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

$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &C1 &C2 &C3 &C4 &C5 &C6 &C7 &C8 &C9 &C10\\ \hline C1 &0 &0.099 &0.048 &0.07 &0.084 &0.081 &0.081 &0.011 &0.044 &0.095\\ \hline C2 &0.077 &0 &0.018 &0.077 &0.059 &0.044 &0.055 &0.044 &0.07 &0.092\\ \hline C3 &0.073 &0.029 &0 &0.051 &0.048 &0.037 &0.048 &0.059 &0.088 &0.077\\ \hline C4 &0.121 &0.037 &0.018 &0 &0.059 &0.07 &0.07 &0.07 &0.07 &0.073\\ \hline C5 &0.121 &0.037 &0.073 &0.037 &0 &0.099 &0.062 &0.073 &0.092 &0.084\\ \hline C6 &0.073 &0.092 &0.048 &0.077 &0.007 &0 &0.084 &0.081 &0.077 &0.077\\ \hline C7 &0.081 &0.113 &0.037 &0.037 &0.092 &0.066 &0 &0.088 &0.073 &0.037\\ \hline C8 &0.037 &0.048 &0.048 &0.04 &0.095 &0.092 &0.077 &0 &0.073 &0.088\\ \hline C9 &0.073 &0.04 &0.077 &0.037 &0.033 &0.026 &0.081 &0.077 &0 &0.113\\ \hline C10 &0.037 &0.073 &0.051 &0.037 &0.077 &0.077 &0.081 &0.077 &0.04 &0\\ \hline \end{array} $$

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

　　综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &C1 &C2 &C3 &C4 &C5 &C6 &C7 &C8 &C9 &C10\\ \hline C1 &0.106 &0.183 &0.11 &0.138 &0.164 &0.166 &0.173 &0.103 &0.137 &0.198\\ \hline C2 &0.163 &0.08 &0.077 &0.135 &0.133 &0.124 &0.14 &0.121 &0.147 &0.183\\ \hline C3 &0.154 &0.104 &0.057 &0.108 &0.119 &0.112 &0.129 &0.13 &0.159 &0.166\\ \hline C4 &0.21 &0.126 &0.084 &0.07 &0.141 &0.156 &0.162 &0.15 &0.155 &0.177\\ \hline C5 &0.222 &0.137 &0.143 &0.115 &0.095 &0.192 &0.169 &0.165 &0.187 &0.202\\ \hline C6 &0.169 &0.176 &0.109 &0.144 &0.097 &0.09 &0.177 &0.163 &0.164 &0.183\\ \hline C7 &0.181 &0.196 &0.103 &0.11 &0.173 &0.156 &0.1 &0.171 &0.165 &0.152\\ \hline C8 &0.138 &0.135 &0.112 &0.108 &0.172 &0.175 &0.169 &0.09 &0.162 &0.19\\ \hline C9 &0.159 &0.122 &0.132 &0.099 &0.114 &0.109 &0.164 &0.152 &0.084 &0.204\\ \hline C10 &0.13 &0.151 &0.109 &0.101 &0.15 &0.156 &0.164 &0.154 &0.126 &0.1\\ \hline \end{array} $$

$T$的平均数$\bar{x} $ 与总体标准差$ \sigma $的求解

均值$\bar{x} $

$\bar{x}= 0.1418587929301 $

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

$\sigma = 0.034647755294855 $

区段截取最小边界$ \lambda_{min}= \bar{x} $

$\lambda_{min} = 0.1418587929301 $

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

$\lambda_{max} = 0.17650654822496 $

\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} =0.1418587929301$

　　　$ \lambda_{max} =0.17650654822496$

$$ \tilde A=\begin{array}{c|c|c|c|c|c|c}{M_{10 \times10}} &C1 &C2 &C3 &C4 &C5 &C6 &C7 &C8 &C9 &C10\\ \hline C1 &0 &1 &0 &0 &0.16371 &0.16643 &0.173 &0 &0 &1\\ \hline C2 &0.16324 &0 &0 &0 &0 &0 &0 &0 &0.14661 &1\\ \hline C3 &0.1538 &0 &0 &0 &0 &0 &0 &0 &0.15943 &0.1661\\ \hline C4 &1 &0 &0 &0 &0 &0.15576 &0.16228 &0.14973 &0.15457 &1\\ \hline C5 &1 &0 &0.14324 &0 &0 &1 &0.16858 &0.16521 &1 &1\\ \hline C6 &0.16941 &0.17632 &0 &0.14401 &0 &0 &1 &0.16311 &0.16424 &1\\ \hline C7 &1 &1 &0 &0 &0.17327 &0.15576 &0 &0.17059 &0.16531 &0.15175\\ \hline C8 &0 &0 &0 &0 &0.1716 &0.17526 &0.16893 &0 &0.16181 &1\\ \hline C9 &0.15852 &0 &0 &0 &0 &0 &0.16445 &0.15241 &0 &1\\ \hline C10 &0 &0.15095 &0 &0 &0.15031 &0.15557 &0.16392 &0.15362 &0 &0\\ \hline \end{array} $$

序号	阈值集合中——特征阈值	聚类特征-对应截距$\lambda $数值区段
1	0.14324	0<$\lambda$<0.14324
2	0.14401	0.1432<$\lambda$<0.14401
3	0.16392	0.144<$\lambda$<0.16392
4	0.16445	0.1639<$\lambda$<0.16445
5	0.1661	0.1644<$\lambda$<0.1661
6	0.17059	0.1661<$\lambda$<0.17059
7	0.173	0.1706<$\lambda$<0.173
8	0.17327	0.173<$\lambda$<0.17327
9	0.17526	0.1733<$\lambda$<0.17526
10	1	0.1753<$\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