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

$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{11 \times11}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10 &F11\\ \hline F1 &0 &0 &0 &0 &0.083 &0 &0.083 &0.083 &0.167 &0.167 &0.083\\ \hline F2 &0 &0 &0 &0 &0 &0 &0.083 &0.083 &0.167 &0.25 &0.083\\ \hline F3 &0 &0 &0 &0 &0 &0.083 &0.167 &0.083 &0.083 &0.083 &0.25\\ \hline F4 &0.083 &0.167 &0.167 &0 &0 &0 &0.083 &0 &0 &0 &0.083\\ \hline F5 &0 &0.25 &0.25 &0 &0 &0 &0.083 &0 &0 &0 &0.083\\ \hline F6 &0.083 &0 &0 &0 &0 &0 &0.167 &0.167 &0.25 &0.167 &0.167\\ \hline F7 &0 &0 &0 &0 &0 &0 &0 &0.167 &0.25 &0.25 &0.167\\ \hline F8 &0 &0 &0 &0 &0 &0 &0 &0 &0.25 &0.25 &0.25\\ \hline F9 &0.25 &0 &0.25 &0 &0 &0 &0.083 &0 &0 &0.25 &0.167\\ \hline F10 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline F11 &0.25 &0 &0 &0.333 &0 &0 &0 &0 &0 &0.083 &0\\ \hline \end{array} $$

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

　　综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{11 \times11}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10 &F11\\ \hline F1 &0.139 &0.037 &0.107 &0.082 &0.095 &0.009 &0.156 &0.134 &0.28 &0.373 &0.247\\ \hline F2 &0.129 &0.015 &0.081 &0.074 &0.011 &0.007 &0.139 &0.126 &0.266 &0.435 &0.223\\ \hline F3 &0.196 &0.029 &0.093 &0.149 &0.016 &0.091 &0.251 &0.167 &0.256 &0.352 &0.447\\ \hline F4 &0.194 &0.185 &0.223 &0.086 &0.016 &0.019 &0.176 &0.083 &0.151 &0.224 &0.257\\ \hline F5 &0.126 &0.269 &0.312 &0.098 &0.011 &0.026 &0.196 &0.096 &0.171 &0.259 &0.293\\ \hline F6 &0.319 &0.031 &0.145 &0.145 &0.027 &0.012 &0.274 &0.256 &0.456 &0.524 &0.434\\ \hline F7 &0.192 &0.024 &0.116 &0.118 &0.016 &0.01 &0.081 &0.209 &0.371 &0.494 &0.354\\ \hline F8 &0.189 &0.025 &0.107 &0.129 &0.016 &0.009 &0.076 &0.041 &0.326 &0.441 &0.386\\ \hline F9 &0.408 &0.03 &0.327 &0.131 &0.034 &0.027 &0.208 &0.103 &0.185 &0.514 &0.394\\ \hline F10 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline F11 &0.35 &0.071 &0.101 &0.383 &0.029 &0.008 &0.098 &0.061 &0.12 &0.251 &0.148\\ \hline \end{array} $$

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$

$$\tilde B=\begin{array} {c|c|c}{M_{11 \times11}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10 &F11\\ \hline F1 &1 &0.0375 &0.1074 &0.0825 &0.095 &0.009 &0.1556 &0.1345 &0.2799 &0.3728 &0.2474\\ \hline F2 &0.1289 &1 &0.0815 &0.0743 &0.0107 &0.0068 &0.1393 &0.1265 &0.2656 &0.4346 &0.223\\ \hline F3 &0.1957 &0.0289 &1 &0.149 &0.0163 &0.0911 &0.2511 &0.1668 &0.2558 &0.3518 &0.4471\\ \hline F4 &0.1942 &0.185 &0.2228 &1 &0.0162 &0.0186 &0.1763 &0.0826 &0.1511 &0.2242 &0.2574\\ \hline F5 &0.1263 &0.2689 &0.3117 &0.0976 &1 &0.026 &0.1958 &0.0959 &0.1713 &0.2587 &0.2927\\ \hline F6 &0.3188 &0.0307 &0.1447 &0.1446 &0.0266 &1 &0.2742 &0.2556 &0.4557 &0.5241 &0.4338\\ \hline F7 &0.1918 &0.0237 &0.1163 &0.118 &0.016 &0.0097 &1 &0.2094 &0.3707 &0.494 &0.3541\\ \hline F8 &0.1894 &0.0254 &0.1069 &0.1285 &0.0158 &0.0089 &0.0764 &1 &0.3263 &0.4414 &0.3855\\ \hline F9 &0.408 &0.0304 &0.3266 &0.1315 &0.034 &0.0272 &0.208 &0.103 &1 &0.5142 &0.3944\\ \hline F10 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1 &0\\ \hline F11 &0.3496 &0.071 &0.1011 &0.3826 &0.0291 &0.0084 &0.0976 &0.0612 &0.1203 &0.2513 &1\\ \hline \end{array} $$

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。

$$\tilde R=\begin{array} {c|c|c}{M_{11 \times11}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10 &F11\\ \hline F1 &1 &0.185 &0.2799 &0.2799 &0.095 &0.0911 &0.2511 &0.2094 &0.2799 &0.3728 &0.2799\\ \hline F2 &0.2656 &1 &0.2656 &0.2656 &0.095 &0.0911 &0.2511 &0.2094 &0.2656 &0.4346 &0.2656\\ \hline F3 &0.3496 &0.185 &1 &0.3826 &0.095 &0.0911 &0.2511 &0.2094 &0.2799 &0.3518 &0.4471\\ \hline F4 &0.2574 &0.185 &0.2574 &1 &0.095 &0.0911 &0.2511 &0.2094 &0.2574 &0.2574 &0.2574\\ \hline F5 &0.3117 &0.2689 &0.3117 &0.3117 &1 &0.0911 &0.2511 &0.2094 &0.2799 &0.3117 &0.3117\\ \hline F6 &0.408 &0.185 &0.3266 &0.3826 &0.095 &1 &0.2742 &0.2556 &0.4557 &0.5241 &0.4338\\ \hline F7 &0.3707 &0.185 &0.3266 &0.3707 &0.095 &0.0911 &1 &0.2094 &0.3707 &0.494 &0.3707\\ \hline F8 &0.3496 &0.185 &0.3263 &0.3826 &0.095 &0.0911 &0.2511 &1 &0.3263 &0.4414 &0.3855\\ \hline F9 &0.408 &0.185 &0.3266 &0.3826 &0.095 &0.0911 &0.2511 &0.2094 &1 &0.5142 &0.3944\\ \hline F10 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1 &0\\ \hline F11 &0.3496 &0.185 &0.2799 &0.3826 &0.095 &0.0911 &0.2511 &0.2094 &0.2799 &0.3496 &1\\ \hline \end{array} $$

由阈值集合$\ddot \Delta $　得出综合影响矩阵$T$对应 31个结构。

序号	阈值集合中——特征阈值	聚类特征-对应截距$\lambda $数值区段
1	0.09107	0<$\lambda$<0.09107
2	0.09495	0.0911<$\lambda$<0.09495
3	0.18501	0.095<$\lambda$<0.18501
4	0.20944	0.185<$\lambda$<0.20944
5	0.25113	0.2094<$\lambda$<0.25113
6	0.25555	0.2511<$\lambda$<0.25555
7	0.25745	0.2556<$\lambda$<0.25745
8	0.26558	0.2574<$\lambda$<0.26558
9	0.26889	0.2656<$\lambda$<0.26889
10	0.27416	0.2689<$\lambda$<0.27416
11	0.27985	0.2742<$\lambda$<0.27985
12	0.3117	0.2799<$\lambda$<0.3117
13	0.3263	0.3117<$\lambda$<0.3263
14	0.32662	0.3263<$\lambda$<0.32662
15	0.34958	0.3266<$\lambda$<0.34958
16	0.35179	0.3496<$\lambda$<0.35179
17	0.37065	0.3518<$\lambda$<0.37065
18	0.37281	0.3707<$\lambda$<0.37281
19	0.38255	0.3728<$\lambda$<0.38255
20	0.38552	0.3826<$\lambda$<0.38552
21	0.39441	0.3855<$\lambda$<0.39441
22	0.40804	0.3944<$\lambda$<0.40804
23	0.43377	0.408<$\lambda$<0.43377
24	0.43459	0.4338<$\lambda$<0.43459
25	0.44137	0.4346<$\lambda$<0.44137
26	0.44708	0.4414<$\lambda$<0.44708
27	0.45575	0.4471<$\lambda$<0.45575
28	0.49399	0.4557<$\lambda$<0.49399
29	0.5142	0.494<$\lambda$<0.5142
30	0.52406	0.5142<$\lambda$<0.52406
31	1	0.5241<$\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

$$\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{11 \times4}} &Di &Ci &Mi &Ri\\ \hline F1 &1.661 &2.242 &3.903 &-0.581\\ \hline F2 &1.506 &0.717 &2.223 &0.79\\ \hline F3 &2.046 &1.612 &3.658 &0.435\\ \hline F4 &1.614 &1.394 &3.009 &0.22\\ \hline F5 &1.855 &0.27 &2.125 &1.585\\ \hline F6 &2.621 &0.218 &2.838 &2.403\\ \hline F7 &1.985 &1.655 &3.64 &0.329\\ \hline F8 &1.746 &1.276 &3.022 &0.469\\ \hline F9 &2.362 &2.581 &4.944 &-0.219\\ \hline F10 &0 &3.867 &3.867 &-3.867\\ \hline F11 &1.62 &3.183 &4.803 &-1.563\\ \hline \end{array} $$

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：