流程图


输入

直接影响矩阵

参数设置

第一、归一化方法的设置

第二、截距值的获得

输出结果

第一、一组成对的对抗层级拓扑图

第二、带综合影响值的MR的直角坐标几何分布图

选择规范化方式

选择截距方式

原始矩阵(直接影响矩阵)为


$$Ori=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{13 \times13}} &S1 &S2 &S3 &S4 &S5 &S6 &S7 &S8 &S9 &S10 &S11 &S12 &S13\\ \hline S1 &0 &10 &11 &10 &21 &25 &13 &20 &29 &25 &24 &18 &27\\ \hline S2 &13 &0 &14 &6 &19 &21 &23 &16 &10 &18 &20 &15 &29\\ \hline S3 &17 &10 &0 &20 &24 &29 &16 &29 &30 &34 &27 &18 &26\\ \hline S4 &16 &11 &11 &0 &18 &9 &4 &18 &8 &12 &14 &15 &12\\ \hline S5 &11 &13 &24 &16 &0 &19 &11 &13 &24 &35 &18 &15 &29\\ \hline S6 &10 &15 &17 &30 &26 &0 &11 &12 &11 &26 &25 &14 &29\\ \hline S7 &13 &13 &7 &13 &6 &15 &0 &10 &6 &19 &22 &13 &16\\ \hline S8 &15 &15 &18 &10 &13 &11 &7 &0 &26 &14 &15 &19 &26\\ \hline S9 &22 &17 &29 &12 &30 &21 &6 &29 &0 &34 &19 &16 &26\\ \hline S10 &14 &7 &29 &29 &12 &18 &8 &25 &34 &0 &10 &33 &26\\ \hline S11 &14 &7 &10 &22 &16 &22 &5 &20 &26 &24 &0 &19 &30\\ \hline S12 &17 &14 &15 &6 &10 &3 &7 &23 &24 &19 &15 &0 &6\\ \hline S13 &23 &22 &26 &23 &20 &15 &12 &30 &27 &29 &24 &20 &0\\ \hline \end{array} $$

规范直接关系矩阵求解过程 $$ \require{cancel} \require{AMScd} \begin{CD} O @>>>N \\ \end{CD} $$


  • $$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{13 \times13}} &S1 &S2 &S3 &S4 &S5 &S6 &S7 &S8 &S9 &S10 &S11 &S12 &S13\\ \hline S1 &0 &0.025 &0.027 &0.025 &0.052 &0.062 &0.032 &0.05 &0.072 &0.062 &0.06 &0.045 &0.067\\ \hline S2 &0.032 &0 &0.035 &0.015 &0.047 &0.052 &0.057 &0.04 &0.025 &0.045 &0.05 &0.037 &0.072\\ \hline S3 &0.042 &0.025 &0 &0.05 &0.06 &0.072 &0.04 &0.072 &0.075 &0.084 &0.067 &0.045 &0.065\\ \hline S4 &0.04 &0.027 &0.027 &0 &0.045 &0.022 &0.01 &0.045 &0.02 &0.03 &0.035 &0.037 &0.03\\ \hline S5 &0.027 &0.032 &0.06 &0.04 &0 &0.047 &0.027 &0.032 &0.06 &0.087 &0.045 &0.037 &0.072\\ \hline S6 &0.025 &0.037 &0.042 &0.075 &0.065 &0 &0.027 &0.03 &0.027 &0.065 &0.062 &0.035 &0.072\\ \hline S7 &0.032 &0.032 &0.017 &0.032 &0.015 &0.037 &0 &0.025 &0.015 &0.047 &0.055 &0.032 &0.04\\ \hline S8 &0.037 &0.037 &0.045 &0.025 &0.032 &0.027 &0.017 &0 &0.065 &0.035 &0.037 &0.047 &0.065\\ \hline S9 &0.055 &0.042 &0.072 &0.03 &0.075 &0.052 &0.015 &0.072 &0 &0.084 &0.047 &0.04 &0.065\\ \hline S10 &0.035 &0.017 &0.072 &0.072 &0.03 &0.045 &0.02 &0.062 &0.084 &0 &0.025 &0.082 &0.065\\ \hline S11 &0.035 &0.017 &0.025 &0.055 &0.04 &0.055 &0.012 &0.05 &0.065 &0.06 &0 &0.047 &0.075\\ \hline S12 &0.042 &0.035 &0.037 &0.015 &0.025 &0.007 &0.017 &0.057 &0.06 &0.047 &0.037 &0 &0.015\\ \hline S13 &0.057 &0.055 &0.065 &0.057 &0.05 &0.037 &0.03 &0.075 &0.067 &0.072 &0.06 &0.05 &0\\ \hline \end{array} $$

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


  综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{13 \times13}} &S1 &S2 &S3 &S4 &S5 &S6 &S7 &S8 &S9 &S10 &S11 &S12 &S13\\ \hline S1 &0.049 &0.065 &0.085 &0.078 &0.106 &0.112 &0.062 &0.112 &0.136 &0.134 &0.115 &0.1 &0.136\\ \hline S2 &0.073 &0.035 &0.083 &0.062 &0.093 &0.096 &0.082 &0.094 &0.083 &0.107 &0.099 &0.085 &0.131\\ \hline S3 &0.098 &0.072 &0.069 &0.111 &0.123 &0.131 &0.074 &0.145 &0.151 &0.167 &0.132 &0.111 &0.147\\ \hline S4 &0.069 &0.052 &0.062 &0.032 &0.078 &0.056 &0.03 &0.084 &0.064 &0.076 &0.071 &0.072 &0.075\\ \hline S5 &0.075 &0.071 &0.115 &0.092 &0.056 &0.098 &0.057 &0.097 &0.125 &0.155 &0.1 &0.093 &0.139\\ \hline S6 &0.071 &0.074 &0.095 &0.122 &0.114 &0.05 &0.056 &0.091 &0.092 &0.132 &0.114 &0.088 &0.136\\ \hline S7 &0.063 &0.057 &0.053 &0.066 &0.051 &0.07 &0.02 &0.066 &0.059 &0.092 &0.09 &0.069 &0.085\\ \hline S8 &0.077 &0.07 &0.091 &0.067 &0.078 &0.071 &0.043 &0.055 &0.118 &0.096 &0.085 &0.092 &0.12\\ \hline S9 &0.106 &0.085 &0.134 &0.089 &0.133 &0.111 &0.05 &0.141 &0.079 &0.163 &0.111 &0.103 &0.143\\ \hline S10 &0.085 &0.06 &0.128 &0.121 &0.088 &0.097 &0.051 &0.128 &0.15 &0.077 &0.085 &0.136 &0.133\\ \hline S11 &0.079 &0.055 &0.079 &0.101 &0.091 &0.1 &0.04 &0.108 &0.124 &0.125 &0.053 &0.098 &0.136\\ \hline S12 &0.074 &0.061 &0.076 &0.05 &0.063 &0.046 &0.039 &0.1 &0.105 &0.096 &0.076 &0.04 &0.066\\ \hline S13 &0.11 &0.098 &0.126 &0.113 &0.111 &0.097 &0.064 &0.145 &0.142 &0.152 &0.123 &0.113 &0.083\\ \hline \end{array} $$

区段截取的处理


$T$的相关统计数据求解

平均数,均值 $\bar{x}$ 

$\bar{x}= 0.091796973077219 $

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

$\sigma = 0.030916125686689 $

样本标准差一:$S=\sqrt { \frac {\sum \limits_{i=1}^{n^2} ({x_i-\bar{x}})^2 }{n^2-1} }$ ( $n$为要素的数目)

$S = 0.031008001448484 $

样本标准差二:$ \bar {S}=\sqrt { \frac {\sum \limits_{i=1}^{n^2} ({x_i-\bar{x}})^2 }{n^2-n} } $ ( $n$为要素的数目)

$ \bar {S}= 0.032178523838602 $

标准误差 $\sigma_{s}= \frac {\sigma}{n }$ ( $n$为要素的数目)

$\sigma_{s}= 0.0070613056213246 $

方差 $ {\sigma}^{2}= \sigma ^{2} $

$\sigma^{2}= 0.00095580682747518 $

选择的截距方式为:$\lambda= \bar{x}+ \sigma_{s}$

$\lambda=0.098858278698544 $

\begin{CD} T@>\lambda=0.098858278698544>> A \\ \end{CD}

$$ a_{ij}= \begin{cases} 1 , \text{ $e_i$}\rightarrow \text{$e_j$ 当: $ t_{ij} > \lambda=0.098858278698544 $} \\ 0, \text{ $e_i$}\rightarrow \text{$e_j$ 当: $ t_{ij} < \lambda=0.098858278698544 $} \end{cases} $$

$\lambda= 0.098858278698544$ 截取后的关系矩阵$ A$

$$ A=\begin{array}{c|c|c|c|c|c|c}{M_{13 \times13}} &S1 &S2 &S3 &S4 &S5 &S6 &S7 &S8 &S9 &S10 &S11 &S12 &S13\\ \hline S1 &0 &0 &0 &0 &1 &1 &0 &1 &1 &1 &1 &1 &1\\ \hline S2 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1 &1 &0 &1\\ \hline S3 &0 &0 &0 &1 &1 &1 &0 &1 &1 &1 &1 &1 &1\\ \hline S4 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline S5 &0 &0 &1 &0 &0 &0 &0 &0 &1 &1 &1 &0 &1\\ \hline S6 &0 &0 &0 &1 &1 &0 &0 &0 &0 &1 &1 &0 &1\\ \hline S7 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline S8 &0 &0 &0 &0 &0 &0 &0 &0 &1 &0 &0 &0 &1\\ \hline S9 &1 &0 &1 &0 &1 &1 &0 &1 &0 &1 &1 &1 &1\\ \hline S10 &0 &0 &1 &1 &0 &0 &0 &1 &1 &0 &0 &1 &1\\ \hline S11 &0 &0 &0 &1 &0 &1 &0 &1 &1 &1 &0 &0 &1\\ \hline S12 &0 &0 &0 &0 &0 &0 &0 &1 &1 &0 &0 &0 &0\\ \hline S13 &1 &0 &1 &1 &1 &0 &0 &1 &1 &1 &1 &1 &0\\ \hline \end{array} $$