DEMATEL-ANP流程图如下:
原始矩阵(直接影响矩阵)O为
$$\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{16 \times16}} &A1 &A2 &A3 &A4 &A5 &B1 &B2 &B3 &C1 &C2 &C3 &C4 &D1 &D2 &D3 &D4\\ \hline A1 &0 &37 &38 &36 &32 &40 &32 &34 &38 &32 &33 &31 &23 &28 &35 &33\\ \hline A2 &43 &0 &40 &41 &36 &40 &38 &40 &45 &39 &43 &43 &41 &38 &37 &35\\ \hline A3 &37 &41 &0 &43 &41 &38 &36 &41 &45 &42 &41 &43 &32 &34 &41 &39\\ \hline A4 &39 &40 &42 &0 &39 &40 &43 &42 &38 &37 &39 &41 &46 &43 &40 &42\\ \hline A5 &32 &28 &31 &33 &0 &26 &24 &25 &29 &27 &21 &23 &22 &21 &27 &24\\ \hline B1 &41 &39 &40 &42 &39 &0 &44 &46 &38 &38 &42 &39 &43 &41 &40 &42\\ \hline B2 &33 &34 &32 &35 &27 &38 &0 &39 &32 &30 &26 &27 &28 &32 &33 &32\\ \hline B3 &36 &37 &33 &38 &34 &41 &37 &0 &33 &29 &28 &30 &31 &32 &37 &32\\ \hline C1 &46 &46 &39 &42 &35 &40 &38 &35 &0 &41 &37 &38 &31 &36 &41 &36\\ \hline C2 &33 &31 &32 &30 &31 &28 &26 &28 &36 &0 &34 &33 &27 &26 &29 &25\\ \hline C3 &31 &32 &29 &32 &33 &31 &32 &28 &35 &30 &0 &26 &29 &31 &33 &22\\ \hline C4 &33 &32 &30 &33 &29 &33 &34 &33 &31 &32 &31 &0 &28 &30 &32 &24\\ \hline D1 &33 &35 &32 &34 &25 &34 &32 &30 &29 &24 &28 &32 &0 &34 &32 &31\\ \hline D2 &34 &37 &32 &33 &25 &31 &33 &28 &32 &27 &25 &34 &30 &0 &31 &29\\ \hline D3 &35 &36 &31 &42 &31 &33 &32 &28 &34 &33 &27 &34 &29 &33 &0 &31\\ \hline D4 &44 &37 &42 &45 &38 &44 &42 &43 &46 &35 &39 &42 &38 &40 &44 &0\\ \hline \end{array} $$
规范直接关系矩阵N
综合影响矩阵T
综合影响矩阵T
$T=\mathcal{N}(I-\mathcal{N})^{-1}$
$$\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} $$
未加权超矩阵Un
$$ \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 &0.1774 &0.1919 &0.192 &0.191 &0.1901 &0.1902 &0.1881 &0.1882 &0.1888 &0.1878 &0.1882 &0.1871 &0.1851 &0.1871 &0.1887 &0.1885\\ \hline A2 &0.2237 &0.2078 &0.2227 &0.2228 &0.2215 &0.2199 &0.22 &0.22 &0.2207 &0.22 &0.2216 &0.2212 &0.222 &0.2208 &0.2191 &0.2188\\ \hline A3 &0.2202 &0.2221 &0.2056 &0.2221 &0.2222 &0.2178 &0.2179 &0.219 &0.2194 &0.2199 &0.2195 &0.2199 &0.2171 &0.2179 &0.2192 &0.219\\ \hline A4 &0.226 &0.2268 &0.2272 &0.2113 &0.2264 &0.2236 &0.2256 &0.2244 &0.2219 &0.2228 &0.2236 &0.2241 &0.2277 &0.2264 &0.2238 &0.2253\\ \hline A5 &0.1527 &0.1515 &0.1525 &0.1529 &0.1398 &0.1486 &0.1484 &0.1484 &0.1491 &0.1494 &0.147 &0.1477 &0.1481 &0.1478 &0.1492 &0.1485\\ \hline B1 &0.3782 &0.377 &0.3787 &0.3777 &0.3793 &0.3592 &0.3875 &0.3878 &0.378 &0.3794 &0.3823 &0.3802 &0.3815 &0.3794 &0.3776 &0.3797\\ \hline B2 &0.3021 &0.3027 &0.3024 &0.3024 &0.3001 &0.3114 &0.2857 &0.3111 &0.3027 &0.3027 &0.3002 &0.301 &0.3003 &0.3024 &0.3021 &0.3022\\ \hline B3 &0.3197 &0.3203 &0.3189 &0.32 &0.3206 &0.3294 &0.3267 &0.3011 &0.3193 &0.3179 &0.3175 &0.3188 &0.3182 &0.3182 &0.3204 &0.318\\ \hline C1 &0.2979 &0.2982 &0.2964 &0.2968 &0.2946 &0.2966 &0.2959 &0.2953 &0.2802 &0.3022 &0.3002 &0.3014 &0.2945 &0.2959 &0.2966 &0.2986\\ \hline C2 &0.2313 &0.2306 &0.2323 &0.2305 &0.2321 &0.2301 &0.2292 &0.2309 &0.2379 &0.2175 &0.2373 &0.2372 &0.2315 &0.23 &0.2302 &0.2314\\ \hline C3 &0.2323 &0.233 &0.2328 &0.2335 &0.2351 &0.2335 &0.2343 &0.2329 &0.2393 &0.2369 &0.2195 &0.2354 &0.2347 &0.2347 &0.2342 &0.2318\\ \hline C4 &0.2385 &0.2382 &0.2385 &0.2392 &0.2382 &0.2398 &0.2406 &0.2409 &0.2426 &0.2433 &0.2429 &0.226 &0.2394 &0.2394 &0.2389 &0.2382\\ \hline D1 &0.23 &0.231 &0.2305 &0.2296 &0.229 &0.2309 &0.2303 &0.2305 &0.2287 &0.2285 &0.2306 &0.23 &0.2174 &0.2355 &0.2342 &0.236\\ \hline D2 &0.2287 &0.2302 &0.2287 &0.2274 &0.2272 &0.2277 &0.229 &0.2276 &0.2283 &0.2283 &0.2272 &0.2292 &0.2329 &0.2148 &0.2318 &0.2331\\ \hline D3 &0.241 &0.2416 &0.2402 &0.2433 &0.2424 &0.2405 &0.2404 &0.2396 &0.2412 &0.2434 &0.2403 &0.241 &0.2445 &0.2451 &0.2277 &0.2463\\ \hline D4 &0.3003 &0.2972 &0.3006 &0.2997 &0.3014 &0.3009 &0.3003 &0.3023 &0.3019 &0.2999 &0.3019 &0.2998 &0.3053 &0.3046 &0.3064 &0.2846\\ \hline \end{array} $$
加权超矩阵W
加权超矩阵依据其定义有:每列加起来的为1。
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。这类计算要重新处理。 $$\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limit W:
权重的求解
归一化求子系统的权重
$$sys-\omega=\begin{array}{c|c|c|c|c|c|c}{M_{4 \times1}} &权重\\ \hline A &0.325\\ \hline B &0.1931\\ \hline C &0.2356\\ \hline D &0.2464\\ \hline \end{array} $$所有子系统内部权重
A系统权重如下: $$ \begin{array}{c|c|c|c|c|c|c}{M_{5 \times1}} &权重\\ \hline A1 &0.1883\\ \hline A2 &0.22\\ \hline A3 &0.2186\\ \hline A4 &0.224\\ \hline A5 &0.1491\\ \hline \end{array} $$B系统权重如下: $$ \begin{array}{c|c|c|c|c|c|c}{M_{3 \times1}} &权重\\ \hline B1 &0.3786\\ \hline B2 &0.3022\\ \hline B3 &0.3192\\ \hline \end{array} $$C系统权重如下: $$ \begin{array}{c|c|c|c|c|c|c}{M_{4 \times1}} &权重\\ \hline C1 &0.2962\\ \hline C2 &0.2313\\ \hline C3 &0.2334\\ \hline C4 &0.2391\\ \hline \end{array} $$D系统权重如下: $$ \begin{array}{c|c|c|c|c|c|c}{M_{4 \times1}} &权重\\ \hline D1 &0.2303\\ \hline D2 &0.2284\\ \hline D3 &0.2412\\ \hline D4 &0.3001\\ \hline \end{array} $$