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 &0.06 &0.061 &0.058 &0.052 &0.065 &0.052 &0.055 &0.061 &0.052 &0.053 &0.05 &0.037 &0.045 &0.057 &0.053\\ \hline A2 &0.069 &0 &0.065 &0.066 &0.058 &0.065 &0.061 &0.065 &0.073 &0.063 &0.069 &0.069 &0.066 &0.061 &0.06 &0.057\\ \hline A3 &0.06 &0.066 &0 &0.069 &0.066 &0.061 &0.058 &0.066 &0.073 &0.068 &0.066 &0.069 &0.052 &0.055 &0.066 &0.063\\ \hline A4 &0.063 &0.065 &0.068 &0 &0.063 &0.065 &0.069 &0.068 &0.061 &0.06 &0.063 &0.066 &0.074 &0.069 &0.065 &0.068\\ \hline A5 &0.052 &0.045 &0.05 &0.053 &0 &0.042 &0.039 &0.04 &0.047 &0.044 &0.034 &0.037 &0.036 &0.034 &0.044 &0.039\\ \hline B1 &0.066 &0.063 &0.065 &0.068 &0.063 &0 &0.071 &0.074 &0.061 &0.061 &0.068 &0.063 &0.069 &0.066 &0.065 &0.068\\ \hline B2 &0.053 &0.055 &0.052 &0.057 &0.044 &0.061 &0 &0.063 &0.052 &0.048 &0.042 &0.044 &0.045 &0.052 &0.053 &0.052\\ \hline B3 &0.058 &0.06 &0.053 &0.061 &0.055 &0.066 &0.06 &0 &0.053 &0.047 &0.045 &0.048 &0.05 &0.052 &0.06 &0.052\\ \hline C1 &0.074 &0.074 &0.063 &0.068 &0.057 &0.065 &0.061 &0.057 &0 &0.066 &0.06 &0.061 &0.05 &0.058 &0.066 &0.058\\ \hline C2 &0.053 &0.05 &0.052 &0.048 &0.05 &0.045 &0.042 &0.045 &0.058 &0 &0.055 &0.053 &0.044 &0.042 &0.047 &0.04\\ \hline C3 &0.05 &0.052 &0.047 &0.052 &0.053 &0.05 &0.052 &0.045 &0.057 &0.048 &0 &0.042 &0.047 &0.05 &0.053 &0.036\\ \hline C4 &0.053 &0.052 &0.048 &0.053 &0.047 &0.053 &0.055 &0.053 &0.05 &0.052 &0.05 &0 &0.045 &0.048 &0.052 &0.039\\ \hline D1 &0.053 &0.057 &0.052 &0.055 &0.04 &0.055 &0.052 &0.048 &0.047 &0.039 &0.045 &0.052 &0 &0.055 &0.052 &0.05\\ \hline D2 &0.055 &0.06 &0.052 &0.053 &0.04 &0.05 &0.053 &0.045 &0.052 &0.044 &0.04 &0.055 &0.048 &0 &0.05 &0.047\\ \hline D3 &0.057 &0.058 &0.05 &0.068 &0.05 &0.053 &0.052 &0.045 &0.055 &0.053 &0.044 &0.055 &0.047 &0.053 &0 &0.05\\ \hline D4 &0.071 &0.06 &0.068 &0.073 &0.061 &0.071 &0.068 &0.069 &0.074 &0.057 &0.063 &0.068 &0.061 &0.065 &0.071 &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 &0.284 &0.337 &0.329 &0.344 &0.307 &0.339 &0.32 &0.322 &0.338 &0.308 &0.308 &0.316 &0.285 &0.303 &0.329 &0.3\\ \hline A2 &0.398 &0.329 &0.378 &0.4 &0.356 &0.386 &0.375 &0.377 &0.395 &0.362 &0.366 &0.378 &0.354 &0.361 &0.379 &0.345\\ \hline A3 &0.387 &0.388 &0.315 &0.401 &0.362 &0.381 &0.37 &0.376 &0.393 &0.364 &0.361 &0.376 &0.339 &0.354 &0.383 &0.349\\ \hline A4 &0.398 &0.395 &0.387 &0.344 &0.366 &0.392 &0.388 &0.385 &0.391 &0.364 &0.366 &0.381 &0.366 &0.374 &0.389 &0.361\\ \hline A5 &0.274 &0.265 &0.262 &0.279 &0.204 &0.26 &0.252 &0.252 &0.266 &0.246 &0.236 &0.248 &0.231 &0.238 &0.26 &0.235\\ \hline B1 &0.402 &0.395 &0.385 &0.409 &0.367 &0.333 &0.391 &0.393 &0.393 &0.367 &0.371 &0.38 &0.363 &0.373 &0.391 &0.362\\ \hline B2 &0.322 &0.32 &0.308 &0.329 &0.287 &0.323 &0.259 &0.317 &0.316 &0.292 &0.286 &0.297 &0.281 &0.297 &0.313 &0.287\\ \hline B3 &0.341 &0.339 &0.324 &0.349 &0.311 &0.342 &0.33 &0.272 &0.332 &0.305 &0.302 &0.316 &0.299 &0.311 &0.334 &0.3\\ \hline C1 &0.394 &0.39 &0.369 &0.393 &0.348 &0.378 &0.368 &0.362 &0.32 &0.357 &0.35 &0.364 &0.332 &0.351 &0.377 &0.339\\ \hline C2 &0.304 &0.297 &0.29 &0.303 &0.277 &0.291 &0.282 &0.283 &0.304 &0.23 &0.281 &0.289 &0.263 &0.271 &0.29 &0.261\\ \hline C3 &0.303 &0.301 &0.288 &0.308 &0.282 &0.297 &0.293 &0.286 &0.305 &0.278 &0.231 &0.281 &0.268 &0.281 &0.298 &0.258\\ \hline C4 &0.312 &0.307 &0.296 &0.316 &0.282 &0.306 &0.302 &0.299 &0.305 &0.287 &0.284 &0.246 &0.272 &0.285 &0.303 &0.267\\ \hline D1 &0.314 &0.314 &0.301 &0.32 &0.277 &0.31 &0.301 &0.297 &0.304 &0.277 &0.282 &0.298 &0.231 &0.293 &0.305 &0.279\\ \hline D2 &0.313 &0.314 &0.298 &0.316 &0.275 &0.303 &0.3 &0.292 &0.306 &0.279 &0.275 &0.298 &0.275 &0.238 &0.301 &0.274\\ \hline D3 &0.33 &0.327 &0.311 &0.344 &0.298 &0.321 &0.313 &0.306 &0.324 &0.301 &0.292 &0.312 &0.287 &0.303 &0.267 &0.29\\ \hline D4 &0.411 &0.396 &0.392 &0.418 &0.37 &0.403 &0.392 &0.392 &0.408 &0.366 &0.371 &0.388 &0.36 &0.375 &0.4 &0.302\\ \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 &0.0518 &0.0622 &0.0629 &0.0617 &0.0617 &0.0631 &0.0612 &0.0618 &0.0625 &0.0617 &0.0621 &0.061 &0.0593 &0.0605 &0.0619 &0.0624\\ \hline A2 &0.0725 &0.0607 &0.0722 &0.0718 &0.0717 &0.072 &0.0717 &0.0723 &0.0732 &0.0726 &0.0738 &0.0732 &0.0736 &0.0722 &0.0713 &0.0718\\ \hline A3 &0.0705 &0.0717 &0.0603 &0.0719 &0.0728 &0.071 &0.0707 &0.0722 &0.0728 &0.0731 &0.0728 &0.0728 &0.0705 &0.0706 &0.0719 &0.0726\\ \hline A4 &0.0725 &0.073 &0.0739 &0.0618 &0.0736 &0.0731 &0.0742 &0.074 &0.0724 &0.073 &0.0737 &0.0738 &0.0762 &0.0748 &0.0732 &0.075\\ \hline A5 &0.0499 &0.0489 &0.0501 &0.05 &0.041 &0.0485 &0.0481 &0.0484 &0.0493 &0.0494 &0.0476 &0.0479 &0.0481 &0.0475 &0.0488 &0.0488\\ \hline B1 &0.0733 &0.073 &0.0736 &0.0734 &0.0739 &0.0621 &0.0747 &0.0754 &0.0727 &0.0736 &0.0748 &0.0735 &0.0756 &0.0745 &0.0735 &0.0753\\ \hline B2 &0.0586 &0.059 &0.0588 &0.059 &0.0578 &0.0602 &0.0494 &0.0608 &0.0585 &0.0587 &0.0575 &0.0575 &0.0584 &0.0592 &0.0589 &0.0597\\ \hline B3 &0.0622 &0.0626 &0.0619 &0.0626 &0.0627 &0.0638 &0.063 &0.0522 &0.0616 &0.0612 &0.0609 &0.0612 &0.0622 &0.062 &0.0628 &0.0625\\ \hline C1 &0.0718 &0.072 &0.0705 &0.0706 &0.0699 &0.0705 &0.0702 &0.0695 &0.0592 &0.0717 &0.0706 &0.0704 &0.0691 &0.0701 &0.0708 &0.0706\\ \hline C2 &0.0553 &0.0549 &0.0555 &0.0544 &0.0557 &0.0542 &0.0538 &0.0544 &0.0563 &0.0462 &0.0566 &0.0559 &0.0548 &0.0541 &0.0545 &0.0542\\ \hline C3 &0.0552 &0.0556 &0.0551 &0.0554 &0.0567 &0.0554 &0.0559 &0.0548 &0.0564 &0.0558 &0.0465 &0.0543 &0.0558 &0.0561 &0.056 &0.0537\\ \hline C4 &0.0569 &0.0568 &0.0565 &0.0567 &0.0567 &0.0571 &0.0576 &0.0574 &0.0565 &0.0575 &0.0573 &0.0477 &0.0567 &0.0569 &0.0569 &0.0555\\ \hline D1 &0.0572 &0.0579 &0.0574 &0.0574 &0.0558 &0.0577 &0.0574 &0.0569 &0.0563 &0.0555 &0.0568 &0.0576 &0.0481 &0.0585 &0.0573 &0.058\\ \hline D2 &0.0571 &0.058 &0.057 &0.0567 &0.0554 &0.0565 &0.0573 &0.056 &0.0567 &0.056 &0.0555 &0.0577 &0.0572 &0.0476 &0.0566 &0.057\\ \hline D3 &0.0601 &0.0605 &0.0594 &0.0617 &0.0599 &0.0597 &0.0597 &0.0586 &0.0599 &0.0605 &0.0588 &0.0604 &0.0597 &0.0604 &0.0503 &0.0603\\ \hline D4 &0.0749 &0.0732 &0.0749 &0.075 &0.0744 &0.0752 &0.0749 &0.0753 &0.0756 &0.0735 &0.0747 &0.0751 &0.0748 &0.0749 &0.0753 &0.0628\\ \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 &0.0729 &0.0729 &0.0729 &0.0729 &0.0729 &0.0729 &0.0729 &0.0729 &0.0729 &0.0729 &0.0729 &0.0729 &0.0729 &0.0729 &0.0729 &0.0729\\ \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 &0.0562 &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 &0.0739 &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

$$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{16 \times1}} &权重\\ \hline A1 &0.06119\\ \hline A2 &0.07153\\ \hline A3 &0.07104\\ \hline A4 &0.07286\\ \hline A5 &0.04843\\ \hline B1 &0.07315\\ \hline B2 &0.05835\\ \hline B3 &0.06163\\ \hline C1 &0.06978\\ \hline C2 &0.05448\\ \hline C3 &0.05497\\ \hline C4 &0.05632\\ \hline D1 &0.05671\\ \hline D2 &0.05624\\ \hline D3 &0.05942\\ \hline D4 &0.0739\\ \hline \end{array} $$$$\omega=\begin{array}{c|c|c|c|c|c|c}{M_{1 \times16}} &A1 &A2 &A3 &A4 &A5 &B1 &B2 &B3 &C1 &C2 &C3 &C4 &D1 &D2 &D3 &D4\\ \hline 权重 &0.06119 &0.07153 &0.07104 &0.07286 &0.04843 &0.07315 &0.05835 &0.06163 &0.06978 &0.05448 &0.05497 &0.05632 &0.05671 &0.05624 &0.05942 &0.0739\\ \hline \end{array} $$

归一化求子系统的权重

$$\omega =\begin{array}{c|c|c|c|c|c|c}{M_{4 \times1}} &权重\\ \hline A &0.325\\ \hline B &0.1931\\ \hline C &0.2355\\ \hline D &0.2463\\ \hline \end{array} $$$$\omega =\begin{array}{c|c|c|c|c|c|c}{M_{1 \times4}} &A &B &C &D\\ \hline 权重 &0.325 &0.1931 &0.2355 &0.2463\\ \hline \end{array} $$