特征结构的计算与说明

原始矩阵（直接影响矩阵）为

$$Ori=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{18 \times18}} &S1 &S2 &S3 &S4 &S5 &S6 &S7 &S8 &S9 &S10 &S11 &S12 &S13 &S14 &S15 &S16 &S17 &S18\\ \hline S1 &0 &8 &0 &8 &8 &8 &5 &0 &8 &5 &11 &8 &5 &5 &5 &3 &3 &9\\ \hline S2 &0 &0 &0 &5 &8 &8 &6 &11 &6 &3 &3 &5 &5 &0 &0 &3 &3 &9\\ \hline S3 &0 &8 &0 &11 &0 &0 &6 &11 &3 &0 &3 &3 &5 &3 &0 &5 &0 &11\\ \hline S4 &3 &3 &3 &0 &6 &6 &0 &0 &0 &0 &0 &0 &0 &8 &8 &6 &6 &6\\ \hline S5 &3 &6 &0 &6 &0 &0 &6 &5 &8 &9 &9 &6 &9 &6 &9 &0 &0 &6\\ \hline S6 &6 &6 &9 &0 &3 &0 &0 &8 &8 &8 &8 &3 &6 &9 &6 &3 &3 &3\\ \hline S7 &6 &3 &9 &6 &3 &6 &0 &12 &0 &0 &0 &0 &9 &9 &9 &6 &6 &12\\ \hline S8 &0 &12 &12 &0 &6 &10 &12 &0 &12 &4 &4 &9 &9 &9 &3 &3 &3 &3\\ \hline S9 &10 &6 &3 &3 &9 &9 &0 &12 &0 &6 &7 &3 &6 &7 &3 &3 &0 &6\\ \hline S10 &7 &2 &0 &6 &10 &6 &0 &3 &7 &0 &0 &6 &3 &0 &4 &0 &3 &0\\ \hline S11 &9 &3 &3 &3 &0 &9 &0 &3 &3 &0 &0 &3 &9 &12 &6 &6 &6 &12\\ \hline S12 &9 &6 &3 &6 &6 &3 &0 &9 &3 &6 &3 &0 &3 &3 &6 &3 &12 &3\\ \hline S13 &6 &6 &6 &6 &6 &9 &3 &9 &6 &0 &12 &3 &0 &9 &12 &9 &12 &12\\ \hline S14 &6 &0 &3 &8 &5 &7 &7 &7 &5 &0 &9 &4 &9 &0 &9 &6 &9 &3\\ \hline S15 &6 &0 &0 &9 &9 &6 &9 &3 &3 &0 &6 &6 &9 &3 &0 &0 &0 &0\\ \hline S16 &3 &3 &0 &0 &0 &3 &3 &3 &3 &0 &3 &3 &3 &0 &0 &0 &0 &3\\ \hline S17 &3 &0 &7 &7 &3 &3 &3 &7 &8 &6 &6 &7 &6 &6 &6 &6 &0 &8\\ \hline S18 &3 &0 &6 &3 &6 &3 &3 &3 &6 &0 &6 &3 &6 &3 &0 &3 &9 &0\\ \hline \end{array} $$

规范直接关系矩阵求解过程 $$ \require{cancel} \require{AMScd} \begin{CD} O @>>>N \\ \end{CD} $$

$$\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 &0.063 &0 &0.063 &0.063 &0.063 &0.04 &0 &0.063 &0.04 &0.087 &0.063 &0.04 &0.04 &0.04 &0.024 &0.024 &0.071\\ \hline S2 &0 &0 &0 &0.04 &0.063 &0.063 &0.048 &0.087 &0.048 &0.024 &0.024 &0.04 &0.04 &0 &0 &0.024 &0.024 &0.071\\ \hline S3 &0 &0.063 &0 &0.087 &0 &0 &0.048 &0.087 &0.024 &0 &0.024 &0.024 &0.04 &0.024 &0 &0.04 &0 &0.087\\ \hline S4 &0.024 &0.024 &0.024 &0 &0.048 &0.048 &0 &0 &0 &0 &0 &0 &0 &0.063 &0.063 &0.048 &0.048 &0.048\\ \hline S5 &0.024 &0.048 &0 &0.048 &0 &0 &0.048 &0.04 &0.063 &0.071 &0.071 &0.048 &0.071 &0.048 &0.071 &0 &0 &0.048\\ \hline S6 &0.048 &0.048 &0.071 &0 &0.024 &0 &0 &0.063 &0.063 &0.063 &0.063 &0.024 &0.048 &0.071 &0.048 &0.024 &0.024 &0.024\\ \hline S7 &0.048 &0.024 &0.071 &0.048 &0.024 &0.048 &0 &0.095 &0 &0 &0 &0 &0.071 &0.071 &0.071 &0.048 &0.048 &0.095\\ \hline S8 &0 &0.095 &0.095 &0 &0.048 &0.079 &0.095 &0 &0.095 &0.032 &0.032 &0.071 &0.071 &0.071 &0.024 &0.024 &0.024 &0.024\\ \hline S9 &0.079 &0.048 &0.024 &0.024 &0.071 &0.071 &0 &0.095 &0 &0.048 &0.056 &0.024 &0.048 &0.056 &0.024 &0.024 &0 &0.048\\ \hline S10 &0.056 &0.016 &0 &0.048 &0.079 &0.048 &0 &0.024 &0.056 &0 &0 &0.048 &0.024 &0 &0.032 &0 &0.024 &0\\ \hline S11 &0.071 &0.024 &0.024 &0.024 &0 &0.071 &0 &0.024 &0.024 &0 &0 &0.024 &0.071 &0.095 &0.048 &0.048 &0.048 &0.095\\ \hline S12 &0.071 &0.048 &0.024 &0.048 &0.048 &0.024 &0 &0.071 &0.024 &0.048 &0.024 &0 &0.024 &0.024 &0.048 &0.024 &0.095 &0.024\\ \hline S13 &0.048 &0.048 &0.048 &0.048 &0.048 &0.071 &0.024 &0.071 &0.048 &0 &0.095 &0.024 &0 &0.071 &0.095 &0.071 &0.095 &0.095\\ \hline S14 &0.048 &0 &0.024 &0.063 &0.04 &0.056 &0.056 &0.056 &0.04 &0 &0.071 &0.032 &0.071 &0 &0.071 &0.048 &0.071 &0.024\\ \hline S15 &0.048 &0 &0 &0.071 &0.071 &0.048 &0.071 &0.024 &0.024 &0 &0.048 &0.048 &0.071 &0.024 &0 &0 &0 &0\\ \hline S16 &0.024 &0.024 &0 &0 &0 &0.024 &0.024 &0.024 &0.024 &0 &0.024 &0.024 &0.024 &0 &0 &0 &0 &0.024\\ \hline S17 &0.024 &0 &0.056 &0.056 &0.024 &0.024 &0.024 &0.056 &0.063 &0.048 &0.048 &0.056 &0.048 &0.048 &0.048 &0.048 &0 &0.063\\ \hline S18 &0.024 &0 &0.048 &0.024 &0.048 &0.024 &0.024 &0.024 &0.048 &0 &0.048 &0.024 &0.048 &0.024 &0 &0.024 &0.071 &0\\ \hline \end{array} $$

综合影响矩阵求解过程 $$\begin{CD} N @>>>T \\ \end{CD} $$

　　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 &0.088 &0.133 &0.068 &0.146 &0.153 &0.163 &0.1 &0.108 &0.153 &0.09 &0.182 &0.134 &0.145 &0.14 &0.131 &0.092 &0.107 &0.177\\ \hline S2 &0.066 &0.064 &0.064 &0.101 &0.133 &0.141 &0.099 &0.171 &0.124 &0.067 &0.1 &0.098 &0.124 &0.083 &0.073 &0.077 &0.088 &0.153\\ \hline S3 &0.053 &0.115 &0.055 &0.139 &0.063 &0.073 &0.096 &0.159 &0.087 &0.03 &0.086 &0.073 &0.111 &0.093 &0.06 &0.09 &0.061 &0.161\\ \hline S4 &0.066 &0.059 &0.059 &0.049 &0.094 &0.096 &0.04 &0.056 &0.052 &0.027 &0.057 &0.042 &0.06 &0.112 &0.109 &0.082 &0.087 &0.101\\ \hline S5 &0.105 &0.113 &0.063 &0.127 &0.089 &0.1 &0.107 &0.136 &0.145 &0.111 &0.158 &0.114 &0.168 &0.139 &0.155 &0.064 &0.079 &0.145\\ \hline S6 &0.124 &0.119 &0.132 &0.084 &0.11 &0.098 &0.066 &0.163 &0.151 &0.107 &0.154 &0.096 &0.148 &0.16 &0.128 &0.087 &0.096 &0.125\\ \hline S7 &0.121 &0.099 &0.144 &0.133 &0.111 &0.145 &0.075 &0.196 &0.096 &0.045 &0.101 &0.076 &0.176 &0.167 &0.157 &0.117 &0.127 &0.198\\ \hline S8 &0.099 &0.182 &0.177 &0.104 &0.15 &0.193 &0.17 &0.141 &0.199 &0.09 &0.145 &0.153 &0.195 &0.184 &0.129 &0.106 &0.118 &0.155\\ \hline S9 &0.156 &0.126 &0.093 &0.107 &0.16 &0.171 &0.071 &0.193 &0.1 &0.099 &0.155 &0.101 &0.154 &0.153 &0.113 &0.089 &0.08 &0.151\\ \hline S10 &0.106 &0.065 &0.04 &0.099 &0.136 &0.107 &0.04 &0.087 &0.113 &0.038 &0.064 &0.094 &0.087 &0.062 &0.089 &0.039 &0.069 &0.064\\ \hline S11 &0.144 &0.088 &0.089 &0.102 &0.082 &0.161 &0.063 &0.118 &0.11 &0.043 &0.097 &0.092 &0.166 &0.181 &0.128 &0.111 &0.124 &0.188\\ \hline S12 &0.137 &0.112 &0.083 &0.123 &0.127 &0.111 &0.062 &0.157 &0.11 &0.093 &0.109 &0.07 &0.116 &0.108 &0.124 &0.081 &0.158 &0.116\\ \hline S13 &0.15 &0.138 &0.137 &0.155 &0.157 &0.196 &0.112 &0.201 &0.166 &0.062 &0.218 &0.12 &0.14 &0.197 &0.203 &0.157 &0.191 &0.228\\ \hline S14 &0.132 &0.077 &0.098 &0.149 &0.127 &0.157 &0.122 &0.16 &0.132 &0.05 &0.17 &0.106 &0.179 &0.108 &0.165 &0.119 &0.151 &0.137\\ \hline S15 &0.112 &0.06 &0.055 &0.135 &0.137 &0.124 &0.118 &0.104 &0.092 &0.039 &0.123 &0.1 &0.15 &0.106 &0.079 &0.055 &0.066 &0.087\\ \hline S16 &0.052 &0.05 &0.026 &0.027 &0.031 &0.059 &0.045 &0.061 &0.055 &0.017 &0.057 &0.048 &0.059 &0.035 &0.03 &0.024 &0.029 &0.061\\ \hline S17 &0.102 &0.071 &0.119 &0.134 &0.108 &0.117 &0.085 &0.152 &0.147 &0.09 &0.136 &0.122 &0.144 &0.138 &0.129 &0.11 &0.076 &0.16\\ \hline S18 &0.08 &0.053 &0.096 &0.083 &0.103 &0.09 &0.067 &0.098 &0.11 &0.035 &0.115 &0.074 &0.119 &0.094 &0.064 &0.073 &0.123 &0.079\\ \hline \end{array} $$

从综合影响矩阵$T$到ISM的处理过程简介

模糊相乘矩阵有$ \tilde B=T+I$

$$\tilde B=\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 &0.1331 &0.0683 &0.1463 &0.1531 &0.1625 &0.0999 &0.1077 &0.1529 &0.0898 &0.1819 &0.1336 &0.1454 &0.1397 &0.1313 &0.0918 &0.1072 &0.1773\\ \hline S2 &0.0657 &1 &0.0636 &0.1012 &0.133 &0.1409 &0.0993 &0.1705 &0.1241 &0.0666 &0.1003 &0.0978 &0.1243 &0.0835 &0.0729 &0.0772 &0.0883 &0.1533\\ \hline S3 &0.0528 &0.1151 &1 &0.1393 &0.0633 &0.0734 &0.0955 &0.1586 &0.0873 &0.0296 &0.0861 &0.0725 &0.1111 &0.0934 &0.0603 &0.0896 &0.0612 &0.1613\\ \hline S4 &0.0662 &0.0593 &0.0588 &1 &0.0937 &0.0965 &0.0399 &0.0562 &0.0519 &0.0272 &0.0569 &0.042 &0.0603 &0.1116 &0.1093 &0.0819 &0.0867 &0.1007\\ \hline S5 &0.1049 &0.1133 &0.0634 &0.1275 &1 &0.0996 &0.1072 &0.1365 &0.1455 &0.1115 &0.1582 &0.1144 &0.168 &0.139 &0.1554 &0.0641 &0.0794 &0.1455\\ \hline S6 &0.124 &0.1191 &0.1323 &0.0841 &0.1095 &1 &0.0665 &0.1627 &0.1513 &0.1068 &0.1544 &0.0962 &0.1476 &0.1599 &0.128 &0.0872 &0.0964 &0.1247\\ \hline S7 &0.1211 &0.099 &0.1443 &0.1331 &0.1114 &0.145 &1 &0.1955 &0.0965 &0.0448 &0.1013 &0.0761 &0.1762 &0.167 &0.1565 &0.1169 &0.1269 &0.1982\\ \hline S8 &0.0986 &0.1825 &0.1766 &0.1044 &0.1504 &0.1933 &0.17 &1 &0.1988 &0.0899 &0.1445 &0.1529 &0.1952 &0.1842 &0.1289 &0.1058 &0.118 &0.1555\\ \hline S9 &0.1565 &0.1261 &0.0931 &0.1066 &0.1597 &0.1709 &0.0705 &0.1934 &1 &0.0986 &0.1549 &0.1013 &0.1536 &0.1532 &0.113 &0.0892 &0.0796 &0.1514\\ \hline S10 &0.106 &0.0654 &0.0401 &0.0992 &0.1359 &0.1068 &0.04 &0.0871 &0.1131 &1 &0.0639 &0.0938 &0.0873 &0.0624 &0.0895 &0.0389 &0.0694 &0.0642\\ \hline S11 &0.1438 &0.0884 &0.0886 &0.1023 &0.0824 &0.1605 &0.0625 &0.118 &0.1104 &0.0432 &1 &0.0915 &0.1656 &0.1807 &0.1282 &0.1114 &0.1241 &0.1882\\ \hline S12 &0.1373 &0.1125 &0.0833 &0.1228 &0.1274 &0.1113 &0.0619 &0.1575 &0.1097 &0.093 &0.109 &1 &0.1155 &0.1083 &0.1238 &0.0814 &0.1575 &0.1159\\ \hline S13 &0.1498 &0.1384 &0.1373 &0.1549 &0.1571 &0.1959 &0.112 &0.2014 &0.1661 &0.062 &0.2177 &0.1197 &1 &0.1965 &0.2028 &0.157 &0.1912 &0.2282\\ \hline S14 &0.1317 &0.0774 &0.0983 &0.1488 &0.1275 &0.1572 &0.1222 &0.1601 &0.1324 &0.0498 &0.1702 &0.1063 &0.1786 &1 &0.165 &0.1191 &0.1507 &0.1367\\ \hline S15 &0.1119 &0.0601 &0.0553 &0.1349 &0.1366 &0.1237 &0.1178 &0.1037 &0.0919 &0.0391 &0.1228 &0.1 &0.1502 &0.1063 &1 &0.0552 &0.066 &0.0875\\ \hline S16 &0.0515 &0.0504 &0.0258 &0.0271 &0.0306 &0.0588 &0.0449 &0.0606 &0.0552 &0.0174 &0.0566 &0.0479 &0.0591 &0.0349 &0.0297 &1 &0.0289 &0.0612\\ \hline S17 &0.102 &0.0713 &0.1192 &0.1341 &0.1076 &0.117 &0.0851 &0.1517 &0.1465 &0.0897 &0.1356 &0.1221 &0.144 &0.1382 &0.1289 &0.1105 &1 &0.1596\\ \hline S18 &0.0795 &0.0526 &0.0957 &0.0828 &0.1031 &0.0899 &0.0674 &0.0979 &0.1097 &0.0352 &0.1145 &0.0736 &0.1187 &0.0941 &0.0638 &0.0729 &0.1231 &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。

$$\tilde R=\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 &0.1786 &0.1766 &0.1549 &0.1597 &0.1786 &0.17 &0.1786 &0.1786 &0.1115 &0.1819 &0.1529 &0.1786 &0.1807 &0.1786 &0.157 &0.1786 &0.1819\\ \hline S2 &0.1565 &1 &0.1705 &0.1549 &0.1597 &0.1705 &0.17 &0.1705 &0.1705 &0.1115 &0.1705 &0.1529 &0.1705 &0.1705 &0.1705 &0.157 &0.1705 &0.1705\\ \hline S3 &0.1565 &0.1586 &1 &0.1549 &0.1586 &0.1586 &0.1586 &0.1586 &0.1586 &0.1115 &0.1586 &0.1529 &0.1586 &0.1586 &0.1586 &0.157 &0.1586 &0.1613\\ \hline S4 &0.1116 &0.1116 &0.1116 &1 &0.1116 &0.1116 &0.1116 &0.1116 &0.1116 &0.1115 &0.1116 &0.1116 &0.1116 &0.1116 &0.1116 &0.1116 &0.1116 &0.1116\\ \hline S5 &0.1565 &0.168 &0.168 &0.1549 &1 &0.168 &0.168 &0.168 &0.168 &0.1115 &0.168 &0.1529 &0.168 &0.168 &0.168 &0.157 &0.168 &0.168\\ \hline S6 &0.1565 &0.1627 &0.1627 &0.1549 &0.1597 &1 &0.1627 &0.1627 &0.1627 &0.1115 &0.1627 &0.1529 &0.1627 &0.1627 &0.1627 &0.157 &0.1627 &0.1627\\ \hline S7 &0.1565 &0.1825 &0.1766 &0.1549 &0.1597 &0.1952 &1 &0.1955 &0.1955 &0.1115 &0.1952 &0.1529 &0.1952 &0.1952 &0.1952 &0.157 &0.1912 &0.1982\\ \hline S8 &0.1565 &0.1825 &0.1766 &0.1549 &0.1597 &0.1952 &0.17 &1 &0.1988 &0.1115 &0.1952 &0.1529 &0.1952 &0.1952 &0.1952 &0.157 &0.1912 &0.1952\\ \hline S9 &0.1565 &0.1825 &0.1766 &0.1549 &0.1597 &0.1934 &0.17 &0.1934 &1 &0.1115 &0.1934 &0.1529 &0.1934 &0.1934 &0.1934 &0.157 &0.1912 &0.1934\\ \hline S10 &0.1359 &0.1359 &0.1359 &0.1359 &0.1359 &0.1359 &0.1359 &0.1359 &0.1359 &1 &0.1359 &0.1359 &0.1359 &0.1359 &0.1359 &0.1359 &0.1359 &0.1359\\ \hline S11 &0.1565 &0.1786 &0.1766 &0.1549 &0.1597 &0.1786 &0.17 &0.1786 &0.1786 &0.1115 &1 &0.1529 &0.1786 &0.1807 &0.1786 &0.157 &0.1786 &0.1882\\ \hline S12 &0.1565 &0.1575 &0.1575 &0.1549 &0.1575 &0.1575 &0.1575 &0.1575 &0.1575 &0.1115 &0.1575 &1 &0.1575 &0.1575 &0.1575 &0.157 &0.1575 &0.1575\\ \hline S13 &0.1565 &0.1825 &0.1766 &0.1549 &0.1597 &0.1959 &0.17 &0.2014 &0.1988 &0.1115 &0.2177 &0.1529 &1 &0.1965 &0.2028 &0.157 &0.1912 &0.2282\\ \hline S14 &0.1565 &0.1786 &0.1766 &0.1549 &0.1597 &0.1786 &0.17 &0.1786 &0.1786 &0.1115 &0.1786 &0.1529 &0.1786 &1 &0.1786 &0.157 &0.1786 &0.1786\\ \hline S15 &0.1502 &0.1502 &0.1502 &0.1502 &0.1502 &0.1502 &0.1502 &0.1502 &0.1502 &0.1115 &0.1502 &0.1502 &0.1502 &0.1502 &1 &0.1502 &0.1502 &0.1502\\ \hline S16 &0.0612 &0.0612 &0.0612 &0.0612 &0.0612 &0.0612 &0.0612 &0.0612 &0.0612 &0.0612 &0.0612 &0.0612 &0.0612 &0.0612 &0.0612 &1 &0.0612 &0.0612\\ \hline S17 &0.1517 &0.1517 &0.1517 &0.1517 &0.1517 &0.1517 &0.1517 &0.1517 &0.1517 &0.1115 &0.1517 &0.1517 &0.1517 &0.1517 &0.1517 &0.1517 &1 &0.1596\\ \hline S18 &0.1231 &0.1231 &0.1231 &0.1231 &0.1231 &0.1231 &0.1231 &0.1231 &0.1231 &0.1115 &0.1231 &0.1231 &0.1231 &0.1231 &0.1231 &0.1231 &0.1231 &1\\ \hline \end{array} $$

由阈值集合$\ddot \Delta $　得出综合影响矩阵$T$对应 40个结构。

序号	阈值集合中——特征阈值	聚类特征-对应截距$\lambda $数值区段
1	0.06122	0<$\lambda$<0.06122
2	0.11149	0.06122<$\lambda$<0.11149
3	0.11157	0.11149<$\lambda$<0.11157
4	0.12314	0.11157<$\lambda$<0.12314
5	0.13592	0.12314<$\lambda$<0.13592
6	0.1502	0.13592<$\lambda$<0.1502
7	0.15172	0.1502<$\lambda$<0.15172
8	0.15285	0.15172<$\lambda$<0.15285
9	0.15489	0.15285<$\lambda$<0.15489
10	0.15649	0.15489<$\lambda$<0.15649
11	0.15696	0.15649<$\lambda$<0.15696
12	0.15748	0.15696<$\lambda$<0.15748
13	0.1575	0.15748<$\lambda$<0.1575
14	0.1586	0.1575<$\lambda$<0.1586
15	0.15957	0.1586<$\lambda$<0.15957
16	0.15973	0.15957<$\lambda$<0.15973
17	0.16127	0.15973<$\lambda$<0.16127
18	0.16269	0.16127<$\lambda$<0.16269
19	0.16801	0.16269<$\lambda$<0.16801
20	0.16998	0.16801<$\lambda$<0.16998
21	0.17055	0.16998<$\lambda$<0.17055
22	0.17657	0.17055<$\lambda$<0.17657
23	0.17857	0.17657<$\lambda$<0.17857
24	0.18068	0.17857<$\lambda$<0.18068
25	0.18194	0.18068<$\lambda$<0.18194
26	0.18249	0.18194<$\lambda$<0.18249
27	0.18824	0.18249<$\lambda$<0.18824
28	0.19116	0.18824<$\lambda$<0.19116
29	0.19335	0.19116<$\lambda$<0.19335
30	0.19524	0.19335<$\lambda$<0.19524
31	0.19554	0.19524<$\lambda$<0.19554
32	0.19592	0.19554<$\lambda$<0.19592
33	0.1965	0.19592<$\lambda$<0.1965
34	0.19816	0.1965<$\lambda$<0.19816
35	0.19883	0.19816<$\lambda$<0.19883
36	0.20139	0.19883<$\lambda$<0.20139
37	0.20281	0.20139<$\lambda$<0.20281
38	0.21773	0.20281<$\lambda$<0.21773
39	0.22816	0.21773<$\lambda$<0.22816
40	1	0.22816<$\lambda$<1

特征结构——不含孤立子系统

截距范围：0.123138738<$\lambda$<0.135922213

$$A_t=\begin{array} {c|c|c|c|c|c|c|c}{M_{18 \times18}} &S1 &S2 &S3 &S4 &S5 &S6 &S7 &S8 &S9 &S10 &S11 &S12 &S13 &S14 &S15 &S16 &S17 &S18\\ \hline S1 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S2 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S3 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S4 & & & &1 & & & & & & & & & & & & & & \\ \hline S5 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S6 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S7 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S8 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S9 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S10 &1 &1 &1 &1 &1 &1 &1 &1 &1 &1 &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S11 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S12 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S13 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S14 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S15 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S16 & & & & & & & & & & & & & & & &1 & & \\ \hline S17 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S18 & & & & & & & & & & & & & & & & & &1\\ \hline \end{array} $$

$$WS_t=\begin{array}{c|c|c|c|c|c|c}{M_{18 \times18}} &S1 &S2 &S3 &S4 &S5 &S6 &S7 &S8 &S9 &S10 &S11 &S12 &S13 &S14 &S15 &S16 &S17 &S18\\ \hline S1 &0 &1 &1 &0.1463 &1 &1 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &0.1773\\ \hline S2 &1 &0 &1 &0 &1 &1 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &0.1533\\ \hline S3 &1 &1 &0 &0.1393 &1 &1 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &0.1613\\ \hline S4 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline S5 &1 &1 &1 &0 &0 &1 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &0.1455\\ \hline S6 &1 &1 &1 &0 &1 &0 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &0\\ \hline S7 &1 &1 &1 &0 &1 &1 &0 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &0.1982\\ \hline S8 &1 &1 &1 &0 &1 &1 &1 &0 &1 &0 &1 &1 &1 &1 &1 &0 &1 &0.1555\\ \hline S9 &1 &1 &1 &0 &1 &1 &1 &1 &0 &0 &1 &1 &1 &1 &1 &0 &1 &0.1514\\ \hline S10 &0 &0 &0 &0 &0.1359 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline S11 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &0 &1 &1 &1 &1 &0 &1 &0.1882\\ \hline S12 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &0 &1 &1 &1 &0 &1 &0\\ \hline S13 &1 &1 &1 &0.1549 &1 &1 &1 &1 &1 &0 &1 &1 &0 &1 &1 &0.157 &1 &0.2282\\ \hline S14 &1 &1 &1 &0.1488 &1 &1 &1 &1 &1 &0 &1 &1 &1 &0 &1 &0 &1 &0.1367\\ \hline S15 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &1 &1 &1 &0 &0 &1 &0\\ \hline S16 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline S17 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &0 &0.1596\\ \hline S18 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline \end{array} $$

含孤立子系统的特征结构

截距范围：0.135922213<$\lambda$<0.150204661

$$A_s=\begin{array} {c|c|c|c|c|c|c|c}{M_{18 \times18}} &S1 &S2 &S3 &S4 &S5 &S6 &S7 &S8 &S9 &S10 &S11 &S12 &S13 &S14 &S15 &S16 &S17 &S18\\ \hline S1 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S2 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S3 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S4 & & & &1 & & & & & & & & & & & & & & \\ \hline S5 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S6 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S7 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S8 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S9 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S10 & & & & & & & & & &1 & & & & & & & & \\ \hline S11 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S12 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S13 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S14 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S15 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S16 & & & & & & & & & & & & & & & &1 & & \\ \hline S17 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S18 & & & & & & & & & & & & & & & & & &1\\ \hline \end{array} $$

$$WS_s=\begin{array}{c|c|c|c|c|c|c}{M_{18 \times18}} &S1 &S2 &S3 &S4 &S5 &S6 &S7 &S8 &S9 &S10 &S11 &S12 &S13 &S14 &S15 &S16 &S17 &S18\\ \hline S1 &0 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &0.1773\\ \hline S2 &1 &0 &1 &0 &1 &1 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &0.1533\\ \hline S3 &1 &1 &0 &0 &1 &1 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &0.1613\\ \hline S4 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline S5 &1 &1 &1 &0 &0 &1 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &0\\ \hline S6 &1 &1 &1 &0 &1 &0 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &0\\ \hline S7 &1 &1 &1 &0 &1 &1 &0 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &0.1982\\ \hline S8 &1 &1 &1 &0 &1 &1 &1 &0 &1 &0 &1 &1 &1 &1 &1 &0 &1 &0.1555\\ \hline S9 &1 &1 &1 &0 &1 &1 &1 &1 &0 &0 &1 &1 &1 &1 &1 &0 &1 &0.1514\\ \hline S10 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline S11 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &0 &1 &1 &1 &1 &0 &1 &0.1882\\ \hline S12 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &0 &1 &1 &1 &0 &1 &0\\ \hline S13 &1 &1 &1 &0.1549 &1 &1 &1 &1 &1 &0 &1 &1 &0 &1 &1 &0.157 &1 &0.2282\\ \hline S14 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &1 &1 &0 &1 &0 &1 &0\\ \hline S15 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &1 &1 &1 &0 &0 &1 &0\\ \hline S16 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline S17 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &0 &0.1596\\ \hline S18 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline \end{array} $$

由综合影响矩阵求影响度、被影响度、中心度、原因度 \begin{CD} T @>>>\{D|C|M|R \} \\ \end{CD}

　　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

$$\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{18 \times4}} &Di &Ci &Mi &Ri\\ \hline S1 &2.31 &1.891 &4.201 &0.418\\ \hline S2 &1.826 &1.728 &3.554 &0.098\\ \hline S3 &1.605 &1.599 &3.204 &0.006\\ \hline S4 &1.248 &1.998 &3.246 &-0.75\\ \hline S5 &2.123 &2.072 &4.195 &0.051\\ \hline S6 &2.148 &2.301 &4.449 &-0.153\\ \hline S7 &2.285 &1.538 &3.823 &0.747\\ \hline S8 &2.691 &2.46 &5.151 &0.23\\ \hline S9 &2.271 &2.143 &4.414 &0.128\\ \hline S10 &1.401 &1.132 &2.533 &0.269\\ \hline S11 &2.087 &2.226 &4.313 &-0.139\\ \hline S12 &1.998 &1.712 &3.71 &0.287\\ \hline S13 &2.928 &2.441 &5.368 &0.487\\ \hline S14 &2.34 &2.261 &4.6 &0.079\\ \hline S15 &1.741 &2.066 &3.807 &-0.325\\ \hline S16 &0.764 &1.573 &2.338 &-0.809\\ \hline S17 &2.139 &1.831 &3.97 &0.309\\ \hline S18 &1.553 &2.488 &4.041 &-0.935\\ \hline \end{array} $$

无孤立系统的中心度、原因度坐标体系综合影响关系特征结构图表

有孤立系统的中心度、原因度坐标体系综合影响关系特征结构图表

特征结构论文写作相关注意事项

数据来源即直接影响矩阵$O$的详细说明。直接影响矩阵O是整个流程中的输入。

参数选择。规范化（归一化）方法需要重点说明，采用不同的归一化方法会导致不同的结果。

输出结果为，1、带影响值的对抗层级拓扑图。2、带影响值的M,R直角坐标图

模糊可达矩阵，及阈值集合是一个重点。即综合影响矩阵$T$与对抗层级拓扑图是1对多的关系。

DEMATEL-ISM联用中特征突变结构的计算

特征结构的计算与说明

原始矩阵（直接影响矩阵）为

规范直接关系矩阵求解过程 $$ \require{cancel} \require{AMScd} \begin{CD} O @>>>N \\ \end{CD} $$

综合影响矩阵求解过程 $$\begin{CD} N @>>>T \\ \end{CD} $$

从综合影响矩阵$T$到ISM的处理过程简介

特征结构——不含孤立子系统

含孤立子系统的特征结构

由综合影响矩阵求影响度、被影响度、中心度、原因度 \begin{CD} T @>>>\{D|C|M|R \} \\ \end{CD}

求解原理

结果

无孤立系统的中心度、原因度坐标体系综合影响关系特征结构图表

有孤立系统的中心度、原因度坐标体系综合影响关系特征结构图表

特征结构论文写作相关注意事项