原始矩阵（直接影响矩阵）为

$$Ori=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{16 \times16}} &A1 &A2 &A3 &A4 &A5 &B1 &B2 &B3 &C1 &C2 &C3 &C4 &D1 &D2 &D3 &D4\\ \hline A1 &0 &37 &38 &36 &32 &40 &32 &34 &38 &32 &33 &31 &23 &28 &35 &33\\ \hline A2 &43 &0 &40 &41 &36 &40 &38 &40 &45 &39 &43 &43 &41 &38 &37 &35\\ \hline A3 &37 &41 &0 &43 &41 &38 &36 &41 &45 &42 &41 &43 &32 &34 &41 &39\\ \hline A4 &39 &40 &42 &0 &39 &40 &43 &42 &38 &37 &39 &41 &46 &43 &40 &42\\ \hline A5 &32 &28 &31 &33 &0 &26 &24 &25 &29 &27 &21 &23 &22 &21 &27 &24\\ \hline B1 &41 &39 &40 &42 &39 &0 &44 &46 &38 &38 &42 &39 &43 &41 &40 &42\\ \hline B2 &33 &34 &32 &35 &27 &38 &0 &39 &32 &30 &26 &27 &28 &32 &33 &32\\ \hline B3 &36 &37 &33 &38 &34 &41 &37 &0 &33 &29 &28 &30 &31 &32 &37 &32\\ \hline C1 &46 &46 &39 &42 &35 &40 &38 &35 &0 &41 &37 &38 &31 &36 &41 &36\\ \hline C2 &33 &31 &32 &30 &31 &28 &26 &28 &36 &0 &34 &33 &27 &26 &29 &25\\ \hline C3 &31 &32 &29 &32 &33 &31 &32 &28 &35 &30 &0 &26 &29 &31 &33 &22\\ \hline C4 &33 &32 &30 &33 &29 &33 &34 &33 &31 &32 &31 &0 &28 &30 &32 &24\\ \hline D1 &33 &35 &32 &34 &25 &34 &32 &30 &29 &24 &28 &32 &0 &34 &32 &31\\ \hline D2 &34 &37 &32 &33 &25 &31 &33 &28 &32 &27 &25 &34 &30 &0 &31 &29\\ \hline D3 &35 &36 &31 &42 &31 &33 &32 &28 &34 &33 &27 &34 &29 &33 &0 &31\\ \hline D4 &44 &37 &42 &45 &38 &44 &42 &43 &46 &35 &39 &42 &38 &40 &44 &0\\ \hline \end{array} $$

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}} &A1 &A2 &A3 &A4 &A5 &B1 &B2 &B3 &C1 &C2 &C3 &C4 &D1 &D2 &D3 &D4\\ \hline A1 &0 &0.066 &0.068 &0.064 &0.057 &0.072 &0.057 &0.061 &0.068 &0.057 &0.059 &0.055 &0.041 &0.05 &0.063 &0.059\\ \hline A2 &0.077 &0 &0.072 &0.073 &0.064 &0.072 &0.068 &0.072 &0.081 &0.07 &0.077 &0.077 &0.073 &0.068 &0.066 &0.063\\ \hline A3 &0.066 &0.073 &0 &0.077 &0.073 &0.068 &0.064 &0.073 &0.081 &0.075 &0.073 &0.077 &0.057 &0.061 &0.073 &0.07\\ \hline A4 &0.07 &0.072 &0.075 &0 &0.07 &0.072 &0.077 &0.075 &0.068 &0.066 &0.07 &0.073 &0.082 &0.077 &0.072 &0.075\\ \hline A5 &0.057 &0.05 &0.055 &0.059 &0 &0.047 &0.043 &0.045 &0.052 &0.048 &0.038 &0.041 &0.039 &0.038 &0.048 &0.043\\ \hline B1 &0.073 &0.07 &0.072 &0.075 &0.07 &0 &0.079 &0.082 &0.068 &0.068 &0.075 &0.07 &0.077 &0.073 &0.072 &0.075\\ \hline B2 &0.059 &0.061 &0.057 &0.063 &0.048 &0.068 &0 &0.07 &0.057 &0.054 &0.047 &0.048 &0.05 &0.057 &0.059 &0.057\\ \hline B3 &0.064 &0.066 &0.059 &0.068 &0.061 &0.073 &0.066 &0 &0.059 &0.052 &0.05 &0.054 &0.055 &0.057 &0.066 &0.057\\ \hline C1 &0.082 &0.082 &0.07 &0.075 &0.063 &0.072 &0.068 &0.063 &0 &0.073 &0.066 &0.068 &0.055 &0.064 &0.073 &0.064\\ \hline C2 &0.059 &0.055 &0.057 &0.054 &0.055 &0.05 &0.047 &0.05 &0.064 &0 &0.061 &0.059 &0.048 &0.047 &0.052 &0.045\\ \hline C3 &0.055 &0.057 &0.052 &0.057 &0.059 &0.055 &0.057 &0.05 &0.063 &0.054 &0 &0.047 &0.052 &0.055 &0.059 &0.039\\ \hline C4 &0.059 &0.057 &0.054 &0.059 &0.052 &0.059 &0.061 &0.059 &0.055 &0.057 &0.055 &0 &0.05 &0.054 &0.057 &0.043\\ \hline D1 &0.059 &0.063 &0.057 &0.061 &0.045 &0.061 &0.057 &0.054 &0.052 &0.043 &0.05 &0.057 &0 &0.061 &0.057 &0.055\\ \hline D2 &0.061 &0.066 &0.057 &0.059 &0.045 &0.055 &0.059 &0.05 &0.057 &0.048 &0.045 &0.061 &0.054 &0 &0.055 &0.052\\ \hline D3 &0.063 &0.064 &0.055 &0.075 &0.055 &0.059 &0.057 &0.05 &0.061 &0.059 &0.048 &0.061 &0.052 &0.059 &0 &0.055\\ \hline D4 &0.079 &0.066 &0.075 &0.081 &0.068 &0.079 &0.075 &0.077 &0.082 &0.063 &0.07 &0.075 &0.068 &0.072 &0.079 &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}} &A1 &A2 &A3 &A4 &A5 &B1 &B2 &B3 &C1 &C2 &C3 &C4 &D1 &D2 &D3 &D4\\ \hline A1 &0.784 &0.836 &0.812 &0.856 &0.765 &0.834 &0.803 &0.802 &0.835 &0.767 &0.766 &0.791 &0.727 &0.763 &0.819 &0.744\\ \hline A2 &0.988 &0.905 &0.942 &0.999 &0.891 &0.964 &0.939 &0.938 &0.977 &0.899 &0.901 &0.935 &0.872 &0.901 &0.951 &0.863\\ \hline A3 &0.973 &0.967 &0.869 &0.996 &0.894 &0.955 &0.93 &0.934 &0.971 &0.898 &0.893 &0.93 &0.853 &0.889 &0.951 &0.864\\ \hline A4 &0.999 &0.988 &0.961 &0.948 &0.911 &0.98 &0.963 &0.957 &0.982 &0.91 &0.91 &0.948 &0.895 &0.924 &0.972 &0.889\\ \hline A5 &0.675 &0.66 &0.645 &0.686 &0.562 &0.652 &0.633 &0.632 &0.66 &0.61 &0.598 &0.624 &0.582 &0.603 &0.648 &0.586\\ \hline B1 &1.006 &0.991 &0.961 &1.022 &0.915 &0.917 &0.968 &0.967 &0.986 &0.916 &0.918 &0.949 &0.894 &0.924 &0.976 &0.892\\ \hline B2 &0.804 &0.795 &0.768 &0.818 &0.724 &0.795 &0.714 &0.776 &0.79 &0.731 &0.721 &0.751 &0.704 &0.737 &0.781 &0.71\\ \hline B3 &0.851 &0.842 &0.81 &0.866 &0.773 &0.841 &0.816 &0.751 &0.833 &0.767 &0.763 &0.795 &0.745 &0.775 &0.828 &0.747\\ \hline C1 &0.971 &0.959 &0.919 &0.978 &0.869 &0.942 &0.918 &0.909 &0.881 &0.882 &0.872 &0.907 &0.837 &0.877 &0.936 &0.845\\ \hline C2 &0.754 &0.742 &0.72 &0.76 &0.685 &0.731 &0.711 &0.711 &0.748 &0.635 &0.689 &0.714 &0.658 &0.682 &0.726 &0.655\\ \hline C3 &0.757 &0.75 &0.722 &0.769 &0.694 &0.742 &0.727 &0.717 &0.752 &0.691 &0.638 &0.708 &0.667 &0.696 &0.739 &0.656\\ \hline C4 &0.777 &0.766 &0.74 &0.788 &0.703 &0.762 &0.746 &0.741 &0.763 &0.71 &0.706 &0.68 &0.681 &0.71 &0.754 &0.674\\ \hline D1 &0.783 &0.776 &0.748 &0.795 &0.701 &0.769 &0.748 &0.742 &0.765 &0.702 &0.706 &0.739 &0.638 &0.721 &0.759 &0.69\\ \hline D2 &0.778 &0.774 &0.742 &0.787 &0.696 &0.758 &0.744 &0.733 &0.764 &0.701 &0.696 &0.737 &0.683 &0.658 &0.751 &0.682\\ \hline D3 &0.82 &0.812 &0.779 &0.843 &0.742 &0.801 &0.781 &0.771 &0.807 &0.748 &0.735 &0.775 &0.717 &0.751 &0.738 &0.721\\ \hline D4 &1.022 &0.999 &0.975 &1.038 &0.923 &1.001 &0.976 &0.973 &1.01 &0.921 &0.924 &0.964 &0.896 &0.933 &0.993 &0.832\\ \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}} &A1 &A2 &A3 &A4 &A5 &B1 &B2 &B3 &C1 &C2 &C3 &C4 &D1 &D2 &D3 &D4\\ \hline A1 &0.0571 &0.0616 &0.0619 &0.0614 &0.0614 &0.062 &0.0612 &0.0615 &0.0618 &0.0614 &0.0616 &0.0611 &0.0604 &0.0609 &0.0615 &0.0617\\ \hline A2 &0.0719 &0.0667 &0.0718 &0.0716 &0.0716 &0.0717 &0.0716 &0.0718 &0.0722 &0.072 &0.0725 &0.0722 &0.0724 &0.0718 &0.0714 &0.0716\\ \hline A3 &0.0708 &0.0713 &0.0663 &0.0714 &0.0718 &0.071 &0.0709 &0.0715 &0.0718 &0.0719 &0.0718 &0.0718 &0.0708 &0.0709 &0.0714 &0.0717\\ \hline A4 &0.0727 &0.0729 &0.0733 &0.0679 &0.0732 &0.0729 &0.0734 &0.0733 &0.0726 &0.0729 &0.0732 &0.0732 &0.0743 &0.0736 &0.0729 &0.0737\\ \hline A5 &0.0491 &0.0487 &0.0492 &0.0491 &0.0452 &0.0485 &0.0483 &0.0484 &0.0488 &0.0489 &0.0481 &0.0482 &0.0483 &0.0481 &0.0486 &0.0486\\ \hline B1 &0.0732 &0.073 &0.0733 &0.0732 &0.0735 &0.0682 &0.0738 &0.0741 &0.0729 &0.0733 &0.0738 &0.0733 &0.0742 &0.0737 &0.0733 &0.074\\ \hline B2 &0.0585 &0.0586 &0.0585 &0.0586 &0.0581 &0.0592 &0.0544 &0.0594 &0.0584 &0.0585 &0.058 &0.058 &0.0584 &0.0587 &0.0586 &0.0589\\ \hline B3 &0.0619 &0.0621 &0.0617 &0.0621 &0.0621 &0.0626 &0.0622 &0.0575 &0.0616 &0.0614 &0.0613 &0.0614 &0.0619 &0.0618 &0.0622 &0.062\\ \hline C1 &0.0707 &0.0707 &0.0701 &0.0701 &0.0698 &0.0701 &0.07 &0.0696 &0.0651 &0.0706 &0.0701 &0.07 &0.0695 &0.0699 &0.0702 &0.0701\\ \hline C2 &0.0549 &0.0547 &0.0549 &0.0545 &0.055 &0.0544 &0.0542 &0.0545 &0.0553 &0.0508 &0.0554 &0.0551 &0.0546 &0.0543 &0.0545 &0.0544\\ \hline C3 &0.0551 &0.0553 &0.055 &0.0552 &0.0558 &0.0552 &0.0554 &0.0549 &0.0556 &0.0554 &0.0513 &0.0547 &0.0554 &0.0555 &0.0555 &0.0545\\ \hline C4 &0.0566 &0.0565 &0.0564 &0.0565 &0.0565 &0.0567 &0.0569 &0.0568 &0.0564 &0.0569 &0.0567 &0.0525 &0.0565 &0.0566 &0.0566 &0.056\\ \hline D1 &0.057 &0.0573 &0.057 &0.057 &0.0563 &0.0572 &0.0571 &0.0568 &0.0566 &0.0562 &0.0568 &0.0571 &0.0529 &0.0575 &0.057 &0.0573\\ \hline D2 &0.0566 &0.057 &0.0566 &0.0565 &0.0559 &0.0564 &0.0567 &0.0561 &0.0565 &0.0562 &0.0559 &0.0569 &0.0567 &0.0525 &0.0564 &0.0566\\ \hline D3 &0.0597 &0.0599 &0.0594 &0.0604 &0.0596 &0.0596 &0.0595 &0.0591 &0.0596 &0.0599 &0.0591 &0.0599 &0.0595 &0.0599 &0.0554 &0.0598\\ \hline D4 &0.0744 &0.0736 &0.0744 &0.0744 &0.0742 &0.0745 &0.0744 &0.0745 &0.0747 &0.0738 &0.0743 &0.0745 &0.0743 &0.0744 &0.0746 &0.0691\\ \hline \end{array} $$

极限超矩阵求解：

$$limit W=\begin{array}{c|c|c|c|c|c|c}{M_{16 \times16}} &A1 &A2 &A3 &A4 &A5 &B1 &B2 &B3 &C1 &C2 &C3 &C4 &D1 &D2 &D3 &D4\\ \hline A1 &0.0612 &0.0612 &0.0612 &0.0612 &0.0612 &0.0612 &0.0612 &0.0612 &0.0612 &0.0612 &0.0612 &0.0612 &0.0612 &0.0612 &0.0612 &0.0612\\ \hline A2 &0.0715 &0.0715 &0.0715 &0.0715 &0.0715 &0.0715 &0.0715 &0.0715 &0.0715 &0.0715 &0.0715 &0.0715 &0.0715 &0.0715 &0.0715 &0.0715\\ \hline A3 &0.071 &0.071 &0.071 &0.071 &0.071 &0.071 &0.071 &0.071 &0.071 &0.071 &0.071 &0.071 &0.071 &0.071 &0.071 &0.071\\ \hline A4 &0.0728 &0.0728 &0.0728 &0.0728 &0.0728 &0.0728 &0.0728 &0.0728 &0.0728 &0.0728 &0.0728 &0.0728 &0.0728 &0.0728 &0.0728 &0.0728\\ \hline A5 &0.0484 &0.0484 &0.0484 &0.0484 &0.0484 &0.0484 &0.0484 &0.0484 &0.0484 &0.0484 &0.0484 &0.0484 &0.0484 &0.0484 &0.0484 &0.0484\\ \hline B1 &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 B2 &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 B3 &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 C1 &0.0698 &0.0698 &0.0698 &0.0698 &0.0698 &0.0698 &0.0698 &0.0698 &0.0698 &0.0698 &0.0698 &0.0698 &0.0698 &0.0698 &0.0698 &0.0698\\ \hline C2 &0.0545 &0.0545 &0.0545 &0.0545 &0.0545 &0.0545 &0.0545 &0.0545 &0.0545 &0.0545 &0.0545 &0.0545 &0.0545 &0.0545 &0.0545 &0.0545\\ \hline C3 &0.055 &0.055 &0.055 &0.055 &0.055 &0.055 &0.055 &0.055 &0.055 &0.055 &0.055 &0.055 &0.055 &0.055 &0.055 &0.055\\ \hline C4 &0.0563 &0.0563 &0.0563 &0.0563 &0.0563 &0.0563 &0.0563 &0.0563 &0.0563 &0.0563 &0.0563 &0.0563 &0.0563 &0.0563 &0.0563 &0.0563\\ \hline D1 &0.0567 &0.0567 &0.0567 &0.0567 &0.0567 &0.0567 &0.0567 &0.0567 &0.0567 &0.0567 &0.0567 &0.0567 &0.0567 &0.0567 &0.0567 &0.0567\\ \hline D2 &0.0563 &0.0563 &0.0563 &0.0563 &0.0563 &0.0563 &0.0563 &0.0563 &0.0563 &0.0563 &0.0563 &0.0563 &0.0563 &0.0563 &0.0563 &0.0563\\ \hline D3 &0.0594 &0.0594 &0.0594 &0.0594 &0.0594 &0.0594 &0.0594 &0.0594 &0.0594 &0.0594 &0.0594 &0.0594 &0.0594 &0.0594 &0.0594 &0.0594\\ \hline D4 &0.0739 &0.0739 &0.0739 &0.0739 &0.0739 &0.0739 &0.0739 &0.0739 &0.0739 &0.0739 &0.0739 &0.0739 &0.0739 &0.0739 &0.0739 &0.0739\\ \hline \end{array} $$

权重的求解

$$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{16 \times1}} &权重\\ \hline A1 &0.06118\\ \hline A2 &0.0715\\ \hline A3 &0.07103\\ \hline A4 &0.07281\\ \hline A5 &0.04845\\ \hline B1 &0.07312\\ \hline B2 &0.05836\\ \hline B3 &0.06163\\ \hline C1 &0.06977\\ \hline C2 &0.05449\\ \hline C3 &0.05498\\ \hline C4 &0.05632\\ \hline D1 &0.05673\\ \hline D2 &0.05626\\ \hline D3 &0.05942\\ \hline D4 &0.07394\\ \hline \end{array} $$$$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{1 \times16}} &A1 &A2 &A3 &A4 &A5 &B1 &B2 &B3 &C1 &C2 &C3 &C4 &D1 &D2 &D3 &D4\\ \hline 权重 &0.06118 &0.0715 &0.07103 &0.07281 &0.04845 &0.07312 &0.05836 &0.06163 &0.06977 &0.05449 &0.05498 &0.05632 &0.05673 &0.05626 &0.05942 &0.07394\\ \hline \end{array} $$

归一化求子系统的权重

$$\omega =\begin{array}{c|c|c|c|c|c|c}{M_{4 \times1}} &权重\\ \hline A &0.325\\ \hline B &0.1931\\ \hline C &0.2356\\ \hline D &0.2464\\ \hline \end{array} $$$$\omega =\begin{array}{c|c|c|c|c|c|c}{M_{1 \times4}} &A &B &C &D\\ \hline 权重 &0.325 &0.1931 &0.2356 &0.2464\\ \hline \end{array} $$