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

$$Ori=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10\\ \hline F1 &0 &3 &3 &1 &3 &2 &2 &3 &2 &0\\ \hline F2 &1 &0 &5 &1 &0 &2 &5 &2 &1 &5\\ \hline F3 &0 &0 &0 &0 &2 &0 &3 &0 &4 &1\\ \hline F4 &3 &0 &5 &0 &0 &0 &3 &0 &0 &0\\ \hline F5 &3 &0 &0 &0 &0 &0 &0 &0 &5 &3\\ \hline F6 &0 &5 &3 &1 &2 &0 &3 &0 &1 &1\\ \hline F7 &2 &1 &0 &0 &0 &0 &0 &0 &0 &1\\ \hline F8 &0 &3 &3 &1 &0 &0 &1 &0 &0 &2\\ \hline F9 &0 &1 &1 &0 &0 &0 &2 &0 &0 &3\\ \hline F10 &0 &0 &4 &0 &1 &1 &2 &0 &0 &0\\ \hline \end{array} $$

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

$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10\\ \hline F1 &0 &0.136 &0.136 &0.045 &0.136 &0.091 &0.091 &0.136 &0.091 &0\\ \hline F2 &0.045 &0 &0.227 &0.045 &0 &0.091 &0.227 &0.091 &0.045 &0.227\\ \hline F3 &0 &0 &0 &0 &0.091 &0 &0.136 &0 &0.182 &0.045\\ \hline F4 &0.136 &0 &0.227 &0 &0 &0 &0.136 &0 &0 &0\\ \hline F5 &0.136 &0 &0 &0 &0 &0 &0 &0 &0.227 &0.136\\ \hline F6 &0 &0.227 &0.136 &0.045 &0.091 &0 &0.136 &0 &0.045 &0.045\\ \hline F7 &0.091 &0.045 &0 &0 &0 &0 &0 &0 &0 &0.045\\ \hline F8 &0 &0.136 &0.136 &0.045 &0 &0 &0.045 &0 &0 &0.091\\ \hline F9 &0 &0.045 &0.045 &0 &0 &0 &0.091 &0 &0 &0.136\\ \hline F10 &0 &0 &0.182 &0 &0.045 &0.045 &0.091 &0 &0 &0\\ \hline \end{array} $$

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

　　综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10\\ \hline F1 &0.068 &0.217 &0.287 &0.072 &0.19 &0.124 &0.252 &0.165 &0.208 &0.149\\ \hline F2 &0.102 &0.081 &0.372 &0.064 &0.074 &0.122 &0.38 &0.112 &0.148 &0.326\\ \hline F3 &0.033 &0.026 &0.043 &0.003 &0.105 &0.01 &0.183 &0.007 &0.218 &0.107\\ \hline F4 &0.167 &0.045 &0.283 &0.012 &0.053 &0.022 &0.219 &0.027 &0.082 &0.055\\ \hline F5 &0.153 &0.047 &0.09 &0.011 &0.041 &0.027 &0.086 &0.025 &0.27 &0.201\\ \hline F6 &0.065 &0.269 &0.269 &0.064 &0.136 &0.038 &0.285 &0.033 &0.145 &0.175\\ \hline F7 &0.103 &0.07 &0.053 &0.01 &0.024 &0.019 &0.047 &0.02 &0.028 &0.076\\ \hline F8 &0.033 &0.159 &0.227 &0.056 &0.035 &0.025 &0.147 &0.019 &0.061 &0.16\\ \hline F9 &0.019 &0.06 &0.098 &0.005 &0.021 &0.015 &0.141 &0.008 &0.028 &0.169\\ \hline F10 &0.025 &0.025 &0.211 &0.005 &0.075 &0.052 &0.145 &0.006 &0.061 &0.043\\ \hline \end{array} $$

$T$的平均数$\bar{x} $ 与总体标准差$ \sigma $的求解

均值$\bar{x} $

$\bar{x}= 0.10227169111374 $

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

$\sigma = 0.090382711033727 $

区段截取最小边界$ \lambda_{min}= \bar{x} $

$\lambda_{min} = 0.10227169111374 $

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

$\lambda_{max} = 0.19265440214747 $

\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} =0.10227169111374$

　　　$ \lambda_{max} =0.19265440214747$

$$ \tilde A=\begin{array}{c|c|c|c|c|c|c}{M_{10 \times10}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10\\ \hline F1 &0 &1 &1 &0 &0.18982 &0.12365 &1 &0.16545 &1 &0.14882\\ \hline F2 &0.10249 &0 &1 &0 &0 &0.12242 &1 &0.11226 &0.14849 &1\\ \hline F3 &0 &0 &0 &0 &0.10501 &0 &0.18273 &0 &1 &0.10672\\ \hline F4 &0.16714 &0 &1 &0 &0 &0 &1 &0 &0 &0\\ \hline F5 &0.15344 &0 &0 &0 &0 &0 &0 &0 &1 &1\\ \hline F6 &0 &1 &1 &0 &0.13571 &0 &1 &0 &0.14513 &0.17483\\ \hline F7 &0.10294 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline F8 &0 &0.1585 &1 &0 &0 &0 &0.1474 &0 &0 &0.15979\\ \hline F9 &0 &0 &0 &0 &0 &0 &0.14052 &0 &0 &0.16883\\ \hline F10 &0 &0 &1 &0 &0 &0 &0.14524 &0 &0 &0\\ \hline \end{array} $$

序号	阈值集合中——特征阈值	聚类特征-对应截距$\lambda $数值区段
1	0.10294	0<$\lambda$<0.10294
2	0.10501	0.1029<$\lambda$<0.10501
3	0.12242	0.105<$\lambda$<0.12242
4	0.12365	0.1224<$\lambda$<0.12365
5	0.13571	0.1237<$\lambda$<0.13571
6	0.15344	0.1357<$\lambda$<0.15344
7	0.1585	0.1534<$\lambda$<0.1585
8	0.16545	0.1585<$\lambda$<0.16545
9	0.16714	0.1655<$\lambda$<0.16714
10	0.16883	0.1671<$\lambda$<0.16883
11	0.18273	0.1688<$\lambda$<0.18273
12	0.18982	0.1827<$\lambda$<0.18982
13	1	0.1898<$\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