模糊可达矩阵的运算

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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 $

$$\tilde B=\begin{array} {c|c|c}{M_{12 \times12}} &甲 &乙 &丙 &丁 &戊 &己 &庚 &辛 &壬 &癸 &乾 &坤\\ \hline 甲 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0.59 &0 &0\\ \hline 乙 &0.69 &1 &0 &0 &0 &0 &0 &0.05 &0 &0 &0 &0\\ \hline 丙 &0.95 &0 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline 丁 &0 &0 &0 &1 &0 &0.48 &0 &0 &0 &0 &0.37 &0\\ \hline 戊 &0 &0 &0 &0 &1 &0 &0 &0.29 &0 &0 &0 &0\\ \hline 己 &0 &0 &0 &0.34 &0 &1 &0 &0 &0 &0.03 &0 &0\\ \hline 庚 &0 &0 &0.28 &0 &0 &0.82 &1 &0 &0 &0 &0 &0\\ \hline 辛 &0 &0 &0 &0 &0 &0.36 &0 &1 &0 &0 &0 &0\\ \hline 壬 &0 &0 &0.73 &0 &0 &0 &0 &0 &1 &0 &0 &0.19\\ \hline 癸 &0 &0 &0 &0.04 &0 &0 &0.72 &0 &0 &1 &0 &0\\ \hline 乾 &0 &0 &0.2 &0 &0 &0 &0 &0 &0 &0 &1 &0.19\\ \hline 坤 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1\\ \hline \end{array} $$

基于选择的算子对求解模糊可达矩阵 $ \tilde R $

$$\tilde B_{1}=\begin{array} {c|c|c}{M_{12 \times12}} &甲 &乙 &丙 &丁 &戊 &己 &庚 &辛 &壬 &癸 &乾 &坤\\ \hline 甲 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0.59 &0 &0\\ \hline 乙 &0.69 &1 &0 &0 &0 &0 &0 &0.05 &0 &0 &0 &0\\ \hline 丙 &0.95 &0 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline 丁 &0 &0 &0 &1 &0 &0.48 &0 &0 &0 &0 &0.37 &0\\ \hline 戊 &0 &0 &0 &0 &1 &0 &0 &0.29 &0 &0 &0 &0\\ \hline 己 &0 &0 &0 &0.34 &0 &1 &0 &0 &0 &0.03 &0 &0\\ \hline 庚 &0 &0 &0.28 &0 &0 &0.82 &1 &0 &0 &0 &0 &0\\ \hline 辛 &0 &0 &0 &0 &0 &0.36 &0 &1 &0 &0 &0 &0\\ \hline 壬 &0 &0 &0.73 &0 &0 &0 &0 &0 &1 &0 &0 &0.19\\ \hline 癸 &0 &0 &0 &0.04 &0 &0 &0.72 &0 &0 &1 &0 &0\\ \hline 乾 &0 &0 &0.2 &0 &0 &0 &0 &0 &0 &0 &1 &0.19\\ \hline 坤 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1\\ \hline \end{array} $$$$\tilde B_{2}=\begin{array} {c|c|c}{M_{12 \times12}} &甲 &乙 &丙 &丁 &戊 &己 &庚 &辛 &壬 &癸 &乾 &坤\\ \hline 甲 &1 &0 &0 &0.04 &0 &0 &0.59 &0 &0 &0.59 &0 &0\\ \hline 乙 &0.69 &1 &0 &0 &0 &0.05 &0 &0.05 &0 &0.59 &0 &0\\ \hline 丙 &0.95 &0 &1 &0 &0 &0 &0 &0 &0 &0.59 &0 &0\\ \hline 丁 &0 &0 &0.2 &1 &0 &0.48 &0 &0 &0 &0.03 &0.37 &0.19\\ \hline 戊 &0 &0 &0 &0 &1 &0.29 &0 &0.29 &0 &0 &0 &0\\ \hline 己 &0 &0 &0 &0.34 &0 &1 &0.03 &0 &0 &0.03 &0.34 &0\\ \hline 庚 &0.28 &0 &0.28 &0.34 &0 &0.82 &1 &0 &0 &0.03 &0 &0\\ \hline 辛 &0 &0 &0 &0.34 &0 &0.36 &0 &1 &0 &0.03 &0 &0\\ \hline 壬 &0.73 &0 &0.73 &0 &0 &0 &0 &0 &1 &0 &0 &0.19\\ \hline 癸 &0 &0 &0.28 &0.04 &0 &0.72 &0.72 &0 &0 &1 &0.04 &0\\ \hline 乾 &0.2 &0 &0.2 &0 &0 &0 &0 &0 &0 &0 &1 &0.19\\ \hline 坤 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1\\ \hline \end{array} $$$$\tilde B_{3}=\begin{array} {c|c|c}{M_{12 \times12}} &甲 &乙 &丙 &丁 &戊 &己 &庚 &辛 &壬 &癸 &乾 &坤\\ \hline 甲 &1 &0 &0.28 &0.04 &0 &0.59 &0.59 &0 &0 &0.59 &0.04 &0\\ \hline 乙 &0.69 &1 &0 &0.05 &0 &0.05 &0.59 &0.05 &0 &0.59 &0 &0\\ \hline 丙 &0.95 &0 &1 &0.04 &0 &0 &0.59 &0 &0 &0.59 &0 &0\\ \hline 丁 &0.2 &0 &0.2 &1 &0 &0.48 &0.03 &0 &0 &0.03 &0.37 &0.19\\ \hline 戊 &0 &0 &0 &0.29 &1 &0.29 &0 &0.29 &0 &0.03 &0 &0\\ \hline 己 &0 &0 &0.2 &0.34 &0 &1 &0.03 &0 &0 &0.03 &0.34 &0.19\\ \hline 庚 &0.28 &0 &0.28 &0.34 &0 &0.82 &1 &0 &0 &0.28 &0.34 &0\\ \hline 辛 &0 &0 &0 &0.34 &0 &0.36 &0.03 &1 &0 &0.03 &0.34 &0\\ \hline 壬 &0.73 &0 &0.73 &0 &0 &0 &0 &0 &1 &0.59 &0 &0.19\\ \hline 癸 &0.28 &0 &0.28 &0.34 &0 &0.72 &0.72 &0 &0 &1 &0.04 &0.04\\ \hline 乾 &0.2 &0 &0.2 &0 &0 &0 &0 &0 &0 &0.2 &1 &0.19\\ \hline 坤 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1\\ \hline \end{array} $$$$\tilde B_{4}=\begin{array} {c|c|c}{M_{12 \times12}} &甲 &乙 &丙 &丁 &戊 &己 &庚 &辛 &壬 &癸 &乾 &坤\\ \hline 甲 &1 &0 &0.28 &0.34 &0 &0.59 &0.59 &0 &0 &0.59 &0.04 &0.04\\ \hline 乙 &0.69 &1 &0.28 &0.05 &0 &0.59 &0.59 &0.05 &0 &0.59 &0.05 &0\\ \hline 丙 &0.95 &0 &1 &0.04 &0 &0.59 &0.59 &0 &0 &0.59 &0.04 &0\\ \hline 丁 &0.2 &0 &0.2 &1 &0 &0.48 &0.03 &0 &0 &0.2 &0.37 &0.19\\ \hline 戊 &0 &0 &0 &0.29 &1 &0.29 &0.03 &0.29 &0 &0.03 &0.29 &0\\ \hline 己 &0.2 &0 &0.2 &0.34 &0 &1 &0.03 &0 &0 &0.03 &0.34 &0.19\\ \hline 庚 &0.28 &0 &0.28 &0.34 &0 &0.82 &1 &0 &0 &0.28 &0.34 &0.19\\ \hline 辛 &0 &0 &0.2 &0.34 &0 &0.36 &0.03 &1 &0 &0.03 &0.34 &0.19\\ \hline 壬 &0.73 &0 &0.73 &0.04 &0 &0 &0.59 &0 &1 &0.59 &0 &0.19\\ \hline 癸 &0.28 &0 &0.28 &0.34 &0 &0.72 &0.72 &0 &0 &1 &0.34 &0.04\\ \hline 乾 &0.2 &0 &0.2 &0.04 &0 &0 &0.2 &0 &0 &0.2 &1 &0.19\\ \hline 坤 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1\\ \hline \end{array} $$$$\tilde B_{5}=\begin{array} {c|c|c}{M_{12 \times12}} &甲 &乙 &丙 &丁 &戊 &己 &庚 &辛 &壬 &癸 &乾 &坤\\ \hline 甲 &1 &0 &0.28 &0.34 &0 &0.59 &0.59 &0 &0 &0.59 &0.34 &0.04\\ \hline 乙 &0.69 &1 &0.28 &0.34 &0 &0.59 &0.59 &0.05 &0 &0.59 &0.05 &0.05\\ \hline 丙 &0.95 &0 &1 &0.34 &0 &0.59 &0.59 &0 &0 &0.59 &0.04 &0.04\\ \hline 丁 &0.2 &0 &0.2 &1 &0 &0.48 &0.2 &0 &0 &0.2 &0.37 &0.19\\ \hline 戊 &0 &0 &0.2 &0.29 &1 &0.29 &0.03 &0.29 &0 &0.03 &0.29 &0.19\\ \hline 己 &0.2 &0 &0.2 &0.34 &0 &1 &0.03 &0 &0 &0.2 &0.34 &0.19\\ \hline 庚 &0.28 &0 &0.28 &0.34 &0 &0.82 &1 &0 &0 &0.28 &0.34 &0.19\\ \hline 辛 &0.2 &0 &0.2 &0.34 &0 &0.36 &0.03 &1 &0 &0.03 &0.34 &0.19\\ \hline 壬 &0.73 &0 &0.73 &0.04 &0 &0.59 &0.59 &0 &1 &0.59 &0.04 &0.19\\ \hline 癸 &0.28 &0 &0.28 &0.34 &0 &0.72 &0.72 &0 &0 &1 &0.34 &0.19\\ \hline 乾 &0.2 &0 &0.2 &0.04 &0 &0.2 &0.2 &0 &0 &0.2 &1 &0.19\\ \hline 坤 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1\\ \hline \end{array} $$$$\tilde B_{6}=\begin{array} {c|c|c}{M_{12 \times12}} &甲 &乙 &丙 &丁 &戊 &己 &庚 &辛 &壬 &癸 &乾 &坤\\ \hline 甲 &1 &0 &0.28 &0.34 &0 &0.59 &0.59 &0 &0 &0.59 &0.34 &0.19\\ \hline 乙 &0.69 &1 &0.28 &0.34 &0 &0.59 &0.59 &0.05 &0 &0.59 &0.34 &0.05\\ \hline 丙 &0.95 &0 &1 &0.34 &0 &0.59 &0.59 &0 &0 &0.59 &0.34 &0.04\\ \hline 丁 &0.2 &0 &0.2 &1 &0 &0.48 &0.2 &0 &0 &0.2 &0.37 &0.19\\ \hline 戊 &0.2 &0 &0.2 &0.29 &1 &0.29 &0.03 &0.29 &0 &0.03 &0.29 &0.19\\ \hline 己 &0.2 &0 &0.2 &0.34 &0 &1 &0.2 &0 &0 &0.2 &0.34 &0.19\\ \hline 庚 &0.28 &0 &0.28 &0.34 &0 &0.82 &1 &0 &0 &0.28 &0.34 &0.19\\ \hline 辛 &0.2 &0 &0.2 &0.34 &0 &0.36 &0.03 &1 &0 &0.2 &0.34 &0.19\\ \hline 壬 &0.73 &0 &0.73 &0.34 &0 &0.59 &0.59 &0 &1 &0.59 &0.04 &0.19\\ \hline 癸 &0.28 &0 &0.28 &0.34 &0 &0.72 &0.72 &0 &0 &1 &0.34 &0.19\\ \hline 乾 &0.2 &0 &0.2 &0.2 &0 &0.2 &0.2 &0 &0 &0.2 &1 &0.19\\ \hline 坤 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1\\ \hline \end{array} $$$$\tilde B_{7}=\begin{array} {c|c|c}{M_{12 \times12}} &甲 &乙 &丙 &丁 &戊 &己 &庚 &辛 &壬 &癸 &乾 &坤\\ \hline 甲 &1 &0 &0.28 &0.34 &0 &0.59 &0.59 &0 &0 &0.59 &0.34 &0.19\\ \hline 乙 &0.69 &1 &0.28 &0.34 &0 &0.59 &0.59 &0.05 &0 &0.59 &0.34 &0.19\\ \hline 丙 &0.95 &0 &1 &0.34 &0 &0.59 &0.59 &0 &0 &0.59 &0.34 &0.19\\ \hline 丁 &0.2 &0 &0.2 &1 &0 &0.48 &0.2 &0 &0 &0.2 &0.37 &0.19\\ \hline 戊 &0.2 &0 &0.2 &0.29 &1 &0.29 &0.03 &0.29 &0 &0.2 &0.29 &0.19\\ \hline 己 &0.2 &0 &0.2 &0.34 &0 &1 &0.2 &0 &0 &0.2 &0.34 &0.19\\ \hline 庚 &0.28 &0 &0.28 &0.34 &0 &0.82 &1 &0 &0 &0.28 &0.34 &0.19\\ \hline 辛 &0.2 &0 &0.2 &0.34 &0 &0.36 &0.2 &1 &0 &0.2 &0.34 &0.19\\ \hline 壬 &0.73 &0 &0.73 &0.34 &0 &0.59 &0.59 &0 &1 &0.59 &0.34 &0.19\\ \hline 癸 &0.28 &0 &0.28 &0.34 &0 &0.72 &0.72 &0 &0 &1 &0.34 &0.19\\ \hline 乾 &0.2 &0 &0.2 &0.2 &0 &0.2 &0.2 &0 &0 &0.2 &1 &0.19\\ \hline 坤 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1\\ \hline \end{array} $$$$\tilde B_{8}=\begin{array} {c|c|c}{M_{12 \times12}} &甲 &乙 &丙 &丁 &戊 &己 &庚 &辛 &壬 &癸 &乾 &坤\\ \hline 甲 &1 &0 &0.28 &0.34 &0 &0.59 &0.59 &0 &0 &0.59 &0.34 &0.19\\ \hline 乙 &0.69 &1 &0.28 &0.34 &0 &0.59 &0.59 &0.05 &0 &0.59 &0.34 &0.19\\ \hline 丙 &0.95 &0 &1 &0.34 &0 &0.59 &0.59 &0 &0 &0.59 &0.34 &0.19\\ \hline 丁 &0.2 &0 &0.2 &1 &0 &0.48 &0.2 &0 &0 &0.2 &0.37 &0.19\\ \hline 戊 &0.2 &0 &0.2 &0.29 &1 &0.29 &0.2 &0.29 &0 &0.2 &0.29 &0.19\\ \hline 己 &0.2 &0 &0.2 &0.34 &0 &1 &0.2 &0 &0 &0.2 &0.34 &0.19\\ \hline 庚 &0.28 &0 &0.28 &0.34 &0 &0.82 &1 &0 &0 &0.28 &0.34 &0.19\\ \hline 辛 &0.2 &0 &0.2 &0.34 &0 &0.36 &0.2 &1 &0 &0.2 &0.34 &0.19\\ \hline 壬 &0.73 &0 &0.73 &0.34 &0 &0.59 &0.59 &0 &1 &0.59 &0.34 &0.19\\ \hline 癸 &0.28 &0 &0.28 &0.34 &0 &0.72 &0.72 &0 &0 &1 &0.34 &0.19\\ \hline 乾 &0.2 &0 &0.2 &0.2 &0 &0.2 &0.2 &0 &0 &0.2 &1 &0.19\\ \hline 坤 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1\\ \hline \end{array} $$$$\tilde B_{9}=\begin{array} {c|c|c}{M_{12 \times12}} &甲 &乙 &丙 &丁 &戊 &己 &庚 &辛 &壬 &癸 &乾 &坤\\ \hline 甲 &1 &0 &0.28 &0.34 &0 &0.59 &0.59 &0 &0 &0.59 &0.34 &0.19\\ \hline 乙 &0.69 &1 &0.28 &0.34 &0 &0.59 &0.59 &0.05 &0 &0.59 &0.34 &0.19\\ \hline 丙 &0.95 &0 &1 &0.34 &0 &0.59 &0.59 &0 &0 &0.59 &0.34 &0.19\\ \hline 丁 &0.2 &0 &0.2 &1 &0 &0.48 &0.2 &0 &0 &0.2 &0.37 &0.19\\ \hline 戊 &0.2 &0 &0.2 &0.29 &1 &0.29 &0.2 &0.29 &0 &0.2 &0.29 &0.19\\ \hline 己 &0.2 &0 &0.2 &0.34 &0 &1 &0.2 &0 &0 &0.2 &0.34 &0.19\\ \hline 庚 &0.28 &0 &0.28 &0.34 &0 &0.82 &1 &0 &0 &0.28 &0.34 &0.19\\ \hline 辛 &0.2 &0 &0.2 &0.34 &0 &0.36 &0.2 &1 &0 &0.2 &0.34 &0.19\\ \hline 壬 &0.73 &0 &0.73 &0.34 &0 &0.59 &0.59 &0 &1 &0.59 &0.34 &0.19\\ \hline 癸 &0.28 &0 &0.28 &0.34 &0 &0.72 &0.72 &0 &0 &1 &0.34 &0.19\\ \hline 乾 &0.2 &0 &0.2 &0.2 &0 &0.2 &0.2 &0 &0 &0.2 &1 &0.19\\ \hline 坤 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1\\ \hline \end{array} $$

模糊可达矩阵 $ \tilde R = \tilde B_{ 9}$

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