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

$$ \require{cancel} \require{AMScd} \begin{CD} O @>>>N \\ \end{CD} $$
$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{12 \times12}} &T1 &T2 &T3 &K1 &K2 &K3 &H1 &H2 &H3 &R1 &R2 &R3\\ \hline T1 &0 &0.129 &0.129 &0 &0.081 &0.048 &0.048 &0.097 &0.113 &0.113 &0.113 &0.129\\ \hline T2 &0.129 &0 &0 &0.048 &0.048 &0.048 &0.065 &0.048 &0.048 &0.048 &0.065 &0.129\\ \hline T3 &0.129 &0 &0 &0.048 &0 &0.048 &0.065 &0.113 &0.048 &0.113 &0.081 &0.097\\ \hline K1 &0.129 &0 &0.065 &0 &0 &0.048 &0.065 &0.081 &0.048 &0.113 &0.097 &0.081\\ \hline K2 &0.129 &0 &0 &0.016 &0 &0.048 &0.065 &0.065 &0.081 &0.129 &0.113 &0.048\\ \hline K3 &0.129 &0 &0.048 &0.032 &0.113 &0 &0.113 &0.113 &0.113 &0.113 &0.113 &0.048\\ \hline H1 &0.129 &0 &0.065 &0.048 &0 &0 &0 &0.048 &0.065 &0.048 &0 &0.097\\ \hline H2 &0.016 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline H3 &0.129 &0 &0 &0.081 &0.048 &0.048 &0.097 &0 &0 &0.081 &0.048 &0.016\\ \hline R1 &0.129 &0 &0.048 &0.048 &0 &0 &0 &0.113 &0 &0 &0 &0.016\\ \hline R2 &0.129 &0 &0.065 &0.145 &0.065 &0.065 &0.065 &0.113 &0.065 &0.065 &0 &0.016\\ \hline R3 &0.065 &0 &0 &0.113 &0.048 &0.113 &0.113 &0.113 &0.113 &0 &0.032 &0\\ \hline \end{array} $$

综合影响矩阵求解过程

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

综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{12 \times12}} &T1 &T2 &T3 &K1 &K2 &K3 &H1 &H2 &H3 &R1 &R2 &R3\\ \hline T1 &0.252 &0.161 &0.218 &0.133 &0.166 &0.15 &0.191 &0.288 &0.254 &0.272 &0.239 &0.26\\ \hline T2 &0.299 &0.039 &0.083 &0.14 &0.118 &0.126 &0.17 &0.193 &0.166 &0.171 &0.164 &0.228\\ \hline T3 &0.296 &0.038 &0.085 &0.137 &0.067 &0.119 &0.161 &0.256 &0.156 &0.227 &0.171 &0.193\\ \hline K1 &0.301 &0.039 &0.149 &0.094 &0.068 &0.12 &0.163 &0.23 &0.158 &0.231 &0.189 &0.181\\ \hline K2 &0.296 &0.038 &0.085 &0.106 &0.067 &0.115 &0.158 &0.204 &0.183 &0.243 &0.2 &0.142\\ \hline K3 &0.35 &0.045 &0.15 &0.144 &0.188 &0.089 &0.232 &0.287 &0.243 &0.268 &0.23 &0.173\\ \hline H1 &0.247 &0.032 &0.123 &0.111 &0.048 &0.058 &0.077 &0.153 &0.145 &0.137 &0.075 &0.172\\ \hline H2 &0.02 &0.003 &0.004 &0.002 &0.003 &0.002 &0.003 &0.005 &0.004 &0.004 &0.004 &0.004\\ \hline H3 &0.276 &0.036 &0.079 &0.149 &0.103 &0.105 &0.176 &0.125 &0.097 &0.189 &0.134 &0.11\\ \hline R1 &0.197 &0.025 &0.09 &0.08 &0.03 &0.034 &0.044 &0.178 &0.052 &0.06 &0.051 &0.07\\ \hline R2 &0.318 &0.041 &0.156 &0.226 &0.13 &0.138 &0.171 &0.266 &0.181 &0.208 &0.116 &0.134\\ \hline R3 &0.24 &0.031 &0.08 &0.19 &0.113 &0.175 &0.212 &0.24 &0.217 &0.13 &0.132 &0.1\\ \hline \end{array} $$

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。 $$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{12 \times12}} &T1 &T2 &T3 &K1 &K2 &K3 &H1 &H2 &H3 &R1 &R2 &R3\\ \hline T1 &0.0814 &0.306 &0.1676 &0.0878 &0.1506 &0.1221 &0.1084 &0.1188 &0.1367 &0.1272 &0.1399 &0.1473\\ \hline T2 &0.0966 &0.073 &0.064 &0.0924 &0.1072 &0.1019 &0.0967 &0.0797 &0.0894 &0.0798 &0.096 &0.1291\\ \hline T3 &0.0957 &0.0723 &0.0654 &0.0908 &0.0608 &0.0966 &0.0918 &0.1057 &0.0843 &0.106 &0.1005 &0.1091\\ \hline K1 &0.0973 &0.0735 &0.1145 &0.062 &0.062 &0.0975 &0.0928 &0.0947 &0.0853 &0.1081 &0.1108 &0.1022\\ \hline K2 &0.0957 &0.0723 &0.0656 &0.0702 &0.061 &0.0933 &0.0897 &0.0842 &0.0985 &0.1134 &0.1172 &0.0806\\ \hline K3 &0.1132 &0.0856 &0.1151 &0.0955 &0.1708 &0.072 &0.1319 &0.1182 &0.1312 &0.1251 &0.1348 &0.0981\\ \hline H1 &0.0798 &0.0603 &0.0943 &0.0733 &0.0437 &0.0474 &0.0438 &0.0632 &0.0781 &0.0641 &0.044 &0.0973\\ \hline H2 &0.0065 &0.0049 &0.0027 &0.0014 &0.0024 &0.002 &0.0017 &0.0019 &0.0022 &0.0021 &0.0023 &0.0024\\ \hline H3 &0.0893 &0.0675 &0.061 &0.0983 &0.0934 &0.0854 &0.1002 &0.0517 &0.052 &0.0885 &0.0788 &0.0622\\ \hline R1 &0.0636 &0.048 &0.0688 &0.0529 &0.0273 &0.0277 &0.0251 &0.0734 &0.028 &0.028 &0.0298 &0.0395\\ \hline R2 &0.1031 &0.0779 &0.1194 &0.1496 &0.1184 &0.1121 &0.0974 &0.1095 &0.0974 &0.0973 &0.0682 &0.0756\\ \hline R3 &0.0777 &0.0587 &0.0616 &0.1259 &0.1024 &0.142 &0.1205 &0.099 &0.117 &0.0606 &0.0777 &0.0567\\ \hline \end{array} $$

极限超矩阵求解：

$$limit W=\begin{array}{c|c|c|c|c|c|c}{M_{12 \times12}} &T1 &T2 &T3 &K1 &K2 &K3 &H1 &H2 &H3 &R1 &R2 &R3\\ \hline T1 &0.1416 &0.1416 &0.1416 &0.1416 &0.1416 &0.1416 &0.1416 &0.1416 &0.1416 &0.1416 &0.1416 &0.1416\\ \hline T2 &0.0942 &0.0942 &0.0942 &0.0942 &0.0942 &0.0942 &0.0942 &0.0942 &0.0942 &0.0942 &0.0942 &0.0942\\ \hline T3 &0.0885 &0.0885 &0.0885 &0.0885 &0.0885 &0.0885 &0.0885 &0.0885 &0.0885 &0.0885 &0.0885 &0.0885\\ \hline K1 &0.0913 &0.0913 &0.0913 &0.0913 &0.0913 &0.0913 &0.0913 &0.0913 &0.0913 &0.0913 &0.0913 &0.0913\\ \hline K2 &0.0865 &0.0865 &0.0865 &0.0865 &0.0865 &0.0865 &0.0865 &0.0865 &0.0865 &0.0865 &0.0865 &0.0865\\ \hline K3 &0.1135 &0.1135 &0.1135 &0.1135 &0.1135 &0.1135 &0.1135 &0.1135 &0.1135 &0.1135 &0.1135 &0.1135\\ \hline H1 &0.0666 &0.0666 &0.0666 &0.0666 &0.0666 &0.0666 &0.0666 &0.0666 &0.0666 &0.0666 &0.0666 &0.0666\\ \hline H2 &0.003 &0.003 &0.003 &0.003 &0.003 &0.003 &0.003 &0.003 &0.003 &0.003 &0.003 &0.003\\ \hline H3 &0.0795 &0.0795 &0.0795 &0.0795 &0.0795 &0.0795 &0.0795 &0.0795 &0.0795 &0.0795 &0.0795 &0.0795\\ \hline R1 &0.0419 &0.0419 &0.0419 &0.0419 &0.0419 &0.0419 &0.0419 &0.0419 &0.0419 &0.0419 &0.0419 &0.0419\\ \hline R2 &0.1016 &0.1016 &0.1016 &0.1016 &0.1016 &0.1016 &0.1016 &0.1016 &0.1016 &0.1016 &0.1016 &0.1016\\ \hline R3 &0.0917 &0.0917 &0.0917 &0.0917 &0.0917 &0.0917 &0.0917 &0.0917 &0.0917 &0.0917 &0.0917 &0.0917\\ \hline \end{array} $$

权重的求解

$$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{12 \times1}} &权重\\ \hline T1 &0.14159\\ \hline T2 &0.09423\\ \hline T3 &0.08845\\ \hline K1 &0.09135\\ \hline K2 &0.08654\\ \hline K3 &0.11346\\ \hline H1 &0.06659\\ \hline H2 &0.00302\\ \hline H3 &0.07954\\ \hline R1 &0.04189\\ \hline R2 &0.10161\\ \hline R3 &0.09172\\ \hline \end{array} $$$$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{1 \times12}} &T1 &T2 &T3 &K1 &K2 &K3 &H1 &H2 &H3 &R1 &R2 &R3\\ \hline 权重 &0.14159 &0.09423 &0.08845 &0.09135 &0.08654 &0.11346 &0.06659 &0.00302 &0.07954 &0.04189 &0.10161 &0.09172\\ \hline \end{array} $$

归一化求子系统的权重

$$\omega =\begin{array}{c|c|c|c|c|c|c}{M_{4 \times1}} &权重\\ \hline T &0.3243\\ \hline K &0.2913\\ \hline H &0.1491\\ \hline R &0.2352\\ \hline \end{array} $$$$\omega =\begin{array}{c|c|c|c|c|c|c}{M_{1 \times4}} &T &K &H &R\\ \hline 权重 &0.3243 &0.2913 &0.1491 &0.2352\\ \hline \end{array} $$