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

$$ \require{cancel} \require{AMScd} \begin{CD} O @>>>N \\ \end{CD} $$
$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{12 \times12}} &B1 &B2 &B3 &E1 &E2 &E3 &Q1 &Q2 &Q3 &R1 &R2 &R3\\ \hline B1 &0 &0.09 &0.09 &0.09 &0.115 &0.09 &0.051 &0.09 &0.09 &0.09 &0.09 &0.115\\ \hline B2 &0.038 &0 &0 &0.038 &0.038 &0.038 &0.051 &0.038 &0.038 &0.038 &0.051 &0.038\\ \hline B3 &0.038 &0 &0 &0.038 &0 &0.038 &0.051 &0.09 &0.038 &0.09 &0.064 &0.051\\ \hline E1 &0.051 &0 &0.051 &0 &0 &0.038 &0.051 &0.064 &0.038 &0.09 &0.077 &0.077\\ \hline E2 &0.064 &0 &0 &0.013 &0 &0.038 &0.051 &0.051 &0.064 &0.09 &0.09 &0.013\\ \hline E3 &0.077 &0.064 &0.038 &0.026 &0.09 &0 &0.09 &0.09 &0.09 &0.09 &0.09 &0.013\\ \hline Q1 &0.09 &0 &0.051 &0.038 &0 &0 &0 &0.038 &0.051 &0.038 &0 &0.038\\ \hline Q2 &0.103 &0.077 &0.038 &0.051 &0 &0 &0.013 &0 &0 &0.103 &0.038 &0.013\\ \hline Q3 &0.103 &0.103 &0.051 &0.064 &0 &0 &0.013 &0 &0 &0.064 &0.038 &0.013\\ \hline R1 &0.103 &0.103 &0.038 &0.038 &0 &0 &0 &0 &0 &0 &0 &0.013\\ \hline R2 &0.103 &0.103 &0.051 &0.115 &0.051 &0.051 &0.051 &0.051 &0.051 &0.051 &0 &0.013\\ \hline R3 &0.051 &0.103 &0 &0.09 &0.038 &0.09 &0.051 &0.09 &0.09 &0 &0.026 &0\\ \hline \end{array} $$

综合影响矩阵求解过程

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

综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{12 \times12}} &B1 &B2 &B3 &E1 &E2 &E3 &Q1 &Q2 &Q3 &R1 &R2 &R3\\ \hline B1 &0.149 &0.207 &0.161 &0.197 &0.171 &0.158 &0.135 &0.192 &0.183 &0.219 &0.188 &0.183\\ \hline B2 &0.103 &0.055 &0.036 &0.087 &0.066 &0.068 &0.086 &0.083 &0.08 &0.095 &0.092 &0.071\\ \hline B3 &0.118 &0.07 &0.044 &0.098 &0.032 &0.072 &0.089 &0.138 &0.084 &0.154 &0.109 &0.088\\ \hline E1 &0.135 &0.077 &0.097 &0.068 &0.037 &0.078 &0.095 &0.122 &0.091 &0.158 &0.126 &0.117\\ \hline E2 &0.141 &0.07 &0.046 &0.073 &0.034 &0.071 &0.088 &0.098 &0.109 &0.153 &0.133 &0.051\\ \hline E3 &0.19 &0.156 &0.1 &0.112 &0.133 &0.051 &0.146 &0.161 &0.156 &0.189 &0.16 &0.071\\ \hline Q1 &0.14 &0.05 &0.084 &0.083 &0.026 &0.031 &0.03 &0.08 &0.087 &0.09 &0.04 &0.073\\ \hline Q2 &0.163 &0.133 &0.077 &0.104 &0.034 &0.037 &0.051 &0.05 &0.044 &0.159 &0.084 &0.056\\ \hline Q3 &0.163 &0.157 &0.09 &0.118 &0.035 &0.04 &0.054 &0.054 &0.047 &0.125 &0.088 &0.058\\ \hline R1 &0.14 &0.137 &0.065 &0.076 &0.028 &0.031 &0.031 &0.04 &0.036 &0.045 &0.039 &0.047\\ \hline R2 &0.2 &0.18 &0.109 &0.188 &0.097 &0.102 &0.111 &0.127 &0.12 &0.15 &0.078 &0.076\\ \hline R3 &0.146 &0.176 &0.054 &0.157 &0.081 &0.13 &0.106 &0.154 &0.149 &0.092 &0.095 &0.051\\ \hline \end{array} $$

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。 $$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{12 \times12}} &B1 &B2 &B3 &E1 &E2 &E3 &Q1 &Q2 &Q3 &R1 &R2 &R3\\ \hline B1 &0.0834 &0.1412 &0.1672 &0.1447 &0.2215 &0.1814 &0.1318 &0.1482 &0.1544 &0.1345 &0.1523 &0.1944\\ \hline B2 &0.0577 &0.0372 &0.0378 &0.0641 &0.0854 &0.0785 &0.0839 &0.0636 &0.0678 &0.0581 &0.075 &0.0748\\ \hline B3 &0.0658 &0.0479 &0.0457 &0.072 &0.041 &0.0828 &0.0873 &0.1065 &0.0706 &0.0943 &0.0882 &0.0936\\ \hline E1 &0.0757 &0.0525 &0.1004 &0.0501 &0.0473 &0.0901 &0.0927 &0.0938 &0.0769 &0.0973 &0.1021 &0.1243\\ \hline E2 &0.0789 &0.048 &0.0475 &0.054 &0.0442 &0.0819 &0.0866 &0.0758 &0.0916 &0.0937 &0.1081 &0.0539\\ \hline E3 &0.1062 &0.1061 &0.1042 &0.082 &0.1721 &0.0586 &0.1426 &0.1237 &0.1317 &0.1158 &0.13 &0.0752\\ \hline Q1 &0.0783 &0.0343 &0.0871 &0.0608 &0.0332 &0.0351 &0.0297 &0.0613 &0.0732 &0.0552 &0.0326 &0.0773\\ \hline Q2 &0.0911 &0.0905 &0.08 &0.0761 &0.0436 &0.043 &0.0496 &0.0383 &0.0372 &0.0977 &0.0683 &0.0592\\ \hline Q3 &0.0914 &0.1066 &0.0936 &0.0866 &0.0455 &0.0458 &0.0529 &0.0413 &0.0397 &0.077 &0.0714 &0.062\\ \hline R1 &0.0783 &0.0935 &0.0673 &0.0559 &0.0362 &0.0352 &0.0304 &0.0309 &0.0301 &0.0279 &0.0316 &0.0503\\ \hline R2 &0.1118 &0.1227 &0.1135 &0.1385 &0.1259 &0.1176 &0.1089 &0.0981 &0.1008 &0.092 &0.0633 &0.0804\\ \hline R3 &0.0815 &0.1196 &0.0556 &0.1152 &0.1041 &0.15 &0.1035 &0.1185 &0.1261 &0.0565 &0.0771 &0.0545\\ \hline \end{array} $$

极限超矩阵求解：

$$limit W=\begin{array}{c|c|c|c|c|c|c}{M_{12 \times12}} &B1 &B2 &B3 &E1 &E2 &E3 &Q1 &Q2 &Q3 &R1 &R2 &R3\\ \hline B1 &0.1517 &0.1517 &0.1517 &0.1517 &0.1517 &0.1517 &0.1517 &0.1517 &0.1517 &0.1517 &0.1517 &0.1517\\ \hline B2 &0.0657 &0.0657 &0.0657 &0.0657 &0.0657 &0.0657 &0.0657 &0.0657 &0.0657 &0.0657 &0.0657 &0.0657\\ \hline B3 &0.0744 &0.0744 &0.0744 &0.0744 &0.0744 &0.0744 &0.0744 &0.0744 &0.0744 &0.0744 &0.0744 &0.0744\\ \hline E1 &0.0841 &0.0841 &0.0841 &0.0841 &0.0841 &0.0841 &0.0841 &0.0841 &0.0841 &0.0841 &0.0841 &0.0841\\ \hline E2 &0.0728 &0.0728 &0.0728 &0.0728 &0.0728 &0.0728 &0.0728 &0.0728 &0.0728 &0.0728 &0.0728 &0.0728\\ \hline E3 &0.1086 &0.1086 &0.1086 &0.1086 &0.1086 &0.1086 &0.1086 &0.1086 &0.1086 &0.1086 &0.1086 &0.1086\\ \hline Q1 &0.0563 &0.0563 &0.0563 &0.0563 &0.0563 &0.0563 &0.0563 &0.0563 &0.0563 &0.0563 &0.0563 &0.0563\\ \hline Q2 &0.0656 &0.0656 &0.0656 &0.0656 &0.0656 &0.0656 &0.0656 &0.0656 &0.0656 &0.0656 &0.0656 &0.0656\\ \hline Q3 &0.0692 &0.0692 &0.0692 &0.0692 &0.0692 &0.0692 &0.0692 &0.0692 &0.0692 &0.0692 &0.0692 &0.0692\\ \hline R1 &0.0496 &0.0496 &0.0496 &0.0496 &0.0496 &0.0496 &0.0496 &0.0496 &0.0496 &0.0496 &0.0496 &0.0496\\ \hline R2 &0.1056 &0.1056 &0.1056 &0.1056 &0.1056 &0.1056 &0.1056 &0.1056 &0.1056 &0.1056 &0.1056 &0.1056\\ \hline R3 &0.0964 &0.0964 &0.0964 &0.0964 &0.0964 &0.0964 &0.0964 &0.0964 &0.0964 &0.0964 &0.0964 &0.0964\\ \hline \end{array} $$

权重的求解

$$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{12 \times1}} &权重\\ \hline B1 &0.15168\\ \hline B2 &0.06573\\ \hline B3 &0.07437\\ \hline E1 &0.08413\\ \hline E2 &0.07276\\ \hline E3 &0.10858\\ \hline Q1 &0.05634\\ \hline Q2 &0.06561\\ \hline Q3 &0.06918\\ \hline R1 &0.04958\\ \hline R2 &0.1056\\ \hline R3 &0.09643\\ \hline \end{array} $$$$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{1 \times12}} &B1 &B2 &B3 &E1 &E2 &E3 &Q1 &Q2 &Q3 &R1 &R2 &R3\\ \hline 权重 &0.15168 &0.06573 &0.07437 &0.08413 &0.07276 &0.10858 &0.05634 &0.06561 &0.06918 &0.04958 &0.1056 &0.09643\\ \hline \end{array} $$

归一化求子系统的权重

$$\omega =\begin{array}{c|c|c|c|c|c|c}{M_{4 \times1}} &权重\\ \hline B &0.2918\\ \hline E &0.2655\\ \hline Q &0.1911\\ \hline R &0.2516\\ \hline \end{array} $$$$\omega =\begin{array}{c|c|c|c|c|c|c}{M_{1 \times4}} &B &E &Q &R\\ \hline 权重 &0.2918 &0.2655 &0.1911 &0.2516\\ \hline \end{array} $$