决策与实验室-模糊解释结构模型在线计算，DEMATEL-FISM

原始矩阵（直接影响矩阵）为

$$Ori=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{9 \times9}} &A &B &C &D &E &F &G &H &I\\ \hline A &0 &3 &1 &5 &8 &8 &3 &5 &0\\ \hline B &5 &0 &6 &4 &3 &2 &5 &8 &6\\ \hline C &4 &6 &0 &7 &1 &2 &9 &3 &1\\ \hline D &3 &6 &9 &0 &8 &9 &11 &5 &3\\ \hline E &8 &9 &2 &11 &0 &10 &9 &2 &5\\ \hline F &5 &8 &0 &10 &8 &0 &9 &4 &6\\ \hline G &0 &11 &6 &5 &9 &10 &0 &9 &0\\ \hline H &9 &10 &5 &3 &5 &3 &7 &0 &6\\ \hline I &5 &7 &1 &8 &10 &6 &5 &3 &0\\ \hline \end{array} $$

规范直接关系矩阵求解过程 $$ \require{cancel} \require{AMScd} \begin{CD} O @>>>N \\ \end{CD} $$

$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{9 \times9}} &A &B &C &D &E &F &G &H &I\\ \hline A &0 &0.054 &0.018 &0.089 &0.143 &0.143 &0.054 &0.089 &0\\ \hline B &0.089 &0 &0.107 &0.071 &0.054 &0.036 &0.089 &0.143 &0.107\\ \hline C &0.071 &0.107 &0 &0.125 &0.018 &0.036 &0.161 &0.054 &0.018\\ \hline D &0.054 &0.107 &0.161 &0 &0.143 &0.161 &0.196 &0.089 &0.054\\ \hline E &0.143 &0.161 &0.036 &0.196 &0 &0.179 &0.161 &0.036 &0.089\\ \hline F &0.089 &0.143 &0 &0.179 &0.143 &0 &0.161 &0.071 &0.107\\ \hline G &0 &0.196 &0.107 &0.089 &0.161 &0.179 &0 &0.161 &0\\ \hline H &0.161 &0.179 &0.089 &0.054 &0.089 &0.054 &0.125 &0 &0.107\\ \hline I &0.089 &0.125 &0.018 &0.143 &0.179 &0.107 &0.089 &0.054 &0\\ \hline \end{array} $$

综合影响矩阵求解过程 $$\begin{CD} N @>>>T \\ \end{CD} $$

　　综合影响矩阵如下

$T=\mathcal{N}(I-\mathcal{N})^{-1}$

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{9 \times9}} &A &B &C &D &E &F &G &H &I\\ \hline A &0.284 &0.487 &0.256 &0.464 &0.502 &0.503 &0.474 &0.381 &0.221\\ \hline B &0.387 &0.469 &0.359 &0.468 &0.452 &0.43 &0.529 &0.455 &0.324\\ \hline C &0.32 &0.507 &0.239 &0.458 &0.37 &0.384 &0.535 &0.346 &0.212\\ \hline D &0.469 &0.76 &0.509 &0.573 &0.686 &0.7 &0.807 &0.542 &0.369\\ \hline E &0.56 &0.822 &0.418 &0.767 &0.597 &0.748 &0.8 &0.519 &0.415\\ \hline F &0.484 &0.758 &0.36 &0.703 &0.676 &0.547 &0.747 &0.51 &0.406\\ \hline G &0.41 &0.793 &0.443 &0.616 &0.657 &0.669 &0.598 &0.574 &0.318\\ \hline H &0.505 &0.713 &0.391 &0.534 &0.562 &0.526 &0.641 &0.396 &0.368\\ \hline I &0.451 &0.682 &0.336 &0.629 &0.652 &0.593 &0.633 &0.448 &0.282\\ \hline \end{array} $$

从综合影响矩阵$T$到ISM的处理过程简介

模糊相乘矩阵有$ \tilde B=T+I$

$$\tilde B=\begin{array} {c|c|c}{M_{9 \times9}} &A &B &C &D &E &F &G &H &I\\ \hline A &1 &0.4874 &0.2565 &0.4643 &0.5021 &0.5031 &0.4737 &0.3814 &0.2213\\ \hline B &0.3867 &1 &0.3586 &0.4677 &0.452 &0.4299 &0.5288 &0.4545 &0.3239\\ \hline C &0.32 &0.5067 &1 &0.4576 &0.37 &0.3845 &0.5348 &0.3462 &0.2122\\ \hline D &0.4691 &0.76 &0.5087 &1 &0.6857 &0.7004 &0.8073 &0.5422 &0.3692\\ \hline E &0.5597 &0.8221 &0.4178 &0.7667 &1 &0.7477 &0.7999 &0.5195 &0.415\\ \hline F &0.4839 &0.7579 &0.3598 &0.7032 &0.6756 &1 &0.7467 &0.5099 &0.406\\ \hline G &0.4096 &0.7927 &0.4428 &0.6159 &0.6573 &0.6691 &1 &0.5737 &0.3177\\ \hline H &0.5046 &0.7127 &0.3911 &0.5338 &0.562 &0.5262 &0.6406 &1 &0.368\\ \hline I &0.4511 &0.6817 &0.3362 &0.6287 &0.6522 &0.5928 &0.6331 &0.4479 &1\\ \hline \end{array} $$

模糊可达矩阵$ \tilde R$　由模糊相乘矩阵根据最大最小算子一直乘下去直到不变。

$$\tilde R=\begin{array} {c|c|c}{M_{9 \times9}} &A &B &C &D &E &F &G &H &I\\ \hline A &1 &0.5031 &0.5031 &0.5031 &0.5031 &0.5031 &0.5031 &0.5031 &0.415\\ \hline B &0.5288 &1 &0.5087 &0.5288 &0.5288 &0.5288 &0.5288 &0.5288 &0.415\\ \hline C &0.5348 &0.5348 &1 &0.5348 &0.5348 &0.5348 &0.5348 &0.5348 &0.415\\ \hline D &0.5597 &0.7927 &0.5087 &1 &0.6857 &0.7004 &0.8073 &0.5737 &0.415\\ \hline E &0.5597 &0.8221 &0.5087 &0.7667 &1 &0.7477 &0.7999 &0.5737 &0.415\\ \hline F &0.5597 &0.7579 &0.5087 &0.7032 &0.6857 &1 &0.7467 &0.5737 &0.415\\ \hline G &0.5597 &0.7927 &0.5087 &0.6691 &0.6691 &0.6691 &1 &0.5737 &0.415\\ \hline H &0.5597 &0.7127 &0.5087 &0.6406 &0.6406 &0.6406 &0.6406 &1 &0.415\\ \hline I &0.5597 &0.6817 &0.5087 &0.6522 &0.6522 &0.6522 &0.6522 &0.5737 &1\\ \hline \end{array} $$

24个结构数量分布图（瀑布图）

由阈值集合$\ddot \Delta $　得出综合影响矩阵$T$对应 24个结构。

序号	阈值集合中——特征阈值	聚类特征-对应截距$\lambda $数值区段
1	0.41497	0<$\lambda$<0.41497
2	0.50306	0.415<$\lambda$<0.50306
3	0.50866	0.5031<$\lambda$<0.50866
4	0.52882	0.5087<$\lambda$<0.52882
5	0.53482	0.5288<$\lambda$<0.53482
6	0.55974	0.5348<$\lambda$<0.55974
7	0.57365	0.5597<$\lambda$<0.57365
8	0.64059	0.5737<$\lambda$<0.64059
9	0.65222	0.6406<$\lambda$<0.65222
10	0.66914	0.6522<$\lambda$<0.66914
11	0.6817	0.6691<$\lambda$<0.6817
12	0.68571	0.6817<$\lambda$<0.68571
13	0.7004	0.6857<$\lambda$<0.7004
14	0.70322	0.7004<$\lambda$<0.70322
15	0.7127	0.7032<$\lambda$<0.7127
16	0.74671	0.7127<$\lambda$<0.74671
17	0.74774	0.7467<$\lambda$<0.74774
18	0.75785	0.7477<$\lambda$<0.75785
19	0.76665	0.7579<$\lambda$<0.76665
20	0.79266	0.7667<$\lambda$<0.79266
21	0.79993	0.7927<$\lambda$<0.79993
22	0.8073	0.7999<$\lambda$<0.8073
23	0.82212	0.8073<$\lambda$<0.82212
24	1	0.8221<$\lambda$<1

由综合影响矩阵求影响度、被影响度、中心度、原因度 \begin{CD} T @>>>\{D|C|M|R \} \\ \end{CD}

　　影响度、被影响度、中心度与原因度是四种度量要素在系统里影响程度的度量值。都是根据综合影响矩阵计算得出。

求解原理

影响度 $D$	$$ D_i=\sum \limits_{j=1}^{n}{t_{ij}},(i=1,2,3,\cdots,n) $$
被影响度 $C$	$$ C_i=\sum \limits_{j=1}^{n}{t_{ji}},(i=1,2,3,\cdots,n) $$
中心度 $M$	$$ M_i=D_i+C_i $$
原因度 $ R$	$$ R_i=D_i-C_i $$

结果

影响度、被影响度、中心度、原因度

$$\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{9 \times4}} &Di &Ci &Mi &Ri\\ \hline A &3.574 &3.869 &7.443 &-0.295\\ \hline B &3.871 &5.99 &9.861 &-2.119\\ \hline C &3.371 &3.31 &6.681 &0.061\\ \hline D &5.416 &5.211 &10.627 &0.205\\ \hline E &5.645 &5.154 &10.799 &0.492\\ \hline F &5.19 &5.101 &10.29 &0.089\\ \hline G &5.077 &5.763 &10.84 &-0.686\\ \hline H &4.635 &4.171 &8.806 &0.464\\ \hline I &4.706 &2.916 &7.622 &1.79\\ \hline \end{array} $$

基于综合影响矩阵T截距

DEMATEL-ISM联用

原始矩阵（直接影响矩阵）为

规范直接关系矩阵求解过程 $$ \require{cancel} \require{AMScd} \begin{CD} O @>>>N \\ \end{CD} $$

综合影响矩阵求解过程 $$\begin{CD} N @>>>T \\ \end{CD} $$

从综合影响矩阵$T$到ISM的处理过程简介

由综合影响矩阵求影响度、被影响度、中心度、原因度 \begin{CD} T @>>>\{D|C|M|R \} \\ \end{CD}

求解原理

结果

绘制中心度与原因度建构的散点图图表

DEMATEL-FISM流程图如下：