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 $$ \require{cancel} \require{AMScd} \begin{CD} O @>>>N \\ \end{CD} $$

$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{9 \times9}} &A &B &C &D &E &F &G &H &I\\ \hline A &0 &0.05 &0.017 &0.083 &0.133 &0.133 &0.05 &0.083 &0\\ \hline B &0.083 &0 &0.1 &0.067 &0.05 &0.033 &0.083 &0.133 &0.1\\ \hline C &0.067 &0.1 &0 &0.117 &0.017 &0.033 &0.15 &0.05 &0.017\\ \hline D &0.05 &0.1 &0.15 &0 &0.133 &0.15 &0.183 &0.083 &0.05\\ \hline E &0.133 &0.15 &0.033 &0.183 &0 &0.167 &0.15 &0.033 &0.083\\ \hline F &0.083 &0.133 &0 &0.167 &0.133 &0 &0.15 &0.067 &0.1\\ \hline G &0 &0.183 &0.1 &0.083 &0.15 &0.167 &0 &0.15 &0\\ \hline H &0.15 &0.167 &0.083 &0.05 &0.083 &0.05 &0.117 &0 &0.1\\ \hline I &0.083 &0.117 &0.017 &0.133 &0.167 &0.1 &0.083 &0.05 &0\\ \hline \end{array} $$

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

　　综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{9 \times9}} &A &B &C &D &E &F &G &H &I\\ \hline A &0.19 &0.339 &0.174 &0.333 &0.37 &0.371 &0.331 &0.275 &0.149\\ \hline B &0.281 &0.314 &0.266 &0.33 &0.316 &0.296 &0.375 &0.338 &0.242\\ \hline C &0.23 &0.365 &0.161 &0.334 &0.252 &0.267 &0.396 &0.247 &0.145\\ \hline D &0.326 &0.536 &0.378 &0.385 &0.492 &0.507 &0.588 &0.384 &0.259\\ \hline E &0.407 &0.587 &0.288 &0.56 &0.401 &0.544 &0.573 &0.357 &0.298\\ \hline F &0.344 &0.541 &0.241 &0.512 &0.488 &0.367 &0.537 &0.358 &0.297\\ \hline G &0.277 &0.578 &0.322 &0.434 &0.475 &0.487 &0.402 &0.422 &0.215\\ \hline H &0.377 &0.519 &0.283 &0.37 &0.398 &0.366 &0.457 &0.265 &0.271\\ \hline I &0.323 &0.485 &0.229 &0.456 &0.479 &0.424 &0.445 &0.311 &0.189\\ \hline \end{array} $$

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$

$$\tilde B=\begin{array} {c|c|c}{M_{9 \times9}} &A &B &C &D &E &F &G &H &I\\ \hline A &1 &0.339 &0.1745 &0.333 &0.3698 &0.3712 &0.3306 &0.275 &0.1489\\ \hline B &0.2813 &1 &0.2658 &0.3297 &0.3158 &0.2959 &0.3752 &0.338 &0.242\\ \hline C &0.2295 &0.3651 &1 &0.3343 &0.2525 &0.2666 &0.3961 &0.2466 &0.1449\\ \hline D &0.3262 &0.536 &0.3783 &1 &0.4922 &0.5068 &0.5878 &0.3843 &0.2593\\ \hline E &0.4067 &0.5873 &0.2883 &0.5597 &1 &0.5442 &0.5735 &0.3572 &0.2984\\ \hline F &0.3443 &0.5409 &0.2415 &0.5125 &0.4875 &1 &0.5372 &0.3584 &0.2969\\ \hline G &0.2766 &0.5781 &0.3223 &0.4342 &0.4753 &0.4875 &1 &0.4218 &0.2154\\ \hline H &0.3766 &0.519 &0.2827 &0.3705 &0.3983 &0.3655 &0.4572 &1 &0.2714\\ \hline I &0.3234 &0.4852 &0.2285 &0.4556 &0.4793 &0.4238 &0.4453 &0.3115 &1\\ \hline \end{array} $$

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。

$$\tilde R=\begin{array} {c|c|c}{M_{9 \times9}} &A &B &C &D &E &F &G &H &I\\ \hline A &1 &0.3712 &0.3712 &0.3712 &0.3712 &0.3712 &0.3712 &0.3712 &0.2984\\ \hline B &0.3752 &1 &0.3752 &0.3752 &0.3752 &0.3752 &0.3752 &0.3752 &0.2984\\ \hline C &0.3961 &0.3961 &1 &0.3961 &0.3961 &0.3961 &0.3961 &0.3961 &0.2984\\ \hline D &0.4067 &0.5781 &0.3783 &1 &0.4922 &0.5068 &0.5878 &0.4218 &0.2984\\ \hline E &0.4067 &0.5873 &0.3783 &0.5597 &1 &0.5442 &0.5735 &0.4218 &0.2984\\ \hline F &0.4067 &0.5409 &0.3783 &0.5125 &0.4922 &1 &0.5372 &0.4218 &0.2984\\ \hline G &0.4067 &0.5781 &0.3783 &0.4875 &0.4875 &0.4875 &1 &0.4218 &0.2984\\ \hline H &0.4067 &0.519 &0.3783 &0.4572 &0.4572 &0.4572 &0.4572 &1 &0.2984\\ \hline I &0.4067 &0.4852 &0.3783 &0.4793 &0.4793 &0.4793 &0.4793 &0.4218 &1\\ \hline \end{array} $$

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 $数值区段
1	0.29841	0<$\lambda$<0.29841
2	0.37116	0.2984<$\lambda$<0.37116
3	0.37522	0.3712<$\lambda$<0.37522
4	0.37825	0.3752<$\lambda$<0.37825
5	0.39612	0.3783<$\lambda$<0.39612
6	0.40675	0.3961<$\lambda$<0.40675
7	0.42177	0.4067<$\lambda$<0.42177
8	0.45722	0.4218<$\lambda$<0.45722
9	0.47929	0.4572<$\lambda$<0.47929
10	0.4852	0.4793<$\lambda$<0.4852
11	0.48746	0.4852<$\lambda$<0.48746
12	0.49218	0.4875<$\lambda$<0.49218
13	0.50679	0.4922<$\lambda$<0.50679
14	0.51247	0.5068<$\lambda$<0.51247
15	0.51901	0.5125<$\lambda$<0.51901
16	0.53725	0.519<$\lambda$<0.53725
17	0.54092	0.5372<$\lambda$<0.54092
18	0.54416	0.5409<$\lambda$<0.54416
19	0.55968	0.5442<$\lambda$<0.55968
20	0.57345	0.5597<$\lambda$<0.57345
21	0.57815	0.5735<$\lambda$<0.57815
22	0.58733	0.5781<$\lambda$<0.58733
23	0.58783	0.5873<$\lambda$<0.58783
24	1	0.5878<$\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

$$\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{9 \times4}} &Di &Ci &Mi &Ri\\ \hline A &2.532 &2.755 &5.287 &-0.223\\ \hline B &2.758 &4.265 &7.022 &-1.507\\ \hline C &2.397 &2.343 &4.74 &0.054\\ \hline D &3.855 &3.714 &7.569 &0.141\\ \hline E &4.016 &3.672 &7.688 &0.345\\ \hline F &3.687 &3.629 &7.315 &0.058\\ \hline G &3.613 &4.104 &7.717 &-0.492\\ \hline H &3.307 &2.958 &6.265 &0.348\\ \hline I &3.341 &2.066 &5.407 &1.275\\ \hline \end{array} $$

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：