基于综合影响矩阵的对抗解释结构模型联合分析法

规范化方法选择（参数选择）：

原始矩阵（直接影响矩阵）为

$$Ori=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{18 \times18}} &S1 &S2 &S3 &S4 &S5 &S6 &S7 &S8 &S9 &S10 &S11 &S12 &S13 &S14 &S15 &S16 &S17 &S18\\ \hline S1 &0 &41 &46 &22 &44 &39 &31 &11 &10 &39 &49 &31 &49 &28 &49 &41 &11 &10\\ \hline S2 &39 &0 &22 &50 &22 &41 &31 &13 &11 &22 &11 &13 &13 &21 &39 &29 &30 &40\\ \hline S3 &50 &21 &0 &40 &50 &50 &30 &10 &28 &40 &40 &11 &40 &10 &40 &49 &31 &38\\ \hline S4 &12 &41 &11 &0 &14 &12 &11 &12 &12 &41 &10 &49 &39 &41 &41 &12 &41 &50\\ \hline S5 &21 &21 &39 &31 &0 &21 &20 &10 &11 &31 &11 &31 &22 &31 &40 &30 &31 &31\\ \hline S6 &31 &41 &40 &40 &40 &0 &40 &11 &11 &30 &28 &11 &13 &11 &11 &11 &21 &20\\ \hline S7 &31 &32 &40 &30 &40 &41 &0 &10 &10 &31 &22 &41 &40 &31 &22 &12 &22 &41\\ \hline S8 &21 &40 &19 &40 &10 &31 &10 &0 &23 &10 &10 &50 &10 &37 &40 &10 &32 &41\\ \hline S9 &10 &20 &10 &10 &10 &10 &10 &39 &0 &40 &21 &40 &10 &11 &40 &13 &10 &40\\ \hline S10 &10 &22 &20 &11 &31 &20 &22 &10 &12 &0 &21 &50 &21 &22 &31 &21 &40 &40\\ \hline S11 &31 &12 &29 &11 &12 &21 &31 &10 &10 &31 &0 &20 &21 &10 &10 &41 &10 &10\\ \hline S12 &12 &40 &10 &10 &12 &12 &13 &10 &10 &30 &13 &0 &10 &32 &50 &10 &29 &47\\ \hline S13 &20 &21 &10 &10 &21 &19 &40 &10 &10 &20 &19 &40 &0 &10 &22 &10 &19 &31\\ \hline S14 &21 &39 &10 &10 &10 &10 &21 &10 &19 &12 &10 &41 &32 &0 &45 &31 &40 &42\\ \hline S15 &10 &22 &11 &10 &30 &10 &11 &10 &11 &22 &11 &28 &21 &31 &0 &12 &19 &19\\ \hline S16 &40 &40 &40 &30 &40 &30 &40 &10 &10 &30 &41 &10 &10 &10 &10 &0 &10 &12\\ \hline S17 &30 &40 &38 &11 &21 &40 &40 &10 &10 &20 &19 &10 &11 &12 &20 &10 &0 &39\\ \hline S18 &21 &21 &28 &10 &30 &40 &40 &10 &19 &20 &28 &10 &20 &21 &29 &19 &40 &0\\ \hline \end{array} $$

规范直接关系矩阵求解过程

$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{18 \times18}} &S1 &S2 &S3 &S4 &S5 &S6 &S7 &S8 &S9 &S10 &S11 &S12 &S13 &S14 &S15 &S16 &S17 &S18\\ \hline S1 &0 &0.071 &0.08 &0.038 &0.076 &0.067 &0.054 &0.019 &0.017 &0.067 &0.085 &0.054 &0.085 &0.048 &0.085 &0.071 &0.019 &0.017\\ \hline S2 &0.067 &0 &0.038 &0.087 &0.038 &0.071 &0.054 &0.022 &0.019 &0.038 &0.019 &0.022 &0.022 &0.036 &0.067 &0.05 &0.052 &0.069\\ \hline S3 &0.087 &0.036 &0 &0.069 &0.087 &0.087 &0.052 &0.017 &0.048 &0.069 &0.069 &0.019 &0.069 &0.017 &0.069 &0.085 &0.054 &0.066\\ \hline S4 &0.021 &0.071 &0.019 &0 &0.024 &0.021 &0.019 &0.021 &0.021 &0.071 &0.017 &0.085 &0.067 &0.071 &0.071 &0.021 &0.071 &0.087\\ \hline S5 &0.036 &0.036 &0.067 &0.054 &0 &0.036 &0.035 &0.017 &0.019 &0.054 &0.019 &0.054 &0.038 &0.054 &0.069 &0.052 &0.054 &0.054\\ \hline S6 &0.054 &0.071 &0.069 &0.069 &0.069 &0 &0.069 &0.019 &0.019 &0.052 &0.048 &0.019 &0.022 &0.019 &0.019 &0.019 &0.036 &0.035\\ \hline S7 &0.054 &0.055 &0.069 &0.052 &0.069 &0.071 &0 &0.017 &0.017 &0.054 &0.038 &0.071 &0.069 &0.054 &0.038 &0.021 &0.038 &0.071\\ \hline S8 &0.036 &0.069 &0.033 &0.069 &0.017 &0.054 &0.017 &0 &0.04 &0.017 &0.017 &0.087 &0.017 &0.064 &0.069 &0.017 &0.055 &0.071\\ \hline S9 &0.017 &0.035 &0.017 &0.017 &0.017 &0.017 &0.017 &0.067 &0 &0.069 &0.036 &0.069 &0.017 &0.019 &0.069 &0.022 &0.017 &0.069\\ \hline S10 &0.017 &0.038 &0.035 &0.019 &0.054 &0.035 &0.038 &0.017 &0.021 &0 &0.036 &0.087 &0.036 &0.038 &0.054 &0.036 &0.069 &0.069\\ \hline S11 &0.054 &0.021 &0.05 &0.019 &0.021 &0.036 &0.054 &0.017 &0.017 &0.054 &0 &0.035 &0.036 &0.017 &0.017 &0.071 &0.017 &0.017\\ \hline S12 &0.021 &0.069 &0.017 &0.017 &0.021 &0.021 &0.022 &0.017 &0.017 &0.052 &0.022 &0 &0.017 &0.055 &0.087 &0.017 &0.05 &0.081\\ \hline S13 &0.035 &0.036 &0.017 &0.017 &0.036 &0.033 &0.069 &0.017 &0.017 &0.035 &0.033 &0.069 &0 &0.017 &0.038 &0.017 &0.033 &0.054\\ \hline S14 &0.036 &0.067 &0.017 &0.017 &0.017 &0.017 &0.036 &0.017 &0.033 &0.021 &0.017 &0.071 &0.055 &0 &0.078 &0.054 &0.069 &0.073\\ \hline S15 &0.017 &0.038 &0.019 &0.017 &0.052 &0.017 &0.019 &0.017 &0.019 &0.038 &0.019 &0.048 &0.036 &0.054 &0 &0.021 &0.033 &0.033\\ \hline S16 &0.069 &0.069 &0.069 &0.052 &0.069 &0.052 &0.069 &0.017 &0.017 &0.052 &0.071 &0.017 &0.017 &0.017 &0.017 &0 &0.017 &0.021\\ \hline S17 &0.052 &0.069 &0.066 &0.019 &0.036 &0.069 &0.069 &0.017 &0.017 &0.035 &0.033 &0.017 &0.019 &0.021 &0.035 &0.017 &0 &0.067\\ \hline S18 &0.036 &0.036 &0.048 &0.017 &0.052 &0.069 &0.069 &0.017 &0.033 &0.035 &0.048 &0.017 &0.035 &0.036 &0.05 &0.033 &0.069 &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_{18 \times18}} &S1 &S2 &S3 &S4 &S5 &S6 &S7 &S8 &S9 &S10 &S11 &S12 &S13 &S14 &S15 &S16 &S17 &S18\\ \hline S1 &0.136 &0.227 &0.214 &0.16 &0.22 &0.209 &0.198 &0.082 &0.09 &0.215 &0.199 &0.199 &0.206 &0.165 &0.248 &0.188 &0.16 &0.189\\ \hline S2 &0.175 &0.138 &0.155 &0.184 &0.161 &0.19 &0.173 &0.075 &0.08 &0.163 &0.119 &0.146 &0.129 &0.137 &0.205 &0.146 &0.17 &0.21\\ \hline S3 &0.223 &0.206 &0.151 &0.193 &0.239 &0.236 &0.206 &0.085 &0.122 &0.227 &0.194 &0.176 &0.199 &0.143 &0.241 &0.206 &0.199 &0.241\\ \hline S4 &0.124 &0.197 &0.125 &0.092 &0.137 &0.136 &0.135 &0.071 &0.079 &0.183 &0.108 &0.198 &0.161 &0.163 &0.205 &0.111 &0.185 &0.223\\ \hline S5 &0.141 &0.165 &0.174 &0.147 &0.118 &0.152 &0.15 &0.067 &0.078 &0.171 &0.114 &0.169 &0.137 &0.147 &0.202 &0.144 &0.166 &0.19\\ \hline S6 &0.158 &0.194 &0.177 &0.165 &0.183 &0.118 &0.18 &0.069 &0.076 &0.17 &0.14 &0.137 &0.125 &0.114 &0.154 &0.115 &0.149 &0.171\\ \hline S7 &0.173 &0.201 &0.193 &0.161 &0.2 &0.202 &0.135 &0.075 &0.084 &0.189 &0.145 &0.202 &0.182 &0.161 &0.194 &0.13 &0.17 &0.227\\ \hline S8 &0.138 &0.196 &0.137 &0.16 &0.129 &0.164 &0.13 &0.051 &0.096 &0.134 &0.108 &0.197 &0.114 &0.157 &0.203 &0.108 &0.168 &0.207\\ \hline S9 &0.096 &0.133 &0.099 &0.089 &0.104 &0.105 &0.104 &0.104 &0.046 &0.156 &0.105 &0.159 &0.091 &0.095 &0.172 &0.092 &0.107 &0.173\\ \hline S10 &0.114 &0.155 &0.135 &0.105 &0.157 &0.14 &0.144 &0.063 &0.074 &0.109 &0.12 &0.187 &0.124 &0.124 &0.175 &0.12 &0.171 &0.193\\ \hline S11 &0.135 &0.121 &0.136 &0.095 &0.114 &0.127 &0.142 &0.056 &0.062 &0.145 &0.077 &0.124 &0.113 &0.089 &0.12 &0.142 &0.103 &0.122\\ \hline S12 &0.103 &0.167 &0.103 &0.092 &0.112 &0.113 &0.114 &0.057 &0.064 &0.141 &0.095 &0.092 &0.095 &0.129 &0.189 &0.091 &0.14 &0.187\\ \hline S13 &0.115 &0.135 &0.103 &0.091 &0.125 &0.122 &0.155 &0.056 &0.061 &0.125 &0.104 &0.157 &0.077 &0.092 &0.141 &0.088 &0.12 &0.158\\ \hline S14 &0.131 &0.182 &0.117 &0.103 &0.123 &0.124 &0.142 &0.064 &0.084 &0.127 &0.102 &0.172 &0.141 &0.086 &0.197 &0.134 &0.168 &0.194\\ \hline S15 &0.087 &0.122 &0.091 &0.08 &0.125 &0.093 &0.095 &0.051 &0.057 &0.114 &0.079 &0.126 &0.1 &0.115 &0.092 &0.083 &0.109 &0.125\\ \hline S16 &0.175 &0.194 &0.18 &0.151 &0.185 &0.169 &0.182 &0.067 &0.075 &0.172 &0.164 &0.135 &0.121 &0.113 &0.152 &0.099 &0.13 &0.157\\ \hline S17 &0.151 &0.184 &0.168 &0.112 &0.147 &0.178 &0.175 &0.063 &0.071 &0.144 &0.121 &0.123 &0.113 &0.107 &0.157 &0.106 &0.105 &0.19\\ \hline S18 &0.138 &0.157 &0.154 &0.11 &0.162 &0.178 &0.177 &0.065 &0.087 &0.147 &0.137 &0.128 &0.129 &0.124 &0.173 &0.121 &0.172 &0.13\\ \hline \end{array} $$

模糊可达矩阵FR的求解

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}$

模糊相乘矩阵求解 FB=T+I即综合影响矩阵中主对角线全部变成1

$$FB=\begin{array} {c|c|c}{M_{18 \times18}} &S1 &S2 &S3 &S4 &S5 &S6 &S7 &S8 &S9 &S10 &S11 &S12 &S13 &S14 &S15 &S16 &S17 &S18\\ \hline S1 &1 &0.2273 &0.2141 &0.1596 &0.2203 &0.2092 &0.1978 &0.0816 &0.0898 &0.2152 &0.1991 &0.1995 &0.2062 &0.1646 &0.2475 &0.1883 &0.1602 &0.1888\\ \hline S2 &0.1752 &1 &0.1547 &0.1837 &0.1614 &0.1903 &0.1734 &0.0749 &0.0796 &0.1633 &0.1193 &0.146 &0.1295 &0.1367 &0.2054 &0.1457 &0.1696 &0.2095\\ \hline S3 &0.2225 &0.2058 &1 &0.1935 &0.2391 &0.2359 &0.2057 &0.0848 &0.1222 &0.2267 &0.194 &0.1756 &0.1991 &0.1425 &0.2412 &0.2056 &0.1988 &0.2405\\ \hline S4 &0.1237 &0.1966 &0.1251 &1 &0.137 &0.1356 &0.1353 &0.0708 &0.0786 &0.183 &0.1081 &0.1983 &0.1611 &0.1634 &0.2046 &0.1115 &0.1846 &0.2232\\ \hline S5 &0.1414 &0.1652 &0.1736 &0.1466 &1 &0.1518 &0.1497 &0.0674 &0.0776 &0.1708 &0.1138 &0.1688 &0.1374 &0.1468 &0.2017 &0.1438 &0.1664 &0.1903\\ \hline S6 &0.1583 &0.1941 &0.1773 &0.1645 &0.1828 &1 &0.1803 &0.0686 &0.0764 &0.1702 &0.1403 &0.1366 &0.1246 &0.1142 &0.154 &0.115 &0.1486 &0.1713\\ \hline S7 &0.1735 &0.2012 &0.1925 &0.1606 &0.2004 &0.2015 &1 &0.0748 &0.0845 &0.1891 &0.1454 &0.2024 &0.1818 &0.1608 &0.194 &0.1299 &0.1695 &0.2269\\ \hline S8 &0.1378 &0.1958 &0.1373 &0.1597 &0.1291 &0.1645 &0.1299 &1 &0.0964 &0.1344 &0.1076 &0.1974 &0.1143 &0.1572 &0.2029 &0.1077 &0.1677 &0.2068\\ \hline S9 &0.0957 &0.1326 &0.0991 &0.0893 &0.1044 &0.1054 &0.1038 &0.1044 &1 &0.1555 &0.1055 &0.1588 &0.0908 &0.0947 &0.1718 &0.0923 &0.107 &0.1735\\ \hline S10 &0.1144 &0.1554 &0.1348 &0.1051 &0.157 &0.1404 &0.1438 &0.0632 &0.0736 &1 &0.1204 &0.1873 &0.1242 &0.1241 &0.1752 &0.1199 &0.1708 &0.1932\\ \hline S11 &0.1351 &0.1207 &0.1358 &0.0946 &0.114 &0.1266 &0.1421 &0.0558 &0.0616 &0.145 &1 &0.1244 &0.1135 &0.0893 &0.1201 &0.1416 &0.1028 &0.1218\\ \hline S12 &0.1034 &0.1672 &0.1032 &0.0915 &0.112 &0.113 &0.1142 &0.0571 &0.0635 &0.1413 &0.0947 &1 &0.0948 &0.1291 &0.1894 &0.0909 &0.1404 &0.1868\\ \hline S13 &0.1145 &0.1347 &0.1033 &0.0906 &0.1251 &0.1223 &0.155 &0.0559 &0.0613 &0.1255 &0.104 &0.1566 &1 &0.092 &0.1412 &0.0883 &0.1196 &0.1583\\ \hline S14 &0.131 &0.182 &0.1167 &0.1027 &0.1225 &0.1239 &0.1417 &0.0635 &0.0841 &0.1275 &0.1024 &0.1718 &0.1409 &1 &0.1965 &0.1341 &0.1682 &0.1943\\ \hline S15 &0.0865 &0.1224 &0.0907 &0.0797 &0.1248 &0.0931 &0.0953 &0.0507 &0.0573 &0.1145 &0.0793 &0.1255 &0.1001 &0.115 &1 &0.0825 &0.1088 &0.1252\\ \hline S16 &0.1751 &0.1936 &0.1802 &0.1506 &0.1854 &0.169 &0.1823 &0.0674 &0.075 &0.1723 &0.1641 &0.1354 &0.121 &0.1126 &0.1524 &1 &0.13 &0.157\\ \hline S17 &0.1506 &0.1836 &0.1678 &0.1116 &0.1466 &0.1777 &0.1748 &0.0634 &0.0711 &0.1444 &0.1211 &0.1228 &0.1129 &0.1072 &0.1569 &0.106 &1 &0.1896\\ \hline S18 &0.1379 &0.1573 &0.1545 &0.1099 &0.1622 &0.178 &0.1775 &0.0653 &0.0867 &0.1473 &0.1369 &0.1277 &0.1285 &0.1236 &0.1732 &0.1214 &0.1716 &1\\ \hline \end{array} $$

模糊可达矩阵FR

$$FR=\begin{array} {c|c|c}{M_{18 \times18}} &S1 &S2 &S3 &S4 &S5 &S6 &S7 &S8 &S9 &S10 &S11 &S12 &S13 &S14 &S15 &S16 &S17 &S18\\ \hline S1 &1 &0.2273 &0.2141 &0.1935 &0.2203 &0.2141 &0.2057 &0.1044 &0.1222 &0.2152 &0.1991 &0.2024 &0.2062 &0.1646 &0.2475 &0.2056 &0.1988 &0.2141\\ \hline S2 &0.1803 &1 &0.1803 &0.1837 &0.1828 &0.1903 &0.1803 &0.1044 &0.1222 &0.183 &0.1803 &0.1837 &0.1803 &0.1646 &0.2054 &0.1803 &0.1837 &0.2095\\ \hline S3 &0.2225 &0.2225 &1 &0.1935 &0.2391 &0.2359 &0.2057 &0.1044 &0.1222 &0.2267 &0.1991 &0.2024 &0.2062 &0.1646 &0.2412 &0.2056 &0.1988 &0.2405\\ \hline S4 &0.1803 &0.1966 &0.1803 &1 &0.1828 &0.1903 &0.1803 &0.1044 &0.1222 &0.183 &0.1803 &0.1983 &0.1803 &0.1646 &0.2046 &0.1803 &0.1846 &0.2232\\ \hline S5 &0.178 &0.178 &0.178 &0.178 &1 &0.178 &0.178 &0.1044 &0.1222 &0.178 &0.178 &0.178 &0.178 &0.1646 &0.2017 &0.178 &0.178 &0.1903\\ \hline S6 &0.1803 &0.1941 &0.1803 &0.1837 &0.1828 &1 &0.1803 &0.1044 &0.1222 &0.183 &0.1803 &0.1837 &0.1803 &0.1646 &0.1941 &0.1803 &0.1837 &0.1941\\ \hline S7 &0.1925 &0.2012 &0.1925 &0.1925 &0.2004 &0.2015 &1 &0.1044 &0.1222 &0.1925 &0.1925 &0.2024 &0.1925 &0.1646 &0.2012 &0.1925 &0.1925 &0.2269\\ \hline S8 &0.1803 &0.1958 &0.1803 &0.1837 &0.1828 &0.1903 &0.1803 &1 &0.1222 &0.183 &0.1803 &0.1974 &0.1803 &0.1646 &0.2029 &0.1803 &0.1837 &0.2068\\ \hline S9 &0.1735 &0.1735 &0.1735 &0.1735 &0.1735 &0.1735 &0.1735 &0.1044 &1 &0.1735 &0.1735 &0.1735 &0.1735 &0.1646 &0.1735 &0.1735 &0.1735 &0.1735\\ \hline S10 &0.178 &0.178 &0.178 &0.178 &0.178 &0.178 &0.178 &0.1044 &0.1222 &1 &0.178 &0.1873 &0.178 &0.1646 &0.1873 &0.178 &0.178 &0.1932\\ \hline S11 &0.145 &0.145 &0.145 &0.145 &0.145 &0.145 &0.145 &0.1044 &0.1222 &0.145 &1 &0.145 &0.145 &0.145 &0.145 &0.145 &0.145 &0.145\\ \hline S12 &0.178 &0.178 &0.178 &0.178 &0.178 &0.178 &0.178 &0.1044 &0.1222 &0.178 &0.178 &1 &0.178 &0.1646 &0.1894 &0.178 &0.178 &0.1868\\ \hline S13 &0.1583 &0.1583 &0.1583 &0.1583 &0.1583 &0.1583 &0.1583 &0.1044 &0.1222 &0.1583 &0.1583 &0.1583 &1 &0.1583 &0.1583 &0.1583 &0.1583 &0.1583\\ \hline S14 &0.1803 &0.182 &0.1803 &0.182 &0.182 &0.182 &0.1803 &0.1044 &0.1222 &0.182 &0.1803 &0.182 &0.1803 &1 &0.1965 &0.1803 &0.182 &0.1943\\ \hline S15 &0.1255 &0.1255 &0.1255 &0.1255 &0.1255 &0.1255 &0.1255 &0.1044 &0.1222 &0.1255 &0.1255 &0.1255 &0.1255 &0.1255 &1 &0.1255 &0.1255 &0.1255\\ \hline S16 &0.1823 &0.1936 &0.1823 &0.1837 &0.1854 &0.1903 &0.1823 &0.1044 &0.1222 &0.183 &0.1823 &0.1837 &0.1823 &0.1646 &0.1936 &1 &0.1837 &0.1936\\ \hline S17 &0.1803 &0.1836 &0.1803 &0.1836 &0.1828 &0.1836 &0.1803 &0.1044 &0.1222 &0.183 &0.1803 &0.1836 &0.1803 &0.1646 &0.1836 &0.1803 &1 &0.1896\\ \hline S18 &0.178 &0.178 &0.178 &0.178 &0.178 &0.178 &0.178 &0.1044 &0.1222 &0.178 &0.178 &0.178 &0.178 &0.1646 &0.178 &0.178 &0.178 &1\\ \hline \end{array} $$

模糊可达矩阵FR中阈值集合分析

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。

63个结构数量分布图（瀑布图）

特征结构分析

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 63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	特征阈值	聚类对应截距$\lambda $区段	该结构的数目	互不连通区域数目	层级数	系统包含几个回路	最大回路要素数目
1	0.10443	0<$\lambda$<0.10443	17	1	1	1	18
2	0.12223	0.10443<$\lambda$<0.12223	17	1	2	1	17
3	0.12555	0.12223<$\lambda$<0.12555	15	1	2	1	16
4	0.14503	0.12555<$\lambda$<0.14503	15	1	3	1	15
5	0.15827	0.14503<$\lambda$<0.15827	15	1	3	1	14
6	0.1646	0.15827<$\lambda$<0.1646	14	1	3	1	13
7	0.17349	0.1646<$\lambda$<0.17349	15	1	3	1	12
8	0.17802	0.17349<$\lambda$<0.17802	49	2	3	1	12
9	0.18033	0.17802<$\lambda$<0.18033	36	2	5	1	8
10	0.18196	0.18033<$\lambda$<0.18196	7	2	5	2	4
11	0.18226	0.18196<$\lambda$<0.18226	5	2	5	2	4
12	0.18276	0.18226<$\lambda$<0.18276	5	2	6	2	4
13	0.18297	0.18276<$\lambda$<0.18297	6	2	6	2	4
14	0.18364	0.18297<$\lambda$<0.18364	5	2	5	2	4
15	0.18368	0.18364<$\lambda$<0.18368	11	2	5	2	3
16	0.18459	0.18368<$\lambda$<0.18459	1	2	4	2	3
17	0.18535	0.18459<$\lambda$<0.18535	1	2	4	2	3
18	0.18682	0.18535<$\lambda$<0.18682	1	2	4	2	3
19	0.18727	0.18682<$\lambda$<0.18727	2	2	4	2	3
20	0.18944	0.18727<$\lambda$<0.18944	1	2	4	2	3
21	0.18964	0.18944<$\lambda$<0.18964	1	2	4	2	3
22	0.19029	0.18964<$\lambda$<0.19029	4	2	4	2	3
23	0.19034	0.19029<$\lambda$<0.19034	1	2	4	1	3
24	0.19253	0.19034<$\lambda$<0.19253	8	2	4	1	3
25	0.19321	0.19253<$\lambda$<0.19321	1	2	5	1	2
26	0.19347	0.19321<$\lambda$<0.19347	2	2	5	1	2
27	0.19361	0.19347<$\lambda$<0.19361	3	2	5	1	2
28	0.19409	0.19361<$\lambda$<0.19409	3	2	5	1	2
29	0.19431	0.19409<$\lambda$<0.19431	1	2	4	1	2
30	0.19577	0.19431<$\lambda$<0.19577	1	2	4	1	2
31	0.1965	0.19577<$\lambda$<0.1965	1	2	4	1	2
32	0.19665	0.1965<$\lambda$<0.19665	1	3	4	1	2
33	0.19738	0.19665<$\lambda$<0.19738	1	3	4	1	2
34	0.19827	0.19738<$\lambda$<0.19827	1	3	4	1	2
35	0.19879	0.19827<$\lambda$<0.19879	2	3	4	1	2
36	0.19911	0.19879<$\lambda$<0.19911	2	4	4	1	2
37	0.20039	0.19911<$\lambda$<0.20039	1	5	4	1	2
38	0.20122	0.20039<$\lambda$<0.20122	2	5	4	1	2
39	0.20154	0.20122<$\lambda$<0.20154	1	5	3	1	2
40	0.20171	0.20154<$\lambda$<0.20171	1	5	3	1	2
41	0.20238	0.20171<$\lambda$<0.20238	3	5	3	1	2
42	0.20291	0.20238<$\lambda$<0.20291	1	6	3	1	2
43	0.2046	0.20291<$\lambda$<0.2046	1	6	3	1	2
44	0.20539	0.2046<$\lambda$<0.20539	1	6	3	1	2
45	0.20556	0.20539<$\lambda$<0.20556	2	6	3	1	2
46	0.20572	0.20556<$\lambda$<0.20572	2	7	3	1	2
47	0.20616	0.20572<$\lambda$<0.20616	2	7	3	1	2
48	0.20682	0.20616<$\lambda$<0.20682	1	8	3	1	2
49	0.20955	0.20682<$\lambda$<0.20955	1	9	3	1	2
50	0.21405	0.20955<$\lambda$<0.21405	3	9	2	1	2
51	0.21517	0.21405<$\lambda$<0.21517	1	9	3	0	1
52	0.22026	0.21517<$\lambda$<0.22026	1	9	3	0	1
53	0.22252	0.22026<$\lambda$<0.22252	2	9	3	0	1
54	0.22316	0.22252<$\lambda$<0.22316	1	9	2	0	1
55	0.22667	0.22316<$\lambda$<0.22667	1	10	2	0	1
56	0.22685	0.22667<$\lambda$<0.22685	1	11	2	0	1
57	0.22732	0.22685<$\lambda$<0.22732	1	12	2	0	1
58	0.23592	0.22732<$\lambda$<0.23592	1	13	2	0	1
59	0.23914	0.23592<$\lambda$<0.23914	1	14	2	0	1
60	0.24051	0.23914<$\lambda$<0.24051	1	15	2	0	1
61	0.24119	0.24051<$\lambda$<0.24119	1	16	2	0	1
62	0.24753	0.24119<$\lambda$<0.24753	1	17	2	0	1
63	1	0.24753<$\lambda$<1	18	18	1	0	1

选择特征结构的原则

第一、层级数最多的，理由越能体现要素之间的因果关系

层级数目与随着截距值的增加，总体趋势是逐渐增多，随后变少。

第二、孤立系统少的。比如独立区块等于要素的数目这种就没有意义。

独立区域的数目与随着截距值的增加，是单调的递增关系。

第三、系统包含的回路数目，回路数目越多越好

回路数目与截距值的关系是，随着截距值的增加，总体趋势是逐渐增多，随后减少。

第四、没有大回路的，比如最大回路中含5个以上的要素属于大回路

如果存在回路，所有回路中所含的要素数目的最大值，随着截距值的增加，是单调的递减关系。

第五、在瀑布图中，数目大的，即结构数量多的。

某个结构的数目，同截距值的大小，没有必然的联系。

上面五项原则会发现，对于T矩阵来说，截距通常是在平均数+标准差附近；对于模糊可达矩阵FR来说，截距通常是FR（去掉主对角线的值）的平均数附近

按照上述原则选取其中排名最靠前的五个结构

序号	聚类对应截距$\lambda $区段	该结构的数目	互不连通区域数目	层级数	包含回路数目	最大回路要素数目
13	0.18276<$\lambda$<0.18297	6	2	6	2	4
12	0.18226<$\lambda$<0.18276	5	2	6	2	4
15	0.18364<$\lambda$<0.18368	11	2	5	2	3
10	0.18033<$\lambda$<0.18196	7	2	5	2	4
11	0.18196<$\lambda$<0.18226	5	2	5	2	4

T-AISM

前置流程图说明

DEMATEL-T-AISM流程图与说明