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 $
$$\tilde B=\begin{array} {c|c|c}{M_{12 \times12}} &甲 &乙 &丙 &丁 &戊 &己 &庚 &辛 &壬 &癸 &乾 &坤\\
\hline 甲 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.62 &0\\
\hline 乙 &0 &1 &0.74 &0 &0 &0 &0 &0.06 &0 &0 &0 &0\\
\hline 丙 &0 &0 &1 &0 &0 &0.22 &0 &0 &0 &0 &0 &0\\
\hline 丁 &0 &0 &0.48 &1 &0 &0 &0 &0 &0 &0 &0 &0\\
\hline 戊 &0 &0.51 &0.02 &0 &1 &0 &0 &0 &0 &0 &0 &0\\
\hline 己 &0 &0.33 &0 &0 &0 &1 &0 &0 &0 &0.13 &0 &0\\
\hline 庚 &0 &0.97 &0 &0 &0 &0 &1 &0 &0 &0 &0 &0\\
\hline 辛 &0 &0 &0 &0.23 &0 &0 &0 &1 &0 &0 &0 &0\\
\hline 壬 &0 &0 &0.72 &0 &0 &0 &0 &0 &1 &0 &0 &0.6\\
\hline 癸 &0 &0 &0 &0.75 &0 &0 &0 &0 &0 &1 &0.54 &0\\
\hline 乾 &0 &0 &0 &0 &0 &0 &0.44 &0 &0 &0 &1 &0\\
\hline 坤 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1\\
\hline \end{array} $$
基于选择的算子对求解模糊可达矩阵 $ \tilde R $
$$\tilde B_{1}=\begin{array} {c|c|c}{M_{12 \times12}} &甲 &乙 &丙 &丁 &戊 &己 &庚 &辛 &壬 &癸 &乾 &坤\\
\hline 甲 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.62 &0\\
\hline 乙 &0 &1 &0.74 &0 &0 &0 &0 &0.06 &0 &0 &0 &0\\
\hline 丙 &0 &0 &1 &0 &0 &0.22 &0 &0 &0 &0 &0 &0\\
\hline 丁 &0 &0 &0.48 &1 &0 &0 &0 &0 &0 &0 &0 &0\\
\hline 戊 &0 &0.51 &0.02 &0 &1 &0 &0 &0 &0 &0 &0 &0\\
\hline 己 &0 &0.33 &0 &0 &0 &1 &0 &0 &0 &0.13 &0 &0\\
\hline 庚 &0 &0.97 &0 &0 &0 &0 &1 &0 &0 &0 &0 &0\\
\hline 辛 &0 &0 &0 &0.23 &0 &0 &0 &1 &0 &0 &0 &0\\
\hline 壬 &0 &0 &0.72 &0 &0 &0 &0 &0 &1 &0 &0 &0.6\\
\hline 癸 &0 &0 &0 &0.75 &0 &0 &0 &0 &0 &1 &0.54 &0\\
\hline 乾 &0 &0 &0 &0 &0 &0 &0.44 &0 &0 &0 &1 &0\\
\hline 坤 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1\\
\hline \end{array} $$$$\tilde B_{2}=\begin{array} {c|c|c}{M_{12 \times12}} &甲 &乙 &丙 &丁 &戊 &己 &庚 &辛 &壬 &癸 &乾 &坤\\
\hline 甲 &1 &0 &0 &0 &0 &0 &0.44 &0 &0 &0 &0.62 &0\\
\hline 乙 &0 &1 &0.74 &0.06 &0 &0.22 &0 &0.06 &0 &0 &0 &0\\
\hline 丙 &0 &0.22 &1 &0 &0 &0.22 &0 &0 &0 &0.13 &0 &0\\
\hline 丁 &0 &0 &0.48 &1 &0 &0.22 &0 &0 &0 &0 &0 &0\\
\hline 戊 &0 &0.51 &0.51 &0 &1 &0.02 &0 &0.06 &0 &0 &0 &0\\
\hline 己 &0 &0.33 &0.33 &0.13 &0 &1 &0 &0.06 &0 &0.13 &0.13 &0\\
\hline 庚 &0 &0.97 &0.74 &0 &0 &0 &1 &0.06 &0 &0 &0 &0\\
\hline 辛 &0 &0 &0.23 &0.23 &0 &0 &0 &1 &0 &0 &0 &0\\
\hline 壬 &0 &0 &0.72 &0 &0 &0.22 &0 &0 &1 &0 &0 &0.6\\
\hline 癸 &0 &0 &0.48 &0.75 &0 &0 &0.44 &0 &0 &1 &0.54 &0\\
\hline 乾 &0 &0.44 &0 &0 &0 &0 &0.44 &0 &0 &0 &1 &0\\
\hline 坤 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1\\
\hline \end{array} $$$$\tilde B_{3}=\begin{array} {c|c|c}{M_{12 \times12}} &甲 &乙 &丙 &丁 &戊 &己 &庚 &辛 &壬 &癸 &乾 &坤\\
\hline 甲 &1 &0.44 &0 &0 &0 &0 &0.44 &0 &0 &0 &0.62 &0\\
\hline 乙 &0 &1 &0.74 &0.06 &0 &0.22 &0 &0.06 &0 &0.13 &0 &0\\
\hline 丙 &0 &0.22 &1 &0.13 &0 &0.22 &0 &0.06 &0 &0.13 &0.13 &0\\
\hline 丁 &0 &0.22 &0.48 &1 &0 &0.22 &0 &0 &0 &0.13 &0 &0\\
\hline 戊 &0 &0.51 &0.51 &0.06 &1 &0.22 &0 &0.06 &0 &0.02 &0 &0\\
\hline 己 &0 &0.33 &0.33 &0.13 &0 &1 &0.13 &0.06 &0 &0.13 &0.13 &0\\
\hline 庚 &0 &0.97 &0.74 &0.06 &0 &0.22 &1 &0.06 &0 &0 &0 &0\\
\hline 辛 &0 &0 &0.23 &0.23 &0 &0.22 &0 &1 &0 &0 &0 &0\\
\hline 壬 &0 &0.22 &0.72 &0 &0 &0.22 &0 &0 &1 &0.13 &0 &0.6\\
\hline 癸 &0 &0.44 &0.48 &0.75 &0 &0.22 &0.44 &0 &0 &1 &0.54 &0\\
\hline 乾 &0 &0.44 &0.44 &0 &0 &0 &0.44 &0.06 &0 &0 &1 &0\\
\hline 坤 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1\\
\hline \end{array} $$$$\tilde B_{4}=\begin{array} {c|c|c}{M_{12 \times12}} &甲 &乙 &丙 &丁 &戊 &己 &庚 &辛 &壬 &癸 &乾 &坤\\
\hline 甲 &1 &0.44 &0.44 &0 &0 &0 &0.44 &0.06 &0 &0 &0.62 &0\\
\hline 乙 &0 &1 &0.74 &0.13 &0 &0.22 &0 &0.06 &0 &0.13 &0.13 &0\\
\hline 丙 &0 &0.22 &1 &0.13 &0 &0.22 &0.13 &0.06 &0 &0.13 &0.13 &0\\
\hline 丁 &0 &0.22 &0.48 &1 &0 &0.22 &0 &0.06 &0 &0.13 &0.13 &0\\
\hline 戊 &0 &0.51 &0.51 &0.06 &1 &0.22 &0 &0.06 &0 &0.13 &0.02 &0\\
\hline 己 &0 &0.33 &0.33 &0.13 &0 &1 &0.13 &0.06 &0 &0.13 &0.13 &0\\
\hline 庚 &0 &0.97 &0.74 &0.06 &0 &0.22 &1 &0.06 &0 &0.13 &0 &0\\
\hline 辛 &0 &0.22 &0.23 &0.23 &0 &0.22 &0 &1 &0 &0.13 &0 &0\\
\hline 壬 &0 &0.22 &0.72 &0.13 &0 &0.22 &0 &0.06 &1 &0.13 &0.13 &0.6\\
\hline 癸 &0 &0.44 &0.48 &0.75 &0 &0.22 &0.44 &0.06 &0 &1 &0.54 &0\\
\hline 乾 &0 &0.44 &0.44 &0.06 &0 &0.22 &0.44 &0.06 &0 &0 &1 &0\\
\hline 坤 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1\\
\hline \end{array} $$$$\tilde B_{5}=\begin{array} {c|c|c}{M_{12 \times12}} &甲 &乙 &丙 &丁 &戊 &己 &庚 &辛 &壬 &癸 &乾 &坤\\
\hline 甲 &1 &0.44 &0.44 &0.06 &0 &0.22 &0.44 &0.06 &0 &0 &0.62 &0\\
\hline 乙 &0 &1 &0.74 &0.13 &0 &0.22 &0.13 &0.06 &0 &0.13 &0.13 &0\\
\hline 丙 &0 &0.22 &1 &0.13 &0 &0.22 &0.13 &0.06 &0 &0.13 &0.13 &0\\
\hline 丁 &0 &0.22 &0.48 &1 &0 &0.22 &0.13 &0.06 &0 &0.13 &0.13 &0\\
\hline 戊 &0 &0.51 &0.51 &0.13 &1 &0.22 &0.02 &0.06 &0 &0.13 &0.13 &0\\
\hline 己 &0 &0.33 &0.33 &0.13 &0 &1 &0.13 &0.06 &0 &0.13 &0.13 &0\\
\hline 庚 &0 &0.97 &0.74 &0.13 &0 &0.22 &1 &0.06 &0 &0.13 &0.13 &0\\
\hline 辛 &0 &0.22 &0.23 &0.23 &0 &0.22 &0 &1 &0 &0.13 &0.13 &0\\
\hline 壬 &0 &0.22 &0.72 &0.13 &0 &0.22 &0.13 &0.06 &1 &0.13 &0.13 &0.6\\
\hline 癸 &0 &0.44 &0.48 &0.75 &0 &0.22 &0.44 &0.06 &0 &1 &0.54 &0\\
\hline 乾 &0 &0.44 &0.44 &0.06 &0 &0.22 &0.44 &0.06 &0 &0.13 &1 &0\\
\hline 坤 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1\\
\hline \end{array} $$$$\tilde B_{6}=\begin{array} {c|c|c}{M_{12 \times12}} &甲 &乙 &丙 &丁 &戊 &己 &庚 &辛 &壬 &癸 &乾 &坤\\
\hline 甲 &1 &0.44 &0.44 &0.06 &0 &0.22 &0.44 &0.06 &0 &0.13 &0.62 &0\\
\hline 乙 &0 &1 &0.74 &0.13 &0 &0.22 &0.13 &0.06 &0 &0.13 &0.13 &0\\
\hline 丙 &0 &0.22 &1 &0.13 &0 &0.22 &0.13 &0.06 &0 &0.13 &0.13 &0\\
\hline 丁 &0 &0.22 &0.48 &1 &0 &0.22 &0.13 &0.06 &0 &0.13 &0.13 &0\\
\hline 戊 &0 &0.51 &0.51 &0.13 &1 &0.22 &0.13 &0.06 &0 &0.13 &0.13 &0\\
\hline 己 &0 &0.33 &0.33 &0.13 &0 &1 &0.13 &0.06 &0 &0.13 &0.13 &0\\
\hline 庚 &0 &0.97 &0.74 &0.13 &0 &0.22 &1 &0.06 &0 &0.13 &0.13 &0\\
\hline 辛 &0 &0.22 &0.23 &0.23 &0 &0.22 &0.13 &1 &0 &0.13 &0.13 &0\\
\hline 壬 &0 &0.22 &0.72 &0.13 &0 &0.22 &0.13 &0.06 &1 &0.13 &0.13 &0.6\\
\hline 癸 &0 &0.44 &0.48 &0.75 &0 &0.22 &0.44 &0.06 &0 &1 &0.54 &0\\
\hline 乾 &0 &0.44 &0.44 &0.13 &0 &0.22 &0.44 &0.06 &0 &0.13 &1 &0\\
\hline 坤 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1\\
\hline \end{array} $$$$\tilde B_{7}=\begin{array} {c|c|c}{M_{12 \times12}} &甲 &乙 &丙 &丁 &戊 &己 &庚 &辛 &壬 &癸 &乾 &坤\\
\hline 甲 &1 &0.44 &0.44 &0.13 &0 &0.22 &0.44 &0.06 &0 &0.13 &0.62 &0\\
\hline 乙 &0 &1 &0.74 &0.13 &0 &0.22 &0.13 &0.06 &0 &0.13 &0.13 &0\\
\hline 丙 &0 &0.22 &1 &0.13 &0 &0.22 &0.13 &0.06 &0 &0.13 &0.13 &0\\
\hline 丁 &0 &0.22 &0.48 &1 &0 &0.22 &0.13 &0.06 &0 &0.13 &0.13 &0\\
\hline 戊 &0 &0.51 &0.51 &0.13 &1 &0.22 &0.13 &0.06 &0 &0.13 &0.13 &0\\
\hline 己 &0 &0.33 &0.33 &0.13 &0 &1 &0.13 &0.06 &0 &0.13 &0.13 &0\\
\hline 庚 &0 &0.97 &0.74 &0.13 &0 &0.22 &1 &0.06 &0 &0.13 &0.13 &0\\
\hline 辛 &0 &0.22 &0.23 &0.23 &0 &0.22 &0.13 &1 &0 &0.13 &0.13 &0\\
\hline 壬 &0 &0.22 &0.72 &0.13 &0 &0.22 &0.13 &0.06 &1 &0.13 &0.13 &0.6\\
\hline 癸 &0 &0.44 &0.48 &0.75 &0 &0.22 &0.44 &0.06 &0 &1 &0.54 &0\\
\hline 乾 &0 &0.44 &0.44 &0.13 &0 &0.22 &0.44 &0.06 &0 &0.13 &1 &0\\
\hline 坤 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1\\
\hline \end{array} $$$$\tilde B_{8}=\begin{array} {c|c|c}{M_{12 \times12}} &甲 &乙 &丙 &丁 &戊 &己 &庚 &辛 &壬 &癸 &乾 &坤\\
\hline 甲 &1 &0.44 &0.44 &0.13 &0 &0.22 &0.44 &0.06 &0 &0.13 &0.62 &0\\
\hline 乙 &0 &1 &0.74 &0.13 &0 &0.22 &0.13 &0.06 &0 &0.13 &0.13 &0\\
\hline 丙 &0 &0.22 &1 &0.13 &0 &0.22 &0.13 &0.06 &0 &0.13 &0.13 &0\\
\hline 丁 &0 &0.22 &0.48 &1 &0 &0.22 &0.13 &0.06 &0 &0.13 &0.13 &0\\
\hline 戊 &0 &0.51 &0.51 &0.13 &1 &0.22 &0.13 &0.06 &0 &0.13 &0.13 &0\\
\hline 己 &0 &0.33 &0.33 &0.13 &0 &1 &0.13 &0.06 &0 &0.13 &0.13 &0\\
\hline 庚 &0 &0.97 &0.74 &0.13 &0 &0.22 &1 &0.06 &0 &0.13 &0.13 &0\\
\hline 辛 &0 &0.22 &0.23 &0.23 &0 &0.22 &0.13 &1 &0 &0.13 &0.13 &0\\
\hline 壬 &0 &0.22 &0.72 &0.13 &0 &0.22 &0.13 &0.06 &1 &0.13 &0.13 &0.6\\
\hline 癸 &0 &0.44 &0.48 &0.75 &0 &0.22 &0.44 &0.06 &0 &1 &0.54 &0\\
\hline 乾 &0 &0.44 &0.44 &0.13 &0 &0.22 &0.44 &0.06 &0 &0.13 &1 &0\\
\hline 坤 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1\\
\hline \end{array} $$ 模糊可达矩阵 $ \tilde R = \tilde B_{ 8}$
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