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 &0.049 &0.052 &0.062 &0.051 &0.057 &0.059 &0.058 &0.062 &0.009 &0.01 &0.056 &0.062 &0.016 &0.049 &0.007\\ \hline C2 &0.058 &0 &0.035 &0.061 &0.062 &0.015 &0.02 &0.05 &0.062 &0.011 &0.036 &0.029 &0.035 &0.035 &0.029 &0.019\\ \hline C3 &0.052 &0.016 &0 &0.061 &0.021 &0.049 &0.007 &0.062 &0.059 &0.002 &0.002 &0.038 &0.046 &0.031 &0.045 &0.021\\ \hline C4 &0.049 &0.035 &0.014 &0 &0.061 &0.05 &0.017 &0.05 &0.057 &0.008 &0.015 &0.035 &0.06 &0.022 &0.042 &0.015\\ \hline C5 &0.062 &0.059 &0.055 &0.049 &0 &0.034 &0.033 &0.045 &0.06 &0.012 &0.015 &0.059 &0.061 &0.029 &0.042 &0.021\\ \hline E1 &0.015 &0.01 &0.006 &0.049 &0.017 &0 &0.043 &0.035 &0.061 &0.023 &0.031 &0.016 &0.06 &0.024 &0.06 &0.039\\ \hline E2 &0.014 &0.049 &0.007 &0.06 &0.022 &0.057 &0 &0.049 &0.058 &0.06 &0.055 &0.015 &0.058 &0.043 &0.047 &0.057\\ \hline E3 &0.049 &0.022 &0.017 &0.062 &0.029 &0.034 &0.036 &0 &0.042 &0.016 &0.043 &0.014 &0.06 &0.024 &0.029 &0.043\\ \hline F1 &0.059 &0.062 &0.045 &0.06 &0.06 &0.05 &0.057 &0.058 &0 &0.015 &0.014 &0.008 &0.014 &0.035 &0.014 &0.042\\ \hline F2 &0.007 &0.011 &0.001 &0.007 &0.008 &0.021 &0.024 &0.014 &0.011 &0 &0.054 &0.011 &0.01 &0.042 &0.017 &0.045\\ \hline F3 &0.031 &0.042 &0.007 &0.008 &0.017 &0.055 &0.056 &0.062 &0.017 &0.057 &0 &0.009 &0.01 &0.049 &0.053 &0.052\\ \hline U1 &0.049 &0.06 &0.049 &0.045 &0.01 &0.043 &0.022 &0.055 &0.032 &0.014 &0.028 &0 &0.058 &0.05 &0.039 &0.021\\ \hline U2 &0.049 &0.034 &0.042 &0.052 &0.035 &0.05 &0.048 &0.056 &0.045 &0.015 &0.014 &0.061 &0 &0.009 &0.004 &0.057\\ \hline D1 &0.014 &0.007 &0.025 &0.048 &0.045 &0.06 &0.048 &0.044 &0.016 &0.007 &0.057 &0.007 &0.045 &0 &0.053 &0.062\\ \hline D2 &0.042 &0.049 &0.008 &0.058 &0.048 &0.057 &0.028 &0.062 &0.06 &0.029 &0.023 &0.056 &0.035 &0.062 &0 &0.021\\ \hline D3 &0.008 &0.007 &0.006 &0.061 &0.015 &0.062 &0.057 &0.05 &0.006 &0.045 &0.05 &0.059 &0.022 &0.05 &0.062 &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 &0.059 &0.1 &0.089 &0.134 &0.101 &0.12 &0.109 &0.129 &0.127 &0.038 &0.05 &0.1 &0.125 &0.064 &0.101 &0.057\\ \hline C2 &0.105 &0.045 &0.068 &0.121 &0.105 &0.072 &0.067 &0.11 &0.115 &0.035 &0.068 &0.068 &0.088 &0.074 &0.075 &0.059\\ \hline C3 &0.095 &0.056 &0.031 &0.117 &0.063 &0.1 &0.051 &0.116 &0.109 &0.024 &0.033 &0.074 &0.096 &0.067 &0.086 &0.059\\ \hline C4 &0.094 &0.078 &0.047 &0.061 &0.101 &0.101 &0.062 &0.107 &0.108 &0.032 &0.047 &0.073 &0.11 &0.059 &0.084 &0.055\\ \hline C5 &0.115 &0.107 &0.092 &0.12 &0.051 &0.097 &0.084 &0.115 &0.122 &0.039 &0.053 &0.102 &0.12 &0.074 &0.092 &0.067\\ \hline E1 &0.055 &0.049 &0.033 &0.101 &0.055 &0.051 &0.083 &0.088 &0.105 &0.047 &0.062 &0.05 &0.103 &0.06 &0.097 &0.077\\ \hline E2 &0.065 &0.093 &0.04 &0.125 &0.07 &0.118 &0.053 &0.115 &0.114 &0.089 &0.096 &0.057 &0.113 &0.089 &0.098 &0.105\\ \hline E3 &0.09 &0.062 &0.046 &0.117 &0.07 &0.087 &0.08 &0.058 &0.092 &0.041 &0.074 &0.052 &0.106 &0.061 &0.073 &0.081\\ \hline F1 &0.107 &0.104 &0.077 &0.124 &0.104 &0.107 &0.103 &0.12 &0.06 &0.042 &0.052 &0.05 &0.073 &0.076 &0.066 &0.083\\ \hline F2 &0.028 &0.03 &0.014 &0.037 &0.028 &0.05 &0.049 &0.045 &0.035 &0.016 &0.073 &0.029 &0.035 &0.063 &0.043 &0.067\\ \hline F3 &0.069 &0.076 &0.032 &0.065 &0.055 &0.104 &0.097 &0.113 &0.065 &0.082 &0.038 &0.043 &0.058 &0.087 &0.096 &0.091\\ \hline U1 &0.096 &0.1 &0.08 &0.108 &0.056 &0.099 &0.069 &0.116 &0.087 &0.039 &0.063 &0.04 &0.111 &0.089 &0.085 &0.064\\ \hline U2 &0.095 &0.077 &0.073 &0.114 &0.077 &0.105 &0.093 &0.116 &0.099 &0.041 &0.05 &0.099 &0.056 &0.05 &0.054 &0.096\\ \hline D1 &0.057 &0.047 &0.051 &0.105 &0.083 &0.113 &0.092 &0.101 &0.067 &0.035 &0.09 &0.046 &0.094 &0.04 &0.098 &0.101\\ \hline D2 &0.094 &0.096 &0.045 &0.125 &0.096 &0.117 &0.08 &0.127 &0.119 &0.056 &0.063 &0.096 &0.096 &0.105 &0.053 &0.069\\ \hline D3 &0.051 &0.048 &0.033 &0.115 &0.054 &0.115 &0.099 &0.107 &0.057 &0.072 &0.086 &0.092 &0.074 &0.09 &0.107 &0.044\\ \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 &0.0461 &0.0857 &0.1048 &0.0794 &0.0865 &0.0774 &0.0861 &0.0764 &0.0858 &0.0525 &0.0501 &0.0937 &0.0855 &0.0556 &0.0775 &0.0484\\ \hline C2 &0.0824 &0.0386 &0.0805 &0.0718 &0.0894 &0.0462 &0.0526 &0.0653 &0.0775 &0.0484 &0.0681 &0.0633 &0.0604 &0.0647 &0.057 &0.0506\\ \hline C3 &0.0745 &0.0482 &0.036 &0.0695 &0.0539 &0.0643 &0.0399 &0.0691 &0.0735 &0.0325 &0.0333 &0.0692 &0.0656 &0.0579 &0.0659 &0.05\\ \hline C4 &0.0741 &0.0663 &0.0554 &0.0361 &0.0863 &0.0649 &0.049 &0.0638 &0.0732 &0.0437 &0.047 &0.0684 &0.0752 &0.0516 &0.0644 &0.0468\\ \hline C5 &0.0906 &0.0917 &0.1079 &0.0708 &0.0437 &0.0621 &0.0659 &0.0682 &0.0824 &0.0542 &0.053 &0.0954 &0.0826 &0.0643 &0.0706 &0.0572\\ \hline E1 &0.0434 &0.0417 &0.0384 &0.0599 &0.0474 &0.0327 &0.0654 &0.0522 &0.0707 &0.0644 &0.0623 &0.0465 &0.0705 &0.0526 &0.0742 &0.0651\\ \hline E2 &0.0508 &0.0795 &0.047 &0.0741 &0.0602 &0.0756 &0.0421 &0.0682 &0.077 &0.1219 &0.0961 &0.0533 &0.0772 &0.0772 &0.075 &0.0892\\ \hline E3 &0.0708 &0.0531 &0.0543 &0.069 &0.0595 &0.0556 &0.0627 &0.0343 &0.0618 &0.0558 &0.0742 &0.0481 &0.073 &0.0535 &0.0555 &0.0691\\ \hline F1 &0.0837 &0.0887 &0.0906 &0.0735 &0.0889 &0.0686 &0.0808 &0.0713 &0.0406 &0.0577 &0.0519 &0.0466 &0.0502 &0.0664 &0.0503 &0.071\\ \hline F2 &0.0216 &0.0259 &0.0164 &0.0218 &0.0237 &0.0323 &0.0385 &0.0265 &0.0233 &0.0224 &0.0733 &0.0267 &0.024 &0.0546 &0.0328 &0.0572\\ \hline F3 &0.0539 &0.0654 &0.0374 &0.0382 &0.0471 &0.0671 &0.0762 &0.0673 &0.0439 &0.1125 &0.0377 &0.0397 &0.0397 &0.0754 &0.0733 &0.0774\\ \hline U1 &0.0753 &0.0858 &0.0938 &0.0638 &0.0481 &0.0639 &0.0541 &0.069 &0.059 &0.0536 &0.063 &0.0375 &0.0761 &0.0772 &0.065 &0.0542\\ \hline U2 &0.0746 &0.0661 &0.0864 &0.0677 &0.0655 &0.0676 &0.0735 &0.0691 &0.0671 &0.0563 &0.0501 &0.0926 &0.0387 &0.0439 &0.0414 &0.0819\\ \hline D1 &0.0446 &0.0405 &0.0598 &0.0621 &0.071 &0.0724 &0.0723 &0.0603 &0.0455 &0.0488 &0.0901 &0.0428 &0.0647 &0.0352 &0.075 &0.0863\\ \hline D2 &0.0739 &0.0817 &0.0526 &0.0739 &0.0825 &0.0754 &0.0628 &0.0756 &0.0801 &0.0765 &0.0636 &0.09 &0.0655 &0.0913 &0.0405 &0.0585\\ \hline D3 &0.0399 &0.0409 &0.0387 &0.0684 &0.0463 &0.0739 &0.0781 &0.0634 &0.0386 &0.0988 &0.0863 &0.086 &0.0509 &0.0786 &0.0816 &0.0371\\ \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 &0.0576 &0.0576 &0.0576 &0.0576 &0.0576 &0.0576 &0.0576 &0.0576 &0.0576 &0.0576 &0.0576 &0.0576 &0.0576 &0.0576 &0.0576 &0.0576\\ \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 &0.0707 &0.0707 &0.0707 &0.0707 &0.0707 &0.0707 &0.0707 &0.0707 &0.0707 &0.0707 &0.0707 &0.0707 &0.0707 &0.0707 &0.0707 &0.0707\\ \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 &0.068 &0.068 &0.068 &0.068 &0.068 &0.068 &0.068 &0.068 &0.068 &0.068 &0.068 &0.068 &0.068 &0.068 &0.068 &0.068\\ \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 &0.0579 &0.0579 &0.0579 &0.0579 &0.0579 &0.0579 &0.0579 &0.0579 &0.0579 &0.0579 &0.0579 &0.0579 &0.0579 &0.0579 &0.0579 &0.0579\\ \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 &0.0713 &0.0713 &0.0713 &0.0713 &0.0713 &0.0713 &0.0713 &0.0713 &0.0713 &0.0713 &0.0713 &0.0713 &0.0713 &0.0713 &0.0713 &0.0713\\ \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

$$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{16 \times1}} &权重\\ \hline C1 &0.07517\\ \hline C2 &0.0644\\ \hline C3 &0.05757\\ \hline C4 &0.06152\\ \hline C5 &0.07314\\ \hline E1 &0.0555\\ \hline E2 &0.07065\\ \hline E3 &0.05971\\ \hline F1 &0.06795\\ \hline F2 &0.03244\\ \hline F3 &0.0579\\ \hline U1 &0.065\\ \hline U2 &0.06535\\ \hline D1 &0.06085\\ \hline D2 &0.07134\\ \hline D3 &0.0615\\ \hline \end{array} $$$$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{1 \times16}} &C1 &C2 &C3 &C4 &C5 &E1 &E2 &E3 &F1 &F2 &F3 &U1 &U2 &D1 &D2 &D3\\ \hline 权重 &0.07517 &0.0644 &0.05757 &0.06152 &0.07314 &0.0555 &0.07065 &0.05971 &0.06795 &0.03244 &0.0579 &0.065 &0.06535 &0.06085 &0.07134 &0.0615\\ \hline \end{array} $$

归一化求子系统的权重

$$\omega =\begin{array}{c|c|c|c|c|c|c}{M_{5 \times1}} &权重\\ \hline C &0.3318\\ \hline E &0.1859\\ \hline F &0.1583\\ \hline U &0.1303\\ \hline D &0.1937\\ \hline \end{array} $$$$\omega =\begin{array}{c|c|c|c|c|c|c}{M_{1 \times5}} &C &E &F &U &D\\ \hline 权重 &0.3318 &0.1859 &0.1583 &0.1303 &0.1937\\ \hline \end{array} $$