原始矩阵（直接影响矩阵）为

$$Ori=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{12 \times12}} &B1 &B2 &B3 &E1 &E2 &E3 &Q1 &Q2 &Q3 &R1 &R2 &R3\\ \hline B1 &0 &7 &7 &7 &9 &7 &4 &7 &7 &7 &7 &9\\ \hline B2 &3 &0 &0 &3 &3 &3 &4 &3 &3 &3 &4 &3\\ \hline B3 &3 &0 &0 &3 &0 &3 &4 &7 &3 &7 &5 &4\\ \hline E1 &4 &0 &4 &0 &0 &3 &4 &5 &3 &7 &6 &6\\ \hline E2 &5 &0 &0 &1 &0 &3 &4 &4 &5 &7 &7 &1\\ \hline E3 &6 &5 &3 &2 &7 &0 &7 &7 &7 &7 &7 &1\\ \hline Q1 &7 &0 &4 &3 &0 &0 &0 &3 &4 &3 &0 &3\\ \hline Q2 &8 &6 &3 &4 &0 &0 &1 &0 &0 &8 &3 &1\\ \hline Q3 &8 &8 &4 &5 &0 &0 &1 &0 &0 &5 &3 &1\\ \hline R1 &8 &8 &3 &3 &0 &0 &0 &0 &0 &0 &0 &1\\ \hline R2 &8 &8 &4 &9 &4 &4 &4 &4 &4 &4 &0 &1\\ \hline R3 &4 &8 &0 &7 &3 &7 &4 &7 &7 &0 &2 &0\\ \hline \end{array} $$

规范直接关系矩阵求解过程

$$ \require{cancel} \require{AMScd} \begin{CD} O @>>>N \\ \end{CD} $$
$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{12 \times12}} &B1 &B2 &B3 &E1 &E2 &E3 &Q1 &Q2 &Q3 &R1 &R2 &R3\\ \hline B1 &0 &0.109 &0.109 &0.109 &0.141 &0.109 &0.063 &0.109 &0.109 &0.109 &0.109 &0.141\\ \hline B2 &0.047 &0 &0 &0.047 &0.047 &0.047 &0.063 &0.047 &0.047 &0.047 &0.063 &0.047\\ \hline B3 &0.047 &0 &0 &0.047 &0 &0.047 &0.063 &0.109 &0.047 &0.109 &0.078 &0.063\\ \hline E1 &0.063 &0 &0.063 &0 &0 &0.047 &0.063 &0.078 &0.047 &0.109 &0.094 &0.094\\ \hline E2 &0.078 &0 &0 &0.016 &0 &0.047 &0.063 &0.063 &0.078 &0.109 &0.109 &0.016\\ \hline E3 &0.094 &0.078 &0.047 &0.031 &0.109 &0 &0.109 &0.109 &0.109 &0.109 &0.109 &0.016\\ \hline Q1 &0.109 &0 &0.063 &0.047 &0 &0 &0 &0.047 &0.063 &0.047 &0 &0.047\\ \hline Q2 &0.125 &0.094 &0.047 &0.063 &0 &0 &0.016 &0 &0 &0.125 &0.047 &0.016\\ \hline Q3 &0.125 &0.125 &0.063 &0.078 &0 &0 &0.016 &0 &0 &0.078 &0.047 &0.016\\ \hline R1 &0.125 &0.125 &0.047 &0.047 &0 &0 &0 &0 &0 &0 &0 &0.016\\ \hline R2 &0.125 &0.125 &0.063 &0.141 &0.063 &0.063 &0.063 &0.063 &0.063 &0.063 &0 &0.016\\ \hline R3 &0.063 &0.125 &0 &0.109 &0.047 &0.109 &0.063 &0.109 &0.109 &0 &0.031 &0\\ \hline \end{array} $$

综合影响矩阵求解过程

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

综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{12 \times12}} &B1 &B2 &B3 &E1 &E2 &E3 &Q1 &Q2 &Q3 &R1 &R2 &R3\\ \hline B1 &0.297 &0.348 &0.258 &0.328 &0.258 &0.248 &0.229 &0.316 &0.298 &0.37 &0.308 &0.284\\ \hline B2 &0.176 &0.11 &0.073 &0.145 &0.103 &0.108 &0.133 &0.137 &0.131 &0.161 &0.147 &0.114\\ \hline B3 &0.203 &0.138 &0.088 &0.166 &0.065 &0.117 &0.141 &0.21 &0.14 &0.24 &0.172 &0.14\\ \hline E1 &0.231 &0.151 &0.155 &0.135 &0.074 &0.128 &0.152 &0.196 &0.154 &0.251 &0.197 &0.178\\ \hline E2 &0.231 &0.137 &0.09 &0.136 &0.069 &0.115 &0.14 &0.161 &0.17 &0.239 &0.202 &0.094\\ \hline E3 &0.318 &0.263 &0.171 &0.204 &0.2 &0.105 &0.225 &0.256 &0.246 &0.309 &0.254 &0.134\\ \hline Q1 &0.215 &0.101 &0.128 &0.136 &0.052 &0.061 &0.063 &0.13 &0.135 &0.151 &0.081 &0.115\\ \hline Q2 &0.251 &0.208 &0.125 &0.169 &0.067 &0.074 &0.093 &0.1 &0.09 &0.242 &0.14 &0.1\\ \hline Q3 &0.254 &0.238 &0.142 &0.188 &0.069 &0.078 &0.099 &0.107 &0.095 &0.204 &0.147 &0.104\\ \hline R1 &0.208 &0.2 &0.101 &0.124 &0.054 &0.059 &0.062 &0.079 &0.071 &0.092 &0.077 &0.082\\ \hline R2 &0.326 &0.288 &0.18 &0.293 &0.156 &0.166 &0.183 &0.216 &0.201 &0.259 &0.154 &0.14\\ \hline R3 &0.253 &0.276 &0.108 &0.248 &0.132 &0.195 &0.172 &0.241 &0.231 &0.182 &0.169 &0.105\\ \hline \end{array} $$

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。 $$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{12 \times12}} &B1 &B2 &B3 &E1 &E2 &E3 &Q1 &Q2 &Q3 &R1 &R2 &R3\\ \hline B1 &0.1001 &0.1417 &0.1596 &0.1442 &0.1988 &0.1707 &0.1355 &0.1472 &0.1517 &0.1371 &0.1502 &0.1787\\ \hline B2 &0.0595 &0.0446 &0.0452 &0.064 &0.0794 &0.0743 &0.0785 &0.0636 &0.067 &0.0596 &0.0719 &0.0714\\ \hline B3 &0.0686 &0.056 &0.0541 &0.073 &0.0501 &0.0802 &0.0836 &0.0977 &0.0715 &0.0889 &0.084 &0.088\\ \hline E1 &0.0778 &0.0615 &0.0955 &0.0595 &0.0571 &0.0881 &0.0899 &0.091 &0.0785 &0.0931 &0.0963 &0.1121\\ \hline E2 &0.078 &0.0559 &0.0556 &0.0599 &0.0528 &0.0794 &0.0829 &0.0749 &0.0867 &0.0883 &0.0984 &0.0594\\ \hline E3 &0.1075 &0.107 &0.1058 &0.0896 &0.154 &0.072 &0.1331 &0.1192 &0.1253 &0.1142 &0.1241 &0.0845\\ \hline Q1 &0.0724 &0.041 &0.0791 &0.0601 &0.04 &0.0417 &0.0369 &0.0606 &0.069 &0.056 &0.0395 &0.0723\\ \hline Q2 &0.0848 &0.0846 &0.077 &0.0742 &0.0512 &0.0508 &0.0549 &0.0466 &0.0457 &0.0897 &0.0685 &0.0627\\ \hline Q3 &0.0856 &0.0967 &0.0875 &0.0826 &0.0534 &0.0538 &0.0583 &0.0499 &0.0485 &0.0754 &0.0718 &0.0656\\ \hline R1 &0.0703 &0.0814 &0.0626 &0.0546 &0.0414 &0.0406 &0.0365 &0.0369 &0.0362 &0.0342 &0.0375 &0.0515\\ \hline R2 &0.1099 &0.1172 &0.1113 &0.1289 &0.1202 &0.1143 &0.1083 &0.1003 &0.1022 &0.096 &0.0753 &0.0881\\ \hline R3 &0.0853 &0.1124 &0.0667 &0.1092 &0.1017 &0.1341 &0.1016 &0.112 &0.1178 &0.0674 &0.0825 &0.0657\\ \hline \end{array} $$

极限超矩阵求解：

$$limit W=\begin{array}{c|c|c|c|c|c|c}{M_{12 \times12}} &B1 &B2 &B3 &E1 &E2 &E3 &Q1 &Q2 &Q3 &R1 &R2 &R3\\ \hline B1 &0.1493 &0.1493 &0.1493 &0.1493 &0.1493 &0.1493 &0.1493 &0.1493 &0.1493 &0.1493 &0.1493 &0.1493\\ \hline B2 &0.0652 &0.0652 &0.0652 &0.0652 &0.0652 &0.0652 &0.0652 &0.0652 &0.0652 &0.0652 &0.0652 &0.0652\\ \hline B3 &0.0745 &0.0745 &0.0745 &0.0745 &0.0745 &0.0745 &0.0745 &0.0745 &0.0745 &0.0745 &0.0745 &0.0745\\ \hline E1 &0.0838 &0.0838 &0.0838 &0.0838 &0.0838 &0.0838 &0.0838 &0.0838 &0.0838 &0.0838 &0.0838 &0.0838\\ \hline E2 &0.0732 &0.0732 &0.0732 &0.0732 &0.0732 &0.0732 &0.0732 &0.0732 &0.0732 &0.0732 &0.0732 &0.0732\\ \hline E3 &0.1088 &0.1088 &0.1088 &0.1088 &0.1088 &0.1088 &0.1088 &0.1088 &0.1088 &0.1088 &0.1088 &0.1088\\ \hline Q1 &0.0568 &0.0568 &0.0568 &0.0568 &0.0568 &0.0568 &0.0568 &0.0568 &0.0568 &0.0568 &0.0568 &0.0568\\ \hline Q2 &0.0666 &0.0666 &0.0666 &0.0666 &0.0666 &0.0666 &0.0666 &0.0666 &0.0666 &0.0666 &0.0666 &0.0666\\ \hline Q3 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07\\ \hline R1 &0.0502 &0.0502 &0.0502 &0.0502 &0.0502 &0.0502 &0.0502 &0.0502 &0.0502 &0.0502 &0.0502 &0.0502\\ \hline R2 &0.1056 &0.1056 &0.1056 &0.1056 &0.1056 &0.1056 &0.1056 &0.1056 &0.1056 &0.1056 &0.1056 &0.1056\\ \hline R3 &0.0961 &0.0961 &0.0961 &0.0961 &0.0961 &0.0961 &0.0961 &0.0961 &0.0961 &0.0961 &0.0961 &0.0961\\ \hline \end{array} $$

权重的求解

$$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{12 \times1}} &权重\\ \hline B1 &0.14931\\ \hline B2 &0.06525\\ \hline B3 &0.07447\\ \hline E1 &0.08376\\ \hline E2 &0.07325\\ \hline E3 &0.10875\\ \hline Q1 &0.05677\\ \hline Q2 &0.06658\\ \hline Q3 &0.06999\\ \hline R1 &0.05019\\ \hline R2 &0.1056\\ \hline R3 &0.09609\\ \hline \end{array} $$$$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{1 \times12}} &B1 &B2 &B3 &E1 &E2 &E3 &Q1 &Q2 &Q3 &R1 &R2 &R3\\ \hline 权重 &0.14931 &0.06525 &0.07447 &0.08376 &0.07325 &0.10875 &0.05677 &0.06658 &0.06999 &0.05019 &0.1056 &0.09609\\ \hline \end{array} $$

归一化求子系统的权重

$$\omega =\begin{array}{c|c|c|c|c|c|c}{M_{4 \times1}} &权重\\ \hline B &0.289\\ \hline E &0.2658\\ \hline Q &0.1933\\ \hline R &0.2519\\ \hline \end{array} $$$$\omega =\begin{array}{c|c|c|c|c|c|c}{M_{1 \times4}} &B &E &Q &R\\ \hline 权重 &0.289 &0.2658 &0.1933 &0.2519\\ \hline \end{array} $$