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 &0.075 &0 &0.075 &0.075 &0.075 &0.047 &0 &0.075 &0.047 &0.104 &0.075 &0.047 &0.047 &0.047 &0.028 &0.028 &0.085\\ \hline S2 &0 &0 &0 &0.047 &0.075 &0.075 &0.057 &0.104 &0.057 &0.028 &0.028 &0.047 &0.047 &0 &0 &0.028 &0.028 &0.085\\ \hline S3 &0 &0.075 &0 &0.104 &0 &0 &0.057 &0.104 &0.028 &0 &0.028 &0.028 &0.047 &0.028 &0 &0.047 &0 &0.104\\ \hline S4 &0.028 &0.028 &0.028 &0 &0.057 &0.057 &0 &0 &0 &0 &0 &0 &0 &0.075 &0.075 &0.057 &0.057 &0.057\\ \hline S5 &0.028 &0.057 &0 &0.057 &0 &0 &0.057 &0.047 &0.075 &0.085 &0.085 &0.057 &0.085 &0.057 &0.085 &0 &0 &0.057\\ \hline S6 &0.057 &0.057 &0.085 &0 &0.028 &0 &0 &0.075 &0.075 &0.075 &0.075 &0.028 &0.057 &0.085 &0.057 &0.028 &0.028 &0.028\\ \hline S7 &0.057 &0.028 &0.085 &0.057 &0.028 &0.057 &0 &0.113 &0 &0 &0 &0 &0.085 &0.085 &0.085 &0.057 &0.057 &0.113\\ \hline S8 &0 &0.113 &0.113 &0 &0.057 &0.094 &0.113 &0 &0.113 &0.038 &0.038 &0.085 &0.085 &0.085 &0.028 &0.028 &0.028 &0.028\\ \hline S9 &0.094 &0.057 &0.028 &0.028 &0.085 &0.085 &0 &0.113 &0 &0.057 &0.066 &0.028 &0.057 &0.066 &0.028 &0.028 &0 &0.057\\ \hline S10 &0.066 &0.019 &0 &0.057 &0.094 &0.057 &0 &0.028 &0.066 &0 &0 &0.057 &0.028 &0 &0.038 &0 &0.028 &0\\ \hline S11 &0.085 &0.028 &0.028 &0.028 &0 &0.085 &0 &0.028 &0.028 &0 &0 &0.028 &0.085 &0.113 &0.057 &0.057 &0.057 &0.113\\ \hline S12 &0.085 &0.057 &0.028 &0.057 &0.057 &0.028 &0 &0.085 &0.028 &0.057 &0.028 &0 &0.028 &0.028 &0.057 &0.028 &0.113 &0.028\\ \hline S13 &0.057 &0.057 &0.057 &0.057 &0.057 &0.085 &0.028 &0.085 &0.057 &0 &0.113 &0.028 &0 &0.085 &0.113 &0.085 &0.113 &0.113\\ \hline S14 &0.057 &0 &0.028 &0.075 &0.047 &0.066 &0.066 &0.066 &0.047 &0 &0.085 &0.038 &0.085 &0 &0.085 &0.057 &0.085 &0.028\\ \hline S15 &0.057 &0 &0 &0.085 &0.085 &0.057 &0.085 &0.028 &0.028 &0 &0.057 &0.057 &0.085 &0.028 &0 &0 &0 &0\\ \hline S16 &0.028 &0.028 &0 &0 &0 &0.028 &0.028 &0.028 &0.028 &0 &0.028 &0.028 &0.028 &0 &0 &0 &0 &0.028\\ \hline S17 &0.028 &0 &0.066 &0.066 &0.028 &0.028 &0.028 &0.066 &0.075 &0.057 &0.057 &0.066 &0.057 &0.057 &0.057 &0.057 &0 &0.075\\ \hline S18 &0.028 &0 &0.057 &0.028 &0.057 &0.028 &0.028 &0.028 &0.057 &0 &0.057 &0.028 &0.057 &0.028 &0 &0.028 &0.085 &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 &0.195 &0.238 &0.157 &0.266 &0.279 &0.302 &0.19 &0.243 &0.282 &0.16 &0.322 &0.239 &0.288 &0.274 &0.254 &0.184 &0.215 &0.327\\ \hline S2 &0.15 &0.143 &0.139 &0.194 &0.236 &0.254 &0.177 &0.295 &0.23 &0.123 &0.205 &0.181 &0.241 &0.187 &0.165 &0.152 &0.175 &0.275\\ \hline S3 &0.123 &0.193 &0.12 &0.228 &0.142 &0.163 &0.165 &0.268 &0.174 &0.071 &0.175 &0.141 &0.212 &0.186 &0.139 &0.159 &0.134 &0.272\\ \hline S4 &0.126 &0.113 &0.11 &0.108 &0.163 &0.172 &0.087 &0.128 &0.116 &0.061 &0.125 &0.093 &0.134 &0.189 &0.182 &0.137 &0.149 &0.181\\ \hline S5 &0.209 &0.21 &0.147 &0.238 &0.198 &0.221 &0.195 &0.269 &0.266 &0.181 &0.287 &0.211 &0.307 &0.266 &0.276 &0.146 &0.177 &0.281\\ \hline S6 &0.231 &0.219 &0.229 &0.188 &0.222 &0.219 &0.149 &0.302 &0.275 &0.177 &0.284 &0.191 &0.284 &0.291 &0.243 &0.174 &0.196 &0.258\\ \hline S7 &0.231 &0.199 &0.249 &0.251 &0.228 &0.28 &0.164 &0.346 &0.216 &0.105 &0.227 &0.171 &0.324 &0.306 &0.282 &0.214 &0.238 &0.351\\ \hline S8 &0.223 &0.313 &0.301 &0.234 &0.293 &0.358 &0.288 &0.307 &0.355 &0.17 &0.297 &0.276 &0.368 &0.346 &0.268 &0.214 &0.243 &0.324\\ \hline S9 &0.274 &0.232 &0.187 &0.219 &0.287 &0.312 &0.158 &0.343 &0.221 &0.171 &0.291 &0.202 &0.298 &0.29 &0.232 &0.18 &0.182 &0.296\\ \hline S10 &0.181 &0.129 &0.094 &0.175 &0.222 &0.194 &0.093 &0.174 &0.197 &0.08 &0.143 &0.162 &0.175 &0.141 &0.167 &0.092 &0.136 &0.148\\ \hline S11 &0.252 &0.179 &0.176 &0.206 &0.186 &0.29 &0.141 &0.245 &0.224 &0.1 &0.215 &0.182 &0.302 &0.312 &0.241 &0.201 &0.228 &0.329\\ \hline S12 &0.24 &0.205 &0.165 &0.227 &0.236 &0.227 &0.138 &0.286 &0.219 &0.158 &0.222 &0.155 &0.238 &0.222 &0.232 &0.161 &0.262 &0.239\\ \hline S13 &0.29 &0.267 &0.26 &0.301 &0.308 &0.37 &0.226 &0.384 &0.325 &0.141 &0.393 &0.244 &0.313 &0.37 &0.363 &0.281 &0.336 &0.418\\ \hline S14 &0.248 &0.176 &0.196 &0.271 &0.25 &0.298 &0.22 &0.307 &0.261 &0.114 &0.311 &0.209 &0.33 &0.24 &0.297 &0.218 &0.268 &0.283\\ \hline S15 &0.202 &0.135 &0.126 &0.232 &0.237 &0.231 &0.196 &0.212 &0.187 &0.088 &0.229 &0.18 &0.268 &0.211 &0.171 &0.124 &0.147 &0.195\\ \hline S16 &0.092 &0.088 &0.057 &0.064 &0.07 &0.107 &0.078 &0.112 &0.1 &0.039 &0.104 &0.084 &0.11 &0.079 &0.069 &0.054 &0.065 &0.113\\ \hline S17 &0.204 &0.16 &0.212 &0.245 &0.218 &0.239 &0.169 &0.286 &0.267 &0.155 &0.259 &0.219 &0.277 &0.264 &0.243 &0.2 &0.171 &0.297\\ \hline S18 &0.155 &0.119 &0.166 &0.162 &0.188 &0.181 &0.13 &0.195 &0.199 &0.079 &0.209 &0.142 &0.22 &0.186 &0.143 &0.138 &0.206 &0.174\\ \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 &0.2384 &0.1574 &0.266 &0.2789 &0.3015 &0.1904 &0.2428 &0.2822 &0.1604 &0.3223 &0.2385 &0.2879 &0.274 &0.254 &0.1836 &0.2152 &0.3268\\ \hline S2 &0.1496 &1 &0.1389 &0.1935 &0.2357 &0.2544 &0.1766 &0.295 &0.2295 &0.1229 &0.2047 &0.1808 &0.2406 &0.1868 &0.1654 &0.1515 &0.1751 &0.2753\\ \hline S3 &0.1234 &0.1932 &1 &0.2283 &0.1425 &0.1631 &0.1646 &0.2678 &0.1737 &0.0712 &0.175 &0.1414 &0.2116 &0.1859 &0.1388 &0.1588 &0.1342 &0.2724\\ \hline S4 &0.1259 &0.113 &0.1103 &1 &0.1626 &0.1717 &0.0872 &0.1278 &0.1159 &0.061 &0.1253 &0.0932 &0.1339 &0.1893 &0.1817 &0.1367 &0.1489 &0.181\\ \hline S5 &0.2086 &0.2098 &0.1466 &0.238 &1 &0.2209 &0.195 &0.2687 &0.2664 &0.1813 &0.2868 &0.2107 &0.3068 &0.2657 &0.276 &0.1459 &0.1766 &0.2812\\ \hline S6 &0.2311 &0.2187 &0.2287 &0.1881 &0.2219 &1 &0.1487 &0.3016 &0.2754 &0.1768 &0.2838 &0.1907 &0.2842 &0.291 &0.2434 &0.1739 &0.1963 &0.2583\\ \hline S7 &0.2308 &0.1989 &0.2488 &0.2507 &0.2284 &0.28 &1 &0.346 &0.2161 &0.1055 &0.2273 &0.171 &0.3241 &0.3055 &0.2824 &0.2137 &0.2376 &0.3511\\ \hline S8 &0.2226 &0.3133 &0.3007 &0.2343 &0.2929 &0.3575 &0.2879 &1 &0.355 &0.17 &0.2973 &0.2758 &0.3682 &0.3457 &0.2684 &0.2145 &0.2432 &0.3237\\ \hline S9 &0.2743 &0.2323 &0.1873 &0.2191 &0.2868 &0.312 &0.1577 &0.3435 &1 &0.1712 &0.2912 &0.2017 &0.2982 &0.29 &0.2322 &0.1802 &0.1819 &0.2961\\ \hline S10 &0.1812 &0.1288 &0.0944 &0.1752 &0.2221 &0.1938 &0.0926 &0.1741 &0.1972 &1 &0.1427 &0.1615 &0.1748 &0.1413 &0.1674 &0.0917 &0.1356 &0.148\\ \hline S11 &0.2517 &0.1787 &0.1756 &0.2064 &0.1863 &0.2895 &0.1413 &0.2445 &0.2239 &0.0997 &1 &0.1823 &0.3016 &0.3124 &0.2413 &0.201 &0.2278 &0.3293\\ \hline S12 &0.2397 &0.2045 &0.1655 &0.2268 &0.2363 &0.227 &0.1378 &0.2859 &0.2194 &0.1577 &0.2223 &1 &0.2375 &0.2224 &0.2318 &0.1613 &0.2616 &0.239\\ \hline S13 &0.2903 &0.2666 &0.2605 &0.3011 &0.3082 &0.3698 &0.2262 &0.3837 &0.3254 &0.1411 &0.3933 &0.2444 &1 &0.37 &0.3633 &0.2809 &0.3364 &0.418\\ \hline S14 &0.2477 &0.1756 &0.196 &0.2715 &0.2499 &0.2981 &0.2198 &0.3072 &0.2605 &0.1137 &0.3114 &0.2086 &0.3302 &1 &0.2965 &0.2185 &0.268 &0.2826\\ \hline S15 &0.2022 &0.1349 &0.1256 &0.2319 &0.2368 &0.2312 &0.1958 &0.2119 &0.1871 &0.088 &0.2288 &0.1805 &0.2675 &0.2113 &1 &0.1241 &0.147 &0.1954\\ \hline S16 &0.0917 &0.0881 &0.0575 &0.0636 &0.0697 &0.1073 &0.0781 &0.1117 &0.1004 &0.0392 &0.1038 &0.0844 &0.1097 &0.0788 &0.0686 &1 &0.0645 &0.113\\ \hline S17 &0.2038 &0.1605 &0.2123 &0.2449 &0.2175 &0.2395 &0.1685 &0.2859 &0.267 &0.1553 &0.2592 &0.219 &0.2773 &0.2636 &0.2431 &0.2002 &1 &0.2967\\ \hline S18 &0.1554 &0.1187 &0.1665 &0.1622 &0.1878 &0.1809 &0.1299 &0.1954 &0.1995 &0.0787 &0.2092 &0.1425 &0.2199 &0.1864 &0.1432 &0.1384 &0.2056 &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 &0.3124 &0.3007 &0.3011 &0.3082 &0.3124 &0.2879 &0.3124 &0.3124 &0.1813 &0.3223 &0.2758 &0.3124 &0.3124 &0.3124 &0.2809 &0.3124 &0.3268\\ \hline S2 &0.2903 &1 &0.295 &0.295 &0.295 &0.295 &0.2879 &0.295 &0.295 &0.1813 &0.295 &0.2758 &0.295 &0.295 &0.295 &0.2809 &0.295 &0.295\\ \hline S3 &0.2678 &0.2678 &1 &0.2678 &0.2678 &0.2678 &0.2678 &0.2678 &0.2678 &0.1813 &0.2678 &0.2678 &0.2678 &0.2678 &0.2678 &0.2678 &0.2678 &0.2724\\ \hline S4 &0.1893 &0.1893 &0.1893 &1 &0.1893 &0.1893 &0.1893 &0.1893 &0.1893 &0.1813 &0.1893 &0.1893 &0.1893 &0.1893 &0.1893 &0.1893 &0.1893 &0.1893\\ \hline S5 &0.2903 &0.3068 &0.3007 &0.3011 &1 &0.3068 &0.2879 &0.3068 &0.3068 &0.1813 &0.3068 &0.2758 &0.3068 &0.3068 &0.3068 &0.2809 &0.3068 &0.3068\\ \hline S6 &0.2903 &0.3016 &0.3007 &0.3011 &0.3016 &1 &0.2879 &0.3016 &0.3016 &0.1813 &0.3016 &0.2758 &0.3016 &0.3016 &0.3016 &0.2809 &0.3016 &0.3016\\ \hline S7 &0.2903 &0.3133 &0.3007 &0.3011 &0.3082 &0.346 &1 &0.346 &0.346 &0.1813 &0.346 &0.2758 &0.346 &0.346 &0.346 &0.2809 &0.3364 &0.3511\\ \hline S8 &0.2903 &0.3133 &0.3007 &0.3011 &0.3082 &0.3682 &0.2879 &1 &0.355 &0.1813 &0.3682 &0.2758 &0.3682 &0.3682 &0.3633 &0.2809 &0.3364 &0.3682\\ \hline S9 &0.2903 &0.3133 &0.3007 &0.3011 &0.3082 &0.3435 &0.2879 &0.3435 &1 &0.1813 &0.3435 &0.2758 &0.3435 &0.3435 &0.3435 &0.2809 &0.3364 &0.3435\\ \hline S10 &0.2221 &0.2221 &0.2221 &0.2221 &0.2221 &0.2221 &0.2221 &0.2221 &0.2221 &1 &0.2221 &0.2221 &0.2221 &0.2221 &0.2221 &0.2221 &0.2221 &0.2221\\ \hline S11 &0.2903 &0.3124 &0.3007 &0.3011 &0.3082 &0.3124 &0.2879 &0.3124 &0.3124 &0.1813 &1 &0.2758 &0.3124 &0.3124 &0.3124 &0.2809 &0.3124 &0.3293\\ \hline S12 &0.2859 &0.2859 &0.2859 &0.2859 &0.2859 &0.2859 &0.2859 &0.2859 &0.2859 &0.1813 &0.2859 &1 &0.2859 &0.2859 &0.2859 &0.2809 &0.2859 &0.2859\\ \hline S13 &0.2903 &0.3133 &0.3007 &0.3011 &0.3082 &0.3698 &0.2879 &0.3837 &0.355 &0.1813 &0.3933 &0.2758 &1 &0.37 &0.3633 &0.2809 &0.3364 &0.418\\ \hline S14 &0.2903 &0.3133 &0.3007 &0.3011 &0.3082 &0.3302 &0.2879 &0.3302 &0.3302 &0.1813 &0.3302 &0.2758 &0.3302 &1 &0.3302 &0.2809 &0.3302 &0.3302\\ \hline S15 &0.2675 &0.2675 &0.2675 &0.2675 &0.2675 &0.2675 &0.2675 &0.2675 &0.2675 &0.1813 &0.2675 &0.2675 &0.2675 &0.2675 &1 &0.2675 &0.2675 &0.2675\\ \hline S16 &0.113 &0.113 &0.113 &0.113 &0.113 &0.113 &0.113 &0.113 &0.113 &0.113 &0.113 &0.113 &0.113 &0.113 &0.113 &1 &0.113 &0.113\\ \hline S17 &0.2859 &0.2859 &0.2859 &0.2859 &0.2859 &0.2859 &0.2859 &0.2859 &0.2859 &0.1813 &0.2859 &0.2758 &0.2859 &0.2859 &0.2859 &0.2809 &1 &0.2967\\ \hline S18 &0.2199 &0.2199 &0.2199 &0.2199 &0.2199 &0.2199 &0.2199 &0.2199 &0.2199 &0.1813 &0.2199 &0.2199 &0.2199 &0.2199 &0.2199 &0.2199 &0.2199 &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 $数值区段
1	0.11298	0<$\lambda$<0.11298
2	0.18131	0.11298<$\lambda$<0.18131
3	0.18927	0.18131<$\lambda$<0.18927
4	0.21991	0.18927<$\lambda$<0.21991
5	0.22206	0.21991<$\lambda$<0.22206
6	0.26753	0.22206<$\lambda$<0.26753
7	0.2678	0.26753<$\lambda$<0.2678
8	0.2724	0.2678<$\lambda$<0.2724
9	0.27579	0.2724<$\lambda$<0.27579
10	0.2809	0.27579<$\lambda$<0.2809
11	0.2859	0.2809<$\lambda$<0.2859
12	0.28593	0.2859<$\lambda$<0.28593
13	0.28794	0.28593<$\lambda$<0.28794
14	0.29026	0.28794<$\lambda$<0.29026
15	0.29499	0.29026<$\lambda$<0.29499
16	0.29666	0.29499<$\lambda$<0.29666
17	0.30067	0.29666<$\lambda$<0.30067
18	0.30106	0.30067<$\lambda$<0.30106
19	0.3016	0.30106<$\lambda$<0.3016
20	0.3068	0.3016<$\lambda$<0.3068
21	0.30823	0.3068<$\lambda$<0.30823
22	0.31238	0.30823<$\lambda$<0.31238
23	0.31328	0.31238<$\lambda$<0.31328
24	0.32228	0.31328<$\lambda$<0.32228
25	0.32681	0.32228<$\lambda$<0.32681
26	0.32928	0.32681<$\lambda$<0.32928
27	0.33016	0.32928<$\lambda$<0.33016
28	0.3364	0.33016<$\lambda$<0.3364
29	0.34348	0.3364<$\lambda$<0.34348
30	0.34596	0.34348<$\lambda$<0.34596
31	0.35109	0.34596<$\lambda$<0.35109
32	0.35503	0.35109<$\lambda$<0.35503
33	0.3633	0.35503<$\lambda$<0.3633
34	0.36824	0.3633<$\lambda$<0.36824
35	0.36977	0.36824<$\lambda$<0.36977
36	0.36997	0.36977<$\lambda$<0.36997
37	0.38365	0.36997<$\lambda$<0.38365
38	0.39328	0.38365<$\lambda$<0.39328
39	0.41804	0.39328<$\lambda$<0.41804
40	1	0.41804<$\lambda$<1

特征结构——不含孤立子系统

截距范围：0.219907689<$\lambda$<0.222060794

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

$$WS_t=\begin{array}{c|c|c|c|c|c|c}{M_{18 \times18}} &S1 &S2 &S3 &S4 &S5 &S6 &S7 &S8 &S9 &S10 &S11 &S12 &S13 &S14 &S15 &S16 &S17 &S18\\ \hline S1 &0 &1 &1 &0.266 &1 &1 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &0.3268\\ \hline S2 &1 &0 &1 &0 &1 &1 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &0.2753\\ \hline S3 &1 &1 &0 &0.2283 &1 &1 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &0.2724\\ \hline S4 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline S5 &1 &1 &1 &0.238 &0 &1 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &0.2812\\ \hline S6 &1 &1 &1 &0 &1 &0 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &0.2583\\ \hline S7 &1 &1 &1 &0.2507 &1 &1 &0 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &0.3511\\ \hline S8 &1 &1 &1 &0.2343 &1 &1 &1 &0 &1 &0 &1 &1 &1 &1 &1 &0 &1 &0.3237\\ \hline S9 &1 &1 &1 &0 &1 &1 &1 &1 &0 &0 &1 &1 &1 &1 &1 &0 &1 &0.2961\\ \hline S10 &0 &0 &0 &0 &0.2221 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline S11 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &0 &1 &1 &1 &1 &0 &1 &0.3293\\ \hline S12 &1 &1 &1 &0.2268 &1 &1 &1 &1 &1 &0 &1 &0 &1 &1 &1 &0 &1 &0.239\\ \hline S13 &1 &1 &1 &0.3011 &1 &1 &1 &1 &1 &0 &1 &1 &0 &1 &1 &0.2809 &1 &0.418\\ \hline S14 &1 &1 &1 &0.2715 &1 &1 &1 &1 &1 &0 &1 &1 &1 &0 &1 &0 &1 &0.2826\\ \hline S15 &1 &1 &1 &0.2319 &1 &1 &1 &1 &1 &0 &1 &1 &1 &1 &0 &0 &1 &0\\ \hline S16 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline S17 &1 &1 &1 &0.2449 &1 &1 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &0 &0.2967\\ \hline S18 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline \end{array} $$

含孤立子系统的特征结构

截距范围：0.222060794<$\lambda$<0.26752734

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

$$WS_s=\begin{array}{c|c|c|c|c|c|c}{M_{18 \times18}} &S1 &S2 &S3 &S4 &S5 &S6 &S7 &S8 &S9 &S10 &S11 &S12 &S13 &S14 &S15 &S16 &S17 &S18\\ \hline S1 &0 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &0.3268\\ \hline S2 &1 &0 &1 &0 &1 &1 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &0.2753\\ \hline S3 &1 &1 &0 &0 &1 &1 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &0.2724\\ \hline S4 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline S5 &1 &1 &1 &0 &0 &1 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &0.2812\\ \hline S6 &1 &1 &1 &0 &1 &0 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &0\\ \hline S7 &1 &1 &1 &0 &1 &1 &0 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &0.3511\\ \hline S8 &1 &1 &1 &0 &1 &1 &1 &0 &1 &0 &1 &1 &1 &1 &1 &0 &1 &0.3237\\ \hline S9 &1 &1 &1 &0 &1 &1 &1 &1 &0 &0 &1 &1 &1 &1 &1 &0 &1 &0.2961\\ \hline S10 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline S11 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &0 &1 &1 &1 &1 &0 &1 &0.3293\\ \hline S12 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &0 &1 &1 &1 &0 &1 &0\\ \hline S13 &1 &1 &1 &0.3011 &1 &1 &1 &1 &1 &0 &1 &1 &0 &1 &1 &0.2809 &1 &0.418\\ \hline S14 &1 &1 &1 &0.2715 &1 &1 &1 &1 &1 &0 &1 &1 &1 &0 &1 &0 &1 &0.2826\\ \hline S15 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &1 &1 &1 &0 &0 &1 &0\\ \hline S16 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline S17 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &0 &0.2967\\ \hline S18 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline \end{array} $$

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

$$\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{18 \times4}} &Di &Ci &Mi &Ri\\ \hline S1 &4.415 &3.625 &8.04 &0.79\\ \hline S2 &3.519 &3.317 &6.836 &0.202\\ \hline S3 &3.066 &3.092 &6.158 &-0.027\\ \hline S4 &2.374 &3.81 &6.183 &-1.436\\ \hline S5 &4.083 &3.962 &8.045 &0.121\\ \hline S6 &4.132 &4.418 &8.55 &-0.286\\ \hline S7 &4.382 &2.962 &7.345 &1.42\\ \hline S8 &5.178 &4.7 &9.878 &0.478\\ \hline S9 &4.377 &4.116 &8.493 &0.261\\ \hline S10 &2.703 &2.174 &4.877 &0.529\\ \hline S11 &4.008 &4.299 &8.307 &-0.291\\ \hline S12 &3.831 &3.282 &7.113 &0.55\\ \hline S13 &5.592 &4.687 &10.279 &0.905\\ \hline S14 &4.496 &4.36 &8.856 &0.136\\ \hline S15 &3.371 &3.969 &7.34 &-0.598\\ \hline S16 &1.484 &3.029 &4.513 &-1.545\\ \hline S17 &4.086 &3.527 &7.612 &0.559\\ \hline S18 &2.994 &4.762 &7.756 &-1.768\\ \hline \end{array} $$

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