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 $

$$\tilde B=\begin{array} {c|c|c}{M_{12 \times12}} &子 &丑 &寅 &卯 &辰 &巳 &午 &未 &申 &酉 &戌 &亥\\ \hline 子 &1 &0 &0 &0.52 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline 丑 &0 &1 &0 &0 &0 &0.87 &0 &0 &0 &0 &0 &0\\ \hline 寅 &0 &0 &1 &0 &0 &0 &0 &0 &0 &0.47 &0.28 &0\\ \hline 卯 &0 &0 &0 &1 &0 &0 &0 &0.65 &0 &0 &0 &0\\ \hline 辰 &0 &0 &0.47 &0.72 &1 &0 &0 &0 &0.15 &0 &0 &0\\ \hline 巳 &0 &0 &0 &0.58 &0 &1 &0 &0 &0 &0 &0 &0\\ \hline 午 &0.34 &0 &0.11 &0 &0 &0 &1 &0 &0 &0 &0 &0\\ \hline 未 &0 &0 &0.32 &0 &0 &0 &0 &1 &0 &0 &0 &0\\ \hline 申 &0 &0.29 &0 &0 &0 &0 &0 &0 &1 &0 &0 &0\\ \hline 酉 &0 &0 &0 &0 &0 &0 &0 &0 &0.83 &1 &0 &0\\ \hline 戌 &0 &0 &0 &0 &0 &0.22 &0 &0.83 &0 &0 &1 &0\\ \hline 亥 &0 &0 &0 &0.5 &0 &0 &0 &0 &0 &0.23 &0 &1\\ \hline \end{array} $$

基于选择的算子对求解模糊可达矩阵 $ \tilde R $

$$\tilde B_{1}=\begin{array} {c|c|c}{M_{12 \times12}} &子 &丑 &寅 &卯 &辰 &巳 &午 &未 &申 &酉 &戌 &亥\\ \hline 子 &1 &0 &0 &0.52 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline 丑 &0 &1 &0 &0 &0 &0.87 &0 &0 &0 &0 &0 &0\\ \hline 寅 &0 &0 &1 &0 &0 &0 &0 &0 &0 &0.47 &0.28 &0\\ \hline 卯 &0 &0 &0 &1 &0 &0 &0 &0.65 &0 &0 &0 &0\\ \hline 辰 &0 &0 &0.47 &0.72 &1 &0 &0 &0 &0.15 &0 &0 &0\\ \hline 巳 &0 &0 &0 &0.58 &0 &1 &0 &0 &0 &0 &0 &0\\ \hline 午 &0.34 &0 &0.11 &0 &0 &0 &1 &0 &0 &0 &0 &0\\ \hline 未 &0 &0 &0.32 &0 &0 &0 &0 &1 &0 &0 &0 &0\\ \hline 申 &0 &0.29 &0 &0 &0 &0 &0 &0 &1 &0 &0 &0\\ \hline 酉 &0 &0 &0 &0 &0 &0 &0 &0 &0.83 &1 &0 &0\\ \hline 戌 &0 &0 &0 &0 &0 &0.22 &0 &0.83 &0 &0 &1 &0\\ \hline 亥 &0 &0 &0 &0.5 &0 &0 &0 &0 &0 &0.23 &0 &1\\ \hline \end{array} $$$$\tilde B_{2}=\begin{array} {c|c|c}{M_{12 \times12}} &子 &丑 &寅 &卯 &辰 &巳 &午 &未 &申 &酉 &戌 &亥\\ \hline 子 &1 &0 &0 &0.52 &0 &0 &0 &0.52 &0 &0 &0 &0\\ \hline 丑 &0 &1 &0 &0.58 &0 &0.87 &0 &0 &0 &0 &0 &0\\ \hline 寅 &0 &0 &1 &0 &0 &0.22 &0 &0.28 &0.47 &0.47 &0.28 &0\\ \hline 卯 &0 &0 &0.32 &1 &0 &0 &0 &0.65 &0 &0 &0 &0\\ \hline 辰 &0 &0.15 &0.47 &0.72 &1 &0 &0 &0.65 &0.15 &0.47 &0.28 &0\\ \hline 巳 &0 &0 &0 &0.58 &0 &1 &0 &0.58 &0 &0 &0 &0\\ \hline 午 &0.34 &0 &0.11 &0.34 &0 &0 &1 &0 &0 &0.11 &0.11 &0\\ \hline 未 &0 &0 &0.32 &0 &0 &0 &0 &1 &0 &0.32 &0.28 &0\\ \hline 申 &0 &0.29 &0 &0 &0 &0.29 &0 &0 &1 &0 &0 &0\\ \hline 酉 &0 &0.29 &0 &0 &0 &0 &0 &0 &0.83 &1 &0 &0\\ \hline 戌 &0 &0 &0.32 &0.22 &0 &0.22 &0 &0.83 &0 &0 &1 &0\\ \hline 亥 &0 &0 &0 &0.5 &0 &0 &0 &0.5 &0.23 &0.23 &0 &1\\ \hline \end{array} $$$$\tilde B_{3}=\begin{array} {c|c|c}{M_{12 \times12}} &子 &丑 &寅 &卯 &辰 &巳 &午 &未 &申 &酉 &戌 &亥\\ \hline 子 &1 &0 &0.32 &0.52 &0 &0 &0 &0.52 &0 &0 &0 &0\\ \hline 丑 &0 &1 &0 &0.58 &0 &0.87 &0 &0.58 &0 &0 &0 &0\\ \hline 寅 &0 &0.29 &1 &0.22 &0 &0.22 &0 &0.28 &0.47 &0.47 &0.28 &0\\ \hline 卯 &0 &0 &0.32 &1 &0 &0 &0 &0.65 &0 &0.32 &0.28 &0\\ \hline 辰 &0 &0.15 &0.47 &0.72 &1 &0.22 &0 &0.65 &0.47 &0.47 &0.28 &0\\ \hline 巳 &0 &0 &0.32 &0.58 &0 &1 &0 &0.58 &0 &0 &0 &0\\ \hline 午 &0.34 &0 &0.11 &0.34 &0 &0.11 &1 &0.34 &0.11 &0.11 &0.11 &0\\ \hline 未 &0 &0 &0.32 &0 &0 &0.22 &0 &1 &0.32 &0.32 &0.28 &0\\ \hline 申 &0 &0.29 &0 &0.29 &0 &0.29 &0 &0 &1 &0 &0 &0\\ \hline 酉 &0 &0.29 &0 &0 &0 &0.29 &0 &0 &0.83 &1 &0 &0\\ \hline 戌 &0 &0 &0.32 &0.22 &0 &0.22 &0 &0.83 &0 &0.32 &1 &0\\ \hline 亥 &0 &0.23 &0.32 &0.5 &0 &0 &0 &0.5 &0.23 &0.23 &0 &1\\ \hline \end{array} $$$$\tilde B_{4}=\begin{array} {c|c|c}{M_{12 \times12}} &子 &丑 &寅 &卯 &辰 &巳 &午 &未 &申 &酉 &戌 &亥\\ \hline 子 &1 &0 &0.32 &0.52 &0 &0 &0 &0.52 &0 &0.32 &0.28 &0\\ \hline 丑 &0 &1 &0.32 &0.58 &0 &0.87 &0 &0.58 &0 &0 &0 &0\\ \hline 寅 &0 &0.29 &1 &0.22 &0 &0.29 &0 &0.28 &0.47 &0.47 &0.28 &0\\ \hline 卯 &0 &0 &0.32 &1 &0 &0.22 &0 &0.65 &0.32 &0.32 &0.28 &0\\ \hline 辰 &0 &0.29 &0.47 &0.72 &1 &0.22 &0 &0.65 &0.47 &0.47 &0.28 &0\\ \hline 巳 &0 &0 &0.32 &0.58 &0 &1 &0 &0.58 &0 &0.32 &0.28 &0\\ \hline 午 &0.34 &0.11 &0.32 &0.34 &0 &0.11 &1 &0.34 &0.11 &0.11 &0.11 &0\\ \hline 未 &0 &0.29 &0.32 &0.22 &0 &0.22 &0 &1 &0.32 &0.32 &0.28 &0\\ \hline 申 &0 &0.29 &0 &0.29 &0 &0.29 &0 &0.29 &1 &0 &0 &0\\ \hline 酉 &0 &0.29 &0 &0.29 &0 &0.29 &0 &0 &0.83 &1 &0 &0\\ \hline 戌 &0 &0 &0.32 &0.22 &0 &0.22 &0 &0.83 &0.32 &0.32 &1 &0\\ \hline 亥 &0 &0.23 &0.32 &0.5 &0 &0.23 &0 &0.5 &0.23 &0.32 &0.28 &1\\ \hline \end{array} $$$$\tilde B_{5}=\begin{array} {c|c|c}{M_{12 \times12}} &子 &丑 &寅 &卯 &辰 &巳 &午 &未 &申 &酉 &戌 &亥\\ \hline 子 &1 &0 &0.32 &0.52 &0 &0.22 &0 &0.52 &0.32 &0.32 &0.28 &0\\ \hline 丑 &0 &1 &0.32 &0.58 &0 &0.87 &0 &0.58 &0 &0.32 &0.28 &0\\ \hline 寅 &0 &0.29 &1 &0.29 &0 &0.29 &0 &0.28 &0.47 &0.47 &0.28 &0\\ \hline 卯 &0 &0.29 &0.32 &1 &0 &0.22 &0 &0.65 &0.32 &0.32 &0.28 &0\\ \hline 辰 &0 &0.29 &0.47 &0.72 &1 &0.29 &0 &0.65 &0.47 &0.47 &0.28 &0\\ \hline 巳 &0 &0 &0.32 &0.58 &0 &1 &0 &0.58 &0.32 &0.32 &0.28 &0\\ \hline 午 &0.34 &0.11 &0.32 &0.34 &0 &0.11 &1 &0.34 &0.11 &0.32 &0.28 &0\\ \hline 未 &0 &0.29 &0.32 &0.22 &0 &0.29 &0 &1 &0.32 &0.32 &0.28 &0\\ \hline 申 &0 &0.29 &0.29 &0.29 &0 &0.29 &0 &0.29 &1 &0 &0 &0\\ \hline 酉 &0 &0.29 &0 &0.29 &0 &0.29 &0 &0.29 &0.83 &1 &0 &0\\ \hline 戌 &0 &0.29 &0.32 &0.22 &0 &0.22 &0 &0.83 &0.32 &0.32 &1 &0\\ \hline 亥 &0 &0.23 &0.32 &0.5 &0 &0.23 &0 &0.5 &0.32 &0.32 &0.28 &1\\ \hline \end{array} $$$$\tilde B_{6}=\begin{array} {c|c|c}{M_{12 \times12}} &子 &丑 &寅 &卯 &辰 &巳 &午 &未 &申 &酉 &戌 &亥\\ \hline 子 &1 &0.29 &0.32 &0.52 &0 &0.22 &0 &0.52 &0.32 &0.32 &0.28 &0\\ \hline 丑 &0 &1 &0.32 &0.58 &0 &0.87 &0 &0.58 &0.32 &0.32 &0.28 &0\\ \hline 寅 &0 &0.29 &1 &0.29 &0 &0.29 &0 &0.29 &0.47 &0.47 &0.28 &0\\ \hline 卯 &0 &0.29 &0.32 &1 &0 &0.29 &0 &0.65 &0.32 &0.32 &0.28 &0\\ \hline 辰 &0 &0.29 &0.47 &0.72 &1 &0.29 &0 &0.65 &0.47 &0.47 &0.28 &0\\ \hline 巳 &0 &0.29 &0.32 &0.58 &0 &1 &0 &0.58 &0.32 &0.32 &0.28 &0\\ \hline 午 &0.34 &0.11 &0.32 &0.34 &0 &0.22 &1 &0.34 &0.32 &0.32 &0.28 &0\\ \hline 未 &0 &0.29 &0.32 &0.29 &0 &0.29 &0 &1 &0.32 &0.32 &0.28 &0\\ \hline 申 &0 &0.29 &0.29 &0.29 &0 &0.29 &0 &0.29 &1 &0.29 &0.28 &0\\ \hline 酉 &0 &0.29 &0.29 &0.29 &0 &0.29 &0 &0.29 &0.83 &1 &0 &0\\ \hline 戌 &0 &0.29 &0.32 &0.22 &0 &0.29 &0 &0.83 &0.32 &0.32 &1 &0\\ \hline 亥 &0 &0.29 &0.32 &0.5 &0 &0.23 &0 &0.5 &0.32 &0.32 &0.28 &1\\ \hline \end{array} $$$$\tilde B_{7}=\begin{array} {c|c|c}{M_{12 \times12}} &子 &丑 &寅 &卯 &辰 &巳 &午 &未 &申 &酉 &戌 &亥\\ \hline 子 &1 &0.29 &0.32 &0.52 &0 &0.29 &0 &0.52 &0.32 &0.32 &0.28 &0\\ \hline 丑 &0 &1 &0.32 &0.58 &0 &0.87 &0 &0.58 &0.32 &0.32 &0.28 &0\\ \hline 寅 &0 &0.29 &1 &0.29 &0 &0.29 &0 &0.29 &0.47 &0.47 &0.28 &0\\ \hline 卯 &0 &0.29 &0.32 &1 &0 &0.29 &0 &0.65 &0.32 &0.32 &0.28 &0\\ \hline 辰 &0 &0.29 &0.47 &0.72 &1 &0.29 &0 &0.65 &0.47 &0.47 &0.28 &0\\ \hline 巳 &0 &0.29 &0.32 &0.58 &0 &1 &0 &0.58 &0.32 &0.32 &0.28 &0\\ \hline 午 &0.34 &0.29 &0.32 &0.34 &0 &0.22 &1 &0.34 &0.32 &0.32 &0.28 &0\\ \hline 未 &0 &0.29 &0.32 &0.29 &0 &0.29 &0 &1 &0.32 &0.32 &0.28 &0\\ \hline 申 &0 &0.29 &0.29 &0.29 &0 &0.29 &0 &0.29 &1 &0.29 &0.28 &0\\ \hline 酉 &0 &0.29 &0.29 &0.29 &0 &0.29 &0 &0.29 &0.83 &1 &0.28 &0\\ \hline 戌 &0 &0.29 &0.32 &0.29 &0 &0.29 &0 &0.83 &0.32 &0.32 &1 &0\\ \hline 亥 &0 &0.29 &0.32 &0.5 &0 &0.29 &0 &0.5 &0.32 &0.32 &0.28 &1\\ \hline \end{array} $$$$\tilde B_{8}=\begin{array} {c|c|c}{M_{12 \times12}} &子 &丑 &寅 &卯 &辰 &巳 &午 &未 &申 &酉 &戌 &亥\\ \hline 子 &1 &0.29 &0.32 &0.52 &0 &0.29 &0 &0.52 &0.32 &0.32 &0.28 &0\\ \hline 丑 &0 &1 &0.32 &0.58 &0 &0.87 &0 &0.58 &0.32 &0.32 &0.28 &0\\ \hline 寅 &0 &0.29 &1 &0.29 &0 &0.29 &0 &0.29 &0.47 &0.47 &0.28 &0\\ \hline 卯 &0 &0.29 &0.32 &1 &0 &0.29 &0 &0.65 &0.32 &0.32 &0.28 &0\\ \hline 辰 &0 &0.29 &0.47 &0.72 &1 &0.29 &0 &0.65 &0.47 &0.47 &0.28 &0\\ \hline 巳 &0 &0.29 &0.32 &0.58 &0 &1 &0 &0.58 &0.32 &0.32 &0.28 &0\\ \hline 午 &0.34 &0.29 &0.32 &0.34 &0 &0.29 &1 &0.34 &0.32 &0.32 &0.28 &0\\ \hline 未 &0 &0.29 &0.32 &0.29 &0 &0.29 &0 &1 &0.32 &0.32 &0.28 &0\\ \hline 申 &0 &0.29 &0.29 &0.29 &0 &0.29 &0 &0.29 &1 &0.29 &0.28 &0\\ \hline 酉 &0 &0.29 &0.29 &0.29 &0 &0.29 &0 &0.29 &0.83 &1 &0.28 &0\\ \hline 戌 &0 &0.29 &0.32 &0.29 &0 &0.29 &0 &0.83 &0.32 &0.32 &1 &0\\ \hline 亥 &0 &0.29 &0.32 &0.5 &0 &0.29 &0 &0.5 &0.32 &0.32 &0.28 &1\\ \hline \end{array} $$$$\tilde B_{9}=\begin{array} {c|c|c}{M_{12 \times12}} &子 &丑 &寅 &卯 &辰 &巳 &午 &未 &申 &酉 &戌 &亥\\ \hline 子 &1 &0.29 &0.32 &0.52 &0 &0.29 &0 &0.52 &0.32 &0.32 &0.28 &0\\ \hline 丑 &0 &1 &0.32 &0.58 &0 &0.87 &0 &0.58 &0.32 &0.32 &0.28 &0\\ \hline 寅 &0 &0.29 &1 &0.29 &0 &0.29 &0 &0.29 &0.47 &0.47 &0.28 &0\\ \hline 卯 &0 &0.29 &0.32 &1 &0 &0.29 &0 &0.65 &0.32 &0.32 &0.28 &0\\ \hline 辰 &0 &0.29 &0.47 &0.72 &1 &0.29 &0 &0.65 &0.47 &0.47 &0.28 &0\\ \hline 巳 &0 &0.29 &0.32 &0.58 &0 &1 &0 &0.58 &0.32 &0.32 &0.28 &0\\ \hline 午 &0.34 &0.29 &0.32 &0.34 &0 &0.29 &1 &0.34 &0.32 &0.32 &0.28 &0\\ \hline 未 &0 &0.29 &0.32 &0.29 &0 &0.29 &0 &1 &0.32 &0.32 &0.28 &0\\ \hline 申 &0 &0.29 &0.29 &0.29 &0 &0.29 &0 &0.29 &1 &0.29 &0.28 &0\\ \hline 酉 &0 &0.29 &0.29 &0.29 &0 &0.29 &0 &0.29 &0.83 &1 &0.28 &0\\ \hline 戌 &0 &0.29 &0.32 &0.29 &0 &0.29 &0 &0.83 &0.32 &0.32 &1 &0\\ \hline 亥 &0 &0.29 &0.32 &0.5 &0 &0.29 &0 &0.5 &0.32 &0.32 &0.28 &1\\ \hline \end{array} $$

模糊可达矩阵 $ \tilde R = \tilde B_{ 9}$

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