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
$$\tilde B=\begin{array} {c|c|c}{M_{10 \times10}} &A &B &C &D &E &F &G &H &I &J\\ \hline A &1 &0.43 &0.15 &0 &0 &0 &0 &0 &0 &0\\ \hline B &0 &1 &0.58 &0 &0 &0 &0 &0 &0 &0\\ \hline C &0 &0 &1 &0 &0 &0.69 &0 &0 &0 &0.98\\ \hline D &0 &0 &0 &1 &0 &0 &0 &0 &0 &0.85\\ \hline E &0.87 &0 &0.53 &0 &1 &0 &0 &0 &0.58 &0\\ \hline F &0 &0 &0 &0 &0 &1 &0.8 &0 &0 &0.14\\ \hline G &0 &0 &0 &0 &0.77 &0 &1 &0 &0 &0\\ \hline H &0.52 &0 &0 &0 &0 &0 &0 &1 &0 &0\\ \hline I &0.75 &0 &0 &0 &0 &0 &0 &0 &1 &0.91\\ \hline J &0 &0 &0.57 &0 &0.36 &0 &0 &0 &0 &1\\ \hline \end{array} $$
求解过程
$$\tilde B_{1}=\begin{array} {c|c|c}{M_{10 \times10}} &A &B &C &D &E &F &G &H &I &J\\ \hline A &1 &0.43 &0.15 &0 &0 &0 &0 &0 &0 &0\\ \hline B &0 &1 &0.58 &0 &0 &0 &0 &0 &0 &0\\ \hline C &0 &0 &1 &0 &0 &0.69 &0 &0 &0 &0.98\\ \hline D &0 &0 &0 &1 &0 &0 &0 &0 &0 &0.85\\ \hline E &0.87 &0 &0.53 &0 &1 &0 &0 &0 &0.58 &0\\ \hline F &0 &0 &0 &0 &0 &1 &0.8 &0 &0 &0.14\\ \hline G &0 &0 &0 &0 &0.77 &0 &1 &0 &0 &0\\ \hline H &0.52 &0 &0 &0 &0 &0 &0 &1 &0 &0\\ \hline I &0.75 &0 &0 &0 &0 &0 &0 &0 &1 &0.91\\ \hline J &0 &0 &0.57 &0 &0.36 &0 &0 &0 &0 &1\\ \hline \end{array} $$$$\tilde B_{2}=\begin{array} {c|c|c}{M_{10 \times10}} &A &B &C &D &E &F &G &H &I &J\\ \hline A &1 &0.43 &0.43 &0 &0 &0.15 &0 &0 &0 &0.15\\ \hline B &0 &1 &0.58 &0 &0 &0.58 &0 &0 &0 &0.58\\ \hline C &0 &0 &1 &0 &0.36 &0.69 &0.69 &0 &0 &0.98\\ \hline D &0 &0 &0.57 &1 &0.36 &0 &0 &0 &0 &0.85\\ \hline E &0.87 &0.43 &0.53 &0 &1 &0.53 &0 &0 &0.58 &0.58\\ \hline F &0 &0 &0.14 &0 &0.77 &1 &0.8 &0 &0 &0.14\\ \hline G &0.77 &0 &0.53 &0 &0.77 &0 &1 &0 &0.58 &0\\ \hline H &0.52 &0.43 &0.15 &0 &0 &0 &0 &1 &0 &0\\ \hline I &0.75 &0.43 &0.57 &0 &0.36 &0 &0 &0 &1 &0.91\\ \hline J &0.36 &0 &0.57 &0 &0.36 &0.57 &0 &0 &0.36 &1\\ \hline \end{array} $$$$\tilde B_{3}=\begin{array} {c|c|c}{M_{10 \times10}} &A &B &C &D &E &F &G &H &I &J\\ \hline A &1 &0.43 &0.43 &0 &0.15 &0.43 &0.15 &0 &0 &0.43\\ \hline B &0 &1 &0.58 &0 &0.36 &0.58 &0.58 &0 &0 &0.58\\ \hline C &0.36 &0 &1 &0 &0.69 &0.69 &0.69 &0 &0.36 &0.98\\ \hline D &0.36 &0 &0.57 &1 &0.36 &0.57 &0 &0 &0.36 &0.85\\ \hline E &0.87 &0.43 &0.57 &0 &1 &0.53 &0.53 &0 &0.58 &0.58\\ \hline F &0.77 &0 &0.53 &0 &0.77 &1 &0.8 &0 &0.58 &0.14\\ \hline G &0.77 &0.43 &0.53 &0 &0.77 &0.53 &1 &0 &0.58 &0.58\\ \hline H &0.52 &0.43 &0.43 &0 &0 &0.15 &0 &1 &0 &0.15\\ \hline I &0.75 &0.43 &0.57 &0 &0.36 &0.57 &0 &0 &1 &0.91\\ \hline J &0.36 &0.36 &0.57 &0 &0.36 &0.57 &0.57 &0 &0.36 &1\\ \hline \end{array} $$$$\tilde B_{4}=\begin{array} {c|c|c}{M_{10 \times10}} &A &B &C &D &E &F &G &H &I &J\\ \hline A &1 &0.43 &0.43 &0 &0.36 &0.43 &0.43 &0 &0.15 &0.43\\ \hline B &0.36 &1 &0.58 &0 &0.58 &0.58 &0.58 &0 &0.36 &0.58\\ \hline C &0.69 &0.36 &1 &0 &0.69 &0.69 &0.69 &0 &0.58 &0.98\\ \hline D &0.36 &0.36 &0.57 &1 &0.36 &0.57 &0.57 &0 &0.36 &0.85\\ \hline E &0.87 &0.43 &0.57 &0 &1 &0.57 &0.53 &0 &0.58 &0.58\\ \hline F &0.77 &0.43 &0.53 &0 &0.77 &1 &0.8 &0 &0.58 &0.58\\ \hline G &0.77 &0.43 &0.57 &0 &0.77 &0.53 &1 &0 &0.58 &0.58\\ \hline H &0.52 &0.43 &0.43 &0 &0.15 &0.43 &0.15 &1 &0 &0.43\\ \hline I &0.75 &0.43 &0.57 &0 &0.36 &0.57 &0.57 &0 &1 &0.91\\ \hline J &0.36 &0.36 &0.57 &0 &0.57 &0.57 &0.57 &0 &0.36 &1\\ \hline \end{array} $$$$\tilde B_{5}=\begin{array} {c|c|c}{M_{10 \times10}} &A &B &C &D &E &F &G &H &I &J\\ \hline A &1 &0.43 &0.43 &0 &0.43 &0.43 &0.43 &0 &0.36 &0.43\\ \hline B &0.58 &1 &0.58 &0 &0.58 &0.58 &0.58 &0 &0.58 &0.58\\ \hline C &0.69 &0.43 &1 &0 &0.69 &0.69 &0.69 &0 &0.58 &0.98\\ \hline D &0.36 &0.36 &0.57 &1 &0.57 &0.57 &0.57 &0 &0.36 &0.85\\ \hline E &0.87 &0.43 &0.57 &0 &1 &0.57 &0.57 &0 &0.58 &0.58\\ \hline F &0.77 &0.43 &0.57 &0 &0.77 &1 &0.8 &0 &0.58 &0.58\\ \hline G &0.77 &0.43 &0.57 &0 &0.77 &0.57 &1 &0 &0.58 &0.58\\ \hline H &0.52 &0.43 &0.43 &0 &0.36 &0.43 &0.43 &1 &0.15 &0.43\\ \hline I &0.75 &0.43 &0.57 &0 &0.57 &0.57 &0.57 &0 &1 &0.91\\ \hline J &0.57 &0.36 &0.57 &0 &0.57 &0.57 &0.57 &0 &0.57 &1\\ \hline \end{array} $$$$\tilde B_{6}=\begin{array} {c|c|c}{M_{10 \times10}} &A &B &C &D &E &F &G &H &I &J\\ \hline A &1 &0.43 &0.43 &0 &0.43 &0.43 &0.43 &0 &0.43 &0.43\\ \hline B &0.58 &1 &0.58 &0 &0.58 &0.58 &0.58 &0 &0.58 &0.58\\ \hline C &0.69 &0.43 &1 &0 &0.69 &0.69 &0.69 &0 &0.58 &0.98\\ \hline D &0.57 &0.36 &0.57 &1 &0.57 &0.57 &0.57 &0 &0.57 &0.85\\ \hline E &0.87 &0.43 &0.57 &0 &1 &0.57 &0.57 &0 &0.58 &0.58\\ \hline F &0.77 &0.43 &0.57 &0 &0.77 &1 &0.8 &0 &0.58 &0.58\\ \hline G &0.77 &0.43 &0.57 &0 &0.77 &0.57 &1 &0 &0.58 &0.58\\ \hline H &0.52 &0.43 &0.43 &0 &0.43 &0.43 &0.43 &1 &0.36 &0.43\\ \hline I &0.75 &0.43 &0.57 &0 &0.57 &0.57 &0.57 &0 &1 &0.91\\ \hline J &0.57 &0.43 &0.57 &0 &0.57 &0.57 &0.57 &0 &0.57 &1\\ \hline \end{array} $$$$\tilde B_{7}=\begin{array} {c|c|c}{M_{10 \times10}} &A &B &C &D &E &F &G &H &I &J\\ \hline A &1 &0.43 &0.43 &0 &0.43 &0.43 &0.43 &0 &0.43 &0.43\\ \hline B &0.58 &1 &0.58 &0 &0.58 &0.58 &0.58 &0 &0.58 &0.58\\ \hline C &0.69 &0.43 &1 &0 &0.69 &0.69 &0.69 &0 &0.58 &0.98\\ \hline D &0.57 &0.43 &0.57 &1 &0.57 &0.57 &0.57 &0 &0.57 &0.85\\ \hline E &0.87 &0.43 &0.57 &0 &1 &0.57 &0.57 &0 &0.58 &0.58\\ \hline F &0.77 &0.43 &0.57 &0 &0.77 &1 &0.8 &0 &0.58 &0.58\\ \hline G &0.77 &0.43 &0.57 &0 &0.77 &0.57 &1 &0 &0.58 &0.58\\ \hline H &0.52 &0.43 &0.43 &0 &0.43 &0.43 &0.43 &1 &0.43 &0.43\\ \hline I &0.75 &0.43 &0.57 &0 &0.57 &0.57 &0.57 &0 &1 &0.91\\ \hline J &0.57 &0.43 &0.57 &0 &0.57 &0.57 &0.57 &0 &0.57 &1\\ \hline \end{array} $$$$\tilde B_{8}=\begin{array} {c|c|c}{M_{10 \times10}} &A &B &C &D &E &F &G &H &I &J\\ \hline A &1 &0.43 &0.43 &0 &0.43 &0.43 &0.43 &0 &0.43 &0.43\\ \hline B &0.58 &1 &0.58 &0 &0.58 &0.58 &0.58 &0 &0.58 &0.58\\ \hline C &0.69 &0.43 &1 &0 &0.69 &0.69 &0.69 &0 &0.58 &0.98\\ \hline D &0.57 &0.43 &0.57 &1 &0.57 &0.57 &0.57 &0 &0.57 &0.85\\ \hline E &0.87 &0.43 &0.57 &0 &1 &0.57 &0.57 &0 &0.58 &0.58\\ \hline F &0.77 &0.43 &0.57 &0 &0.77 &1 &0.8 &0 &0.58 &0.58\\ \hline G &0.77 &0.43 &0.57 &0 &0.77 &0.57 &1 &0 &0.58 &0.58\\ \hline H &0.52 &0.43 &0.43 &0 &0.43 &0.43 &0.43 &1 &0.43 &0.43\\ \hline I &0.75 &0.43 &0.57 &0 &0.57 &0.57 &0.57 &0 &1 &0.91\\ \hline J &0.57 &0.43 &0.57 &0 &0.57 &0.57 &0.57 &0 &0.57 &1\\ \hline \end{array} $$
模糊可达矩阵 $ \tilde R = \tilde B_{ 8}$
模糊可达矩阵
$$\tilde R=\begin{array} {c|c|c}{M_{10 \times10}} &A &B &C &D &E &F &G &H &I &J\\ \hline A &1 &0.43 &0.43 &0 &0.43 &0.43 &0.43 &0 &0.43 &0.43\\ \hline B &0.58 &1 &0.58 &0 &0.58 &0.58 &0.58 &0 &0.58 &0.58\\ \hline C &0.69 &0.43 &1 &0 &0.69 &0.69 &0.69 &0 &0.58 &0.98\\ \hline D &0.57 &0.43 &0.57 &1 &0.57 &0.57 &0.57 &0 &0.57 &0.85\\ \hline E &0.87 &0.43 &0.57 &0 &1 &0.57 &0.57 &0 &0.58 &0.58\\ \hline F &0.77 &0.43 &0.57 &0 &0.77 &1 &0.8 &0 &0.58 &0.58\\ \hline G &0.77 &0.43 &0.57 &0 &0.77 &0.57 &1 &0 &0.58 &0.58\\ \hline H &0.52 &0.43 &0.43 &0 &0.43 &0.43 &0.43 &1 &0.43 &0.43\\ \hline I &0.75 &0.43 &0.57 &0 &0.57 &0.57 &0.57 &0 &1 &0.91\\ \hline J &0.57 &0.43 &0.57 &0 &0.57 &0.57 &0.57 &0 &0.57 &1\\ \hline \end{array} $$