 &0.5387 &0.1835 &0.258 &0.3115 &0.4613\\ \hline 九条沟 &0.1799 &0.2119 &0.3832 &0.6163 &0.1644 &0.3348 &0.367 &0.3837\\ \hline 沱口 &0.2803 &0.3548 &0.4834 &0.5626 &0.064 &0.1919 &0.2668 &0.4374\\ \hline 红砂啧 &0.2559 &0.2559 &0.3844 &0.5363 &0.0885 &0.2909 &0.3658 &0.4637\\ \hline 晒网坝 &0.2011 &0.2118 &0.3617 &0.5284 &0.1433 &0.335 &0.3885 &0.4716\\ \hline 盐码头 &0.2385 &0.4409 &0.4623 &0.5517 &0.1058 &0.1058 &0.2879 &0.4483\\ \hline \end{array} $$$$6列矩阵=\begin{array}{c|c|c|c|c|c|c}{M_{13 \times6}} &-P_{a}3 &-P_{a}4 &-P_{a}5 &+Q_{a}3 &+Q_{a}4 &+Q_{a}5\\ \hline 白沙 &0.3125 &0.3125 &0.3855 &0.2342 &0.4377 &0.6145\\ \hline 黄谦 &0.3031 &0.5065 &0.6794 &0.2437 &0.2437 &0.3206\\ \hline 望龙门 &0.3672 &0.4529 &0.6819 &0.1795 &0.2973 &0.3181\\ \hline 寸滩 &0.3622 &0.4586 &0.7084 &0.1846 &0.2916 &0.2916\\ \hline 黄草峡 &0.2201 &0.4021 &0.6207 &0.3267 &0.3481 &0.3793\\ \hline 鸭嘴石 &0.4027 &0.5313 &0.552 &0.1441 &0.2189 &0.448\\ \hline 美女啧 &0.3194 &0.4264 &0.4264 &0.2274 &0.3238 &0.5736\\ \hline 米市圈 &0.2888 &0.4387 &0.5387 &0.258 &0.3115 &0.4613\\ \hline 九条沟 &0.2119 &0.3832 &0.6163 &0.3348 &0.367 &0.3837\\ \hline 沱口 &0.3548 &0.4834 &0.5626 &0.1919 &0.2668 &0.4374\\ \hline 红砂啧 &0.2559 &0.3844 &0.5363 &0.2909 &0.3658 &0.4637\\ \hline 晒网坝 &0.2118 &0.3617 &0.5284 &0.335 &0.3885 &0.4716\\ \hline 盐码头 &0.4409 &0.4623 &0.5517 &0.1058 &0.2879 &0.4483\\ \hline \end{array} $$$$4列矩阵=\begin{array}{c|c|c|c|c|c|c}{M_{13 \times4}} &-P_{a}4 &-P_{a}5 &+Q_{a}4 &+Q_{a}5\\ \hline 白沙 &0.3125 &0.3855 &0.4377 &0.6145\\ \hline 黄谦 &0.5065 &0.6794 &0.2437 &0.3206\\ \hline 望龙门 &0.4529 &0.6819 &0.2973 &0.3181\\ \hline 寸滩 &0.4586 &0.7084 &0.2916 &0.2916\\ \hline 黄草峡 &0.4021 &0.6207 &0.3481 &0.3793\\ \hline 鸭嘴石 &0.5313 &0.552 &0.2189 &0.448\\ \hline 美女啧 &0.4264 &0.4264 &0.3238 &0.5736\\ \hline 米市圈 &0.4387 &0.5387 &0.3115 &0.4613\\ \hline 九条沟 &0.3832 &0.6163 &0.367 &0.3837\\ \hline 沱口 &0.4834 &0.5626 &0.2668 &0.4374\\ \hline 红砂啧 &0.3844 &0.5363 &0.3658 &0.4637\\ \hline 晒网坝 &0.3617 &0.5284 &0.3885 &0.4716\\ \hline 盐码头 &0.4623 &0.5517 &0.2879 &0.4483\\ \hline \end{array} $$$$2列矩阵=\begin{array}{c|c|c|c|c|c|c}{M_{13 \times2}} &-P_{a}5 &+Q_{a}5\\ \hline 白沙 &0.3855 &0.6145\\ \hline 黄谦 &0.6794 &0.3206\\ \hline 望龙门 &0.6819 &0.3181\\ \hline 寸滩 &0.7084 &0.2916\\ \hline 黄草峡 &0.6207 &0.3793\\ \hline 鸭嘴石 &0.552 &0.448\\ \hline 美女啧 &0.4264 &0.5736\\ \hline 米市圈 &0.5387 &0.4613\\ \hline 九条沟 &0.6163 &0.3837\\ \hline 沱口 &0.5626 &0.4374\\ \hline 红砂啧 &0.5363 &0.4637\\ \hline 晒网坝 &0.5284 &0.4716\\ \hline 盐码头 &0.5517 &0.4483\\ \hline \end{array} $$去重显示拓扑层级图
没有重复的拓扑层级图