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 &0.068 &0.109 &0.108 &0.11 &0.098 &0.112 &0.102 &0.104 &0.11 &0.099 &0.099 &0.1 &0.086 &0.094 &0.106 &0.097\\ \hline A2 &0.129 &0.079 &0.122 &0.128 &0.113 &0.124 &0.12 &0.121 &0.13 &0.117 &0.121 &0.124 &0.116 &0.116 &0.12 &0.11\\ \hline A3 &0.122 &0.125 &0.075 &0.129 &0.119 &0.121 &0.117 &0.122 &0.129 &0.12 &0.118 &0.124 &0.106 &0.111 &0.124 &0.114\\ \hline A4 &0.126 &0.126 &0.125 &0.082 &0.118 &0.125 &0.126 &0.125 &0.123 &0.116 &0.118 &0.123 &0.123 &0.123 &0.124 &0.119\\ \hline A5 &0.09 &0.085 &0.087 &0.092 &0.048 &0.083 &0.079 &0.08 &0.086 &0.08 &0.073 &0.077 &0.073 &0.073 &0.083 &0.075\\ \hline B1 &0.128 &0.125 &0.123 &0.131 &0.118 &0.08 &0.128 &0.13 &0.124 &0.117 &0.121 &0.121 &0.12 &0.121 &0.125 &0.119\\ \hline B2 &0.103 &0.103 &0.099 &0.106 &0.09 &0.107 &0.062 &0.106 &0.101 &0.093 &0.089 &0.092 &0.089 &0.096 &0.101 &0.094\\ \hline B3 &0.11 &0.11 &0.103 &0.113 &0.101 &0.114 &0.108 &0.065 &0.105 &0.096 &0.094 &0.099 &0.096 &0.099 &0.109 &0.097\\ \hline C1 &0.13 &0.129 &0.119 &0.127 &0.111 &0.122 &0.118 &0.114 &0.077 &0.117 &0.113 &0.117 &0.104 &0.112 &0.122 &0.109\\ \hline C2 &0.098 &0.095 &0.094 &0.096 &0.09 &0.091 &0.088 &0.09 &0.101 &0.055 &0.094 &0.095 &0.084 &0.085 &0.092 &0.082\\ \hline C3 &0.097 &0.097 &0.092 &0.099 &0.093 &0.095 &0.095 &0.09 &0.1 &0.09 &0.055 &0.088 &0.087 &0.091 &0.097 &0.079\\ \hline C4 &0.1 &0.099 &0.094 &0.101 &0.09 &0.099 &0.099 &0.097 &0.097 &0.094 &0.092 &0.059 &0.087 &0.092 &0.097 &0.083\\ \hline D1 &0.101 &0.102 &0.097 &0.103 &0.086 &0.101 &0.097 &0.094 &0.095 &0.085 &0.089 &0.096 &0.055 &0.097 &0.098 &0.091\\ \hline D2 &0.101 &0.104 &0.096 &0.101 &0.085 &0.097 &0.097 &0.092 &0.098 &0.088 &0.085 &0.098 &0.089 &0.057 &0.096 &0.088\\ \hline D3 &0.106 &0.106 &0.099 &0.115 &0.095 &0.102 &0.1 &0.095 &0.104 &0.098 &0.091 &0.101 &0.091 &0.098 &0.064 &0.094\\ \hline D4 &0.133 &0.124 &0.127 &0.135 &0.118 &0.131 &0.127 &0.127 &0.133 &0.115 &0.119 &0.126 &0.116 &0.121 &0.13 &0.072\\ \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 &0.127 &0.2088 &0.2092 &0.2035 &0.1982 &0.1986 &0.1871 &0.1879 &0.1908 &0.1857 &0.1878 &0.1821 &0.171 &0.1821 &0.1905 &0.1893\\ \hline A2 &0.2409 &0.1501 &0.2351 &0.2355 &0.2282 &0.2191 &0.22 &0.2199 &0.2239 &0.2201 &0.2285 &0.2264 &0.2308 &0.2242 &0.2149 &0.2134\\ \hline A3 &0.2276 &0.2384 &0.1457 &0.2387 &0.2386 &0.2142 &0.2149 &0.2209 &0.2231 &0.2256 &0.2235 &0.2255 &0.2102 &0.2147 &0.2219 &0.2209\\ \hline A4 &0.2353 &0.2401 &0.2421 &0.152 &0.2374 &0.2217 &0.2327 &0.2265 &0.2131 &0.2182 &0.2224 &0.2249 &0.2443 &0.2375 &0.2234 &0.2309\\ \hline A5 &0.1692 &0.1627 &0.1679 &0.1703 &0.0976 &0.1463 &0.1453 &0.1448 &0.1491 &0.1505 &0.1379 &0.1411 &0.1436 &0.1416 &0.1494 &0.1455\\ \hline B1 &0.3765 &0.3701 &0.3794 &0.3738 &0.3827 &0.2655 &0.4301 &0.4311 &0.3754 &0.3831 &0.399 &0.3879 &0.3943 &0.3829 &0.3732 &0.3849\\ \hline B2 &0.3014 &0.3046 &0.3031 &0.3029 &0.2906 &0.3557 &0.2076 &0.3529 &0.3051 &0.3047 &0.2913 &0.2951 &0.292 &0.3032 &0.3014 &0.3023\\ \hline B3 &0.3221 &0.3253 &0.3175 &0.3233 &0.3267 &0.3788 &0.3623 &0.216 &0.3195 &0.3122 &0.3096 &0.3169 &0.3137 &0.3139 &0.3254 &0.3129\\ \hline C1 &0.3055 &0.307 &0.2976 &0.2998 &0.2877 &0.2986 &0.2947 &0.2914 &0.2043 &0.33 &0.3188 &0.3263 &0.2869 &0.2949 &0.2988 &0.3097\\ \hline C2 &0.2312 &0.2272 &0.2367 &0.2269 &0.2355 &0.2244 &0.2199 &0.2292 &0.269 &0.1541 &0.2651 &0.2651 &0.2323 &0.224 &0.2253 &0.2319\\ \hline C3 &0.2273 &0.2312 &0.2297 &0.2336 &0.2424 &0.2339 &0.238 &0.2306 &0.2673 &0.2529 &0.1554 &0.2447 &0.2401 &0.2402 &0.2375 &0.2242\\ \hline C4 &0.2359 &0.2346 &0.236 &0.2397 &0.2344 &0.2431 &0.2473 &0.2487 &0.2594 &0.263 &0.2607 &0.164 &0.2407 &0.2409 &0.2383 &0.2342\\ \hline D1 &0.2287 &0.2343 &0.2314 &0.2267 &0.2232 &0.2337 &0.2304 &0.2312 &0.2214 &0.2203 &0.232 &0.2285 &0.1568 &0.2592 &0.2522 &0.2636\\ \hline D2 &0.23 &0.2382 &0.2302 &0.2231 &0.2219 &0.2247 &0.2316 &0.2244 &0.2279 &0.2279 &0.2221 &0.2326 &0.254 &0.1525 &0.2479 &0.2557\\ \hline D3 &0.2407 &0.2437 &0.2359 &0.2529 &0.2479 &0.2378 &0.2371 &0.2327 &0.2412 &0.2536 &0.2364 &0.2406 &0.26 &0.2635 &0.1644 &0.2713\\ \hline D4 &0.3007 &0.2839 &0.3025 &0.2973 &0.307 &0.3038 &0.3009 &0.3117 &0.3095 &0.2982 &0.3095 &0.2983 &0.3292 &0.3247 &0.3354 &0.2094\\ \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 &0.039 &0.0637 &0.0652 &0.0624 &0.0625 &0.0658 &0.0612 &0.0627 &0.0644 &0.0625 &0.0633 &0.0609 &0.0567 &0.0594 &0.0628 &0.064\\ \hline A2 &0.0739 &0.0458 &0.0733 &0.0722 &0.072 &0.0726 &0.072 &0.0734 &0.0756 &0.074 &0.077 &0.0757 &0.0765 &0.0732 &0.0709 &0.0722\\ \hline A3 &0.0698 &0.0727 &0.0454 &0.0732 &0.0753 &0.071 &0.0703 &0.0738 &0.0753 &0.0759 &0.0753 &0.0754 &0.0697 &0.0701 &0.0732 &0.0747\\ \hline A4 &0.0722 &0.0732 &0.0754 &0.0466 &0.0749 &0.0735 &0.0761 &0.0756 &0.072 &0.0734 &0.0749 &0.0752 &0.081 &0.0775 &0.0737 &0.0781\\ \hline A5 &0.0519 &0.0496 &0.0523 &0.0522 &0.0308 &0.0485 &0.0475 &0.0484 &0.0503 &0.0506 &0.0464 &0.0472 &0.0476 &0.0462 &0.0493 &0.0492\\ \hline B1 &0.0737 &0.0728 &0.0743 &0.0739 &0.0751 &0.0468 &0.077 &0.0785 &0.0722 &0.0743 &0.0772 &0.074 &0.079 &0.0763 &0.0739 &0.0783\\ \hline B2 &0.059 &0.0599 &0.0594 &0.0599 &0.0571 &0.0627 &0.0372 &0.0643 &0.0587 &0.0591 &0.0564 &0.0563 &0.0585 &0.0604 &0.0597 &0.0615\\ \hline B3 &0.063 &0.064 &0.0622 &0.0639 &0.0641 &0.0668 &0.0649 &0.0393 &0.0614 &0.0606 &0.0599 &0.0605 &0.0629 &0.0626 &0.0644 &0.0637\\ \hline C1 &0.0746 &0.075 &0.0715 &0.0717 &0.0702 &0.0715 &0.0708 &0.069 &0.0446 &0.0744 &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 &0.0528 &0.0543 &0.0588 &0.0347 &0.0596 &0.0579 &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 &0.0349 &0.0534 &0.057 &0.0575 &0.0575 &0.052\\ \hline C4 &0.0577 &0.0573 &0.0567 &0.0573 &0.0572 &0.0582 &0.0594 &0.0589 &0.0567 &0.0592 &0.0586 &0.0358 &0.0572 &0.0577 &0.0577 &0.0543\\ \hline D1 &0.0579 &0.0595 &0.0583 &0.0582 &0.0545 &0.0591 &0.0584 &0.0572 &0.0557 &0.0538 &0.0568 &0.0587 &0.0362 &0.0608 &0.058 &0.0597\\ \hline D2 &0.0583 &0.0605 &0.058 &0.0573 &0.0542 &0.0568 &0.0587 &0.0555 &0.0573 &0.0557 &0.0544 &0.0597 &0.0586 &0.0358 &0.057 &0.0579\\ \hline D3 &0.0609 &0.0619 &0.0595 &0.0649 &0.0606 &0.0602 &0.0601 &0.0575 &0.0607 &0.062 &0.0578 &0.0618 &0.06 &0.0618 &0.0378 &0.0614\\ \hline D4 &0.0761 &0.0721 &0.0762 &0.0763 &0.075 &0.0768 &0.0763 &0.0771 &0.0778 &0.0729 &0.0757 &0.0766 &0.0759 &0.0762 &0.0771 &0.0474\\ \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
$$sys-\omega=\begin{array}{c|c|c|c|c|c|c}{M_{4 \times1}} &权重\\ \hline A &0.3252\\ \hline B &0.1932\\ \hline C &0.2355\\ \hline D &0.2461\\ \hline \end{array} $$所有子系统内部权重
A系统权重如下: $$ \begin{array}{c|c|c|c|c|c|c}{M_{5 \times1}} &权重\\ \hline A1 &0.1882\\ \hline A2 &0.2201\\ \hline A3 &0.2185\\ \hline A4 &0.2244\\ \hline A5 &0.1488\\ \hline \end{array} $$B系统权重如下: $$ \begin{array}{c|c|c|c|c|c|c}{M_{3 \times1}} &权重\\ \hline B1 &0.379\\ \hline B2 &0.302\\ \hline B3 &0.3189\\ \hline \end{array} $$C系统权重如下: $$ \begin{array}{c|c|c|c|c|c|c}{M_{4 \times1}} &权重\\ \hline C1 &0.2964\\ \hline C2 &0.2312\\ \hline C3 &0.2333\\ \hline C4 &0.2391\\ \hline \end{array} $$D系统权重如下: $$ \begin{array}{c|c|c|c|c|c|c}{M_{4 \times1}} &权重\\ \hline D1 &0.2302\\ \hline D2 &0.2284\\ \hline D3 &0.2415\\ \hline D4 &0.2999\\ \hline \end{array} $$