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

$$ \require{cancel} \require{AMScd} \begin{CD} O @>>>N \\ \end{CD} $$
$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{12 \times12}} &B1 &B2 &B3 &E1 &E2 &E3 &Q1 &Q2 &Q3 &R1 &R2 &R3\\ \hline B1 &0 &0.069 &0.069 &0.069 &0.089 &0.069 &0.04 &0.069 &0.069 &0.069 &0.069 &0.089\\ \hline B2 &0.03 &0 &0 &0.03 &0.03 &0.03 &0.04 &0.03 &0.03 &0.03 &0.04 &0.03\\ \hline B3 &0.03 &0 &0 &0.03 &0 &0.03 &0.04 &0.069 &0.03 &0.069 &0.05 &0.04\\ \hline E1 &0.04 &0 &0.04 &0 &0 &0.03 &0.04 &0.05 &0.03 &0.069 &0.059 &0.059\\ \hline E2 &0.05 &0 &0 &0.01 &0 &0.03 &0.04 &0.04 &0.05 &0.069 &0.069 &0.01\\ \hline E3 &0.059 &0.05 &0.03 &0.02 &0.069 &0 &0.069 &0.069 &0.069 &0.069 &0.069 &0.01\\ \hline Q1 &0.069 &0 &0.04 &0.03 &0 &0 &0 &0.03 &0.04 &0.03 &0 &0.03\\ \hline Q2 &0.079 &0.059 &0.03 &0.04 &0 &0 &0.01 &0 &0 &0.079 &0.03 &0.01\\ \hline Q3 &0.079 &0.079 &0.04 &0.05 &0 &0 &0.01 &0 &0 &0.05 &0.03 &0.01\\ \hline R1 &0.079 &0.079 &0.03 &0.03 &0 &0 &0 &0 &0 &0 &0 &0.01\\ \hline R2 &0.079 &0.079 &0.04 &0.089 &0.04 &0.04 &0.04 &0.04 &0.04 &0.04 &0 &0.01\\ \hline R3 &0.04 &0.079 &0 &0.069 &0.03 &0.069 &0.04 &0.069 &0.069 &0 &0.02 &0\\ \hline \end{array} $$

综合影响矩阵求解过程

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

综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{12 \times12}} &B1 &B2 &B3 &E1 &E2 &E3 &Q1 &Q2 &Q3 &R1 &R2 &R3\\ \hline B1 &0.071 &0.124 &0.102 &0.119 &0.114 &0.101 &0.079 &0.118 &0.113 &0.13 &0.116 &0.12\\ \hline B2 &0.06 &0.026 &0.017 &0.053 &0.043 &0.043 &0.056 &0.05 &0.049 &0.056 &0.059 &0.044\\ \hline B3 &0.068 &0.034 &0.021 &0.058 &0.015 &0.045 &0.057 &0.091 &0.051 &0.099 &0.07 &0.056\\ \hline E1 &0.08 &0.037 &0.061 &0.033 &0.017 &0.048 &0.06 &0.076 &0.054 &0.101 &0.081 &0.078\\ \hline E2 &0.086 &0.034 &0.022 &0.039 &0.016 &0.044 &0.056 &0.061 &0.07 &0.098 &0.089 &0.027\\ \hline E3 &0.113 &0.093 &0.059 &0.06 &0.089 &0.023 &0.095 &0.102 &0.1 &0.116 &0.102 &0.037\\ \hline Q1 &0.092 &0.024 &0.055 &0.051 &0.012 &0.015 &0.014 &0.049 &0.056 &0.054 &0.019 &0.046\\ \hline Q2 &0.107 &0.086 &0.048 &0.064 &0.016 &0.018 &0.028 &0.023 &0.021 &0.105 &0.051 &0.031\\ \hline Q3 &0.106 &0.104 &0.058 &0.075 &0.017 &0.019 &0.029 &0.025 &0.022 &0.078 &0.053 &0.032\\ \hline R1 &0.095 &0.094 &0.042 &0.047 &0.014 &0.015 &0.015 &0.019 &0.017 &0.021 &0.019 &0.027\\ \hline R2 &0.124 &0.114 &0.067 &0.122 &0.061 &0.063 &0.068 &0.075 &0.072 &0.086 &0.038 &0.04\\ \hline R3 &0.084 &0.113 &0.025 &0.1 &0.049 &0.088 &0.065 &0.099 &0.097 &0.044 &0.053 &0.024\\ \hline \end{array} $$

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。 $$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{12 \times12}} &B1 &B2 &B3 &E1 &E2 &E3 &Q1 &Q2 &Q3 &R1 &R2 &R3\\ \hline B1 &0.0654 &0.1406 &0.1763 &0.1454 &0.2467 &0.1928 &0.1275 &0.149 &0.1569 &0.1317 &0.1544 &0.2125\\ \hline B2 &0.0555 &0.0293 &0.0299 &0.0641 &0.0918 &0.083 &0.0894 &0.0636 &0.0685 &0.0566 &0.0784 &0.0788\\ \hline B3 &0.0624 &0.0387 &0.0365 &0.0707 &0.0315 &0.0859 &0.0915 &0.1158 &0.07 &0.1001 &0.093 &0.1002\\ \hline E1 &0.0732 &0.0423 &0.1057 &0.0399 &0.0369 &0.0923 &0.0959 &0.0968 &0.0752 &0.102 &0.1087 &0.1379\\ \hline E2 &0.0795 &0.0389 &0.0384 &0.0474 &0.0348 &0.085 &0.0908 &0.0771 &0.0968 &0.0995 &0.1186 &0.0485\\ \hline E3 &0.1044 &0.105 &0.1022 &0.0737 &0.192 &0.0448 &0.1527 &0.1287 &0.1384 &0.1173 &0.1362 &0.0654\\ \hline Q1 &0.0847 &0.0271 &0.0955 &0.0616 &0.026 &0.0278 &0.0224 &0.062 &0.0776 &0.0545 &0.0253 &0.0823\\ \hline Q2 &0.0981 &0.0969 &0.0832 &0.0781 &0.035 &0.0343 &0.0443 &0.0295 &0.0285 &0.1063 &0.0681 &0.0548\\ \hline Q3 &0.0979 &0.1175 &0.1002 &0.0909 &0.0366 &0.0368 &0.0472 &0.0322 &0.0306 &0.0787 &0.0709 &0.0573\\ \hline R1 &0.0873 &0.1069 &0.0726 &0.0573 &0.0299 &0.0288 &0.0238 &0.0244 &0.0235 &0.0214 &0.0252 &0.0482\\ \hline R2 &0.1142 &0.1293 &0.1159 &0.1491 &0.132 &0.1212 &0.1093 &0.0955 &0.0993 &0.0875 &0.0502 &0.0715\\ \hline R3 &0.0774 &0.1275 &0.0437 &0.1218 &0.1067 &0.1673 &0.1052 &0.1253 &0.1346 &0.0446 &0.071 &0.0427\\ \hline \end{array} $$

极限超矩阵求解：

$$limit W=\begin{array}{c|c|c|c|c|c|c}{M_{12 \times12}} &B1 &B2 &B3 &E1 &E2 &E3 &Q1 &Q2 &Q3 &R1 &R2 &R3\\ \hline B1 &0.1543 &0.1543 &0.1543 &0.1543 &0.1543 &0.1543 &0.1543 &0.1543 &0.1543 &0.1543 &0.1543 &0.1543\\ \hline B2 &0.0662 &0.0662 &0.0662 &0.0662 &0.0662 &0.0662 &0.0662 &0.0662 &0.0662 &0.0662 &0.0662 &0.0662\\ \hline B3 &0.0743 &0.0743 &0.0743 &0.0743 &0.0743 &0.0743 &0.0743 &0.0743 &0.0743 &0.0743 &0.0743 &0.0743\\ \hline E1 &0.0845 &0.0845 &0.0845 &0.0845 &0.0845 &0.0845 &0.0845 &0.0845 &0.0845 &0.0845 &0.0845 &0.0845\\ \hline E2 &0.0722 &0.0722 &0.0722 &0.0722 &0.0722 &0.0722 &0.0722 &0.0722 &0.0722 &0.0722 &0.0722 &0.0722\\ \hline E3 &0.1084 &0.1084 &0.1084 &0.1084 &0.1084 &0.1084 &0.1084 &0.1084 &0.1084 &0.1084 &0.1084 &0.1084\\ \hline Q1 &0.0559 &0.0559 &0.0559 &0.0559 &0.0559 &0.0559 &0.0559 &0.0559 &0.0559 &0.0559 &0.0559 &0.0559\\ \hline Q2 &0.0646 &0.0646 &0.0646 &0.0646 &0.0646 &0.0646 &0.0646 &0.0646 &0.0646 &0.0646 &0.0646 &0.0646\\ \hline Q3 &0.0683 &0.0683 &0.0683 &0.0683 &0.0683 &0.0683 &0.0683 &0.0683 &0.0683 &0.0683 &0.0683 &0.0683\\ \hline R1 &0.049 &0.049 &0.049 &0.049 &0.049 &0.049 &0.049 &0.049 &0.049 &0.049 &0.049 &0.049\\ \hline R2 &0.1056 &0.1056 &0.1056 &0.1056 &0.1056 &0.1056 &0.1056 &0.1056 &0.1056 &0.1056 &0.1056 &0.1056\\ \hline R3 &0.0967 &0.0967 &0.0967 &0.0967 &0.0967 &0.0967 &0.0967 &0.0967 &0.0967 &0.0967 &0.0967 &0.0967\\ \hline \end{array} $$

权重的求解

$$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{12 \times1}} &权重\\ \hline B1 &0.15427\\ \hline B2 &0.06622\\ \hline B3 &0.07426\\ \hline E1 &0.08454\\ \hline E2 &0.07219\\ \hline E3 &0.10836\\ \hline Q1 &0.05591\\ \hline Q2 &0.0646\\ \hline Q3 &0.06834\\ \hline R1 &0.04895\\ \hline R2 &0.10561\\ \hline R3 &0.09675\\ \hline \end{array} $$$$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{1 \times12}} &B1 &B2 &B3 &E1 &E2 &E3 &Q1 &Q2 &Q3 &R1 &R2 &R3\\ \hline 权重 &0.15427 &0.06622 &0.07426 &0.08454 &0.07219 &0.10836 &0.05591 &0.0646 &0.06834 &0.04895 &0.10561 &0.09675\\ \hline \end{array} $$

归一化求子系统的权重

$$\omega =\begin{array}{c|c|c|c|c|c|c}{M_{4 \times1}} &权重\\ \hline B &0.2947\\ \hline E &0.2651\\ \hline Q &0.1889\\ \hline R &0.2513\\ \hline \end{array} $$$$\omega =\begin{array}{c|c|c|c|c|c|c}{M_{1 \times4}} &B &E &Q &R\\ \hline 权重 &0.2947 &0.2651 &0.1889 &0.2513\\ \hline \end{array} $$