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

$$Ori=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &C1 &C2 &C3 &C4 &C5 &C6 &C7 &C8 &C9 &C10\\ \hline C1 &0 &27 &13 &19 &23 &22 &22 &3 &12 &26\\ \hline C2 &21 &0 &5 &21 &16 &12 &15 &12 &19 &25\\ \hline C3 &20 &8 &0 &14 &13 &10 &13 &16 &24 &21\\ \hline C4 &33 &10 &5 &0 &16 &19 &19 &19 &19 &20\\ \hline C5 &33 &10 &20 &10 &0 &27 &17 &20 &25 &23\\ \hline C6 &20 &25 &13 &21 &2 &0 &23 &22 &21 &21\\ \hline C7 &22 &31 &10 &10 &25 &18 &0 &24 &20 &10\\ \hline C8 &10 &13 &13 &11 &26 &25 &21 &0 &20 &24\\ \hline C9 &20 &11 &21 &10 &9 &7 &22 &21 &0 &31\\ \hline C10 &10 &20 &14 &10 &21 &21 &22 &21 &11 &0\\ \hline \end{array} $$

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

$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &C1 &C2 &C3 &C4 &C5 &C6 &C7 &C8 &C9 &C10\\ \hline C1 &0 &0.134 &0.065 &0.095 &0.114 &0.109 &0.109 &0.015 &0.06 &0.129\\ \hline C2 &0.104 &0 &0.025 &0.104 &0.08 &0.06 &0.075 &0.06 &0.095 &0.124\\ \hline C3 &0.1 &0.04 &0 &0.07 &0.065 &0.05 &0.065 &0.08 &0.119 &0.104\\ \hline C4 &0.164 &0.05 &0.025 &0 &0.08 &0.095 &0.095 &0.095 &0.095 &0.1\\ \hline C5 &0.164 &0.05 &0.1 &0.05 &0 &0.134 &0.085 &0.1 &0.124 &0.114\\ \hline C6 &0.1 &0.124 &0.065 &0.104 &0.01 &0 &0.114 &0.109 &0.104 &0.104\\ \hline C7 &0.109 &0.154 &0.05 &0.05 &0.124 &0.09 &0 &0.119 &0.1 &0.05\\ \hline C8 &0.05 &0.065 &0.065 &0.055 &0.129 &0.124 &0.104 &0 &0.1 &0.119\\ \hline C9 &0.1 &0.055 &0.104 &0.05 &0.045 &0.035 &0.109 &0.104 &0 &0.154\\ \hline C10 &0.05 &0.1 &0.07 &0.05 &0.104 &0.104 &0.109 &0.104 &0.055 &0\\ \hline \end{array} $$

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

　　综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &C1 &C2 &C3 &C4 &C5 &C6 &C7 &C8 &C9 &C10\\ \hline C1 &0.384 &0.459 &0.304 &0.355 &0.423 &0.438 &0.463 &0.348 &0.404 &0.524\\ \hline C2 &0.431 &0.298 &0.243 &0.33 &0.359 &0.358 &0.393 &0.347 &0.39 &0.475\\ \hline C3 &0.407 &0.32 &0.209 &0.286 &0.331 &0.332 &0.368 &0.349 &0.397 &0.441\\ \hline C4 &0.513 &0.38 &0.266 &0.259 &0.388 &0.419 &0.443 &0.403 &0.42 &0.49\\ \hline C5 &0.559 &0.42 &0.364 &0.341 &0.351 &0.492 &0.481 &0.45 &0.491 &0.556\\ \hline C6 &0.465 &0.448 &0.301 &0.361 &0.335 &0.334 &0.466 &0.425 &0.438 &0.502\\ \hline C7 &0.487 &0.48 &0.299 &0.322 &0.44 &0.429 &0.372 &0.44 &0.446 &0.471\\ \hline C8 &0.422 &0.392 &0.306 &0.312 &0.429 &0.446 &0.454 &0.328 &0.433 &0.51\\ \hline C9 &0.429 &0.358 &0.319 &0.286 &0.34 &0.343 &0.43 &0.393 &0.312 &0.507\\ \hline C10 &0.393 &0.397 &0.288 &0.29 &0.387 &0.404 &0.43 &0.396 &0.37 &0.372\\ \hline \end{array} $$

$T$的平均数$\bar{x} $ 与总体标准差$ \sigma $的求解

均值$\bar{x} $

$\bar{x}= 0.39391941578953 $

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

$\sigma = 0.071189593207685 $

区段截取最小边界$ \lambda_{min}= \bar{x} $

$\lambda_{min} = 0.39391941578953 $

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

$\lambda_{max} = 0.46510900899721 $

\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} =0.39391941578953$

　　　$ \lambda_{max} =0.46510900899721$

$$ \tilde A=\begin{array}{c|c|c|c|c|c|c}{M_{10 \times10}} &C1 &C2 &C3 &C4 &C5 &C6 &C7 &C8 &C9 &C10\\ \hline C1 &0 &0.45921 &0 &0 &0.42256 &0.43784 &0.46268 &0 &0.40355 &1\\ \hline C2 &0.43146 &0 &0 &0 &0 &0 &0 &0 &0 &1\\ \hline C3 &0.40718 &0 &0 &0 &0 &0 &0 &0 &0.39727 &0.44105\\ \hline C4 &1 &0 &0 &0 &0 &0.41861 &0.44296 &0.40278 &0.4201 &1\\ \hline C5 &1 &0.42041 &0 &0 &0 &1 &1 &0.44986 &1 &1\\ \hline C6 &0.46462 &0.44833 &0 &0 &0 &0 &1 &0.42509 &0.43751 &1\\ \hline C7 &1 &1 &0 &0 &0.4399 &0.42869 &0 &0.44038 &0.44613 &1\\ \hline C8 &0.42173 &0 &0 &0 &0.42941 &0.44613 &0.45402 &0 &0.43343 &1\\ \hline C9 &0.42862 &0 &0 &0 &0 &0 &0.42964 &0 &0 &1\\ \hline C10 &0 &0.39697 &0 &0 &0 &0.40446 &0.42982 &0.39605 &0 &0\\ \hline \end{array} $$

序号	阈值集合中——特征阈值	聚类特征-对应截距$\lambda $数值区段
1	0.42982	0<$\lambda$<0.42982
2	0.43146	0.4298<$\lambda$<0.43146
3	0.4399	0.4315<$\lambda$<0.4399
4	0.44038	0.4399<$\lambda$<0.44038
5	0.44105	0.4404<$\lambda$<0.44105
6	0.44613	0.441<$\lambda$<0.44613
7	0.44613	0.4461<$\lambda$<0.44613
8	0.44986	0.4461<$\lambda$<0.44986
9	0.45402	0.4499<$\lambda$<0.45402
10	0.46268	0.454<$\lambda$<0.46268
11	1	0.4627<$\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