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 $
$$\tilde B=\begin{array} {c|c|c}{M_{12 \times12}} &A1 &A2 &A3 &A4 &A5 &A6 &A7 &A8 &A9 &A10 &A11 &A12\\
\hline A1 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.2 &0\\
\hline A2 &0 &1 &0 &0 &0 &0.05 &0 &0 &0 &0 &0 &0\\
\hline A3 &0 &0 &1 &0 &0 &0 &0 &0 &0.18 &0 &0 &0\\
\hline A4 &0 &0 &0.04 &1 &0 &0 &0 &0 &0 &0.01 &0 &0\\
\hline A5 &0 &0 &0.56 &0 &1 &0 &0 &0.09 &0 &0 &0 &0.43\\
\hline A6 &0 &0 &0 &0 &0.53 &1 &0 &0 &0 &0 &0 &0\\
\hline A7 &0 &0 &0 &0 &0 &0 &1 &0 &0 &0.85 &0 &0\\
\hline A8 &0 &0.81 &0 &0 &0 &0 &0 &1 &0 &0 &0 &0\\
\hline A9 &0 &0 &0 &0 &0.29 &0 &0 &0 &1 &0 &0 &0\\
\hline A10 &0.33 &0 &0 &0 &0 &0 &0 &0 &0 &1 &0 &0\\
\hline A11 &0 &0 &0 &0 &0 &0.05 &0 &0.39 &0 &0.1 &1 &0\\
\hline A12 &0 &0 &0 &0.18 &0 &0 &0 &0 &0 &0 &0 &1\\
\hline \end{array} $$
基于选择的算子对求解模糊可达矩阵 $ \tilde R $
$$\tilde B_{1}=\begin{array} {c|c|c}{M_{12 \times12}} &A1 &A2 &A3 &A4 &A5 &A6 &A7 &A8 &A9 &A10 &A11 &A12\\
\hline A1 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.2 &0\\
\hline A2 &0 &1 &0 &0 &0 &0.05 &0 &0 &0 &0 &0 &0\\
\hline A3 &0 &0 &1 &0 &0 &0 &0 &0 &0.18 &0 &0 &0\\
\hline A4 &0 &0 &0.04 &1 &0 &0 &0 &0 &0 &0.01 &0 &0\\
\hline A5 &0 &0 &0.56 &0 &1 &0 &0 &0.09 &0 &0 &0 &0.43\\
\hline A6 &0 &0 &0 &0 &0.53 &1 &0 &0 &0 &0 &0 &0\\
\hline A7 &0 &0 &0 &0 &0 &0 &1 &0 &0 &0.85 &0 &0\\
\hline A8 &0 &0.81 &0 &0 &0 &0 &0 &1 &0 &0 &0 &0\\
\hline A9 &0 &0 &0 &0 &0.29 &0 &0 &0 &1 &0 &0 &0\\
\hline A10 &0.33 &0 &0 &0 &0 &0 &0 &0 &0 &1 &0 &0\\
\hline A11 &0 &0 &0 &0 &0 &0.05 &0 &0.39 &0 &0.1 &1 &0\\
\hline A12 &0 &0 &0 &0.18 &0 &0 &0 &0 &0 &0 &0 &1\\
\hline \end{array} $$$$\tilde B_{2}=\begin{array} {c|c|c}{M_{12 \times12}} &A1 &A2 &A3 &A4 &A5 &A6 &A7 &A8 &A9 &A10 &A11 &A12\\
\hline A1 &1 &0 &0 &0 &0 &0.05 &0 &0.2 &0 &0.1 &0.2 &0\\
\hline A2 &0 &1 &0 &0 &0.05 &0.05 &0 &0 &0 &0 &0 &0\\
\hline A3 &0 &0 &1 &0 &0.18 &0 &0 &0 &0.18 &0 &0 &0\\
\hline A4 &0.01 &0 &0.04 &1 &0 &0 &0 &0 &0.04 &0.01 &0 &0\\
\hline A5 &0 &0.09 &0.56 &0.18 &1 &0 &0 &0.09 &0.18 &0 &0 &0.43\\
\hline A6 &0 &0 &0.53 &0 &0.53 &1 &0 &0.09 &0 &0 &0 &0.43\\
\hline A7 &0.33 &0 &0 &0 &0 &0 &1 &0 &0 &0.85 &0 &0\\
\hline A8 &0 &0.81 &0 &0 &0 &0.05 &0 &1 &0 &0 &0 &0\\
\hline A9 &0 &0 &0.29 &0 &0.29 &0 &0 &0.09 &1 &0 &0 &0.29\\
\hline A10 &0.33 &0 &0 &0 &0 &0 &0 &0 &0 &1 &0.2 &0\\
\hline A11 &0.1 &0.39 &0 &0 &0.05 &0.05 &0 &0.39 &0 &0.1 &1 &0\\
\hline A12 &0 &0 &0.04 &0.18 &0 &0 &0 &0 &0 &0.01 &0 &1\\
\hline \end{array} $$$$\tilde B_{3}=\begin{array} {c|c|c}{M_{12 \times12}} &A1 &A2 &A3 &A4 &A5 &A6 &A7 &A8 &A9 &A10 &A11 &A12\\
\hline A1 &1 &0.2 &0 &0 &0.05 &0.05 &0 &0.2 &0 &0.1 &0.2 &0\\
\hline A2 &0 &1 &0.05 &0 &0.05 &0.05 &0 &0.05 &0 &0 &0 &0.05\\
\hline A3 &0 &0 &1 &0 &0.18 &0 &0 &0.09 &0.18 &0 &0 &0.18\\
\hline A4 &0.01 &0 &0.04 &1 &0.04 &0 &0 &0 &0.04 &0.01 &0.01 &0\\
\hline A5 &0 &0.09 &0.56 &0.18 &1 &0.05 &0 &0.09 &0.18 &0.01 &0 &0.43\\
\hline A6 &0 &0.09 &0.53 &0.18 &0.53 &1 &0 &0.09 &0.18 &0 &0 &0.43\\
\hline A7 &0.33 &0 &0 &0 &0 &0 &1 &0 &0 &0.85 &0.2 &0\\
\hline A8 &0 &0.81 &0 &0 &0.05 &0.05 &0 &1 &0 &0 &0 &0\\
\hline A9 &0 &0.09 &0.29 &0.18 &0.29 &0 &0 &0.09 &1 &0 &0 &0.29\\
\hline A10 &0.33 &0 &0 &0 &0 &0.05 &0 &0.2 &0 &1 &0.2 &0\\
\hline A11 &0.1 &0.39 &0.05 &0 &0.05 &0.05 &0 &0.39 &0 &0.1 &1 &0.05\\
\hline A12 &0.01 &0 &0.04 &0.18 &0 &0 &0 &0 &0.04 &0.01 &0 &1\\
\hline \end{array} $$$$\tilde B_{4}=\begin{array} {c|c|c}{M_{12 \times12}} &A1 &A2 &A3 &A4 &A5 &A6 &A7 &A8 &A9 &A10 &A11 &A12\\
\hline A1 &1 &0.2 &0.05 &0 &0.05 &0.05 &0 &0.2 &0 &0.1 &0.2 &0.05\\
\hline A2 &0 &1 &0.05 &0.05 &0.05 &0.05 &0 &0.05 &0.05 &0 &0 &0.05\\
\hline A3 &0 &0.09 &1 &0.18 &0.18 &0 &0 &0.09 &0.18 &0 &0 &0.18\\
\hline A4 &0.01 &0 &0.04 &1 &0.04 &0.01 &0 &0.04 &0.04 &0.01 &0.01 &0.04\\
\hline A5 &0.01 &0.09 &0.56 &0.18 &1 &0.05 &0 &0.09 &0.18 &0.01 &0 &0.43\\
\hline A6 &0 &0.09 &0.53 &0.18 &0.53 &1 &0 &0.09 &0.18 &0.01 &0 &0.43\\
\hline A7 &0.33 &0 &0 &0 &0 &0.05 &1 &0.2 &0 &0.85 &0.2 &0\\
\hline A8 &0 &0.81 &0.05 &0 &0.05 &0.05 &0 &1 &0 &0 &0 &0.05\\
\hline A9 &0 &0.09 &0.29 &0.18 &0.29 &0.05 &0 &0.09 &1 &0.01 &0 &0.29\\
\hline A10 &0.33 &0.2 &0 &0 &0.05 &0.05 &0 &0.2 &0 &1 &0.2 &0\\
\hline A11 &0.1 &0.39 &0.05 &0.05 &0.05 &0.05 &0 &0.39 &0.05 &0.1 &1 &0.05\\
\hline A12 &0.01 &0 &0.04 &0.18 &0.04 &0 &0 &0 &0.04 &0.01 &0.01 &1\\
\hline \end{array} $$$$\tilde B_{5}=\begin{array} {c|c|c}{M_{12 \times12}} &A1 &A2 &A3 &A4 &A5 &A6 &A7 &A8 &A9 &A10 &A11 &A12\\
\hline A1 &1 &0.2 &0.05 &0.05 &0.05 &0.05 &0 &0.2 &0.05 &0.1 &0.2 &0.05\\
\hline A2 &0 &1 &0.05 &0.05 &0.05 &0.05 &0 &0.05 &0.05 &0.01 &0 &0.05\\
\hline A3 &0 &0.09 &1 &0.18 &0.18 &0.05 &0 &0.09 &0.18 &0.01 &0 &0.18\\
\hline A4 &0.01 &0.04 &0.04 &1 &0.04 &0.01 &0 &0.04 &0.04 &0.01 &0.01 &0.04\\
\hline A5 &0.01 &0.09 &0.56 &0.18 &1 &0.05 &0 &0.09 &0.18 &0.01 &0.01 &0.43\\
\hline A6 &0.01 &0.09 &0.53 &0.18 &0.53 &1 &0 &0.09 &0.18 &0.01 &0 &0.43\\
\hline A7 &0.33 &0.2 &0 &0 &0.05 &0.05 &1 &0.2 &0 &0.85 &0.2 &0\\
\hline A8 &0 &0.81 &0.05 &0.05 &0.05 &0.05 &0 &1 &0.05 &0 &0 &0.05\\
\hline A9 &0.01 &0.09 &0.29 &0.18 &0.29 &0.05 &0 &0.09 &1 &0.01 &0 &0.29\\
\hline A10 &0.33 &0.2 &0.05 &0 &0.05 &0.05 &0 &0.2 &0 &1 &0.2 &0.05\\
\hline A11 &0.1 &0.39 &0.05 &0.05 &0.05 &0.05 &0 &0.39 &0.05 &0.1 &1 &0.05\\
\hline A12 &0.01 &0 &0.04 &0.18 &0.04 &0.01 &0 &0.04 &0.04 &0.01 &0.01 &1\\
\hline \end{array} $$$$\tilde B_{6}=\begin{array} {c|c|c}{M_{12 \times12}} &A1 &A2 &A3 &A4 &A5 &A6 &A7 &A8 &A9 &A10 &A11 &A12\\
\hline A1 &1 &0.2 &0.05 &0.05 &0.05 &0.05 &0 &0.2 &0.05 &0.1 &0.2 &0.05\\
\hline A2 &0.01 &1 &0.05 &0.05 &0.05 &0.05 &0 &0.05 &0.05 &0.01 &0 &0.05\\
\hline A3 &0.01 &0.09 &1 &0.18 &0.18 &0.05 &0 &0.09 &0.18 &0.01 &0 &0.18\\
\hline A4 &0.01 &0.04 &0.04 &1 &0.04 &0.04 &0 &0.04 &0.04 &0.01 &0.01 &0.04\\
\hline A5 &0.01 &0.09 &0.56 &0.18 &1 &0.05 &0 &0.09 &0.18 &0.01 &0.01 &0.43\\
\hline A6 &0.01 &0.09 &0.53 &0.18 &0.53 &1 &0 &0.09 &0.18 &0.01 &0.01 &0.43\\
\hline A7 &0.33 &0.2 &0.05 &0 &0.05 &0.05 &1 &0.2 &0 &0.85 &0.2 &0.05\\
\hline A8 &0 &0.81 &0.05 &0.05 &0.05 &0.05 &0 &1 &0.05 &0.01 &0 &0.05\\
\hline A9 &0.01 &0.09 &0.29 &0.18 &0.29 &0.05 &0 &0.09 &1 &0.01 &0.01 &0.29\\
\hline A10 &0.33 &0.2 &0.05 &0.05 &0.05 &0.05 &0 &0.2 &0.05 &1 &0.2 &0.05\\
\hline A11 &0.1 &0.39 &0.05 &0.05 &0.05 &0.05 &0 &0.39 &0.05 &0.1 &1 &0.05\\
\hline A12 &0.01 &0.04 &0.04 &0.18 &0.04 &0.01 &0 &0.04 &0.04 &0.01 &0.01 &1\\
\hline \end{array} $$$$\tilde B_{7}=\begin{array} {c|c|c}{M_{12 \times12}} &A1 &A2 &A3 &A4 &A5 &A6 &A7 &A8 &A9 &A10 &A11 &A12\\
\hline A1 &1 &0.2 &0.05 &0.05 &0.05 &0.05 &0 &0.2 &0.05 &0.1 &0.2 &0.05\\
\hline A2 &0.01 &1 &0.05 &0.05 &0.05 &0.05 &0 &0.05 &0.05 &0.01 &0.01 &0.05\\
\hline A3 &0.01 &0.09 &1 &0.18 &0.18 &0.05 &0 &0.09 &0.18 &0.01 &0.01 &0.18\\
\hline A4 &0.01 &0.04 &0.04 &1 &0.04 &0.04 &0 &0.04 &0.04 &0.01 &0.01 &0.04\\
\hline A5 &0.01 &0.09 &0.56 &0.18 &1 &0.05 &0 &0.09 &0.18 &0.01 &0.01 &0.43\\
\hline A6 &0.01 &0.09 &0.53 &0.18 &0.53 &1 &0 &0.09 &0.18 &0.01 &0.01 &0.43\\
\hline A7 &0.33 &0.2 &0.05 &0.05 &0.05 &0.05 &1 &0.2 &0.05 &0.85 &0.2 &0.05\\
\hline A8 &0.01 &0.81 &0.05 &0.05 &0.05 &0.05 &0 &1 &0.05 &0.01 &0 &0.05\\
\hline A9 &0.01 &0.09 &0.29 &0.18 &0.29 &0.05 &0 &0.09 &1 &0.01 &0.01 &0.29\\
\hline A10 &0.33 &0.2 &0.05 &0.05 &0.05 &0.05 &0 &0.2 &0.05 &1 &0.2 &0.05\\
\hline A11 &0.1 &0.39 &0.05 &0.05 &0.05 &0.05 &0 &0.39 &0.05 &0.1 &1 &0.05\\
\hline A12 &0.01 &0.04 &0.04 &0.18 &0.04 &0.04 &0 &0.04 &0.04 &0.01 &0.01 &1\\
\hline \end{array} $$$$\tilde B_{8}=\begin{array} {c|c|c}{M_{12 \times12}} &A1 &A2 &A3 &A4 &A5 &A6 &A7 &A8 &A9 &A10 &A11 &A12\\
\hline A1 &1 &0.2 &0.05 &0.05 &0.05 &0.05 &0 &0.2 &0.05 &0.1 &0.2 &0.05\\
\hline A2 &0.01 &1 &0.05 &0.05 &0.05 &0.05 &0 &0.05 &0.05 &0.01 &0.01 &0.05\\
\hline A3 &0.01 &0.09 &1 &0.18 &0.18 &0.05 &0 &0.09 &0.18 &0.01 &0.01 &0.18\\
\hline A4 &0.01 &0.04 &0.04 &1 &0.04 &0.04 &0 &0.04 &0.04 &0.01 &0.01 &0.04\\
\hline A5 &0.01 &0.09 &0.56 &0.18 &1 &0.05 &0 &0.09 &0.18 &0.01 &0.01 &0.43\\
\hline A6 &0.01 &0.09 &0.53 &0.18 &0.53 &1 &0 &0.09 &0.18 &0.01 &0.01 &0.43\\
\hline A7 &0.33 &0.2 &0.05 &0.05 &0.05 &0.05 &1 &0.2 &0.05 &0.85 &0.2 &0.05\\
\hline A8 &0.01 &0.81 &0.05 &0.05 &0.05 &0.05 &0 &1 &0.05 &0.01 &0.01 &0.05\\
\hline A9 &0.01 &0.09 &0.29 &0.18 &0.29 &0.05 &0 &0.09 &1 &0.01 &0.01 &0.29\\
\hline A10 &0.33 &0.2 &0.05 &0.05 &0.05 &0.05 &0 &0.2 &0.05 &1 &0.2 &0.05\\
\hline A11 &0.1 &0.39 &0.05 &0.05 &0.05 &0.05 &0 &0.39 &0.05 &0.1 &1 &0.05\\
\hline A12 &0.01 &0.04 &0.04 &0.18 &0.04 &0.04 &0 &0.04 &0.04 &0.01 &0.01 &1\\
\hline \end{array} $$$$\tilde B_{9}=\begin{array} {c|c|c}{M_{12 \times12}} &A1 &A2 &A3 &A4 &A5 &A6 &A7 &A8 &A9 &A10 &A11 &A12\\
\hline A1 &1 &0.2 &0.05 &0.05 &0.05 &0.05 &0 &0.2 &0.05 &0.1 &0.2 &0.05\\
\hline A2 &0.01 &1 &0.05 &0.05 &0.05 &0.05 &0 &0.05 &0.05 &0.01 &0.01 &0.05\\
\hline A3 &0.01 &0.09 &1 &0.18 &0.18 &0.05 &0 &0.09 &0.18 &0.01 &0.01 &0.18\\
\hline A4 &0.01 &0.04 &0.04 &1 &0.04 &0.04 &0 &0.04 &0.04 &0.01 &0.01 &0.04\\
\hline A5 &0.01 &0.09 &0.56 &0.18 &1 &0.05 &0 &0.09 &0.18 &0.01 &0.01 &0.43\\
\hline A6 &0.01 &0.09 &0.53 &0.18 &0.53 &1 &0 &0.09 &0.18 &0.01 &0.01 &0.43\\
\hline A7 &0.33 &0.2 &0.05 &0.05 &0.05 &0.05 &1 &0.2 &0.05 &0.85 &0.2 &0.05\\
\hline A8 &0.01 &0.81 &0.05 &0.05 &0.05 &0.05 &0 &1 &0.05 &0.01 &0.01 &0.05\\
\hline A9 &0.01 &0.09 &0.29 &0.18 &0.29 &0.05 &0 &0.09 &1 &0.01 &0.01 &0.29\\
\hline A10 &0.33 &0.2 &0.05 &0.05 &0.05 &0.05 &0 &0.2 &0.05 &1 &0.2 &0.05\\
\hline A11 &0.1 &0.39 &0.05 &0.05 &0.05 &0.05 &0 &0.39 &0.05 &0.1 &1 &0.05\\
\hline A12 &0.01 &0.04 &0.04 &0.18 &0.04 &0.04 &0 &0.04 &0.04 &0.01 &0.01 &1\\
\hline \end{array} $$ 模糊可达矩阵 $ \tilde R = \tilde B_{ 9}$
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