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 &0.075 &0.079 &0.094 &0.077 &0.087 &0.09 &0.088 &0.094 &0.013 &0.015 &0.085 &0.094 &0.025 &0.075 &0.011\\ \hline C2 &0.087 &0 &0.054 &0.093 &0.094 &0.023 &0.031 &0.075 &0.094 &0.016 &0.054 &0.043 &0.052 &0.054 &0.043 &0.028\\ \hline C3 &0.078 &0.024 &0 &0.092 &0.032 &0.075 &0.011 &0.094 &0.09 &0.003 &0.003 &0.058 &0.07 &0.047 &0.068 &0.032\\ \hline C4 &0.074 &0.054 &0.021 &0 &0.092 &0.075 &0.026 &0.076 &0.086 &0.013 &0.022 &0.053 &0.09 &0.033 &0.064 &0.023\\ \hline C5 &0.094 &0.09 &0.084 &0.074 &0 &0.051 &0.05 &0.069 &0.092 &0.018 &0.022 &0.089 &0.092 &0.044 &0.063 &0.032\\ \hline E1 &0.022 &0.016 &0.01 &0.075 &0.026 &0 &0.065 &0.053 &0.092 &0.034 &0.047 &0.024 &0.092 &0.037 &0.09 &0.059\\ \hline E2 &0.021 &0.074 &0.011 &0.092 &0.034 &0.086 &0 &0.074 &0.088 &0.09 &0.084 &0.022 &0.088 &0.065 &0.072 &0.087\\ \hline E3 &0.074 &0.034 &0.026 &0.094 &0.045 &0.051 &0.055 &0 &0.064 &0.024 &0.065 &0.021 &0.09 &0.037 &0.044 &0.065\\ \hline F1 &0.09 &0.094 &0.068 &0.09 &0.09 &0.076 &0.086 &0.088 &0 &0.023 &0.021 &0.012 &0.021 &0.053 &0.021 &0.063\\ \hline F2 &0.011 &0.016 &0.001 &0.011 &0.012 &0.032 &0.037 &0.021 &0.016 &0 &0.082 &0.016 &0.016 &0.063 &0.026 &0.068\\ \hline F3 &0.047 &0.063 &0.011 &0.012 &0.026 &0.084 &0.084 &0.094 &0.026 &0.087 &0 &0.013 &0.015 &0.074 &0.081 &0.079\\ \hline U1 &0.074 &0.092 &0.074 &0.068 &0.016 &0.066 &0.034 &0.084 &0.048 &0.021 &0.042 &0 &0.088 &0.076 &0.058 &0.031\\ \hline U2 &0.074 &0.052 &0.064 &0.079 &0.053 &0.076 &0.073 &0.085 &0.068 &0.022 &0.021 &0.093 &0 &0.013 &0.007 &0.086\\ \hline D1 &0.021 &0.011 &0.037 &0.073 &0.068 &0.09 &0.073 &0.067 &0.024 &0.011 &0.086 &0.011 &0.068 &0 &0.08 &0.094\\ \hline D2 &0.064 &0.074 &0.012 &0.087 &0.073 &0.087 &0.042 &0.094 &0.091 &0.043 &0.035 &0.085 &0.053 &0.094 &0 &0.032\\ \hline D3 &0.013 &0.011 &0.01 &0.092 &0.022 &0.094 &0.087 &0.076 &0.008 &0.068 &0.075 &0.089 &0.034 &0.076 &0.094 &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 &0.371 &0.409 &0.323 &0.572 &0.413 &0.517 &0.439 &0.557 &0.519 &0.213 &0.288 &0.385 &0.509 &0.34 &0.433 &0.34\\ \hline C2 &0.398 &0.289 &0.265 &0.496 &0.38 &0.396 &0.337 &0.475 &0.45 &0.185 &0.282 &0.302 &0.406 &0.319 &0.352 &0.305\\ \hline C3 &0.364 &0.288 &0.195 &0.467 &0.301 &0.415 &0.295 &0.46 &0.421 &0.157 &0.217 &0.296 &0.397 &0.291 &0.35 &0.287\\ \hline C4 &0.372 &0.328 &0.227 &0.395 &0.364 &0.426 &0.321 &0.458 &0.43 &0.175 &0.244 &0.303 &0.427 &0.288 &0.356 &0.29\\ \hline C5 &0.445 &0.41 &0.321 &0.537 &0.33 &0.47 &0.392 &0.524 &0.499 &0.209 &0.285 &0.38 &0.491 &0.346 &0.41 &0.345\\ \hline E1 &0.29 &0.264 &0.187 &0.424 &0.276 &0.327 &0.33 &0.401 &0.397 &0.188 &0.253 &0.249 &0.389 &0.273 &0.353 &0.304\\ \hline E2 &0.357 &0.377 &0.233 &0.53 &0.349 &0.491 &0.341 &0.51 &0.473 &0.281 &0.346 &0.304 &0.465 &0.363 &0.411 &0.397\\ \hline E3 &0.356 &0.296 &0.217 &0.465 &0.31 &0.397 &0.339 &0.374 &0.395 &0.186 &0.28 &0.264 &0.412 &0.285 &0.332 &0.323\\ \hline F1 &0.41 &0.384 &0.283 &0.517 &0.389 &0.461 &0.401 &0.504 &0.384 &0.203 &0.27 &0.286 &0.399 &0.333 &0.353 &0.352\\ \hline F2 &0.157 &0.152 &0.098 &0.21 &0.15 &0.218 &0.192 &0.22 &0.187 &0.094 &0.202 &0.14 &0.186 &0.199 &0.185 &0.21\\ \hline F3 &0.313 &0.308 &0.187 &0.378 &0.28 &0.413 &0.357 &0.444 &0.344 &0.245 &0.224 &0.241 &0.33 &0.318 &0.36 &0.332\\ \hline U1 &0.386 &0.37 &0.281 &0.48 &0.31 &0.439 &0.342 &0.487 &0.413 &0.193 &0.278 &0.263 &0.442 &0.343 &0.37 &0.315\\ \hline U2 &0.383 &0.337 &0.272 &0.49 &0.338 &0.447 &0.378 &0.487 &0.43 &0.197 &0.259 &0.35 &0.362 &0.287 &0.325 &0.362\\ \hline D1 &0.31 &0.278 &0.225 &0.455 &0.333 &0.442 &0.362 &0.446 &0.364 &0.184 &0.309 &0.259 &0.4 &0.26 &0.376 &0.359\\ \hline D2 &0.407 &0.387 &0.246 &0.537 &0.392 &0.494 &0.383 &0.534 &0.487 &0.232 &0.299 &0.365 &0.448 &0.388 &0.347 &0.345\\ \hline D3 &0.301 &0.279 &0.198 &0.47 &0.291 &0.446 &0.373 &0.454 &0.349 &0.238 &0.306 &0.326 &0.371 &0.336 &0.39 &0.274\\ \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 &0.0661 &0.0793 &0.0858 &0.077 &0.0793 &0.076 &0.0787 &0.0759 &0.0794 &0.0671 &0.0663 &0.0817 &0.0791 &0.0685 &0.0759 &0.0661\\ \hline C2 &0.0708 &0.056 &0.0704 &0.0669 &0.0729 &0.0582 &0.0603 &0.0647 &0.0689 &0.0583 &0.0651 &0.0641 &0.0631 &0.0642 &0.0617 &0.0594\\ \hline C3 &0.0647 &0.0558 &0.0519 &0.063 &0.0579 &0.0611 &0.0528 &0.0627 &0.0643 &0.0495 &0.05 &0.0629 &0.0617 &0.0586 &0.0614 &0.0559\\ \hline C4 &0.0662 &0.0636 &0.0603 &0.0532 &0.07 &0.0627 &0.0574 &0.0625 &0.0658 &0.055 &0.0562 &0.0642 &0.0663 &0.058 &0.0624 &0.0565\\ \hline C5 &0.0792 &0.0794 &0.0853 &0.0724 &0.0634 &0.0692 &0.0703 &0.0714 &0.0763 &0.0658 &0.0655 &0.0807 &0.0762 &0.0697 &0.0718 &0.0672\\ \hline E1 &0.0516 &0.0512 &0.0497 &0.0572 &0.0531 &0.0481 &0.0592 &0.0546 &0.0606 &0.0592 &0.0582 &0.0527 &0.0605 &0.0549 &0.0619 &0.0592\\ \hline E2 &0.0636 &0.0732 &0.062 &0.0714 &0.067 &0.0722 &0.061 &0.0696 &0.0723 &0.0884 &0.0797 &0.0645 &0.0723 &0.073 &0.072 &0.0772\\ \hline E3 &0.0633 &0.0575 &0.0578 &0.0627 &0.0596 &0.0584 &0.0608 &0.051 &0.0603 &0.0585 &0.0644 &0.0559 &0.064 &0.0574 &0.0582 &0.0628\\ \hline F1 &0.073 &0.0746 &0.0754 &0.0697 &0.0747 &0.0678 &0.0718 &0.0688 &0.0588 &0.064 &0.0621 &0.0606 &0.062 &0.067 &0.0619 &0.0684\\ \hline F2 &0.0279 &0.0295 &0.026 &0.0282 &0.0288 &0.0321 &0.0343 &0.03 &0.0285 &0.0295 &0.0466 &0.0298 &0.0289 &0.04 &0.0325 &0.0408\\ \hline F3 &0.0556 &0.0597 &0.0499 &0.0509 &0.0537 &0.0607 &0.0639 &0.0606 &0.0526 &0.077 &0.0516 &0.0512 &0.0513 &0.064 &0.0631 &0.0646\\ \hline U1 &0.0686 &0.0718 &0.0748 &0.0647 &0.0596 &0.0646 &0.0613 &0.0664 &0.0632 &0.0607 &0.0641 &0.0557 &0.0688 &0.069 &0.0649 &0.0613\\ \hline U2 &0.0682 &0.0654 &0.0723 &0.066 &0.0649 &0.0658 &0.0677 &0.0663 &0.0657 &0.0619 &0.0597 &0.0743 &0.0563 &0.0577 &0.057 &0.0704\\ \hline D1 &0.0552 &0.054 &0.0599 &0.0613 &0.064 &0.065 &0.0649 &0.0608 &0.0557 &0.0577 &0.0711 &0.055 &0.0622 &0.0523 &0.066 &0.0698\\ \hline D2 &0.0724 &0.075 &0.0656 &0.0723 &0.0753 &0.0727 &0.0686 &0.0728 &0.0744 &0.0728 &0.0689 &0.0775 &0.0696 &0.0781 &0.0609 &0.0671\\ \hline D3 &0.0536 &0.0542 &0.0528 &0.0633 &0.0558 &0.0656 &0.0668 &0.0618 &0.0534 &0.0747 &0.0704 &0.0691 &0.0577 &0.0676 &0.0684 &0.0534\\ \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 &0.0754 &0.0754 &0.0754 &0.0754 &0.0754 &0.0754 &0.0754 &0.0754 &0.0754 &0.0754 &0.0754 &0.0754 &0.0754 &0.0754 &0.0754 &0.0754\\ \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 &0.0588 &0.0588 &0.0588 &0.0588 &0.0588 &0.0588 &0.0588 &0.0588 &0.0588 &0.0588 &0.0588 &0.0588 &0.0588 &0.0588 &0.0588 &0.0588\\ \hline C4 &0.0617 &0.0617 &0.0617 &0.0617 &0.0617 &0.0617 &0.0617 &0.0617 &0.0617 &0.0617 &0.0617 &0.0617 &0.0617 &0.0617 &0.0617 &0.0617\\ \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 &0.0557 &0.0557 &0.0557 &0.0557 &0.0557 &0.0557 &0.0557 &0.0557 &0.0557 &0.0557 &0.0557 &0.0557 &0.0557 &0.0557 &0.0557 &0.0557\\ \hline E2 &0.0704 &0.0704 &0.0704 &0.0704 &0.0704 &0.0704 &0.0704 &0.0704 &0.0704 &0.0704 &0.0704 &0.0704 &0.0704 &0.0704 &0.0704 &0.0704\\ \hline E3 &0.0596 &0.0596 &0.0596 &0.0596 &0.0596 &0.0596 &0.0596 &0.0596 &0.0596 &0.0596 &0.0596 &0.0596 &0.0596 &0.0596 &0.0596 &0.0596\\ \hline F1 &0.0677 &0.0677 &0.0677 &0.0677 &0.0677 &0.0677 &0.0677 &0.0677 &0.0677 &0.0677 &0.0677 &0.0677 &0.0677 &0.0677 &0.0677 &0.0677\\ \hline F2 &0.032 &0.032 &0.032 &0.032 &0.032 &0.032 &0.032 &0.032 &0.032 &0.032 &0.032 &0.032 &0.032 &0.032 &0.032 &0.032\\ \hline F3 &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 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 &0.0651 &0.0651 &0.0651 &0.0651 &0.0651 &0.0651 &0.0651 &0.0651 &0.0651 &0.0651 &0.0651 &0.0651 &0.0651 &0.0651 &0.0651 &0.0651\\ \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 &0.0612 &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 \end{array} $$

权重的求解

$$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{16 \times1}} &权重\\ \hline C1 &0.07541\\ \hline C2 &0.06438\\ \hline C3 &0.0588\\ \hline C4 &0.06168\\ \hline C5 &0.073\\ \hline E1 &0.05573\\ \hline E2 &0.07044\\ \hline E3 &0.05963\\ \hline F1 &0.06769\\ \hline F2 &0.032\\ \hline F3 &0.05756\\ \hline U1 &0.06502\\ \hline U2 &0.06506\\ \hline D1 &0.06093\\ \hline D2 &0.07144\\ \hline D3 &0.06123\\ \hline \end{array} $$$$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{1 \times16}} &C1 &C2 &C3 &C4 &C5 &E1 &E2 &E3 &F1 &F2 &F3 &U1 &U2 &D1 &D2 &D3\\ \hline 权重 &0.07541 &0.06438 &0.0588 &0.06168 &0.073 &0.05573 &0.07044 &0.05963 &0.06769 &0.032 &0.05756 &0.06502 &0.06506 &0.06093 &0.07144 &0.06123\\ \hline \end{array} $$

归一化求子系统的权重

$$\omega =\begin{array}{c|c|c|c|c|c|c}{M_{5 \times1}} &权重\\ \hline C &0.3333\\ \hline E &0.1858\\ \hline F &0.1573\\ \hline U &0.1301\\ \hline D &0.1936\\ \hline \end{array} $$$$\omega =\begin{array}{c|c|c|c|c|c|c}{M_{1 \times5}} &C &E &F &U &D\\ \hline 权重 &0.3333 &0.1858 &0.1573 &0.1301 &0.1936\\ \hline \end{array} $$