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

$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &C1 &C2 &C3 &C4 &C5 &C6 &C7 &C8 &C9 &C10\\ \hline C1 &0 &0.146 &0.07 &0.103 &0.124 &0.119 &0.119 &0.016 &0.065 &0.141\\ \hline C2 &0.114 &0 &0.027 &0.114 &0.086 &0.065 &0.081 &0.065 &0.103 &0.135\\ \hline C3 &0.108 &0.043 &0 &0.076 &0.07 &0.054 &0.07 &0.086 &0.13 &0.114\\ \hline C4 &0.178 &0.054 &0.027 &0 &0.086 &0.103 &0.103 &0.103 &0.103 &0.108\\ \hline C5 &0.178 &0.054 &0.108 &0.054 &0 &0.146 &0.092 &0.108 &0.135 &0.124\\ \hline C6 &0.108 &0.135 &0.07 &0.114 &0.011 &0 &0.124 &0.119 &0.114 &0.114\\ \hline C7 &0.119 &0.168 &0.054 &0.054 &0.135 &0.097 &0 &0.13 &0.108 &0.054\\ \hline C8 &0.054 &0.07 &0.07 &0.059 &0.141 &0.135 &0.114 &0 &0.108 &0.13\\ \hline C9 &0.108 &0.059 &0.114 &0.054 &0.049 &0.038 &0.119 &0.114 &0 &0.168\\ \hline C10 &0.054 &0.108 &0.076 &0.054 &0.114 &0.114 &0.119 &0.114 &0.059 &0\\ \hline \end{array} $$

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

　　综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &C1 &C2 &C3 &C4 &C5 &C6 &C7 &C8 &C9 &C10\\ \hline C1 &0.679 &0.732 &0.502 &0.57 &0.681 &0.71 &0.754 &0.606 &0.678 &0.852\\ \hline C2 &0.7 &0.531 &0.416 &0.522 &0.588 &0.597 &0.651 &0.579 &0.636 &0.767\\ \hline C3 &0.662 &0.544 &0.371 &0.466 &0.547 &0.558 &0.612 &0.57 &0.632 &0.717\\ \hline C4 &0.81 &0.64 &0.455 &0.462 &0.638 &0.683 &0.726 &0.658 &0.689 &0.807\\ \hline C5 &0.892 &0.713 &0.583 &0.574 &0.626 &0.792 &0.799 &0.738 &0.796 &0.914\\ \hline C6 &0.764 &0.718 &0.497 &0.575 &0.586 &0.596 &0.756 &0.687 &0.712 &0.826\\ \hline C7 &0.796 &0.759 &0.5 &0.539 &0.705 &0.705 &0.662 &0.71 &0.729 &0.801\\ \hline C8 &0.716 &0.655 &0.501 &0.521 &0.685 &0.715 &0.741 &0.581 &0.706 &0.832\\ \hline C9 &0.702 &0.601 &0.501 &0.479 &0.572 &0.586 &0.695 &0.633 &0.557 &0.807\\ \hline C10 &0.666 &0.644 &0.469 &0.484 &0.623 &0.653 &0.696 &0.637 &0.621 &0.662\\ \hline \end{array} $$

$T$的平均数$\bar{x} $ 与总体标准差$ \sigma $的求解

均值$\bar{x} $

$\bar{x}= 0.64989300004208 $

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

$\sigma = 0.10876611872427 $

区段截取最小边界$ \lambda_{min}= \bar{x} $

$\lambda_{min} = 0.64989300004208 $

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

$\lambda_{max} = 0.75865911876635 $

\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} =0.64989300004208$

　　　$ \lambda_{max} =0.75865911876635$

$$ \tilde A=\begin{array}{c|c|c|c|c|c|c}{M_{10 \times10}} &C1 &C2 &C3 &C4 &C5 &C6 &C7 &C8 &C9 &C10\\ \hline C1 &0.67909 &0.73174 &0 &0 &0.68111 &0.7099 &0.75442 &0 &0.67807 &1\\ \hline C2 &0.70026 &0 &0 &0 &0 &0 &0.65105 &0 &0 &1\\ \hline C3 &0.66164 &0 &0 &0 &0 &0 &0 &0 &0 &0.71681\\ \hline C4 &1 &0 &0 &0 &0 &0.68298 &0.72648 &0.65835 &0.68887 &1\\ \hline C5 &1 &0.71321 &0 &0 &0 &1 &1 &0.73781 &1 &1\\ \hline C6 &1 &0.71808 &0 &0 &0 &0 &0.75627 &0.68695 &0.71235 &1\\ \hline C7 &1 &0.75859 &0 &0 &0.70464 &0.70519 &0.6616 &0.70995 &0.729 &1\\ \hline C8 &0.71592 &0.65524 &0 &0 &0.68485 &0.71514 &0.74125 &0 &0.70647 &1\\ \hline C9 &0.70193 &0 &0 &0 &0 &0 &0.69488 &0 &0 &1\\ \hline C10 &0.66601 &0 &0 &0 &0 &0.65294 &0.69631 &0 &0 &0.66208\\ \hline \end{array} $$

序号	阈值集合中——特征阈值	聚类特征-对应截距$\lambda $数值区段
1	0.69631	0<$\lambda$<0.69631
2	0.70026	0.6963<$\lambda$<0.70026
3	0.70193	0.7003<$\lambda$<0.70193
4	0.70464	0.7019<$\lambda$<0.70464
5	0.70995	0.7046<$\lambda$<0.70995
6	0.71514	0.7099<$\lambda$<0.71514
7	0.71681	0.7151<$\lambda$<0.71681
8	0.729	0.7168<$\lambda$<0.729
9	0.73781	0.729<$\lambda$<0.73781
10	0.74125	0.7378<$\lambda$<0.74125
11	0.75442	0.7412<$\lambda$<0.75442
12	0.75627	0.7544<$\lambda$<0.75627
13	0.75859	0.7563<$\lambda$<0.75859
14	1	0.7586<$\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