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

$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{9 \times9}} &A &B &C &D &E &F &G &H &I\\ \hline A &0 &0.039 &0.013 &0.065 &0.104 &0.104 &0.039 &0.065 &0\\ \hline B &0.065 &0 &0.078 &0.052 &0.039 &0.026 &0.065 &0.104 &0.078\\ \hline C &0.052 &0.078 &0 &0.091 &0.013 &0.026 &0.118 &0.039 &0.013\\ \hline D &0.039 &0.078 &0.118 &0 &0.104 &0.118 &0.144 &0.065 &0.039\\ \hline E &0.104 &0.118 &0.026 &0.144 &0 &0.131 &0.118 &0.026 &0.065\\ \hline F &0.065 &0.104 &0 &0.131 &0.104 &0 &0.118 &0.052 &0.078\\ \hline G &0 &0.144 &0.078 &0.065 &0.118 &0.131 &0 &0.118 &0\\ \hline H &0.118 &0.131 &0.065 &0.039 &0.065 &0.039 &0.091 &0 &0.078\\ \hline I &0.065 &0.091 &0.013 &0.104 &0.131 &0.078 &0.065 &0.039 &0\\ \hline \end{array} $$

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

　　综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{9 \times9}} &A &B &C &D &E &F &G &H &I\\ \hline A &0.07 &0.143 &0.069 &0.155 &0.186 &0.188 &0.141 &0.131 &0.055\\ \hline B &0.137 &0.115 &0.136 &0.146 &0.135 &0.121 &0.17 &0.175 &0.127\\ \hline C &0.108 &0.173 &0.061 &0.166 &0.1 &0.111 &0.203 &0.112 &0.058\\ \hline D &0.138 &0.237 &0.196 &0.142 &0.231 &0.243 &0.287 &0.173 &0.113\\ \hline E &0.198 &0.271 &0.118 &0.275 &0.149 &0.265 &0.268 &0.145 &0.141\\ \hline F &0.157 &0.249 &0.089 &0.251 &0.231 &0.136 &0.254 &0.157 &0.147\\ \hline G &0.104 &0.283 &0.157 &0.192 &0.229 &0.239 &0.148 &0.212 &0.082\\ \hline H &0.196 &0.254 &0.135 &0.155 &0.179 &0.154 &0.211 &0.098 &0.137\\ \hline I &0.151 &0.222 &0.089 &0.219 &0.24 &0.195 &0.195 &0.132 &0.068\\ \hline \end{array} $$

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$

$$\tilde B=\begin{array} {c|c|c}{M_{9 \times9}} &A &B &C &D &E &F &G &H &I\\ \hline A &1 &0.1434 &0.0687 &0.1551 &0.1865 &0.1878 &0.1412 &0.1311 &0.0554\\ \hline B &0.1365 &1 &0.1362 &0.146 &0.1355 &0.1207 &0.1695 &0.175 &0.1269\\ \hline C &0.1078 &0.1727 &1 &0.1655 &0.0995 &0.1113 &0.2028 &0.112 &0.0579\\ \hline D &0.1381 &0.2369 &0.1958 &1 &0.2307 &0.2431 &0.2868 &0.1728 &0.1135\\ \hline E &0.1982 &0.2715 &0.1185 &0.2754 &1 &0.2649 &0.2675 &0.1447 &0.1407\\ \hline F &0.1572 &0.249 &0.0892 &0.2511 &0.2315 &1 &0.2536 &0.1571 &0.1469\\ \hline G &0.104 &0.2834 &0.157 &0.1919 &0.2286 &0.2394 &1 &0.2117 &0.082\\ \hline H &0.1964 &0.2537 &0.1354 &0.1553 &0.1789 &0.1536 &0.2109 &1 &0.1375\\ \hline I &0.1508 &0.2217 &0.0892 &0.2191 &0.24 &0.1954 &0.1954 &0.1321 &1\\ \hline \end{array} $$

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。

$$\tilde R=\begin{array} {c|c|c}{M_{9 \times9}} &A &B &C &D &E &F &G &H &I\\ \hline A &1 &0.1878 &0.1878 &0.1878 &0.1878 &0.1878 &0.1878 &0.1878 &0.1469\\ \hline B &0.175 &1 &0.175 &0.175 &0.175 &0.175 &0.175 &0.175 &0.1469\\ \hline C &0.1982 &0.2028 &1 &0.2028 &0.2028 &0.2028 &0.2028 &0.2028 &0.1469\\ \hline D &0.1982 &0.2834 &0.1958 &1 &0.2315 &0.2431 &0.2868 &0.2117 &0.1469\\ \hline E &0.1982 &0.2754 &0.1958 &0.2754 &1 &0.2649 &0.2754 &0.2117 &0.1469\\ \hline F &0.1982 &0.2536 &0.1958 &0.2511 &0.2315 &1 &0.2536 &0.2117 &0.1469\\ \hline G &0.1982 &0.2834 &0.1958 &0.2394 &0.2315 &0.2394 &1 &0.2117 &0.1469\\ \hline H &0.1982 &0.2537 &0.1958 &0.2109 &0.2109 &0.2109 &0.2109 &1 &0.1469\\ \hline I &0.1982 &0.24 &0.1958 &0.24 &0.24 &0.24 &0.24 &0.2117 &1\\ \hline \end{array} $$

20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 20个结构。

序号	阈值集合中——特征阈值	聚类特征-对应截距$\lambda $数值区段
1	0.14693	0<$\lambda$<0.14693
2	0.17498	0.1469<$\lambda$<0.17498
3	0.18779	0.175<$\lambda$<0.18779
4	0.19579	0.1878<$\lambda$<0.19579
5	0.19818	0.1958<$\lambda$<0.19818
6	0.20276	0.1982<$\lambda$<0.20276
7	0.21088	0.2028<$\lambda$<0.21088
8	0.21172	0.2109<$\lambda$<0.21172
9	0.23147	0.2117<$\lambda$<0.23147
10	0.23944	0.2315<$\lambda$<0.23944
11	0.24003	0.2394<$\lambda$<0.24003
12	0.24314	0.24<$\lambda$<0.24314
13	0.25105	0.2431<$\lambda$<0.25105
14	0.2536	0.2511<$\lambda$<0.2536
15	0.25375	0.2536<$\lambda$<0.25375
16	0.26487	0.2537<$\lambda$<0.26487
17	0.27536	0.2649<$\lambda$<0.27536
18	0.28338	0.2754<$\lambda$<0.28338
19	0.28677	0.2834<$\lambda$<0.28677
20	1	0.2868<$\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

$$\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{9 \times4}} &Di &Ci &Mi &Ri\\ \hline A &1.139 &1.259 &2.398 &-0.12\\ \hline B &1.261 &1.947 &3.208 &-0.686\\ \hline C &1.09 &1.051 &2.141 &0.04\\ \hline D &1.759 &1.701 &3.46 &0.058\\ \hline E &1.83 &1.68 &3.51 &0.15\\ \hline F &1.671 &1.652 &3.323 &0.019\\ \hline G &1.646 &1.876 &3.522 &-0.23\\ \hline H &1.519 &1.334 &2.854 &0.185\\ \hline I &1.512 &0.929 &2.441 &0.583\\ \hline \end{array} $$

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：