模糊可达矩阵的运算
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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 $
$$\tilde B=\begin{array} {c|c|c}{M_{12 \times12}} &E1 &E2 &E3 &E4 &E5 &E6 &E7 &E8 &E9 &E10 &E11 &E12\\
\hline E1 &1 &0 &0 &0 &0 &0 &0.59 &0 &0 &0 &0.98 &0\\
\hline E2 &0 &1 &0 &0 &0.76 &0 &0 &0 &0 &0 &0 &0\\
\hline E3 &0 &0.18 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0\\
\hline E4 &0.11 &0 &0 &1 &0 &0 &0 &0 &0 &0 &0 &0\\
\hline E5 &0 &0 &0.83 &0 &1 &0 &0.16 &0 &0 &0 &0 &0\\
\hline E6 &0 &0 &0 &0 &0 &1 &0 &0 &0 &0.72 &0 &0\\
\hline E7 &0 &0 &0 &0 &0 &0.2 &1 &0 &0 &0 &0 &0\\
\hline E8 &0 &0 &0 &0 &0 &0 &0.53 &1 &0 &0 &0 &0\\
\hline E9 &0 &0 &0 &0.6 &0 &0 &0 &0 &1 &0 &0 &0.83\\
\hline E10 &0.19 &0 &0 &0 &0 &0 &0 &0 &0 &1 &0 &0\\
\hline E11 &0 &0.76 &0.76 &0 &0 &0 &0 &0 &0 &0 &1 &0\\
\hline E12 &0.05 &0 &0.81 &0 &0 &0 &0 &0 &0 &0 &0 &1\\
\hline \end{array} $$
基于选择的算子对求解模糊可达矩阵 $ \tilde R $
$$\tilde B_{1}=\begin{array} {c|c|c}{M_{12 \times12}} &E1 &E2 &E3 &E4 &E5 &E6 &E7 &E8 &E9 &E10 &E11 &E12\\
\hline E1 &1 &0 &0 &0 &0 &0 &0.59 &0 &0 &0 &0.98 &0\\
\hline E2 &0 &1 &0 &0 &0.76 &0 &0 &0 &0 &0 &0 &0\\
\hline E3 &0 &0.18 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0\\
\hline E4 &0.11 &0 &0 &1 &0 &0 &0 &0 &0 &0 &0 &0\\
\hline E5 &0 &0 &0.83 &0 &1 &0 &0.16 &0 &0 &0 &0 &0\\
\hline E6 &0 &0 &0 &0 &0 &1 &0 &0 &0 &0.72 &0 &0\\
\hline E7 &0 &0 &0 &0 &0 &0.2 &1 &0 &0 &0 &0 &0\\
\hline E8 &0 &0 &0 &0 &0 &0 &0.53 &1 &0 &0 &0 &0\\
\hline E9 &0 &0 &0 &0.6 &0 &0 &0 &0 &1 &0 &0 &0.83\\
\hline E10 &0.19 &0 &0 &0 &0 &0 &0 &0 &0 &1 &0 &0\\
\hline E11 &0 &0.76 &0.76 &0 &0 &0 &0 &0 &0 &0 &1 &0\\
\hline E12 &0.05 &0 &0.81 &0 &0 &0 &0 &0 &0 &0 &0 &1\\
\hline \end{array} $$$$\tilde B_{2}=\begin{array} {c|c|c}{M_{12 \times12}} &E1 &E2 &E3 &E4 &E5 &E6 &E7 &E8 &E9 &E10 &E11 &E12\\
\hline E1 &1 &0.76 &0.76 &0 &0 &0.2 &0.59 &0 &0 &0 &0.98 &0\\
\hline E2 &0 &1 &0.76 &0 &0.76 &0 &0.16 &0 &0 &0 &0 &0\\
\hline E3 &0 &0.18 &1 &0 &0.18 &0 &0 &0 &0 &0 &0 &0\\
\hline E4 &0.11 &0 &0 &1 &0 &0 &0.11 &0 &0 &0 &0.11 &0\\
\hline E5 &0 &0.18 &0.83 &0 &1 &0.16 &0.16 &0 &0 &0 &0 &0\\
\hline E6 &0.19 &0 &0 &0 &0 &1 &0 &0 &0 &0.72 &0 &0\\
\hline E7 &0 &0 &0 &0 &0 &0.2 &1 &0 &0 &0.2 &0 &0\\
\hline E8 &0 &0 &0 &0 &0 &0.2 &0.53 &1 &0 &0 &0 &0\\
\hline E9 &0.11 &0 &0.81 &0.6 &0 &0 &0 &0 &1 &0 &0 &0.83\\
\hline E10 &0.19 &0 &0 &0 &0 &0 &0.19 &0 &0 &1 &0.19 &0\\
\hline E11 &0 &0.76 &0.76 &0 &0.76 &0 &0 &0 &0 &0 &1 &0\\
\hline E12 &0.05 &0.18 &0.81 &0 &0 &0 &0.05 &0 &0 &0 &0.05 &1\\
\hline \end{array} $$$$\tilde B_{3}=\begin{array} {c|c|c}{M_{12 \times12}} &E1 &E2 &E3 &E4 &E5 &E6 &E7 &E8 &E9 &E10 &E11 &E12\\
\hline E1 &1 &0.76 &0.76 &0 &0.76 &0.2 &0.59 &0 &0 &0.2 &0.98 &0\\
\hline E2 &0 &1 &0.76 &0 &0.76 &0.16 &0.16 &0 &0 &0 &0 &0\\
\hline E3 &0 &0.18 &1 &0 &0.18 &0 &0.16 &0 &0 &0 &0 &0\\
\hline E4 &0.11 &0.11 &0.11 &1 &0 &0.11 &0.11 &0 &0 &0 &0.11 &0\\
\hline E5 &0 &0.18 &0.83 &0 &1 &0.16 &0.16 &0 &0 &0.16 &0 &0\\
\hline E6 &0.19 &0 &0 &0 &0 &1 &0.19 &0 &0 &0.72 &0.19 &0\\
\hline E7 &0.19 &0 &0 &0 &0 &0.2 &1 &0 &0 &0.2 &0 &0\\
\hline E8 &0 &0 &0 &0 &0 &0.2 &0.53 &1 &0 &0.2 &0 &0\\
\hline E9 &0.11 &0.18 &0.81 &0.6 &0 &0 &0.11 &0 &1 &0 &0.11 &0.83\\
\hline E10 &0.19 &0.19 &0.19 &0 &0 &0.19 &0.19 &0 &0 &1 &0.19 &0\\
\hline E11 &0 &0.76 &0.76 &0 &0.76 &0 &0.16 &0 &0 &0 &1 &0\\
\hline E12 &0.05 &0.18 &0.81 &0 &0.18 &0.05 &0.05 &0 &0 &0 &0.05 &1\\
\hline \end{array} $$$$\tilde B_{4}=\begin{array} {c|c|c}{M_{12 \times12}} &E1 &E2 &E3 &E4 &E5 &E6 &E7 &E8 &E9 &E10 &E11 &E12\\
\hline E1 &1 &0.76 &0.76 &0 &0.76 &0.2 &0.59 &0 &0 &0.2 &0.98 &0\\
\hline E2 &0 &1 &0.76 &0 &0.76 &0.16 &0.16 &0 &0 &0.16 &0 &0\\
\hline E3 &0 &0.18 &1 &0 &0.18 &0.16 &0.16 &0 &0 &0 &0 &0\\
\hline E4 &0.11 &0.11 &0.11 &1 &0.11 &0.11 &0.11 &0 &0 &0.11 &0.11 &0\\
\hline E5 &0.16 &0.18 &0.83 &0 &1 &0.16 &0.16 &0 &0 &0.16 &0 &0\\
\hline E6 &0.19 &0.19 &0.19 &0 &0 &1 &0.19 &0 &0 &0.72 &0.19 &0\\
\hline E7 &0.19 &0 &0 &0 &0 &0.2 &1 &0 &0 &0.2 &0.19 &0\\
\hline E8 &0.19 &0 &0 &0 &0 &0.2 &0.53 &1 &0 &0.2 &0 &0\\
\hline E9 &0.11 &0.18 &0.81 &0.6 &0.18 &0.11 &0.11 &0 &1 &0 &0.11 &0.83\\
\hline E10 &0.19 &0.19 &0.19 &0 &0.19 &0.19 &0.19 &0 &0 &1 &0.19 &0\\
\hline E11 &0 &0.76 &0.76 &0 &0.76 &0.16 &0.16 &0 &0 &0 &1 &0\\
\hline E12 &0.05 &0.18 &0.81 &0 &0.18 &0.05 &0.16 &0 &0 &0.05 &0.05 &1\\
\hline \end{array} $$$$\tilde B_{5}=\begin{array} {c|c|c}{M_{12 \times12}} &E1 &E2 &E3 &E4 &E5 &E6 &E7 &E8 &E9 &E10 &E11 &E12\\
\hline E1 &1 &0.76 &0.76 &0 &0.76 &0.2 &0.59 &0 &0 &0.2 &0.98 &0\\
\hline E2 &0.16 &1 &0.76 &0 &0.76 &0.16 &0.16 &0 &0 &0.16 &0 &0\\
\hline E3 &0 &0.18 &1 &0 &0.18 &0.16 &0.16 &0 &0 &0.16 &0 &0\\
\hline E4 &0.11 &0.11 &0.11 &1 &0.11 &0.11 &0.11 &0 &0 &0.11 &0.11 &0\\
\hline E5 &0.16 &0.18 &0.83 &0 &1 &0.16 &0.16 &0 &0 &0.16 &0.16 &0\\
\hline E6 &0.19 &0.19 &0.19 &0 &0.19 &1 &0.19 &0 &0 &0.72 &0.19 &0\\
\hline E7 &0.19 &0.19 &0.19 &0 &0 &0.2 &1 &0 &0 &0.2 &0.19 &0\\
\hline E8 &0.19 &0 &0 &0 &0 &0.2 &0.53 &1 &0 &0.2 &0.19 &0\\
\hline E9 &0.11 &0.18 &0.81 &0.6 &0.18 &0.11 &0.16 &0 &1 &0.11 &0.11 &0.83\\
\hline E10 &0.19 &0.19 &0.19 &0 &0.19 &0.19 &0.19 &0 &0 &1 &0.19 &0\\
\hline E11 &0 &0.76 &0.76 &0 &0.76 &0.16 &0.16 &0 &0 &0.16 &1 &0\\
\hline E12 &0.05 &0.18 &0.81 &0 &0.18 &0.16 &0.16 &0 &0 &0.05 &0.05 &1\\
\hline \end{array} $$$$\tilde B_{6}=\begin{array} {c|c|c}{M_{12 \times12}} &E1 &E2 &E3 &E4 &E5 &E6 &E7 &E8 &E9 &E10 &E11 &E12\\
\hline E1 &1 &0.76 &0.76 &0 &0.76 &0.2 &0.59 &0 &0 &0.2 &0.98 &0\\
\hline E2 &0.16 &1 &0.76 &0 &0.76 &0.16 &0.16 &0 &0 &0.16 &0.16 &0\\
\hline E3 &0.16 &0.18 &1 &0 &0.18 &0.16 &0.16 &0 &0 &0.16 &0 &0\\
\hline E4 &0.11 &0.11 &0.11 &1 &0.11 &0.11 &0.11 &0 &0 &0.11 &0.11 &0\\
\hline E5 &0.16 &0.18 &0.83 &0 &1 &0.16 &0.16 &0 &0 &0.16 &0.16 &0\\
\hline E6 &0.19 &0.19 &0.19 &0 &0.19 &1 &0.19 &0 &0 &0.72 &0.19 &0\\
\hline E7 &0.19 &0.19 &0.19 &0 &0.19 &0.2 &1 &0 &0 &0.2 &0.19 &0\\
\hline E8 &0.19 &0.19 &0.19 &0 &0 &0.2 &0.53 &1 &0 &0.2 &0.19 &0\\
\hline E9 &0.11 &0.18 &0.81 &0.6 &0.18 &0.16 &0.16 &0 &1 &0.11 &0.11 &0.83\\
\hline E10 &0.19 &0.19 &0.19 &0 &0.19 &0.19 &0.19 &0 &0 &1 &0.19 &0\\
\hline E11 &0.16 &0.76 &0.76 &0 &0.76 &0.16 &0.16 &0 &0 &0.16 &1 &0\\
\hline E12 &0.05 &0.18 &0.81 &0 &0.18 &0.16 &0.16 &0 &0 &0.16 &0.05 &1\\
\hline \end{array} $$$$\tilde B_{7}=\begin{array} {c|c|c}{M_{12 \times12}} &E1 &E2 &E3 &E4 &E5 &E6 &E7 &E8 &E9 &E10 &E11 &E12\\
\hline E1 &1 &0.76 &0.76 &0 &0.76 &0.2 &0.59 &0 &0 &0.2 &0.98 &0\\
\hline E2 &0.16 &1 &0.76 &0 &0.76 &0.16 &0.16 &0 &0 &0.16 &0.16 &0\\
\hline E3 &0.16 &0.18 &1 &0 &0.18 &0.16 &0.16 &0 &0 &0.16 &0.16 &0\\
\hline E4 &0.11 &0.11 &0.11 &1 &0.11 &0.11 &0.11 &0 &0 &0.11 &0.11 &0\\
\hline E5 &0.16 &0.18 &0.83 &0 &1 &0.16 &0.16 &0 &0 &0.16 &0.16 &0\\
\hline E6 &0.19 &0.19 &0.19 &0 &0.19 &1 &0.19 &0 &0 &0.72 &0.19 &0\\
\hline E7 &0.19 &0.19 &0.19 &0 &0.19 &0.2 &1 &0 &0 &0.2 &0.19 &0\\
\hline E8 &0.19 &0.19 &0.19 &0 &0.19 &0.2 &0.53 &1 &0 &0.2 &0.19 &0\\
\hline E9 &0.11 &0.18 &0.81 &0.6 &0.18 &0.16 &0.16 &0 &1 &0.16 &0.11 &0.83\\
\hline E10 &0.19 &0.19 &0.19 &0 &0.19 &0.19 &0.19 &0 &0 &1 &0.19 &0\\
\hline E11 &0.16 &0.76 &0.76 &0 &0.76 &0.16 &0.16 &0 &0 &0.16 &1 &0\\
\hline E12 &0.16 &0.18 &0.81 &0 &0.18 &0.16 &0.16 &0 &0 &0.16 &0.05 &1\\
\hline \end{array} $$$$\tilde B_{8}=\begin{array} {c|c|c}{M_{12 \times12}} &E1 &E2 &E3 &E4 &E5 &E6 &E7 &E8 &E9 &E10 &E11 &E12\\
\hline E1 &1 &0.76 &0.76 &0 &0.76 &0.2 &0.59 &0 &0 &0.2 &0.98 &0\\
\hline E2 &0.16 &1 &0.76 &0 &0.76 &0.16 &0.16 &0 &0 &0.16 &0.16 &0\\
\hline E3 &0.16 &0.18 &1 &0 &0.18 &0.16 &0.16 &0 &0 &0.16 &0.16 &0\\
\hline E4 &0.11 &0.11 &0.11 &1 &0.11 &0.11 &0.11 &0 &0 &0.11 &0.11 &0\\
\hline E5 &0.16 &0.18 &0.83 &0 &1 &0.16 &0.16 &0 &0 &0.16 &0.16 &0\\
\hline E6 &0.19 &0.19 &0.19 &0 &0.19 &1 &0.19 &0 &0 &0.72 &0.19 &0\\
\hline E7 &0.19 &0.19 &0.19 &0 &0.19 &0.2 &1 &0 &0 &0.2 &0.19 &0\\
\hline E8 &0.19 &0.19 &0.19 &0 &0.19 &0.2 &0.53 &1 &0 &0.2 &0.19 &0\\
\hline E9 &0.16 &0.18 &0.81 &0.6 &0.18 &0.16 &0.16 &0 &1 &0.16 &0.11 &0.83\\
\hline E10 &0.19 &0.19 &0.19 &0 &0.19 &0.19 &0.19 &0 &0 &1 &0.19 &0\\
\hline E11 &0.16 &0.76 &0.76 &0 &0.76 &0.16 &0.16 &0 &0 &0.16 &1 &0\\
\hline E12 &0.16 &0.18 &0.81 &0 &0.18 &0.16 &0.16 &0 &0 &0.16 &0.16 &1\\
\hline \end{array} $$$$\tilde B_{9}=\begin{array} {c|c|c}{M_{12 \times12}} &E1 &E2 &E3 &E4 &E5 &E6 &E7 &E8 &E9 &E10 &E11 &E12\\
\hline E1 &1 &0.76 &0.76 &0 &0.76 &0.2 &0.59 &0 &0 &0.2 &0.98 &0\\
\hline E2 &0.16 &1 &0.76 &0 &0.76 &0.16 &0.16 &0 &0 &0.16 &0.16 &0\\
\hline E3 &0.16 &0.18 &1 &0 &0.18 &0.16 &0.16 &0 &0 &0.16 &0.16 &0\\
\hline E4 &0.11 &0.11 &0.11 &1 &0.11 &0.11 &0.11 &0 &0 &0.11 &0.11 &0\\
\hline E5 &0.16 &0.18 &0.83 &0 &1 &0.16 &0.16 &0 &0 &0.16 &0.16 &0\\
\hline E6 &0.19 &0.19 &0.19 &0 &0.19 &1 &0.19 &0 &0 &0.72 &0.19 &0\\
\hline E7 &0.19 &0.19 &0.19 &0 &0.19 &0.2 &1 &0 &0 &0.2 &0.19 &0\\
\hline E8 &0.19 &0.19 &0.19 &0 &0.19 &0.2 &0.53 &1 &0 &0.2 &0.19 &0\\
\hline E9 &0.16 &0.18 &0.81 &0.6 &0.18 &0.16 &0.16 &0 &1 &0.16 &0.16 &0.83\\
\hline E10 &0.19 &0.19 &0.19 &0 &0.19 &0.19 &0.19 &0 &0 &1 &0.19 &0\\
\hline E11 &0.16 &0.76 &0.76 &0 &0.76 &0.16 &0.16 &0 &0 &0.16 &1 &0\\
\hline E12 &0.16 &0.18 &0.81 &0 &0.18 &0.16 &0.16 &0 &0 &0.16 &0.16 &1\\
\hline \end{array} $$$$\tilde B_{10}=\begin{array} {c|c|c}{M_{12 \times12}} &E1 &E2 &E3 &E4 &E5 &E6 &E7 &E8 &E9 &E10 &E11 &E12\\
\hline E1 &1 &0.76 &0.76 &0 &0.76 &0.2 &0.59 &0 &0 &0.2 &0.98 &0\\
\hline E2 &0.16 &1 &0.76 &0 &0.76 &0.16 &0.16 &0 &0 &0.16 &0.16 &0\\
\hline E3 &0.16 &0.18 &1 &0 &0.18 &0.16 &0.16 &0 &0 &0.16 &0.16 &0\\
\hline E4 &0.11 &0.11 &0.11 &1 &0.11 &0.11 &0.11 &0 &0 &0.11 &0.11 &0\\
\hline E5 &0.16 &0.18 &0.83 &0 &1 &0.16 &0.16 &0 &0 &0.16 &0.16 &0\\
\hline E6 &0.19 &0.19 &0.19 &0 &0.19 &1 &0.19 &0 &0 &0.72 &0.19 &0\\
\hline E7 &0.19 &0.19 &0.19 &0 &0.19 &0.2 &1 &0 &0 &0.2 &0.19 &0\\
\hline E8 &0.19 &0.19 &0.19 &0 &0.19 &0.2 &0.53 &1 &0 &0.2 &0.19 &0\\
\hline E9 &0.16 &0.18 &0.81 &0.6 &0.18 &0.16 &0.16 &0 &1 &0.16 &0.16 &0.83\\
\hline E10 &0.19 &0.19 &0.19 &0 &0.19 &0.19 &0.19 &0 &0 &1 &0.19 &0\\
\hline E11 &0.16 &0.76 &0.76 &0 &0.76 &0.16 &0.16 &0 &0 &0.16 &1 &0\\
\hline E12 &0.16 &0.18 &0.81 &0 &0.18 &0.16 &0.16 &0 &0 &0.16 &0.16 &1\\
\hline \end{array} $$ 模糊可达矩阵 $ \tilde R = \tilde B_{ 10}$
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