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 &0.006 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.013 &0 &0 &0 &0 &0 &0 &0\\ \hline A2 &0.055 &0 &0.052 &0.055 &0 &0.003 &0.019 &0.016 &0.042 &0.013 &0.042 &0 &0 &0 &0 &0 &0.01 &0 &0.01 &0 &0 &0.029 &0 &0\\ \hline A3 &0.052 &0.039 &0 &0.042 &0.019 &0.026 &0.058 &0 &0.036 &0 &0.045 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.026 &0\\ \hline A4 &0.055 &0.036 &0.023 &0 &0.006 &0 &0.045 &0.019 &0.029 &0.01 &0.042 &0 &0 &0 &0 &0 &0.026 &0.029 &0 &0 &0 &0 &0 &0\\ \hline B1 &0.036 &0.01 &0.013 &0.006 &0 &0.029 &0.01 &0 &0.01 &0 &0.01 &0 &0 &0 &0 &0 &0 &0 &0 &0.023 &0 &0 &0 &0\\ \hline B2 &0.039 &0.003 &0.01 &0 &0.052 &0 &0.039 &0 &0.036 &0.036 &0.019 &0 &0.023 &0 &0.026 &0.019 &0 &0 &0.029 &0.023 &0 &0 &0 &0\\ \hline C1 &0.049 &0.052 &0.052 &0.052 &0 &0.039 &0 &0.036 &0.055 &0.023 &0.055 &0.036 &0.045 &0.039 &0.045 &0.042 &0.039 &0.045 &0.045 &0.032 &0.039 &0.042 &0.052 &0\\ \hline C2 &0.039 &0.058 &0.036 &0.045 &0.003 &0.026 &0.026 &0 &0.062 &0.026 &0.065 &0.042 &0.055 &0.042 &0.052 &0.032 &0.045 &0.039 &0.052 &0.042 &0.049 &0.052 &0.019 &0\\ \hline C3 &0.052 &0.045 &0.045 &0.065 &0.026 &0.055 &0.045 &0.055 &0 &0.049 &0.026 &0.039 &0.026 &0.052 &0.039 &0.029 &0.045 &0.039 &0.065 &0.052 &0.045 &0.023 &0 &0\\ \hline C4 &0.052 &0.039 &0.052 &0.058 &0.026 &0.055 &0.055 &0.055 &0.058 &0 &0.055 &0.042 &0.042 &0.039 &0.042 &0.045 &0.042 &0.042 &0.055 &0.045 &0.042 &0.029 &0 &0\\ \hline C5 &0.062 &0.045 &0.045 &0.055 &0 &0 &0.042 &0.058 &0.052 &0.036 &0 &0.039 &0.029 &0.042 &0.049 &0.026 &0.039 &0.042 &0.036 &0.042 &0.036 &0.049 &0 &0\\ \hline D1 &0.058 &0.058 &0.045 &0.058 &0 &0.045 &0.042 &0.052 &0.058 &0.042 &0.058 &0 &0.062 &0.045 &0.055 &0.042 &0.065 &0.065 &0.055 &0.058 &0.065 &0.042 &0 &0.01\\ \hline D2 &0.039 &0.052 &0.052 &0.055 &0.019 &0.055 &0.039 &0.045 &0.055 &0.055 &0.049 &0.052 &0 &0.052 &0.065 &0.065 &0.045 &0.055 &0.055 &0.062 &0.055 &0.055 &0.045 &0.016\\ \hline D3 &0.029 &0.032 &0.023 &0.036 &0.026 &0.042 &0.036 &0.036 &0.029 &0.042 &0.042 &0.023 &0.039 &0 &0.052 &0.039 &0.029 &0.039 &0.032 &0.036 &0.029 &0.029 &0.01 &0\\ \hline D4 &0.019 &0.036 &0.013 &0.019 &0.032 &0.062 &0.055 &0.026 &0.023 &0.039 &0.029 &0.016 &0.029 &0.026 &0 &0.036 &0.013 &0.036 &0.019 &0.026 &0.023 &0.023 &0 &0\\ \hline D5 &0.019 &0.039 &0.039 &0.039 &0.036 &0.039 &0.039 &0.036 &0.052 &0.039 &0.045 &0.032 &0.052 &0.042 &0.039 &0 &0.042 &0.055 &0.039 &0.049 &0.036 &0.032 &0 &0\\ \hline E1 &0.045 &0.052 &0.055 &0.045 &0.01 &0.036 &0.026 &0.062 &0.065 &0.045 &0.045 &0.065 &0.052 &0.049 &0.045 &0.045 &0 &0.065 &0.052 &0.042 &0.058 &0.052 &0.049 &0.013\\ \hline E2 &0.042 &0.055 &0.065 &0.055 &0.039 &0.058 &0.032 &0.045 &0.055 &0.042 &0.055 &0.052 &0.055 &0.045 &0.052 &0.049 &0.039 &0 &0.055 &0.052 &0.023 &0.039 &0 &0\\ \hline E3 &0.029 &0.036 &0.055 &0.062 &0.052 &0.045 &0.045 &0.023 &0.042 &0.036 &0.026 &0.013 &0.042 &0.032 &0.039 &0.013 &0.023 &0.026 &0 &0.045 &0.023 &0.019 &0 &0\\ \hline E4 &0.019 &0.026 &0.045 &0.026 &0.023 &0.036 &0.032 &0.052 &0.039 &0.045 &0.029 &0.042 &0.052 &0.055 &0.049 &0.052 &0.042 &0.039 &0.055 &0 &0.036 &0.032 &0 &0\\ \hline E5 &0.045 &0.055 &0.045 &0.042 &0.023 &0.029 &0.042 &0.049 &0.052 &0.039 &0.045 &0.052 &0.045 &0.049 &0.042 &0.036 &0.065 &0.058 &0.049 &0.049 &0 &0.049 &0.055 &0.042\\ \hline E6 &0.036 &0.045 &0.045 &0.052 &0.013 &0.052 &0.042 &0.065 &0.049 &0.036 &0.029 &0.055 &0.065 &0.055 &0.052 &0.032 &0.045 &0.058 &0.065 &0.055 &0.049 &0 &0.058 &0.029\\ \hline F1 &0.042 &0.039 &0.049 &0.055 &0.049 &0.058 &0.045 &0.049 &0.045 &0.052 &0.049 &0.042 &0.065 &0.052 &0.052 &0.049 &0.039 &0.062 &0.052 &0.052 &0.052 &0.065 &0 &0.016\\ \hline F2 &0.036 &0.052 &0.052 &0.045 &0.052 &0.055 &0.055 &0.065 &0.055 &0.052 &0.052 &0.065 &0.049 &0.052 &0.049 &0.052 &0.065 &0.065 &0.058 &0.049 &0.049 &0.065 &0.065 &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 &0.004 &0.004 &0.004 &0.004 &0.002 &0.003 &0.01 &0.004 &0.004 &0.003 &0.004 &0.003 &0.004 &0.003 &0.004 &0.003 &0.016 &0.004 &0.004 &0.003 &0.003 &0.003 &0.002 &0.001\\ \hline A2 &0.101 &0.041 &0.09 &0.098 &0.019 &0.036 &0.06 &0.052 &0.084 &0.043 &0.081 &0.029 &0.032 &0.032 &0.034 &0.027 &0.042 &0.035 &0.046 &0.033 &0.029 &0.057 &0.015 &0.004\\ \hline A3 &0.096 &0.075 &0.038 &0.083 &0.037 &0.056 &0.093 &0.033 &0.075 &0.029 &0.082 &0.026 &0.03 &0.029 &0.032 &0.026 &0.031 &0.033 &0.034 &0.031 &0.027 &0.028 &0.039 &0.004\\ \hline A4 &0.1 &0.076 &0.064 &0.045 &0.024 &0.034 &0.082 &0.056 &0.073 &0.041 &0.082 &0.03 &0.034 &0.033 &0.036 &0.029 &0.058 &0.063 &0.038 &0.035 &0.03 &0.031 &0.015 &0.004\\ \hline B1 &0.05 &0.022 &0.025 &0.02 &0.007 &0.039 &0.023 &0.011 &0.024 &0.011 &0.022 &0.009 &0.011 &0.01 &0.011 &0.009 &0.01 &0.01 &0.012 &0.033 &0.009 &0.009 &0.004 &0.001\\ \hline B2 &0.086 &0.046 &0.054 &0.048 &0.075 &0.041 &0.081 &0.039 &0.082 &0.07 &0.062 &0.032 &0.059 &0.036 &0.065 &0.052 &0.036 &0.039 &0.07 &0.062 &0.033 &0.032 &0.015 &0.004\\ \hline C1 &0.191 &0.184 &0.184 &0.195 &0.07 &0.157 &0.13 &0.155 &0.199 &0.132 &0.187 &0.133 &0.16 &0.148 &0.165 &0.14 &0.148 &0.165 &0.17 &0.15 &0.138 &0.142 &0.099 &0.017\\ \hline C2 &0.184 &0.192 &0.171 &0.192 &0.073 &0.146 &0.157 &0.124 &0.208 &0.137 &0.197 &0.142 &0.171 &0.154 &0.174 &0.133 &0.157 &0.161 &0.179 &0.162 &0.15 &0.153 &0.07 &0.018\\ \hline C3 &0.186 &0.169 &0.169 &0.197 &0.091 &0.164 &0.166 &0.164 &0.138 &0.148 &0.152 &0.129 &0.134 &0.151 &0.151 &0.121 &0.146 &0.149 &0.179 &0.16 &0.136 &0.115 &0.046 &0.015\\ \hline C4 &0.197 &0.174 &0.186 &0.203 &0.095 &0.174 &0.185 &0.175 &0.205 &0.11 &0.189 &0.141 &0.159 &0.149 &0.164 &0.144 &0.153 &0.163 &0.181 &0.164 &0.142 &0.13 &0.05 &0.017\\ \hline C5 &0.188 &0.165 &0.164 &0.183 &0.06 &0.107 &0.156 &0.165 &0.181 &0.131 &0.121 &0.127 &0.133 &0.139 &0.155 &0.114 &0.137 &0.149 &0.147 &0.146 &0.125 &0.137 &0.046 &0.015\\ \hline D1 &0.227 &0.216 &0.204 &0.228 &0.082 &0.185 &0.195 &0.194 &0.231 &0.171 &0.215 &0.12 &0.198 &0.175 &0.198 &0.16 &0.194 &0.206 &0.204 &0.197 &0.182 &0.162 &0.061 &0.03\\ \hline D2 &0.217 &0.218 &0.218 &0.234 &0.108 &0.205 &0.202 &0.196 &0.237 &0.191 &0.215 &0.175 &0.149 &0.189 &0.216 &0.188 &0.183 &0.206 &0.212 &0.209 &0.18 &0.18 &0.106 &0.037\\ \hline D3 &0.142 &0.137 &0.128 &0.148 &0.081 &0.136 &0.137 &0.13 &0.144 &0.127 &0.147 &0.101 &0.13 &0.087 &0.146 &0.117 &0.115 &0.133 &0.131 &0.129 &0.108 &0.108 &0.048 &0.013\\ \hline D4 &0.111 &0.119 &0.098 &0.11 &0.076 &0.136 &0.135 &0.101 &0.116 &0.107 &0.114 &0.078 &0.102 &0.094 &0.078 &0.098 &0.082 &0.11 &0.1 &0.101 &0.085 &0.086 &0.031 &0.01\\ \hline D5 &0.152 &0.161 &0.162 &0.171 &0.098 &0.148 &0.157 &0.146 &0.185 &0.138 &0.167 &0.123 &0.157 &0.142 &0.15 &0.093 &0.142 &0.164 &0.154 &0.157 &0.127 &0.124 &0.046 &0.015\\ \hline E1 &0.218 &0.213 &0.216 &0.221 &0.095 &0.181 &0.183 &0.207 &0.24 &0.177 &0.207 &0.184 &0.193 &0.182 &0.193 &0.166 &0.136 &0.21 &0.205 &0.186 &0.179 &0.174 &0.107 &0.034\\ \hline E2 &0.19 &0.19 &0.2 &0.202 &0.109 &0.179 &0.166 &0.167 &0.204 &0.152 &0.191 &0.15 &0.171 &0.156 &0.174 &0.149 &0.15 &0.123 &0.182 &0.171 &0.125 &0.14 &0.05 &0.016\\ \hline E3 &0.132 &0.128 &0.147 &0.16 &0.099 &0.128 &0.137 &0.105 &0.143 &0.11 &0.12 &0.081 &0.12 &0.107 &0.121 &0.082 &0.098 &0.108 &0.087 &0.125 &0.091 &0.088 &0.035 &0.011\\ \hline E4 &0.151 &0.15 &0.168 &0.16 &0.087 &0.147 &0.152 &0.161 &0.174 &0.145 &0.153 &0.133 &0.159 &0.156 &0.161 &0.143 &0.143 &0.15 &0.171 &0.111 &0.129 &0.125 &0.047 &0.016\\ \hline E5 &0.216 &0.215 &0.206 &0.216 &0.107 &0.174 &0.197 &0.194 &0.227 &0.17 &0.206 &0.172 &0.186 &0.181 &0.189 &0.157 &0.196 &0.204 &0.2 &0.191 &0.123 &0.171 &0.115 &0.062\\ \hline E6 &0.21 &0.209 &0.209 &0.228 &0.101 &0.199 &0.2 &0.211 &0.227 &0.17 &0.194 &0.176 &0.208 &0.19 &0.201 &0.157 &0.18 &0.206 &0.219 &0.2 &0.172 &0.127 &0.119 &0.05\\ \hline F1 &0.217 &0.202 &0.212 &0.23 &0.134 &0.205 &0.204 &0.196 &0.224 &0.185 &0.212 &0.164 &0.207 &0.186 &0.201 &0.171 &0.174 &0.208 &0.206 &0.198 &0.174 &0.187 &0.063 &0.037\\ \hline F2 &0.236 &0.239 &0.24 &0.248 &0.15 &0.224 &0.235 &0.234 &0.26 &0.205 &0.24 &0.204 &0.214 &0.207 &0.22 &0.192 &0.219 &0.234 &0.236 &0.216 &0.191 &0.207 &0.135 &0.025\\ \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
$$\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{24 \times4}} &Di &Ci &Mi &Ri\\ \hline A1 &0.098 &3.802 &3.9 &-3.703\\ \hline A2 &1.121 &3.544 &4.664 &-2.423\\ \hline A3 &1.067 &3.556 &4.623 &-2.489\\ \hline A4 &1.115 &3.825 &4.94 &-2.71\\ \hline B1 &0.391 &1.879 &2.27 &-1.489\\ \hline B2 &1.218 &3.204 &4.423 &-1.986\\ \hline C1 &3.559 &3.443 &7.002 &0.115\\ \hline C2 &3.605 &3.219 &6.824 &0.385\\ \hline C3 &3.378 &3.885 &7.262 &-0.507\\ \hline C4 &3.649 &2.902 &6.552 &0.747\\ \hline C5 &3.189 &3.561 &6.75 &-0.372\\ \hline D1 &4.233 &2.661 &6.894 &1.572\\ \hline D2 &4.47 &3.122 &7.591 &1.348\\ \hline D3 &2.821 &2.935 &5.756 &-0.113\\ \hline D4 &2.278 &3.239 &5.517 &-0.961\\ \hline D5 &3.281 &2.674 &5.955 &0.608\\ \hline E1 &4.305 &2.946 &7.251 &1.359\\ \hline E2 &3.706 &3.233 &6.939 &0.473\\ \hline E3 &2.565 &3.364 &5.93 &-0.799\\ \hline E4 &3.292 &3.168 &6.46 &0.124\\ \hline E5 &4.275 &2.686 &6.961 &1.589\\ \hline E6 &4.363 &2.717 &7.08 &1.645\\ \hline F1 &4.398 &1.364 &5.763 &3.034\\ \hline F2 &5.009 &0.456 &5.465 &4.552\\ \hline \end{array} $$
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 &0.004 &0.004 &0.0041 &0.0017 &0.0034 &0.0097 &0.0037 &0.0044 &0.0032 &0.0039 &0.0033 &0.0036 &0.0033 &0.0036 &0.0031 &0.0157 &0.0038 &0.0038 &0.0034 &0.0032 &0.0032 &0.002 &0.0006\\ \hline A2 &0.1008 &1 &0.0903 &0.0984 &0.0186 &0.0363 &0.0597 &0.0518 &0.0844 &0.0429 &0.0811 &0.0286 &0.0322 &0.0315 &0.0341 &0.027 &0.0425 &0.0352 &0.0456 &0.0334 &0.029 &0.0566 &0.0155 &0.0045\\ \hline A3 &0.0955 &0.0751 &1 &0.0826 &0.0369 &0.056 &0.0932 &0.0333 &0.0755 &0.0293 &0.0816 &0.026 &0.0302 &0.0291 &0.0322 &0.0261 &0.0307 &0.0326 &0.034 &0.0314 &0.0267 &0.0282 &0.039 &0.0037\\ \hline A4 &0.1003 &0.076 &0.064 &1 &0.0245 &0.0339 &0.0822 &0.0555 &0.0733 &0.0408 &0.082 &0.0303 &0.0338 &0.0328 &0.0358 &0.0292 &0.0584 &0.0634 &0.0377 &0.0345 &0.03 &0.0314 &0.0155 &0.004\\ \hline B1 &0.0502 &0.0215 &0.0253 &0.0196 &1 &0.0394 &0.0226 &0.011 &0.0236 &0.0105 &0.022 &0.0087 &0.0106 &0.0099 &0.0113 &0.0093 &0.0103 &0.0104 &0.012 &0.0326 &0.0087 &0.0089 &0.0042 &0.0011\\ \hline B2 &0.0858 &0.0463 &0.0537 &0.0476 &0.0746 &1 &0.0809 &0.0392 &0.0818 &0.07 &0.0618 &0.032 &0.0593 &0.0364 &0.0649 &0.0519 &0.0359 &0.0389 &0.0696 &0.0618 &0.033 &0.0322 &0.0151 &0.0043\\ \hline C1 &0.1909 &0.1836 &0.1839 &0.1953 &0.0702 &0.1567 &1 &0.1553 &0.1989 &0.1316 &0.1868 &0.1334 &0.1603 &0.1476 &0.1652 &0.1401 &0.1476 &0.1647 &0.1695 &0.1498 &0.138 &0.1423 &0.0995 &0.0174\\ \hline C2 &0.1836 &0.1924 &0.1713 &0.192 &0.073 &0.1462 &0.1572 &1 &0.2075 &0.1369 &0.1975 &0.1422 &0.1714 &0.1535 &0.1741 &0.1331 &0.1565 &0.1613 &0.1785 &0.1616 &0.1496 &0.1534 &0.0698 &0.0181\\ \hline C3 &0.1859 &0.1689 &0.1692 &0.1971 &0.0906 &0.1643 &0.1658 &0.1643 &1 &0.1479 &0.152 &0.1289 &0.1343 &0.1513 &0.1508 &0.1211 &0.1465 &0.1494 &0.1792 &0.1596 &0.1363 &0.1154 &0.0462 &0.0152\\ \hline C4 &0.1973 &0.174 &0.1859 &0.203 &0.0953 &0.1735 &0.1852 &0.1747 &0.2051 &1 &0.1894 &0.1406 &0.1585 &0.1488 &0.1641 &0.1445 &0.1527 &0.1626 &0.1807 &0.1639 &0.1421 &0.1301 &0.0505 &0.0165\\ \hline C5 &0.1879 &0.1647 &0.1637 &0.1833 &0.0596 &0.1068 &0.1564 &0.1645 &0.1806 &0.1308 &1 &0.1267 &0.1327 &0.1394 &0.1552 &0.1142 &0.1373 &0.1491 &0.1473 &0.1456 &0.1248 &0.137 &0.0455 &0.0152\\ \hline D1 &0.2266 &0.2157 &0.2038 &0.2282 &0.0824 &0.185 &0.1947 &0.1943 &0.2306 &0.1708 &0.2154 &1 &0.1977 &0.1753 &0.1981 &0.1602 &0.194 &0.206 &0.2036 &0.1968 &0.1816 &0.1615 &0.0607 &0.03\\ \hline D2 &0.2171 &0.2176 &0.2181 &0.2343 &0.1082 &0.2046 &0.2016 &0.1962 &0.2369 &0.1907 &0.2154 &0.175 &1 &0.1889 &0.2155 &0.1884 &0.1829 &0.2057 &0.2123 &0.2087 &0.1796 &0.1803 &0.1058 &0.0373\\ \hline D3 &0.1417 &0.1368 &0.1278 &0.1481 &0.0806 &0.1358 &0.1372 &0.1297 &0.1443 &0.127 &0.1465 &0.1006 &0.13 &1 &0.1465 &0.1172 &0.1151 &0.1329 &0.1313 &0.1286 &0.1075 &0.1081 &0.0482 &0.0131\\ \hline D4 &0.1109 &0.1186 &0.098 &0.1101 &0.0764 &0.1357 &0.1351 &0.1009 &0.1159 &0.1067 &0.1137 &0.0784 &0.1025 &0.0944 &1 &0.0984 &0.0823 &0.1099 &0.0997 &0.1009 &0.085 &0.0857 &0.0315 &0.0101\\ \hline D5 &0.1518 &0.1611 &0.1616 &0.1711 &0.0984 &0.1484 &0.1569 &0.1461 &0.185 &0.1383 &0.1673 &0.1234 &0.1571 &0.1424 &0.1503 &1 &0.1421 &0.1637 &0.1544 &0.1566 &0.127 &0.1243 &0.0459 &0.0153\\ \hline E1 &0.2178 &0.2131 &0.2161 &0.2206 &0.0946 &0.1808 &0.1832 &0.2066 &0.24 &0.1768 &0.2073 &0.1837 &0.1932 &0.1818 &0.1927 &0.1659 &1 &0.2099 &0.2045 &0.1861 &0.1793 &0.174 &0.1073 &0.0341\\ \hline E2 &0.1902 &0.1903 &0.1997 &0.2019 &0.1091 &0.1789 &0.1663 &0.1667 &0.2037 &0.1524 &0.1909 &0.1499 &0.1713 &0.1555 &0.1743 &0.1485 &0.1499 &1 &0.1816 &0.1713 &0.1248 &0.1397 &0.0498 &0.0163\\ \hline E3 &0.1323 &0.1284 &0.147 &0.1605 &0.0994 &0.1282 &0.1367 &0.1054 &0.1434 &0.11 &0.1202 &0.0807 &0.1199 &0.1067 &0.1214 &0.0824 &0.0981 &0.108 &1 &0.1254 &0.0906 &0.0878 &0.0351 &0.011\\ \hline E4 &0.1512 &0.15 &0.1678 &0.1596 &0.0872 &0.1472 &0.1521 &0.1615 &0.1739 &0.1453 &0.1534 &0.133 &0.1591 &0.1555 &0.161 &0.1435 &0.1429 &0.1501 &0.1705 &1 &0.1287 &0.1251 &0.0465 &0.0156\\ \hline E5 &0.2162 &0.2147 &0.2064 &0.2159 &0.1066 &0.174 &0.1965 &0.1943 &0.2267 &0.1701 &0.206 &0.1719 &0.1865 &0.1812 &0.1886 &0.1567 &0.1963 &0.2036 &0.2005 &0.1908 &1 &0.1714 &0.1152 &0.0615\\ \hline E6 &0.2099 &0.2087 &0.209 &0.2279 &0.1006 &0.1991 &0.2004 &0.2109 &0.2272 &0.1704 &0.1945 &0.1762 &0.2078 &0.1896 &0.2015 &0.1567 &0.1805 &0.206 &0.2188 &0.2001 &0.172 &1 &0.1186 &0.0495\\ \hline F1 &0.2172 &0.2022 &0.2118 &0.2304 &0.1341 &0.2053 &0.204 &0.1959 &0.2242 &0.1848 &0.212 &0.1639 &0.2071 &0.1861 &0.2009 &0.1712 &0.174 &0.2085 &0.2063 &0.1975 &0.174 &0.1869 &1 &0.0373\\ \hline F2 &0.2365 &0.2388 &0.2395 &0.2479 &0.1495 &0.2238 &0.2354 &0.2336 &0.2601 &0.2045 &0.2395 &0.2041 &0.2144 &0.2067 &0.22 &0.1924 &0.2186 &0.2344 &0.2359 &0.2163 &0.1907 &0.207 &0.1346 &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
$$\begin{array}{c|c|c|c|c|c|c}{M_{24 \times2}} &R集合之和=D &Q集合之和=C\\ \hline A1 &1.36130530183 &4.89786990142\\ \hline A2 &3.06712922199 &4.67865238901\\ \hline A3 &3.11482473265 &4.66029785281\\ \hline A4 &2.88887044361 &4.91583102424\\ \hline B1 &1.91610544128 &3.54432823162\\ \hline B2 &2.86457341861 &4.51595197752\\ \hline C1 &4.76049036174 &4.4488422118\\ \hline C2 &4.86202368433 &4.43288985001\\ \hline C3 &4.67212225503 &4.82809118374\\ \hline C4 &4.89345081074 &4.34266851334\\ \hline C5 &4.67508343796 &4.59447986743\\ \hline D1 &5.33776037004 &4.28518006792\\ \hline D2 &5.37822711938 &4.37842549775\\ \hline D3 &4.23070235928 &4.35949125491\\ \hline D4 &4.00039252224 &4.47594590482\\ \hline D5 &4.68072826991 &4.32295229368\\ \hline E1 &5.31406006272 &4.32265582912\\ \hline E2 &4.89515688815 &4.4678127892\\ \hline E3 &4.18724005104 &4.59893605176\\ \hline E4 &4.64103615418 &4.42428883646\\ \hline E5 &5.28257949524 &4.26355823088\\ \hline E6 &5.37045788897 &4.2801004665\\ \hline F1 &5.44282756326 &3.43459313261\\ \hline F2 &5.98423583615 &2.34754033177\\ \hline \end{array} $$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。
160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 160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 $数值区段 | TAISM运算过程 |
---|---|---|---|
1 | 0.01571 | 0<$\lambda$<0.01571 | |
2 | 0.03936 | 0.01571<$\lambda$<0.03936 | |
3 | 0.05018 | 0.03936<$\lambda$<0.05018 | |
4 | 0.06155 | 0.05018<$\lambda$<0.06155 | |
5 | 0.08177 | 0.06155<$\lambda$<0.08177 | |
6 | 0.08224 | 0.08177<$\lambda$<0.08224 | |
7 | 0.08584 | 0.08224<$\lambda$<0.08584 | |
8 | 0.09032 | 0.08584<$\lambda$<0.09032 | |
9 | 0.09323 | 0.09032<$\lambda$<0.09323 | |
10 | 0.0955 | 0.09323<$\lambda$<0.0955 | |
11 | 0.09836 | 0.0955<$\lambda$<0.09836 | |
12 | 0.10027 | 0.09836<$\lambda$<0.10027 | |
13 | 0.10077 | 0.10027<$\lambda$<0.10077 | |
14 | 0.11859 | 0.10077<$\lambda$<0.11859 | |
15 | 0.13414 | 0.11859<$\lambda$<0.13414 | |
16 | 0.13456 | 0.13414<$\lambda$<0.13456 | |
17 | 0.13505 | 0.13456<$\lambda$<0.13505 | |
18 | 0.13567 | 0.13505<$\lambda$<0.13567 | |
19 | 0.14339 | 0.13567<$\lambda$<0.14339 | |
20 | 0.14652 | 0.14339<$\lambda$<0.14652 | |
21 | 0.14703 | 0.14652<$\lambda$<0.14703 | |
22 | 0.14808 | 0.14703<$\lambda$<0.14808 | |
23 | 0.14952 | 0.14808<$\lambda$<0.14952 | |
24 | 0.16047 | 0.14952<$\lambda$<0.16047 | |
25 | 0.16468 | 0.16047<$\lambda$<0.16468 | |
26 | 0.1652 | 0.16468<$\lambda$<0.1652 | |
27 | 0.16585 | 0.1652<$\lambda$<0.16585 | |
28 | 0.16725 | 0.16585<$\lambda$<0.16725 | |
29 | 0.16893 | 0.16725<$\lambda$<0.16893 | |
30 | 0.16918 | 0.16893<$\lambda$<0.16918 | |
31 | 0.17134 | 0.16918<$\lambda$<0.17134 | |
32 | 0.17135 | 0.17134<$\lambda$<0.17135 | |
33 | 0.17351 | 0.17135<$\lambda$<0.17351 | |
34 | 0.17394 | 0.17351<$\lambda$<0.17394 | |
35 | 0.17407 | 0.17394<$\lambda$<0.17407 | |
36 | 0.17427 | 0.17407<$\lambda$<0.17427 | |
37 | 0.17465 | 0.17427<$\lambda$<0.17465 | |
38 | 0.17889 | 0.17465<$\lambda$<0.17889 | |
39 | 0.17917 | 0.17889<$\lambda$<0.17917 | |
40 | 0.18028 | 0.17917<$\lambda$<0.18028 | |
41 | 0.18055 | 0.18028<$\lambda$<0.18055 | |
42 | 0.1807 | 0.18055<$\lambda$<0.1807 | |
43 | 0.18156 | 0.1807<$\lambda$<0.18156 | |
44 | 0.18163 | 0.18156<$\lambda$<0.18163 | |
45 | 0.18289 | 0.18163<$\lambda$<0.18289 | |
46 | 0.18332 | 0.18289<$\lambda$<0.18332 | |
47 | 0.18362 | 0.18332<$\lambda$<0.18362 | |
48 | 0.18366 | 0.18362<$\lambda$<0.18366 | |
49 | 0.18389 | 0.18366<$\lambda$<0.18389 | |
50 | 0.18496 | 0.18389<$\lambda$<0.18496 | |
51 | 0.18518 | 0.18496<$\lambda$<0.18518 | |
52 | 0.18587 | 0.18518<$\lambda$<0.18587 | |
53 | 0.18592 | 0.18587<$\lambda$<0.18592 | |
54 | 0.18677 | 0.18592<$\lambda$<0.18677 | |
55 | 0.1869 | 0.18677<$\lambda$<0.1869 | |
56 | 0.18794 | 0.1869<$\lambda$<0.18794 | |
57 | 0.18836 | 0.18794<$\lambda$<0.18836 | |
58 | 0.18893 | 0.18836<$\lambda$<0.18893 | |
59 | 0.1894 | 0.18893<$\lambda$<0.1894 | |
60 | 0.18962 | 0.1894<$\lambda$<0.18962 | |
61 | 0.19023 | 0.18962<$\lambda$<0.19023 | |
62 | 0.19034 | 0.19023<$\lambda$<0.19034 | |
63 | 0.19071 | 0.19034<$\lambda$<0.19071 | |
64 | 0.19074 | 0.19071<$\lambda$<0.19074 | |
65 | 0.19087 | 0.19074<$\lambda$<0.19087 | |
66 | 0.19094 | 0.19087<$\lambda$<0.19094 | |
67 | 0.1924 | 0.19094<$\lambda$<0.1924 | |
68 | 0.19242 | 0.1924<$\lambda$<0.19242 | |
69 | 0.19321 | 0.19242<$\lambda$<0.19321 | |
70 | 0.19403 | 0.19321<$\lambda$<0.19403 | |
71 | 0.19618 | 0.19403<$\lambda$<0.19618 | |
72 | 0.19627 | 0.19618<$\lambda$<0.19627 | |
73 | 0.19652 | 0.19627<$\lambda$<0.19652 | |
74 | 0.19714 | 0.19652<$\lambda$<0.19714 | |
75 | 0.19733 | 0.19714<$\lambda$<0.19733 | |
76 | 0.19747 | 0.19733<$\lambda$<0.19747 | |
77 | 0.1977 | 0.19747<$\lambda$<0.1977 | |
78 | 0.19813 | 0.1977<$\lambda$<0.19813 | |
79 | 0.1989 | 0.19813<$\lambda$<0.1989 | |
80 | 0.19968 | 0.1989<$\lambda$<0.19968 | |
81 | 0.2005 | 0.19968<$\lambda$<0.2005 | |
82 | 0.20158 | 0.2005<$\lambda$<0.20158 | |
83 | 0.20194 | 0.20158<$\lambda$<0.20194 | |
84 | 0.20302 | 0.20194<$\lambda$<0.20302 | |
85 | 0.20358 | 0.20302<$\lambda$<0.20358 | |
86 | 0.2036 | 0.20358<$\lambda$<0.2036 | |
87 | 0.20374 | 0.2036<$\lambda$<0.20374 | |
88 | 0.20381 | 0.20374<$\lambda$<0.20381 | |
89 | 0.20399 | 0.20381<$\lambda$<0.20399 | |
90 | 0.20412 | 0.20399<$\lambda$<0.20412 | |
91 | 0.20451 | 0.20412<$\lambda$<0.20451 | |
92 | 0.20454 | 0.20451<$\lambda$<0.20454 | |
93 | 0.20455 | 0.20454<$\lambda$<0.20455 | |
94 | 0.20514 | 0.20455<$\lambda$<0.20514 | |
95 | 0.20526 | 0.20514<$\lambda$<0.20526 | |
96 | 0.20573 | 0.20526<$\lambda$<0.20573 | |
97 | 0.20596 | 0.20573<$\lambda$<0.20596 | |
98 | 0.20602 | 0.20596<$\lambda$<0.20602 | |
99 | 0.20604 | 0.20602<$\lambda$<0.20604 | |
100 | 0.20642 | 0.20604<$\lambda$<0.20642 | |
101 | 0.20655 | 0.20642<$\lambda$<0.20655 | |
102 | 0.20669 | 0.20655<$\lambda$<0.20669 | |
103 | 0.207 | 0.20669<$\lambda$<0.207 | |
104 | 0.20706 | 0.207<$\lambda$<0.20706 | |
105 | 0.20727 | 0.20706<$\lambda$<0.20727 | |
106 | 0.20751 | 0.20727<$\lambda$<0.20751 | |
107 | 0.20781 | 0.20751<$\lambda$<0.20781 | |
108 | 0.20847 | 0.20781<$\lambda$<0.20847 | |
109 | 0.20866 | 0.20847<$\lambda$<0.20866 | |
110 | 0.20866 | 0.20866<$\lambda$<0.20866 | |
111 | 0.20896 | 0.20866<$\lambda$<0.20896 | |
112 | 0.20987 | 0.20896<$\lambda$<0.20987 | |
113 | 0.20989 | 0.20987<$\lambda$<0.20989 | |
114 | 0.2109 | 0.20989<$\lambda$<0.2109 | |
115 | 0.21181 | 0.2109<$\lambda$<0.21181 | |
116 | 0.21196 | 0.21181<$\lambda$<0.21196 | |
117 | 0.21228 | 0.21196<$\lambda$<0.21228 | |
118 | 0.21311 | 0.21228<$\lambda$<0.21311 | |
119 | 0.21437 | 0.21311<$\lambda$<0.21437 | |
120 | 0.2147 | 0.21437<$\lambda$<0.2147 | |
121 | 0.21537 | 0.2147<$\lambda$<0.21537 | |
122 | 0.21544 | 0.21537<$\lambda$<0.21544 | |
123 | 0.21552 | 0.21544<$\lambda$<0.21552 | |
124 | 0.21573 | 0.21552<$\lambda$<0.21573 | |
125 | 0.21588 | 0.21573<$\lambda$<0.21588 | |
126 | 0.21609 | 0.21588<$\lambda$<0.21609 | |
127 | 0.2162 | 0.21609<$\lambda$<0.2162 | |
128 | 0.21625 | 0.2162<$\lambda$<0.21625 | |
129 | 0.2171 | 0.21625<$\lambda$<0.2171 | |
130 | 0.21724 | 0.2171<$\lambda$<0.21724 | |
131 | 0.2176 | 0.21724<$\lambda$<0.2176 | |
132 | 0.21775 | 0.2176<$\lambda$<0.21775 | |
133 | 0.21812 | 0.21775<$\lambda$<0.21812 | |
134 | 0.21862 | 0.21812<$\lambda$<0.21862 | |
135 | 0.21879 | 0.21862<$\lambda$<0.21879 | |
136 | 0.22003 | 0.21879<$\lambda$<0.22003 | |
137 | 0.22061 | 0.22003<$\lambda$<0.22061 | |
138 | 0.22384 | 0.22061<$\lambda$<0.22384 | |
139 | 0.22423 | 0.22384<$\lambda$<0.22423 | |
140 | 0.22663 | 0.22423<$\lambda$<0.22663 | |
141 | 0.22674 | 0.22663<$\lambda$<0.22674 | |
142 | 0.22724 | 0.22674<$\lambda$<0.22724 | |
143 | 0.22787 | 0.22724<$\lambda$<0.22787 | |
144 | 0.22818 | 0.22787<$\lambda$<0.22818 | |
145 | 0.23043 | 0.22818<$\lambda$<0.23043 | |
146 | 0.23061 | 0.23043<$\lambda$<0.23061 | |
147 | 0.23362 | 0.23061<$\lambda$<0.23362 | |
148 | 0.23429 | 0.23362<$\lambda$<0.23429 | |
149 | 0.23436 | 0.23429<$\lambda$<0.23436 | |
150 | 0.2354 | 0.23436<$\lambda$<0.2354 | |
151 | 0.23585 | 0.2354<$\lambda$<0.23585 | |
152 | 0.23647 | 0.23585<$\lambda$<0.23647 | |
153 | 0.23687 | 0.23647<$\lambda$<0.23687 | |
154 | 0.2388 | 0.23687<$\lambda$<0.2388 | |
155 | 0.23952 | 0.2388<$\lambda$<0.23952 | |
156 | 0.23954 | 0.23952<$\lambda$<0.23954 | |
157 | 0.23996 | 0.23954<$\lambda$<0.23996 | |
158 | 0.24794 | 0.23996<$\lambda$<0.24794 | |
159 | 0.26009 | 0.24794<$\lambda$<0.26009 | |
160 | 1 | 0.26009<$\lambda$<1 |