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 &0.01 &0 &0 &0 &0 &0 &0 &0\\ \hline A2 &0.044 &0 &0.041 &0.044 &0 &0.003 &0.016 &0.013 &0.034 &0.01 &0.034 &0 &0 &0 &0 &0 &0.008 &0 &0.008 &0 &0 &0.023 &0 &0\\ \hline A3 &0.041 &0.031 &0 &0.034 &0.016 &0.021 &0.047 &0 &0.028 &0 &0.036 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.021 &0\\ \hline A4 &0.044 &0.028 &0.018 &0 &0.005 &0 &0.036 &0.016 &0.023 &0.008 &0.034 &0 &0 &0 &0 &0 &0.021 &0.023 &0 &0 &0 &0 &0 &0\\ \hline B1 &0.028 &0.008 &0.01 &0.005 &0 &0.023 &0.008 &0 &0.008 &0 &0.008 &0 &0 &0 &0 &0 &0 &0 &0 &0.018 &0 &0 &0 &0\\ \hline B2 &0.031 &0.003 &0.008 &0 &0.041 &0 &0.031 &0 &0.028 &0.028 &0.016 &0 &0.018 &0 &0.021 &0.016 &0 &0 &0.023 &0.018 &0 &0 &0 &0\\ \hline C1 &0.039 &0.041 &0.041 &0.041 &0 &0.031 &0 &0.028 &0.044 &0.018 &0.044 &0.028 &0.036 &0.031 &0.036 &0.034 &0.031 &0.036 &0.036 &0.026 &0.031 &0.034 &0.041 &0\\ \hline C2 &0.031 &0.047 &0.028 &0.036 &0.003 &0.021 &0.021 &0 &0.049 &0.021 &0.052 &0.034 &0.044 &0.034 &0.041 &0.026 &0.036 &0.031 &0.041 &0.034 &0.039 &0.041 &0.016 &0\\ \hline C3 &0.041 &0.036 &0.036 &0.052 &0.021 &0.044 &0.036 &0.044 &0 &0.039 &0.021 &0.031 &0.021 &0.041 &0.031 &0.023 &0.036 &0.031 &0.052 &0.041 &0.036 &0.018 &0 &0\\ \hline C4 &0.041 &0.031 &0.041 &0.047 &0.021 &0.044 &0.044 &0.044 &0.047 &0 &0.044 &0.034 &0.034 &0.031 &0.034 &0.036 &0.034 &0.034 &0.044 &0.036 &0.034 &0.023 &0 &0\\ \hline C5 &0.049 &0.036 &0.036 &0.044 &0 &0 &0.034 &0.047 &0.041 &0.028 &0 &0.031 &0.023 &0.034 &0.039 &0.021 &0.031 &0.034 &0.028 &0.034 &0.028 &0.039 &0 &0\\ \hline D1 &0.047 &0.047 &0.036 &0.047 &0 &0.036 &0.034 &0.041 &0.047 &0.034 &0.047 &0 &0.049 &0.036 &0.044 &0.034 &0.052 &0.052 &0.044 &0.047 &0.052 &0.034 &0 &0.008\\ \hline D2 &0.031 &0.041 &0.041 &0.044 &0.016 &0.044 &0.031 &0.036 &0.044 &0.044 &0.039 &0.041 &0 &0.041 &0.052 &0.052 &0.036 &0.044 &0.044 &0.049 &0.044 &0.044 &0.036 &0.013\\ \hline D3 &0.023 &0.026 &0.018 &0.028 &0.021 &0.034 &0.028 &0.028 &0.023 &0.034 &0.034 &0.018 &0.031 &0 &0.041 &0.031 &0.023 &0.031 &0.026 &0.028 &0.023 &0.023 &0.008 &0\\ \hline D4 &0.016 &0.028 &0.01 &0.016 &0.026 &0.049 &0.044 &0.021 &0.018 &0.031 &0.023 &0.013 &0.023 &0.021 &0 &0.028 &0.01 &0.028 &0.016 &0.021 &0.018 &0.018 &0 &0\\ \hline D5 &0.016 &0.031 &0.031 &0.031 &0.028 &0.031 &0.031 &0.028 &0.041 &0.031 &0.036 &0.026 &0.041 &0.034 &0.031 &0 &0.034 &0.044 &0.031 &0.039 &0.028 &0.026 &0 &0\\ \hline E1 &0.036 &0.041 &0.044 &0.036 &0.008 &0.028 &0.021 &0.049 &0.052 &0.036 &0.036 &0.052 &0.041 &0.039 &0.036 &0.036 &0 &0.052 &0.041 &0.034 &0.047 &0.041 &0.039 &0.01\\ \hline E2 &0.034 &0.044 &0.052 &0.044 &0.031 &0.047 &0.026 &0.036 &0.044 &0.034 &0.044 &0.041 &0.044 &0.036 &0.041 &0.039 &0.031 &0 &0.044 &0.041 &0.018 &0.031 &0 &0\\ \hline E3 &0.023 &0.028 &0.044 &0.049 &0.041 &0.036 &0.036 &0.018 &0.034 &0.028 &0.021 &0.01 &0.034 &0.026 &0.031 &0.01 &0.018 &0.021 &0 &0.036 &0.018 &0.016 &0 &0\\ \hline E4 &0.016 &0.021 &0.036 &0.021 &0.018 &0.028 &0.026 &0.041 &0.031 &0.036 &0.023 &0.034 &0.041 &0.044 &0.039 &0.041 &0.034 &0.031 &0.044 &0 &0.028 &0.026 &0 &0\\ \hline E5 &0.036 &0.044 &0.036 &0.034 &0.018 &0.023 &0.034 &0.039 &0.041 &0.031 &0.036 &0.041 &0.036 &0.039 &0.034 &0.028 &0.052 &0.047 &0.039 &0.039 &0 &0.039 &0.044 &0.034\\ \hline E6 &0.028 &0.036 &0.036 &0.041 &0.01 &0.041 &0.034 &0.052 &0.039 &0.028 &0.023 &0.044 &0.052 &0.044 &0.041 &0.026 &0.036 &0.047 &0.052 &0.044 &0.039 &0 &0.047 &0.023\\ \hline F1 &0.034 &0.031 &0.039 &0.044 &0.039 &0.047 &0.036 &0.039 &0.036 &0.041 &0.039 &0.034 &0.052 &0.041 &0.041 &0.039 &0.031 &0.049 &0.041 &0.041 &0.041 &0.052 &0 &0.013\\ \hline F2 &0.028 &0.041 &0.041 &0.036 &0.041 &0.044 &0.044 &0.052 &0.044 &0.041 &0.041 &0.052 &0.039 &0.041 &0.039 &0.041 &0.052 &0.052 &0.047 &0.039 &0.039 &0.052 &0.052 &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 &0.002 &0.002 &0.002 &0.002 &0.001 &0.001 &0.006 &0.002 &0.002 &0.001 &0.002 &0.001 &0.001 &0.001 &0.001 &0.001 &0.011 &0.002 &0.002 &0.001 &0.001 &0.001 &0.001 &0\\ \hline A2 &0.063 &0.017 &0.057 &0.062 &0.007 &0.016 &0.033 &0.028 &0.051 &0.022 &0.05 &0.012 &0.013 &0.013 &0.014 &0.011 &0.021 &0.014 &0.022 &0.013 &0.012 &0.034 &0.007 &0.002\\ \hline A3 &0.06 &0.046 &0.016 &0.05 &0.022 &0.032 &0.061 &0.014 &0.045 &0.012 &0.051 &0.01 &0.012 &0.012 &0.013 &0.01 &0.013 &0.013 &0.014 &0.013 &0.011 &0.012 &0.026 &0.001\\ \hline A4 &0.063 &0.045 &0.035 &0.019 &0.012 &0.013 &0.051 &0.03 &0.041 &0.02 &0.05 &0.013 &0.014 &0.013 &0.015 &0.012 &0.034 &0.037 &0.015 &0.014 &0.012 &0.013 &0.006 &0.001\\ \hline B1 &0.035 &0.012 &0.015 &0.01 &0.003 &0.027 &0.013 &0.004 &0.014 &0.004 &0.013 &0.003 &0.004 &0.004 &0.005 &0.004 &0.004 &0.004 &0.005 &0.022 &0.003 &0.004 &0.002 &0\\ \hline B2 &0.05 &0.02 &0.026 &0.02 &0.051 &0.017 &0.048 &0.016 &0.047 &0.042 &0.032 &0.013 &0.033 &0.015 &0.036 &0.029 &0.015 &0.016 &0.04 &0.034 &0.014 &0.013 &0.006 &0.002\\ \hline C1 &0.096 &0.095 &0.095 &0.1 &0.029 &0.079 &0.053 &0.077 &0.102 &0.063 &0.097 &0.068 &0.083 &0.075 &0.085 &0.073 &0.075 &0.085 &0.087 &0.074 &0.071 &0.074 &0.06 &0.007\\ \hline C2 &0.089 &0.101 &0.084 &0.096 &0.031 &0.069 &0.074 &0.051 &0.108 &0.066 &0.105 &0.074 &0.091 &0.079 &0.091 &0.067 &0.081 &0.081 &0.093 &0.082 &0.08 &0.083 &0.036 &0.008\\ \hline C3 &0.096 &0.087 &0.087 &0.105 &0.047 &0.088 &0.085 &0.088 &0.057 &0.079 &0.073 &0.067 &0.065 &0.081 &0.077 &0.061 &0.077 &0.076 &0.098 &0.085 &0.073 &0.056 &0.019 &0.006\\ \hline C4 &0.101 &0.086 &0.096 &0.105 &0.049 &0.092 &0.097 &0.092 &0.106 &0.045 &0.099 &0.073 &0.081 &0.076 &0.083 &0.076 &0.079 &0.083 &0.095 &0.084 &0.074 &0.064 &0.021 &0.007\\ \hline C5 &0.1 &0.085 &0.084 &0.096 &0.024 &0.044 &0.08 &0.09 &0.093 &0.067 &0.049 &0.067 &0.065 &0.073 &0.082 &0.057 &0.071 &0.077 &0.074 &0.075 &0.065 &0.074 &0.019 &0.006\\ \hline D1 &0.114 &0.11 &0.101 &0.115 &0.034 &0.093 &0.095 &0.099 &0.116 &0.086 &0.11 &0.049 &0.104 &0.089 &0.102 &0.082 &0.104 &0.109 &0.104 &0.103 &0.099 &0.082 &0.025 &0.016\\ \hline D2 &0.103 &0.108 &0.109 &0.116 &0.052 &0.105 &0.097 &0.098 &0.118 &0.099 &0.106 &0.091 &0.061 &0.097 &0.113 &0.102 &0.092 &0.105 &0.108 &0.109 &0.094 &0.095 &0.06 &0.022\\ \hline D3 &0.069 &0.068 &0.061 &0.074 &0.043 &0.072 &0.07 &0.067 &0.07 &0.068 &0.076 &0.05 &0.068 &0.036 &0.08 &0.063 &0.058 &0.069 &0.066 &0.066 &0.055 &0.055 &0.023 &0.005\\ \hline D4 &0.053 &0.062 &0.045 &0.052 &0.044 &0.079 &0.076 &0.051 &0.056 &0.058 &0.058 &0.038 &0.053 &0.048 &0.032 &0.054 &0.039 &0.058 &0.048 &0.051 &0.043 &0.044 &0.013 &0.004\\ \hline D5 &0.069 &0.081 &0.081 &0.085 &0.054 &0.076 &0.079 &0.073 &0.095 &0.071 &0.086 &0.063 &0.084 &0.074 &0.076 &0.038 &0.074 &0.088 &0.078 &0.083 &0.066 &0.063 &0.019 &0.006\\ \hline E1 &0.106 &0.107 &0.109 &0.107 &0.042 &0.088 &0.085 &0.108 &0.122 &0.09 &0.102 &0.1 &0.099 &0.093 &0.096 &0.085 &0.056 &0.111 &0.104 &0.092 &0.096 &0.091 &0.062 &0.019\\ \hline E2 &0.094 &0.099 &0.106 &0.104 &0.06 &0.096 &0.081 &0.085 &0.105 &0.079 &0.099 &0.081 &0.091 &0.081 &0.091 &0.079 &0.076 &0.05 &0.095 &0.09 &0.06 &0.072 &0.02 &0.007\\ \hline E3 &0.066 &0.066 &0.081 &0.089 &0.061 &0.07 &0.074 &0.052 &0.075 &0.059 &0.059 &0.038 &0.065 &0.056 &0.064 &0.039 &0.049 &0.054 &0.036 &0.069 &0.046 &0.043 &0.014 &0.004\\ \hline E4 &0.069 &0.071 &0.086 &0.075 &0.044 &0.074 &0.074 &0.086 &0.086 &0.077 &0.074 &0.07 &0.085 &0.085 &0.085 &0.079 &0.074 &0.076 &0.091 &0.046 &0.066 &0.063 &0.019 &0.006\\ \hline E5 &0.105 &0.108 &0.102 &0.104 &0.052 &0.082 &0.096 &0.098 &0.112 &0.084 &0.101 &0.09 &0.094 &0.093 &0.093 &0.078 &0.105 &0.106 &0.101 &0.097 &0.051 &0.089 &0.068 &0.041\\ \hline E6 &0.098 &0.102 &0.102 &0.112 &0.046 &0.101 &0.098 &0.111 &0.111 &0.084 &0.091 &0.093 &0.11 &0.099 &0.102 &0.077 &0.091 &0.107 &0.114 &0.103 &0.089 &0.052 &0.071 &0.032\\ \hline F1 &0.104 &0.097 &0.105 &0.115 &0.074 &0.106 &0.101 &0.099 &0.109 &0.095 &0.105 &0.083 &0.11 &0.096 &0.102 &0.089 &0.086 &0.109 &0.104 &0.101 &0.091 &0.101 &0.026 &0.022\\ \hline F2 &0.109 &0.117 &0.117 &0.118 &0.081 &0.113 &0.117 &0.12 &0.127 &0.103 &0.117 &0.108 &0.107 &0.104 &0.109 &0.099 &0.114 &0.121 &0.119 &0.107 &0.097 &0.11 &0.08 &0.01\\ \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

$$\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{24 \times4}} &Di &Ci &Mi &Ri\\ \hline A1 &0.047 &1.915 &1.963 &-1.868\\ \hline A2 &0.592 &1.793 &2.386 &-1.201\\ \hline A3 &0.569 &1.801 &2.371 &-1.232\\ \hline A4 &0.579 &1.933 &2.512 &-1.354\\ \hline B1 &0.216 &0.962 &1.179 &-0.746\\ \hline B2 &0.634 &1.634 &2.268 &-0.999\\ \hline C1 &1.804 &1.742 &3.546 &0.061\\ \hline C2 &1.82 &1.638 &3.458 &0.181\\ \hline C3 &1.732 &1.969 &3.701 &-0.237\\ \hline C4 &1.864 &1.475 &3.339 &0.389\\ \hline C5 &1.617 &1.804 &3.422 &-0.187\\ \hline D1 &2.143 &1.358 &3.501 &0.785\\ \hline D2 &2.261 &1.593 &3.854 &0.668\\ \hline D3 &1.432 &1.494 &2.925 &-0.062\\ \hline D4 &1.161 &1.647 &2.808 &-0.486\\ \hline D5 &1.662 &1.362 &3.025 &0.3\\ \hline E1 &2.169 &1.499 &3.668 &0.67\\ \hline E2 &1.9 &1.65 &3.55 &0.25\\ \hline E3 &1.328 &1.711 &3.039 &-0.383\\ \hline E4 &1.661 &1.614 &3.275 &0.047\\ \hline E5 &2.15 &1.368 &3.518 &0.781\\ \hline E6 &2.196 &1.388 &3.584 &0.807\\ \hline F1 &2.228 &0.703 &2.931 &1.525\\ \hline F2 &2.524 &0.235 &2.759 &2.289\\ \hline \end{array} $$

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

$$D=\begin{array}{c|c|c|c|c|c|c}{M_{24 \times2}} &|M| &|R|\\ \hline A1 &1.9625747090387 &1.8678447501632\\ \hline A2 &2.3856243738264 &1.2013393297237\\ \hline A3 &2.3705127591425 &1.2318827887094\\ \hline A4 &2.5121725866773 &1.3538044793968\\ \hline B1 &1.1785283147235 &0.74571773758684\\ \hline B2 &2.2682809513662 &0.99934279439943\\ \hline C1 &3.5462416831391 &0.061385326038733\\ \hline C2 &3.4576517176006 &0.18148018332047\\ \hline C3 &3.7010869223493 &0.23695942821396\\ \hline C4 &3.3390334730408 &0.38854646492654\\ \hline C5 &3.4216315435616 &0.18676584032064\\ \hline D1 &3.5011735599517 &0.78479281542866\\ \hline D2 &3.8537589064482 &0.66822845736576\\ \hline D3 &2.9254701267158 &0.061693408262705\\ \hline D4 &2.8076051973743 &0.4858724671659\\ \hline D5 &3.0246053126472 &0.30004575303481\\ \hline E1 &3.6678965491371 &0.66973187322921\\ \hline E2 &3.5500977707107 &0.25028217773693\\ \hline E3 &3.0394026085126 &0.38322151693477\\ \hline E4 &3.2753069277425 &0.047331741967238\\ \hline E5 &3.517863848436 &0.78141946117091\\ \hline E6 &3.5842006959921 &0.8073485588031\\ \hline F1 &2.931027359406 &1.5251264149825\\ \hline F2 &2.7593576103448 &2.2887253128724\\ \hline \end{array} $$

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 &0.0016 &0.0016 &0.0016 &0.0006 &0.0013 &0.0063 &0.0015 &0.0018 &0.0013 &0.0016 &0.0014 &0.0015 &0.0014 &0.0014 &0.0013 &0.0113 &0.0016 &0.0015 &0.0013 &0.0014 &0.0013 &0.001 &0.0002\\ \hline A2 &0.0634 &1 &0.057 &0.0619 &0.0072 &0.0157 &0.0326 &0.0276 &0.0508 &0.0222 &0.0495 &0.0116 &0.0128 &0.0128 &0.0137 &0.0106 &0.0213 &0.0144 &0.0223 &0.0134 &0.0118 &0.034 &0.0065 &0.0018\\ \hline A3 &0.0602 &0.0458 &1 &0.0504 &0.0224 &0.0325 &0.0607 &0.0137 &0.0448 &0.0119 &0.051 &0.0104 &0.012 &0.0118 &0.013 &0.0105 &0.0127 &0.0133 &0.0138 &0.0127 &0.0108 &0.0117 &0.0259 &0.0013\\ \hline A4 &0.0629 &0.045 &0.0353 &1 &0.0119 &0.0135 &0.0508 &0.0303 &0.0414 &0.0201 &0.0499 &0.0126 &0.0136 &0.0134 &0.0145 &0.0118 &0.0338 &0.0369 &0.0154 &0.0139 &0.0123 &0.0131 &0.0064 &0.0014\\ \hline B1 &0.0347 &0.0125 &0.0154 &0.0105 &1 &0.0273 &0.0133 &0.0045 &0.0135 &0.0044 &0.0128 &0.0035 &0.0043 &0.004 &0.0046 &0.0039 &0.0042 &0.0041 &0.005 &0.0219 &0.0035 &0.0035 &0.0016 &0.0003\\ \hline B2 &0.0502 &0.0201 &0.0258 &0.0196 &0.0507 &1 &0.0481 &0.0161 &0.047 &0.0423 &0.0325 &0.0131 &0.0328 &0.015 &0.0365 &0.0288 &0.0147 &0.0158 &0.0397 &0.0343 &0.0136 &0.013 &0.0059 &0.0015\\ \hline C1 &0.0964 &0.0948 &0.0949 &0.0997 &0.0289 &0.0788 &1 &0.0772 &0.1022 &0.0627 &0.0972 &0.0681 &0.0829 &0.0753 &0.0849 &0.0733 &0.0752 &0.0848 &0.0866 &0.0736 &0.0713 &0.0744 &0.0603 &0.0073\\ \hline C2 &0.0895 &0.1008 &0.0836 &0.0959 &0.0308 &0.0695 &0.074 &1 &0.108 &0.0661 &0.1049 &0.0743 &0.091 &0.079 &0.091 &0.0668 &0.0813 &0.081 &0.0928 &0.0822 &0.0798 &0.0825 &0.036 &0.0077\\ \hline C3 &0.096 &0.0865 &0.0866 &0.1053 &0.0472 &0.0882 &0.0854 &0.088 &1 &0.079 &0.0725 &0.0674 &0.0651 &0.0814 &0.0766 &0.0607 &0.0772 &0.0759 &0.0979 &0.085 &0.0729 &0.0558 &0.0188 &0.0062\\ \hline C4 &0.1006 &0.0862 &0.0958 &0.1053 &0.0488 &0.0918 &0.0968 &0.0923 &0.1063 &1 &0.0985 &0.0735 &0.081 &0.0757 &0.0833 &0.0763 &0.0786 &0.0826 &0.0949 &0.0844 &0.0742 &0.0643 &0.0206 &0.0067\\ \hline C5 &0.1 &0.0849 &0.0842 &0.096 &0.0238 &0.0437 &0.0798 &0.0896 &0.0935 &0.0668 &1 &0.0668 &0.0655 &0.0732 &0.0819 &0.0565 &0.0712 &0.0772 &0.0738 &0.0754 &0.0648 &0.0745 &0.0188 &0.0063\\ \hline D1 &0.1144 &0.1104 &0.1007 &0.1153 &0.0336 &0.0927 &0.0954 &0.0994 &0.1165 &0.086 &0.1101 &1 &0.1042 &0.0892 &0.1021 &0.0817 &0.104 &0.109 &0.1043 &0.1026 &0.0988 &0.0822 &0.0251 &0.0162\\ \hline D2 &0.1029 &0.1085 &0.1087 &0.1165 &0.0521 &0.1048 &0.0973 &0.0976 &0.1177 &0.0991 &0.1064 &0.0914 &1 &0.0971 &0.1128 &0.1017 &0.0921 &0.1053 &0.1079 &0.1088 &0.0944 &0.0947 &0.0603 &0.0216\\ \hline D3 &0.0688 &0.0682 &0.0609 &0.0739 &0.043 &0.0717 &0.0697 &0.0666 &0.0702 &0.0681 &0.0759 &0.0499 &0.0681 &1 &0.0797 &0.0629 &0.0581 &0.0692 &0.0661 &0.0663 &0.0551 &0.0553 &0.0232 &0.0053\\ \hline D4 &0.0528 &0.0619 &0.0451 &0.0523 &0.0438 &0.0791 &0.0761 &0.051 &0.0563 &0.0585 &0.0577 &0.0383 &0.0532 &0.0484 &1 &0.054 &0.0385 &0.0583 &0.0484 &0.0513 &0.0433 &0.0437 &0.0128 &0.004\\ \hline D5 &0.0693 &0.0807 &0.081 &0.0847 &0.0538 &0.0757 &0.0788 &0.0734 &0.0954 &0.0715 &0.0856 &0.063 &0.0839 &0.0744 &0.0765 &1 &0.0741 &0.0878 &0.0782 &0.0827 &0.0656 &0.0631 &0.0187 &0.0063\\ \hline E1 &0.1056 &0.1068 &0.1091 &0.1074 &0.0424 &0.0876 &0.0846 &0.1079 &0.1225 &0.0896 &0.1019 &0.0998 &0.099 &0.093 &0.0962 &0.0851 &1 &0.1106 &0.1035 &0.0924 &0.0957 &0.0911 &0.0622 &0.0191\\ \hline E2 &0.0942 &0.099 &0.1064 &0.1038 &0.0596 &0.0956 &0.0809 &0.0855 &0.1046 &0.0786 &0.0993 &0.0808 &0.091 &0.0808 &0.0911 &0.0792 &0.0761 &1 &0.0953 &0.09 &0.0599 &0.0718 &0.0201 &0.0065\\ \hline E3 &0.066 &0.0664 &0.0813 &0.0892 &0.0607 &0.0701 &0.0738 &0.0517 &0.075 &0.0586 &0.0595 &0.0378 &0.0648 &0.0558 &0.0644 &0.0388 &0.0487 &0.0539 &1 &0.0685 &0.0455 &0.0431 &0.0145 &0.0044\\ \hline E4 &0.0686 &0.0712 &0.0857 &0.0751 &0.0444 &0.0741 &0.0744 &0.0856 &0.0859 &0.0767 &0.0739 &0.0704 &0.085 &0.0846 &0.0846 &0.0785 &0.0744 &0.0763 &0.0907 &1 &0.0664 &0.0634 &0.019 &0.0064\\ \hline E5 &0.1048 &0.1084 &0.1015 &0.104 &0.0522 &0.0823 &0.0958 &0.0981 &0.1121 &0.0844 &0.1012 &0.0903 &0.0938 &0.0927 &0.0932 &0.0778 &0.1048 &0.1056 &0.1005 &0.0965 &1 &0.089 &0.0684 &0.0414\\ \hline E6 &0.0984 &0.1023 &0.1024 &0.1125 &0.0465 &0.1013 &0.0976 &0.1107 &0.1111 &0.0835 &0.0906 &0.0931 &0.1099 &0.0986 &0.1023 &0.0768 &0.0911 &0.1066 &0.1142 &0.1029 &0.089 &1 &0.0708 &0.0315\\ \hline F1 &0.1043 &0.0973 &0.1049 &0.1148 &0.0736 &0.1064 &0.1005 &0.0986 &0.1088 &0.0953 &0.105 &0.0833 &0.1095 &0.0959 &0.1021 &0.0887 &0.086 &0.1088 &0.1042 &0.1008 &0.0909 &0.101 &1 &0.0217\\ \hline F2 &0.1094 &0.117 &0.1174 &0.1182 &0.081 &0.1127 &0.1166 &0.1202 &0.1271 &0.1033 &0.1174 &0.1083 &0.1067 &0.1044 &0.1086 &0.0985 &0.1139 &0.1207 &0.1188 &0.1072 &0.0968 &0.1096 &0.08 &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}$
$$FR=\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 &0.0113 &0.0113 &0.0113 &0.0113 &0.0113 &0.0113 &0.0113 &0.0113 &0.0113 &0.0113 &0.0113 &0.0113 &0.0113 &0.0113 &0.0113 &0.0113 &0.0113 &0.0113 &0.0113 &0.0113 &0.0113 &0.0113 &0.0113\\ \hline A2 &0.0634 &1 &0.057 &0.0619 &0.057 &0.057 &0.057 &0.057 &0.057 &0.057 &0.057 &0.057 &0.057 &0.057 &0.057 &0.057 &0.057 &0.057 &0.057 &0.057 &0.057 &0.057 &0.057 &0.0414\\ \hline A3 &0.0607 &0.0607 &1 &0.0607 &0.0607 &0.0607 &0.0607 &0.0607 &0.0607 &0.0607 &0.0607 &0.0607 &0.0607 &0.0607 &0.0607 &0.0607 &0.0607 &0.0607 &0.0607 &0.0607 &0.0607 &0.0607 &0.0607 &0.0414\\ \hline A4 &0.0629 &0.0508 &0.0508 &1 &0.0508 &0.0508 &0.0508 &0.0508 &0.0508 &0.0508 &0.0508 &0.0508 &0.0508 &0.0508 &0.0508 &0.0508 &0.0508 &0.0508 &0.0508 &0.0508 &0.0508 &0.0508 &0.0508 &0.0414\\ \hline B1 &0.0347 &0.0273 &0.0273 &0.0273 &1 &0.0273 &0.0273 &0.0273 &0.0273 &0.0273 &0.0273 &0.0273 &0.0273 &0.0273 &0.0273 &0.0273 &0.0273 &0.0273 &0.0273 &0.0273 &0.0273 &0.0273 &0.0273 &0.0273\\ \hline B2 &0.0502 &0.0481 &0.0481 &0.0481 &0.0507 &1 &0.0481 &0.0481 &0.0481 &0.0481 &0.0481 &0.0481 &0.0481 &0.0481 &0.0481 &0.0481 &0.0481 &0.0481 &0.0481 &0.0481 &0.0481 &0.0481 &0.0481 &0.0414\\ \hline C1 &0.0972 &0.0948 &0.0949 &0.1022 &0.0708 &0.0896 &1 &0.0896 &0.1022 &0.0896 &0.0972 &0.0896 &0.0896 &0.0896 &0.0896 &0.0896 &0.0896 &0.0896 &0.0979 &0.0896 &0.0896 &0.0896 &0.0708 &0.0414\\ \hline C2 &0.1 &0.1008 &0.091 &0.1053 &0.0708 &0.091 &0.091 &1 &0.108 &0.091 &0.1049 &0.091 &0.091 &0.091 &0.091 &0.091 &0.091 &0.091 &0.0979 &0.091 &0.091 &0.091 &0.0708 &0.0414\\ \hline C3 &0.096 &0.088 &0.088 &0.1053 &0.0708 &0.0882 &0.088 &0.088 &1 &0.088 &0.088 &0.088 &0.088 &0.088 &0.088 &0.088 &0.088 &0.088 &0.0979 &0.088 &0.088 &0.088 &0.0708 &0.0414\\ \hline C4 &0.1006 &0.0948 &0.0958 &0.1053 &0.0708 &0.0918 &0.0968 &0.0923 &0.1063 &1 &0.0985 &0.091 &0.091 &0.091 &0.091 &0.091 &0.091 &0.091 &0.0979 &0.091 &0.091 &0.091 &0.0708 &0.0414\\ \hline C5 &0.1 &0.0896 &0.0896 &0.096 &0.0708 &0.0896 &0.0896 &0.0896 &0.0935 &0.0896 &1 &0.0896 &0.0896 &0.0896 &0.0896 &0.0896 &0.0896 &0.0896 &0.0935 &0.0896 &0.0896 &0.0896 &0.0708 &0.0414\\ \hline D1 &0.1144 &0.1104 &0.1064 &0.1153 &0.0708 &0.1042 &0.0973 &0.104 &0.1165 &0.0991 &0.1101 &1 &0.1042 &0.0971 &0.1042 &0.1017 &0.104 &0.109 &0.1043 &0.1042 &0.0988 &0.0947 &0.0708 &0.0414\\ \hline D2 &0.1029 &0.1085 &0.1087 &0.1165 &0.0708 &0.1048 &0.0973 &0.0976 &0.1177 &0.0991 &0.1064 &0.0944 &1 &0.0971 &0.1128 &0.1017 &0.0944 &0.1053 &0.1079 &0.1088 &0.0944 &0.0947 &0.0708 &0.0414\\ \hline D3 &0.0761 &0.0761 &0.0761 &0.0761 &0.0708 &0.0791 &0.0761 &0.0761 &0.0761 &0.0761 &0.0761 &0.0761 &0.0761 &1 &0.0797 &0.0761 &0.0761 &0.0761 &0.0761 &0.0761 &0.0761 &0.0761 &0.0708 &0.0414\\ \hline D4 &0.0761 &0.0761 &0.0761 &0.0761 &0.0708 &0.0791 &0.0761 &0.0761 &0.0761 &0.0761 &0.0761 &0.0761 &0.0761 &0.0761 &1 &0.0761 &0.0761 &0.0761 &0.0761 &0.0761 &0.0761 &0.0761 &0.0708 &0.0414\\ \hline D5 &0.0954 &0.088 &0.088 &0.0954 &0.0708 &0.0882 &0.088 &0.088 &0.0954 &0.088 &0.088 &0.088 &0.088 &0.088 &0.088 &1 &0.088 &0.088 &0.0954 &0.088 &0.088 &0.088 &0.0708 &0.0414\\ \hline E1 &0.1056 &0.1068 &0.1091 &0.1074 &0.0708 &0.0998 &0.0973 &0.1079 &0.1225 &0.0991 &0.1049 &0.0998 &0.0998 &0.0971 &0.0998 &0.0998 &1 &0.1106 &0.1035 &0.0998 &0.0988 &0.0947 &0.0708 &0.0414\\ \hline E2 &0.0993 &0.099 &0.1064 &0.1046 &0.0708 &0.0956 &0.091 &0.091 &0.1046 &0.091 &0.0993 &0.091 &0.091 &0.091 &0.0911 &0.091 &0.091 &1 &0.0979 &0.091 &0.091 &0.091 &0.0708 &0.0414\\ \hline E3 &0.075 &0.075 &0.0813 &0.0892 &0.0708 &0.075 &0.075 &0.075 &0.075 &0.075 &0.075 &0.075 &0.075 &0.075 &0.075 &0.075 &0.075 &0.075 &1 &0.075 &0.075 &0.075 &0.0708 &0.0414\\ \hline E4 &0.0859 &0.0859 &0.0859 &0.0892 &0.0708 &0.0859 &0.0859 &0.0859 &0.0859 &0.0859 &0.0859 &0.0859 &0.0859 &0.0859 &0.0859 &0.0859 &0.0859 &0.0859 &0.0907 &1 &0.0859 &0.0859 &0.0708 &0.0414\\ \hline E5 &0.1048 &0.1084 &0.1056 &0.1053 &0.0708 &0.0998 &0.0973 &0.1048 &0.1121 &0.0991 &0.1048 &0.0998 &0.0998 &0.0971 &0.0998 &0.0998 &0.1048 &0.1056 &0.1035 &0.0998 &1 &0.0947 &0.0708 &0.0414\\ \hline E6 &0.1029 &0.1085 &0.1087 &0.1125 &0.0708 &0.1048 &0.0976 &0.1107 &0.1111 &0.0991 &0.1064 &0.0944 &0.1099 &0.0986 &0.1099 &0.1017 &0.0944 &0.1066 &0.1142 &0.1088 &0.0944 &1 &0.0708 &0.0414\\ \hline F1 &0.1043 &0.1085 &0.1087 &0.1148 &0.0736 &0.1064 &0.1005 &0.101 &0.1095 &0.0991 &0.1064 &0.0944 &0.1095 &0.0986 &0.1095 &0.1017 &0.0944 &0.1088 &0.1079 &0.1088 &0.0944 &0.101 &1 &0.0414\\ \hline F2 &0.1094 &0.117 &0.1174 &0.1182 &0.081 &0.1127 &0.1166 &0.1202 &0.1271 &0.1033 &0.1174 &0.1083 &0.1096 &0.1044 &0.1096 &0.1017 &0.1139 &0.1207 &0.1188 &0.1088 &0.0988 &0.1096 &0.08 &1\\ \hline \end{array} $$

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

$$\begin{array}{c|c|c|c|c|c|c}{M_{24 \times2}} &R集合之和=D &Q集合之和=C\\ \hline A1 &1.26058702913 &3.01779826729\\ \hline A2 &2.30617068146 &2.93419279451\\ \hline A3 &2.37709181642 &2.93223331286\\ \hline A4 &2.17094922913 &3.04390693938\\ \hline B1 &1.63461042862 &2.51793161767\\ \hline B2 &2.10452572521 &2.89266973411\\ \hline C1 &3.03401076343 &2.81635467435\\ \hline C2 &3.07324840951 &2.85292041899\\ \hline C3 &2.97829336229 &2.99460923263\\ \hline C4 &3.07260572416 &2.80333520114\\ \hline C5 &2.99950556163 &2.90067342001\\ \hline D1 &3.28304690858 &2.78756468685\\ \hline D2 &3.25408016322 &2.82918900995\\ \hline D3 &2.71096849859 &2.81041766438\\ \hline D4 &2.70730248793 &2.86978223025\\ \hline D5 &2.97260327548 &2.81657023638\\ \hline E1 &3.24711257834 &2.80234719097\\ \hline E2 &3.08150322989 &2.87187469095\\ \hline E3 &2.70301543292 &2.93623654932\\ \hline E4 &2.9097936611 &2.84955953863\\ \hline E5 &3.22978456423 &2.77602339109\\ \hline E6 &3.27817944124 &2.78568965532\\ \hline F1 &3.303323732 &2.46791497453\\ \hline F2 &3.52445960797 &1.9069768809\\ \hline \end{array} $$

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。

131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 131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 $数值区段 TAISM运算过程
10.011330<$\lambda$<0.01133
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