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

$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &A1 &A2 &A3 &A4 &A5 &A6 &A7 &A8 &A9 &A10\\ \hline A1 &0 &0.046 &0.046 &0.067 &0.081 &0.077 &0.042 &0.046 &0.077 &0.091\\ \hline A2 &0.074 &0 &0.018 &0.074 &0.056 &0.042 &0.053 &0.042 &0.067 &0.088\\ \hline A3 &0.07 &0.028 &0 &0.049 &0.046 &0.035 &0.046 &0.056 &0.084 &0.074\\ \hline A4 &0.116 &0.035 &0.018 &0 &0.056 &0.067 &0.067 &0.067 &0.067 &0.07\\ \hline A5 &0.116 &0.035 &0.07 &0.035 &0 &0.095 &0.06 &0.07 &0.088 &0.081\\ \hline A6 &0.07 &0.088 &0.046 &0.074 &0.007 &0 &0.081 &0.077 &0.074 &0.074\\ \hline A7 &0.077 &0.109 &0.035 &0.035 &0.088 &0.063 &0 &0.084 &0.105 &0.067\\ \hline A8 &0.035 &0.046 &0.046 &0.039 &0.091 &0.088 &0.074 &0 &0.07 &0.084\\ \hline A9 &0.07 &0.039 &0.074 &0.035 &0.102 &0.095 &0.077 &0.074 &0 &0.109\\ \hline A10 &0.035 &0.07 &0.049 &0.035 &0.074 &0.074 &0.077 &0.074 &0.039 &0\\ \hline \end{array} $$

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

　　综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &A1 &A2 &A3 &A4 &A5 &A6 &A7 &A8 &A9 &A10\\ \hline A1 &0.094 &0.117 &0.105 &0.127 &0.162 &0.166 &0.126 &0.13 &0.166 &0.19\\ \hline A2 &0.153 &0.067 &0.073 &0.127 &0.134 &0.126 &0.126 &0.118 &0.147 &0.177\\ \hline A3 &0.145 &0.09 &0.053 &0.101 &0.121 &0.116 &0.116 &0.127 &0.159 &0.16\\ \hline A4 &0.198 &0.108 &0.079 &0.064 &0.141 &0.157 &0.146 &0.148 &0.156 &0.17\\ \hline A5 &0.209 &0.118 &0.136 &0.107 &0.099 &0.193 &0.151 &0.163 &0.188 &0.194\\ \hline A6 &0.159 &0.158 &0.103 &0.136 &0.1 &0.094 &0.161 &0.159 &0.165 &0.177\\ \hline A7 &0.179 &0.185 &0.105 &0.109 &0.184 &0.168 &0.097 &0.177 &0.206 &0.186\\ \hline A8 &0.128 &0.12 &0.106 &0.101 &0.172 &0.176 &0.155 &0.088 &0.162 &0.184\\ \hline A9 &0.173 &0.125 &0.141 &0.109 &0.195 &0.197 &0.171 &0.17 &0.111 &0.222\\ \hline A10 &0.12 &0.136 &0.102 &0.094 &0.149 &0.155 &0.15 &0.149 &0.126 &0.097\\ \hline \end{array} $$

$T$的平均数$\bar{x} $ 与总体标准差$ \sigma $的求解

均值$\bar{x} $

$\bar{x}= 0.14039188317699 $

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

$\sigma = 0.035993934202298 $

区段截取最小边界$ \lambda_{min}= \bar{x} $

$\lambda_{min} = 0.14039188317699 $

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

$\lambda_{max} = 0.17638581737929 $

\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} =0.14039188317699$

　　　$ \lambda_{max} =0.17638581737929$

$$ \tilde A=\begin{array}{c|c|c|c|c|c|c}{M_{10 \times10}} &A1 &A2 &A3 &A4 &A5 &A6 &A7 &A8 &A9 &A10\\ \hline A1 &0 &0 &0 &0 &0.162 &0.16622 &0 &0 &0.166 &1\\ \hline A2 &0.15335 &0 &0 &0 &0 &0 &0 &0 &0.14715 &1\\ \hline A3 &0.14498 &0 &0 &0 &0 &0 &0 &0 &0.15948 &0.16028\\ \hline A4 &1 &0 &0 &0 &0.1414 &0.15668 &0.14594 &0.14753 &0.1565 &0.17037\\ \hline A5 &1 &0 &0 &0 &0 &1 &0.15125 &0.16251 &1 &1\\ \hline A6 &0.15912 &0.15827 &0 &0 &0 &0 &0.16146 &0.15931 &0.16526 &1\\ \hline A7 &1 &1 &0 &0 &1 &0.16829 &0 &1 &1 &1\\ \hline A8 &0 &0 &0 &0 &0.17192 &0.17605 &0.15482 &0 &0.16161 &1\\ \hline A9 &0.17331 &0 &0.14144 &0 &1 &1 &0.17081 &0.17013 &0 &1\\ \hline A10 &0 &0 &0 &0 &0.14901 &0.15454 &0.15012 &0.14861 &0 &0\\ \hline \end{array} $$

序号	阈值集合中——特征阈值	聚类特征-对应截距$\lambda $数值区段
1	0.14144	0<$\lambda$<0.14144
2	0.15454	0.1414<$\lambda$<0.15454
3	0.15948	0.1545<$\lambda$<0.15948
4	0.16028	0.1595<$\lambda$<0.16028
5	0.16526	0.1603<$\lambda$<0.16526
6	0.166	0.1653<$\lambda$<0.166
7	0.16622	0.166<$\lambda$<0.16622
8	0.17081	0.1662<$\lambda$<0.17081
9	0.17192	0.1708<$\lambda$<0.17192
10	0.17605	0.1719<$\lambda$<0.17605
11	1	0.176<$\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