原始矩阵（直接影响矩阵）为

$$Ori=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{12 \times12}} &T1 &T2 &T3 &K1 &K2 &K3 &H1 &H2 &H3 &R1 &R2 &R3\\ \hline T1 &0 &8 &8 &0 &5 &3 &3 &6 &7 &7 &7 &8\\ \hline T2 &8 &0 &0 &3 &3 &3 &4 &3 &3 &3 &4 &8\\ \hline T3 &8 &0 &0 &3 &0 &3 &4 &7 &3 &7 &5 &6\\ \hline K1 &8 &0 &4 &0 &0 &3 &4 &5 &3 &7 &6 &5\\ \hline K2 &8 &0 &0 &1 &0 &3 &4 &4 &5 &8 &7 &3\\ \hline K3 &8 &0 &3 &2 &7 &0 &7 &7 &7 &7 &7 &3\\ \hline H1 &8 &0 &4 &3 &0 &0 &0 &3 &4 &3 &0 &6\\ \hline H2 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline H3 &8 &0 &0 &5 &3 &3 &6 &0 &0 &5 &3 &1\\ \hline R1 &8 &0 &3 &3 &0 &0 &0 &7 &0 &0 &0 &1\\ \hline R2 &8 &0 &4 &9 &4 &4 &4 &7 &4 &4 &0 &1\\ \hline R3 &4 &0 &0 &7 &3 &7 &7 &7 &7 &0 &2 &0\\ \hline \end{array} $$

规范直接关系矩阵求解过程

$$ \require{cancel} \require{AMScd} \begin{CD} O @>>>N \\ \end{CD} $$
$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{12 \times12}} &T1 &T2 &T3 &K1 &K2 &K3 &H1 &H2 &H3 &R1 &R2 &R3\\ \hline T1 &0 &0.081 &0.081 &0 &0.051 &0.03 &0.03 &0.061 &0.071 &0.071 &0.071 &0.081\\ \hline T2 &0.081 &0 &0 &0.03 &0.03 &0.03 &0.04 &0.03 &0.03 &0.03 &0.04 &0.081\\ \hline T3 &0.081 &0 &0 &0.03 &0 &0.03 &0.04 &0.071 &0.03 &0.071 &0.051 &0.061\\ \hline K1 &0.081 &0 &0.04 &0 &0 &0.03 &0.04 &0.051 &0.03 &0.071 &0.061 &0.051\\ \hline K2 &0.081 &0 &0 &0.01 &0 &0.03 &0.04 &0.04 &0.051 &0.081 &0.071 &0.03\\ \hline K3 &0.081 &0 &0.03 &0.02 &0.071 &0 &0.071 &0.071 &0.071 &0.071 &0.071 &0.03\\ \hline H1 &0.081 &0 &0.04 &0.03 &0 &0 &0 &0.03 &0.04 &0.03 &0 &0.061\\ \hline H2 &0.01 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline H3 &0.081 &0 &0 &0.051 &0.03 &0.03 &0.061 &0 &0 &0.051 &0.03 &0.01\\ \hline R1 &0.081 &0 &0.03 &0.03 &0 &0 &0 &0.071 &0 &0 &0 &0.01\\ \hline R2 &0.081 &0 &0.04 &0.091 &0.04 &0.04 &0.04 &0.071 &0.04 &0.04 &0 &0.01\\ \hline R3 &0.04 &0 &0 &0.071 &0.03 &0.071 &0.071 &0.071 &0.071 &0 &0.02 &0\\ \hline \end{array} $$

综合影响矩阵求解过程

$$\begin{CD} N @>>>T \\ \end{CD} $$

综合影响矩阵如下

$T=\mathcal{N}(I-\mathcal{N})^{-1}$

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{12 \times12}} &T1 &T2 &T3 &K1 &K2 &K3 &H1 &H2 &H3 &R1 &R2 &R3\\ \hline T1 &0.065 &0.086 &0.099 &0.035 &0.071 &0.056 &0.066 &0.108 &0.104 &0.109 &0.1 &0.112\\ \hline T2 &0.121 &0.01 &0.021 &0.053 &0.048 &0.05 &0.067 &0.066 &0.06 &0.059 &0.065 &0.104\\ \hline T3 &0.121 &0.01 &0.022 &0.053 &0.017 &0.048 &0.064 &0.107 &0.057 &0.097 &0.072 &0.083\\ \hline K1 &0.122 &0.01 &0.062 &0.024 &0.017 &0.048 &0.064 &0.088 &0.057 &0.099 &0.082 &0.075\\ \hline K2 &0.121 &0.01 &0.022 &0.033 &0.017 &0.046 &0.063 &0.075 &0.075 &0.108 &0.091 &0.052\\ \hline K3 &0.136 &0.011 &0.055 &0.048 &0.088 &0.022 &0.099 &0.113 &0.102 &0.109 &0.099 &0.061\\ \hline H1 &0.108 &0.009 &0.055 &0.045 &0.012 &0.015 &0.019 &0.056 &0.06 &0.052 &0.019 &0.079\\ \hline H2 &0.011 &0.001 &0.001 &0 &0.001 &0.001 &0.001 &0.001 &0.001 &0.001 &0.001 &0.001\\ \hline H3 &0.116 &0.009 &0.021 &0.066 &0.043 &0.043 &0.079 &0.031 &0.024 &0.078 &0.052 &0.034\\ \hline R1 &0.095 &0.008 &0.041 &0.036 &0.007 &0.008 &0.01 &0.087 &0.013 &0.015 &0.013 &0.024\\ \hline R2 &0.127 &0.01 &0.063 &0.108 &0.056 &0.058 &0.066 &0.108 &0.069 &0.077 &0.03 &0.04\\ \hline R3 &0.084 &0.007 &0.02 &0.088 &0.046 &0.085 &0.095 &0.1 &0.096 &0.033 &0.046 &0.025\\ \hline \end{array} $$

加权超矩阵求解：

　求解就是每列归一化，加权超矩阵每列加起来的为1。$加权超矩阵 \mathcal{ \omega} $如下：

注意：当综合影响矩阵中存在某一列的值全部为0的时候需要特殊处理。 $$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{12 \times12}} &T1 &T2 &T3 &K1 &K2 &K3 &H1 &H2 &H3 &R1 &R2 &R3\\ \hline T1 &0.0526 &0.478 &0.2064 &0.0595 &0.1676 &0.1175 &0.0958 &0.1148 &0.1451 &0.1298 &0.1502 &0.1623\\ \hline T2 &0.0984 &0.0542 &0.0427 &0.0895 &0.1129 &0.1039 &0.096 &0.0701 &0.0835 &0.071 &0.0964 &0.1512\\ \hline T3 &0.0985 &0.0543 &0.0453 &0.0891 &0.04 &0.0994 &0.0921 &0.1136 &0.0794 &0.1164 &0.1074 &0.1209\\ \hline K1 &0.0997 &0.0549 &0.1282 &0.0405 &0.0405 &0.0998 &0.0926 &0.0938 &0.0798 &0.118 &0.1229 &0.108\\ \hline K2 &0.099 &0.0545 &0.0458 &0.0561 &0.0407 &0.0964 &0.0904 &0.08 &0.1046 &0.1288 &0.1357 &0.0761\\ \hline K3 &0.1107 &0.061 &0.1148 &0.0818 &0.2086 &0.0452 &0.143 &0.1203 &0.1421 &0.1302 &0.1476 &0.0877\\ \hline H1 &0.0878 &0.0484 &0.1134 &0.0765 &0.0278 &0.0315 &0.0277 &0.0597 &0.0837 &0.0618 &0.0281 &0.1146\\ \hline H2 &0.0088 &0.0048 &0.0021 &0.0006 &0.0017 &0.0012 &0.001 &0.0012 &0.0015 &0.0013 &0.0015 &0.0016\\ \hline H3 &0.0947 &0.0522 &0.0437 &0.1115 &0.1024 &0.0904 &0.1137 &0.033 &0.0335 &0.0926 &0.0771 &0.0491\\ \hline R1 &0.0775 &0.0427 &0.0856 &0.0617 &0.0172 &0.0174 &0.0148 &0.0922 &0.018 &0.0181 &0.0199 &0.0352\\ \hline R2 &0.1036 &0.0571 &0.1312 &0.1835 &0.1315 &0.1203 &0.0955 &0.1147 &0.0954 &0.0923 &0.045 &0.0577\\ \hline R3 &0.0686 &0.0378 &0.0409 &0.1497 &0.1092 &0.1769 &0.1374 &0.1067 &0.1335 &0.0396 &0.0681 &0.0356\\ \hline \end{array} $$

极限超矩阵求解：

$$limit W=\begin{array}{c|c|c|c|c|c|c}{M_{12 \times12}} &T1 &T2 &T3 &K1 &K2 &K3 &H1 &H2 &H3 &R1 &R2 &R3\\ \hline T1 &0.1561 &0.1561 &0.1561 &0.1561 &0.1561 &0.1561 &0.1561 &0.1561 &0.1561 &0.1561 &0.1561 &0.1561\\ \hline T2 &0.0927 &0.0927 &0.0927 &0.0927 &0.0927 &0.0927 &0.0927 &0.0927 &0.0927 &0.0927 &0.0927 &0.0927\\ \hline T3 &0.086 &0.086 &0.086 &0.086 &0.086 &0.086 &0.086 &0.086 &0.086 &0.086 &0.086 &0.086\\ \hline K1 &0.0896 &0.0896 &0.0896 &0.0896 &0.0896 &0.0896 &0.0896 &0.0896 &0.0896 &0.0896 &0.0896 &0.0896\\ \hline K2 &0.0839 &0.0839 &0.0839 &0.0839 &0.0839 &0.0839 &0.0839 &0.0839 &0.0839 &0.0839 &0.0839 &0.0839\\ \hline K3 &0.1118 &0.1118 &0.1118 &0.1118 &0.1118 &0.1118 &0.1118 &0.1118 &0.1118 &0.1118 &0.1118 &0.1118\\ \hline H1 &0.065 &0.065 &0.065 &0.065 &0.065 &0.065 &0.065 &0.065 &0.065 &0.065 &0.065 &0.065\\ \hline H2 &0.0029 &0.0029 &0.0029 &0.0029 &0.0029 &0.0029 &0.0029 &0.0029 &0.0029 &0.0029 &0.0029 &0.0029\\ \hline H3 &0.0783 &0.0783 &0.0783 &0.0783 &0.0783 &0.0783 &0.0783 &0.0783 &0.0783 &0.0783 &0.0783 &0.0783\\ \hline R1 &0.041 &0.041 &0.041 &0.041 &0.041 &0.041 &0.041 &0.041 &0.041 &0.041 &0.041 &0.041\\ \hline R2 &0.1013 &0.1013 &0.1013 &0.1013 &0.1013 &0.1013 &0.1013 &0.1013 &0.1013 &0.1013 &0.1013 &0.1013\\ \hline R3 &0.0916 &0.0916 &0.0916 &0.0916 &0.0916 &0.0916 &0.0916 &0.0916 &0.0916 &0.0916 &0.0916 &0.0916\\ \hline \end{array} $$

权重的求解

$$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{12 \times1}} &权重\\ \hline T1 &0.15609\\ \hline T2 &0.09266\\ \hline T3 &0.086\\ \hline K1 &0.08956\\ \hline K2 &0.08394\\ \hline K3 &0.11178\\ \hline H1 &0.06505\\ \hline H2 &0.00287\\ \hline H3 &0.07827\\ \hline R1 &0.04097\\ \hline R2 &0.10128\\ \hline R3 &0.09155\\ \hline \end{array} $$$$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{1 \times12}} &T1 &T2 &T3 &K1 &K2 &K3 &H1 &H2 &H3 &R1 &R2 &R3\\ \hline 权重 &0.15609 &0.09266 &0.086 &0.08956 &0.08394 &0.11178 &0.06505 &0.00287 &0.07827 &0.04097 &0.10128 &0.09155\\ \hline \end{array} $$

归一化求子系统的权重

$$\omega =\begin{array}{c|c|c|c|c|c|c}{M_{4 \times1}} &权重\\ \hline T &0.3347\\ \hline K &0.2853\\ \hline H &0.1462\\ \hline R &0.2338\\ \hline \end{array} $$$$\omega =\begin{array}{c|c|c|c|c|c|c}{M_{1 \times4}} &T &K &H &R\\ \hline 权重 &0.3347 &0.2853 &0.1462 &0.2338\\ \hline \end{array} $$