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

$$Ori=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &D1 &D2 &D3 &D4 &D5 &D6 &D7 &D8 &D9 &D10\\ \hline D1 &0 &13 &13 &19 &23 &22 &12 &13 &12 &26\\ \hline D2 &21 &0 &5 &21 &16 &12 &15 &12 &19 &25\\ \hline D3 &20 &8 &0 &14 &13 &10 &13 &16 &24 &21\\ \hline D4 &33 &10 &5 &0 &16 &19 &19 &19 &19 &20\\ \hline D5 &33 &10 &20 &10 &0 &27 &17 &20 &25 &23\\ \hline D6 &20 &25 &13 &21 &2 &0 &23 &22 &21 &21\\ \hline D7 &22 &31 &10 &10 &25 &18 &0 &24 &20 &19\\ \hline D8 &10 &13 &13 &11 &26 &25 &21 &0 &20 &24\\ \hline D9 &20 &11 &21 &10 &10 &27 &22 &21 &0 &31\\ \hline D10 &10 &20 &14 &10 &21 &21 &22 &21 &11 &0\\ \hline \end{array} $$

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

$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &D1 &D2 &D3 &D4 &D5 &D6 &D7 &D8 &D9 &D10\\ \hline D1 &0 &0.046 &0.046 &0.068 &0.082 &0.079 &0.043 &0.046 &0.043 &0.093\\ \hline D2 &0.075 &0 &0.018 &0.075 &0.057 &0.043 &0.054 &0.043 &0.068 &0.089\\ \hline D3 &0.071 &0.029 &0 &0.05 &0.046 &0.036 &0.046 &0.057 &0.086 &0.075\\ \hline D4 &0.118 &0.036 &0.018 &0 &0.057 &0.068 &0.068 &0.068 &0.068 &0.071\\ \hline D5 &0.118 &0.036 &0.071 &0.036 &0 &0.096 &0.061 &0.071 &0.089 &0.082\\ \hline D6 &0.071 &0.089 &0.046 &0.075 &0.007 &0 &0.082 &0.079 &0.075 &0.075\\ \hline D7 &0.079 &0.111 &0.036 &0.036 &0.089 &0.064 &0 &0.086 &0.071 &0.068\\ \hline D8 &0.036 &0.046 &0.046 &0.039 &0.093 &0.089 &0.075 &0 &0.071 &0.086\\ \hline D9 &0.071 &0.039 &0.075 &0.036 &0.036 &0.096 &0.079 &0.075 &0 &0.111\\ \hline D10 &0.036 &0.071 &0.05 &0.036 &0.075 &0.075 &0.079 &0.075 &0.039 &0\\ \hline \end{array} $$

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

　　综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &D1 &D2 &D3 &D4 &D5 &D6 &D7 &D8 &D9 &D10\\ \hline D1 &0.09 &0.115 &0.102 &0.126 &0.15 &0.162 &0.122 &0.127 &0.123 &0.185\\ \hline D2 &0.155 &0.068 &0.073 &0.129 &0.127 &0.127 &0.128 &0.12 &0.14 &0.179\\ \hline D3 &0.147 &0.092 &0.054 &0.103 &0.113 &0.117 &0.118 &0.129 &0.153 &0.162\\ \hline D4 &0.2 &0.11 &0.079 &0.065 &0.134 &0.158 &0.148 &0.15 &0.147 &0.173\\ \hline D5 &0.212 &0.12 &0.137 &0.109 &0.088 &0.196 &0.153 &0.165 &0.179 &0.197\\ \hline D6 &0.161 &0.161 &0.104 &0.138 &0.092 &0.095 &0.164 &0.162 &0.157 &0.179\\ \hline D7 &0.176 &0.184 &0.101 &0.107 &0.17 &0.164 &0.093 &0.174 &0.161 &0.181\\ \hline D8 &0.13 &0.122 &0.107 &0.103 &0.165 &0.179 &0.157 &0.089 &0.155 &0.187\\ \hline D9 &0.162 &0.12 &0.135 &0.104 &0.118 &0.187 &0.164 &0.162 &0.09 &0.213\\ \hline D10 &0.122 &0.138 &0.104 &0.096 &0.144 &0.157 &0.153 &0.151 &0.12 &0.099\\ \hline \end{array} $$

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$

$$\tilde B=\begin{array} {c|c|c}{M_{10 \times10}} &D1 &D2 &D3 &D4 &D5 &D6 &D7 &D8 &D9 &D10\\ \hline D1 &1 &0.1154 &0.1019 &0.1256 &0.1502 &0.1622 &0.1224 &0.127 &0.1225 &0.1855\\ \hline D2 &0.1554 &1 &0.0732 &0.1291 &0.1265 &0.1275 &0.1283 &0.1199 &0.1398 &0.179\\ \hline D3 &0.1466 &0.0918 &1 &0.1029 &0.1131 &0.1171 &0.1181 &0.129 &0.1528 &0.1623\\ \hline D4 &0.2002 &0.11 &0.0791 &1 &0.1337 &0.1585 &0.148 &0.1495 &0.147 &0.1725\\ \hline D5 &0.2118 &0.1198 &0.1372 &0.1092 &1 &0.1957 &0.1534 &0.1647 &0.1788 &0.1969\\ \hline D6 &0.1611 &0.1611 &0.1043 &0.1379 &0.0917 &1 &0.1638 &0.1616 &0.1568 &0.1791\\ \hline D7 &0.1756 &0.1841 &0.1014 &0.1073 &0.1701 &0.164 &1 &0.1736 &0.1612 &0.1813\\ \hline D8 &0.1302 &0.1221 &0.1073 &0.1033 &0.1646 &0.1785 &0.1573 &1 &0.1546 &0.1866\\ \hline D9 &0.1624 &0.1198 &0.1345 &0.1038 &0.1184 &0.1874 &0.1639 &0.1624 &1 &0.2129\\ \hline D10 &0.1225 &0.1384 &0.1038 &0.0957 &0.1438 &0.1569 &0.1527 &0.1512 &0.1196 &1\\ \hline \end{array} $$

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。

$$\tilde R=\begin{array} {c|c|c}{M_{10 \times10}} &D1 &D2 &D3 &D4 &D5 &D6 &D7 &D8 &D9 &D10\\ \hline D1 &1 &0.1622 &0.1372 &0.1379 &0.1622 &0.1622 &0.1622 &0.1622 &0.1622 &0.1855\\ \hline D2 &0.1569 &1 &0.1372 &0.1379 &0.1569 &0.1569 &0.1569 &0.1569 &0.1569 &0.179\\ \hline D3 &0.1569 &0.1569 &1 &0.1379 &0.1569 &0.1569 &0.1569 &0.1569 &0.1569 &0.1623\\ \hline D4 &0.2002 &0.1622 &0.1372 &1 &0.1622 &0.1622 &0.1622 &0.1622 &0.1622 &0.1855\\ \hline D5 &0.2118 &0.1639 &0.1372 &0.1379 &1 &0.1957 &0.1639 &0.1647 &0.1788 &0.1969\\ \hline D6 &0.1638 &0.1638 &0.1372 &0.1379 &0.1638 &1 &0.1638 &0.1638 &0.1638 &0.1791\\ \hline D7 &0.1756 &0.1841 &0.1372 &0.1379 &0.1701 &0.1736 &1 &0.1736 &0.1701 &0.1813\\ \hline D8 &0.1646 &0.1639 &0.1372 &0.1379 &0.1646 &0.1785 &0.1639 &1 &0.1646 &0.1866\\ \hline D9 &0.1639 &0.1639 &0.1372 &0.1379 &0.1639 &0.1874 &0.1639 &0.1639 &1 &0.2129\\ \hline D10 &0.1569 &0.1569 &0.1372 &0.1379 &0.1569 &0.1569 &0.1569 &0.1569 &0.1569 &1\\ \hline \end{array} $$

由阈值集合$\ddot \Delta $　得出综合影响矩阵$T$对应 27个结构。

序号	阈值集合中——特征阈值	聚类特征-对应截距$\lambda $数值区段
1	0.1372	0<$\lambda$<0.1372
2	0.1379	0.1372<$\lambda$<0.1379
3	0.15693	0.1379<$\lambda$<0.15693
4	0.16222	0.1569<$\lambda$<0.16222
5	0.16232	0.1622<$\lambda$<0.16232
6	0.16385	0.1623<$\lambda$<0.16385
7	0.16388	0.1638<$\lambda$<0.16388
8	0.16462	0.1639<$\lambda$<0.16462
9	0.16474	0.1646<$\lambda$<0.16474
10	0.17011	0.1647<$\lambda$<0.17011
11	0.17362	0.1701<$\lambda$<0.17362
12	0.17562	0.1736<$\lambda$<0.17562
13	0.17854	0.1756<$\lambda$<0.17854
14	0.17878	0.1785<$\lambda$<0.17878
15	0.179	0.1788<$\lambda$<0.179
16	0.1791	0.179<$\lambda$<0.1791
17	0.18127	0.1791<$\lambda$<0.18127
18	0.18406	0.1813<$\lambda$<0.18406
19	0.18545	0.1841<$\lambda$<0.18545
20	0.18658	0.1855<$\lambda$<0.18658
21	0.18736	0.1866<$\lambda$<0.18736
22	0.19571	0.1874<$\lambda$<0.19571
23	0.19695	0.1957<$\lambda$<0.19695
24	0.20023	0.1969<$\lambda$<0.20023
25	0.21175	0.2002<$\lambda$<0.21175
26	0.21288	0.2118<$\lambda$<0.21288
27	1	0.2129<$\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

$$\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times4}} &Di &Ci &Mi &Ri\\ \hline D1 &1.302 &1.555 &2.858 &-0.253\\ \hline D2 &1.247 &1.23 &2.477 &0.016\\ \hline D3 &1.187 &0.996 &2.184 &0.191\\ \hline D4 &1.364 &1.08 &2.444 &0.284\\ \hline D5 &1.556 &1.301 &2.857 &0.255\\ \hline D6 &1.413 &1.543 &2.955 &-0.13\\ \hline D7 &1.512 &1.401 &2.913 &0.111\\ \hline D8 &1.394 &1.428 &2.822 &-0.035\\ \hline D9 &1.455 &1.423 &2.879 &0.032\\ \hline D10 &1.283 &1.755 &3.038 &-0.472\\ \hline \end{array} $$

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：