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
$$\tilde B=\begin{array} {c|c|c}{M_{10 \times10}} &A &B &C &D &E &F &G &H &I &J\\ \hline A &1 &0.84 &0 &0 &0.19 &0 &0 &0 &0 &0\\ \hline B &0 &1 &0 &0.44 &0 &0.17 &0 &0 &0 &0\\ \hline C &0 &0 &1 &0 &0.25 &0 &0 &0 &0 &0\\ \hline D &0 &0 &0 &1 &0.08 &0 &0.99 &0 &0 &0\\ \hline E &0 &0 &0 &0 &1 &0 &0.17 &0 &0 &0.44\\ \hline F &0.39 &0 &0 &0 &0 &1 &0 &0 &0 &0\\ \hline G &0 &0 &0 &0 &0 &0 &1 &0 &0 &0\\ \hline H &0.56 &0 &0 &0 &0 &0 &0 &1 &0 &0.06\\ \hline I &0 &0.48 &0 &0 &0.44 &0 &0.94 &0 &1 &0.09\\ \hline J &0 &0 &0.77 &0 &0 &0 &0 &0.56 &0 &1\\ \hline \end{array} $$
求解过程
$$\tilde B_{1}=\begin{array} {c|c|c}{M_{10 \times10}} &A &B &C &D &E &F &G &H &I &J\\ \hline A &1 &0.84 &0 &0 &0.19 &0 &0 &0 &0 &0\\ \hline B &0 &1 &0 &0.44 &0 &0.17 &0 &0 &0 &0\\ \hline C &0 &0 &1 &0 &0.25 &0 &0 &0 &0 &0\\ \hline D &0 &0 &0 &1 &0.08 &0 &0.99 &0 &0 &0\\ \hline E &0 &0 &0 &0 &1 &0 &0.17 &0 &0 &0.44\\ \hline F &0.39 &0 &0 &0 &0 &1 &0 &0 &0 &0\\ \hline G &0 &0 &0 &0 &0 &0 &1 &0 &0 &0\\ \hline H &0.56 &0 &0 &0 &0 &0 &0 &1 &0 &0.06\\ \hline I &0 &0.48 &0 &0 &0.44 &0 &0.94 &0 &1 &0.09\\ \hline J &0 &0 &0.77 &0 &0 &0 &0 &0.56 &0 &1\\ \hline \end{array} $$$$\tilde B_{2}=\begin{array} {c|c|c}{M_{10 \times10}} &A &B &C &D &E &F &G &H &I &J\\ \hline A &1 &0.84 &0 &0.44 &0.19 &0.17 &0.17 &0 &0 &0.19\\ \hline B &0.17 &1 &0 &0.44 &0.08 &0.17 &0.44 &0 &0 &0\\ \hline C &0 &0 &1 &0 &0.25 &0 &0.17 &0 &0 &0.25\\ \hline D &0 &0 &0 &1 &0.08 &0 &0.99 &0 &0 &0.08\\ \hline E &0 &0 &0.44 &0 &1 &0 &0.17 &0.44 &0 &0.44\\ \hline F &0.39 &0.39 &0 &0 &0.19 &1 &0 &0 &0 &0\\ \hline G &0 &0 &0 &0 &0 &0 &1 &0 &0 &0\\ \hline H &0.56 &0.56 &0.06 &0 &0.19 &0 &0 &1 &0 &0.06\\ \hline I &0 &0.48 &0.09 &0.44 &0.44 &0.17 &0.94 &0.09 &1 &0.44\\ \hline J &0.56 &0 &0.77 &0 &0.25 &0 &0 &0.56 &0 &1\\ \hline \end{array} $$$$\tilde B_{3}=\begin{array} {c|c|c}{M_{10 \times10}} &A &B &C &D &E &F &G &H &I &J\\ \hline A &1 &0.84 &0.19 &0.44 &0.19 &0.17 &0.44 &0.19 &0 &0.19\\ \hline B &0.17 &1 &0 &0.44 &0.17 &0.17 &0.44 &0 &0 &0.08\\ \hline C &0 &0 &1 &0 &0.25 &0 &0.17 &0.25 &0 &0.25\\ \hline D &0 &0 &0.08 &1 &0.08 &0 &0.99 &0.08 &0 &0.08\\ \hline E &0.44 &0 &0.44 &0 &1 &0 &0.17 &0.44 &0 &0.44\\ \hline F &0.39 &0.39 &0 &0.39 &0.19 &1 &0.17 &0 &0 &0.19\\ \hline G &0 &0 &0 &0 &0 &0 &1 &0 &0 &0\\ \hline H &0.56 &0.56 &0.06 &0.44 &0.19 &0.17 &0.17 &1 &0 &0.19\\ \hline I &0.17 &0.48 &0.44 &0.44 &0.44 &0.17 &0.94 &0.44 &1 &0.44\\ \hline J &0.56 &0.56 &0.77 &0 &0.25 &0 &0.17 &0.56 &0 &1\\ \hline \end{array} $$$$\tilde B_{4}=\begin{array} {c|c|c}{M_{10 \times10}} &A &B &C &D &E &F &G &H &I &J\\ \hline A &1 &0.84 &0.19 &0.44 &0.19 &0.17 &0.44 &0.19 &0 &0.19\\ \hline B &0.17 &1 &0.08 &0.44 &0.17 &0.17 &0.44 &0.08 &0 &0.17\\ \hline C &0.25 &0 &1 &0 &0.25 &0 &0.17 &0.25 &0 &0.25\\ \hline D &0.08 &0 &0.08 &1 &0.08 &0 &0.99 &0.08 &0 &0.08\\ \hline E &0.44 &0.44 &0.44 &0 &1 &0 &0.17 &0.44 &0 &0.44\\ \hline F &0.39 &0.39 &0.19 &0.39 &0.19 &1 &0.39 &0.19 &0 &0.19\\ \hline G &0 &0 &0 &0 &0 &0 &1 &0 &0 &0\\ \hline H &0.56 &0.56 &0.19 &0.44 &0.19 &0.17 &0.44 &1 &0 &0.19\\ \hline I &0.44 &0.48 &0.44 &0.44 &0.44 &0.17 &0.94 &0.44 &1 &0.44\\ \hline J &0.56 &0.56 &0.77 &0.44 &0.25 &0.17 &0.17 &0.56 &0 &1\\ \hline \end{array} $$$$\tilde B_{5}=\begin{array} {c|c|c}{M_{10 \times10}} &A &B &C &D &E &F &G &H &I &J\\ \hline A &1 &0.84 &0.19 &0.44 &0.19 &0.17 &0.44 &0.19 &0 &0.19\\ \hline B &0.17 &1 &0.17 &0.44 &0.17 &0.17 &0.44 &0.17 &0 &0.17\\ \hline C &0.25 &0.25 &1 &0 &0.25 &0 &0.17 &0.25 &0 &0.25\\ \hline D &0.08 &0.08 &0.08 &1 &0.08 &0 &0.99 &0.08 &0 &0.08\\ \hline E &0.44 &0.44 &0.44 &0.44 &1 &0.17 &0.17 &0.44 &0 &0.44\\ \hline F &0.39 &0.39 &0.19 &0.39 &0.19 &1 &0.39 &0.19 &0 &0.19\\ \hline G &0 &0 &0 &0 &0 &0 &1 &0 &0 &0\\ \hline H &0.56 &0.56 &0.19 &0.44 &0.19 &0.17 &0.44 &1 &0 &0.19\\ \hline I &0.44 &0.48 &0.44 &0.44 &0.44 &0.17 &0.94 &0.44 &1 &0.44\\ \hline J &0.56 &0.56 &0.77 &0.44 &0.25 &0.17 &0.44 &0.56 &0 &1\\ \hline \end{array} $$$$\tilde B_{6}=\begin{array} {c|c|c}{M_{10 \times10}} &A &B &C &D &E &F &G &H &I &J\\ \hline A &1 &0.84 &0.19 &0.44 &0.19 &0.17 &0.44 &0.19 &0 &0.19\\ \hline B &0.17 &1 &0.17 &0.44 &0.17 &0.17 &0.44 &0.17 &0 &0.17\\ \hline C &0.25 &0.25 &1 &0.25 &0.25 &0.17 &0.17 &0.25 &0 &0.25\\ \hline D &0.08 &0.08 &0.08 &1 &0.08 &0.08 &0.99 &0.08 &0 &0.08\\ \hline E &0.44 &0.44 &0.44 &0.44 &1 &0.17 &0.44 &0.44 &0 &0.44\\ \hline F &0.39 &0.39 &0.19 &0.39 &0.19 &1 &0.39 &0.19 &0 &0.19\\ \hline G &0 &0 &0 &0 &0 &0 &1 &0 &0 &0\\ \hline H &0.56 &0.56 &0.19 &0.44 &0.19 &0.17 &0.44 &1 &0 &0.19\\ \hline I &0.44 &0.48 &0.44 &0.44 &0.44 &0.17 &0.94 &0.44 &1 &0.44\\ \hline J &0.56 &0.56 &0.77 &0.44 &0.25 &0.17 &0.44 &0.56 &0 &1\\ \hline \end{array} $$$$\tilde B_{7}=\begin{array} {c|c|c}{M_{10 \times10}} &A &B &C &D &E &F &G &H &I &J\\ \hline A &1 &0.84 &0.19 &0.44 &0.19 &0.17 &0.44 &0.19 &0 &0.19\\ \hline B &0.17 &1 &0.17 &0.44 &0.17 &0.17 &0.44 &0.17 &0 &0.17\\ \hline C &0.25 &0.25 &1 &0.25 &0.25 &0.17 &0.25 &0.25 &0 &0.25\\ \hline D &0.08 &0.08 &0.08 &1 &0.08 &0.08 &0.99 &0.08 &0 &0.08\\ \hline E &0.44 &0.44 &0.44 &0.44 &1 &0.17 &0.44 &0.44 &0 &0.44\\ \hline F &0.39 &0.39 &0.19 &0.39 &0.19 &1 &0.39 &0.19 &0 &0.19\\ \hline G &0 &0 &0 &0 &0 &0 &1 &0 &0 &0\\ \hline H &0.56 &0.56 &0.19 &0.44 &0.19 &0.17 &0.44 &1 &0 &0.19\\ \hline I &0.44 &0.48 &0.44 &0.44 &0.44 &0.17 &0.94 &0.44 &1 &0.44\\ \hline J &0.56 &0.56 &0.77 &0.44 &0.25 &0.17 &0.44 &0.56 &0 &1\\ \hline \end{array} $$$$\tilde B_{8}=\begin{array} {c|c|c}{M_{10 \times10}} &A &B &C &D &E &F &G &H &I &J\\ \hline A &1 &0.84 &0.19 &0.44 &0.19 &0.17 &0.44 &0.19 &0 &0.19\\ \hline B &0.17 &1 &0.17 &0.44 &0.17 &0.17 &0.44 &0.17 &0 &0.17\\ \hline C &0.25 &0.25 &1 &0.25 &0.25 &0.17 &0.25 &0.25 &0 &0.25\\ \hline D &0.08 &0.08 &0.08 &1 &0.08 &0.08 &0.99 &0.08 &0 &0.08\\ \hline E &0.44 &0.44 &0.44 &0.44 &1 &0.17 &0.44 &0.44 &0 &0.44\\ \hline F &0.39 &0.39 &0.19 &0.39 &0.19 &1 &0.39 &0.19 &0 &0.19\\ \hline G &0 &0 &0 &0 &0 &0 &1 &0 &0 &0\\ \hline H &0.56 &0.56 &0.19 &0.44 &0.19 &0.17 &0.44 &1 &0 &0.19\\ \hline I &0.44 &0.48 &0.44 &0.44 &0.44 &0.17 &0.94 &0.44 &1 &0.44\\ \hline J &0.56 &0.56 &0.77 &0.44 &0.25 &0.17 &0.44 &0.56 &0 &1\\ \hline \end{array} $$
模糊可达矩阵 $ \tilde R = \tilde B_{ 8}$
模糊可达矩阵
$$\tilde R=\begin{array} {c|c|c}{M_{10 \times10}} &A &B &C &D &E &F &G &H &I &J\\ \hline A &1 &0.84 &0.19 &0.44 &0.19 &0.17 &0.44 &0.19 &0 &0.19\\ \hline B &0.17 &1 &0.17 &0.44 &0.17 &0.17 &0.44 &0.17 &0 &0.17\\ \hline C &0.25 &0.25 &1 &0.25 &0.25 &0.17 &0.25 &0.25 &0 &0.25\\ \hline D &0.08 &0.08 &0.08 &1 &0.08 &0.08 &0.99 &0.08 &0 &0.08\\ \hline E &0.44 &0.44 &0.44 &0.44 &1 &0.17 &0.44 &0.44 &0 &0.44\\ \hline F &0.39 &0.39 &0.19 &0.39 &0.19 &1 &0.39 &0.19 &0 &0.19\\ \hline G &0 &0 &0 &0 &0 &0 &1 &0 &0 &0\\ \hline H &0.56 &0.56 &0.19 &0.44 &0.19 &0.17 &0.44 &1 &0 &0.19\\ \hline I &0.44 &0.48 &0.44 &0.44 &0.44 &0.17 &0.94 &0.44 &1 &0.44\\ \hline J &0.56 &0.56 &0.77 &0.44 &0.25 &0.17 &0.44 &0.56 &0 &1\\ \hline \end{array} $$