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

$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10\\ \hline F1 &0 &0.125 &0.125 &0.042 &0.125 &0.083 &0.083 &0.125 &0.083 &0\\ \hline F2 &0.042 &0 &0.208 &0.042 &0 &0.083 &0.208 &0.083 &0.042 &0.208\\ \hline F3 &0 &0 &0 &0 &0.083 &0 &0.125 &0 &0.167 &0.042\\ \hline F4 &0.125 &0 &0.208 &0 &0 &0 &0.125 &0 &0 &0\\ \hline F5 &0.125 &0 &0 &0 &0 &0 &0 &0 &0.208 &0.125\\ \hline F6 &0 &0.208 &0.125 &0.042 &0.083 &0 &0.125 &0 &0.042 &0.042\\ \hline F7 &0.083 &0.042 &0 &0 &0 &0 &0 &0 &0 &0.042\\ \hline F8 &0 &0.125 &0.125 &0.042 &0 &0 &0.042 &0 &0 &0.083\\ \hline F9 &0 &0.042 &0.042 &0 &0 &0 &0.083 &0 &0 &0.125\\ \hline F10 &0 &0 &0.167 &0 &0.042 &0.042 &0.083 &0 &0 &0\\ \hline \end{array} $$

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

　　综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10\\ \hline F1 &0.054 &0.189 &0.243 &0.062 &0.166 &0.108 &0.209 &0.147 &0.175 &0.118\\ \hline F2 &0.086 &0.064 &0.323 &0.057 &0.058 &0.108 &0.328 &0.099 &0.122 &0.284\\ \hline F3 &0.026 &0.02 &0.033 &0.002 &0.094 &0.008 &0.161 &0.005 &0.195 &0.091\\ \hline F4 &0.149 &0.035 &0.251 &0.009 &0.043 &0.017 &0.189 &0.022 &0.065 &0.042\\ \hline F5 &0.137 &0.037 &0.071 &0.009 &0.032 &0.022 &0.067 &0.02 &0.241 &0.175\\ \hline F6 &0.052 &0.239 &0.229 &0.056 &0.117 &0.03 &0.242 &0.026 &0.12 &0.144\\ \hline F7 &0.092 &0.061 &0.042 &0.008 &0.019 &0.015 &0.036 &0.017 &0.022 &0.065\\ \hline F8 &0.026 &0.141 &0.197 &0.05 &0.027 &0.02 &0.123 &0.015 &0.047 &0.137\\ \hline F9 &0.015 &0.053 &0.083 &0.004 &0.016 &0.012 &0.122 &0.006 &0.021 &0.15\\ \hline F10 &0.02 &0.02 &0.188 &0.004 &0.065 &0.046 &0.126 &0.004 &0.049 &0.034\\ \hline \end{array} $$

$T$的平均数$\bar{x} $ 与总体标准差$ \sigma $的求解

均值$\bar{x} $

$\bar{x}= 0.087269003128053 $

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

$\sigma = 0.07914841797361 $

区段截取最小边界$ \lambda_{min}= \bar{x} $

$\lambda_{min} = 0.087269003128053 $

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

$\lambda_{max} = 0.16641742110166 $

\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} =0.087269003128053$

　　　$ \lambda_{max} =0.16641742110166$

$$ \tilde A=\begin{array}{c|c|c|c|c|c|c}{M_{10 \times10}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10\\ \hline F1 &0 &1 &1 &0 &0.16592 &0.10846 &1 &0.14747 &1 &0.11764\\ \hline F2 &0 &0 &1 &0 &0 &0.10771 &1 &0.09945 &0.12195 &1\\ \hline F3 &0 &0 &0 &0 &0.09378 &0 &0.16083 &0 &1 &0.09081\\ \hline F4 &0.14874 &0 &1 &0 &0 &0 &1 &0 &0 &0\\ \hline F5 &0.13732 &0 &0 &0 &0 &0 &0 &0 &1 &1\\ \hline F6 &0 &1 &1 &0 &0.11745 &0 &1 &0 &0.1199 &0.14432\\ \hline F7 &0.09224 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline F8 &0 &0.14127 &1 &0 &0 &0 &0.12265 &0 &0 &0.13746\\ \hline F9 &0 &0 &0 &0 &0 &0 &0.12248 &0 &0 &0.15025\\ \hline F10 &0 &0 &1 &0 &0 &0 &0.12605 &0 &0 &0\\ \hline \end{array} $$

序号	阈值集合中——特征阈值	聚类特征-对应截距$\lambda $数值区段
1	0.09224	0<$\lambda$<0.09224
2	0.09378	0.0922<$\lambda$<0.09378
3	0.10771	0.0938<$\lambda$<0.10771
4	0.10846	0.1077<$\lambda$<0.10846
5	0.11745	0.1085<$\lambda$<0.11745
6	0.13732	0.1175<$\lambda$<0.13732
7	0.14127	0.1373<$\lambda$<0.14127
8	0.14747	0.1413<$\lambda$<0.14747
9	0.14874	0.1475<$\lambda$<0.14874
10	0.15025	0.1487<$\lambda$<0.15025
11	0.16083	0.1502<$\lambda$<0.16083
12	0.16592	0.1608<$\lambda$<0.16592
13	1	0.1659<$\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