G-Sharpen-DEMATEL,灰色决策与实验室方法在线计算

流程图

灰度的操作

第一、每位专家打分为E共n个专家

第二、每个打分可以拆解我上界与下界两个值。

$$ \begin{array} {|c|c|c|c|} \hline {　值域范围　} &{5分制}& {表述一}& {表述二} & {下界}& { 上界} \\ \hline 0&0 &\color{red}{非常傻逼} &\color{blue}{垃圾} & \color{red}{ 0 } & \color{blue}{0 } \\ \hline 0-0.25&1 &\color{red}{真傻逼} &\color{blue}{有点挫} & \color{red}{ 0 } & \color{blue}{0.25} \\ \hline 0.25-0.5&2 &\color{red}{恩} &\color{blue}{还行} & \color{red}{ 0.25 } & \color{blue}{0.5} \\ \hline 0.5-0.75&3 &\color{red}{有点牛逼} &\color{blue}{好} & \color{red}{ 0.5 } & \color{blue}{0.75} \\ \hline 0.75-1 &4 &\color{red}{大神} &\color{blue}{哇塞} & \color{red}{ 0.75 } & \color{blue}{1} \\ \hline 1 &5 &\color{red}{永远的神} &\color{blue}{神一样的存在} & \color{red}{ 1 } & \color{blue}{1} \\ \hline \end{array} $$

第三、下界的值相加求平均值（不求亦可以）得到 min 直接影响矩阵，上界的值相加求平均值（不求亦可以）得到 Max直接影响矩阵

清晰化上界矩阵与下界清晰化的算法

上界矩阵：$O_{max}=UP=(u)_{n \times n}$

下界矩阵：$O_{min}=DOWN=(v)_{n \times n}$

清晰化矩阵：$O_{sharp}=SHARPEN=(s)_{n \times n}$

$ \tilde u_{ij}= \frac {u_{ij} - Min (u_{j})} { Max(u_{j})- Min (v_{j})} $

$ \tilde v_{ij}= \frac {v_{ij} - Min (v_{j})} { Max(u_{j})- Min (v_{j})} $

$ y_{ij}= \frac {　\tilde　v_{ij} (1- \tilde v_{ij})+\tilde u_{ij}^2 } {1-　\tilde v_{ij} + \tilde　u_{ij} } $

$ s_{ij}= y_{ij}[(Max(u_{j})- Min (v_{j})) ]+ Min (v_{j})$

由于主对角线中的值都为0，即 $Min (u_{j})=0 ,Min (v_{j})=0$ 故上述四个公式简化如下

$ \tilde u_{ij}= \frac {u_{ij} } { Max(u_{j})} $

$ \tilde v_{ij}= \frac {v_{ij} } { Max(u_{j})} $

$ y_{ij}= \frac {　\tilde　v_{ij} (1- \tilde v_{ij})+\tilde u_{ij}^2 } {1-　\tilde v_{ij} + \tilde　u_{ij} } $

$ s_{ij}= y_{ij}(Max(u_{j}))$

$ s_{ij}= Max(u_{j}) \frac {　\tilde　v_{ij} (1- \tilde v_{ij})+(\tilde u_{ij})^2 } {1-\tilde v_{ij} + \tilde　u_{ij} }$

$ s_{ij}= Max(u_{j}) \frac {　\tilde　v_{ij} - (\tilde v_{ij})^2+(\tilde u_{ij})^2 } {1-\tilde v_{ij} + \tilde　u_{ij} }$

$ s_{ij}= \frac{v_{ij}- \frac {(v_{ij})^2}{Max(u_{j})}+\frac {( u_{ij})^2}{Max(u_{j})}} {1- \frac {v_{ij}}{ Max(u_{j})} + \frac {u_{ij}}{Max(u_{j})} }$

$ s_{ij}= \frac{v_{ij}Max(u_{j})- (v_{ij})^2+( u_{ij})^2} {Max(u_{j})-v_{ij} + u_{ij}}$

归一化方法选择，选择参数

三组数据分析

总共有7位专家打分$$上界求和 =\begin{array}{c|c|c|c|c|c|c}{M_{10 \times10}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10\\ \hline F1 &0 &4.75 &4.5 &1.75 &5.25 &3.5 &4.5 &4.75 &2.75 &1.25\\ \hline F2 &2 &0 &6.25 &1.75 &0 &5 &6.25 &3.5 &2.25 &7\\ \hline F3 &4.75 &1 &0 &0 &3.5 &0 &5.25 &0 &7 &1.75\\ \hline F4 &5.25 &1.5 &6.25 &0 &0 &1 &5.25 &0 &2.75 &2.5\\ \hline F5 &5.25 &0.75 &0 &0 &0 &0 &0 &0.75 &7 &5.5\\ \hline F6 &1.75 &6.25 &5.25 &2.25 &3.5 &0 &5.25 &0 &1.75 &1.75\\ \hline F7 &3.5 &2.5 &0 &1 &0 &0 &0 &0 &2.25 &1.75\\ \hline F8 &3 &5.25 &5 &1.75 &0 &0 &1.75 &0 &3 &3.5\\ \hline F9 &1.5 &1.75 &1.75 &2 &0.75 &0 &3.5 &0 &0 &5.25\\ \hline F10 &2 &2.25 &7 &0 &1.75 &2 &3.5 &1.75 &0 &0\\ \hline \end{array} $$$$下界求和 =\begin{array}{c|c|c|c|c|c|c}{M_{10 \times10}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10\\ \hline F1 &0 &3 &2.75 &0 &3.5 &1.75 &2.75 &3 &1.25 &0.75\\ \hline F2 &0.25 &0 &6 &0 &0 &3.25 &6 &1.75 &0.5 &7\\ \hline F3 &3.5 &1 &0 &0 &1.75 &0 &3.5 &0 &5.25 &0\\ \hline F4 &3.5 &1 &6 &0 &0 &0.75 &3.5 &0 &1.75 &1.5\\ \hline F5 &3.5 &0 &0 &0 &0 &0 &0 &0.5 &7 &3.75\\ \hline F6 &1.25 &6 &3.5 &0.5 &1.75 &0 &3.5 &0 &0 &0\\ \hline F7 &1.75 &1 &0 &0.75 &0 &0 &0 &0 &1.5 &0\\ \hline F8 &2.25 &3.5 &3.25 &0 &0 &0 &0 &0 &2.25 &1.75\\ \hline F9 &0.75 &0 &0 &2 &0.5 &0 &1.75 &0 &0 &3.5\\ \hline F10 &1 &1.25 &5.25 &0 &0 &0.5 &1.75 &1.25 &0 &0\\ \hline \end{array} $$均值化与代入清晰化的计算公式后精确到小数点四位数字结果如下：$$Upper =\begin{array}{c|c|c|c|c|c|c}{M_{10 \times10}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10\\ \hline F1 &0 &0.6786 &0.6429 &0.25 &0.75 &0.5 &0.6429 &0.6786 &0.3929 &0.1786\\ \hline F2 &0.2857 &0 &0.8929 &0.25 &0 &0.7143 &0.8929 &0.5 &0.3214 &1\\ \hline F3 &0.6786 &0.1429 &0 &0 &0.5 &0 &0.75 &0 &1 &0.25\\ \hline F4 &0.75 &0.2143 &0.8929 &0 &0 &0.1429 &0.75 &0 &0.3929 &0.3571\\ \hline F5 &0.75 &0.1071 &0 &0 &0 &0 &0 &0.1071 &1 &0.7857\\ \hline F6 &0.25 &0.8929 &0.75 &0.3214 &0.5 &0 &0.75 &0 &0.25 &0.25\\ \hline F7 &0.5 &0.3571 &0 &0.1429 &0 &0 &0 &0 &0.3214 &0.25\\ \hline F8 &0.4286 &0.75 &0.7143 &0.25 &0 &0 &0.25 &0 &0.4286 &0.5\\ \hline F9 &0.2143 &0.25 &0.25 &0.2857 &0.1071 &0 &0.5 &0 &0 &0.75\\ \hline F10 &0.2857 &0.3214 &1 &0 &0.25 &0.2857 &0.5 &0.25 &0 &0\\ \hline \end{array} $$$$Lower =\begin{array}{c|c|c|c|c|c|c}{M_{10 \times10}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10\\ \hline F1 &0 &0.4286 &0.3929 &0 &0.5 &0.25 &0.3929 &0.4286 &0.1786 &0.1071\\ \hline F2 &0.0357 &0 &0.8571 &0 &0 &0.4643 &0.8571 &0.25 &0.0714 &1\\ \hline F3 &0.5 &0.1429 &0 &0 &0.25 &0 &0.5 &0 &0.75 &0\\ \hline F4 &0.5 &0.1429 &0.8571 &0 &0 &0.1071 &0.5 &0 &0.25 &0.2143\\ \hline F5 &0.5 &0 &0 &0 &0 &0 &0 &0.0714 &1 &0.5357\\ \hline F6 &0.1786 &0.8571 &0.5 &0.0714 &0.25 &0 &0.5 &0 &0 &0\\ \hline F7 &0.25 &0.1429 &0 &0.1071 &0 &0 &0 &0 &0.2143 &0\\ \hline F8 &0.3214 &0.5 &0.4643 &0 &0 &0 &0 &0 &0.3214 &0.25\\ \hline F9 &0.1071 &0 &0 &0.2857 &0.0714 &0 &0.25 &0 &0 &0.5\\ \hline F10 &0.1429 &0.1786 &0.75 &0 &0 &0.0714 &0.25 &0.1786 &0 &0\\ \hline \end{array} $$$$Sharpen =\begin{array}{c|c|c|c|c|c|c}{M_{10 \times10}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10\\ \hline F1 &0 &0.5982 &0.5536 &0.0625 &0.6875 &0.375 &0.5536 &0.5982 &0.2659 &0.1227\\ \hline F2 &0.0929 &0 &0.8879 &0.05 &0 &0.6071 &0.8879 &0.35 &0.1357 &1\\ \hline F3 &0.6028 &0.1429 &0 &0 &0.35 &0 &0.65 &0 &0.95 &0.05\\ \hline F4 &0.6641 &0.1587 &0.8915 &0 &0 &0.1126 &0.6641 &0 &0.3042 &0.2635\\ \hline F5 &0.65 &0.0104 &0 &0 &0 &0 &0 &0.0751 &1 &0.6929\\ \hline F6 &0.1971 &0.8915 &0.6641 &0.1417 &0.3594 &0 &0.6641 &0 &0.0547 &0.0547\\ \hline F7 &0.4167 &0.25 &0 &0.1167 &0 &0 &0 &0 &0.271 &0.0833\\ \hline F8 &0.375 &0.6875 &0.6429 &0.0625 &0 &0 &0.0625 &0 &0.375 &0.375\\ \hline F9 &0.1339 &0.0625 &0.0625 &0.2857 &0.0763 &0 &0.375 &0 &0 &0.6875\\ \hline F10 &0.1786 &0.2188 &0.95 &0 &0.05 &0.1218 &0.35 &0.1952 &0 &0\\ \hline \end{array} $$

数据比对后分别得到直接影响矩阵$ O$为

$$O-Upper=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10\\ \hline F1 &0 &0.679 &0.643 &0.25 &0.75 &0.5 &0.643 &0.679 &0.393 &0.179\\ \hline F2 &0.286 &0 &0.893 &0.25 &0 &0.714 &0.893 &0.5 &0.321 &1\\ \hline F3 &0.679 &0.143 &0 &0 &0.5 &0 &0.75 &0 &1 &0.25\\ \hline F4 &0.75 &0.214 &0.893 &0 &0 &0.143 &0.75 &0 &0.393 &0.357\\ \hline F5 &0.75 &0.107 &0 &0 &0 &0 &0 &0.107 &1 &0.786\\ \hline F6 &0.25 &0.893 &0.75 &0.321 &0.5 &0 &0.75 &0 &0.25 &0.25\\ \hline F7 &0.5 &0.357 &0 &0.143 &0 &0 &0 &0 &0.321 &0.25\\ \hline F8 &0.429 &0.75 &0.714 &0.25 &0 &0 &0.25 &0 &0.429 &0.5\\ \hline F9 &0.214 &0.25 &0.25 &0.286 &0.107 &0 &0.5 &0 &0 &0.75\\ \hline F10 &0.286 &0.321 &1 &0 &0.25 &0.286 &0.5 &0.25 &0 &0\\ \hline \end{array} $$

$$O-Lower=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10\\ \hline F1 &0 &0.429 &0.393 &0 &0.5 &0.25 &0.393 &0.429 &0.179 &0.107\\ \hline F2 &0.036 &0 &0.857 &0 &0 &0.464 &0.857 &0.25 &0.071 &1\\ \hline F3 &0.5 &0.143 &0 &0 &0.25 &0 &0.5 &0 &0.75 &0\\ \hline F4 &0.5 &0.143 &0.857 &0 &0 &0.107 &0.5 &0 &0.25 &0.214\\ \hline F5 &0.5 &0 &0 &0 &0 &0 &0 &0.071 &1 &0.536\\ \hline F6 &0.179 &0.857 &0.5 &0.071 &0.25 &0 &0.5 &0 &0 &0\\ \hline F7 &0.25 &0.143 &0 &0.107 &0 &0 &0 &0 &0.214 &0\\ \hline F8 &0.321 &0.5 &0.464 &0 &0 &0 &0 &0 &0.321 &0.25\\ \hline F9 &0.107 &0 &0 &0.286 &0.071 &0 &0.25 &0 &0 &0.5\\ \hline F10 &0.143 &0.179 &0.75 &0 &0 &0.071 &0.25 &0.179 &0 &0\\ \hline \end{array} $$

$$O-Sharpen=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10\\ \hline F1 &0 &0.598 &0.554 &0.063 &0.688 &0.375 &0.554 &0.598 &0.266 &0.123\\ \hline F2 &0.093 &0 &0.888 &0.05 &0 &0.607 &0.888 &0.35 &0.136 &1\\ \hline F3 &0.603 &0.143 &0 &0 &0.35 &0 &0.65 &0 &0.95 &0.05\\ \hline F4 &0.664 &0.159 &0.891 &0 &0 &0.113 &0.664 &0 &0.304 &0.264\\ \hline F5 &0.65 &0.01 &0 &0 &0 &0 &0 &0.075 &1 &0.693\\ \hline F6 &0.197 &0.891 &0.664 &0.142 &0.359 &0 &0.664 &0 &0.055 &0.055\\ \hline F7 &0.417 &0.25 &0 &0.117 &0 &0 &0 &0 &0.271 &0.083\\ \hline F8 &0.375 &0.688 &0.643 &0.063 &0 &0 &0.063 &0 &0.375 &0.375\\ \hline F9 &0.134 &0.063 &0.063 &0.286 &0.076 &0 &0.375 &0 &0 &0.688\\ \hline F10 &0.179 &0.219 &0.95 &0 &0.05 &0.122 &0.35 &0.195 &0 &0\\ \hline \end{array} $$

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

归一化方法中最大值：5.1428571428571$$\mathcal{N-Upper}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10\\ \hline F1 &0 &0.132 &0.125 &0.049 &0.146 &0.097 &0.125 &0.132 &0.076 &0.035\\ \hline F2 &0.056 &0 &0.174 &0.049 &0 &0.139 &0.174 &0.097 &0.063 &0.194\\ \hline F3 &0.132 &0.028 &0 &0 &0.097 &0 &0.146 &0 &0.194 &0.049\\ \hline F4 &0.146 &0.042 &0.174 &0 &0 &0.028 &0.146 &0 &0.076 &0.069\\ \hline F5 &0.146 &0.021 &0 &0 &0 &0 &0 &0.021 &0.194 &0.153\\ \hline F6 &0.049 &0.174 &0.146 &0.063 &0.097 &0 &0.146 &0 &0.049 &0.049\\ \hline F7 &0.097 &0.069 &0 &0.028 &0 &0 &0 &0 &0.063 &0.049\\ \hline F8 &0.083 &0.146 &0.139 &0.049 &0 &0 &0.049 &0 &0.083 &0.097\\ \hline F9 &0.042 &0.049 &0.049 &0.056 &0.021 &0 &0.097 &0 &0 &0.146\\ \hline F10 &0.056 &0.063 &0.194 &0 &0.049 &0.056 &0.097 &0.049 &0 &0\\ \hline \end{array} $$归一化方法中最大值：3.8214285714286$$\mathcal{N-Lower}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10\\ \hline F1 &0 &0.112 &0.103 &0 &0.131 &0.065 &0.103 &0.112 &0.047 &0.028\\ \hline F2 &0.009 &0 &0.224 &0 &0 &0.121 &0.224 &0.065 &0.019 &0.262\\ \hline F3 &0.131 &0.037 &0 &0 &0.065 &0 &0.131 &0 &0.196 &0\\ \hline F4 &0.131 &0.037 &0.224 &0 &0 &0.028 &0.131 &0 &0.065 &0.056\\ \hline F5 &0.131 &0 &0 &0 &0 &0 &0 &0.019 &0.262 &0.14\\ \hline F6 &0.047 &0.224 &0.131 &0.019 &0.065 &0 &0.131 &0 &0 &0\\ \hline F7 &0.065 &0.037 &0 &0.028 &0 &0 &0 &0 &0.056 &0\\ \hline F8 &0.084 &0.131 &0.121 &0 &0 &0 &0 &0 &0.084 &0.065\\ \hline F9 &0.028 &0 &0 &0.075 &0.019 &0 &0.065 &0 &0 &0.131\\ \hline F10 &0.037 &0.047 &0.196 &0 &0 &0.019 &0.065 &0.047 &0 &0\\ \hline \end{array} $$归一化方法中最大值：4.6524056223948$$\mathcal{N-Sharpen}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10\\ \hline F1 &0 &0.129 &0.119 &0.013 &0.148 &0.081 &0.119 &0.129 &0.057 &0.026\\ \hline F2 &0.02 &0 &0.191 &0.011 &0 &0.131 &0.191 &0.075 &0.029 &0.215\\ \hline F3 &0.13 &0.031 &0 &0 &0.075 &0 &0.14 &0 &0.204 &0.011\\ \hline F4 &0.143 &0.034 &0.192 &0 &0 &0.024 &0.143 &0 &0.065 &0.057\\ \hline F5 &0.14 &0.002 &0 &0 &0 &0 &0 &0.016 &0.215 &0.149\\ \hline F6 &0.042 &0.192 &0.143 &0.03 &0.077 &0 &0.143 &0 &0.012 &0.012\\ \hline F7 &0.09 &0.054 &0 &0.025 &0 &0 &0 &0 &0.058 &0.018\\ \hline F8 &0.081 &0.148 &0.138 &0.013 &0 &0 &0.013 &0 &0.081 &0.081\\ \hline F9 &0.029 &0.013 &0.013 &0.061 &0.016 &0 &0.081 &0 &0 &0.148\\ \hline F10 &0.038 &0.047 &0.204 &0 &0.011 &0.026 &0.075 &0.042 &0 &0\\ \hline \end{array} $$

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

　　综合影响矩阵如下

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

Upper综合影响矩阵$$T-Upper=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10\\ \hline F1 &0.198 &0.291 &0.336 &0.118 &0.242 &0.174 &0.353 &0.203 &0.278 &0.246\\ \hline F2 &0.245 &0.174 &0.391 &0.115 &0.117 &0.21 &0.407 &0.167 &0.249 &0.364\\ \hline F3 &0.246 &0.134 &0.13 &0.05 &0.166 &0.054 &0.285 &0.058 &0.308 &0.185\\ \hline F4 &0.28 &0.162 &0.318 &0.051 &0.095 &0.09 &0.32 &0.065 &0.222 &0.203\\ \hline F5 &0.238 &0.121 &0.143 &0.045 &0.073 &0.056 &0.143 &0.078 &0.284 &0.264\\ \hline F6 &0.216 &0.292 &0.32 &0.117 &0.183 &0.077 &0.345 &0.072 &0.221 &0.224\\ \hline F7 &0.158 &0.13 &0.094 &0.056 &0.045 &0.042 &0.097 &0.04 &0.125 &0.124\\ \hline F8 &0.22 &0.254 &0.306 &0.099 &0.085 &0.073 &0.239 &0.067 &0.224 &0.243\\ \hline F9 &0.136 &0.124 &0.163 &0.084 &0.074 &0.045 &0.211 &0.043 &0.09 &0.229\\ \hline F10 &0.179 &0.163 &0.311 &0.042 &0.124 &0.104 &0.245 &0.097 &0.14 &0.122\\ \hline \end{array} $$Lower综合影响矩阵$$T-Lower=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10\\ \hline F1 &0.095 &0.187 &0.216 &0.02 &0.167 &0.097 &0.218 &0.145 &0.166 &0.135\\ \hline F2 &0.123 &0.104 &0.361 &0.023 &0.052 &0.149 &0.361 &0.102 &0.141 &0.326\\ \hline F3 &0.184 &0.082 &0.066 &0.026 &0.1 &0.024 &0.206 &0.032 &0.261 &0.078\\ \hline F4 &0.214 &0.107 &0.311 &0.021 &0.055 &0.058 &0.247 &0.038 &0.171 &0.124\\ \hline F5 &0.178 &0.049 &0.085 &0.026 &0.036 &0.022 &0.08 &0.052 &0.308 &0.208\\ \hline F6 &0.13 &0.28 &0.247 &0.035 &0.104 &0.046 &0.264 &0.04 &0.107 &0.11\\ \hline F7 &0.086 &0.058 &0.04 &0.035 &0.016 &0.014 &0.041 &0.015 &0.079 &0.033\\ \hline F8 &0.143 &0.179 &0.217 &0.015 &0.038 &0.034 &0.109 &0.035 &0.157 &0.145\\ \hline F9 &0.068 &0.03 &0.066 &0.081 &0.034 &0.013 &0.113 &0.018 &0.039 &0.156\\ \hline F10 &0.098 &0.092 &0.251 &0.011 &0.033 &0.037 &0.143 &0.066 &0.079 &0.047\\ \hline \end{array} $$Sharpen综合影响矩阵$$T-Sharpen=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10\\ \hline F1 &0.129 &0.23 &0.265 &0.043 &0.202 &0.126 &0.27 &0.173 &0.203 &0.165\\ \hline F2 &0.144 &0.114 &0.34 &0.039 &0.066 &0.166 &0.343 &0.116 &0.158 &0.3\\ \hline F3 &0.2 &0.093 &0.082 &0.028 &0.119 &0.032 &0.232 &0.039 &0.28 &0.105\\ \hline F4 &0.237 &0.117 &0.293 &0.025 &0.066 &0.063 &0.272 &0.046 &0.178 &0.138\\ \hline F5 &0.195 &0.065 &0.102 &0.024 &0.046 &0.031 &0.097 &0.056 &0.271 &0.224\\ \hline F6 &0.146 &0.26 &0.26 &0.053 &0.126 &0.05 &0.281 &0.046 &0.132 &0.125\\ \hline F7 &0.122 &0.088 &0.059 &0.036 &0.027 &0.024 &0.061 &0.025 &0.094 &0.064\\ \hline F8 &0.16 &0.211 &0.255 &0.034 &0.051 &0.046 &0.148 &0.045 &0.174 &0.175\\ \hline F9 &0.081 &0.053 &0.091 &0.071 &0.04 &0.02 &0.144 &0.023 &0.048 &0.184\\ \hline F10 &0.113 &0.103 &0.27 &0.015 &0.054 &0.051 &0.168 &0.068 &0.093 &0.06\\ \hline \end{array} $$

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}

　　影响度、被影响度、中心度与原因度是四种度量要素在系统里影响程度的度量值。都是根据综合影响矩阵计算得出。

求解原理

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$	$$ R_i=D_i-C_i $$

结果

影响度、被影响度、中心度、原因度

$$\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times4}} &Di &Ci &Mi &Ri\\ \hline F1 &2.438 &2.116 &4.554 &0.321\\ \hline F2 &2.441 &1.845 &4.286 &0.597\\ \hline F3 &1.616 &2.511 &4.127 &-0.895\\ \hline F4 &1.806 &0.778 &2.584 &1.028\\ \hline F5 &1.445 &1.204 &2.649 &0.241\\ \hline F6 &2.068 &0.926 &2.993 &1.142\\ \hline F7 &0.911 &2.644 &3.556 &-1.733\\ \hline F8 &1.81 &0.889 &2.699 &0.92\\ \hline F9 &1.199 &2.142 &3.341 &-0.943\\ \hline F10 &1.526 &2.205 &3.731 &-0.678\\ \hline \end{array} $$$$\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times4}} &Di &Ci &Mi &Ri\\ \hline F1 &1.447 &1.318 &2.765 &0.129\\ \hline F2 &1.742 &1.167 &2.909 &0.575\\ \hline F3 &1.06 &1.861 &2.921 &-0.802\\ \hline F4 &1.347 &0.294 &1.64 &1.053\\ \hline F5 &1.043 &0.635 &1.678 &0.408\\ \hline F6 &1.362 &0.495 &1.857 &0.867\\ \hline F7 &0.419 &1.782 &2.202 &-1.363\\ \hline F8 &1.072 &0.543 &1.615 &0.53\\ \hline F9 &0.618 &1.509 &2.127 &-0.891\\ \hline F10 &0.858 &1.363 &2.221 &-0.505\\ \hline \end{array} $$$$\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times4}} &Di &Ci &Mi &Ri\\ \hline F1 &1.804 &1.527 &3.331 &0.277\\ \hline F2 &1.786 &1.335 &3.121 &0.451\\ \hline F3 &1.211 &2.018 &3.229 &-0.807\\ \hline F4 &1.435 &0.367 &1.802 &1.068\\ \hline F5 &1.11 &0.795 &1.905 &0.314\\ \hline F6 &1.478 &0.608 &2.086 &0.87\\ \hline F7 &0.6 &2.018 &2.618 &-1.418\\ \hline F8 &1.3 &0.636 &1.936 &0.664\\ \hline F9 &0.756 &1.631 &2.386 &-0.875\\ \hline F10 &0.995 &1.539 &2.534 &-0.545\\ \hline \end{array} $$

绘制中心度与原因度建构的散点图图表

拓扑不变性讨论

原因度数值的排序

$$R-sort=\begin{array}{c|c|c|c|c|c|c}{M_{10 \times6}} &要素 &Upper &要素 &Lower &要素 &Sharpen\\ \hline 1 &F7 &-1.7330140773 &F7 &-1.3632511784 &F7 &-1.4177370056\\ \hline 2 &F9 &-0.9430184394 &F9 &-0.8905922242 &F9 &-0.8748314951\\ \hline 3 &F3 &-0.895187595 &F3 &-0.8017878177 &F3 &-0.806674023\\ \hline 4 &F10 &-0.6784465494 &F10 &-0.5053378006 &F10 &-0.5447399364\\ \hline 5 &F5 &0.2407967234 &F1 &0.128900583 &F1 &0.2774431507\\ \hline 6 &F1 &0.3212742243 &F5 &0.4075462833 &F5 &0.3144838225\\ \hline 7 &F2 &0.5966398016 &F8 &0.5297297666 &F2 &0.4507551265\\ \hline 8 &F8 &0.9203753611 &F2 &0.5750611807 &F8 &0.663583475\\ \hline 9 &F4 &1.0284889977 &F6 &0.866678887 &F6 &0.8697905561\\ \hline 10 &F6 &1.142091553 &F4 &1.0530523203 &F4 &1.0679263293\\ \hline \end{array} $$

中心度数值的排序

$$M-sort=\begin{array}{c|c|c|c|c|c|c}{M_{10 \times6}} &要素 &Upper &要素 &Lower &要素 &Sharpen\\ \hline 1 &F4 &2.5839760292 &F8 &1.6152056095 &F4 &1.8023917526\\ \hline 2 &F5 &2.6493487442 &F4 &1.6401095572 &F5 &1.9046691854\\ \hline 3 &F8 &2.6992975762 &F5 &1.6780034458 &F8 &1.9358637672\\ \hline 4 &F6 &2.9930949692 &F6 &1.8574264596 &F6 &2.0858214526\\ \hline 5 &F9 &3.340599798 &F9 &2.1268651131 &F9 &2.3862428\\ \hline 6 &F7 &3.5557708953 &F7 &2.2015013972 &F10 &2.5338552963\\ \hline 7 &F10 &3.7312880177 &F10 &2.2206730153 &F7 &2.6175893634\\ \hline 8 &F3 &4.1271420805 &F1 &2.7652574954 &F2 &3.1208223377\\ \hline 9 &F2 &4.2859563096 &F2 &2.9090712151 &F3 &3.2288535508\\ \hline 10 &F1 &4.5539829053 &F3 &2.9209553116 &F1 &3.3314722058\\ \hline \end{array} $$

结论

移动轨迹。

GREY-DEMATEL

流程图