解释结构模型(ISM)在线计算

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目前暂时限制到8个要素的输入，输入更多要素需付费。

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$$ \require{cancel} \require{AMScd} \begin{CD} 原始邻接矩阵A @>A+I> >　相乘矩阵B @>连乘> > 可达矩阵R @>可达集等于共同集的抽取> >层级@>代入A >>层次图 \\ \end{CD} $$

你没有输入参数，本处随机给出一个


本系统基本信息为

原始关系矩阵：

$$A=\begin{array} {c|c|c|c|c|c|c|c}{M_{21 \times21}} &A1 &A2 &A3 &A4 &A5 &A6 &A7 &A8 &A9 &A10 &A11 &A12 &A13 &A14 &A15 &A16 &A17 &A18 &A19 &A20 &A21\\ \hline A1 & & & & & & &1 & & & & & &1 & & & &1 & & & & \\ \hline A2 &1 & & & & & & &1 & & & & & & & & & & & & & \\ \hline A3 & & & & & & & &1 & & & & & & & & & & & & & \\ \hline A4 & & & & & & & &1 & & & & & & & & & & & & & \\ \hline A5 & & & & & & & &1 & & & & & & & & & & & & & \\ \hline A6 & & & & & & & & & & & & & & & & & & & & &1\\ \hline A7 & & & & & &1 & & & & & & & & & & & & & & & \\ \hline A8 & & & & & & & & & & & & & & & & & &1 & & & \\ \hline A9 & & & & & & & & & & &1 & & & & & & & & & & \\ \hline A10 & &1 & & & & & & & & & & & & & & & & & & & \\ \hline A11 & & & & & & & & & &1 & & & & & & & & & & & \\ \hline A12 & & & & & & & & &1 & & & & & & & & & & & & \\ \hline A13 & & & & & & & & & & & & & & & & & & &1 & & \\ \hline A14 & & & & & & & & & & & & & & & & & &1 & & & \\ \hline A15 & & & & & & & & & & & &1 & & & & & & & & & \\ \hline A16 & &1 & & & & & & & & & & & & & & & &1 & & & \\ \hline A17 & & & & & & & & & & &1 & & & & & & & & & & \\ \hline A18 & & & & & & & &1 & & & & & & &1 & & & & & & \\ \hline A19 & & & & & &1 & & & & & & & & & & & & & & & \\ \hline A20 & &1 & & & & & & & & & & & & & & & & & & & \\ \hline A21 & & & & & & & & & & & & & & & & & & & & & \\ \hline \end{array} $$

邻接相乘矩阵为：

$$B=\begin{array} {c|c|c|c|c|c|c|c}{M_{21 \times21}} &A1 &A2 &A3 &A4 &A5 &A6 &A7 &A8 &A9 &A10 &A11 &A12 &A13 &A14 &A15 &A16 &A17 &A18 &A19 &A20 &A21\\ \hline A1 &1 & & & & & &1 & & & & & &1 & & & &1 & & & & \\ \hline A2 &1 &1 & & & & & &1 & & & & & & & & & & & & & \\ \hline A3 & & &1 & & & & &1 & & & & & & & & & & & & & \\ \hline A4 & & & &1 & & & &1 & & & & & & & & & & & & & \\ \hline A5 & & & & &1 & & &1 & & & & & & & & & & & & & \\ \hline A6 & & & & & &1 & & & & & & & & & & & & & & &1\\ \hline A7 & & & & & &1 &1 & & & & & & & & & & & & & & \\ \hline A8 & & & & & & & &1 & & & & & & & & & &1 & & & \\ \hline A9 & & & & & & & & &1 & &1 & & & & & & & & & & \\ \hline A10 & &1 & & & & & & & &1 & & & & & & & & & & & \\ \hline A11 & & & & & & & & & &1 &1 & & & & & & & & & & \\ \hline A12 & & & & & & & & &1 & & &1 & & & & & & & & & \\ \hline A13 & & & & & & & & & & & & &1 & & & & & &1 & & \\ \hline A14 & & & & & & & & & & & & & &1 & & & &1 & & & \\ \hline A15 & & & & & & & & & & & &1 & & &1 & & & & & & \\ \hline A16 & &1 & & & & & & & & & & & & & &1 & &1 & & & \\ \hline A17 & & & & & & & & & & &1 & & & & & &1 & & & & \\ \hline A18 & & & & & & & &1 & & & & & & &1 & & &1 & & & \\ \hline A19 & & & & & &1 & & & & & & & & & & & & &1 & & \\ \hline A20 & &1 & & & & & & & & & & & & & & & & & &1 & \\ \hline A21 & & & & & & & & & & & & & & & & & & & & &1\\ \hline \end{array} $$

可达矩阵为：

$$R=\begin{array} {c|c|c|c|c|c|c|c}{M_{21 \times21}} &A1 &A2 &A3 &A4 &A5 &A6 &A7 &A8 &A9 &A10 &A11 &A12 &A13 &A14 &A15 &A16 &A17 &A18 &A19 &A20 &A21\\ \hline A1 &1 &1 & & & &1 &1 &1 &1 &1 &1 &1 &1 & &1 & &1 &1 &1 & &1\\ \hline A2 &1 &1 & & & &1 &1 &1 &1 &1 &1 &1 &1 & &1 & &1 &1 &1 & &1\\ \hline A3 &1 &1 &1 & & &1 &1 &1 &1 &1 &1 &1 &1 & &1 & &1 &1 &1 & &1\\ \hline A4 &1 &1 & &1 & &1 &1 &1 &1 &1 &1 &1 &1 & &1 & &1 &1 &1 & &1\\ \hline A5 &1 &1 & & &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 & &1 &1 &1 & &1\\ \hline A6 & & & & & &1 & & & & & & & & & & & & & & &1\\ \hline A7 & & & & & &1 &1 & & & & & & & & & & & & & &1\\ \hline A8 &1 &1 & & & &1 &1 &1 &1 &1 &1 &1 &1 & &1 & &1 &1 &1 & &1\\ \hline A9 &1 &1 & & & &1 &1 &1 &1 &1 &1 &1 &1 & &1 & &1 &1 &1 & &1\\ \hline A10 &1 &1 & & & &1 &1 &1 &1 &1 &1 &1 &1 & &1 & &1 &1 &1 & &1\\ \hline A11 &1 &1 & & & &1 &1 &1 &1 &1 &1 &1 &1 & &1 & &1 &1 &1 & &1\\ \hline A12 &1 &1 & & & &1 &1 &1 &1 &1 &1 &1 &1 & &1 & &1 &1 &1 & &1\\ \hline A13 & & & & & &1 & & & & & & &1 & & & & & &1 & &1\\ \hline A14 &1 &1 & & & &1 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 & &1\\ \hline A15 &1 &1 & & & &1 &1 &1 &1 &1 &1 &1 &1 & &1 & &1 &1 &1 & &1\\ \hline A16 &1 &1 & & & &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 & &1\\ \hline A17 &1 &1 & & & &1 &1 &1 &1 &1 &1 &1 &1 & &1 & &1 &1 &1 & &1\\ \hline A18 &1 &1 & & & &1 &1 &1 &1 &1 &1 &1 &1 & &1 & &1 &1 &1 & &1\\ \hline A19 & & & & & &1 & & & & & & & & & & & & &1 & &1\\ \hline A20 &1 &1 & & & &1 &1 &1 &1 &1 &1 &1 &1 & &1 & &1 &1 &1 &1 &1\\ \hline A21 & & & & & & & & & & & & & & & & & & & & &1\\ \hline \end{array} $$

抽取的过程如下

结果优先——UP型抽取过程
$$\begin{array} {c|c|c|c|c|c|c|c}{} & R_{e} & T_{e} \\\hline A1&A1,A2,A6,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19,A21&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A2&A1,A2,A6,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19,A21&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A3&A1,A2,A3,A6,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19,A21&A3 \\\hline A4&A1,A2,A4,A6,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19,A21&A4 \\\hline A5&A1,A2,A5,A6,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19,A21&A5 \\\hline A6&A6,A21&A6 \\\hline A7&A6,A7,A21&A7 \\\hline A8&A1,A2,A6,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19,A21&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A9&A1,A2,A6,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19,A21&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A10&A1,A2,A6,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19,A21&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A11&A1,A2,A6,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19,A21&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A12&A1,A2,A6,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19,A21&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A13&A6,A13,A19,A21&A13 \\\hline A14&A1,A2,A6,A7,A8,A9,A10,A11,A12,A13,A14,A15,A17,A18,A19,A21&A14 \\\hline A15&A1,A2,A6,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19,A21&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A16&A1,A2,A6,A7,A8,A9,A10,A11,A12,A13,A15,A16,A17,A18,A19,A21&A16 \\\hline A17&A1,A2,A6,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19,A21&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A18&A1,A2,A6,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19,A21&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A19&A6,A19,A21&A19 \\\hline A20&A1,A2,A6,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19,A20,A21&A20 \\\hline A21&\color{red}{\fbox{A21}}&\color{red}{\fbox{A21}} \\\hline \end{array} $$
抽取出A21　剩余的情况如下
$$\begin{array} {c|c|c|c|c|c|c|c}{} & R_{e} & T_{e} \\\hline A1&A1,A2,A6,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A2&A1,A2,A6,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A3&A1,A2,A3,A6,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19&A3 \\\hline A4&A1,A2,A4,A6,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19&A4 \\\hline A5&A1,A2,A5,A6,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19&A5 \\\hline A6&\color{red}{\fbox{A6}}&\color{red}{\fbox{A6}} \\\hline A7&A6,A7&A7 \\\hline A8&A1,A2,A6,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A9&A1,A2,A6,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A10&A1,A2,A6,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A11&A1,A2,A6,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A12&A1,A2,A6,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A13&A6,A13,A19&A13 \\\hline A14&A1,A2,A6,A7,A8,A9,A10,A11,A12,A13,A14,A15,A17,A18,A19&A14 \\\hline A15&A1,A2,A6,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A16&A1,A2,A6,A7,A8,A9,A10,A11,A12,A13,A15,A16,A17,A18,A19&A16 \\\hline A17&A1,A2,A6,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A18&A1,A2,A6,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A19&A6,A19&A19 \\\hline A20&A1,A2,A6,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19,A20&A20 \\\hline \end{array} $$
抽取出A6　剩余的情况如下
$$\begin{array} {c|c|c|c|c|c|c|c}{} & R_{e} & T_{e} \\\hline A1&A1,A2,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A2&A1,A2,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A3&A1,A2,A3,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19&A3 \\\hline A4&A1,A2,A4,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19&A4 \\\hline A5&A1,A2,A5,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19&A5 \\\hline A7&\color{red}{\fbox{A7}}&\color{red}{\fbox{A7}} \\\hline A8&A1,A2,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A9&A1,A2,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A10&A1,A2,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A11&A1,A2,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A12&A1,A2,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A13&A13,A19&A13 \\\hline A14&A1,A2,A7,A8,A9,A10,A11,A12,A13,A14,A15,A17,A18,A19&A14 \\\hline A15&A1,A2,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A16&A1,A2,A7,A8,A9,A10,A11,A12,A13,A15,A16,A17,A18,A19&A16 \\\hline A17&A1,A2,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A18&A1,A2,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A19&\color{red}{\fbox{A19}}&\color{red}{\fbox{A19}} \\\hline A20&A1,A2,A7,A8,A9,A10,A11,A12,A13,A15,A17,A18,A19,A20&A20 \\\hline \end{array} $$
抽取出A7、A19　剩余的情况如下
$$\begin{array} {c|c|c|c|c|c|c|c}{} & R_{e} & T_{e} \\\hline A1&A1,A2,A8,A9,A10,A11,A12,A13,A15,A17,A18&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A2&A1,A2,A8,A9,A10,A11,A12,A13,A15,A17,A18&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A3&A1,A2,A3,A8,A9,A10,A11,A12,A13,A15,A17,A18&A3 \\\hline A4&A1,A2,A4,A8,A9,A10,A11,A12,A13,A15,A17,A18&A4 \\\hline A5&A1,A2,A5,A8,A9,A10,A11,A12,A13,A15,A17,A18&A5 \\\hline A8&A1,A2,A8,A9,A10,A11,A12,A13,A15,A17,A18&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A9&A1,A2,A8,A9,A10,A11,A12,A13,A15,A17,A18&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A10&A1,A2,A8,A9,A10,A11,A12,A13,A15,A17,A18&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A11&A1,A2,A8,A9,A10,A11,A12,A13,A15,A17,A18&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A12&A1,A2,A8,A9,A10,A11,A12,A13,A15,A17,A18&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A13&\color{red}{\fbox{A13}}&\color{red}{\fbox{A13}} \\\hline A14&A1,A2,A8,A9,A10,A11,A12,A13,A14,A15,A17,A18&A14 \\\hline A15&A1,A2,A8,A9,A10,A11,A12,A13,A15,A17,A18&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A16&A1,A2,A8,A9,A10,A11,A12,A13,A15,A16,A17,A18&A16 \\\hline A17&A1,A2,A8,A9,A10,A11,A12,A13,A15,A17,A18&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A18&A1,A2,A8,A9,A10,A11,A12,A13,A15,A17,A18&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18 \\\hline A20&A1,A2,A8,A9,A10,A11,A12,A13,A15,A17,A18,A20&A20 \\\hline \end{array} $$
抽取出A13　剩余的情况如下
$$\begin{array} {c|c|c|c|c|c|c|c}{} & R_{e} & T_{e} \\\hline A1&\color{red}{\fbox{A1,A2,A8,A9,A10,A11,A12,A15,A17,A18}}&\color{red}{\fbox{A1,A2,A8,A9,A10,A11,A12,A15,A17,A18}} \\\hline A2&\color{red}{\fbox{A1,A2,A8,A9,A10,A11,A12,A15,A17,A18}}&\color{red}{\fbox{A1,A2,A8,A9,A10,A11,A12,A15,A17,A18}} \\\hline A3&A1,A2,A3,A8,A9,A10,A11,A12,A15,A17,A18&A3 \\\hline A4&A1,A2,A4,A8,A9,A10,A11,A12,A15,A17,A18&A4 \\\hline A5&A1,A2,A5,A8,A9,A10,A11,A12,A15,A17,A18&A5 \\\hline A8&\color{red}{\fbox{A1,A2,A8,A9,A10,A11,A12,A15,A17,A18}}&\color{red}{\fbox{A1,A2,A8,A9,A10,A11,A12,A15,A17,A18}} \\\hline A9&\color{red}{\fbox{A1,A2,A8,A9,A10,A11,A12,A15,A17,A18}}&\color{red}{\fbox{A1,A2,A8,A9,A10,A11,A12,A15,A17,A18}} \\\hline A10&\color{red}{\fbox{A1,A2,A8,A9,A10,A11,A12,A15,A17,A18}}&\color{red}{\fbox{A1,A2,A8,A9,A10,A11,A12,A15,A17,A18}} \\\hline A11&\color{red}{\fbox{A1,A2,A8,A9,A10,A11,A12,A15,A17,A18}}&\color{red}{\fbox{A1,A2,A8,A9,A10,A11,A12,A15,A17,A18}} \\\hline A12&\color{red}{\fbox{A1,A2,A8,A9,A10,A11,A12,A15,A17,A18}}&\color{red}{\fbox{A1,A2,A8,A9,A10,A11,A12,A15,A17,A18}} \\\hline A14&A1,A2,A8,A9,A10,A11,A12,A14,A15,A17,A18&A14 \\\hline A15&\color{red}{\fbox{A1,A2,A8,A9,A10,A11,A12,A15,A17,A18}}&\color{red}{\fbox{A1,A2,A8,A9,A10,A11,A12,A15,A17,A18}} \\\hline A16&A1,A2,A8,A9,A10,A11,A12,A15,A16,A17,A18&A16 \\\hline A17&\color{red}{\fbox{A1,A2,A8,A9,A10,A11,A12,A15,A17,A18}}&\color{red}{\fbox{A1,A2,A8,A9,A10,A11,A12,A15,A17,A18}} \\\hline A18&\color{red}{\fbox{A1,A2,A8,A9,A10,A11,A12,A15,A17,A18}}&\color{red}{\fbox{A1,A2,A8,A9,A10,A11,A12,A15,A17,A18}} \\\hline A20&A1,A2,A8,A9,A10,A11,A12,A15,A17,A18,A20&A20 \\\hline \end{array} $$
抽取出A1、A2、A8、A9、A10、A11、A12、A15、A17、A18　剩余的情况如下
$$\begin{array} {c|c|c|c|c|c|c|c}{} & R_{e} & T_{e} \\\hline A3&\color{red}{\fbox{A3}}&\color{red}{\fbox{A3}} \\\hline A4&\color{red}{\fbox{A4}}&\color{red}{\fbox{A4}} \\\hline A5&\color{red}{\fbox{A5}}&\color{red}{\fbox{A5}} \\\hline A14&\color{red}{\fbox{A14}}&\color{red}{\fbox{A14}} \\\hline A16&\color{red}{\fbox{A16}}&\color{red}{\fbox{A16}} \\\hline A20&\color{red}{\fbox{A20}}&\color{red}{\fbox{A20}} \\\hline \end{array} $$
抽取出A3、A4、A5、A14、A16、A20　剩余的情况如下

抽取方式的结果如下

层级 结果优先——UP型
第0层 A21
第1层 A6
第2层 A7,A19
第3层 A13
第4层 A1,A2,A8,A9,A10,A11,A12,A15,A17,A18
第5层 A3,A4,A5,A14,A16,A20

绘制层次图

A1
A2
A3
A4
A5
A6
A7
A8
A9
A10
A11
A12
A13
A14
A15
A16
A17
A18
A19
A20
A21
第0层
第1层
第2层
第3层
第4层
第5层
如需用到其它方法如：扯蛋模型
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