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

$$ \require{cancel} \require{AMScd} \begin{CD} O @>>>N \\ \end{CD} $$
$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{12 \times12}} &T1 &T2 &T3 &K1 &K2 &K3 &H1 &H2 &H3 &R1 &R2 &R3\\ \hline T1 &0 &0.104 &0.104 &0 &0.065 &0.039 &0.039 &0.078 &0.091 &0.091 &0.091 &0.104\\ \hline T2 &0.104 &0 &0 &0.039 &0.039 &0.039 &0.052 &0.039 &0.039 &0.039 &0.052 &0.104\\ \hline T3 &0.104 &0 &0 &0.039 &0 &0.039 &0.052 &0.091 &0.039 &0.091 &0.065 &0.078\\ \hline K1 &0.104 &0 &0.052 &0 &0 &0.039 &0.052 &0.065 &0.039 &0.091 &0.078 &0.065\\ \hline K2 &0.104 &0 &0 &0.013 &0 &0.039 &0.052 &0.052 &0.065 &0.104 &0.091 &0.039\\ \hline K3 &0.104 &0 &0.039 &0.026 &0.091 &0 &0.091 &0.091 &0.091 &0.091 &0.091 &0.039\\ \hline H1 &0.104 &0 &0.052 &0.039 &0 &0 &0 &0.039 &0.052 &0.039 &0 &0.078\\ \hline H2 &0.013 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline H3 &0.104 &0 &0 &0.065 &0.039 &0.039 &0.078 &0 &0 &0.065 &0.039 &0.013\\ \hline R1 &0.104 &0 &0.039 &0.039 &0 &0 &0 &0.091 &0 &0 &0 &0.013\\ \hline R2 &0.104 &0 &0.052 &0.117 &0.052 &0.052 &0.052 &0.091 &0.052 &0.052 &0 &0.013\\ \hline R3 &0.052 &0 &0 &0.091 &0.039 &0.091 &0.091 &0.091 &0.091 &0 &0.026 &0\\ \hline \end{array} $$

综合影响矩阵求解过程

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

综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{12 \times12}} &T1 &T2 &T3 &K1 &K2 &K3 &H1 &H2 &H3 &R1 &R2 &R3\\ \hline T1 &0.127 &0.117 &0.144 &0.068 &0.107 &0.09 &0.11 &0.172 &0.159 &0.168 &0.152 &0.167\\ \hline T2 &0.186 &0.019 &0.041 &0.084 &0.074 &0.078 &0.104 &0.11 &0.098 &0.098 &0.101 &0.152\\ \hline T3 &0.185 &0.019 &0.043 &0.083 &0.034 &0.074 &0.099 &0.162 &0.092 &0.146 &0.109 &0.124\\ \hline K1 &0.188 &0.02 &0.094 &0.047 &0.034 &0.074 &0.1 &0.139 &0.093 &0.148 &0.122 &0.114\\ \hline K2 &0.186 &0.019 &0.043 &0.058 &0.034 &0.071 &0.097 &0.121 &0.115 &0.159 &0.132 &0.084\\ \hline K3 &0.213 &0.022 &0.089 &0.082 &0.127 &0.044 &0.149 &0.176 &0.155 &0.167 &0.148 &0.1\\ \hline H1 &0.16 &0.017 &0.08 &0.069 &0.024 &0.03 &0.038 &0.091 &0.092 &0.082 &0.037 &0.115\\ \hline H2 &0.015 &0.002 &0.002 &0.001 &0.001 &0.001 &0.001 &0.002 &0.002 &0.002 &0.002 &0.002\\ \hline H3 &0.175 &0.018 &0.041 &0.097 &0.065 &0.066 &0.116 &0.062 &0.048 &0.119 &0.081 &0.06\\ \hline R1 &0.135 &0.014 &0.06 &0.053 &0.015 &0.017 &0.021 &0.123 &0.026 &0.03 &0.026 &0.04\\ \hline R2 &0.197 &0.02 &0.097 &0.154 &0.084 &0.087 &0.104 &0.165 &0.109 &0.124 &0.059 &0.072\\ \hline R3 &0.139 &0.014 &0.04 &0.128 &0.071 &0.12 &0.14 &0.152 &0.142 &0.065 &0.076 &0.049\\ \hline \end{array} $$

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。 $$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{12 \times12}} &T1 &T2 &T3 &K1 &K2 &K3 &H1 &H2 &H3 &R1 &R2 &R3\\ \hline T1 &0.0666 &0.3879 &0.1863 &0.0736 &0.1593 &0.12 &0.1021 &0.1167 &0.1409 &0.1284 &0.1451 &0.155\\ \hline T2 &0.0974 &0.0639 &0.0531 &0.0909 &0.1103 &0.1032 &0.0965 &0.0747 &0.0865 &0.0751 &0.0962 &0.1405\\ \hline T3 &0.0971 &0.0637 &0.0554 &0.0901 &0.0502 &0.0981 &0.0919 &0.1099 &0.0818 &0.1113 &0.104 &0.1151\\ \hline K1 &0.0985 &0.0646 &0.1215 &0.051 &0.051 &0.0987 &0.0926 &0.0944 &0.0824 &0.1132 &0.117 &0.1052\\ \hline K2 &0.0974 &0.0639 &0.0558 &0.063 &0.0507 &0.0948 &0.09 &0.0821 &0.1016 &0.1213 &0.1267 &0.0781\\ \hline K3 &0.112 &0.0735 &0.1149 &0.0885 &0.1902 &0.058 &0.1376 &0.1192 &0.1368 &0.1278 &0.1414 &0.0926\\ \hline H1 &0.0839 &0.055 &0.1039 &0.0749 &0.0354 &0.0394 &0.0355 &0.0614 &0.081 &0.0628 &0.0358 &0.1063\\ \hline H2 &0.0077 &0.005 &0.0024 &0.001 &0.0021 &0.0016 &0.0013 &0.0015 &0.0018 &0.0017 &0.0019 &0.002\\ \hline H3 &0.0921 &0.0604 &0.0526 &0.1049 &0.0979 &0.0878 &0.1071 &0.042 &0.0425 &0.0907 &0.078 &0.0555\\ \hline R1 &0.0707 &0.0464 &0.0775 &0.0572 &0.0221 &0.0224 &0.0196 &0.0832 &0.0228 &0.0229 &0.0248 &0.0375\\ \hline R2 &0.1034 &0.0678 &0.1254 &0.1668 &0.1249 &0.1162 &0.0964 &0.1121 &0.0963 &0.0949 &0.0564 &0.0664\\ \hline R3 &0.0731 &0.0479 &0.0511 &0.1381 &0.106 &0.1599 &0.1295 &0.1028 &0.1256 &0.0499 &0.0728 &0.0457\\ \hline \end{array} $$

极限超矩阵求解：

$$limit W=\begin{array}{c|c|c|c|c|c|c}{M_{12 \times12}} &T1 &T2 &T3 &K1 &K2 &K3 &H1 &H2 &H3 &R1 &R2 &R3\\ \hline T1 &0.1486 &0.1486 &0.1486 &0.1486 &0.1486 &0.1486 &0.1486 &0.1486 &0.1486 &0.1486 &0.1486 &0.1486\\ \hline T2 &0.0935 &0.0935 &0.0935 &0.0935 &0.0935 &0.0935 &0.0935 &0.0935 &0.0935 &0.0935 &0.0935 &0.0935\\ \hline T3 &0.0872 &0.0872 &0.0872 &0.0872 &0.0872 &0.0872 &0.0872 &0.0872 &0.0872 &0.0872 &0.0872 &0.0872\\ \hline K1 &0.0905 &0.0905 &0.0905 &0.0905 &0.0905 &0.0905 &0.0905 &0.0905 &0.0905 &0.0905 &0.0905 &0.0905\\ \hline K2 &0.0853 &0.0853 &0.0853 &0.0853 &0.0853 &0.0853 &0.0853 &0.0853 &0.0853 &0.0853 &0.0853 &0.0853\\ \hline K3 &0.1126 &0.1126 &0.1126 &0.1126 &0.1126 &0.1126 &0.1126 &0.1126 &0.1126 &0.1126 &0.1126 &0.1126\\ \hline H1 &0.0658 &0.0658 &0.0658 &0.0658 &0.0658 &0.0658 &0.0658 &0.0658 &0.0658 &0.0658 &0.0658 &0.0658\\ \hline H2 &0.0029 &0.0029 &0.0029 &0.0029 &0.0029 &0.0029 &0.0029 &0.0029 &0.0029 &0.0029 &0.0029 &0.0029\\ \hline H3 &0.0789 &0.0789 &0.0789 &0.0789 &0.0789 &0.0789 &0.0789 &0.0789 &0.0789 &0.0789 &0.0789 &0.0789\\ \hline R1 &0.0414 &0.0414 &0.0414 &0.0414 &0.0414 &0.0414 &0.0414 &0.0414 &0.0414 &0.0414 &0.0414 &0.0414\\ \hline R2 &0.1015 &0.1015 &0.1015 &0.1015 &0.1015 &0.1015 &0.1015 &0.1015 &0.1015 &0.1015 &0.1015 &0.1015\\ \hline R3 &0.0917 &0.0917 &0.0917 &0.0917 &0.0917 &0.0917 &0.0917 &0.0917 &0.0917 &0.0917 &0.0917 &0.0917\\ \hline \end{array} $$

权重的求解

$$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{12 \times1}} &权重\\ \hline T1 &0.14861\\ \hline T2 &0.09349\\ \hline T3 &0.08725\\ \hline K1 &0.09045\\ \hline K2 &0.08525\\ \hline K3 &0.11264\\ \hline H1 &0.0658\\ \hline H2 &0.00294\\ \hline H3 &0.07894\\ \hline R1 &0.04142\\ \hline R2 &0.10149\\ \hline R3 &0.09171\\ \hline \end{array} $$$$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{1 \times12}} &T1 &T2 &T3 &K1 &K2 &K3 &H1 &H2 &H3 &R1 &R2 &R3\\ \hline 权重 &0.14861 &0.09349 &0.08725 &0.09045 &0.08525 &0.11264 &0.0658 &0.00294 &0.07894 &0.04142 &0.10149 &0.09171\\ \hline \end{array} $$

归一化求子系统的权重

$$\omega =\begin{array}{c|c|c|c|c|c|c}{M_{4 \times1}} &权重\\ \hline T &0.3294\\ \hline K &0.2884\\ \hline H &0.1477\\ \hline R &0.2346\\ \hline \end{array} $$$$\omega =\begin{array}{c|c|c|c|c|c|c}{M_{1 \times4}} &T &K &H &R\\ \hline 权重 &0.3294 &0.2884 &0.1477 &0.2346\\ \hline \end{array} $$