模糊可达矩阵的运算


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模糊乘算子 模糊加算子



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 $


$$\tilde B=\begin{array} {c|c|c}{M_{12 \times12}} &t1 &t2 &t3 &t4 &t5 &t6 &t7 &t8 &t9 &t10 &t11 &t12\\ \hline t1 &1 &0 &0 &0 &0 &0.64 &0 &0 &0 &0 &0 &0\\ \hline t2 &0 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0.84 &0\\ \hline t3 &0.77 &0 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline t4 &0 &0 &0 &1 &0 &0 &0 &0.03 &0 &0 &0 &0\\ \hline t5 &0.9 &0 &0 &0 &1 &0 &0 &0 &0 &0 &0 &0\\ \hline t6 &0 &0 &0 &0 &0 &1 &0 &0.69 &0 &0 &0.56 &0\\ \hline t7 &0 &0 &0 &0.7 &0 &0 &1 &0 &0 &0 &0 &0\\ \hline t8 &0.94 &0 &0 &0.9 &0 &0 &0 &1 &0 &0.8 &0 &0\\ \hline t9 &0 &0 &0 &0 &0 &0 &0 &0 &1 &0 &0 &0.35\\ \hline t10 &0.64 &0 &0 &0 &0 &0 &0.8 &0.93 &0 &1 &0 &0\\ \hline t11 &0 &0 &0 &0.67 &0 &0 &0 &0 &0 &0.98 &1 &0\\ \hline t12 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.26 &0 &1\\ \hline \end{array} $$

基于选择的算子对求解模糊可达矩阵 $ \tilde R $


$$\tilde B_{1}=\begin{array} {c|c|c}{M_{12 \times12}} &t1 &t2 &t3 &t4 &t5 &t6 &t7 &t8 &t9 &t10 &t11 &t12\\ \hline t1 &1 &0 &0 &0 &0 &0.64 &0 &0 &0 &0 &0 &0\\ \hline t2 &0 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0.84 &0\\ \hline t3 &0.77 &0 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline t4 &0 &0 &0 &1 &0 &0 &0 &0.03 &0 &0 &0 &0\\ \hline t5 &0.9 &0 &0 &0 &1 &0 &0 &0 &0 &0 &0 &0\\ \hline t6 &0 &0 &0 &0 &0 &1 &0 &0.69 &0 &0 &0.56 &0\\ \hline t7 &0 &0 &0 &0.7 &0 &0 &1 &0 &0 &0 &0 &0\\ \hline t8 &0.94 &0 &0 &0.9 &0 &0 &0 &1 &0 &0.8 &0 &0\\ \hline t9 &0 &0 &0 &0 &0 &0 &0 &0 &1 &0 &0 &0.35\\ \hline t10 &0.64 &0 &0 &0 &0 &0 &0.8 &0.93 &0 &1 &0 &0\\ \hline t11 &0 &0 &0 &0.67 &0 &0 &0 &0 &0 &0.98 &1 &0\\ \hline t12 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.26 &0 &1\\ \hline \end{array} $$$$\tilde B_{2}=\begin{array} {c|c|c}{M_{12 \times12}} &t1 &t2 &t3 &t4 &t5 &t6 &t7 &t8 &t9 &t10 &t11 &t12\\ \hline t1 &1 &0 &0 &0 &0 &0.64 &0 &0.64 &0 &0 &0.56 &0\\ \hline t2 &0 &1 &0 &0.67 &0 &0 &0 &0 &0 &0.84 &0.84 &0\\ \hline t3 &0.77 &0 &1 &0 &0 &0.64 &0 &0 &0 &0 &0 &0\\ \hline t4 &0.03 &0 &0 &1 &0 &0 &0 &0.03 &0 &0.03 &0 &0\\ \hline t5 &0.9 &0 &0 &0 &1 &0.64 &0 &0 &0 &0 &0 &0\\ \hline t6 &0.69 &0 &0 &0.69 &0 &1 &0 &0.69 &0 &0.69 &0.56 &0\\ \hline t7 &0 &0 &0 &0.7 &0 &0 &1 &0.03 &0 &0 &0 &0\\ \hline t8 &0.94 &0 &0 &0.9 &0 &0.64 &0.8 &1 &0 &0.8 &0 &0\\ \hline t9 &0 &0 &0 &0 &0 &0 &0 &0 &1 &0.26 &0 &0.35\\ \hline t10 &0.93 &0 &0 &0.9 &0 &0.64 &0.8 &0.93 &0 &1 &0 &0\\ \hline t11 &0.64 &0 &0 &0.67 &0 &0 &0.8 &0.93 &0 &0.98 &1 &0\\ \hline t12 &0.26 &0 &0 &0 &0 &0 &0.26 &0.26 &0 &0.26 &0 &1\\ \hline \end{array} $$$$\tilde B_{3}=\begin{array} {c|c|c}{M_{12 \times12}} &t1 &t2 &t3 &t4 &t5 &t6 &t7 &t8 &t9 &t10 &t11 &t12\\ \hline t1 &1 &0 &0 &0.64 &0 &0.64 &0 &0.64 &0 &0.64 &0.56 &0\\ \hline t2 &0.64 &1 &0 &0.67 &0 &0 &0.8 &0.84 &0 &0.84 &0.84 &0\\ \hline t3 &0.77 &0 &1 &0 &0 &0.64 &0 &0.64 &0 &0 &0.56 &0\\ \hline t4 &0.03 &0 &0 &1 &0 &0.03 &0.03 &0.03 &0 &0.03 &0 &0\\ \hline t5 &0.9 &0 &0 &0 &1 &0.64 &0 &0.64 &0 &0 &0.56 &0\\ \hline t6 &0.69 &0 &0 &0.69 &0 &1 &0.69 &0.69 &0 &0.69 &0.56 &0\\ \hline t7 &0.03 &0 &0 &0.7 &0 &0 &1 &0.03 &0 &0.03 &0 &0\\ \hline t8 &0.94 &0 &0 &0.9 &0 &0.64 &0.8 &1 &0 &0.8 &0.56 &0\\ \hline t9 &0.26 &0 &0 &0 &0 &0 &0.26 &0.26 &1 &0.26 &0 &0.35\\ \hline t10 &0.93 &0 &0 &0.9 &0 &0.64 &0.8 &0.93 &0 &1 &0.56 &0\\ \hline t11 &0.93 &0 &0 &0.9 &0 &0.64 &0.8 &0.93 &0 &0.98 &1 &0\\ \hline t12 &0.26 &0 &0 &0.26 &0 &0.26 &0.26 &0.26 &0 &0.26 &0 &1\\ \hline \end{array} $$$$\tilde B_{4}=\begin{array} {c|c|c}{M_{12 \times12}} &t1 &t2 &t3 &t4 &t5 &t6 &t7 &t8 &t9 &t10 &t11 &t12\\ \hline t1 &1 &0 &0 &0.64 &0 &0.64 &0.64 &0.64 &0 &0.64 &0.56 &0\\ \hline t2 &0.84 &1 &0 &0.84 &0 &0.64 &0.8 &0.84 &0 &0.84 &0.84 &0\\ \hline t3 &0.77 &0 &1 &0.64 &0 &0.64 &0 &0.64 &0 &0.64 &0.56 &0\\ \hline t4 &0.03 &0 &0 &1 &0 &0.03 &0.03 &0.03 &0 &0.03 &0.03 &0\\ \hline t5 &0.9 &0 &0 &0.64 &1 &0.64 &0 &0.64 &0 &0.64 &0.56 &0\\ \hline t6 &0.69 &0 &0 &0.69 &0 &1 &0.69 &0.69 &0 &0.69 &0.56 &0\\ \hline t7 &0.03 &0 &0 &0.7 &0 &0.03 &1 &0.03 &0 &0.03 &0 &0\\ \hline t8 &0.94 &0 &0 &0.9 &0 &0.64 &0.8 &1 &0 &0.8 &0.56 &0\\ \hline t9 &0.26 &0 &0 &0.26 &0 &0.26 &0.26 &0.26 &1 &0.26 &0 &0.35\\ \hline t10 &0.93 &0 &0 &0.9 &0 &0.64 &0.8 &0.93 &0 &1 &0.56 &0\\ \hline t11 &0.93 &0 &0 &0.9 &0 &0.64 &0.8 &0.93 &0 &0.98 &1 &0\\ \hline t12 &0.26 &0 &0 &0.26 &0 &0.26 &0.26 &0.26 &0 &0.26 &0.26 &1\\ \hline \end{array} $$$$\tilde B_{5}=\begin{array} {c|c|c}{M_{12 \times12}} &t1 &t2 &t3 &t4 &t5 &t6 &t7 &t8 &t9 &t10 &t11 &t12\\ \hline t1 &1 &0 &0 &0.64 &0 &0.64 &0.64 &0.64 &0 &0.64 &0.56 &0\\ \hline t2 &0.84 &1 &0 &0.84 &0 &0.64 &0.8 &0.84 &0 &0.84 &0.84 &0\\ \hline t3 &0.77 &0 &1 &0.64 &0 &0.64 &0.64 &0.64 &0 &0.64 &0.56 &0\\ \hline t4 &0.03 &0 &0 &1 &0 &0.03 &0.03 &0.03 &0 &0.03 &0.03 &0\\ \hline t5 &0.9 &0 &0 &0.64 &1 &0.64 &0.64 &0.64 &0 &0.64 &0.56 &0\\ \hline t6 &0.69 &0 &0 &0.69 &0 &1 &0.69 &0.69 &0 &0.69 &0.56 &0\\ \hline t7 &0.03 &0 &0 &0.7 &0 &0.03 &1 &0.03 &0 &0.03 &0.03 &0\\ \hline t8 &0.94 &0 &0 &0.9 &0 &0.64 &0.8 &1 &0 &0.8 &0.56 &0\\ \hline t9 &0.26 &0 &0 &0.26 &0 &0.26 &0.26 &0.26 &1 &0.26 &0.26 &0.35\\ \hline t10 &0.93 &0 &0 &0.9 &0 &0.64 &0.8 &0.93 &0 &1 &0.56 &0\\ \hline t11 &0.93 &0 &0 &0.9 &0 &0.64 &0.8 &0.93 &0 &0.98 &1 &0\\ \hline t12 &0.26 &0 &0 &0.26 &0 &0.26 &0.26 &0.26 &0 &0.26 &0.26 &1\\ \hline \end{array} $$$$\tilde B_{6}=\begin{array} {c|c|c}{M_{12 \times12}} &t1 &t2 &t3 &t4 &t5 &t6 &t7 &t8 &t9 &t10 &t11 &t12\\ \hline t1 &1 &0 &0 &0.64 &0 &0.64 &0.64 &0.64 &0 &0.64 &0.56 &0\\ \hline t2 &0.84 &1 &0 &0.84 &0 &0.64 &0.8 &0.84 &0 &0.84 &0.84 &0\\ \hline t3 &0.77 &0 &1 &0.64 &0 &0.64 &0.64 &0.64 &0 &0.64 &0.56 &0\\ \hline t4 &0.03 &0 &0 &1 &0 &0.03 &0.03 &0.03 &0 &0.03 &0.03 &0\\ \hline t5 &0.9 &0 &0 &0.64 &1 &0.64 &0.64 &0.64 &0 &0.64 &0.56 &0\\ \hline t6 &0.69 &0 &0 &0.69 &0 &1 &0.69 &0.69 &0 &0.69 &0.56 &0\\ \hline t7 &0.03 &0 &0 &0.7 &0 &0.03 &1 &0.03 &0 &0.03 &0.03 &0\\ \hline t8 &0.94 &0 &0 &0.9 &0 &0.64 &0.8 &1 &0 &0.8 &0.56 &0\\ \hline t9 &0.26 &0 &0 &0.26 &0 &0.26 &0.26 &0.26 &1 &0.26 &0.26 &0.35\\ \hline t10 &0.93 &0 &0 &0.9 &0 &0.64 &0.8 &0.93 &0 &1 &0.56 &0\\ \hline t11 &0.93 &0 &0 &0.9 &0 &0.64 &0.8 &0.93 &0 &0.98 &1 &0\\ \hline t12 &0.26 &0 &0 &0.26 &0 &0.26 &0.26 &0.26 &0 &0.26 &0.26 &1\\ \hline \end{array} $$

模糊可达矩阵 $ \tilde R = \tilde B_{ 6}$


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