流程图如下：
流程图说明：蓝色部分为完整的DEMATEL部分及拓展；绿色部分为MACMIC及拓展；灰色部分为TAISM（综合对抗解释结构模型）。
输入数据一个：直接影响矩阵$O$
DEMATEL部分输出结果两个：
第一、中心度M与原因度R构成的直角坐标散点图
第二、由中心度M的绝对值与原因度R通过对抗哈斯图技术（AHDT）得到的对抗层级拓扑图（亦称为对抗哈斯图）
MICMAC部分输出结果两个：
第一、驱动力D与依赖力C构成的直角坐标散点图
第二、由（D、C）通过对抗哈斯图技术（AHDT）得到的对抗层级拓扑图（亦称为对抗哈斯图）
TAISM部分输出结果有n个：
带综合影响值的层级拓扑图中的综合影响值来自模糊可达矩阵
输出的结构数目等于模糊可达矩阵中不重复的值——即阈值集合中的阈值数目。
选择直接影响矩阵O的归一化方式
原始矩阵（直接影响矩阵）O为
$$Ori=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{24 \times24}} &A1 &A2 &A3 &A4 &B1 &B2 &C1 &C2 &C3 &C4 &C5 &D1 &D2 &D3 &D4 &D5 &E1 &E2 &E3 &E4 &E5 &E6 &F1 &F2\\ \hline A1 &0 &0 &0 &0 &0 &0 &2 &0 &0 &0 &0 &0 &0 &0 &0 &0 &4 &0 &0 &0 &0 &0 &0 &0\\ \hline A2 &17 &0 &16 &17 &0 &1 &6 &5 &13 &4 &13 &0 &0 &0 &0 &0 &3 &0 &3 &0 &0 &9 &0 &0\\ \hline A3 &16 &12 &0 &13 &6 &8 &18 &0 &11 &0 &14 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &8 &0\\ \hline A4 &17 &11 &7 &0 &2 &0 &14 &6 &9 &3 &13 &0 &0 &0 &0 &0 &8 &9 &0 &0 &0 &0 &0 &0\\ \hline B1 &11 &3 &4 &2 &0 &9 &3 &0 &3 &0 &3 &0 &0 &0 &0 &0 &0 &0 &0 &7 &0 &0 &0 &0\\ \hline B2 &12 &1 &3 &0 &16 &0 &12 &0 &11 &11 &6 &0 &7 &0 &8 &6 &0 &0 &9 &7 &0 &0 &0 &0\\ \hline C1 &15 &16 &16 &16 &0 &12 &0 &11 &17 &7 &17 &11 &14 &12 &14 &13 &12 &14 &14 &10 &12 &13 &16 &0\\ \hline C2 &12 &18 &11 &14 &1 &8 &8 &0 &19 &8 &20 &13 &17 &13 &16 &10 &14 &12 &16 &13 &15 &16 &6 &0\\ \hline C3 &16 &14 &14 &20 &8 &17 &14 &17 &0 &15 &8 &12 &8 &16 &12 &9 &14 &12 &20 &16 &14 &7 &0 &0\\ \hline C4 &16 &12 &16 &18 &8 &17 &17 &17 &18 &0 &17 &13 &13 &12 &13 &14 &13 &13 &17 &14 &13 &9 &0 &0\\ \hline C5 &19 &14 &14 &17 &0 &0 &13 &18 &16 &11 &0 &12 &9 &13 &15 &8 &12 &13 &11 &13 &11 &15 &0 &0\\ \hline D1 &18 &18 &14 &18 &0 &14 &13 &16 &18 &13 &18 &0 &19 &14 &17 &13 &20 &20 &17 &18 &20 &13 &0 &3\\ \hline D2 &12 &16 &16 &17 &6 &17 &12 &14 &17 &17 &15 &16 &0 &16 &20 &20 &14 &17 &17 &19 &17 &17 &14 &5\\ \hline D3 &9 &10 &7 &11 &8 &13 &11 &11 &9 &13 &13 &7 &12 &0 &16 &12 &9 &12 &10 &11 &9 &9 &3 &0\\ \hline D4 &6 &11 &4 &6 &10 &19 &17 &8 &7 &12 &9 &5 &9 &8 &0 &11 &4 &11 &6 &8 &7 &7 &0 &0\\ \hline D5 &6 &12 &12 &12 &11 &12 &12 &11 &16 &12 &14 &10 &16 &13 &12 &0 &13 &17 &12 &15 &11 &10 &0 &0\\ \hline E1 &14 &16 &17 &14 &3 &11 &8 &19 &20 &14 &14 &20 &16 &15 &14 &14 &0 &20 &16 &13 &18 &16 &15 &4\\ \hline E2 &13 &17 &20 &17 &12 &18 &10 &14 &17 &13 &17 &16 &17 &14 &16 &15 &12 &0 &17 &16 &7 &12 &0 &0\\ \hline E3 &9 &11 &17 &19 &16 &14 &14 &7 &13 &11 &8 &4 &13 &10 &12 &4 &7 &8 &0 &14 &7 &6 &0 &0\\ \hline E4 &6 &8 &14 &8 &7 &11 &10 &16 &12 &14 &9 &13 &16 &17 &15 &16 &13 &12 &17 &0 &11 &10 &0 &0\\ \hline E5 &14 &17 &14 &13 &7 &9 &13 &15 &16 &12 &14 &16 &14 &15 &13 &11 &20 &18 &15 &15 &0 &15 &17 &13\\ \hline E6 &11 &14 &14 &16 &4 &16 &13 &20 &15 &11 &9 &17 &20 &17 &16 &10 &14 &18 &20 &17 &15 &0 &18 &9\\ \hline F1 &13 &12 &15 &17 &15 &18 &14 &15 &14 &16 &15 &13 &20 &16 &16 &15 &12 &19 &16 &16 &16 &20 &0 &5\\ \hline F2 &11 &16 &16 &14 &16 &17 &17 &20 &17 &16 &16 &20 &15 &16 &15 &16 &20 &20 &18 &15 &15 &20 &20 &0\\ \hline \end{array} $$
规范化矩阵
- $$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{24 \times24}} &A1 &A2 &A3 &A4 &B1 &B2 &C1 &C2 &C3 &C4 &C5 &D1 &D2 &D3 &D4 &D5 &E1 &E2 &E3 &E4 &E5 &E6 &F1 &F2\\ \hline A1 &0 &0 &0 &0 &0 &0 &0.004 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.008 &0 &0 &0 &0 &0 &0 &0\\ \hline A2 &0.034 &0 &0.032 &0.034 &0 &0.002 &0.012 &0.01 &0.026 &0.008 &0.026 &0 &0 &0 &0 &0 &0.006 &0 &0.006 &0 &0 &0.018 &0 &0\\ \hline A3 &0.032 &0.024 &0 &0.026 &0.012 &0.016 &0.036 &0 &0.022 &0 &0.028 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.016 &0\\ \hline A4 &0.034 &0.022 &0.014 &0 &0.004 &0 &0.028 &0.012 &0.018 &0.006 &0.026 &0 &0 &0 &0 &0 &0.016 &0.018 &0 &0 &0 &0 &0 &0\\ \hline B1 &0.022 &0.006 &0.008 &0.004 &0 &0.018 &0.006 &0 &0.006 &0 &0.006 &0 &0 &0 &0 &0 &0 &0 &0 &0.014 &0 &0 &0 &0\\ \hline B2 &0.024 &0.002 &0.006 &0 &0.032 &0 &0.024 &0 &0.022 &0.022 &0.012 &0 &0.014 &0 &0.016 &0.012 &0 &0 &0.018 &0.014 &0 &0 &0 &0\\ \hline C1 &0.03 &0.032 &0.032 &0.032 &0 &0.024 &0 &0.022 &0.034 &0.014 &0.034 &0.022 &0.028 &0.024 &0.028 &0.026 &0.024 &0.028 &0.028 &0.02 &0.024 &0.026 &0.032 &0\\ \hline C2 &0.024 &0.036 &0.022 &0.028 &0.002 &0.016 &0.016 &0 &0.038 &0.016 &0.041 &0.026 &0.034 &0.026 &0.032 &0.02 &0.028 &0.024 &0.032 &0.026 &0.03 &0.032 &0.012 &0\\ \hline C3 &0.032 &0.028 &0.028 &0.041 &0.016 &0.034 &0.028 &0.034 &0 &0.03 &0.016 &0.024 &0.016 &0.032 &0.024 &0.018 &0.028 &0.024 &0.041 &0.032 &0.028 &0.014 &0 &0\\ \hline C4 &0.032 &0.024 &0.032 &0.036 &0.016 &0.034 &0.034 &0.034 &0.036 &0 &0.034 &0.026 &0.026 &0.024 &0.026 &0.028 &0.026 &0.026 &0.034 &0.028 &0.026 &0.018 &0 &0\\ \hline C5 &0.038 &0.028 &0.028 &0.034 &0 &0 &0.026 &0.036 &0.032 &0.022 &0 &0.024 &0.018 &0.026 &0.03 &0.016 &0.024 &0.026 &0.022 &0.026 &0.022 &0.03 &0 &0\\ \hline D1 &0.036 &0.036 &0.028 &0.036 &0 &0.028 &0.026 &0.032 &0.036 &0.026 &0.036 &0 &0.038 &0.028 &0.034 &0.026 &0.041 &0.041 &0.034 &0.036 &0.041 &0.026 &0 &0.006\\ \hline D2 &0.024 &0.032 &0.032 &0.034 &0.012 &0.034 &0.024 &0.028 &0.034 &0.034 &0.03 &0.032 &0 &0.032 &0.041 &0.041 &0.028 &0.034 &0.034 &0.038 &0.034 &0.034 &0.028 &0.01\\ \hline D3 &0.018 &0.02 &0.014 &0.022 &0.016 &0.026 &0.022 &0.022 &0.018 &0.026 &0.026 &0.014 &0.024 &0 &0.032 &0.024 &0.018 &0.024 &0.02 &0.022 &0.018 &0.018 &0.006 &0\\ \hline D4 &0.012 &0.022 &0.008 &0.012 &0.02 &0.038 &0.034 &0.016 &0.014 &0.024 &0.018 &0.01 &0.018 &0.016 &0 &0.022 &0.008 &0.022 &0.012 &0.016 &0.014 &0.014 &0 &0\\ \hline D5 &0.012 &0.024 &0.024 &0.024 &0.022 &0.024 &0.024 &0.022 &0.032 &0.024 &0.028 &0.02 &0.032 &0.026 &0.024 &0 &0.026 &0.034 &0.024 &0.03 &0.022 &0.02 &0 &0\\ \hline E1 &0.028 &0.032 &0.034 &0.028 &0.006 &0.022 &0.016 &0.038 &0.041 &0.028 &0.028 &0.041 &0.032 &0.03 &0.028 &0.028 &0 &0.041 &0.032 &0.026 &0.036 &0.032 &0.03 &0.008\\ \hline E2 &0.026 &0.034 &0.041 &0.034 &0.024 &0.036 &0.02 &0.028 &0.034 &0.026 &0.034 &0.032 &0.034 &0.028 &0.032 &0.03 &0.024 &0 &0.034 &0.032 &0.014 &0.024 &0 &0\\ \hline E3 &0.018 &0.022 &0.034 &0.038 &0.032 &0.028 &0.028 &0.014 &0.026 &0.022 &0.016 &0.008 &0.026 &0.02 &0.024 &0.008 &0.014 &0.016 &0 &0.028 &0.014 &0.012 &0 &0\\ \hline E4 &0.012 &0.016 &0.028 &0.016 &0.014 &0.022 &0.02 &0.032 &0.024 &0.028 &0.018 &0.026 &0.032 &0.034 &0.03 &0.032 &0.026 &0.024 &0.034 &0 &0.022 &0.02 &0 &0\\ \hline E5 &0.028 &0.034 &0.028 &0.026 &0.014 &0.018 &0.026 &0.03 &0.032 &0.024 &0.028 &0.032 &0.028 &0.03 &0.026 &0.022 &0.041 &0.036 &0.03 &0.03 &0 &0.03 &0.034 &0.026\\ \hline E6 &0.022 &0.028 &0.028 &0.032 &0.008 &0.032 &0.026 &0.041 &0.03 &0.022 &0.018 &0.034 &0.041 &0.034 &0.032 &0.02 &0.028 &0.036 &0.041 &0.034 &0.03 &0 &0.036 &0.018\\ \hline F1 &0.026 &0.024 &0.03 &0.034 &0.03 &0.036 &0.028 &0.03 &0.028 &0.032 &0.03 &0.026 &0.041 &0.032 &0.032 &0.03 &0.024 &0.038 &0.032 &0.032 &0.032 &0.041 &0 &0.01\\ \hline F2 &0.022 &0.032 &0.032 &0.028 &0.032 &0.034 &0.034 &0.041 &0.034 &0.032 &0.032 &0.041 &0.03 &0.032 &0.03 &0.032 &0.041 &0.041 &0.036 &0.03 &0.03 &0.041 &0.041 &0\\ \hline \end{array} $$
综合影响矩阵求解过程
综合影响矩阵如下
$T=\mathcal{N}(I-\mathcal{N})^{-1}$
$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{24 \times24}} &A1 &A2 &A3 &A4 &B1 &B2 &C1 &C2 &C3 &C4 &C5 &D1 &D2 &D3 &D4 &D5 &E1 &E2 &E3 &E4 &E5 &E6 &F1 &F2\\ \hline A1 &0.001 &0.001 &0.001 &0.001 &0 &0.001 &0.005 &0.001 &0.001 &0.001 &0.001 &0.001 &0.001 &0.001 &0.001 &0.001 &0.008 &0.001 &0.001 &0.001 &0.001 &0.001 &0 &0\\ \hline A2 &0.044 &0.008 &0.04 &0.043 &0.003 &0.008 &0.02 &0.017 &0.034 &0.014 &0.034 &0.005 &0.006 &0.006 &0.006 &0.005 &0.012 &0.007 &0.013 &0.006 &0.006 &0.023 &0.003 &0.001\\ \hline A3 &0.042 &0.031 &0.008 &0.034 &0.015 &0.021 &0.043 &0.006 &0.03 &0.006 &0.035 &0.005 &0.006 &0.005 &0.006 &0.005 &0.006 &0.006 &0.006 &0.006 &0.005 &0.006 &0.019 &0.001\\ \hline A4 &0.043 &0.03 &0.022 &0.009 &0.007 &0.006 &0.035 &0.019 &0.027 &0.012 &0.034 &0.006 &0.006 &0.006 &0.007 &0.005 &0.022 &0.024 &0.007 &0.006 &0.006 &0.006 &0.003 &0.001\\ \hline B1 &0.025 &0.008 &0.01 &0.007 &0.002 &0.02 &0.009 &0.002 &0.009 &0.002 &0.008 &0.002 &0.002 &0.002 &0.002 &0.002 &0.002 &0.002 &0.002 &0.016 &0.002 &0.002 &0.001 &0\\ \hline B2 &0.033 &0.01 &0.015 &0.009 &0.037 &0.008 &0.032 &0.008 &0.031 &0.029 &0.02 &0.006 &0.021 &0.007 &0.024 &0.018 &0.007 &0.007 &0.026 &0.022 &0.006 &0.006 &0.003 &0.001\\ \hline C1 &0.057 &0.057 &0.057 &0.06 &0.014 &0.046 &0.025 &0.045 &0.061 &0.035 &0.059 &0.041 &0.05 &0.045 &0.051 &0.045 &0.045 &0.051 &0.052 &0.043 &0.043 &0.045 &0.041 &0.003\\ \hline C2 &0.051 &0.062 &0.048 &0.056 &0.015 &0.039 &0.041 &0.024 &0.066 &0.037 &0.065 &0.045 &0.056 &0.048 &0.055 &0.039 &0.049 &0.048 &0.056 &0.049 &0.049 &0.051 &0.022 &0.004\\ \hline C3 &0.058 &0.052 &0.052 &0.065 &0.029 &0.055 &0.051 &0.055 &0.027 &0.049 &0.041 &0.041 &0.037 &0.051 &0.046 &0.036 &0.047 &0.045 &0.062 &0.053 &0.045 &0.032 &0.009 &0.003\\ \hline C4 &0.06 &0.05 &0.058 &0.064 &0.029 &0.057 &0.059 &0.057 &0.064 &0.021 &0.06 &0.045 &0.048 &0.045 &0.049 &0.047 &0.047 &0.049 &0.058 &0.051 &0.045 &0.037 &0.01 &0.003\\ \hline C5 &0.062 &0.051 &0.051 &0.059 &0.011 &0.02 &0.048 &0.056 &0.057 &0.04 &0.023 &0.041 &0.038 &0.045 &0.05 &0.033 &0.043 &0.047 &0.043 &0.046 &0.039 &0.047 &0.009 &0.003\\ \hline D1 &0.068 &0.066 &0.058 &0.068 &0.016 &0.054 &0.055 &0.059 &0.069 &0.051 &0.066 &0.023 &0.064 &0.053 &0.061 &0.049 &0.065 &0.067 &0.062 &0.062 &0.062 &0.049 &0.012 &0.01\\ \hline D2 &0.058 &0.063 &0.064 &0.068 &0.029 &0.063 &0.055 &0.057 &0.069 &0.06 &0.062 &0.056 &0.029 &0.058 &0.069 &0.064 &0.054 &0.063 &0.064 &0.066 &0.058 &0.058 &0.039 &0.014\\ \hline D3 &0.039 &0.04 &0.034 &0.043 &0.027 &0.044 &0.041 &0.04 &0.04 &0.042 &0.046 &0.029 &0.042 &0.017 &0.05 &0.039 &0.034 &0.042 &0.039 &0.04 &0.033 &0.033 &0.013 &0.002\\ \hline D4 &0.03 &0.038 &0.024 &0.029 &0.029 &0.052 &0.049 &0.03 &0.032 &0.037 &0.034 &0.022 &0.032 &0.029 &0.015 &0.034 &0.021 &0.036 &0.028 &0.031 &0.026 &0.026 &0.006 &0.002\\ \hline D5 &0.037 &0.047 &0.048 &0.049 &0.034 &0.045 &0.046 &0.043 &0.057 &0.043 &0.051 &0.038 &0.052 &0.045 &0.045 &0.018 &0.045 &0.055 &0.046 &0.051 &0.04 &0.038 &0.009 &0.003\\ \hline E1 &0.06 &0.063 &0.065 &0.062 &0.022 &0.05 &0.046 &0.066 &0.073 &0.053 &0.059 &0.063 &0.059 &0.056 &0.056 &0.051 &0.026 &0.068 &0.061 &0.054 &0.059 &0.056 &0.041 &0.012\\ \hline E2 &0.055 &0.06 &0.066 &0.062 &0.038 &0.059 &0.046 &0.051 &0.063 &0.047 &0.06 &0.051 &0.056 &0.049 &0.056 &0.049 &0.045 &0.024 &0.058 &0.055 &0.034 &0.043 &0.009 &0.003\\ \hline E3 &0.038 &0.04 &0.052 &0.057 &0.041 &0.044 &0.046 &0.03 &0.046 &0.036 &0.034 &0.021 &0.041 &0.034 &0.04 &0.021 &0.028 &0.032 &0.017 &0.043 &0.027 &0.025 &0.007 &0.002\\ \hline E4 &0.037 &0.04 &0.051 &0.042 &0.026 &0.044 &0.043 &0.053 &0.05 &0.047 &0.042 &0.043 &0.053 &0.053 &0.052 &0.05 &0.045 &0.045 &0.056 &0.022 &0.04 &0.038 &0.009 &0.003\\ \hline E5 &0.06 &0.064 &0.059 &0.059 &0.03 &0.046 &0.055 &0.058 &0.065 &0.049 &0.058 &0.055 &0.055 &0.055 &0.054 &0.045 &0.065 &0.064 &0.059 &0.057 &0.024 &0.054 &0.046 &0.03\\ \hline E6 &0.055 &0.059 &0.059 &0.065 &0.025 &0.06 &0.056 &0.068 &0.064 &0.048 &0.05 &0.057 &0.068 &0.06 &0.061 &0.044 &0.054 &0.064 &0.069 &0.062 &0.054 &0.025 &0.048 &0.022\\ \hline F1 &0.059 &0.055 &0.061 &0.067 &0.047 &0.064 &0.058 &0.058 &0.062 &0.057 &0.061 &0.049 &0.067 &0.058 &0.061 &0.054 &0.05 &0.066 &0.062 &0.06 &0.055 &0.063 &0.012 &0.014\\ \hline F2 &0.06 &0.067 &0.068 &0.066 &0.051 &0.066 &0.068 &0.072 &0.073 &0.061 &0.068 &0.067 &0.062 &0.062 &0.063 &0.059 &0.069 &0.073 &0.07 &0.062 &0.057 &0.067 &0.054 &0.005\\ \hline \end{array} $$
由综合影响矩阵求影响度D、被影响度C、中心度M、原因度R
影响度、被影响度、中心度与原因度是四种度量要素在系统里影响程度的度量值。都是根据综合影响矩阵计算得出。
求解原理
| 影响度 $D$ | $$ D_i=\sum \limits_{j=1}^{n}{t_{ij}},(i=1,2,3,\cdots,n) $$ |
| 被影响度 $C$ | $$ C_i=\sum \limits_{j=1}^{n}{t_{ji}},(i=1,2,3,\cdots,n) $$ |
| 中心度 $M$ | $$ M_i=D_i+C_i $$ |
| 原因度 $ R$ | $$ R_i=D_i-C_i $$ |
结果
影响度、被影响度、中心度、原因度
$$\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{24 \times4}} &Di &Ci &Mi &Ri\\ \hline A1 &0.027 &1.131 &1.158 &-1.104\\ \hline A2 &0.364 &1.063 &1.427 &-0.7\\ \hline A3 &0.352 &1.069 &1.421 &-0.716\\ \hline A4 &0.351 &1.145 &1.495 &-0.794\\ \hline B1 &0.138 &0.576 &0.714 &-0.438\\ \hline B2 &0.385 &0.975 &1.36 &-0.589\\ \hline C1 &1.071 &1.033 &2.104 &0.038\\ \hline C2 &1.076 &0.976 &2.052 &0.101\\ \hline C3 &1.038 &1.169 &2.207 &-0.131\\ \hline C4 &1.113 &0.878 &1.991 &0.236\\ \hline C5 &0.961 &1.071 &2.031 &-0.11\\ \hline D1 &1.271 &0.811 &2.082 &0.46\\ \hline D2 &1.34 &0.951 &2.29 &0.389\\ \hline D3 &0.851 &0.89 &1.74 &-0.039\\ \hline D4 &0.692 &0.98 &1.672 &-0.288\\ \hline D5 &0.986 &0.812 &1.798 &0.174\\ \hline E1 &1.281 &0.893 &2.173 &0.388\\ \hline E2 &1.139 &0.985 &2.124 &0.154\\ \hline E3 &0.802 &1.019 &1.821 &-0.217\\ \hline E4 &0.982 &0.962 &1.944 &0.02\\ \hline E5 &1.267 &0.816 &2.083 &0.452\\ \hline E6 &1.296 &0.83 &2.125 &0.466\\ \hline F1 &1.322 &0.423 &1.745 &0.899\\ \hline F2 &1.491 &0.142 &1.632 &1.349\\ \hline \end{array} $$
绘制中心度M与原因度R建构的散点图点击右键可以保存到本地
DEMATEL中的对抗哈斯图技术( AHDT)
中心度绝对值，原因度绝对值组成的决策矩阵D
其中|M|与 |R|都是正向指标，即数值越大越优
MICMAC处理过程
模糊相乘矩阵有$ \tilde B=T+I$
$$\tilde B=\begin{array} {c|c|c}{M_{24 \times24}} &A1 &A2 &A3 &A4 &B1 &B2 &C1 &C2 &C3 &C4 &C5 &D1 &D2 &D3 &D4 &D5 &E1 &E2 &E3 &E4 &E5 &E6 &F1 &F2\\ \hline A1 &1 &0.0007 &0.0008 &0.0007 &0.0002 &0.0006 &0.0045 &0.0007 &0.0008 &0.0006 &0.0007 &0.0007 &0.0007 &0.0006 &0.0007 &0.0006 &0.0085 &0.0008 &0.0007 &0.0006 &0.0007 &0.0006 &0.0005 &0.0001\\ \hline A2 &0.0438 &1 &0.0396 &0.0429 &0.0033 &0.008 &0.0203 &0.017 &0.0343 &0.0135 &0.0337 &0.0054 &0.0058 &0.006 &0.0063 &0.0048 &0.0125 &0.0068 &0.0128 &0.0062 &0.0055 &0.023 &0.0031 &0.0008\\ \hline A3 &0.0416 &0.0312 &1 &0.0342 &0.0152 &0.0215 &0.043 &0.0065 &0.0299 &0.0056 &0.0352 &0.0048 &0.0055 &0.0054 &0.006 &0.0048 &0.006 &0.0062 &0.0065 &0.0059 &0.005 &0.0056 &0.0186 &0.0006\\ \hline A4 &0.0434 &0.03 &0.0223 &1 &0.007 &0.0061 &0.0349 &0.019 &0.0267 &0.0117 &0.0339 &0.006 &0.0063 &0.0063 &0.0068 &0.0055 &0.0223 &0.0244 &0.0072 &0.0064 &0.0057 &0.0063 &0.0031 &0.0006\\ \hline B1 &0.0253 &0.0082 &0.0105 &0.0065 &1 &0.02 &0.0087 &0.0021 &0.0088 &0.0021 &0.0084 &0.0016 &0.002 &0.0019 &0.0022 &0.0018 &0.002 &0.0019 &0.0024 &0.0159 &0.0016 &0.0016 &0.0007 &0.0001\\ \hline B2 &0.0332 &0.0102 &0.0145 &0.0092 &0.0367 &1 &0.0322 &0.0075 &0.0308 &0.0286 &0.02 &0.0061 &0.0209 &0.0071 &0.0235 &0.0184 &0.0069 &0.0074 &0.0259 &0.0218 &0.0064 &0.006 &0.0027 &0.0006\\ \hline C1 &0.0571 &0.0572 &0.0572 &0.0595 &0.0136 &0.0465 &1 &0.045 &0.0614 &0.0351 &0.0591 &0.0407 &0.0501 &0.0449 &0.051 &0.0447 &0.0448 &0.051 &0.0517 &0.0425 &0.043 &0.0453 &0.041 &0.0035\\ \hline C2 &0.0514 &0.0616 &0.048 &0.0561 &0.0151 &0.0389 &0.041 &1 &0.0657 &0.0375 &0.0649 &0.0453 &0.0562 &0.0475 &0.0554 &0.0393 &0.0493 &0.0476 &0.0562 &0.0489 &0.0494 &0.0515 &0.0217 &0.0037\\ \hline C3 &0.0579 &0.0518 &0.0518 &0.0653 &0.0286 &0.0549 &0.0513 &0.0547 &1 &0.049 &0.0406 &0.0411 &0.037 &0.0509 &0.0455 &0.0356 &0.0474 &0.0452 &0.0618 &0.0526 &0.0453 &0.0317 &0.0088 &0.0029\\ \hline C4 &0.06 &0.0501 &0.0577 &0.0637 &0.0293 &0.0566 &0.059 &0.0568 &0.0643 &1 &0.0598 &0.0448 &0.0484 &0.0451 &0.0495 &0.0469 &0.0473 &0.0491 &0.0581 &0.0508 &0.0452 &0.0373 &0.0097 &0.0031\\ \hline C5 &0.062 &0.0511 &0.0506 &0.0586 &0.0109 &0.0205 &0.0477 &0.0564 &0.0565 &0.04 &1 &0.0409 &0.0379 &0.0447 &0.0503 &0.0329 &0.0431 &0.0466 &0.0434 &0.0456 &0.0392 &0.0468 &0.0089 &0.003\\ \hline D1 &0.0678 &0.0661 &0.0584 &0.0683 &0.0157 &0.0545 &0.055 &0.0594 &0.0689 &0.0508 &0.0659 &1 &0.064 &0.053 &0.0614 &0.0487 &0.0647 &0.067 &0.0625 &0.0624 &0.0622 &0.049 &0.0119 &0.01\\ \hline D2 &0.0575 &0.0635 &0.0636 &0.068 &0.0294 &0.0628 &0.0552 &0.057 &0.0686 &0.0601 &0.0618 &0.0556 &1 &0.0584 &0.0688 &0.0636 &0.0544 &0.063 &0.0642 &0.0662 &0.0578 &0.0579 &0.0394 &0.0142\\ \hline D3 &0.0393 &0.0399 &0.0341 &0.0433 &0.0266 &0.044 &0.0414 &0.04 &0.0401 &0.0423 &0.0459 &0.029 &0.0416 &1 &0.0502 &0.0391 &0.0344 &0.042 &0.039 &0.0399 &0.033 &0.0331 &0.0132 &0.0025\\ \hline D4 &0.0296 &0.0377 &0.0244 &0.0292 &0.0286 &0.0523 &0.0492 &0.0303 &0.0321 &0.037 &0.0343 &0.0219 &0.0322 &0.0291 &1 &0.0342 &0.0212 &0.0361 &0.0276 &0.0305 &0.0258 &0.026 &0.006 &0.0018\\ \hline D5 &0.0372 &0.0474 &0.0476 &0.0493 &0.034 &0.0451 &0.0464 &0.0433 &0.0575 &0.0431 &0.0512 &0.0376 &0.0521 &0.0453 &0.0455 &1 &0.0451 &0.0547 &0.0463 &0.0508 &0.0395 &0.0376 &0.0088 &0.0029\\ \hline E1 &0.0604 &0.0628 &0.0646 &0.0615 &0.0223 &0.0499 &0.0459 &0.0657 &0.0732 &0.0532 &0.0589 &0.0628 &0.0593 &0.0556 &0.0563 &0.0511 &1 &0.0678 &0.0613 &0.0537 &0.0593 &0.0555 &0.0411 &0.0123\\ \hline E2 &0.0547 &0.06 &0.0659 &0.0623 &0.0376 &0.0592 &0.0461 &0.0512 &0.0627 &0.0473 &0.0602 &0.0505 &0.0562 &0.0491 &0.0555 &0.0491 &0.0452 &1 &0.0582 &0.055 &0.0337 &0.0432 &0.0093 &0.003\\ \hline E3 &0.0385 &0.04 &0.0518 &0.057 &0.0414 &0.0442 &0.046 &0.0298 &0.0456 &0.0363 &0.0345 &0.0209 &0.0406 &0.0341 &0.0397 &0.0215 &0.0284 &0.0316 &1 &0.0433 &0.0268 &0.0249 &0.0068 &0.002\\ \hline E4 &0.0367 &0.0398 &0.0512 &0.0415 &0.0265 &0.0437 &0.0428 &0.0528 &0.0499 &0.0472 &0.0418 &0.0434 &0.0527 &0.0532 &0.0517 &0.0496 &0.0452 &0.0454 &0.0561 &1 &0.04 &0.0377 &0.0089 &0.003\\ \hline E5 &0.0599 &0.0642 &0.0587 &0.059 &0.0301 &0.0458 &0.055 &0.058 &0.0652 &0.0491 &0.0585 &0.0552 &0.0552 &0.0555 &0.054 &0.0453 &0.065 &0.0639 &0.0591 &0.0572 &1 &0.0538 &0.0457 &0.0298\\ \hline E6 &0.0545 &0.059 &0.0591 &0.0653 &0.0251 &0.0603 &0.056 &0.0677 &0.0639 &0.048 &0.0496 &0.0572 &0.0676 &0.0598 &0.0608 &0.0441 &0.0538 &0.0644 &0.0695 &0.0618 &0.0537 &1 &0.0476 &0.022\\ \hline F1 &0.059 &0.0551 &0.061 &0.0672 &0.0466 &0.0644 &0.0582 &0.0582 &0.0621 &0.0575 &0.0611 &0.0495 &0.0674 &0.0578 &0.0607 &0.0536 &0.0499 &0.0662 &0.0616 &0.0601 &0.0554 &0.0633 &1 &0.0142\\ \hline F2 &0.0597 &0.0675 &0.0677 &0.0664 &0.0508 &0.0665 &0.0679 &0.0723 &0.073 &0.0612 &0.0677 &0.0668 &0.0622 &0.0618 &0.0629 &0.059 &0.0693 &0.0726 &0.0701 &0.0623 &0.0575 &0.0674 &0.0536 &1\\ \hline \end{array} $$模糊可达矩阵$ \tilde R$ 由模糊相乘矩阵根据最大最小算子一直乘下去直到不变。
- FR：模糊可达矩阵的求解
- $FB= T +I$
- $FB^{(k-1)}≠FB^{k}=FB^{(k+1)}= FR$
- $FR 为模糊可达矩阵$
- $FB 为模糊相乘矩阵$
- $FB 主对角线为1$
- $FB= \begin{array} {c|c|c|c|c|c|c|c}{ FB_{n \times n}} &1 &2 &{\cdots} &n \\ \hline 1 & \color{blue}{1}&{b_{12}}&{\cdots}&{b_{1n}}\\ \hline 2 & {b_{21}}&\color{blue}{1}&{\cdots}&{b_{2n}}\\ \hline {\vdots} &{\vdots}&{\vdots}&\color{blue}{1}&{\vdots}\\ \hline n & {b_{n1}}&{b_{n2}}&{\cdots}&\color{blue}{1}\\ \hline \end{array}$
- $FB 主对角线为1$
- $ 设FC =FB \times FB \quad FC=\left[ c_{ij} \right]_{n \times n} \quad FB=\left[ b_{ij} \right]_{n \times n}$
- $ \begin{equation}\begin{split} c_{ij}&=\sum_{k=1}^n b_{ik}\odot b_{kj} \\ &=(b_{i1} \odot b_{1j}) \oplus (b_{i2} \odot b_{2j}) \oplus (b_{i3} \odot b_{3j}) \cdots \oplus \cdots(b_{in} \odot b_{nj})\\ \end{split}\end{equation}$
- 模糊算子采用查德算子，即最大最小算子，格式如下。
- $ \begin{equation}\begin{split} c_{ij}&=\sum_{k=1}^n b_{ik} \land b_{kj} \\ &=(b_{i1} \land b_{1j}) \vee (b_{i2} \land b_{2j}) \vee (b_{i3} \land b_{3j}) \cdots \vee \cdots(b_{in} \land b_{nj})\\ \end{split}\end{equation}$
由模糊可达矩阵MICMAC坐标图
模糊可达矩阵构成的决策矩阵如下
$$\begin{array}{c|c|c|c|c|c|c}{M_{24 \times2}} &R集合之和=D &Q集合之和=C\\ \hline A1 &1.19535112439 &2.25008332204\\ \hline A2 &1.90845335928 &2.18865508904\\ \hline A3 &1.9755308288 &2.19903077089\\ \hline A4 &1.8070013867 &2.26226000256\\ \hline B1 &1.46522346819 &2.00505579333\\ \hline B2 &1.74427399468 &2.18606367872\\ \hline C1 &2.27104091423 &2.13413957713\\ \hline C2 &2.29145646683 &2.16755096959\\ \hline C3 &2.23973095675 &2.22735732487\\ \hline C4 &2.28289411214 &2.13112232375\\ \hline C5 &2.25664704681 &2.18229847812\\ \hline D1 &2.40336455617 &2.13152200132\\ \hline D2 &2.3667689117 &2.15755757191\\ \hline D3 &2.10941168672 &2.13173532967\\ \hline D4 &2.11049163765 &2.17823819913\\ \hline D5 &2.2298584265 &2.15470243376\\ \hline E1 &2.38924415704 &2.13823461274\\ \hline E2 &2.29126737837 &2.17554527332\\ \hline E3 &2.05884162578 &2.21262946972\\ \hline E4 &2.18712609123 &2.16715190387\\ \hline E5 &2.38102323357 &2.1258716758\\ \hline E6 &2.39551647133 &2.12817479653\\ \hline F1 &2.40383817275 &1.99173643586\\ \hline F2 &2.51705662343 &1.65469559739\\ \hline \end{array} $$其中D是负向指标；C是正向指标
D表示驱动，影响力，是原因，原因成份的数值越大，层级越低，
TAISM处理过程
模糊可达矩阵FR中除数字0外不重复的值作为元素构成的集合称为阈值集合。
显然，阈值集合中元素的数目即为其对应层次拓扑图的数目。
113个结构数量分布图（瀑布图）
由模糊可达矩阵的阈值集合$\ddot \Delta $ 元素的数目得出 在(0,1]的截距值范围内得到 113个结构。
其中模糊可达矩阵(0,1]的截距值范围内取截距，得到的截矩阵为可达矩阵
设截距值为$\lambda $ ，$T$的 截距阵为 $A$ ,$R$为 $A$的可达矩阵。
$R$即为 模糊可达矩阵 $FR$ 的 $\lambda $ 截距阵
| 序号 | 阈值集合中——特征阈值 | 聚类特征-对应截距$\lambda $数值区段 | TAISM运算过程 |
|---|---|---|---|
| 1 | 0.00849 | 0<$\lambda$<0.00849 | |
| 2 | 0.02 | 0.00849<$\lambda$<0.02 | |
| 3 | 0.02527 | 0.02<$\lambda$<0.02527 | |
| 4 | 0.02982 | 0.02527<$\lambda$<0.02982 | |
| 5 | 0.03223 | 0.02982<$\lambda$<0.03223 | |
| 6 | 0.03321 | 0.03223<$\lambda$<0.03321 | |
| 7 | 0.03494 | 0.03321<$\lambda$<0.03494 | |
| 8 | 0.03673 | 0.03494<$\lambda$<0.03673 | |
| 9 | 0.0396 | 0.03673<$\lambda$<0.0396 | |
| 10 | 0.04287 | 0.0396<$\lambda$<0.04287 | |
| 11 | 0.04299 | 0.04287<$\lambda$<0.04299 | |
| 12 | 0.04338 | 0.04299<$\lambda$<0.04338 | |
| 13 | 0.04381 | 0.04338<$\lambda$<0.04381 | |
| 14 | 0.04601 | 0.04381<$\lambda$<0.04601 | |
| 15 | 0.04659 | 0.04601<$\lambda$<0.04659 | |
| 16 | 0.0476 | 0.04659<$\lambda$<0.0476 | |
| 17 | 0.04917 | 0.0476<$\lambda$<0.04917 | |
| 18 | 0.05018 | 0.04917<$\lambda$<0.05018 | |
| 19 | 0.05079 | 0.05018<$\lambda$<0.05079 | |
| 20 | 0.05176 | 0.05079<$\lambda$<0.05176 | |
| 21 | 0.05228 | 0.05176<$\lambda$<0.05228 | |
| 22 | 0.05281 | 0.05228<$\lambda$<0.05281 | |
| 23 | 0.05323 | 0.05281<$\lambda$<0.05323 | |
| 24 | 0.05355 | 0.05323<$\lambda$<0.05355 | |
| 25 | 0.05474 | 0.05355<$\lambda$<0.05474 | |
| 26 | 0.05492 | 0.05474<$\lambda$<0.05492 | |
| 27 | 0.05609 | 0.05492<$\lambda$<0.05609 | |
| 28 | 0.05616 | 0.05609<$\lambda$<0.05616 | |
| 29 | 0.0562 | 0.05616<$\lambda$<0.0562 | |
| 30 | 0.0564 | 0.0562<$\lambda$<0.0564 | |
| 31 | 0.05652 | 0.0564<$\lambda$<0.05652 | |
| 32 | 0.05657 | 0.05652<$\lambda$<0.05657 | |
| 33 | 0.0568 | 0.05657<$\lambda$<0.0568 | |
| 34 | 0.05704 | 0.0568<$\lambda$<0.05704 | |
| 35 | 0.05717 | 0.05704<$\lambda$<0.05717 | |
| 36 | 0.05722 | 0.05717<$\lambda$<0.05722 | |
| 37 | 0.05746 | 0.05722<$\lambda$<0.05746 | |
| 38 | 0.05769 | 0.05746<$\lambda$<0.05769 | |
| 39 | 0.05783 | 0.05769<$\lambda$<0.05783 | |
| 40 | 0.05788 | 0.05783<$\lambda$<0.05788 | |
| 41 | 0.05795 | 0.05788<$\lambda$<0.05795 | |
| 42 | 0.05836 | 0.05795<$\lambda$<0.05836 | |
| 43 | 0.05863 | 0.05836<$\lambda$<0.05863 | |
| 44 | 0.05897 | 0.05863<$\lambda$<0.05897 | |
| 45 | 0.05907 | 0.05897<$\lambda$<0.05907 | |
| 46 | 0.05925 | 0.05907<$\lambda$<0.05925 | |
| 47 | 0.05979 | 0.05925<$\lambda$<0.05979 | |
| 48 | 0.0598 | 0.05979<$\lambda$<0.0598 | |
| 49 | 0.06 | 0.0598<$\lambda$<0.06 | |
| 50 | 0.06001 | 0.06<$\lambda$<0.06001 | |
| 51 | 0.06007 | 0.06001<$\lambda$<0.06007 | |
| 52 | 0.06017 | 0.06007<$\lambda$<0.06017 | |
| 53 | 0.06117 | 0.06017<$\lambda$<0.06117 | |
| 54 | 0.0614 | 0.06117<$\lambda$<0.0614 | |
| 55 | 0.06157 | 0.0614<$\lambda$<0.06157 | |
| 56 | 0.06175 | 0.06157<$\lambda$<0.06175 | |
| 57 | 0.06178 | 0.06175<$\lambda$<0.06178 | |
| 58 | 0.0618 | 0.06178<$\lambda$<0.0618 | |
| 59 | 0.06196 | 0.0618<$\lambda$<0.06196 | |
| 60 | 0.06223 | 0.06196<$\lambda$<0.06223 | |
| 61 | 0.06272 | 0.06223<$\lambda$<0.06272 | |
| 62 | 0.06276 | 0.06272<$\lambda$<0.06276 | |
| 63 | 0.06276 | 0.06276<$\lambda$<0.06276 | |
| 64 | 0.06277 | 0.06276<$\lambda$<0.06277 | |
| 65 | 0.06304 | 0.06277<$\lambda$<0.06304 | |
| 66 | 0.06326 | 0.06304<$\lambda$<0.06326 | |
| 67 | 0.0635 | 0.06326<$\lambda$<0.0635 | |
| 68 | 0.06363 | 0.0635<$\lambda$<0.06363 | |
| 69 | 0.06365 | 0.06363<$\lambda$<0.06365 | |
| 70 | 0.06399 | 0.06365<$\lambda$<0.06399 | |
| 71 | 0.06417 | 0.06399<$\lambda$<0.06417 | |
| 72 | 0.06424 | 0.06417<$\lambda$<0.06424 | |
| 73 | 0.06426 | 0.06424<$\lambda$<0.06426 | |
| 74 | 0.06435 | 0.06426<$\lambda$<0.06435 | |
| 75 | 0.06435 | 0.06435<$\lambda$<0.06435 | |
| 76 | 0.06473 | 0.06435<$\lambda$<0.06473 | |
| 77 | 0.06495 | 0.06473<$\lambda$<0.06495 | |
| 78 | 0.06503 | 0.06495<$\lambda$<0.06503 | |
| 79 | 0.06516 | 0.06503<$\lambda$<0.06516 | |
| 80 | 0.0653 | 0.06516<$\lambda$<0.0653 | |
| 81 | 0.06567 | 0.0653<$\lambda$<0.06567 | |
| 82 | 0.06572 | 0.06567<$\lambda$<0.06572 | |
| 83 | 0.06587 | 0.06572<$\lambda$<0.06587 | |
| 84 | 0.06589 | 0.06587<$\lambda$<0.06589 | |
| 85 | 0.0661 | 0.06589<$\lambda$<0.0661 | |
| 86 | 0.06616 | 0.0661<$\lambda$<0.06616 | |
| 87 | 0.06619 | 0.06616<$\lambda$<0.06619 | |
| 88 | 0.06645 | 0.06619<$\lambda$<0.06645 | |
| 89 | 0.06682 | 0.06645<$\lambda$<0.06682 | |
| 90 | 0.06704 | 0.06682<$\lambda$<0.06704 | |
| 91 | 0.06737 | 0.06704<$\lambda$<0.06737 | |
| 92 | 0.06741 | 0.06737<$\lambda$<0.06741 | |
| 93 | 0.06748 | 0.06741<$\lambda$<0.06748 | |
| 94 | 0.06757 | 0.06748<$\lambda$<0.06757 | |
| 95 | 0.06766 | 0.06757<$\lambda$<0.06766 | |
| 96 | 0.06768 | 0.06766<$\lambda$<0.06768 | |
| 97 | 0.06772 | 0.06768<$\lambda$<0.06772 | |
| 98 | 0.06776 | 0.06772<$\lambda$<0.06776 | |
| 99 | 0.06782 | 0.06776<$\lambda$<0.06782 | |
| 100 | 0.06795 | 0.06782<$\lambda$<0.06795 | |
| 101 | 0.06802 | 0.06795<$\lambda$<0.06802 | |
| 102 | 0.06834 | 0.06802<$\lambda$<0.06834 | |
| 103 | 0.06864 | 0.06834<$\lambda$<0.06864 | |
| 104 | 0.06883 | 0.06864<$\lambda$<0.06883 | |
| 105 | 0.06895 | 0.06883<$\lambda$<0.06895 | |
| 106 | 0.06929 | 0.06895<$\lambda$<0.06929 | |
| 107 | 0.06946 | 0.06929<$\lambda$<0.06946 | |
| 108 | 0.07007 | 0.06946<$\lambda$<0.07007 | |
| 109 | 0.07226 | 0.07007<$\lambda$<0.07226 | |
| 110 | 0.0726 | 0.07226<$\lambda$<0.0726 | |
| 111 | 0.07301 | 0.0726<$\lambda$<0.07301 | |
| 112 | 0.07322 | 0.07301<$\lambda$<0.07322 | |
| 113 | 1 | 0.07322<$\lambda$<1 |