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

$$Ori=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{11 \times11}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10 &F11\\ \hline F1 &0 &0 &0 &0 &1 &0 &1 &1 &2 &2 &1\\ \hline F2 &0 &0 &0 &0 &0 &0 &1 &1 &2 &3 &1\\ \hline F3 &0 &0 &0 &0 &0 &1 &2 &1 &1 &1 &3\\ \hline F4 &1 &2 &2 &0 &0 &0 &1 &0 &0 &0 &1\\ \hline F5 &0 &3 &3 &0 &0 &0 &1 &0 &0 &0 &1\\ \hline F6 &1 &0 &0 &0 &0 &0 &2 &2 &3 &2 &2\\ \hline F7 &0 &0 &0 &0 &0 &0 &0 &2 &3 &3 &2\\ \hline F8 &0 &0 &0 &0 &0 &0 &0 &0 &3 &3 &3\\ \hline F9 &3 &0 &3 &0 &0 &0 &1 &0 &0 &3 &2\\ \hline F10 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline F11 &3 &0 &0 &4 &0 &0 &0 &0 &0 &1 &0\\ \hline \end{array} $$

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

$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{11 \times11}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10 &F11\\ \hline F1 &0 &0 &0 &0 &0.056 &0 &0.056 &0.056 &0.111 &0.111 &0.056\\ \hline F2 &0 &0 &0 &0 &0 &0 &0.056 &0.056 &0.111 &0.167 &0.056\\ \hline F3 &0 &0 &0 &0 &0 &0.056 &0.111 &0.056 &0.056 &0.056 &0.167\\ \hline F4 &0.056 &0.111 &0.111 &0 &0 &0 &0.056 &0 &0 &0 &0.056\\ \hline F5 &0 &0.167 &0.167 &0 &0 &0 &0.056 &0 &0 &0 &0.056\\ \hline F6 &0.056 &0 &0 &0 &0 &0 &0.111 &0.111 &0.167 &0.111 &0.111\\ \hline F7 &0 &0 &0 &0 &0 &0 &0 &0.111 &0.167 &0.167 &0.111\\ \hline F8 &0 &0 &0 &0 &0 &0 &0 &0 &0.167 &0.167 &0.167\\ \hline F9 &0.167 &0 &0.167 &0 &0 &0 &0.056 &0 &0 &0.167 &0.111\\ \hline F10 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline F11 &0.167 &0 &0 &0.222 &0 &0 &0 &0 &0 &0.056 &0\\ \hline \end{array} $$

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

　　综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{11 \times11}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10 &F11\\ \hline F1 &0.043 &0.012 &0.036 &0.023 &0.058 &0.002 &0.075 &0.069 &0.144 &0.174 &0.105\\ \hline F2 &0.041 &0.003 &0.026 &0.022 &0.002 &0.001 &0.07 &0.067 &0.141 &0.225 &0.099\\ \hline F3 &0.062 &0.006 &0.024 &0.05 &0.003 &0.057 &0.133 &0.082 &0.11 &0.138 &0.224\\ \hline F4 &0.084 &0.115 &0.123 &0.024 &0.005 &0.007 &0.085 &0.028 &0.049 &0.069 &0.109\\ \hline F5 &0.031 &0.17 &0.179 &0.027 &0.002 &0.01 &0.092 &0.033 &0.055 &0.08 &0.121\\ \hline F6 &0.129 &0.006 &0.044 &0.043 &0.007 &0.002 &0.139 &0.137 &0.231 &0.224 &0.193\\ \hline F7 &0.064 &0.005 &0.038 &0.037 &0.004 &0.002 &0.022 &0.12 &0.2 &0.243 &0.168\\ \hline F8 &0.067 &0.006 &0.036 &0.045 &0.004 &0.002 &0.021 &0.009 &0.182 &0.224 &0.204\\ \hline F9 &0.209 &0.006 &0.183 &0.04 &0.012 &0.01 &0.095 &0.034 &0.057 &0.243 &0.18\\ \hline F10 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline F11 &0.192 &0.028 &0.033 &0.232 &0.011 &0.002 &0.032 &0.018 &0.035 &0.1 &0.042\\ \hline \end{array} $$

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$

$$\tilde B=\begin{array} {c|c|c}{M_{11 \times11}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10 &F11\\ \hline F1 &1 &0.0123 &0.0362 &0.0234 &0.0579 &0.002 &0.0754 &0.0692 &0.1437 &0.1741 &0.1053\\ \hline F2 &0.0412 &1 &0.0263 &0.0219 &0.0023 &0.0015 &0.0702 &0.0674 &0.1406 &0.2252 &0.0985\\ \hline F3 &0.0616 &0.0061 &1 &0.0499 &0.0034 &0.0569 &0.133 &0.0818 &0.1097 &0.1376 &0.2244\\ \hline F4 &0.0836 &0.1146 &0.1227 &1 &0.0046 &0.0068 &0.0853 &0.0281 &0.0489 &0.069 &0.109\\ \hline F5 &0.0314 &0.1699 &0.1791 &0.0269 &1 &0.0099 &0.0924 &0.0325 &0.0548 &0.0795 &0.1211\\ \hline F6 &0.1287 &0.006 &0.0444 &0.0429 &0.0071 &1 &0.1394 &0.1368 &0.2305 &0.2243 &0.1929\\ \hline F7 &0.0636 &0.0047 &0.0381 &0.0374 &0.0035 &0.0021 &1 &0.1197 &0.2003 &0.2432 &0.1684\\ \hline F8 &0.0669 &0.0056 &0.036 &0.0453 &0.0037 &0.002 &0.0211 &1 &0.182 &0.2239 &0.2036\\ \hline F9 &0.209 &0.0064 &0.1826 &0.04 &0.0116 &0.0101 &0.095 &0.0338 &1 &0.2432 &0.18\\ \hline F10 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1 &0\\ \hline F11 &0.1924 &0.0275 &0.0333 &0.2315 &0.0107 &0.0019 &0.0315 &0.0178 &0.0348 &0.0999 &1\\ \hline \end{array} $$

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。

$$\tilde R=\begin{array} {c|c|c}{M_{11 \times11}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10 &F11\\ \hline F1 &1 &0.1146 &0.1437 &0.1437 &0.0579 &0.0569 &0.133 &0.1197 &0.1437 &0.1741 &0.1437\\ \hline F2 &0.1406 &1 &0.1406 &0.1406 &0.0579 &0.0569 &0.133 &0.1197 &0.1406 &0.2252 &0.1406\\ \hline F3 &0.1924 &0.1146 &1 &0.2244 &0.0579 &0.0569 &0.133 &0.1197 &0.1437 &0.1741 &0.2244\\ \hline F4 &0.1227 &0.1146 &0.1227 &1 &0.0579 &0.0569 &0.1227 &0.1197 &0.1227 &0.1227 &0.1227\\ \hline F5 &0.1791 &0.1699 &0.1791 &0.1791 &1 &0.0569 &0.133 &0.1197 &0.1437 &0.1741 &0.1791\\ \hline F6 &0.209 &0.1146 &0.1826 &0.1929 &0.0579 &1 &0.1394 &0.1368 &0.2305 &0.2305 &0.1929\\ \hline F7 &0.2003 &0.1146 &0.1826 &0.1826 &0.0579 &0.0569 &1 &0.1197 &0.2003 &0.2432 &0.1826\\ \hline F8 &0.1924 &0.1146 &0.182 &0.2036 &0.0579 &0.0569 &0.133 &1 &0.182 &0.2239 &0.2036\\ \hline F9 &0.209 &0.1146 &0.1826 &0.1826 &0.0579 &0.0569 &0.133 &0.1197 &1 &0.2432 &0.1826\\ \hline F10 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1 &0\\ \hline F11 &0.1924 &0.1146 &0.1437 &0.2315 &0.0579 &0.0569 &0.133 &0.1197 &0.1437 &0.1741 &1\\ \hline \end{array} $$

由阈值集合$\ddot \Delta $　得出综合影响矩阵$T$对应 28个结构。

序号	阈值集合中——特征阈值	聚类特征-对应截距$\lambda $数值区段
1	0.05691	0<$\lambda$<0.05691
2	0.05794	0.0569<$\lambda$<0.05794
3	0.11458	0.0579<$\lambda$<0.11458
4	0.11967	0.1146<$\lambda$<0.11967
5	0.12272	0.1197<$\lambda$<0.12272
6	0.13296	0.1227<$\lambda$<0.13296
7	0.13682	0.133<$\lambda$<0.13682
8	0.13938	0.1368<$\lambda$<0.13938
9	0.14064	0.1394<$\lambda$<0.14064
10	0.14369	0.1406<$\lambda$<0.14369
11	0.16995	0.1437<$\lambda$<0.16995
12	0.17405	0.1699<$\lambda$<0.17405
13	0.17908	0.1741<$\lambda$<0.17908
14	0.18201	0.1791<$\lambda$<0.18201
15	0.18259	0.182<$\lambda$<0.18259
16	0.19239	0.1826<$\lambda$<0.19239
17	0.19294	0.1924<$\lambda$<0.19294
18	0.2003	0.1929<$\lambda$<0.2003
19	0.20363	0.2003<$\lambda$<0.20363
20	0.209	0.2036<$\lambda$<0.209
21	0.22386	0.209<$\lambda$<0.22386
22	0.22437	0.2239<$\lambda$<0.22437
23	0.22519	0.2244<$\lambda$<0.22519
24	0.23053	0.2252<$\lambda$<0.23053
25	0.2315	0.2305<$\lambda$<0.2315
26	0.24318	0.2315<$\lambda$<0.24318
27	0.24323	0.2432<$\lambda$<0.24323
28	1	0.2432<$\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

$$\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{11 \times4}} &Di &Ci &Mi &Ri\\ \hline F1 &0.742 &0.921 &1.664 &-0.179\\ \hline F2 &0.698 &0.356 &1.054 &0.342\\ \hline F3 &0.889 &0.723 &1.612 &0.166\\ \hline F4 &0.697 &0.543 &1.24 &0.153\\ \hline F5 &0.799 &0.107 &0.906 &0.692\\ \hline F6 &1.155 &0.096 &1.251 &1.06\\ \hline F7 &0.903 &0.765 &1.668 &0.138\\ \hline F8 &0.799 &0.596 &1.394 &0.203\\ \hline F9 &1.069 &1.203 &2.272 &-0.134\\ \hline F10 &0 &1.72 &1.72 &-1.72\\ \hline F11 &0.723 &1.445 &2.168 &-0.722\\ \hline \end{array} $$

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：