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

$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &A1 &A2 &A3 &A4 &A5 &A6 &A7 &A8 &A9 &A10\\ \hline A1 &0 &0.068 &0.068 &0.099 &0.12 &0.115 &0.063 &0.068 &0.115 &0.135\\ \hline A2 &0.109 &0 &0.026 &0.109 &0.083 &0.063 &0.078 &0.063 &0.099 &0.13\\ \hline A3 &0.104 &0.042 &0 &0.073 &0.068 &0.052 &0.068 &0.083 &0.125 &0.109\\ \hline A4 &0.172 &0.052 &0.026 &0 &0.083 &0.099 &0.099 &0.099 &0.099 &0.104\\ \hline A5 &0.172 &0.052 &0.104 &0.052 &0 &0.141 &0.089 &0.104 &0.13 &0.12\\ \hline A6 &0.104 &0.13 &0.068 &0.109 &0.01 &0 &0.12 &0.115 &0.109 &0.109\\ \hline A7 &0.115 &0.161 &0.052 &0.052 &0.13 &0.094 &0 &0.125 &0.156 &0.099\\ \hline A8 &0.052 &0.068 &0.068 &0.057 &0.135 &0.13 &0.109 &0 &0.104 &0.125\\ \hline A9 &0.104 &0.057 &0.109 &0.052 &0.151 &0.141 &0.115 &0.109 &0 &0.161\\ \hline A10 &0.052 &0.104 &0.073 &0.052 &0.109 &0.109 &0.115 &0.109 &0.057 &0\\ \hline \end{array} $$

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

　　综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &A1 &A2 &A3 &A4 &A5 &A6 &A7 &A8 &A9 &A10\\ \hline A1 &0.62 &0.56 &0.476 &0.522 &0.693 &0.73 &0.626 &0.64 &0.734 &0.822\\ \hline A2 &0.659 &0.45 &0.398 &0.49 &0.611 &0.626 &0.584 &0.58 &0.66 &0.751\\ \hline A3 &0.627 &0.468 &0.357 &0.44 &0.575 &0.593 &0.552 &0.574 &0.658 &0.707\\ \hline A4 &0.763 &0.545 &0.435 &0.429 &0.662 &0.713 &0.65 &0.66 &0.717 &0.79\\ \hline A5 &0.842 &0.609 &0.559 &0.537 &0.659 &0.828 &0.716 &0.74 &0.827 &0.897\\ \hline A6 &0.721 &0.626 &0.477 &0.541 &0.616 &0.634 &0.684 &0.688 &0.742 &0.814\\ \hline A7 &0.814 &0.714 &0.524 &0.549 &0.796 &0.807 &0.651 &0.773 &0.866 &0.901\\ \hline A8 &0.675 &0.568 &0.48 &0.489 &0.711 &0.748 &0.671 &0.583 &0.733 &0.818\\ \hline A9 &0.811 &0.635 &0.58 &0.552 &0.814 &0.852 &0.761 &0.769 &0.736 &0.956\\ \hline A10 &0.623 &0.558 &0.447 &0.451 &0.641 &0.676 &0.627 &0.632 &0.643 &0.648\\ \hline \end{array} $$

$T$的平均数$\bar{x} $ 与总体标准差$ \sigma $的求解

均值$\bar{x} $

$\bar{x}= 0.6518567345602 $

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

$\sigma = 0.12424744973134 $

区段截取最小边界$ \lambda_{min}= \bar{x} $

$\lambda_{min} = 0.6518567345602 $

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

$\lambda_{max} = 0.77610418429154 $

\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} =0.6518567345602$

　　　$ \lambda_{max} =0.77610418429154$

$$ \tilde A=\begin{array}{c|c|c|c|c|c|c}{M_{10 \times10}} &A1 &A2 &A3 &A4 &A5 &A6 &A7 &A8 &A9 &A10\\ \hline A1 &0 &0 &0 &0 &0.69303 &0.72971 &0 &0 &0.73384 &1\\ \hline A2 &0.65943 &0 &0 &0 &0 &0 &0 &0 &0.65995 &0.7511\\ \hline A3 &0 &0 &0 &0 &0 &0 &0 &0 &0.65778 &0.70663\\ \hline A4 &0.76318 &0 &0 &0 &0.66154 &0.71276 &0 &0.66009 &0.71685 &1\\ \hline A5 &1 &0 &0 &0 &0.65922 &1 &0.71572 &0.74044 &1 &1\\ \hline A6 &0.72108 &0 &0 &0 &0 &0 &0.68359 &0.68821 &0.74177 &1\\ \hline A7 &1 &0.71446 &0 &0 &1 &1 &0 &0.77281 &1 &1\\ \hline A8 &0.6746 &0 &0 &0 &0.71111 &0.74778 &0.67086 &0 &0.73289 &1\\ \hline A9 &1 &0 &0 &0 &1 &1 &0.76088 &0.76945 &0.73584 &1\\ \hline A10 &0 &0 &0 &0 &0 &0.67595 &0 &0 &0 &0\\ \hline \end{array} $$

序号	阈值集合中——特征阈值	聚类特征-对应截距$\lambda $数值区段
1	0.67595	0<$\lambda$<0.67595
2	0.70663	0.6759<$\lambda$<0.70663
3	0.71446	0.7066<$\lambda$<0.71446
4	0.73384	0.7145<$\lambda$<0.73384
5	0.74177	0.7338<$\lambda$<0.74177
6	0.74778	0.7418<$\lambda$<0.74778
7	0.7511	0.7478<$\lambda$<0.7511
8	0.76088	0.7511<$\lambda$<0.76088
9	0.76318	0.7609<$\lambda$<0.76318
10	0.76945	0.7632<$\lambda$<0.76945
11	0.77281	0.7695<$\lambda$<0.77281
12	1	0.7728<$\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