选择的模糊算子对如下
$$ \begin{array} {c|c}{OP} & 模糊乘 \odot & 模糊加 \oplus \\ \hline 名称 &\color{red}{取最小} &\color{blue}{取最大} \\ \hline 计算公式 &\color{red}{min(p,q)} &\color{blue}{max(p,q) } \\ \hline \end{array} $$
模糊相乘矩阵
$$\tilde B=\begin{array} {c|c|c}{M_{10 \times10}} &甲 &乙 &丙 &丁 &戊 &己 &庚 &辛 &壬 &癸\\ \hline 甲 &1 &0 &0 &0 &0 &0 &0.68 &0 &0.45 &0\\ \hline 乙 &0 &1 &0.01 &0 &0 &0.35 &0 &0 &0 &0\\ \hline 丙 &0 &0 &1 &0 &0 &0 &0 &0 &0 &0\\ \hline 丁 &0 &0 &0 &1 &0 &0 &0 &0 &0 &0\\ \hline 戊 &0 &0 &0 &0 &1 &0.44 &0 &0 &0 &0\\ \hline 己 &0 &0 &0 &0 &0 &1 &0 &0 &0 &0.96\\ \hline 庚 &0 &0.8 &0 &0 &0 &0.57 &1 &0 &0 &0.16\\ \hline 辛 &0 &0 &0.31 &0 &0.6 &0 &0 &1 &0.4 &0\\ \hline 壬 &0 &0 &0.99 &0.87 &0 &0 &0 &0.68 &1 &0\\ \hline 癸 &0.39 &0 &0.76 &0.45 &0 &0.03 &0 &0 &0 &1\\ \hline \end{array} $$
求解过程
$$\tilde B_{1}=\begin{array} {c|c|c}{M_{10 \times10}} &甲 &乙 &丙 &丁 &戊 &己 &庚 &辛 &壬 &癸\\ \hline 甲 &1 &0 &0 &0 &0 &0 &0.68 &0 &0.45 &0\\ \hline 乙 &0 &1 &0.01 &0 &0 &0.35 &0 &0 &0 &0\\ \hline 丙 &0 &0 &1 &0 &0 &0 &0 &0 &0 &0\\ \hline 丁 &0 &0 &0 &1 &0 &0 &0 &0 &0 &0\\ \hline 戊 &0 &0 &0 &0 &1 &0.44 &0 &0 &0 &0\\ \hline 己 &0 &0 &0 &0 &0 &1 &0 &0 &0 &0.96\\ \hline 庚 &0 &0.8 &0 &0 &0 &0.57 &1 &0 &0 &0.16\\ \hline 辛 &0 &0 &0.31 &0 &0.6 &0 &0 &1 &0.4 &0\\ \hline 壬 &0 &0 &0.99 &0.87 &0 &0 &0 &0.68 &1 &0\\ \hline 癸 &0.39 &0 &0.76 &0.45 &0 &0.03 &0 &0 &0 &1\\ \hline \end{array} $$$$\tilde B_{2}=\begin{array} {c|c|c}{M_{10 \times10}} &甲 &乙 &丙 &丁 &戊 &己 &庚 &辛 &壬 &癸\\ \hline 甲 &1 &0.68 &0.45 &0.45 &0 &0.57 &0.68 &0.45 &0.45 &0.16\\ \hline 乙 &0 &1 &0.01 &0 &0 &0.35 &0 &0 &0 &0.35\\ \hline 丙 &0 &0 &1 &0 &0 &0 &0 &0 &0 &0\\ \hline 丁 &0 &0 &0 &1 &0 &0 &0 &0 &0 &0\\ \hline 戊 &0 &0 &0 &0 &1 &0.44 &0 &0 &0 &0.44\\ \hline 己 &0.39 &0 &0.76 &0.45 &0 &1 &0 &0 &0 &0.96\\ \hline 庚 &0.16 &0.8 &0.16 &0.16 &0 &0.57 &1 &0 &0 &0.57\\ \hline 辛 &0 &0 &0.4 &0.4 &0.6 &0.44 &0 &1 &0.4 &0\\ \hline 壬 &0 &0 &0.99 &0.87 &0.6 &0 &0 &0.68 &1 &0\\ \hline 癸 &0.39 &0 &0.76 &0.45 &0 &0.03 &0.39 &0 &0.39 &1\\ \hline \end{array} $$$$\tilde B_{3}=\begin{array} {c|c|c}{M_{10 \times10}} &甲 &乙 &丙 &丁 &戊 &己 &庚 &辛 &壬 &癸\\ \hline 甲 &1 &0.68 &0.45 &0.45 &0.45 &0.57 &0.68 &0.45 &0.45 &0.57\\ \hline 乙 &0.35 &1 &0.35 &0.35 &0 &0.35 &0 &0 &0 &0.35\\ \hline 丙 &0 &0 &1 &0 &0 &0 &0 &0 &0 &0\\ \hline 丁 &0 &0 &0 &1 &0 &0 &0 &0 &0 &0\\ \hline 戊 &0.39 &0 &0.44 &0.44 &1 &0.44 &0 &0 &0 &0.44\\ \hline 己 &0.39 &0 &0.76 &0.45 &0 &1 &0.39 &0 &0.39 &0.96\\ \hline 庚 &0.39 &0.8 &0.57 &0.45 &0 &0.57 &1 &0 &0.16 &0.57\\ \hline 辛 &0 &0 &0.4 &0.4 &0.6 &0.44 &0 &1 &0.4 &0.44\\ \hline 壬 &0 &0 &0.99 &0.87 &0.6 &0.44 &0 &0.68 &1 &0\\ \hline 癸 &0.39 &0.39 &0.76 &0.45 &0 &0.39 &0.39 &0.39 &0.39 &1\\ \hline \end{array} $$$$\tilde B_{4}=\begin{array} {c|c|c}{M_{10 \times10}} &甲 &乙 &丙 &丁 &戊 &己 &庚 &辛 &壬 &癸\\ \hline 甲 &1 &0.68 &0.57 &0.45 &0.45 &0.57 &0.68 &0.45 &0.45 &0.57\\ \hline 乙 &0.35 &1 &0.35 &0.35 &0 &0.35 &0.35 &0 &0.35 &0.35\\ \hline 丙 &0 &0 &1 &0 &0 &0 &0 &0 &0 &0\\ \hline 丁 &0 &0 &0 &1 &0 &0 &0 &0 &0 &0\\ \hline 戊 &0.39 &0 &0.44 &0.44 &1 &0.44 &0.39 &0 &0.39 &0.44\\ \hline 己 &0.39 &0.39 &0.76 &0.45 &0 &1 &0.39 &0.39 &0.39 &0.96\\ \hline 庚 &0.39 &0.8 &0.57 &0.45 &0 &0.57 &1 &0.16 &0.39 &0.57\\ \hline 辛 &0.39 &0 &0.44 &0.44 &0.6 &0.44 &0 &1 &0.4 &0.44\\ \hline 壬 &0 &0 &0.99 &0.87 &0.6 &0.44 &0 &0.68 &1 &0.44\\ \hline 癸 &0.39 &0.39 &0.76 &0.45 &0.39 &0.39 &0.39 &0.39 &0.39 &1\\ \hline \end{array} $$$$\tilde B_{5}=\begin{array} {c|c|c}{M_{10 \times10}} &甲 &乙 &丙 &丁 &戊 &己 &庚 &辛 &壬 &癸\\ \hline 甲 &1 &0.68 &0.57 &0.45 &0.45 &0.57 &0.68 &0.45 &0.45 &0.57\\ \hline 乙 &0.35 &1 &0.35 &0.35 &0 &0.35 &0.35 &0.35 &0.35 &0.35\\ \hline 丙 &0 &0 &1 &0 &0 &0 &0 &0 &0 &0\\ \hline 丁 &0 &0 &0 &1 &0 &0 &0 &0 &0 &0\\ \hline 戊 &0.39 &0.39 &0.44 &0.44 &1 &0.44 &0.39 &0.39 &0.39 &0.44\\ \hline 己 &0.39 &0.39 &0.76 &0.45 &0.39 &1 &0.39 &0.39 &0.39 &0.96\\ \hline 庚 &0.39 &0.8 &0.57 &0.45 &0.16 &0.57 &1 &0.39 &0.39 &0.57\\ \hline 辛 &0.39 &0 &0.44 &0.44 &0.6 &0.44 &0.39 &1 &0.4 &0.44\\ \hline 壬 &0.39 &0 &0.99 &0.87 &0.6 &0.44 &0 &0.68 &1 &0.44\\ \hline 癸 &0.39 &0.39 &0.76 &0.45 &0.39 &0.39 &0.39 &0.39 &0.39 &1\\ \hline \end{array} $$$$\tilde B_{6}=\begin{array} {c|c|c}{M_{10 \times10}} &甲 &乙 &丙 &丁 &戊 &己 &庚 &辛 &壬 &癸\\ \hline 甲 &1 &0.68 &0.57 &0.45 &0.45 &0.57 &0.68 &0.45 &0.45 &0.57\\ \hline 乙 &0.35 &1 &0.35 &0.35 &0.35 &0.35 &0.35 &0.35 &0.35 &0.35\\ \hline 丙 &0 &0 &1 &0 &0 &0 &0 &0 &0 &0\\ \hline 丁 &0 &0 &0 &1 &0 &0 &0 &0 &0 &0\\ \hline 戊 &0.39 &0.39 &0.44 &0.44 &1 &0.44 &0.39 &0.39 &0.39 &0.44\\ \hline 己 &0.39 &0.39 &0.76 &0.45 &0.39 &1 &0.39 &0.39 &0.39 &0.96\\ \hline 庚 &0.39 &0.8 &0.57 &0.45 &0.39 &0.57 &1 &0.39 &0.39 &0.57\\ \hline 辛 &0.39 &0.39 &0.44 &0.44 &0.6 &0.44 &0.39 &1 &0.4 &0.44\\ \hline 壬 &0.39 &0 &0.99 &0.87 &0.6 &0.44 &0.39 &0.68 &1 &0.44\\ \hline 癸 &0.39 &0.39 &0.76 &0.45 &0.39 &0.39 &0.39 &0.39 &0.39 &1\\ \hline \end{array} $$$$\tilde B_{7}=\begin{array} {c|c|c}{M_{10 \times10}} &甲 &乙 &丙 &丁 &戊 &己 &庚 &辛 &壬 &癸\\ \hline 甲 &1 &0.68 &0.57 &0.45 &0.45 &0.57 &0.68 &0.45 &0.45 &0.57\\ \hline 乙 &0.35 &1 &0.35 &0.35 &0.35 &0.35 &0.35 &0.35 &0.35 &0.35\\ \hline 丙 &0 &0 &1 &0 &0 &0 &0 &0 &0 &0\\ \hline 丁 &0 &0 &0 &1 &0 &0 &0 &0 &0 &0\\ \hline 戊 &0.39 &0.39 &0.44 &0.44 &1 &0.44 &0.39 &0.39 &0.39 &0.44\\ \hline 己 &0.39 &0.39 &0.76 &0.45 &0.39 &1 &0.39 &0.39 &0.39 &0.96\\ \hline 庚 &0.39 &0.8 &0.57 &0.45 &0.39 &0.57 &1 &0.39 &0.39 &0.57\\ \hline 辛 &0.39 &0.39 &0.44 &0.44 &0.6 &0.44 &0.39 &1 &0.4 &0.44\\ \hline 壬 &0.39 &0.39 &0.99 &0.87 &0.6 &0.44 &0.39 &0.68 &1 &0.44\\ \hline 癸 &0.39 &0.39 &0.76 &0.45 &0.39 &0.39 &0.39 &0.39 &0.39 &1\\ \hline \end{array} $$$$\tilde B_{8}=\begin{array} {c|c|c}{M_{10 \times10}} &甲 &乙 &丙 &丁 &戊 &己 &庚 &辛 &壬 &癸\\ \hline 甲 &1 &0.68 &0.57 &0.45 &0.45 &0.57 &0.68 &0.45 &0.45 &0.57\\ \hline 乙 &0.35 &1 &0.35 &0.35 &0.35 &0.35 &0.35 &0.35 &0.35 &0.35\\ \hline 丙 &0 &0 &1 &0 &0 &0 &0 &0 &0 &0\\ \hline 丁 &0 &0 &0 &1 &0 &0 &0 &0 &0 &0\\ \hline 戊 &0.39 &0.39 &0.44 &0.44 &1 &0.44 &0.39 &0.39 &0.39 &0.44\\ \hline 己 &0.39 &0.39 &0.76 &0.45 &0.39 &1 &0.39 &0.39 &0.39 &0.96\\ \hline 庚 &0.39 &0.8 &0.57 &0.45 &0.39 &0.57 &1 &0.39 &0.39 &0.57\\ \hline 辛 &0.39 &0.39 &0.44 &0.44 &0.6 &0.44 &0.39 &1 &0.4 &0.44\\ \hline 壬 &0.39 &0.39 &0.99 &0.87 &0.6 &0.44 &0.39 &0.68 &1 &0.44\\ \hline 癸 &0.39 &0.39 &0.76 &0.45 &0.39 &0.39 &0.39 &0.39 &0.39 &1\\ \hline \end{array} $$
模糊可达矩阵 $ \tilde R = \tilde B_{ 8}$
模糊可达矩阵
$$\tilde R=\begin{array} {c|c|c}{M_{10 \times10}} &甲 &乙 &丙 &丁 &戊 &己 &庚 &辛 &壬 &癸\\ \hline 甲 &1 &0.68 &0.57 &0.45 &0.45 &0.57 &0.68 &0.45 &0.45 &0.57\\ \hline 乙 &0.35 &1 &0.35 &0.35 &0.35 &0.35 &0.35 &0.35 &0.35 &0.35\\ \hline 丙 &0 &0 &1 &0 &0 &0 &0 &0 &0 &0\\ \hline 丁 &0 &0 &0 &1 &0 &0 &0 &0 &0 &0\\ \hline 戊 &0.39 &0.39 &0.44 &0.44 &1 &0.44 &0.39 &0.39 &0.39 &0.44\\ \hline 己 &0.39 &0.39 &0.76 &0.45 &0.39 &1 &0.39 &0.39 &0.39 &0.96\\ \hline 庚 &0.39 &0.8 &0.57 &0.45 &0.39 &0.57 &1 &0.39 &0.39 &0.57\\ \hline 辛 &0.39 &0.39 &0.44 &0.44 &0.6 &0.44 &0.39 &1 &0.4 &0.44\\ \hline 壬 &0.39 &0.39 &0.99 &0.87 &0.6 &0.44 &0.39 &0.68 &1 &0.44\\ \hline 癸 &0.39 &0.39 &0.76 &0.45 &0.39 &0.39 &0.39 &0.39 &0.39 &1\\ \hline \end{array} $$