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

$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &C1 &C2 &C3 &C4 &C5 &C6 &C7 &C8 &C9 &C10\\ \hline C1 &0 &0.107 &0.052 &0.075 &0.091 &0.087 &0.087 &0.012 &0.048 &0.103\\ \hline C2 &0.083 &0 &0.02 &0.083 &0.063 &0.048 &0.059 &0.048 &0.075 &0.099\\ \hline C3 &0.079 &0.032 &0 &0.056 &0.052 &0.04 &0.052 &0.063 &0.095 &0.083\\ \hline C4 &0.131 &0.04 &0.02 &0 &0.063 &0.075 &0.075 &0.075 &0.075 &0.079\\ \hline C5 &0.131 &0.04 &0.079 &0.04 &0 &0.107 &0.067 &0.079 &0.099 &0.091\\ \hline C6 &0.079 &0.099 &0.052 &0.083 &0.008 &0 &0.091 &0.087 &0.083 &0.083\\ \hline C7 &0.087 &0.123 &0.04 &0.04 &0.099 &0.071 &0 &0.095 &0.079 &0.04\\ \hline C8 &0.04 &0.052 &0.052 &0.044 &0.103 &0.099 &0.083 &0 &0.079 &0.095\\ \hline C9 &0.079 &0.044 &0.083 &0.04 &0.036 &0.028 &0.087 &0.083 &0 &0.123\\ \hline C10 &0.04 &0.079 &0.056 &0.04 &0.083 &0.083 &0.087 &0.083 &0.044 &0\\ \hline \end{array} $$

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

　　综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &C1 &C2 &C3 &C4 &C5 &C6 &C7 &C8 &C9 &C10\\ \hline C1 &0.139 &0.22 &0.135 &0.167 &0.198 &0.202 &0.211 &0.133 &0.17 &0.24\\ \hline C2 &0.198 &0.107 &0.098 &0.161 &0.162 &0.154 &0.173 &0.149 &0.178 &0.222\\ \hline C3 &0.187 &0.131 &0.075 &0.131 &0.146 &0.14 &0.159 &0.158 &0.191 &0.202\\ \hline C4 &0.25 &0.158 &0.106 &0.093 &0.172 &0.19 &0.199 &0.182 &0.189 &0.217\\ \hline C5 &0.267 &0.173 &0.173 &0.144 &0.125 &0.231 &0.208 &0.202 &0.227 &0.248\\ \hline C6 &0.207 &0.212 &0.134 &0.173 &0.127 &0.119 &0.215 &0.197 &0.2 &0.224\\ \hline C7 &0.221 &0.234 &0.128 &0.137 &0.208 &0.191 &0.133 &0.206 &0.202 &0.192\\ \hline C8 &0.173 &0.167 &0.137 &0.134 &0.206 &0.211 &0.206 &0.119 &0.197 &0.232\\ \hline C9 &0.193 &0.152 &0.157 &0.123 &0.143 &0.139 &0.199 &0.184 &0.112 &0.244\\ \hline C10 &0.163 &0.183 &0.132 &0.125 &0.181 &0.188 &0.199 &0.186 &0.157 &0.133\\ \hline \end{array} $$

$T$的平均数$\bar{x} $ 与总体标准差$ \sigma $的求解

均值$\bar{x} $

$\bar{x}= 0.17424953075379 $

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

$\sigma = 0.039569492962048 $

区段截取最小边界$ \lambda_{min}= \bar{x} $

$\lambda_{min} = 0.17424953075379 $

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

$\lambda_{max} = 0.21381902371583 $

\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} =0.17424953075379$

　　　$ \lambda_{max} =0.21381902371583$

$$ \tilde A=\begin{array}{c|c|c|c|c|c|c}{M_{10 \times10}} &C1 &C2 &C3 &C4 &C5 &C6 &C7 &C8 &C9 &C10\\ \hline C1 &0 &1 &0 &0 &0.19766 &0.20187 &0.21061 &0 &0 &1\\ \hline C2 &0.19826 &0 &0 &0 &0 &0 &0 &0 &0.17829 &1\\ \hline C3 &0.18681 &0 &0 &0 &0 &0 &0 &0 &0.19103 &0.20195\\ \hline C4 &1 &0 &0 &0 &0 &0.18992 &0.19857 &0.18249 &0.18884 &1\\ \hline C5 &1 &0 &0 &0 &0 &1 &0.20844 &0.20197 &1 &1\\ \hline C6 &0.20747 &0.21228 &0 &0 &0 &0 &1 &0.19743 &0.19978 &1\\ \hline C7 &1 &1 &0 &0 &0.20847 &0.19093 &0 &0.20597 &0.20174 &0.1917\\ \hline C8 &0 &0 &0 &0 &0.20575 &0.21101 &0.20592 &0 &0.19713 &1\\ \hline C9 &0.19341 &0 &0 &0 &0 &0 &0.19916 &0.18406 &0 &1\\ \hline C10 &0 &0.18307 &0 &0 &0.18141 &0.18821 &0.19864 &0.18553 &0 &0\\ \hline \end{array} $$

序号	阈值集合中——特征阈值	聚类特征-对应截距$\lambda $数值区段
1	0.19864	0<$\lambda$<0.19864
2	0.19916	0.1986<$\lambda$<0.19916
3	0.20195	0.1992<$\lambda$<0.20195
4	0.20597	0.202<$\lambda$<0.20597
5	0.20847	0.206<$\lambda$<0.20847
6	0.21061	0.2085<$\lambda$<0.21061
7	0.21101	0.2106<$\lambda$<0.21101
8	1	0.211<$\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