决策与实验室-区段截取解释结构模型在线计算，DEMATEL-SectionISM

原始矩阵（直接影响矩阵）为

$$Ori=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &A1 &A2 &A3 &A4 &A5 &A6 &A7 &A8 &A9 &A10\\ \hline A1 &0 &13 &13 &19 &23 &22 &12 &13 &22 &26\\ \hline A2 &21 &0 &5 &21 &16 &12 &15 &12 &19 &25\\ \hline A3 &20 &8 &0 &14 &13 &10 &13 &16 &24 &21\\ \hline A4 &33 &10 &5 &0 &16 &19 &19 &19 &19 &20\\ \hline A5 &33 &10 &20 &10 &0 &27 &17 &20 &25 &23\\ \hline A6 &20 &25 &13 &21 &2 &0 &23 &22 &21 &21\\ \hline A7 &22 &31 &10 &10 &25 &18 &0 &24 &30 &19\\ \hline A8 &10 &13 &13 &11 &26 &25 &21 &0 &20 &24\\ \hline A9 &20 &11 &21 &10 &29 &27 &22 &21 &0 &31\\ \hline A10 &10 &20 &14 &10 &21 &21 &22 &21 &11 &0\\ \hline \end{array} $$

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

$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &A1 &A2 &A3 &A4 &A5 &A6 &A7 &A8 &A9 &A10\\ \hline A1 &0 &0.062 &0.062 &0.09 &0.11 &0.105 &0.057 &0.062 &0.105 &0.124\\ \hline A2 &0.1 &0 &0.024 &0.1 &0.076 &0.057 &0.071 &0.057 &0.09 &0.119\\ \hline A3 &0.095 &0.038 &0 &0.067 &0.062 &0.048 &0.062 &0.076 &0.114 &0.1\\ \hline A4 &0.157 &0.048 &0.024 &0 &0.076 &0.09 &0.09 &0.09 &0.09 &0.095\\ \hline A5 &0.157 &0.048 &0.095 &0.048 &0 &0.129 &0.081 &0.095 &0.119 &0.11\\ \hline A6 &0.095 &0.119 &0.062 &0.1 &0.01 &0 &0.11 &0.105 &0.1 &0.1\\ \hline A7 &0.105 &0.148 &0.048 &0.048 &0.119 &0.086 &0 &0.114 &0.143 &0.09\\ \hline A8 &0.048 &0.062 &0.062 &0.052 &0.124 &0.119 &0.1 &0 &0.095 &0.114\\ \hline A9 &0.095 &0.052 &0.1 &0.048 &0.138 &0.129 &0.105 &0.1 &0 &0.148\\ \hline A10 &0.048 &0.095 &0.067 &0.048 &0.1 &0.1 &0.105 &0.1 &0.052 &0\\ \hline \end{array} $$

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

　　综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &A1 &A2 &A3 &A4 &A5 &A6 &A7 &A8 &A9 &A10\\ \hline A1 &0.335 &0.325 &0.28 &0.316 &0.414 &0.433 &0.36 &0.37 &0.435 &0.49\\ \hline A2 &0.394 &0.242 &0.224 &0.302 &0.359 &0.361 &0.342 &0.335 &0.39 &0.45\\ \hline A3 &0.374 &0.267 &0.193 &0.262 &0.335 &0.339 &0.322 &0.339 &0.397 &0.419\\ \hline A4 &0.47 &0.312 &0.244 &0.231 &0.387 &0.42 &0.385 &0.39 &0.421 &0.463\\ \hline A5 &0.512 &0.347 &0.338 &0.309 &0.356 &0.495 &0.417 &0.436 &0.491 &0.526\\ \hline A6 &0.425 &0.383 &0.279 &0.33 &0.339 &0.341 &0.41 &0.41 &0.438 &0.477\\ \hline A7 &0.479 &0.439 &0.301 &0.315 &0.475 &0.469 &0.351 &0.459 &0.52 &0.522\\ \hline A8 &0.383 &0.331 &0.283 &0.283 &0.429 &0.448 &0.4 &0.315 &0.432 &0.484\\ \hline A9 &0.474 &0.364 &0.351 &0.316 &0.49 &0.508 &0.45 &0.454 &0.398 &0.571\\ \hline A10 &0.355 &0.338 &0.266 &0.262 &0.382 &0.402 &0.377 &0.379 &0.368 &0.349\\ \hline \end{array} $$

$T$的平均数$\bar{x} $ 与总体标准差$ \sigma $的求解

均值$\bar{x} $

$\bar{x}= 0.38154067215708 $

总体标准差$\sigma=\sqrt { \frac {\sum \limits_{i=1}^{n^2} ({x_i-\bar{x}})^2 }{n^2} }　$

$\sigma = 0.077335472070474 $

区段截取最小边界$ \lambda_{min}= \bar{x} $

$\lambda_{min} = 0.38154067215708 $

区段截取最大边界$\lambda_{max}= \bar{x} +\sigma $

$\lambda_{max} = 0.45887614422755 $

\begin{CD} T@>区段截取>> \tilde A \\ \end{CD}

$$ \tilde a_{ij}= \begin{cases} 1 , \text{ $e_i$}\rightarrow \text{$e_j$ 当： $ t_{ij} ＞ \lambda_{max} $} \\ t_{ij} , \text{ $e_i$}\rightarrow \text{$e_j $ 当：$\lambda_{min} ≤ t_{ij} ≤ \lambda_{max}$ } \\ 0, \text{ $e_i$}\rightarrow \text{$e_j$ 当：　$ t_{ij} ＜ \lambda_{min} $} \end{cases} $$

$[\lambda_{min}- \lambda_{max} ] $ 截取后的模糊矩阵$ \tilde A$

　　　$ \lambda_{min} =0.38154067215708$

　　　$ \lambda_{max} =0.45887614422755$

$$ \tilde A=\begin{array}{c|c|c|c|c|c|c}{M_{10 \times10}} &A1 &A2 &A3 &A4 &A5 &A6 &A7 &A8 &A9 &A10\\ \hline A1 &0 &0 &0 &0 &0.4143 &0.43347 &0 &0 &0.43494 &1\\ \hline A2 &0.39398 &0 &0 &0 &0 &0 &0 &0 &0.38963 &0.44983\\ \hline A3 &0 &0 &0 &0 &0 &0 &0 &0 &0.39725 &0.41929\\ \hline A4 &1 &0 &0 &0 &0.38665 &0.41959 &0.38451 &0.39003 &0.42106 &1\\ \hline A5 &1 &0 &0 &0 &0 &1 &0.41694 &0.43551 &1 &1\\ \hline A6 &0.42463 &0.38277 &0 &0 &0 &0 &0.41 &0.41045 &0.43799 &1\\ \hline A7 &1 &0.43939 &0 &0 &1 &1 &0 &1 &1 &1\\ \hline A8 &0.38331 &0 &0 &0 &0.42899 &0.44805 &0.39991 &0 &0.43165 &1\\ \hline A9 &1 &0 &0 &0 &1 &1 &0.45021 &0.45359 &0.39776 &1\\ \hline A10 &0 &0 &0 &0 &0.38243 &0.40171 &0 &0 &0 &0\\ \hline \end{array} $$

序号	阈值集合中——特征阈值	聚类特征-对应截距$\lambda $数值区段
1	0.40171	0<$\lambda$<0.40171
2	0.41929	0.4017<$\lambda$<0.41929
3	0.43494	0.4193<$\lambda$<0.43494
4	0.43799	0.4349<$\lambda$<0.43799
5	0.43939	0.438<$\lambda$<0.43939
6	0.44805	0.4394<$\lambda$<0.44805
7	0.44983	0.448<$\lambda$<0.44983
8	0.45021	0.4498<$\lambda$<0.45021
9	0.45359	0.4502<$\lambda$<0.45359
10	1	0.4536<$\lambda$<1

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$	$$ R_i=D_i-C_i $$

基于综合影响矩阵T区段截取

DEMATEL-SecISM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 $$\begin{CD} N @>>>T \\ \end{CD} $$

区段截取的处理

$T$的平均数$\bar{x} $ 与总体标准差$ \sigma $的求解

\begin{CD} T@>区段截取>> \tilde A \\ \end{CD}

$\tilde A$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

基于综合影响矩阵T区段截取

DEMATEL-SecISM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 $$\begin{CD} N @>>>T \\ \end{CD} $$

区段截取的处理

$T$的 平均数$\bar{x} $ 与 总体标准差$ \sigma $的求解

\begin{CD} T@>区段截取>> \tilde A \\ \end{CD}

$\tilde A$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

$T$的平均数$\bar{x} $ 与总体标准差$ \sigma $的求解