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
$$\tilde B=\begin{array} {c|c|c}{M_{10 \times10}} &A &B &C &D &E &F &G &H &I &J\\ \hline A &1 &0 &0 &0.38 &0 &0 &0 &0 &0 &0\\ \hline B &0 &1 &0 &0 &0.47 &0 &0 &0 &0 &0.94\\ \hline C &0 &0 &1 &0 &0.23 &0 &0 &0 &0 &0.4\\ \hline D &0 &0 &0 &1 &0 &0 &0 &0 &0.13 &0\\ \hline E &0 &0 &0 &0.16 &1 &0 &0 &0 &0 &0\\ \hline F &0 &0 &0 &0 &0 &1 &0.76 &0.22 &0 &0\\ \hline G &0 &0 &0 &0.75 &0 &0.45 &1 &0.97 &0 &0\\ \hline H &0.81 &0.52 &0 &0 &0 &0 &0.12 &1 &0 &0.54\\ \hline I &0 &0.06 &0.24 &0 &0 &0 &0 &0 &1 &0\\ \hline J &0 &0 &0 &0 &0 &0.98 &0 &0 &0 &1\\ \hline \end{array} $$
求解过程
$$\tilde B_{1}=\begin{array} {c|c|c}{M_{10 \times10}} &A &B &C &D &E &F &G &H &I &J\\ \hline A &1 &0 &0 &0.38 &0 &0 &0 &0 &0 &0\\ \hline B &0 &1 &0 &0 &0.47 &0 &0 &0 &0 &0.94\\ \hline C &0 &0 &1 &0 &0.23 &0 &0 &0 &0 &0.4\\ \hline D &0 &0 &0 &1 &0 &0 &0 &0 &0.13 &0\\ \hline E &0 &0 &0 &0.16 &1 &0 &0 &0 &0 &0\\ \hline F &0 &0 &0 &0 &0 &1 &0.76 &0.22 &0 &0\\ \hline G &0 &0 &0 &0.75 &0 &0.45 &1 &0.97 &0 &0\\ \hline H &0.81 &0.52 &0 &0 &0 &0 &0.12 &1 &0 &0.54\\ \hline I &0 &0.06 &0.24 &0 &0 &0 &0 &0 &1 &0\\ \hline J &0 &0 &0 &0 &0 &0.98 &0 &0 &0 &1\\ \hline \end{array} $$$$\tilde B_{2}=\begin{array} {c|c|c}{M_{10 \times10}} &A &B &C &D &E &F &G &H &I &J\\ \hline A &1 &0 &0 &0.38 &0 &0 &0 &0 &0.13 &0\\ \hline B &0 &1 &0 &0.16 &0.47 &0.94 &0 &0 &0 &0.94\\ \hline C &0 &0 &1 &0.16 &0.23 &0.4 &0 &0 &0 &0.4\\ \hline D &0 &0.06 &0.13 &1 &0 &0 &0 &0 &0.13 &0\\ \hline E &0 &0 &0 &0.16 &1 &0 &0 &0 &0.13 &0\\ \hline F &0.22 &0.22 &0 &0.75 &0 &1 &0.76 &0.76 &0 &0.22\\ \hline G &0.81 &0.52 &0 &0.75 &0 &0.45 &1 &0.97 &0.13 &0.54\\ \hline H &0.81 &0.52 &0 &0.38 &0.47 &0.54 &0.12 &1 &0 &0.54\\ \hline I &0 &0.06 &0.24 &0 &0.23 &0 &0 &0 &1 &0.24\\ \hline J &0 &0 &0 &0 &0 &0.98 &0.76 &0.22 &0 &1\\ \hline \end{array} $$$$\tilde B_{3}=\begin{array} {c|c|c}{M_{10 \times10}} &A &B &C &D &E &F &G &H &I &J\\ \hline A &1 &0.06 &0.13 &0.38 &0 &0 &0 &0 &0.13 &0\\ \hline B &0 &1 &0 &0.16 &0.47 &0.94 &0.76 &0.22 &0.13 &0.94\\ \hline C &0 &0 &1 &0.16 &0.23 &0.4 &0.4 &0.22 &0.13 &0.4\\ \hline D &0 &0.06 &0.13 &1 &0.13 &0 &0 &0 &0.13 &0.13\\ \hline E &0 &0.06 &0.13 &0.16 &1 &0 &0 &0 &0.13 &0\\ \hline F &0.76 &0.52 &0 &0.75 &0.22 &1 &0.76 &0.76 &0.13 &0.54\\ \hline G &0.81 &0.52 &0.13 &0.75 &0.47 &0.54 &1 &0.97 &0.13 &0.54\\ \hline H &0.81 &0.52 &0 &0.38 &0.47 &0.54 &0.54 &1 &0.13 &0.54\\ \hline I &0 &0.06 &0.24 &0.16 &0.23 &0.24 &0 &0 &1 &0.24\\ \hline J &0.22 &0.22 &0 &0.75 &0 &0.98 &0.76 &0.76 &0 &1\\ \hline \end{array} $$$$\tilde B_{4}=\begin{array} {c|c|c}{M_{10 \times10}} &A &B &C &D &E &F &G &H &I &J\\ \hline A &1 &0.06 &0.13 &0.38 &0.13 &0 &0 &0 &0.13 &0.13\\ \hline B &0.22 &1 &0.13 &0.75 &0.47 &0.94 &0.76 &0.76 &0.13 &0.94\\ \hline C &0.22 &0.22 &1 &0.4 &0.23 &0.4 &0.4 &0.4 &0.13 &0.4\\ \hline D &0 &0.06 &0.13 &1 &0.13 &0.13 &0 &0 &0.13 &0.13\\ \hline E &0 &0.06 &0.13 &0.16 &1 &0 &0 &0 &0.13 &0.13\\ \hline F &0.76 &0.52 &0.13 &0.75 &0.47 &1 &0.76 &0.76 &0.13 &0.54\\ \hline G &0.81 &0.52 &0.13 &0.75 &0.47 &0.54 &1 &0.97 &0.13 &0.54\\ \hline H &0.81 &0.52 &0.13 &0.54 &0.47 &0.54 &0.54 &1 &0.13 &0.54\\ \hline I &0 &0.06 &0.24 &0.16 &0.23 &0.24 &0.24 &0.22 &1 &0.24\\ \hline J &0.76 &0.52 &0 &0.75 &0.22 &0.98 &0.76 &0.76 &0.13 &1\\ \hline \end{array} $$$$\tilde B_{5}=\begin{array} {c|c|c}{M_{10 \times10}} &A &B &C &D &E &F &G &H &I &J\\ \hline A &1 &0.06 &0.13 &0.38 &0.13 &0.13 &0 &0 &0.13 &0.13\\ \hline B &0.76 &1 &0.13 &0.75 &0.47 &0.94 &0.76 &0.76 &0.13 &0.94\\ \hline C &0.4 &0.4 &1 &0.4 &0.23 &0.4 &0.4 &0.4 &0.13 &0.4\\ \hline D &0 &0.06 &0.13 &1 &0.13 &0.13 &0.13 &0.13 &0.13 &0.13\\ \hline E &0 &0.06 &0.13 &0.16 &1 &0.13 &0 &0 &0.13 &0.13\\ \hline F &0.76 &0.52 &0.13 &0.75 &0.47 &1 &0.76 &0.76 &0.13 &0.54\\ \hline G &0.81 &0.52 &0.13 &0.75 &0.47 &0.54 &1 &0.97 &0.13 &0.54\\ \hline H &0.81 &0.52 &0.13 &0.54 &0.47 &0.54 &0.54 &1 &0.13 &0.54\\ \hline I &0.22 &0.22 &0.24 &0.24 &0.23 &0.24 &0.24 &0.24 &1 &0.24\\ \hline J &0.76 &0.52 &0.13 &0.75 &0.47 &0.98 &0.76 &0.76 &0.13 &1\\ \hline \end{array} $$$$\tilde B_{6}=\begin{array} {c|c|c}{M_{10 \times10}} &A &B &C &D &E &F &G &H &I &J\\ \hline A &1 &0.06 &0.13 &0.38 &0.13 &0.13 &0.13 &0.13 &0.13 &0.13\\ \hline B &0.76 &1 &0.13 &0.75 &0.47 &0.94 &0.76 &0.76 &0.13 &0.94\\ \hline C &0.4 &0.4 &1 &0.4 &0.4 &0.4 &0.4 &0.4 &0.13 &0.4\\ \hline D &0.13 &0.13 &0.13 &1 &0.13 &0.13 &0.13 &0.13 &0.13 &0.13\\ \hline E &0 &0.06 &0.13 &0.16 &1 &0.13 &0.13 &0.13 &0.13 &0.13\\ \hline F &0.76 &0.52 &0.13 &0.75 &0.47 &1 &0.76 &0.76 &0.13 &0.54\\ \hline G &0.81 &0.52 &0.13 &0.75 &0.47 &0.54 &1 &0.97 &0.13 &0.54\\ \hline H &0.81 &0.52 &0.13 &0.54 &0.47 &0.54 &0.54 &1 &0.13 &0.54\\ \hline I &0.24 &0.24 &0.24 &0.24 &0.23 &0.24 &0.24 &0.24 &1 &0.24\\ \hline J &0.76 &0.52 &0.13 &0.75 &0.47 &0.98 &0.76 &0.76 &0.13 &1\\ \hline \end{array} $$$$\tilde B_{7}=\begin{array} {c|c|c}{M_{10 \times10}} &A &B &C &D &E &F &G &H &I &J\\ \hline A &1 &0.13 &0.13 &0.38 &0.13 &0.13 &0.13 &0.13 &0.13 &0.13\\ \hline B &0.76 &1 &0.13 &0.75 &0.47 &0.94 &0.76 &0.76 &0.13 &0.94\\ \hline C &0.4 &0.4 &1 &0.4 &0.4 &0.4 &0.4 &0.4 &0.13 &0.4\\ \hline D &0.13 &0.13 &0.13 &1 &0.13 &0.13 &0.13 &0.13 &0.13 &0.13\\ \hline E &0.13 &0.13 &0.13 &0.16 &1 &0.13 &0.13 &0.13 &0.13 &0.13\\ \hline F &0.76 &0.52 &0.13 &0.75 &0.47 &1 &0.76 &0.76 &0.13 &0.54\\ \hline G &0.81 &0.52 &0.13 &0.75 &0.47 &0.54 &1 &0.97 &0.13 &0.54\\ \hline H &0.81 &0.52 &0.13 &0.54 &0.47 &0.54 &0.54 &1 &0.13 &0.54\\ \hline I &0.24 &0.24 &0.24 &0.24 &0.24 &0.24 &0.24 &0.24 &1 &0.24\\ \hline J &0.76 &0.52 &0.13 &0.75 &0.47 &0.98 &0.76 &0.76 &0.13 &1\\ \hline \end{array} $$$$\tilde B_{8}=\begin{array} {c|c|c}{M_{10 \times10}} &A &B &C &D &E &F &G &H &I &J\\ \hline A &1 &0.13 &0.13 &0.38 &0.13 &0.13 &0.13 &0.13 &0.13 &0.13\\ \hline B &0.76 &1 &0.13 &0.75 &0.47 &0.94 &0.76 &0.76 &0.13 &0.94\\ \hline C &0.4 &0.4 &1 &0.4 &0.4 &0.4 &0.4 &0.4 &0.13 &0.4\\ \hline D &0.13 &0.13 &0.13 &1 &0.13 &0.13 &0.13 &0.13 &0.13 &0.13\\ \hline E &0.13 &0.13 &0.13 &0.16 &1 &0.13 &0.13 &0.13 &0.13 &0.13\\ \hline F &0.76 &0.52 &0.13 &0.75 &0.47 &1 &0.76 &0.76 &0.13 &0.54\\ \hline G &0.81 &0.52 &0.13 &0.75 &0.47 &0.54 &1 &0.97 &0.13 &0.54\\ \hline H &0.81 &0.52 &0.13 &0.54 &0.47 &0.54 &0.54 &1 &0.13 &0.54\\ \hline I &0.24 &0.24 &0.24 &0.24 &0.24 &0.24 &0.24 &0.24 &1 &0.24\\ \hline J &0.76 &0.52 &0.13 &0.75 &0.47 &0.98 &0.76 &0.76 &0.13 &1\\ \hline \end{array} $$
模糊可达矩阵 $ \tilde R = \tilde B_{ 8}$
模糊可达矩阵
$$\tilde R=\begin{array} {c|c|c}{M_{10 \times10}} &A &B &C &D &E &F &G &H &I &J\\ \hline A &1 &0.13 &0.13 &0.38 &0.13 &0.13 &0.13 &0.13 &0.13 &0.13\\ \hline B &0.76 &1 &0.13 &0.75 &0.47 &0.94 &0.76 &0.76 &0.13 &0.94\\ \hline C &0.4 &0.4 &1 &0.4 &0.4 &0.4 &0.4 &0.4 &0.13 &0.4\\ \hline D &0.13 &0.13 &0.13 &1 &0.13 &0.13 &0.13 &0.13 &0.13 &0.13\\ \hline E &0.13 &0.13 &0.13 &0.16 &1 &0.13 &0.13 &0.13 &0.13 &0.13\\ \hline F &0.76 &0.52 &0.13 &0.75 &0.47 &1 &0.76 &0.76 &0.13 &0.54\\ \hline G &0.81 &0.52 &0.13 &0.75 &0.47 &0.54 &1 &0.97 &0.13 &0.54\\ \hline H &0.81 &0.52 &0.13 &0.54 &0.47 &0.54 &0.54 &1 &0.13 &0.54\\ \hline I &0.24 &0.24 &0.24 &0.24 &0.24 &0.24 &0.24 &0.24 &1 &0.24\\ \hline J &0.76 &0.52 &0.13 &0.75 &0.47 &0.98 &0.76 &0.76 &0.13 &1\\ \hline \end{array} $$