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 &0.005 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.009 &0 &0 &0 &0 &0 &0 &0\\ \hline A2 &0.039 &0 &0.037 &0.039 &0 &0.002 &0.014 &0.012 &0.03 &0.009 &0.03 &0 &0 &0 &0 &0 &0.007 &0 &0.007 &0 &0 &0.021 &0 &0\\ \hline A3 &0.037 &0.028 &0 &0.03 &0.014 &0.018 &0.041 &0 &0.025 &0 &0.032 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.018 &0\\ \hline A4 &0.039 &0.025 &0.016 &0 &0.005 &0 &0.032 &0.014 &0.021 &0.007 &0.03 &0 &0 &0 &0 &0 &0.018 &0.021 &0 &0 &0 &0 &0 &0\\ \hline B1 &0.025 &0.007 &0.009 &0.005 &0 &0.021 &0.007 &0 &0.007 &0 &0.007 &0 &0 &0 &0 &0 &0 &0 &0 &0.016 &0 &0 &0 &0\\ \hline B2 &0.028 &0.002 &0.007 &0 &0.037 &0 &0.028 &0 &0.025 &0.025 &0.014 &0 &0.016 &0 &0.018 &0.014 &0 &0 &0.021 &0.016 &0 &0 &0 &0\\ \hline C1 &0.035 &0.037 &0.037 &0.037 &0 &0.028 &0 &0.025 &0.039 &0.016 &0.039 &0.025 &0.032 &0.028 &0.032 &0.03 &0.028 &0.032 &0.032 &0.023 &0.028 &0.03 &0.037 &0\\ \hline C2 &0.028 &0.041 &0.025 &0.032 &0.002 &0.018 &0.018 &0 &0.044 &0.018 &0.046 &0.03 &0.039 &0.03 &0.037 &0.023 &0.032 &0.028 &0.037 &0.03 &0.035 &0.037 &0.014 &0\\ \hline C3 &0.037 &0.032 &0.032 &0.046 &0.018 &0.039 &0.032 &0.039 &0 &0.035 &0.018 &0.028 &0.018 &0.037 &0.028 &0.021 &0.032 &0.028 &0.046 &0.037 &0.032 &0.016 &0 &0\\ \hline C4 &0.037 &0.028 &0.037 &0.041 &0.018 &0.039 &0.039 &0.039 &0.041 &0 &0.039 &0.03 &0.03 &0.028 &0.03 &0.032 &0.03 &0.03 &0.039 &0.032 &0.03 &0.021 &0 &0\\ \hline C5 &0.044 &0.032 &0.032 &0.039 &0 &0 &0.03 &0.041 &0.037 &0.025 &0 &0.028 &0.021 &0.03 &0.035 &0.018 &0.028 &0.03 &0.025 &0.03 &0.025 &0.035 &0 &0\\ \hline D1 &0.041 &0.041 &0.032 &0.041 &0 &0.032 &0.03 &0.037 &0.041 &0.03 &0.041 &0 &0.044 &0.032 &0.039 &0.03 &0.046 &0.046 &0.039 &0.041 &0.046 &0.03 &0 &0.007\\ \hline D2 &0.028 &0.037 &0.037 &0.039 &0.014 &0.039 &0.028 &0.032 &0.039 &0.039 &0.035 &0.037 &0 &0.037 &0.046 &0.046 &0.032 &0.039 &0.039 &0.044 &0.039 &0.039 &0.032 &0.012\\ \hline D3 &0.021 &0.023 &0.016 &0.025 &0.018 &0.03 &0.025 &0.025 &0.021 &0.03 &0.03 &0.016 &0.028 &0 &0.037 &0.028 &0.021 &0.028 &0.023 &0.025 &0.021 &0.021 &0.007 &0\\ \hline D4 &0.014 &0.025 &0.009 &0.014 &0.023 &0.044 &0.039 &0.018 &0.016 &0.028 &0.021 &0.012 &0.021 &0.018 &0 &0.025 &0.009 &0.025 &0.014 &0.018 &0.016 &0.016 &0 &0\\ \hline D5 &0.014 &0.028 &0.028 &0.028 &0.025 &0.028 &0.028 &0.025 &0.037 &0.028 &0.032 &0.023 &0.037 &0.03 &0.028 &0 &0.03 &0.039 &0.028 &0.035 &0.025 &0.023 &0 &0\\ \hline E1 &0.032 &0.037 &0.039 &0.032 &0.007 &0.025 &0.018 &0.044 &0.046 &0.032 &0.032 &0.046 &0.037 &0.035 &0.032 &0.032 &0 &0.046 &0.037 &0.03 &0.041 &0.037 &0.035 &0.009\\ \hline E2 &0.03 &0.039 &0.046 &0.039 &0.028 &0.041 &0.023 &0.032 &0.039 &0.03 &0.039 &0.037 &0.039 &0.032 &0.037 &0.035 &0.028 &0 &0.039 &0.037 &0.016 &0.028 &0 &0\\ \hline E3 &0.021 &0.025 &0.039 &0.044 &0.037 &0.032 &0.032 &0.016 &0.03 &0.025 &0.018 &0.009 &0.03 &0.023 &0.028 &0.009 &0.016 &0.018 &0 &0.032 &0.016 &0.014 &0 &0\\ \hline E4 &0.014 &0.018 &0.032 &0.018 &0.016 &0.025 &0.023 &0.037 &0.028 &0.032 &0.021 &0.03 &0.037 &0.039 &0.035 &0.037 &0.03 &0.028 &0.039 &0 &0.025 &0.023 &0 &0\\ \hline E5 &0.032 &0.039 &0.032 &0.03 &0.016 &0.021 &0.03 &0.035 &0.037 &0.028 &0.032 &0.037 &0.032 &0.035 &0.03 &0.025 &0.046 &0.041 &0.035 &0.035 &0 &0.035 &0.039 &0.03\\ \hline E6 &0.025 &0.032 &0.032 &0.037 &0.009 &0.037 &0.03 &0.046 &0.035 &0.025 &0.021 &0.039 &0.046 &0.039 &0.037 &0.023 &0.032 &0.041 &0.046 &0.039 &0.035 &0 &0.041 &0.021\\ \hline F1 &0.03 &0.028 &0.035 &0.039 &0.035 &0.041 &0.032 &0.035 &0.032 &0.037 &0.035 &0.03 &0.046 &0.037 &0.037 &0.035 &0.028 &0.044 &0.037 &0.037 &0.037 &0.046 &0 &0.012\\ \hline F2 &0.025 &0.037 &0.037 &0.032 &0.037 &0.039 &0.039 &0.046 &0.039 &0.037 &0.037 &0.046 &0.035 &0.037 &0.035 &0.037 &0.046 &0.046 &0.041 &0.035 &0.035 &0.046 &0.046 &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 &0.01 &0.001 &0.001 &0.001 &0.001 &0.001 &0.001 &0\\ \hline A2 &0.053 &0.012 &0.047 &0.051 &0.005 &0.011 &0.026 &0.022 &0.042 &0.017 &0.041 &0.008 &0.009 &0.009 &0.009 &0.007 &0.016 &0.01 &0.017 &0.009 &0.008 &0.028 &0.005 &0.001\\ \hline A3 &0.05 &0.038 &0.011 &0.041 &0.018 &0.026 &0.051 &0.009 &0.037 &0.008 &0.042 &0.007 &0.008 &0.008 &0.009 &0.007 &0.009 &0.009 &0.009 &0.009 &0.007 &0.008 &0.022 &0.001\\ \hline A4 &0.052 &0.037 &0.028 &0.013 &0.009 &0.009 &0.042 &0.024 &0.033 &0.015 &0.041 &0.009 &0.009 &0.009 &0.01 &0.008 &0.027 &0.03 &0.011 &0.009 &0.008 &0.009 &0.004 &0.001\\ \hline B1 &0.03 &0.01 &0.013 &0.008 &0.002 &0.023 &0.011 &0.003 &0.011 &0.003 &0.01 &0.002 &0.003 &0.003 &0.003 &0.003 &0.003 &0.003 &0.003 &0.019 &0.002 &0.002 &0.001 &0\\ \hline B2 &0.041 &0.014 &0.019 &0.013 &0.043 &0.012 &0.039 &0.011 &0.038 &0.035 &0.025 &0.009 &0.026 &0.01 &0.029 &0.023 &0.01 &0.011 &0.032 &0.027 &0.009 &0.009 &0.004 &0.001\\ \hline C1 &0.074 &0.073 &0.073 &0.077 &0.02 &0.06 &0.037 &0.059 &0.079 &0.047 &0.075 &0.052 &0.064 &0.058 &0.065 &0.057 &0.058 &0.065 &0.067 &0.056 &0.055 &0.058 &0.05 &0.005\\ \hline C2 &0.067 &0.078 &0.063 &0.073 &0.022 &0.052 &0.055 &0.035 &0.084 &0.05 &0.082 &0.058 &0.071 &0.061 &0.071 &0.051 &0.063 &0.062 &0.072 &0.063 &0.063 &0.065 &0.028 &0.005\\ \hline C3 &0.074 &0.067 &0.067 &0.083 &0.037 &0.069 &0.066 &0.069 &0.039 &0.062 &0.054 &0.052 &0.049 &0.064 &0.059 &0.046 &0.06 &0.058 &0.077 &0.067 &0.057 &0.042 &0.013 &0.004\\ \hline C4 &0.077 &0.065 &0.074 &0.082 &0.038 &0.072 &0.075 &0.072 &0.082 &0.031 &0.076 &0.057 &0.062 &0.058 &0.064 &0.06 &0.061 &0.063 &0.074 &0.065 &0.058 &0.049 &0.014 &0.005\\ \hline C5 &0.078 &0.066 &0.065 &0.075 &0.016 &0.03 &0.061 &0.071 &0.072 &0.051 &0.034 &0.052 &0.05 &0.057 &0.064 &0.043 &0.055 &0.06 &0.056 &0.058 &0.05 &0.059 &0.013 &0.004\\ \hline D1 &0.088 &0.085 &0.076 &0.088 &0.023 &0.071 &0.072 &0.077 &0.089 &0.066 &0.085 &0.034 &0.081 &0.068 &0.079 &0.063 &0.082 &0.085 &0.08 &0.08 &0.078 &0.063 &0.017 &0.013\\ \hline D2 &0.077 &0.083 &0.083 &0.089 &0.039 &0.081 &0.073 &0.074 &0.089 &0.077 &0.081 &0.071 &0.042 &0.075 &0.088 &0.08 &0.07 &0.081 &0.083 &0.085 &0.074 &0.074 &0.049 &0.017\\ \hline D3 &0.052 &0.052 &0.045 &0.056 &0.034 &0.056 &0.053 &0.051 &0.053 &0.053 &0.059 &0.038 &0.053 &0.024 &0.063 &0.049 &0.045 &0.054 &0.051 &0.051 &0.042 &0.043 &0.017 &0.004\\ \hline D4 &0.039 &0.048 &0.033 &0.039 &0.035 &0.064 &0.061 &0.039 &0.042 &0.046 &0.044 &0.029 &0.041 &0.037 &0.022 &0.043 &0.029 &0.046 &0.036 &0.039 &0.033 &0.034 &0.009 &0.003\\ \hline D5 &0.051 &0.062 &0.062 &0.064 &0.043 &0.058 &0.06 &0.056 &0.074 &0.055 &0.066 &0.048 &0.066 &0.058 &0.059 &0.026 &0.058 &0.069 &0.06 &0.065 &0.051 &0.048 &0.013 &0.004\\ \hline E1 &0.08 &0.081 &0.084 &0.081 &0.031 &0.066 &0.062 &0.084 &0.094 &0.069 &0.077 &0.079 &0.076 &0.072 &0.073 &0.066 &0.038 &0.086 &0.079 &0.07 &0.075 &0.071 &0.05 &0.015\\ \hline E2 &0.072 &0.077 &0.083 &0.08 &0.047 &0.075 &0.061 &0.066 &0.081 &0.061 &0.077 &0.064 &0.071 &0.063 &0.071 &0.062 &0.058 &0.034 &0.074 &0.07 &0.045 &0.055 &0.014 &0.004\\ \hline E3 &0.05 &0.051 &0.065 &0.071 &0.05 &0.055 &0.058 &0.039 &0.058 &0.046 &0.045 &0.028 &0.051 &0.043 &0.05 &0.029 &0.037 &0.041 &0.024 &0.054 &0.035 &0.033 &0.01 &0.003\\ \hline E4 &0.05 &0.053 &0.066 &0.056 &0.034 &0.057 &0.056 &0.067 &0.065 &0.06 &0.055 &0.055 &0.067 &0.067 &0.066 &0.062 &0.058 &0.059 &0.071 &0.032 &0.051 &0.049 &0.013 &0.004\\ \hline E5 &0.079 &0.083 &0.077 &0.078 &0.039 &0.061 &0.072 &0.075 &0.085 &0.064 &0.077 &0.07 &0.072 &0.071 &0.071 &0.059 &0.082 &0.082 &0.077 &0.074 &0.035 &0.069 &0.056 &0.035\\ \hline E6 &0.073 &0.077 &0.077 &0.085 &0.034 &0.078 &0.074 &0.086 &0.084 &0.063 &0.067 &0.073 &0.086 &0.076 &0.079 &0.058 &0.07 &0.082 &0.089 &0.079 &0.069 &0.036 &0.058 &0.026\\ \hline F1 &0.078 &0.073 &0.08 &0.087 &0.058 &0.082 &0.076 &0.075 &0.082 &0.074 &0.08 &0.064 &0.086 &0.074 &0.078 &0.069 &0.065 &0.084 &0.08 &0.078 &0.071 &0.08 &0.018 &0.018\\ \hline F2 &0.08 &0.088 &0.089 &0.088 &0.064 &0.086 &0.089 &0.093 &0.096 &0.079 &0.089 &0.085 &0.081 &0.08 &0.082 &0.076 &0.088 &0.093 &0.091 &0.081 &0.074 &0.086 &0.065 &0.007\\ \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
$$\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{24 \times4}} &Di &Ci &Mi &Ri\\ \hline A1 &0.036 &1.465 &1.501 &-1.43\\ \hline A2 &0.462 &1.375 &1.837 &-0.913\\ \hline A3 &0.446 &1.381 &1.828 &-0.935\\ \hline A4 &0.449 &1.481 &1.93 &-1.032\\ \hline B1 &0.172 &0.741 &0.913 &-0.569\\ \hline B2 &0.492 &1.256 &1.749 &-0.764\\ \hline C1 &1.384 &1.336 &2.72 &0.048\\ \hline C2 &1.393 &1.259 &2.652 &0.135\\ \hline C3 &1.335 &1.511 &2.846 &-0.175\\ \hline C4 &1.434 &1.133 &2.568 &0.301\\ \hline C5 &1.241 &1.384 &2.625 &-0.143\\ \hline D1 &1.643 &1.045 &2.688 &0.598\\ \hline D2 &1.733 &1.225 &2.958 &0.508\\ \hline D3 &1.099 &1.148 &2.247 &-0.049\\ \hline D4 &0.893 &1.265 &2.157 &-0.372\\ \hline D5 &1.275 &1.047 &2.322 &0.228\\ \hline E1 &1.659 &1.152 &2.811 &0.507\\ \hline E2 &1.465 &1.27 &2.734 &0.195\\ \hline E3 &1.028 &1.315 &2.343 &-0.287\\ \hline E4 &1.272 &1.241 &2.513 &0.031\\ \hline E5 &1.643 &1.052 &2.695 &0.591\\ \hline E6 &1.679 &1.069 &2.748 &0.61\\ \hline F1 &1.709 &0.543 &2.252 &1.166\\ \hline F2 &1.931 &0.182 &2.113 &1.75\\ \hline \end{array} $$
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 &0.0011 &0.0011 &0.0011 &0.0004 &0.0009 &0.0054 &0.001 &0.0012 &0.0008 &0.0011 &0.001 &0.001 &0.0009 &0.001 &0.0009 &0.0098 &0.0011 &0.001 &0.0009 &0.0009 &0.0009 &0.0007 &0.0002\\ \hline A2 &0.0527 &1 &0.0475 &0.0515 &0.0049 &0.0112 &0.0257 &0.0216 &0.0417 &0.0172 &0.0408 &0.008 &0.0087 &0.0088 &0.0093 &0.0071 &0.0162 &0.0099 &0.0168 &0.0091 &0.0081 &0.0279 &0.0046 &0.0012\\ \hline A3 &0.05 &0.0377 &1 &0.0415 &0.0184 &0.0263 &0.0511 &0.0095 &0.0365 &0.0082 &0.0423 &0.0071 &0.0082 &0.008 &0.0089 &0.0071 &0.0088 &0.0091 &0.0095 &0.0086 &0.0074 &0.0081 &0.0219 &0.0009\\ \hline A4 &0.0522 &0.0367 &0.028 &1 &0.009 &0.0091 &0.0421 &0.0239 &0.0332 &0.0153 &0.041 &0.0087 &0.0093 &0.0092 &0.0099 &0.008 &0.0274 &0.0299 &0.0106 &0.0095 &0.0084 &0.0091 &0.0045 &0.0009\\ \hline B1 &0.0297 &0.0101 &0.0127 &0.0082 &1 &0.0234 &0.0107 &0.0031 &0.0109 &0.0031 &0.0104 &0.0023 &0.0029 &0.0027 &0.0032 &0.0027 &0.0029 &0.0028 &0.0035 &0.0187 &0.0023 &0.0024 &0.0011 &0.0002\\ \hline B2 &0.0407 &0.0143 &0.0193 &0.0135 &0.0432 &1 &0.0393 &0.011 &0.0379 &0.0347 &0.0254 &0.0089 &0.0261 &0.0104 &0.0292 &0.0229 &0.0101 &0.0108 &0.032 &0.0272 &0.0094 &0.0089 &0.004 &0.001\\ \hline C1 &0.0738 &0.0733 &0.0734 &0.0767 &0.0198 &0.0603 &1 &0.0587 &0.0789 &0.0467 &0.0755 &0.0525 &0.0642 &0.0579 &0.0655 &0.057 &0.0578 &0.0655 &0.0666 &0.0557 &0.0551 &0.0578 &0.0497 &0.0051\\ \hline C2 &0.0675 &0.0784 &0.0631 &0.0731 &0.0216 &0.0518 &0.0549 &1 &0.0839 &0.0496 &0.0822 &0.0578 &0.0712 &0.061 &0.0707 &0.051 &0.0631 &0.0618 &0.0719 &0.0632 &0.0626 &0.0649 &0.0278 &0.0053\\ \hline C3 &0.0742 &0.0667 &0.0667 &0.0826 &0.0366 &0.0693 &0.0659 &0.0691 &1 &0.062 &0.054 &0.0524 &0.0489 &0.0641 &0.0588 &0.0463 &0.0602 &0.0583 &0.0775 &0.0666 &0.0572 &0.0419 &0.0129 &0.0042\\ \hline C4 &0.0774 &0.0654 &0.074 &0.0816 &0.0377 &0.0718 &0.0752 &0.0721 &0.0823 &1 &0.0764 &0.0571 &0.0623 &0.0582 &0.0639 &0.0596 &0.0607 &0.0634 &0.0739 &0.0652 &0.0576 &0.0488 &0.0141 &0.0046\\ \hline C5 &0.0784 &0.0656 &0.065 &0.0747 &0.0161 &0.03 &0.0614 &0.0708 &0.0724 &0.0515 &1 &0.0521 &0.0496 &0.057 &0.0639 &0.0429 &0.0552 &0.0597 &0.0564 &0.0584 &0.0502 &0.0588 &0.013 &0.0043\\ \hline D1 &0.0876 &0.0851 &0.0763 &0.0884 &0.023 &0.0707 &0.0721 &0.0765 &0.0892 &0.0658 &0.0848 &1 &0.0813 &0.0685 &0.0789 &0.0628 &0.0817 &0.0851 &0.0804 &0.0797 &0.0781 &0.0632 &0.0173 &0.0127\\ \hline D2 &0.0766 &0.0826 &0.0828 &0.0886 &0.039 &0.0808 &0.0729 &0.0743 &0.0895 &0.0768 &0.0807 &0.071 &1 &0.075 &0.0878 &0.0802 &0.0705 &0.0811 &0.0828 &0.0845 &0.0736 &0.0738 &0.0486 &0.0174\\ \hline D3 &0.0518 &0.052 &0.0454 &0.0563 &0.0337 &0.056 &0.0535 &0.0514 &0.0528 &0.0534 &0.0588 &0.0379 &0.053 &1 &0.063 &0.0494 &0.0445 &0.0537 &0.0506 &0.0512 &0.0425 &0.0426 &0.0175 &0.0036\\ \hline D4 &0.0394 &0.0481 &0.0331 &0.0389 &0.0353 &0.0641 &0.061 &0.0391 &0.0423 &0.0464 &0.0443 &0.0288 &0.0412 &0.0373 &1 &0.0428 &0.0285 &0.0457 &0.0364 &0.0394 &0.0333 &0.0336 &0.0088 &0.0027\\ \hline D5 &0.0506 &0.0616 &0.0618 &0.0643 &0.0426 &0.0582 &0.0602 &0.0561 &0.0737 &0.0553 &0.0659 &0.0485 &0.0659 &0.0578 &0.0587 &1 &0.0575 &0.069 &0.0599 &0.0646 &0.0507 &0.0485 &0.0128 &0.0043\\ \hline E1 &0.0795 &0.0815 &0.0836 &0.0809 &0.0307 &0.0658 &0.0621 &0.0838 &0.0943 &0.0687 &0.0771 &0.0788 &0.0763 &0.0716 &0.0733 &0.0657 &1 &0.0862 &0.0793 &0.0702 &0.075 &0.0708 &0.0504 &0.0153\\ \hline E2 &0.0715 &0.0768 &0.0834 &0.0801 &0.0471 &0.075 &0.0608 &0.0659 &0.0807 &0.0607 &0.077 &0.0636 &0.0712 &0.0627 &0.0708 &0.0621 &0.0584 &1 &0.0742 &0.0701 &0.0447 &0.0554 &0.0137 &0.0044\\ \hline E3 &0.0502 &0.0513 &0.0647 &0.0711 &0.05 &0.0555 &0.0581 &0.0391 &0.0583 &0.0459 &0.0451 &0.028 &0.0511 &0.0434 &0.0504 &0.0288 &0.037 &0.0411 &1 &0.0542 &0.0348 &0.0326 &0.01 &0.003\\ \hline E4 &0.05 &0.053 &0.0659 &0.0556 &0.0341 &0.0566 &0.0562 &0.067 &0.0652 &0.0599 &0.0554 &0.0551 &0.0667 &0.0669 &0.0659 &0.0622 &0.0577 &0.0586 &0.071 &1 &0.0513 &0.0487 &0.0131 &0.0044\\ \hline E5 &0.0789 &0.0831 &0.0768 &0.078 &0.0395 &0.0611 &0.0723 &0.0751 &0.0851 &0.0641 &0.0766 &0.0703 &0.0717 &0.0714 &0.0707 &0.0591 &0.0822 &0.0818 &0.0768 &0.074 &1 &0.0689 &0.0558 &0.0352\\ \hline E6 &0.0729 &0.0774 &0.0774 &0.0853 &0.0341 &0.0779 &0.0736 &0.0862 &0.0839 &0.0631 &0.0668 &0.0727 &0.0858 &0.0765 &0.0785 &0.058 &0.0697 &0.0825 &0.0887 &0.0794 &0.0689 &1 &0.0579 &0.0264\\ \hline F1 &0.0781 &0.0729 &0.0797 &0.0874 &0.0584 &0.0824 &0.0762 &0.0754 &0.0819 &0.0737 &0.0797 &0.0639 &0.0856 &0.0741 &0.0784 &0.0687 &0.0652 &0.0845 &0.0798 &0.0775 &0.0706 &0.0796 &1 &0.0175\\ \hline F2 &0.0805 &0.0885 &0.0887 &0.0882 &0.0639 &0.0862 &0.0886 &0.0928 &0.0959 &0.0792 &0.0887 &0.0848 &0.0811 &0.08 &0.0823 &0.0759 &0.0885 &0.0932 &0.0908 &0.0814 &0.0743 &0.0856 &0.0653 &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
$$\begin{array}{c|c|c|c|c|c|c}{M_{24 \times2}} &R集合之和=D &Q集合之和=C\\ \hline A1 &1.22630320736 &2.57472404888\\ \hline A2 &2.08878516655 &2.50968468142\\ \hline A3 &2.15943960016 &2.51362095581\\ \hline A4 &1.97095615205 &2.5983033603\\ \hline B1 &1.54440854784 &2.24293310642\\ \hline B2 &1.90510771666 &2.49310848055\\ \hline C1 &2.60458312475 &2.42801127668\\ \hline C2 &2.63052731317 &2.46426874618\\ \hline C3 &2.56070310363 &2.55746259286\\ \hline C4 &2.62518126758 &2.42280458568\\ \hline C5 &2.58215060526 &2.49127063597\\ \hline D1 &2.78335922436 &2.41702990225\\ \hline D2 &2.74675550799 &2.44983694421\\ \hline D3 &2.37432600048 &2.42563059804\\ \hline D4 &2.37336603148 &2.47870149919\\ \hline D5 &2.55211352124 &2.44315671043\\ \hline E1 &2.75616242709 &2.42701050386\\ \hline E2 &2.63348797348 &2.47748823637\\ \hline E3 &2.33543335274 &2.52489092237\\ \hline E4 &2.49822702197 &2.46396759245\\ \hline E5 &2.74566133464 &2.40893499424\\ \hline E6 &2.77253276579 &2.41413195462\\ \hline F1 &2.78667421495 &2.20542863536\\ \hline F2 &2.94760457869 &1.77144879575\\ \hline \end{array} $$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。
119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 119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 $数值区段 | TAISM运算过程 |
|---|---|---|---|
| 1 | 0.00984 | 0<$\lambda$<0.00984 | |
| 2 | 0.0234 | 0.00984<$\lambda$<0.0234 | |
| 3 | 0.02967 | 0.0234<$\lambda$<0.02967 | |
| 4 | 0.03515 | 0.02967<$\lambda$<0.03515 | |
| 5 | 0.0393 | 0.03515<$\lambda$<0.0393 | |
| 6 | 0.04073 | 0.0393<$\lambda$<0.04073 | |
| 7 | 0.04208 | 0.04073<$\lambda$<0.04208 | |
| 8 | 0.04322 | 0.04208<$\lambda$<0.04322 | |
| 9 | 0.04747 | 0.04322<$\lambda$<0.04747 | |
| 10 | 0.0511 | 0.04747<$\lambda$<0.0511 | |
| 11 | 0.0515 | 0.0511<$\lambda$<0.0515 | |
| 12 | 0.0522 | 0.0515<$\lambda$<0.0522 | |
| 13 | 0.05271 | 0.0522<$\lambda$<0.05271 | |
| 14 | 0.05793 | 0.05271<$\lambda$<0.05793 | |
| 15 | 0.05826 | 0.05793<$\lambda$<0.05826 | |
| 16 | 0.05837 | 0.05826<$\lambda$<0.05837 | |
| 17 | 0.06096 | 0.05837<$\lambda$<0.06096 | |
| 18 | 0.06302 | 0.06096<$\lambda$<0.06302 | |
| 19 | 0.06391 | 0.06302<$\lambda$<0.06391 | |
| 20 | 0.06413 | 0.06391<$\lambda$<0.06413 | |
| 21 | 0.06466 | 0.06413<$\lambda$<0.06466 | |
| 22 | 0.0653 | 0.06466<$\lambda$<0.0653 | |
| 23 | 0.06695 | 0.0653<$\lambda$<0.06695 | |
| 24 | 0.06913 | 0.06695<$\lambda$<0.06913 | |
| 25 | 0.06933 | 0.06913<$\lambda$<0.06933 | |
| 26 | 0.07083 | 0.06933<$\lambda$<0.07083 | |
| 27 | 0.07105 | 0.07083<$\lambda$<0.07105 | |
| 28 | 0.07109 | 0.07105<$\lambda$<0.07109 | |
| 29 | 0.07118 | 0.07109<$\lambda$<0.07118 | |
| 30 | 0.07122 | 0.07118<$\lambda$<0.07122 | |
| 31 | 0.07178 | 0.07122<$\lambda$<0.07178 | |
| 32 | 0.07211 | 0.07178<$\lambda$<0.07211 | |
| 33 | 0.07237 | 0.07211<$\lambda$<0.07237 | |
| 34 | 0.07329 | 0.07237<$\lambda$<0.07329 | |
| 35 | 0.07337 | 0.07329<$\lambda$<0.07337 | |
| 36 | 0.07359 | 0.07337<$\lambda$<0.07359 | |
| 37 | 0.07371 | 0.07359<$\lambda$<0.07371 | |
| 38 | 0.07377 | 0.07371<$\lambda$<0.07377 | |
| 39 | 0.07403 | 0.07377<$\lambda$<0.07403 | |
| 40 | 0.07424 | 0.07403<$\lambda$<0.07424 | |
| 41 | 0.07428 | 0.07424<$\lambda$<0.07428 | |
| 42 | 0.07473 | 0.07428<$\lambda$<0.07473 | |
| 43 | 0.07496 | 0.07473<$\lambda$<0.07496 | |
| 44 | 0.07498 | 0.07496<$\lambda$<0.07498 | |
| 45 | 0.07524 | 0.07498<$\lambda$<0.07524 | |
| 46 | 0.07546 | 0.07524<$\lambda$<0.07546 | |
| 47 | 0.07616 | 0.07546<$\lambda$<0.07616 | |
| 48 | 0.07644 | 0.07616<$\lambda$<0.07644 | |
| 49 | 0.07646 | 0.07644<$\lambda$<0.07646 | |
| 50 | 0.07675 | 0.07646<$\lambda$<0.07675 | |
| 51 | 0.07684 | 0.07675<$\lambda$<0.07684 | |
| 52 | 0.07697 | 0.07684<$\lambda$<0.07697 | |
| 53 | 0.07737 | 0.07697<$\lambda$<0.07737 | |
| 54 | 0.07748 | 0.07737<$\lambda$<0.07748 | |
| 55 | 0.07812 | 0.07748<$\lambda$<0.07812 | |
| 56 | 0.07841 | 0.07812<$\lambda$<0.07841 | |
| 57 | 0.07845 | 0.07841<$\lambda$<0.07845 | |
| 58 | 0.07885 | 0.07845<$\lambda$<0.07885 | |
| 59 | 0.07887 | 0.07885<$\lambda$<0.07887 | |
| 60 | 0.07916 | 0.07887<$\lambda$<0.07916 | |
| 61 | 0.07935 | 0.07916<$\lambda$<0.07935 | |
| 62 | 0.07951 | 0.07935<$\lambda$<0.07951 | |
| 63 | 0.07963 | 0.07951<$\lambda$<0.07963 | |
| 64 | 0.07995 | 0.07963<$\lambda$<0.07995 | |
| 65 | 0.08016 | 0.07995<$\lambda$<0.08016 | |
| 66 | 0.08066 | 0.08016<$\lambda$<0.08066 | |
| 67 | 0.08072 | 0.08066<$\lambda$<0.08072 | |
| 68 | 0.08078 | 0.08072<$\lambda$<0.08078 | |
| 69 | 0.08115 | 0.08078<$\lambda$<0.08115 | |
| 70 | 0.08133 | 0.08115<$\lambda$<0.08133 | |
| 71 | 0.0815 | 0.08133<$\lambda$<0.0815 | |
| 72 | 0.08174 | 0.0815<$\lambda$<0.08174 | |
| 73 | 0.08221 | 0.08174<$\lambda$<0.08221 | |
| 74 | 0.08222 | 0.08221<$\lambda$<0.08222 | |
| 75 | 0.08231 | 0.08222<$\lambda$<0.08231 | |
| 76 | 0.08242 | 0.08231<$\lambda$<0.08242 | |
| 77 | 0.08246 | 0.08242<$\lambda$<0.08246 | |
| 78 | 0.08258 | 0.08246<$\lambda$<0.08258 | |
| 79 | 0.08262 | 0.08258<$\lambda$<0.08262 | |
| 80 | 0.08281 | 0.08262<$\lambda$<0.08281 | |
| 81 | 0.08285 | 0.08281<$\lambda$<0.08285 | |
| 82 | 0.08309 | 0.08285<$\lambda$<0.08309 | |
| 83 | 0.08339 | 0.08309<$\lambda$<0.08339 | |
| 84 | 0.08358 | 0.08339<$\lambda$<0.08358 | |
| 85 | 0.08385 | 0.08358<$\lambda$<0.08385 | |
| 86 | 0.08386 | 0.08385<$\lambda$<0.08386 | |
| 87 | 0.08448 | 0.08386<$\lambda$<0.08448 | |
| 88 | 0.08452 | 0.08448<$\lambda$<0.08452 | |
| 89 | 0.08475 | 0.08452<$\lambda$<0.08475 | |
| 90 | 0.0848 | 0.08475<$\lambda$<0.0848 | |
| 91 | 0.08506 | 0.0848<$\lambda$<0.08506 | |
| 92 | 0.08508 | 0.08506<$\lambda$<0.08508 | |
| 93 | 0.08512 | 0.08508<$\lambda$<0.08512 | |
| 94 | 0.08556 | 0.08512<$\lambda$<0.08556 | |
| 95 | 0.0856 | 0.08556<$\lambda$<0.0856 | |
| 96 | 0.08584 | 0.0856<$\lambda$<0.08584 | |
| 97 | 0.08617 | 0.08584<$\lambda$<0.08617 | |
| 98 | 0.0862 | 0.08617<$\lambda$<0.0862 | |
| 99 | 0.08625 | 0.0862<$\lambda$<0.08625 | |
| 100 | 0.08741 | 0.08625<$\lambda$<0.08741 | |
| 101 | 0.08764 | 0.08741<$\lambda$<0.08764 | |
| 102 | 0.08776 | 0.08764<$\lambda$<0.08776 | |
| 103 | 0.08825 | 0.08776<$\lambda$<0.08825 | |
| 104 | 0.08839 | 0.08825<$\lambda$<0.08839 | |
| 105 | 0.08846 | 0.08839<$\lambda$<0.08846 | |
| 106 | 0.08847 | 0.08846<$\lambda$<0.08847 | |
| 107 | 0.0886 | 0.08847<$\lambda$<0.0886 | |
| 108 | 0.08861 | 0.0886<$\lambda$<0.08861 | |
| 109 | 0.08868 | 0.08861<$\lambda$<0.08868 | |
| 110 | 0.08873 | 0.08868<$\lambda$<0.08873 | |
| 111 | 0.08875 | 0.08873<$\lambda$<0.08875 | |
| 112 | 0.08923 | 0.08875<$\lambda$<0.08923 | |
| 113 | 0.08948 | 0.08923<$\lambda$<0.08948 | |
| 114 | 0.09084 | 0.08948<$\lambda$<0.09084 | |
| 115 | 0.09279 | 0.09084<$\lambda$<0.09279 | |
| 116 | 0.09322 | 0.09279<$\lambda$<0.09322 | |
| 117 | 0.09427 | 0.09322<$\lambda$<0.09427 | |
| 118 | 0.0959 | 0.09427<$\lambda$<0.0959 | |
| 119 | 1 | 0.0959<$\lambda$<1 |