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 &0.066 &0.069 &0.082 &0.068 &0.076 &0.079 &0.077 &0.082 &0.012 &0.013 &0.074 &0.082 &0.022 &0.066 &0.01\\ \hline C2 &0.077 &0 &0.047 &0.082 &0.082 &0.02 &0.027 &0.066 &0.082 &0.014 &0.048 &0.038 &0.046 &0.047 &0.038 &0.025\\ \hline C3 &0.069 &0.021 &0 &0.081 &0.028 &0.066 &0.01 &0.082 &0.079 &0.002 &0.002 &0.051 &0.061 &0.041 &0.06 &0.028\\ \hline C4 &0.065 &0.047 &0.019 &0 &0.081 &0.066 &0.023 &0.067 &0.075 &0.011 &0.02 &0.047 &0.079 &0.029 &0.056 &0.02\\ \hline C5 &0.082 &0.079 &0.073 &0.065 &0 &0.045 &0.044 &0.06 &0.08 &0.016 &0.02 &0.078 &0.081 &0.038 &0.055 &0.028\\ \hline E1 &0.02 &0.014 &0.008 &0.066 &0.023 &0 &0.057 &0.046 &0.081 &0.03 &0.042 &0.021 &0.08 &0.032 &0.079 &0.052\\ \hline E2 &0.018 &0.065 &0.01 &0.08 &0.03 &0.076 &0 &0.065 &0.077 &0.079 &0.074 &0.02 &0.077 &0.057 &0.063 &0.076\\ \hline E3 &0.065 &0.029 &0.023 &0.083 &0.039 &0.045 &0.048 &0 &0.056 &0.021 &0.057 &0.018 &0.079 &0.032 &0.039 &0.057\\ \hline F1 &0.079 &0.082 &0.06 &0.079 &0.079 &0.066 &0.076 &0.077 &0 &0.02 &0.018 &0.01 &0.018 &0.047 &0.019 &0.055\\ \hline F2 &0.01 &0.014 &0.001 &0.01 &0.01 &0.028 &0.032 &0.019 &0.014 &0 &0.072 &0.014 &0.014 &0.055 &0.023 &0.06\\ \hline F3 &0.041 &0.056 &0.009 &0.011 &0.023 &0.074 &0.074 &0.083 &0.023 &0.076 &0 &0.011 &0.013 &0.065 &0.071 &0.069\\ \hline U1 &0.065 &0.08 &0.065 &0.06 &0.014 &0.058 &0.029 &0.074 &0.042 &0.019 &0.037 &0 &0.077 &0.066 &0.051 &0.028\\ \hline U2 &0.065 &0.046 &0.056 &0.069 &0.046 &0.066 &0.064 &0.075 &0.06 &0.02 &0.018 &0.082 &0 &0.011 &0.006 &0.076\\ \hline D1 &0.018 &0.01 &0.033 &0.064 &0.06 &0.079 &0.064 &0.059 &0.021 &0.009 &0.076 &0.009 &0.06 &0 &0.07 &0.082\\ \hline D2 &0.056 &0.065 &0.01 &0.077 &0.064 &0.076 &0.037 &0.082 &0.08 &0.038 &0.031 &0.075 &0.047 &0.082 &0 &0.028\\ \hline D3 &0.011 &0.009 &0.008 &0.081 &0.02 &0.083 &0.076 &0.067 &0.007 &0.06 &0.066 &0.078 &0.029 &0.066 &0.082 &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 &0.173 &0.219 &0.181 &0.301 &0.221 &0.271 &0.236 &0.292 &0.278 &0.102 &0.137 &0.211 &0.272 &0.166 &0.228 &0.16\\ \hline C2 &0.219 &0.134 &0.145 &0.265 &0.213 &0.191 &0.167 &0.249 &0.245 &0.09 &0.15 &0.157 &0.208 &0.167 &0.179 &0.15\\ \hline C3 &0.2 &0.143 &0.091 &0.253 &0.153 &0.221 &0.14 &0.249 &0.23 &0.072 &0.099 &0.16 &0.211 &0.152 &0.188 &0.144\\ \hline C4 &0.202 &0.173 &0.115 &0.182 &0.205 &0.225 &0.158 &0.241 &0.233 &0.084 &0.12 &0.161 &0.232 &0.145 &0.188 &0.142\\ \hline C5 &0.244 &0.225 &0.183 &0.278 &0.153 &0.236 &0.2 &0.269 &0.267 &0.102 &0.138 &0.211 &0.263 &0.176 &0.213 &0.17\\ \hline E1 &0.142 &0.129 &0.089 &0.225 &0.138 &0.151 &0.179 &0.206 &0.218 &0.102 &0.136 &0.124 &0.214 &0.141 &0.197 &0.165\\ \hline E2 &0.172 &0.202 &0.11 &0.28 &0.174 &0.261 &0.158 &0.265 &0.251 &0.167 &0.195 &0.148 &0.247 &0.194 &0.218 &0.219\\ \hline E3 &0.193 &0.15 &0.111 &0.251 &0.161 &0.204 &0.179 &0.173 &0.207 &0.096 &0.154 &0.131 &0.225 &0.146 &0.171 &0.175\\ \hline F1 &0.224 &0.213 &0.158 &0.275 &0.215 &0.242 &0.218 &0.267 &0.178 &0.102 &0.133 &0.137 &0.194 &0.174 &0.172 &0.186\\ \hline F2 &0.074 &0.075 &0.044 &0.1 &0.073 &0.115 &0.105 &0.11 &0.09 &0.045 &0.128 &0.07 &0.091 &0.118 &0.098 &0.126\\ \hline F3 &0.16 &0.165 &0.088 &0.18 &0.139 &0.224 &0.199 &0.241 &0.168 &0.149 &0.107 &0.115 &0.158 &0.178 &0.199 &0.186\\ \hline U1 &0.208 &0.206 &0.159 &0.249 &0.15 &0.228 &0.171 &0.258 &0.21 &0.096 &0.144 &0.121 &0.239 &0.187 &0.194 &0.158\\ \hline U2 &0.206 &0.176 &0.151 &0.258 &0.176 &0.236 &0.203 &0.258 &0.225 &0.099 &0.128 &0.198 &0.168 &0.137 &0.154 &0.2\\ \hline D1 &0.15 &0.132 &0.116 &0.238 &0.179 &0.24 &0.196 &0.232 &0.177 &0.091 &0.177 &0.125 &0.211 &0.12 &0.207 &0.203\\ \hline D2 &0.213 &0.208 &0.119 &0.282 &0.21 &0.261 &0.193 &0.283 &0.26 &0.123 &0.152 &0.201 &0.228 &0.216 &0.16 &0.172\\ \hline D3 &0.142 &0.133 &0.093 &0.251 &0.141 &0.244 &0.206 &0.239 &0.164 &0.139 &0.173 &0.184 &0.185 &0.187 &0.218 &0.128\\ \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 &0.0592 &0.0817 &0.0927 &0.0779 &0.0819 &0.0764 &0.0812 &0.0761 &0.0818 &0.0617 &0.0603 &0.086 &0.0814 &0.0638 &0.0763 &0.0597\\ \hline C2 &0.075 &0.0499 &0.0742 &0.0686 &0.0788 &0.0539 &0.0576 &0.0649 &0.0719 &0.0545 &0.0659 &0.0639 &0.0622 &0.0643 &0.06 &0.0561\\ \hline C3 &0.0683 &0.0532 &0.0464 &0.0653 &0.0566 &0.0622 &0.0482 &0.065 &0.0676 &0.0431 &0.0438 &0.0652 &0.0632 &0.0582 &0.0629 &0.0537\\ \hline C4 &0.0691 &0.0647 &0.0589 &0.0471 &0.0758 &0.0634 &0.0544 &0.0629 &0.0685 &0.0507 &0.0527 &0.0658 &0.0695 &0.0556 &0.063 &0.0529\\ \hline C5 &0.0834 &0.0839 &0.0936 &0.0719 &0.0565 &0.0666 &0.0686 &0.0703 &0.0786 &0.0613 &0.0608 &0.0859 &0.0785 &0.0677 &0.0713 &0.0635\\ \hline E1 &0.0487 &0.0479 &0.0456 &0.0581 &0.0511 &0.0426 &0.0615 &0.0538 &0.0641 &0.0612 &0.0597 &0.0506 &0.0639 &0.0541 &0.0662 &0.0614\\ \hline E2 &0.059 &0.0753 &0.0565 &0.0723 &0.0646 &0.0734 &0.0544 &0.0691 &0.0738 &0.1006 &0.0858 &0.0605 &0.0739 &0.0747 &0.0731 &0.0816\\ \hline E3 &0.0659 &0.056 &0.0566 &0.0649 &0.0596 &0.0574 &0.0615 &0.0451 &0.0608 &0.0576 &0.0678 &0.0533 &0.0671 &0.056 &0.0572 &0.0651\\ \hline F1 &0.0768 &0.0795 &0.0808 &0.0711 &0.0797 &0.068 &0.0749 &0.0696 &0.0524 &0.0616 &0.0584 &0.0557 &0.0579 &0.0667 &0.0578 &0.0692\\ \hline F2 &0.0255 &0.0281 &0.0223 &0.0259 &0.0269 &0.0323 &0.036 &0.0287 &0.0265 &0.0273 &0.0564 &0.0286 &0.0271 &0.0454 &0.0328 &0.0468\\ \hline F3 &0.0548 &0.0615 &0.0451 &0.0464 &0.0513 &0.063 &0.0683 &0.0629 &0.0495 &0.09 &0.0471 &0.047 &0.0472 &0.0683 &0.0669 &0.0694\\ \hline U1 &0.071 &0.0767 &0.0816 &0.0644 &0.0557 &0.0643 &0.0587 &0.0674 &0.0618 &0.058 &0.0636 &0.0493 &0.0714 &0.0719 &0.0649 &0.0587\\ \hline U2 &0.0705 &0.0656 &0.0774 &0.0666 &0.065 &0.0664 &0.0697 &0.0673 &0.0662 &0.0599 &0.0562 &0.0808 &0.0501 &0.0527 &0.0515 &0.0744\\ \hline D1 &0.0513 &0.0491 &0.0596 &0.0615 &0.0663 &0.0677 &0.0676 &0.0606 &0.052 &0.0549 &0.078 &0.0508 &0.063 &0.0462 &0.0693 &0.0757\\ \hline D2 &0.073 &0.0774 &0.0612 &0.0729 &0.0779 &0.0736 &0.0665 &0.0738 &0.0764 &0.074 &0.067 &0.0819 &0.0682 &0.0828 &0.0536 &0.064\\ \hline D3 &0.0486 &0.0494 &0.0474 &0.065 &0.0523 &0.0686 &0.0708 &0.0624 &0.0481 &0.0836 &0.0764 &0.075 &0.0554 &0.0717 &0.0732 &0.0478\\ \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 &0.0753 &0.0753 &0.0753 &0.0753 &0.0753 &0.0753 &0.0753 &0.0753 &0.0753 &0.0753 &0.0753 &0.0753 &0.0753 &0.0753 &0.0753 &0.0753\\ \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 &0.0584 &0.0584 &0.0584 &0.0584 &0.0584 &0.0584 &0.0584 &0.0584 &0.0584 &0.0584 &0.0584 &0.0584 &0.0584 &0.0584 &0.0584 &0.0584\\ \hline C4 &0.0616 &0.0616 &0.0616 &0.0616 &0.0616 &0.0616 &0.0616 &0.0616 &0.0616 &0.0616 &0.0616 &0.0616 &0.0616 &0.0616 &0.0616 &0.0616\\ \hline C5 &0.073 &0.073 &0.073 &0.073 &0.073 &0.073 &0.073 &0.073 &0.073 &0.073 &0.073 &0.073 &0.073 &0.073 &0.073 &0.073\\ \hline E1 &0.0556 &0.0556 &0.0556 &0.0556 &0.0556 &0.0556 &0.0556 &0.0556 &0.0556 &0.0556 &0.0556 &0.0556 &0.0556 &0.0556 &0.0556 &0.0556\\ \hline E2 &0.0705 &0.0705 &0.0705 &0.0705 &0.0705 &0.0705 &0.0705 &0.0705 &0.0705 &0.0705 &0.0705 &0.0705 &0.0705 &0.0705 &0.0705 &0.0705\\ \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 &0.0678 &0.0678 &0.0678 &0.0678 &0.0678 &0.0678 &0.0678 &0.0678 &0.0678 &0.0678 &0.0678 &0.0678 &0.0678 &0.0678 &0.0678 &0.0678\\ \hline F2 &0.0322 &0.0322 &0.0322 &0.0322 &0.0322 &0.0322 &0.0322 &0.0322 &0.0322 &0.0322 &0.0322 &0.0322 &0.0322 &0.0322 &0.0322 &0.0322\\ \hline F3 &0.0577 &0.0577 &0.0577 &0.0577 &0.0577 &0.0577 &0.0577 &0.0577 &0.0577 &0.0577 &0.0577 &0.0577 &0.0577 &0.0577 &0.0577 &0.0577\\ \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 &0.0652 &0.0652 &0.0652 &0.0652 &0.0652 &0.0652 &0.0652 &0.0652 &0.0652 &0.0652 &0.0652 &0.0652 &0.0652 &0.0652 &0.0652 &0.0652\\ \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 &0.0613 &0.0613 &0.0613 &0.0613 &0.0613 &0.0613 &0.0613 &0.0613 &0.0613 &0.0613 &0.0613 &0.0613 &0.0613 &0.0613 &0.0613 &0.0613\\ \hline \end{array} $$

权重的求解

$$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{16 \times1}} &权重\\ \hline C1 &0.07532\\ \hline C2 &0.06438\\ \hline C3 &0.05836\\ \hline C4 &0.06161\\ \hline C5 &0.07305\\ \hline E1 &0.05565\\ \hline E2 &0.07052\\ \hline E3 &0.05966\\ \hline F1 &0.06778\\ \hline F2 &0.03217\\ \hline F3 &0.05769\\ \hline U1 &0.06501\\ \hline U2 &0.06516\\ \hline D1 &0.06091\\ \hline D2 &0.0714\\ \hline D3 &0.06134\\ \hline \end{array} $$$$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{1 \times16}} &C1 &C2 &C3 &C4 &C5 &E1 &E2 &E3 &F1 &F2 &F3 &U1 &U2 &D1 &D2 &D3\\ \hline 权重 &0.07532 &0.06438 &0.05836 &0.06161 &0.07305 &0.05565 &0.07052 &0.05966 &0.06778 &0.03217 &0.05769 &0.06501 &0.06516 &0.06091 &0.0714 &0.06134\\ \hline \end{array} $$

归一化求子系统的权重

$$\omega =\begin{array}{c|c|c|c|c|c|c}{M_{5 \times1}} &权重\\ \hline C &0.3327\\ \hline E &0.1858\\ \hline F &0.1576\\ \hline U &0.1302\\ \hline D &0.1936\\ \hline \end{array} $$$$\omega =\begin{array}{c|c|c|c|c|c|c}{M_{1 \times5}} &C &E &F &U &D\\ \hline 权重 &0.3327 &0.1858 &0.1576 &0.1302 &0.1936\\ \hline \end{array} $$