原始矩阵（直接影响矩阵）为

$$Ori=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{16 \times16}} &C1 &C2 &C3 &C4 &C5 &E1 &E2 &E3 &F1 &F2 &F3 &U1 &U2 &D1 &D2 &D3\\ \hline C1 &0 &7.12 &7.52 &8.92 &7.36 &8.24 &8.56 &8.4 &8.92 &1.28 &1.4 &8.08 &8.92 &2.36 &7.12 &1.04\\ \hline C2 &8.32 &0 &5.12 &8.88 &8.92 &2.16 &2.96 &7.16 &8.92 &1.56 &5.16 &4.12 &5 &5.12 &4.12 &2.68\\ \hline C3 &7.44 &2.32 &0 &8.8 &3.08 &7.12 &1.04 &8.92 &8.56 &0.24 &0.26 &5.52 &6.64 &4.48 &6.52 &3.08\\ \hline C4 &7.04 &5.12 &2.04 &0 &8.76 &7.16 &2.48 &7.28 &8.16 &1.2 &2.12 &5.08 &8.6 &3.12 &6.08 &2.2\\ \hline C5 &8.92 &8.56 &7.96 &7.08 &0 &4.84 &4.76 &6.56 &8.72 &1.76 &2.12 &8.48 &8.8 &4.16 &6 &3.04\\ \hline E1 &2.12 &1.5 &0.92 &7.12 &2.48 &0 &6.2 &5.04 &8.76 &3.28 &4.52 &2.24 &8.72 &3.5 &8.6 &5.64\\ \hline E2 &2 &7.04 &1.08 &8.72 &3.24 &8.2 &0 &7.08 &8.4 &8.6 &8 &2.12 &8.4 &6.2 &6.84 &8.24\\ \hline E3 &7.02 &3.2 &2.5 &8.96 &4.24 &4.88 &5.24 &0 &6.12 &2.24 &6.2 &2 &8.6 &3.52 &4.22 &6.2\\ \hline F1 &8.56 &8.92 &6.52 &8.6 &8.6 &7.2 &8.2 &8.4 &0 &2.2 &2 &1.12 &2 &5.08 &2.04 &6\\ \hline F2 &1.04 &1.52 &0.096 &1.08 &1.12 &3.04 &3.52 &2.04 &1.56 &0 &7.8 &1.52 &1.5 &6 &2.52 &6.5\\ \hline F3 &4.5 &6.04 &1 &1.16 &2.52 &8 &8.04 &8.96 &2.5 &8.25 &0 &1.24 &1.4 &7.04 &7.72 &7.5\\ \hline U1 &7.08 &8.72 &7.08 &6.52 &1.5 &6.28 &3.2 &8 &4.56 &2.04 &4 &0 &8.4 &7.2 &5.56 &3\\ \hline U2 &7.04 &4.96 &6.08 &7.52 &5.02 &7.2 &7 &8.12 &6.5 &2.12 &2 &8.88 &0 &1.24 &0.64 &8.2\\ \hline D1 &2 &1.04 &3.56 &6.96 &6.52 &8.6 &6.96 &6.4 &2.28 &1.02 &8.2 &1.02 &6.5 &0 &7.64 &8.92\\ \hline D2 &6.08 &7.02 &1.12 &8.32 &7 &8.24 &4.04 &8.92 &8.68 &4.12 &3.32 &8.12 &5.08 &8.92 &0 &3.04\\ \hline D3 &1.2 &1 &0.92 &8.76 &2.12 &8.96 &8.24 &7.28 &0.8 &6.52 &7.16 &8.52 &3.2 &7.2 &8.92 &0\\ \hline \end{array} $$

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_{16 \times16}} &C1 &C2 &C3 &C4 &C5 &E1 &E2 &E3 &F1 &F2 &F3 &U1 &U2 &D1 &D2 &D3\\ \hline C1 &0 &0.054 &0.057 &0.068 &0.056 &0.062 &0.065 &0.064 &0.068 &0.01 &0.011 &0.061 &0.068 &0.018 &0.054 &0.008\\ \hline C2 &0.063 &0 &0.039 &0.067 &0.068 &0.016 &0.022 &0.054 &0.068 &0.012 &0.039 &0.031 &0.038 &0.039 &0.031 &0.02\\ \hline C3 &0.056 &0.018 &0 &0.067 &0.023 &0.054 &0.008 &0.068 &0.065 &0.002 &0.002 &0.042 &0.05 &0.034 &0.049 &0.023\\ \hline C4 &0.053 &0.039 &0.015 &0 &0.066 &0.054 &0.019 &0.055 &0.062 &0.009 &0.016 &0.038 &0.065 &0.024 &0.046 &0.017\\ \hline C5 &0.068 &0.065 &0.06 &0.054 &0 &0.037 &0.036 &0.05 &0.066 &0.013 &0.016 &0.064 &0.067 &0.032 &0.045 &0.023\\ \hline E1 &0.016 &0.011 &0.007 &0.054 &0.019 &0 &0.047 &0.038 &0.066 &0.025 &0.034 &0.017 &0.066 &0.027 &0.065 &0.043\\ \hline E2 &0.015 &0.053 &0.008 &0.066 &0.025 &0.062 &0 &0.054 &0.064 &0.065 &0.061 &0.016 &0.064 &0.047 &0.052 &0.062\\ \hline E3 &0.053 &0.024 &0.019 &0.068 &0.032 &0.037 &0.04 &0 &0.046 &0.017 &0.047 &0.015 &0.065 &0.027 &0.032 &0.047\\ \hline F1 &0.065 &0.068 &0.049 &0.065 &0.065 &0.055 &0.062 &0.064 &0 &0.017 &0.015 &0.008 &0.015 &0.038 &0.015 &0.045\\ \hline F2 &0.008 &0.012 &0.001 &0.008 &0.008 &0.023 &0.027 &0.015 &0.012 &0 &0.059 &0.012 &0.011 &0.045 &0.019 &0.049\\ \hline F3 &0.034 &0.046 &0.008 &0.009 &0.019 &0.061 &0.061 &0.068 &0.019 &0.062 &0 &0.009 &0.011 &0.053 &0.058 &0.057\\ \hline U1 &0.054 &0.066 &0.054 &0.049 &0.011 &0.048 &0.024 &0.061 &0.035 &0.015 &0.03 &0 &0.064 &0.055 &0.042 &0.023\\ \hline U2 &0.053 &0.038 &0.046 &0.057 &0.038 &0.055 &0.053 &0.062 &0.049 &0.016 &0.015 &0.067 &0 &0.009 &0.005 &0.062\\ \hline D1 &0.015 &0.008 &0.027 &0.053 &0.049 &0.065 &0.053 &0.048 &0.017 &0.008 &0.062 &0.008 &0.049 &0 &0.058 &0.068\\ \hline D2 &0.046 &0.053 &0.008 &0.063 &0.053 &0.062 &0.031 &0.068 &0.066 &0.031 &0.025 &0.062 &0.038 &0.068 &0 &0.023\\ \hline D3 &0.009 &0.008 &0.007 &0.066 &0.016 &0.068 &0.062 &0.055 &0.006 &0.049 &0.054 &0.065 &0.024 &0.055 &0.068 &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_{16 \times16}} &C1 &C2 &C3 &C4 &C5 &E1 &E2 &E3 &F1 &F2 &F3 &U1 &U2 &D1 &D2 &D3\\ \hline C1 &0.079 &0.123 &0.107 &0.166 &0.124 &0.149 &0.133 &0.159 &0.156 &0.05 &0.065 &0.122 &0.153 &0.082 &0.125 &0.075\\ \hline C2 &0.127 &0.061 &0.083 &0.149 &0.126 &0.093 &0.085 &0.136 &0.14 &0.045 &0.083 &0.084 &0.11 &0.092 &0.094 &0.076\\ \hline C3 &0.115 &0.072 &0.041 &0.143 &0.08 &0.123 &0.067 &0.142 &0.132 &0.032 &0.045 &0.091 &0.118 &0.082 &0.106 &0.074\\ \hline C4 &0.115 &0.096 &0.06 &0.082 &0.121 &0.124 &0.08 &0.133 &0.132 &0.041 &0.06 &0.09 &0.133 &0.075 &0.104 &0.071\\ \hline C5 &0.14 &0.13 &0.11 &0.149 &0.069 &0.122 &0.105 &0.143 &0.15 &0.051 &0.068 &0.123 &0.147 &0.093 &0.115 &0.086\\ \hline E1 &0.071 &0.063 &0.043 &0.125 &0.071 &0.069 &0.101 &0.11 &0.127 &0.057 &0.076 &0.063 &0.124 &0.075 &0.117 &0.094\\ \hline E2 &0.084 &0.114 &0.052 &0.154 &0.09 &0.145 &0.072 &0.143 &0.14 &0.104 &0.115 &0.074 &0.138 &0.109 &0.121 &0.127\\ \hline E3 &0.11 &0.078 &0.058 &0.142 &0.087 &0.108 &0.098 &0.078 &0.113 &0.051 &0.089 &0.066 &0.129 &0.077 &0.091 &0.099\\ \hline F1 &0.129 &0.125 &0.093 &0.153 &0.126 &0.132 &0.125 &0.148 &0.081 &0.053 &0.066 &0.065 &0.095 &0.095 &0.085 &0.103\\ \hline F2 &0.036 &0.038 &0.019 &0.048 &0.036 &0.062 &0.06 &0.057 &0.045 &0.022 &0.085 &0.036 &0.045 &0.074 &0.053 &0.079\\ \hline F3 &0.086 &0.093 &0.042 &0.085 &0.07 &0.127 &0.117 &0.138 &0.084 &0.096 &0.05 &0.056 &0.076 &0.104 &0.116 &0.11\\ \hline U1 &0.117 &0.121 &0.095 &0.134 &0.073 &0.124 &0.087 &0.143 &0.11 &0.049 &0.078 &0.054 &0.135 &0.108 &0.105 &0.081\\ \hline U2 &0.116 &0.096 &0.089 &0.141 &0.095 &0.13 &0.114 &0.143 &0.123 &0.052 &0.064 &0.119 &0.076 &0.066 &0.072 &0.116\\ \hline D1 &0.074 &0.062 &0.063 &0.13 &0.101 &0.137 &0.112 &0.126 &0.087 &0.046 &0.107 &0.06 &0.116 &0.055 &0.119 &0.121\\ \hline D2 &0.116 &0.117 &0.058 &0.154 &0.118 &0.145 &0.101 &0.157 &0.146 &0.068 &0.08 &0.117 &0.12 &0.126 &0.072 &0.088\\ \hline D3 &0.067 &0.063 &0.043 &0.141 &0.07 &0.14 &0.12 &0.132 &0.076 &0.085 &0.103 &0.11 &0.095 &0.109 &0.129 &0.059\\ \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_{16 \times16}} &C1 &C2 &C3 &C4 &C5 &E1 &E2 &E3 &F1 &F2 &F3 &U1 &U2 &D1 &D2 &D3\\ \hline C1 &0.0499 &0.0846 &0.1014 &0.079 &0.0852 &0.0771 &0.0846 &0.0763 &0.0847 &0.055 &0.0529 &0.0915 &0.0843 &0.0579 &0.0771 &0.0516\\ \hline C2 &0.0803 &0.0419 &0.0788 &0.0708 &0.0864 &0.0484 &0.054 &0.0652 &0.0759 &0.05 &0.0674 &0.0635 &0.0609 &0.0645 &0.0578 &0.0521\\ \hline C3 &0.0727 &0.0497 &0.0391 &0.0683 &0.0547 &0.0637 &0.0423 &0.0679 &0.0718 &0.0354 &0.0362 &0.0681 &0.065 &0.0579 &0.065 &0.051\\ \hline C4 &0.0727 &0.0659 &0.0565 &0.0393 &0.0832 &0.0645 &0.0505 &0.0636 &0.0719 &0.0456 &0.0485 &0.0677 &0.0735 &0.0527 &0.064 &0.0485\\ \hline C5 &0.0886 &0.0895 &0.1038 &0.0711 &0.0474 &0.0633 &0.0667 &0.0688 &0.0813 &0.0561 &0.0551 &0.0927 &0.0814 &0.0652 &0.0707 &0.0589\\ \hline E1 &0.0449 &0.0435 &0.0404 &0.0594 &0.0485 &0.0355 &0.0643 &0.0526 &0.0688 &0.0635 &0.0616 &0.0477 &0.0686 &0.0531 &0.0719 &0.0641\\ \hline E2 &0.0531 &0.0783 &0.0497 &0.0735 &0.0615 &0.075 &0.0457 &0.0685 &0.076 &0.1159 &0.0933 &0.0554 &0.0762 &0.0765 &0.0745 &0.0871\\ \hline E3 &0.0693 &0.054 &0.055 &0.0678 &0.0595 &0.0562 &0.0624 &0.0374 &0.0615 &0.0564 &0.0724 &0.0496 &0.0713 &0.0542 &0.056 &0.068\\ \hline F1 &0.0817 &0.086 &0.0878 &0.0728 &0.0862 &0.0684 &0.0791 &0.0708 &0.0441 &0.0588 &0.0537 &0.0492 &0.0524 &0.0665 &0.0525 &0.0705\\ \hline F2 &0.0227 &0.0265 &0.018 &0.023 &0.0246 &0.0323 &0.0378 &0.0271 &0.0242 &0.024 &0.0685 &0.0272 &0.0249 &0.052 &0.0329 &0.0543\\ \hline F3 &0.0541 &0.0642 &0.0395 &0.0406 &0.0483 &0.0659 &0.0739 &0.066 &0.0455 &0.1062 &0.0405 &0.0418 &0.0418 &0.0734 &0.0715 &0.0752\\ \hline U1 &0.0741 &0.0832 &0.0903 &0.064 &0.0503 &0.064 &0.0554 &0.0686 &0.0599 &0.0548 &0.0631 &0.0409 &0.0748 &0.0757 &0.0649 &0.0555\\ \hline U2 &0.0734 &0.0659 &0.0838 &0.0674 &0.0653 &0.0673 &0.0724 &0.0686 &0.0668 &0.0573 &0.0518 &0.0892 &0.042 &0.0464 &0.0443 &0.0797\\ \hline D1 &0.0465 &0.043 &0.0597 &0.0619 &0.0696 &0.0711 &0.071 &0.0604 &0.0474 &0.0507 &0.0867 &0.0451 &0.0642 &0.0384 &0.0734 &0.0833\\ \hline D2 &0.0736 &0.0805 &0.0551 &0.0736 &0.0812 &0.0749 &0.0639 &0.0751 &0.0791 &0.0757 &0.0646 &0.0877 &0.0663 &0.0888 &0.0443 &0.0601\\ \hline D3 &0.0424 &0.0433 &0.0411 &0.0674 &0.048 &0.0724 &0.076 &0.0631 &0.0413 &0.0946 &0.0835 &0.0828 &0.0522 &0.0767 &0.0793 &0.0402\\ \hline \end{array} $$

极限超矩阵求解：

$$limit W=\begin{array}{c|c|c|c|c|c|c}{M_{16 \times16}} &C1 &C2 &C3 &C4 &C5 &E1 &E2 &E3 &F1 &F2 &F3 &U1 &U2 &D1 &D2 &D3\\ \hline C1 &0.0752 &0.0752 &0.0752 &0.0752 &0.0752 &0.0752 &0.0752 &0.0752 &0.0752 &0.0752 &0.0752 &0.0752 &0.0752 &0.0752 &0.0752 &0.0752\\ \hline C2 &0.0644 &0.0644 &0.0644 &0.0644 &0.0644 &0.0644 &0.0644 &0.0644 &0.0644 &0.0644 &0.0644 &0.0644 &0.0644 &0.0644 &0.0644 &0.0644\\ \hline C3 &0.0578 &0.0578 &0.0578 &0.0578 &0.0578 &0.0578 &0.0578 &0.0578 &0.0578 &0.0578 &0.0578 &0.0578 &0.0578 &0.0578 &0.0578 &0.0578\\ \hline C4 &0.0615 &0.0615 &0.0615 &0.0615 &0.0615 &0.0615 &0.0615 &0.0615 &0.0615 &0.0615 &0.0615 &0.0615 &0.0615 &0.0615 &0.0615 &0.0615\\ \hline C5 &0.0731 &0.0731 &0.0731 &0.0731 &0.0731 &0.0731 &0.0731 &0.0731 &0.0731 &0.0731 &0.0731 &0.0731 &0.0731 &0.0731 &0.0731 &0.0731\\ \hline E1 &0.0555 &0.0555 &0.0555 &0.0555 &0.0555 &0.0555 &0.0555 &0.0555 &0.0555 &0.0555 &0.0555 &0.0555 &0.0555 &0.0555 &0.0555 &0.0555\\ \hline E2 &0.0706 &0.0706 &0.0706 &0.0706 &0.0706 &0.0706 &0.0706 &0.0706 &0.0706 &0.0706 &0.0706 &0.0706 &0.0706 &0.0706 &0.0706 &0.0706\\ \hline E3 &0.0597 &0.0597 &0.0597 &0.0597 &0.0597 &0.0597 &0.0597 &0.0597 &0.0597 &0.0597 &0.0597 &0.0597 &0.0597 &0.0597 &0.0597 &0.0597\\ \hline F1 &0.0679 &0.0679 &0.0679 &0.0679 &0.0679 &0.0679 &0.0679 &0.0679 &0.0679 &0.0679 &0.0679 &0.0679 &0.0679 &0.0679 &0.0679 &0.0679\\ \hline F2 &0.0324 &0.0324 &0.0324 &0.0324 &0.0324 &0.0324 &0.0324 &0.0324 &0.0324 &0.0324 &0.0324 &0.0324 &0.0324 &0.0324 &0.0324 &0.0324\\ \hline F3 &0.0578 &0.0578 &0.0578 &0.0578 &0.0578 &0.0578 &0.0578 &0.0578 &0.0578 &0.0578 &0.0578 &0.0578 &0.0578 &0.0578 &0.0578 &0.0578\\ \hline U1 &0.065 &0.065 &0.065 &0.065 &0.065 &0.065 &0.065 &0.065 &0.065 &0.065 &0.065 &0.065 &0.065 &0.065 &0.065 &0.065\\ \hline U2 &0.0653 &0.0653 &0.0653 &0.0653 &0.0653 &0.0653 &0.0653 &0.0653 &0.0653 &0.0653 &0.0653 &0.0653 &0.0653 &0.0653 &0.0653 &0.0653\\ \hline D1 &0.0609 &0.0609 &0.0609 &0.0609 &0.0609 &0.0609 &0.0609 &0.0609 &0.0609 &0.0609 &0.0609 &0.0609 &0.0609 &0.0609 &0.0609 &0.0609\\ \hline D2 &0.0714 &0.0714 &0.0714 &0.0714 &0.0714 &0.0714 &0.0714 &0.0714 &0.0714 &0.0714 &0.0714 &0.0714 &0.0714 &0.0714 &0.0714 &0.0714\\ \hline D3 &0.0615 &0.0615 &0.0615 &0.0615 &0.0615 &0.0615 &0.0615 &0.0615 &0.0615 &0.0615 &0.0615 &0.0615 &0.0615 &0.0615 &0.0615 &0.0615\\ \hline \end{array} $$

权重的求解

$$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{16 \times1}} &权重\\ \hline C1 &0.07521\\ \hline C2 &0.06439\\ \hline C3 &0.0578\\ \hline C4 &0.06154\\ \hline C5 &0.07311\\ \hline E1 &0.05554\\ \hline E2 &0.07062\\ \hline E3 &0.05969\\ \hline F1 &0.0679\\ \hline F2 &0.03237\\ \hline F3 &0.05784\\ \hline U1 &0.065\\ \hline U2 &0.06529\\ \hline D1 &0.06087\\ \hline D2 &0.07136\\ \hline D3 &0.06146\\ \hline \end{array} $$$$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{1 \times16}} &C1 &C2 &C3 &C4 &C5 &E1 &E2 &E3 &F1 &F2 &F3 &U1 &U2 &D1 &D2 &D3\\ \hline 权重 &0.07521 &0.06439 &0.0578 &0.06154 &0.07311 &0.05554 &0.07062 &0.05969 &0.0679 &0.03237 &0.05784 &0.065 &0.06529 &0.06087 &0.07136 &0.06146\\ \hline \end{array} $$

归一化求子系统的权重

$$\omega =\begin{array}{c|c|c|c|c|c|c}{M_{5 \times1}} &权重\\ \hline C &0.3321\\ \hline E &0.1858\\ \hline F &0.1581\\ \hline U &0.1303\\ \hline D &0.1937\\ \hline \end{array} $$$$\omega =\begin{array}{c|c|c|c|c|c|c}{M_{1 \times5}} &C &E &F &U &D\\ \hline 权重 &0.3321 &0.1858 &0.1581 &0.1303 &0.1937\\ \hline \end{array} $$