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

$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{9 \times9}} &A &B &C &D &E &F &G &H &I\\ \hline A &0 &0.037 &0.012 &0.061 &0.097 &0.097 &0.037 &0.061 &0\\ \hline B &0.061 &0 &0.073 &0.049 &0.037 &0.024 &0.061 &0.097 &0.073\\ \hline C &0.049 &0.073 &0 &0.085 &0.012 &0.024 &0.11 &0.037 &0.012\\ \hline D &0.037 &0.073 &0.11 &0 &0.097 &0.11 &0.134 &0.061 &0.037\\ \hline E &0.097 &0.11 &0.024 &0.134 &0 &0.122 &0.11 &0.024 &0.061\\ \hline F &0.061 &0.097 &0 &0.122 &0.097 &0 &0.11 &0.049 &0.073\\ \hline G &0 &0.134 &0.073 &0.061 &0.11 &0.122 &0 &0.11 &0\\ \hline H &0.11 &0.122 &0.061 &0.037 &0.061 &0.037 &0.085 &0 &0.073\\ \hline I &0.061 &0.085 &0.012 &0.097 &0.122 &0.073 &0.061 &0.037 &0\\ \hline \end{array} $$

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

　　综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{9 \times9}} &A &B &C &D &E &F &G &H &I\\ \hline A &0.056 &0.119 &0.056 &0.132 &0.162 &0.163 &0.118 &0.112 &0.044\\ \hline B &0.117 &0.091 &0.119 &0.123 &0.113 &0.099 &0.143 &0.153 &0.111\\ \hline C &0.092 &0.148 &0.049 &0.143 &0.081 &0.092 &0.176 &0.095 &0.047\\ \hline D &0.115 &0.199 &0.171 &0.113 &0.197 &0.209 &0.247 &0.146 &0.095\\ \hline E &0.171 &0.231 &0.098 &0.238 &0.119 &0.228 &0.228 &0.119 &0.12\\ \hline F &0.133 &0.212 &0.071 &0.216 &0.198 &0.108 &0.217 &0.132 &0.127\\ \hline G &0.083 &0.244 &0.135 &0.161 &0.196 &0.207 &0.118 &0.184 &0.066\\ \hline H &0.172 &0.219 &0.116 &0.129 &0.151 &0.127 &0.179 &0.078 &0.119\\ \hline I &0.129 &0.188 &0.073 &0.188 &0.208 &0.166 &0.164 &0.11 &0.054\\ \hline \end{array} $$

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$

$$\tilde B=\begin{array} {c|c|c}{M_{9 \times9}} &A &B &C &D &E &F &G &H &I\\ \hline A &1 &0.1192 &0.056 &0.132 &0.1618 &0.163 &0.1176 &0.1124 &0.0442\\ \hline B &0.1173 &1 &0.1186 &0.1228 &0.113 &0.0993 &0.1433 &0.1527 &0.111\\ \hline C &0.0921 &0.1476 &1 &0.1432 &0.081 &0.0921 &0.1765 &0.0946 &0.0474\\ \hline D &0.1148 &0.199 &0.1709 &1 &0.1969 &0.2086 &0.2469 &0.1459 &0.0952\\ \hline E &0.1708 &0.2309 &0.0976 &0.2376 &1 &0.2279 &0.228 &0.1187 &0.1202\\ \hline F &0.1333 &0.2116 &0.0711 &0.2165 &0.198 &1 &0.2168 &0.1318 &0.127\\ \hline G &0.0832 &0.2442 &0.1351 &0.1613 &0.1964 &0.2067 &1 &0.1835 &0.0659\\ \hline H &0.1716 &0.2187 &0.1161 &0.1287 &0.151 &0.1274 &0.1793 &1 &0.1194\\ \hline I &0.1285 &0.188 &0.0725 &0.188 &0.2079 &0.1659 &0.1639 &0.1099 &1\\ \hline \end{array} $$

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。

$$\tilde R=\begin{array} {c|c|c}{M_{9 \times9}} &A &B &C &D &E &F &G &H &I\\ \hline A &1 &0.163 &0.163 &0.163 &0.163 &0.163 &0.163 &0.163 &0.127\\ \hline B &0.1527 &1 &0.1527 &0.1527 &0.1527 &0.1527 &0.1527 &0.1527 &0.127\\ \hline C &0.1716 &0.1765 &1 &0.1765 &0.1765 &0.1765 &0.1765 &0.1765 &0.127\\ \hline D &0.1716 &0.2442 &0.1709 &1 &0.198 &0.2086 &0.2469 &0.1835 &0.127\\ \hline E &0.1716 &0.2376 &0.1709 &0.2376 &1 &0.2279 &0.2376 &0.1835 &0.127\\ \hline F &0.1716 &0.2168 &0.1709 &0.2165 &0.198 &1 &0.2168 &0.1835 &0.127\\ \hline G &0.1716 &0.2442 &0.1709 &0.2067 &0.198 &0.2067 &1 &0.1835 &0.127\\ \hline H &0.1716 &0.2187 &0.1709 &0.1793 &0.1793 &0.1793 &0.1793 &1 &0.127\\ \hline I &0.1716 &0.2079 &0.1709 &0.2079 &0.2079 &0.2079 &0.2079 &0.1835 &1\\ \hline \end{array} $$

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 $数值区段
1	0.12696	0<$\lambda$<0.12696
2	0.1527	0.127<$\lambda$<0.1527
3	0.16302	0.1527<$\lambda$<0.16302
4	0.17086	0.163<$\lambda$<0.17086
5	0.17162	0.1709<$\lambda$<0.17162
6	0.1765	0.1716<$\lambda$<0.1765
7	0.1793	0.1765<$\lambda$<0.1793
8	0.18353	0.1793<$\lambda$<0.18353
9	0.19798	0.1835<$\lambda$<0.19798
10	0.20674	0.198<$\lambda$<0.20674
11	0.20791	0.2067<$\lambda$<0.20791
12	0.2086	0.2079<$\lambda$<0.2086
13	0.21646	0.2086<$\lambda$<0.21646
14	0.21678	0.2165<$\lambda$<0.21678
15	0.21867	0.2168<$\lambda$<0.21867
16	0.2279	0.2187<$\lambda$<0.2279
17	0.23761	0.2279<$\lambda$<0.23761
18	0.24425	0.2376<$\lambda$<0.24425
19	0.24691	0.2442<$\lambda$<0.24691
20	1	0.2469<$\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

$$\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{9 \times4}} &Di &Ci &Mi &Ri\\ \hline A &0.962 &1.067 &2.029 &-0.105\\ \hline B &1.069 &1.65 &2.72 &-0.581\\ \hline C &0.923 &0.887 &1.81 &0.037\\ \hline D &1.491 &1.443 &2.934 &0.048\\ \hline E &1.55 &1.424 &2.975 &0.126\\ \hline F &1.414 &1.399 &2.813 &0.015\\ \hline G &1.395 &1.59 &2.985 &-0.196\\ \hline H &1.29 &1.127 &2.417 &0.163\\ \hline I &1.279 &0.785 &2.064 &0.494\\ \hline \end{array} $$

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：