模糊可达矩阵的运算


论文写作或者计算需要帮助可发邮件到 hwstu # sohu.com 把 #替换成@,请说清来意,不必拐弯抹角,浪费相互之间的时间。

模糊乘算子 模糊加算子



选择的模糊算子对如下


$$ \begin{array} {c|c}{属性} & 模糊乘 \odot & 模糊加 \oplus \\ \hline 名称 &\color{red}{取最小} &\color{blue}{取最大} \\ \hline 计算公式 &\color{red}{min(p,q)} &\color{blue}{max(p,q)} \\ \hline \end{array} $$

模糊相乘矩阵 $ \tilde B $


$$\tilde B=\begin{array} {c|c|c}{M_{12 \times12}} &E1 &E2 &E3 &E4 &E5 &E6 &E7 &E8 &E9 &E10 &E11 &E12\\ \hline E1 &1 &0 &0 &0 &0 &0.07 &0 &0 &0 &0 &0 &0\\ \hline E2 &0.51 &1 &0 &0 &0 &0 &0 &0 &0 &0.75 &0 &0\\ \hline E3 &0 &0.59 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline E4 &0 &0 &0 &1 &0 &0.33 &0 &0 &0 &0 &0 &0\\ \hline E5 &0 &0 &0 &0 &1 &0 &0.07 &0.09 &0 &0 &0 &0\\ \hline E6 &0 &0.7 &0 &0 &0.42 &1 &0 &0.5 &0 &0 &0.61 &0\\ \hline E7 &0 &0 &0 &0 &0 &0 &1 &0.75 &0 &0 &0 &0\\ \hline E8 &0 &0.97 &0 &0.52 &0 &0 &0 &1 &0 &0 &0 &0\\ \hline E9 &0 &0 &0 &0 &0 &0 &0 &0.8 &1 &0 &0 &0\\ \hline E10 &0 &0 &0.23 &0 &0 &0 &0 &0 &0 &1 &0 &0\\ \hline E11 &0 &0 &0 &0 &0 &0 &0 &0 &0.95 &0 &1 &0\\ \hline E12 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1\\ \hline \end{array} $$

基于选择的算子对求解模糊可达矩阵 $ \tilde R $


$$\tilde B_{1}=\begin{array} {c|c|c}{M_{12 \times12}} &E1 &E2 &E3 &E4 &E5 &E6 &E7 &E8 &E9 &E10 &E11 &E12\\ \hline E1 &1 &0 &0 &0 &0 &0.07 &0 &0 &0 &0 &0 &0\\ \hline E2 &0.51 &1 &0 &0 &0 &0 &0 &0 &0 &0.75 &0 &0\\ \hline E3 &0 &0.59 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline E4 &0 &0 &0 &1 &0 &0.33 &0 &0 &0 &0 &0 &0\\ \hline E5 &0 &0 &0 &0 &1 &0 &0.07 &0.09 &0 &0 &0 &0\\ \hline E6 &0 &0.7 &0 &0 &0.42 &1 &0 &0.5 &0 &0 &0.61 &0\\ \hline E7 &0 &0 &0 &0 &0 &0 &1 &0.75 &0 &0 &0 &0\\ \hline E8 &0 &0.97 &0 &0.52 &0 &0 &0 &1 &0 &0 &0 &0\\ \hline E9 &0 &0 &0 &0 &0 &0 &0 &0.8 &1 &0 &0 &0\\ \hline E10 &0 &0 &0.23 &0 &0 &0 &0 &0 &0 &1 &0 &0\\ \hline E11 &0 &0 &0 &0 &0 &0 &0 &0 &0.95 &0 &1 &0\\ \hline E12 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1\\ \hline \end{array} $$$$\tilde B_{2}=\begin{array} {c|c|c}{M_{12 \times12}} &E1 &E2 &E3 &E4 &E5 &E6 &E7 &E8 &E9 &E10 &E11 &E12\\ \hline E1 &1 &0.07 &0 &0 &0.07 &0.07 &0 &0.07 &0 &0 &0.07 &0\\ \hline E2 &0.51 &1 &0.23 &0 &0 &0.07 &0 &0 &0 &0.75 &0 &0\\ \hline E3 &0.51 &0.59 &1 &0 &0 &0 &0 &0 &0 &0.59 &0 &0\\ \hline E4 &0 &0.33 &0 &1 &0.33 &0.33 &0 &0.33 &0 &0 &0.33 &0\\ \hline E5 &0 &0.09 &0 &0.09 &1 &0 &0.07 &0.09 &0 &0 &0 &0\\ \hline E6 &0.51 &0.7 &0 &0.5 &0.42 &1 &0.07 &0.5 &0.61 &0.7 &0.61 &0\\ \hline E7 &0 &0.75 &0 &0.52 &0 &0 &1 &0.75 &0 &0 &0 &0\\ \hline E8 &0.51 &0.97 &0 &0.52 &0 &0.33 &0 &1 &0 &0.75 &0 &0\\ \hline E9 &0 &0.8 &0 &0.52 &0 &0 &0 &0.8 &1 &0 &0 &0\\ \hline E10 &0 &0.23 &0.23 &0 &0 &0 &0 &0 &0 &1 &0 &0\\ \hline E11 &0 &0 &0 &0 &0 &0 &0 &0.8 &0.95 &0 &1 &0\\ \hline E12 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1\\ \hline \end{array} $$$$\tilde B_{3}=\begin{array} {c|c|c}{M_{12 \times12}} &E1 &E2 &E3 &E4 &E5 &E6 &E7 &E8 &E9 &E10 &E11 &E12\\ \hline E1 &1 &0.07 &0 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0\\ \hline E2 &0.51 &1 &0.23 &0 &0.07 &0.07 &0 &0.07 &0 &0.75 &0.07 &0\\ \hline E3 &0.51 &0.59 &1 &0 &0 &0.07 &0 &0 &0 &0.59 &0 &0\\ \hline E4 &0.33 &0.33 &0 &1 &0.33 &0.33 &0.07 &0.33 &0.33 &0.33 &0.33 &0\\ \hline E5 &0.09 &0.09 &0 &0.09 &1 &0.09 &0.07 &0.09 &0 &0.09 &0 &0\\ \hline E6 &0.51 &0.7 &0.23 &0.5 &0.42 &1 &0.07 &0.61 &0.61 &0.7 &0.61 &0\\ \hline E7 &0.51 &0.75 &0 &0.52 &0 &0.33 &1 &0.75 &0 &0.75 &0 &0\\ \hline E8 &0.51 &0.97 &0.23 &0.52 &0.33 &0.33 &0 &1 &0 &0.75 &0.33 &0\\ \hline E9 &0.51 &0.8 &0 &0.52 &0 &0.33 &0 &0.8 &1 &0.75 &0 &0\\ \hline E10 &0.23 &0.23 &0.23 &0 &0 &0 &0 &0 &0 &1 &0 &0\\ \hline E11 &0 &0.8 &0 &0.52 &0 &0 &0 &0.8 &0.95 &0 &1 &0\\ \hline E12 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1\\ \hline \end{array} $$$$\tilde B_{4}=\begin{array} {c|c|c}{M_{12 \times12}} &E1 &E2 &E3 &E4 &E5 &E6 &E7 &E8 &E9 &E10 &E11 &E12\\ \hline E1 &1 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0\\ \hline E2 &0.51 &1 &0.23 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0.75 &0.07 &0\\ \hline E3 &0.51 &0.59 &1 &0 &0.07 &0.07 &0 &0.07 &0 &0.59 &0.07 &0\\ \hline E4 &0.33 &0.33 &0.23 &1 &0.33 &0.33 &0.07 &0.33 &0.33 &0.33 &0.33 &0\\ \hline E5 &0.09 &0.09 &0.09 &0.09 &1 &0.09 &0.07 &0.09 &0 &0.09 &0.09 &0\\ \hline E6 &0.51 &0.7 &0.23 &0.52 &0.42 &1 &0.07 &0.61 &0.61 &0.7 &0.61 &0\\ \hline E7 &0.51 &0.75 &0.23 &0.52 &0.33 &0.33 &1 &0.75 &0 &0.75 &0.33 &0\\ \hline E8 &0.51 &0.97 &0.23 &0.52 &0.33 &0.33 &0.07 &1 &0.33 &0.75 &0.33 &0\\ \hline E9 &0.51 &0.8 &0.23 &0.52 &0.33 &0.33 &0 &0.8 &1 &0.75 &0.33 &0\\ \hline E10 &0.23 &0.23 &0.23 &0 &0 &0.07 &0 &0 &0 &1 &0 &0\\ \hline E11 &0.51 &0.8 &0 &0.52 &0 &0.33 &0 &0.8 &0.95 &0.75 &1 &0\\ \hline E12 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1\\ \hline \end{array} $$$$\tilde B_{5}=\begin{array} {c|c|c}{M_{12 \times12}} &E1 &E2 &E3 &E4 &E5 &E6 &E7 &E8 &E9 &E10 &E11 &E12\\ \hline E1 &1 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0\\ \hline E2 &0.51 &1 &0.23 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0.75 &0.07 &0\\ \hline E3 &0.51 &0.59 &1 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0.59 &0.07 &0\\ \hline E4 &0.33 &0.33 &0.23 &1 &0.33 &0.33 &0.07 &0.33 &0.33 &0.33 &0.33 &0\\ \hline E5 &0.09 &0.09 &0.09 &0.09 &1 &0.09 &0.07 &0.09 &0.09 &0.09 &0.09 &0\\ \hline E6 &0.51 &0.7 &0.23 &0.52 &0.42 &1 &0.07 &0.61 &0.61 &0.7 &0.61 &0\\ \hline E7 &0.51 &0.75 &0.23 &0.52 &0.33 &0.33 &1 &0.75 &0.33 &0.75 &0.33 &0\\ \hline E8 &0.51 &0.97 &0.23 &0.52 &0.33 &0.33 &0.07 &1 &0.33 &0.75 &0.33 &0\\ \hline E9 &0.51 &0.8 &0.23 &0.52 &0.33 &0.33 &0.07 &0.8 &1 &0.75 &0.33 &0\\ \hline E10 &0.23 &0.23 &0.23 &0 &0.07 &0.07 &0 &0.07 &0 &1 &0.07 &0\\ \hline E11 &0.51 &0.8 &0.23 &0.52 &0.33 &0.33 &0 &0.8 &0.95 &0.75 &1 &0\\ \hline E12 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1\\ \hline \end{array} $$$$\tilde B_{6}=\begin{array} {c|c|c}{M_{12 \times12}} &E1 &E2 &E3 &E4 &E5 &E6 &E7 &E8 &E9 &E10 &E11 &E12\\ \hline E1 &1 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0\\ \hline E2 &0.51 &1 &0.23 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0.75 &0.07 &0\\ \hline E3 &0.51 &0.59 &1 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0.59 &0.07 &0\\ \hline E4 &0.33 &0.33 &0.23 &1 &0.33 &0.33 &0.07 &0.33 &0.33 &0.33 &0.33 &0\\ \hline E5 &0.09 &0.09 &0.09 &0.09 &1 &0.09 &0.07 &0.09 &0.09 &0.09 &0.09 &0\\ \hline E6 &0.51 &0.7 &0.23 &0.52 &0.42 &1 &0.07 &0.61 &0.61 &0.7 &0.61 &0\\ \hline E7 &0.51 &0.75 &0.23 &0.52 &0.33 &0.33 &1 &0.75 &0.33 &0.75 &0.33 &0\\ \hline E8 &0.51 &0.97 &0.23 &0.52 &0.33 &0.33 &0.07 &1 &0.33 &0.75 &0.33 &0\\ \hline E9 &0.51 &0.8 &0.23 &0.52 &0.33 &0.33 &0.07 &0.8 &1 &0.75 &0.33 &0\\ \hline E10 &0.23 &0.23 &0.23 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &1 &0.07 &0\\ \hline E11 &0.51 &0.8 &0.23 &0.52 &0.33 &0.33 &0.07 &0.8 &0.95 &0.75 &1 &0\\ \hline E12 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1\\ \hline \end{array} $$$$\tilde B_{7}=\begin{array} {c|c|c}{M_{12 \times12}} &E1 &E2 &E3 &E4 &E5 &E6 &E7 &E8 &E9 &E10 &E11 &E12\\ \hline E1 &1 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0\\ \hline E2 &0.51 &1 &0.23 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0.75 &0.07 &0\\ \hline E3 &0.51 &0.59 &1 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &0.59 &0.07 &0\\ \hline E4 &0.33 &0.33 &0.23 &1 &0.33 &0.33 &0.07 &0.33 &0.33 &0.33 &0.33 &0\\ \hline E5 &0.09 &0.09 &0.09 &0.09 &1 &0.09 &0.07 &0.09 &0.09 &0.09 &0.09 &0\\ \hline E6 &0.51 &0.7 &0.23 &0.52 &0.42 &1 &0.07 &0.61 &0.61 &0.7 &0.61 &0\\ \hline E7 &0.51 &0.75 &0.23 &0.52 &0.33 &0.33 &1 &0.75 &0.33 &0.75 &0.33 &0\\ \hline E8 &0.51 &0.97 &0.23 &0.52 &0.33 &0.33 &0.07 &1 &0.33 &0.75 &0.33 &0\\ \hline E9 &0.51 &0.8 &0.23 &0.52 &0.33 &0.33 &0.07 &0.8 &1 &0.75 &0.33 &0\\ \hline E10 &0.23 &0.23 &0.23 &0.07 &0.07 &0.07 &0.07 &0.07 &0.07 &1 &0.07 &0\\ \hline E11 &0.51 &0.8 &0.23 &0.52 &0.33 &0.33 &0.07 &0.8 &0.95 &0.75 &1 &0\\ \hline E12 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1\\ \hline \end{array} $$

模糊可达矩阵 $ \tilde R = \tilde B_{ 7}$


请联系作者 hwstu # sohu.com