模糊可达矩阵的运算
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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 $
$$\tilde B=\begin{array} {c|c|c}{M_{12 \times12}} &A &B &C &D &E &F &G &H &I &J &K &L\\
\hline A &1 &0.94 &0 &0 &0 &0 &0 &0 &0.78 &0 &0 &0\\
\hline B &0 &1 &0 &0.76 &0 &0 &0 &0 &0 &0 &0 &0\\
\hline C &0 &0 &1 &0 &0 &0 &0 &0 &0 &0.58 &0.75 &0\\
\hline D &0 &0 &0 &1 &0 &0 &0.66 &0 &0 &0 &0 &0\\
\hline E &0 &0 &0.39 &0 &1 &0 &0 &0 &0 &0.66 &0 &0\\
\hline F &0 &0 &0 &0 &0 &1 &0 &0 &0.83 &0 &0.64 &0\\
\hline G &0 &0 &0 &0 &0 &0 &1 &0 &0 &0 &0 &0.55\\
\hline H &0 &0 &0 &0 &0 &0 &0.97 &1 &0 &0 &0 &0.48\\
\hline I &0 &0.69 &0 &0 &0 &0 &0 &0 &1 &0.13 &0 &0\\
\hline J &0 &0.81 &0 &0 &0 &0 &0 &0 &0 &1 &0 &0\\
\hline K &0 &0 &0 &0 &0 &0.93 &0 &0 &0 &0 &1 &0\\
\hline L &0.5 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1\\
\hline \end{array} $$
基于选择的算子对求解模糊可达矩阵 $ \tilde R $
$$\tilde B_{1}=\begin{array} {c|c|c}{M_{12 \times12}} &A &B &C &D &E &F &G &H &I &J &K &L\\
\hline A &1 &0.94 &0 &0 &0 &0 &0 &0 &0.78 &0 &0 &0\\
\hline B &0 &1 &0 &0.76 &0 &0 &0 &0 &0 &0 &0 &0\\
\hline C &0 &0 &1 &0 &0 &0 &0 &0 &0 &0.58 &0.75 &0\\
\hline D &0 &0 &0 &1 &0 &0 &0.66 &0 &0 &0 &0 &0\\
\hline E &0 &0 &0.39 &0 &1 &0 &0 &0 &0 &0.66 &0 &0\\
\hline F &0 &0 &0 &0 &0 &1 &0 &0 &0.83 &0 &0.64 &0\\
\hline G &0 &0 &0 &0 &0 &0 &1 &0 &0 &0 &0 &0.55\\
\hline H &0 &0 &0 &0 &0 &0 &0.97 &1 &0 &0 &0 &0.48\\
\hline I &0 &0.69 &0 &0 &0 &0 &0 &0 &1 &0.13 &0 &0\\
\hline J &0 &0.81 &0 &0 &0 &0 &0 &0 &0 &1 &0 &0\\
\hline K &0 &0 &0 &0 &0 &0.93 &0 &0 &0 &0 &1 &0\\
\hline L &0.5 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1\\
\hline \end{array} $$$$\tilde B_{2}=\begin{array} {c|c|c}{M_{12 \times12}} &A &B &C &D &E &F &G &H &I &J &K &L\\
\hline A &1 &0.94 &0 &0.76 &0 &0 &0 &0 &0.78 &0.13 &0 &0\\
\hline B &0 &1 &0 &0.76 &0 &0 &0.66 &0 &0 &0 &0 &0\\
\hline C &0 &0.58 &1 &0 &0 &0.75 &0 &0 &0 &0.58 &0.75 &0\\
\hline D &0 &0 &0 &1 &0 &0 &0.66 &0 &0 &0 &0 &0.55\\
\hline E &0 &0.66 &0.39 &0 &1 &0 &0 &0 &0 &0.66 &0.39 &0\\
\hline F &0 &0.69 &0 &0 &0 &1 &0 &0 &0.83 &0.13 &0.64 &0\\
\hline G &0.5 &0 &0 &0 &0 &0 &1 &0 &0 &0 &0 &0.55\\
\hline H &0.48 &0 &0 &0 &0 &0 &0.97 &1 &0 &0 &0 &0.55\\
\hline I &0 &0.69 &0 &0.69 &0 &0 &0 &0 &1 &0.13 &0 &0\\
\hline J &0 &0.81 &0 &0.76 &0 &0 &0 &0 &0 &1 &0 &0\\
\hline K &0 &0 &0 &0 &0 &0.93 &0 &0 &0.83 &0 &1 &0\\
\hline L &0.5 &0.5 &0 &0 &0 &0 &0 &0 &0.5 &0 &0 &1\\
\hline \end{array} $$$$\tilde B_{3}=\begin{array} {c|c|c}{M_{12 \times12}} &A &B &C &D &E &F &G &H &I &J &K &L\\
\hline A &1 &0.94 &0 &0.76 &0 &0 &0.66 &0 &0.78 &0.13 &0 &0\\
\hline B &0 &1 &0 &0.76 &0 &0 &0.66 &0 &0 &0 &0 &0.55\\
\hline C &0 &0.58 &1 &0.58 &0 &0.75 &0 &0 &0.75 &0.58 &0.75 &0\\
\hline D &0.5 &0 &0 &1 &0 &0 &0.66 &0 &0 &0 &0 &0.55\\
\hline E &0 &0.66 &0.39 &0.66 &1 &0.39 &0 &0 &0 &0.66 &0.39 &0\\
\hline F &0 &0.69 &0 &0.69 &0 &1 &0 &0 &0.83 &0.13 &0.64 &0\\
\hline G &0.5 &0.5 &0 &0 &0 &0 &1 &0 &0.5 &0 &0 &0.55\\
\hline H &0.5 &0.48 &0 &0 &0 &0 &0.97 &1 &0.48 &0 &0 &0.55\\
\hline I &0 &0.69 &0 &0.69 &0 &0 &0.66 &0 &1 &0.13 &0 &0\\
\hline J &0 &0.81 &0 &0.76 &0 &0 &0.66 &0 &0 &1 &0 &0\\
\hline K &0 &0.69 &0 &0 &0 &0.93 &0 &0 &0.83 &0.13 &1 &0\\
\hline L &0.5 &0.5 &0 &0.5 &0 &0 &0 &0 &0.5 &0.13 &0 &1\\
\hline \end{array} $$$$\tilde B_{4}=\begin{array} {c|c|c}{M_{12 \times12}} &A &B &C &D &E &F &G &H &I &J &K &L\\
\hline A &1 &0.94 &0 &0.76 &0 &0 &0.66 &0 &0.78 &0.13 &0 &0.55\\
\hline B &0.5 &1 &0 &0.76 &0 &0 &0.66 &0 &0 &0 &0 &0.55\\
\hline C &0 &0.69 &1 &0.58 &0 &0.75 &0.58 &0 &0.75 &0.58 &0.75 &0\\
\hline D &0.5 &0.5 &0 &1 &0 &0 &0.66 &0 &0.5 &0 &0 &0.55\\
\hline E &0 &0.66 &0.39 &0.66 &1 &0.39 &0.66 &0 &0.39 &0.66 &0.39 &0\\
\hline F &0 &0.69 &0 &0.69 &0 &1 &0.66 &0 &0.83 &0.13 &0.64 &0\\
\hline G &0.5 &0.5 &0 &0.5 &0 &0 &1 &0 &0.5 &0.13 &0 &0.55\\
\hline H &0.5 &0.5 &0 &0.48 &0 &0 &0.97 &1 &0.5 &0.13 &0 &0.55\\
\hline I &0 &0.69 &0 &0.69 &0 &0 &0.66 &0 &1 &0.13 &0 &0.55\\
\hline J &0 &0.81 &0 &0.76 &0 &0 &0.66 &0 &0 &1 &0 &0.55\\
\hline K &0 &0.69 &0 &0.69 &0 &0.93 &0 &0 &0.83 &0.13 &1 &0\\
\hline L &0.5 &0.5 &0 &0.5 &0 &0 &0.5 &0 &0.5 &0.13 &0 &1\\
\hline \end{array} $$$$\tilde B_{5}=\begin{array} {c|c|c}{M_{12 \times12}} &A &B &C &D &E &F &G &H &I &J &K &L\\
\hline A &1 &0.94 &0 &0.76 &0 &0 &0.66 &0 &0.78 &0.13 &0 &0.55\\
\hline B &0.5 &1 &0 &0.76 &0 &0 &0.66 &0 &0.5 &0 &0 &0.55\\
\hline C &0 &0.69 &1 &0.69 &0 &0.75 &0.58 &0 &0.75 &0.58 &0.75 &0.55\\
\hline D &0.5 &0.5 &0 &1 &0 &0 &0.66 &0 &0.5 &0.13 &0 &0.55\\
\hline E &0 &0.66 &0.39 &0.66 &1 &0.39 &0.66 &0 &0.39 &0.66 &0.39 &0.55\\
\hline F &0 &0.69 &0 &0.69 &0 &1 &0.66 &0 &0.83 &0.13 &0.64 &0.55\\
\hline G &0.5 &0.5 &0 &0.5 &0 &0 &1 &0 &0.5 &0.13 &0 &0.55\\
\hline H &0.5 &0.5 &0 &0.5 &0 &0 &0.97 &1 &0.5 &0.13 &0 &0.55\\
\hline I &0.5 &0.69 &0 &0.69 &0 &0 &0.66 &0 &1 &0.13 &0 &0.55\\
\hline J &0.5 &0.81 &0 &0.76 &0 &0 &0.66 &0 &0 &1 &0 &0.55\\
\hline K &0 &0.69 &0 &0.69 &0 &0.93 &0.66 &0 &0.83 &0.13 &1 &0\\
\hline L &0.5 &0.5 &0 &0.5 &0 &0 &0.5 &0 &0.5 &0.13 &0 &1\\
\hline \end{array} $$$$\tilde B_{6}=\begin{array} {c|c|c}{M_{12 \times12}} &A &B &C &D &E &F &G &H &I &J &K &L\\
\hline A &1 &0.94 &0 &0.76 &0 &0 &0.66 &0 &0.78 &0.13 &0 &0.55\\
\hline B &0.5 &1 &0 &0.76 &0 &0 &0.66 &0 &0.5 &0.13 &0 &0.55\\
\hline C &0.5 &0.69 &1 &0.69 &0 &0.75 &0.66 &0 &0.75 &0.58 &0.75 &0.55\\
\hline D &0.5 &0.5 &0 &1 &0 &0 &0.66 &0 &0.5 &0.13 &0 &0.55\\
\hline E &0.5 &0.66 &0.39 &0.66 &1 &0.39 &0.66 &0 &0.39 &0.66 &0.39 &0.55\\
\hline F &0.5 &0.69 &0 &0.69 &0 &1 &0.66 &0 &0.83 &0.13 &0.64 &0.55\\
\hline G &0.5 &0.5 &0 &0.5 &0 &0 &1 &0 &0.5 &0.13 &0 &0.55\\
\hline H &0.5 &0.5 &0 &0.5 &0 &0 &0.97 &1 &0.5 &0.13 &0 &0.55\\
\hline I &0.5 &0.69 &0 &0.69 &0 &0 &0.66 &0 &1 &0.13 &0 &0.55\\
\hline J &0.5 &0.81 &0 &0.76 &0 &0 &0.66 &0 &0.5 &1 &0 &0.55\\
\hline K &0 &0.69 &0 &0.69 &0 &0.93 &0.66 &0 &0.83 &0.13 &1 &0.55\\
\hline L &0.5 &0.5 &0 &0.5 &0 &0 &0.5 &0 &0.5 &0.13 &0 &1\\
\hline \end{array} $$$$\tilde B_{7}=\begin{array} {c|c|c}{M_{12 \times12}} &A &B &C &D &E &F &G &H &I &J &K &L\\
\hline A &1 &0.94 &0 &0.76 &0 &0 &0.66 &0 &0.78 &0.13 &0 &0.55\\
\hline B &0.5 &1 &0 &0.76 &0 &0 &0.66 &0 &0.5 &0.13 &0 &0.55\\
\hline C &0.5 &0.69 &1 &0.69 &0 &0.75 &0.66 &0 &0.75 &0.58 &0.75 &0.55\\
\hline D &0.5 &0.5 &0 &1 &0 &0 &0.66 &0 &0.5 &0.13 &0 &0.55\\
\hline E &0.5 &0.66 &0.39 &0.66 &1 &0.39 &0.66 &0 &0.5 &0.66 &0.39 &0.55\\
\hline F &0.5 &0.69 &0 &0.69 &0 &1 &0.66 &0 &0.83 &0.13 &0.64 &0.55\\
\hline G &0.5 &0.5 &0 &0.5 &0 &0 &1 &0 &0.5 &0.13 &0 &0.55\\
\hline H &0.5 &0.5 &0 &0.5 &0 &0 &0.97 &1 &0.5 &0.13 &0 &0.55\\
\hline I &0.5 &0.69 &0 &0.69 &0 &0 &0.66 &0 &1 &0.13 &0 &0.55\\
\hline J &0.5 &0.81 &0 &0.76 &0 &0 &0.66 &0 &0.5 &1 &0 &0.55\\
\hline K &0.5 &0.69 &0 &0.69 &0 &0.93 &0.66 &0 &0.83 &0.13 &1 &0.55\\
\hline L &0.5 &0.5 &0 &0.5 &0 &0 &0.5 &0 &0.5 &0.13 &0 &1\\
\hline \end{array} $$$$\tilde B_{8}=\begin{array} {c|c|c}{M_{12 \times12}} &A &B &C &D &E &F &G &H &I &J &K &L\\
\hline A &1 &0.94 &0 &0.76 &0 &0 &0.66 &0 &0.78 &0.13 &0 &0.55\\
\hline B &0.5 &1 &0 &0.76 &0 &0 &0.66 &0 &0.5 &0.13 &0 &0.55\\
\hline C &0.5 &0.69 &1 &0.69 &0 &0.75 &0.66 &0 &0.75 &0.58 &0.75 &0.55\\
\hline D &0.5 &0.5 &0 &1 &0 &0 &0.66 &0 &0.5 &0.13 &0 &0.55\\
\hline E &0.5 &0.66 &0.39 &0.66 &1 &0.39 &0.66 &0 &0.5 &0.66 &0.39 &0.55\\
\hline F &0.5 &0.69 &0 &0.69 &0 &1 &0.66 &0 &0.83 &0.13 &0.64 &0.55\\
\hline G &0.5 &0.5 &0 &0.5 &0 &0 &1 &0 &0.5 &0.13 &0 &0.55\\
\hline H &0.5 &0.5 &0 &0.5 &0 &0 &0.97 &1 &0.5 &0.13 &0 &0.55\\
\hline I &0.5 &0.69 &0 &0.69 &0 &0 &0.66 &0 &1 &0.13 &0 &0.55\\
\hline J &0.5 &0.81 &0 &0.76 &0 &0 &0.66 &0 &0.5 &1 &0 &0.55\\
\hline K &0.5 &0.69 &0 &0.69 &0 &0.93 &0.66 &0 &0.83 &0.13 &1 &0.55\\
\hline L &0.5 &0.5 &0 &0.5 &0 &0 &0.5 &0 &0.5 &0.13 &0 &1\\
\hline \end{array} $$ 模糊可达矩阵 $ \tilde R = \tilde B_{ 8}$
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