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 &0.045 &0.046 &0.043 &0.039 &0.048 &0.039 &0.041 &0.046 &0.039 &0.04 &0.037 &0.028 &0.034 &0.042 &0.04\\ \hline A2 &0.052 &0 &0.048 &0.05 &0.043 &0.048 &0.046 &0.048 &0.054 &0.047 &0.052 &0.052 &0.05 &0.046 &0.045 &0.042\\ \hline A3 &0.045 &0.05 &0 &0.052 &0.05 &0.046 &0.043 &0.05 &0.054 &0.051 &0.05 &0.052 &0.039 &0.041 &0.05 &0.047\\ \hline A4 &0.047 &0.048 &0.051 &0 &0.047 &0.048 &0.052 &0.051 &0.046 &0.045 &0.047 &0.05 &0.056 &0.052 &0.048 &0.051\\ \hline A5 &0.039 &0.034 &0.037 &0.04 &0 &0.031 &0.029 &0.03 &0.035 &0.033 &0.025 &0.028 &0.027 &0.025 &0.033 &0.029\\ \hline B1 &0.05 &0.047 &0.048 &0.051 &0.047 &0 &0.053 &0.056 &0.046 &0.046 &0.051 &0.047 &0.052 &0.05 &0.048 &0.051\\ \hline B2 &0.04 &0.041 &0.039 &0.042 &0.033 &0.046 &0 &0.047 &0.039 &0.036 &0.031 &0.033 &0.034 &0.039 &0.04 &0.039\\ \hline B3 &0.043 &0.045 &0.04 &0.046 &0.041 &0.05 &0.045 &0 &0.04 &0.035 &0.034 &0.036 &0.037 &0.039 &0.045 &0.039\\ \hline C1 &0.056 &0.056 &0.047 &0.051 &0.042 &0.048 &0.046 &0.042 &0 &0.05 &0.045 &0.046 &0.037 &0.043 &0.05 &0.043\\ \hline C2 &0.04 &0.037 &0.039 &0.036 &0.037 &0.034 &0.031 &0.034 &0.043 &0 &0.041 &0.04 &0.033 &0.031 &0.035 &0.03\\ \hline C3 &0.037 &0.039 &0.035 &0.039 &0.04 &0.037 &0.039 &0.034 &0.042 &0.036 &0 &0.031 &0.035 &0.037 &0.04 &0.027\\ \hline C4 &0.04 &0.039 &0.036 &0.04 &0.035 &0.04 &0.041 &0.04 &0.037 &0.039 &0.037 &0 &0.034 &0.036 &0.039 &0.029\\ \hline D1 &0.04 &0.042 &0.039 &0.041 &0.03 &0.041 &0.039 &0.036 &0.035 &0.029 &0.034 &0.039 &0 &0.041 &0.039 &0.037\\ \hline D2 &0.041 &0.045 &0.039 &0.04 &0.03 &0.037 &0.04 &0.034 &0.039 &0.033 &0.03 &0.041 &0.036 &0 &0.037 &0.035\\ \hline D3 &0.042 &0.043 &0.037 &0.051 &0.037 &0.04 &0.039 &0.034 &0.041 &0.04 &0.033 &0.041 &0.035 &0.04 &0 &0.037\\ \hline D4 &0.053 &0.045 &0.051 &0.054 &0.046 &0.053 &0.051 &0.052 &0.056 &0.042 &0.047 &0.051 &0.046 &0.048 &0.053 &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 &0.07 &0.111 &0.11 &0.112 &0.1 &0.114 &0.104 &0.106 &0.112 &0.101 &0.101 &0.102 &0.088 &0.096 &0.108 &0.099\\ \hline A2 &0.131 &0.081 &0.124 &0.13 &0.116 &0.126 &0.122 &0.124 &0.132 &0.119 &0.123 &0.126 &0.119 &0.118 &0.122 &0.112\\ \hline A3 &0.124 &0.127 &0.077 &0.132 &0.121 &0.123 &0.119 &0.124 &0.132 &0.122 &0.121 &0.126 &0.108 &0.113 &0.126 &0.116\\ \hline A4 &0.128 &0.128 &0.128 &0.085 &0.12 &0.127 &0.129 &0.127 &0.126 &0.118 &0.12 &0.126 &0.126 &0.125 &0.127 &0.121\\ \hline A5 &0.092 &0.087 &0.088 &0.094 &0.05 &0.084 &0.08 &0.081 &0.088 &0.081 &0.074 &0.079 &0.074 &0.075 &0.085 &0.076\\ \hline B1 &0.131 &0.127 &0.126 &0.133 &0.121 &0.082 &0.13 &0.132 &0.126 &0.12 &0.124 &0.124 &0.123 &0.123 &0.127 &0.121\\ \hline B2 &0.105 &0.105 &0.1 &0.108 &0.092 &0.109 &0.063 &0.108 &0.102 &0.095 &0.09 &0.094 &0.091 &0.098 &0.103 &0.095\\ \hline B3 &0.112 &0.112 &0.105 &0.115 &0.103 &0.116 &0.11 &0.067 &0.107 &0.097 &0.096 &0.101 &0.098 &0.101 &0.111 &0.099\\ \hline C1 &0.132 &0.131 &0.121 &0.129 &0.113 &0.124 &0.12 &0.116 &0.079 &0.12 &0.115 &0.119 &0.106 &0.114 &0.124 &0.111\\ \hline C2 &0.1 &0.097 &0.096 &0.098 &0.092 &0.093 &0.089 &0.091 &0.103 &0.056 &0.095 &0.097 &0.086 &0.087 &0.094 &0.083\\ \hline C3 &0.099 &0.099 &0.093 &0.101 &0.095 &0.097 &0.097 &0.092 &0.102 &0.092 &0.056 &0.089 &0.088 &0.093 &0.099 &0.081\\ \hline C4 &0.102 &0.1 &0.096 &0.103 &0.092 &0.101 &0.1 &0.099 &0.099 &0.095 &0.094 &0.06 &0.089 &0.093 &0.099 &0.084\\ \hline D1 &0.103 &0.104 &0.099 &0.105 &0.088 &0.103 &0.099 &0.096 &0.097 &0.087 &0.091 &0.098 &0.057 &0.098 &0.1 &0.093\\ \hline D2 &0.103 &0.106 &0.098 &0.103 &0.087 &0.099 &0.099 &0.093 &0.1 &0.09 &0.087 &0.1 &0.091 &0.058 &0.098 &0.09\\ \hline D3 &0.108 &0.108 &0.101 &0.117 &0.097 &0.104 &0.102 &0.097 &0.106 &0.1 &0.093 &0.103 &0.093 &0.1 &0.065 &0.095\\ \hline D4 &0.135 &0.126 &0.129 &0.138 &0.12 &0.133 &0.129 &0.13 &0.136 &0.117 &0.121 &0.128 &0.118 &0.123 &0.133 &0.074\\ \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 &0.0392 &0.0636 &0.0652 &0.0623 &0.0625 &0.0658 &0.0612 &0.0627 &0.0644 &0.0624 &0.0632 &0.0609 &0.0567 &0.0595 &0.0628 &0.064\\ \hline A2 &0.0739 &0.0461 &0.0733 &0.0722 &0.072 &0.0726 &0.072 &0.0734 &0.0756 &0.074 &0.0769 &0.0756 &0.0764 &0.0732 &0.0709 &0.0722\\ \hline A3 &0.0698 &0.0727 &0.0457 &0.0731 &0.0752 &0.071 &0.0703 &0.0737 &0.0753 &0.0758 &0.0752 &0.0753 &0.0697 &0.0701 &0.0732 &0.0747\\ \hline A4 &0.0722 &0.0732 &0.0754 &0.0469 &0.0749 &0.0735 &0.0761 &0.0756 &0.072 &0.0734 &0.0749 &0.0751 &0.0809 &0.0775 &0.0737 &0.078\\ \hline A5 &0.0519 &0.0496 &0.0523 &0.0522 &0.031 &0.0485 &0.0476 &0.0484 &0.0503 &0.0506 &0.0465 &0.0472 &0.0476 &0.0462 &0.0493 &0.0492\\ \hline B1 &0.0737 &0.0728 &0.0743 &0.0739 &0.0751 &0.0472 &0.077 &0.0784 &0.0722 &0.0743 &0.0772 &0.074 &0.079 &0.0763 &0.0739 &0.0782\\ \hline B2 &0.059 &0.0599 &0.0594 &0.0599 &0.0571 &0.0627 &0.0374 &0.0642 &0.0587 &0.0591 &0.0564 &0.0563 &0.0585 &0.0604 &0.0597 &0.0615\\ \hline B3 &0.063 &0.0639 &0.0622 &0.0639 &0.0641 &0.0667 &0.0648 &0.0396 &0.0614 &0.0606 &0.06 &0.0605 &0.0628 &0.0626 &0.0644 &0.0636\\ \hline C1 &0.0746 &0.075 &0.0715 &0.0717 &0.0702 &0.0714 &0.0708 &0.069 &0.0449 &0.0743 &0.0717 &0.0712 &0.0681 &0.0706 &0.0723 &0.0718\\ \hline C2 &0.0565 &0.0555 &0.0569 &0.0543 &0.0574 &0.0537 &0.0529 &0.0543 &0.0587 &0.035 &0.0595 &0.0578 &0.0552 &0.0537 &0.0546 &0.0538\\ \hline C3 &0.0555 &0.0565 &0.0552 &0.0558 &0.0591 &0.056 &0.0572 &0.0546 &0.0584 &0.057 &0.0352 &0.0534 &0.057 &0.0575 &0.0575 &0.052\\ \hline C4 &0.0576 &0.0573 &0.0567 &0.0573 &0.0572 &0.0581 &0.0594 &0.0588 &0.0567 &0.0592 &0.0586 &0.036 &0.0572 &0.0577 &0.0577 &0.0543\\ \hline D1 &0.0579 &0.0595 &0.0583 &0.0582 &0.0546 &0.0591 &0.0584 &0.0572 &0.0557 &0.0539 &0.0568 &0.0586 &0.0364 &0.0608 &0.058 &0.0597\\ \hline D2 &0.0582 &0.0604 &0.058 &0.0573 &0.0543 &0.0568 &0.0587 &0.0555 &0.0573 &0.0557 &0.0544 &0.0597 &0.0586 &0.036 &0.057 &0.0579\\ \hline D3 &0.0609 &0.0619 &0.0595 &0.0648 &0.0606 &0.0601 &0.0601 &0.0576 &0.0606 &0.0619 &0.0579 &0.0618 &0.06 &0.0618 &0.0381 &0.0614\\ \hline D4 &0.0761 &0.0721 &0.0762 &0.0763 &0.075 &0.0768 &0.0763 &0.077 &0.0778 &0.0729 &0.0757 &0.0766 &0.0759 &0.0762 &0.0771 &0.0477\\ \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 &0.0716 &0.0716 &0.0716 &0.0716 &0.0716 &0.0716 &0.0716 &0.0716 &0.0716 &0.0716 &0.0716 &0.0716 &0.0716 &0.0716 &0.0716 &0.0716\\ \hline A3 &0.0711 &0.0711 &0.0711 &0.0711 &0.0711 &0.0711 &0.0711 &0.0711 &0.0711 &0.0711 &0.0711 &0.0711 &0.0711 &0.0711 &0.0711 &0.0711\\ \hline A4 &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 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 &0.0732 &0.0732 &0.0732 &0.0732 &0.0732 &0.0732 &0.0732 &0.0732 &0.0732 &0.0732 &0.0732 &0.0732 &0.0732 &0.0732 &0.0732 &0.0732\\ \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 &0.0549 &0.0549 &0.0549 &0.0549 &0.0549 &0.0549 &0.0549 &0.0549 &0.0549 &0.0549 &0.0549 &0.0549 &0.0549 &0.0549 &0.0549 &0.0549\\ \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 &0.0562 &0.0562 &0.0562 &0.0562 &0.0562 &0.0562 &0.0562 &0.0562 &0.0562 &0.0562 &0.0562 &0.0562 &0.0562 &0.0562 &0.0562 &0.0562\\ \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 &0.0738 &0.0738 &0.0738 &0.0738 &0.0738 &0.0738 &0.0738 &0.0738 &0.0738 &0.0738 &0.0738 &0.0738 &0.0738 &0.0738 &0.0738 &0.0738\\ \hline \end{array} $$

权重的求解

$$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{16 \times1}} &权重\\ \hline A1 &0.06122\\ \hline A2 &0.07158\\ \hline A3 &0.07105\\ \hline A4 &0.07298\\ \hline A5 &0.04838\\ \hline B1 &0.07322\\ \hline B2 &0.05835\\ \hline B3 &0.06162\\ \hline C1 &0.0698\\ \hline C2 &0.05445\\ \hline C3 &0.05493\\ \hline C4 &0.05631\\ \hline D1 &0.05666\\ \hline D2 &0.05621\\ \hline D3 &0.05943\\ \hline D4 &0.07381\\ \hline \end{array} $$$$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{1 \times16}} &A1 &A2 &A3 &A4 &A5 &B1 &B2 &B3 &C1 &C2 &C3 &C4 &D1 &D2 &D3 &D4\\ \hline 权重 &0.06122 &0.07158 &0.07105 &0.07298 &0.04838 &0.07322 &0.05835 &0.06162 &0.0698 &0.05445 &0.05493 &0.05631 &0.05666 &0.05621 &0.05943 &0.07381\\ \hline \end{array} $$

归一化求子系统的权重

$$\omega =\begin{array}{c|c|c|c|c|c|c}{M_{4 \times1}} &权重\\ \hline A &0.3252\\ \hline B &0.1932\\ \hline C &0.2355\\ \hline D &0.2461\\ \hline \end{array} $$$$\omega =\begin{array}{c|c|c|c|c|c|c}{M_{1 \times4}} &A &B &C &D\\ \hline 权重 &0.3252 &0.1932 &0.2355 &0.2461\\ \hline \end{array} $$