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

$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &A1 &A2 &A3 &A4 &A5 &A6 &A7 &A8 &A9 &A10\\ \hline A1 &0 &0.048 &0.048 &0.07 &0.085 &0.081 &0.044 &0.048 &0.081 &0.096\\ \hline A2 &0.078 &0 &0.018 &0.078 &0.059 &0.044 &0.055 &0.044 &0.07 &0.092\\ \hline A3 &0.074 &0.03 &0 &0.052 &0.048 &0.037 &0.048 &0.059 &0.089 &0.078\\ \hline A4 &0.122 &0.037 &0.018 &0 &0.059 &0.07 &0.07 &0.07 &0.07 &0.074\\ \hline A5 &0.122 &0.037 &0.074 &0.037 &0 &0.1 &0.063 &0.074 &0.092 &0.085\\ \hline A6 &0.074 &0.092 &0.048 &0.078 &0.007 &0 &0.085 &0.081 &0.078 &0.078\\ \hline A7 &0.081 &0.114 &0.037 &0.037 &0.092 &0.066 &0 &0.089 &0.111 &0.07\\ \hline A8 &0.037 &0.048 &0.048 &0.041 &0.096 &0.092 &0.078 &0 &0.074 &0.089\\ \hline A9 &0.074 &0.041 &0.078 &0.037 &0.107 &0.1 &0.081 &0.078 &0 &0.114\\ \hline A10 &0.037 &0.074 &0.052 &0.037 &0.078 &0.078 &0.081 &0.078 &0.041 &0\\ \hline \end{array} $$

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

　　综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &A1 &A2 &A3 &A4 &A5 &A6 &A7 &A8 &A9 &A10\\ \hline A1 &0.111 &0.133 &0.119 &0.142 &0.182 &0.187 &0.144 &0.149 &0.187 &0.213\\ \hline A2 &0.172 &0.079 &0.084 &0.141 &0.151 &0.144 &0.143 &0.135 &0.166 &0.198\\ \hline A3 &0.163 &0.103 &0.063 &0.114 &0.138 &0.133 &0.132 &0.144 &0.178 &0.18\\ \hline A4 &0.22 &0.123 &0.091 &0.076 &0.16 &0.177 &0.164 &0.166 &0.177 &0.193\\ \hline A5 &0.233 &0.135 &0.152 &0.122 &0.117 &0.217 &0.172 &0.184 &0.212 &0.22\\ \hline A6 &0.18 &0.176 &0.117 &0.151 &0.118 &0.112 &0.181 &0.179 &0.186 &0.2\\ \hline A7 &0.202 &0.205 &0.12 &0.124 &0.207 &0.191 &0.115 &0.199 &0.231 &0.211\\ \hline A8 &0.147 &0.136 &0.12 &0.115 &0.192 &0.197 &0.174 &0.104 &0.182 &0.207\\ \hline A9 &0.196 &0.143 &0.158 &0.124 &0.218 &0.221 &0.192 &0.192 &0.132 &0.249\\ \hline A10 &0.138 &0.152 &0.115 &0.107 &0.167 &0.174 &0.168 &0.167 &0.145 &0.115\\ \hline \end{array} $$

$T$的平均数$\bar{x} $ 与总体标准差$ \sigma $的求解

均值$\bar{x} $

$\bar{x}= 0.15887482827128 $

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

$\sigma = 0.039276069728989 $

区段截取最小边界$ \lambda_{min}= \bar{x} $

$\lambda_{min} = 0.15887482827128 $

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

$\lambda_{max} = 0.19815089800027 $

\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} =0.15887482827128$

　　　$ \lambda_{max} =0.19815089800027$

$$ \tilde A=\begin{array}{c|c|c|c|c|c|c}{M_{10 \times10}} &A1 &A2 &A3 &A4 &A5 &A6 &A7 &A8 &A9 &A10\\ \hline A1 &0 &0 &0 &0 &0.18172 &0.187 &0 &0 &0.18685 &1\\ \hline A2 &0.17217 &0 &0 &0 &0 &0 &0 &0 &0.16588 &0.19793\\ \hline A3 &0.16283 &0 &0 &0 &0 &0 &0 &0 &0.17825 &0.1804\\ \hline A4 &1 &0 &0 &0 &0.16019 &0.17696 &0.1644 &0.16628 &0.17684 &0.19279\\ \hline A5 &1 &0 &0 &0 &0 &1 &0.17153 &0.18353 &1 &1\\ \hline A6 &0.17958 &0.17624 &0 &0 &0 &0 &0.18096 &0.1789 &0.18633 &1\\ \hline A7 &1 &1 &0 &0 &1 &0.19117 &0 &1 &1 &1\\ \hline A8 &0 &0 &0 &0 &0.19218 &0.19736 &0.17394 &0 &0.18243 &1\\ \hline A9 &0.19631 &0 &0 &0 &1 &1 &0.19245 &0.19202 &0 &1\\ \hline A10 &0 &0 &0 &0 &0.16723 &0.17374 &0.168 &0.16663 &0 &0\\ \hline \end{array} $$

序号	阈值集合中——特征阈值	聚类特征-对应截距$\lambda $数值区段
1	0.17374	0<$\lambda$<0.17374
2	0.17825	0.1737<$\lambda$<0.17825
3	0.1804	0.1782<$\lambda$<0.1804
4	0.18633	0.1804<$\lambda$<0.18633
5	0.18685	0.1863<$\lambda$<0.18685
6	0.187	0.1869<$\lambda$<0.187
7	0.19218	0.187<$\lambda$<0.19218
8	0.19245	0.1922<$\lambda$<0.19245
9	0.19736	0.1925<$\lambda$<0.19736
10	0.19793	0.1974<$\lambda$<0.19793
11	1	0.1979<$\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