原始矩阵（直接影响矩阵）为

$$Ori=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{12 \times12}} &A1 &A2 &A3 &K1 &K2 &K3 &X1 &X2 &X3 &R1 &R2 &R3\\ \hline A1 &0 &7 &7 &7 &7 &7 &7 &7 &7 &7 &7 &9\\ \hline A2 &8 &0 &0 &3 &3 &3 &4 &3 &3 &3 &4 &0\\ \hline A3 &8 &0 &0 &3 &0 &3 &4 &7 &3 &7 &5 &0\\ \hline K1 &8 &0 &4 &0 &0 &3 &4 &5 &3 &7 &6 &0\\ \hline K2 &8 &0 &0 &1 &0 &3 &4 &4 &5 &7 &7 &1\\ \hline K3 &8 &5 &3 &2 &7 &0 &7 &7 &7 &7 &7 &1\\ \hline X1 &8 &0 &4 &3 &0 &0 &0 &3 &4 &3 &0 &3\\ \hline X2 &8 &6 &3 &4 &0 &0 &1 &0 &0 &8 &3 &1\\ \hline X3 &8 &8 &0 &5 &0 &0 &1 &0 &0 &5 &3 &1\\ \hline R1 &8 &8 &3 &3 &0 &0 &0 &0 &0 &0 &0 &1\\ \hline R2 &8 &8 &4 &9 &4 &4 &4 &4 &4 &4 &0 &1\\ \hline R3 &4 &8 &0 &7 &3 &7 &7 &7 &7 &0 &2 &0\\ \hline \end{array} $$

规范直接关系矩阵求解过程

$$ \require{cancel} \require{AMScd} \begin{CD} O @>>>N \\ \end{CD} $$
$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{12 \times12}} &A1 &A2 &A3 &K1 &K2 &K3 &X1 &X2 &X3 &R1 &R2 &R3\\ \hline A1 &0 &0.083 &0.083 &0.083 &0.083 &0.083 &0.083 &0.083 &0.083 &0.083 &0.083 &0.107\\ \hline A2 &0.095 &0 &0 &0.036 &0.036 &0.036 &0.048 &0.036 &0.036 &0.036 &0.048 &0\\ \hline A3 &0.095 &0 &0 &0.036 &0 &0.036 &0.048 &0.083 &0.036 &0.083 &0.06 &0\\ \hline K1 &0.095 &0 &0.048 &0 &0 &0.036 &0.048 &0.06 &0.036 &0.083 &0.071 &0\\ \hline K2 &0.095 &0 &0 &0.012 &0 &0.036 &0.048 &0.048 &0.06 &0.083 &0.083 &0.012\\ \hline K3 &0.095 &0.06 &0.036 &0.024 &0.083 &0 &0.083 &0.083 &0.083 &0.083 &0.083 &0.012\\ \hline X1 &0.095 &0 &0.048 &0.036 &0 &0 &0 &0.036 &0.048 &0.036 &0 &0.036\\ \hline X2 &0.095 &0.071 &0.036 &0.048 &0 &0 &0.012 &0 &0 &0.095 &0.036 &0.012\\ \hline X3 &0.095 &0.095 &0 &0.06 &0 &0 &0.012 &0 &0 &0.06 &0.036 &0.012\\ \hline R1 &0.095 &0.095 &0.036 &0.036 &0 &0 &0 &0 &0 &0 &0 &0.012\\ \hline R2 &0.095 &0.095 &0.048 &0.107 &0.048 &0.048 &0.048 &0.048 &0.048 &0.048 &0 &0.012\\ \hline R3 &0.048 &0.095 &0 &0.083 &0.036 &0.083 &0.083 &0.083 &0.083 &0 &0.024 &0\\ \hline \end{array} $$

综合影响矩阵求解过程

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

综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{12 \times12}} &A1 &A2 &A3 &K1 &K2 &K3 &X1 &X2 &X3 &R1 &R2 &R3\\ \hline A1 &0.159 &0.179 &0.138 &0.172 &0.127 &0.138 &0.161 &0.167 &0.16 &0.19 &0.163 &0.141\\ \hline A2 &0.163 &0.049 &0.034 &0.08 &0.062 &0.064 &0.085 &0.076 &0.075 &0.09 &0.088 &0.026\\ \hline A3 &0.174 &0.06 &0.04 &0.088 &0.028 &0.065 &0.087 &0.126 &0.075 &0.143 &0.101 &0.028\\ \hline K1 &0.175 &0.06 &0.085 &0.054 &0.029 &0.066 &0.088 &0.104 &0.077 &0.143 &0.113 &0.028\\ \hline K2 &0.174 &0.064 &0.039 &0.067 &0.03 &0.067 &0.089 &0.091 &0.101 &0.141 &0.124 &0.04\\ \hline K3 &0.214 &0.138 &0.085 &0.098 &0.118 &0.044 &0.14 &0.144 &0.141 &0.169 &0.145 &0.049\\ \hline X1 &0.148 &0.043 &0.073 &0.074 &0.02 &0.026 &0.033 &0.071 &0.078 &0.08 &0.034 &0.056\\ \hline X2 &0.161 &0.117 &0.067 &0.09 &0.025 &0.03 &0.049 &0.04 &0.036 &0.142 &0.073 &0.035\\ \hline X3 &0.155 &0.136 &0.029 &0.099 &0.025 &0.03 &0.048 &0.038 &0.035 &0.103 &0.072 &0.034\\ \hline R1 &0.14 &0.123 &0.057 &0.066 &0.021 &0.025 &0.031 &0.033 &0.029 &0.038 &0.032 &0.03\\ \hline R2 &0.202 &0.158 &0.092 &0.166 &0.082 &0.089 &0.105 &0.11 &0.103 &0.129 &0.065 &0.044\\ \hline R3 &0.153 &0.156 &0.042 &0.14 &0.069 &0.117 &0.135 &0.138 &0.135 &0.079 &0.082 &0.029\\ \hline \end{array} $$

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。 $$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{12 \times12}} &A1 &A2 &A3 &K1 &K2 &K3 &X1 &X2 &X3 &R1 &R2 &R3\\ \hline A1 &0.0786 &0.1396 &0.1767 &0.1439 &0.2005 &0.1813 &0.1529 &0.1472 &0.1534 &0.1313 &0.149 &0.2609\\ \hline A2 &0.081 &0.0385 &0.0435 &0.0674 &0.0969 &0.0837 &0.0812 &0.0671 &0.0714 &0.0623 &0.0804 &0.048\\ \hline A3 &0.0862 &0.0471 &0.0507 &0.0732 &0.044 &0.0854 &0.083 &0.1103 &0.0721 &0.0987 &0.0926 &0.052\\ \hline K1 &0.0865 &0.047 &0.1096 &0.0451 &0.0451 &0.0868 &0.084 &0.0917 &0.0732 &0.0986 &0.1033 &0.0521\\ \hline K2 &0.0864 &0.0496 &0.0494 &0.0562 &0.0468 &0.0875 &0.0843 &0.08 &0.0966 &0.0973 &0.1134 &0.0746\\ \hline K3 &0.106 &0.1078 &0.1084 &0.082 &0.1867 &0.0584 &0.1332 &0.1268 &0.135 &0.1169 &0.1325 &0.0904\\ \hline X1 &0.0735 &0.0333 &0.0936 &0.0615 &0.0311 &0.0344 &0.031 &0.0621 &0.0747 &0.0552 &0.0316 &0.1044\\ \hline X2 &0.0796 &0.091 &0.0857 &0.0755 &0.0391 &0.04 &0.0469 &0.0355 &0.0344 &0.098 &0.0671 &0.0647\\ \hline X3 &0.077 &0.1059 &0.0378 &0.083 &0.0392 &0.0388 &0.0458 &0.0332 &0.0334 &0.0715 &0.0659 &0.0626\\ \hline R1 &0.0694 &0.096 &0.0731 &0.0556 &0.0328 &0.0332 &0.0298 &0.0291 &0.0281 &0.0261 &0.0297 &0.0558\\ \hline R2 &0.1001 &0.1229 &0.1181 &0.1392 &0.1295 &0.1169 &0.0997 &0.0962 &0.0989 &0.0894 &0.0592 &0.0817\\ \hline R3 &0.0757 &0.1213 &0.0534 &0.1173 &0.1083 &0.1535 &0.128 &0.1209 &0.1289 &0.0545 &0.0754 &0.0528\\ \hline \end{array} $$

极限超矩阵求解：

$$limit W=\begin{array}{c|c|c|c|c|c|c}{M_{12 \times12}} &A1 &A2 &A3 &K1 &K2 &K3 &X1 &X2 &X3 &R1 &R2 &R3\\ \hline A1 &0.157 &0.157 &0.157 &0.157 &0.157 &0.157 &0.157 &0.157 &0.157 &0.157 &0.157 &0.157\\ \hline A2 &0.0701 &0.0701 &0.0701 &0.0701 &0.0701 &0.0701 &0.0701 &0.0701 &0.0701 &0.0701 &0.0701 &0.0701\\ \hline A3 &0.0749 &0.0749 &0.0749 &0.0749 &0.0749 &0.0749 &0.0749 &0.0749 &0.0749 &0.0749 &0.0749 &0.0749\\ \hline K1 &0.0774 &0.0774 &0.0774 &0.0774 &0.0774 &0.0774 &0.0774 &0.0774 &0.0774 &0.0774 &0.0774 &0.0774\\ \hline K2 &0.078 &0.078 &0.078 &0.078 &0.078 &0.078 &0.078 &0.078 &0.078 &0.078 &0.078 &0.078\\ \hline K3 &0.1118 &0.1118 &0.1118 &0.1118 &0.1118 &0.1118 &0.1118 &0.1118 &0.1118 &0.1118 &0.1118 &0.1118\\ \hline X1 &0.0582 &0.0582 &0.0582 &0.0582 &0.0582 &0.0582 &0.0582 &0.0582 &0.0582 &0.0582 &0.0582 &0.0582\\ \hline X2 &0.0637 &0.0637 &0.0637 &0.0637 &0.0637 &0.0637 &0.0637 &0.0637 &0.0637 &0.0637 &0.0637 &0.0637\\ \hline X3 &0.0593 &0.0593 &0.0593 &0.0593 &0.0593 &0.0593 &0.0593 &0.0593 &0.0593 &0.0593 &0.0593 &0.0593\\ \hline R1 &0.0487 &0.0487 &0.0487 &0.0487 &0.0487 &0.0487 &0.0487 &0.0487 &0.0487 &0.0487 &0.0487 &0.0487\\ \hline R2 &0.1034 &0.1034 &0.1034 &0.1034 &0.1034 &0.1034 &0.1034 &0.1034 &0.1034 &0.1034 &0.1034 &0.1034\\ \hline R3 &0.0975 &0.0975 &0.0975 &0.0975 &0.0975 &0.0975 &0.0975 &0.0975 &0.0975 &0.0975 &0.0975 &0.0975\\ \hline \end{array} $$

权重的求解

$$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{12 \times1}} &权重\\ \hline A1 &0.15701\\ \hline A2 &0.07006\\ \hline A3 &0.07487\\ \hline K1 &0.07743\\ \hline K2 &0.07799\\ \hline K3 &0.11181\\ \hline X1 &0.05824\\ \hline X2 &0.06372\\ \hline X3 &0.05934\\ \hline R1 &0.04872\\ \hline R2 &0.10336\\ \hline R3 &0.09747\\ \hline \end{array} $$$$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{1 \times12}} &A1 &A2 &A3 &K1 &K2 &K3 &X1 &X2 &X3 &R1 &R2 &R3\\ \hline 权重 &0.15701 &0.07006 &0.07487 &0.07743 &0.07799 &0.11181 &0.05824 &0.06372 &0.05934 &0.04872 &0.10336 &0.09747\\ \hline \end{array} $$

归一化求子系统的权重

$$\omega =\begin{array}{c|c|c|c|c|c|c}{M_{4 \times1}} &权重\\ \hline A &0.3019\\ \hline K &0.2672\\ \hline X &0.1813\\ \hline R &0.2496\\ \hline \end{array} $$$$\omega =\begin{array}{c|c|c|c|c|c|c}{M_{1 \times4}} &A &K &X &R\\ \hline 权重 &0.3019 &0.2672 &0.1813 &0.2496\\ \hline \end{array} $$