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 &0.074 &0.083 &0.04 &0.08 &0.071 &0.056 &0.02 &0.018 &0.071 &0.089 &0.056 &0.089 &0.051 &0.089 &0.074 &0.02 &0.018\\ \hline S2 &0.071 &0 &0.04 &0.091 &0.04 &0.074 &0.056 &0.024 &0.02 &0.04 &0.02 &0.024 &0.024 &0.038 &0.071 &0.053 &0.054 &0.073\\ \hline S3 &0.091 &0.038 &0 &0.073 &0.091 &0.091 &0.054 &0.018 &0.051 &0.073 &0.073 &0.02 &0.073 &0.018 &0.073 &0.089 &0.056 &0.069\\ \hline S4 &0.022 &0.074 &0.02 &0 &0.025 &0.022 &0.02 &0.022 &0.022 &0.074 &0.018 &0.089 &0.071 &0.074 &0.074 &0.022 &0.074 &0.091\\ \hline S5 &0.038 &0.038 &0.071 &0.056 &0 &0.038 &0.036 &0.018 &0.02 &0.056 &0.02 &0.056 &0.04 &0.056 &0.073 &0.054 &0.056 &0.056\\ \hline S6 &0.056 &0.074 &0.073 &0.073 &0.073 &0 &0.073 &0.02 &0.02 &0.054 &0.051 &0.02 &0.024 &0.02 &0.02 &0.02 &0.038 &0.036\\ \hline S7 &0.056 &0.058 &0.073 &0.054 &0.073 &0.074 &0 &0.018 &0.018 &0.056 &0.04 &0.074 &0.073 &0.056 &0.04 &0.022 &0.04 &0.074\\ \hline S8 &0.038 &0.073 &0.034 &0.073 &0.018 &0.056 &0.018 &0 &0.042 &0.018 &0.018 &0.091 &0.018 &0.067 &0.073 &0.018 &0.058 &0.074\\ \hline S9 &0.018 &0.036 &0.018 &0.018 &0.018 &0.018 &0.018 &0.071 &0 &0.073 &0.038 &0.073 &0.018 &0.02 &0.073 &0.024 &0.018 &0.073\\ \hline S10 &0.018 &0.04 &0.036 &0.02 &0.056 &0.036 &0.04 &0.018 &0.022 &0 &0.038 &0.091 &0.038 &0.04 &0.056 &0.038 &0.073 &0.073\\ \hline S11 &0.056 &0.022 &0.053 &0.02 &0.022 &0.038 &0.056 &0.018 &0.018 &0.056 &0 &0.036 &0.038 &0.018 &0.018 &0.074 &0.018 &0.018\\ \hline S12 &0.022 &0.073 &0.018 &0.018 &0.022 &0.022 &0.024 &0.018 &0.018 &0.054 &0.024 &0 &0.018 &0.058 &0.091 &0.018 &0.053 &0.085\\ \hline S13 &0.036 &0.038 &0.018 &0.018 &0.038 &0.034 &0.073 &0.018 &0.018 &0.036 &0.034 &0.073 &0 &0.018 &0.04 &0.018 &0.034 &0.056\\ \hline S14 &0.038 &0.071 &0.018 &0.018 &0.018 &0.018 &0.038 &0.018 &0.034 &0.022 &0.018 &0.074 &0.058 &0 &0.082 &0.056 &0.073 &0.076\\ \hline S15 &0.018 &0.04 &0.02 &0.018 &0.054 &0.018 &0.02 &0.018 &0.02 &0.04 &0.02 &0.051 &0.038 &0.056 &0 &0.022 &0.034 &0.034\\ \hline S16 &0.073 &0.073 &0.073 &0.054 &0.073 &0.054 &0.073 &0.018 &0.018 &0.054 &0.074 &0.018 &0.018 &0.018 &0.018 &0 &0.018 &0.022\\ \hline S17 &0.054 &0.073 &0.069 &0.02 &0.038 &0.073 &0.073 &0.018 &0.018 &0.036 &0.034 &0.018 &0.02 &0.022 &0.036 &0.018 &0 &0.071\\ \hline S18 &0.038 &0.038 &0.051 &0.018 &0.054 &0.073 &0.073 &0.018 &0.034 &0.036 &0.051 &0.018 &0.036 &0.038 &0.053 &0.034 &0.073 &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 &0.17 &0.271 &0.253 &0.192 &0.261 &0.249 &0.237 &0.099 &0.109 &0.256 &0.233 &0.239 &0.242 &0.197 &0.294 &0.222 &0.197 &0.233\\ \hline S2 &0.206 &0.173 &0.186 &0.213 &0.195 &0.225 &0.207 &0.089 &0.096 &0.197 &0.145 &0.178 &0.157 &0.164 &0.244 &0.173 &0.202 &0.249\\ \hline S3 &0.262 &0.251 &0.188 &0.229 &0.282 &0.279 &0.247 &0.103 &0.144 &0.27 &0.229 &0.216 &0.236 &0.175 &0.289 &0.241 &0.239 &0.289\\ \hline S4 &0.151 &0.232 &0.153 &0.115 &0.167 &0.166 &0.165 &0.085 &0.094 &0.216 &0.132 &0.231 &0.189 &0.191 &0.242 &0.136 &0.217 &0.262\\ \hline S5 &0.17 &0.2 &0.205 &0.173 &0.148 &0.183 &0.181 &0.081 &0.093 &0.203 &0.139 &0.201 &0.165 &0.173 &0.239 &0.17 &0.198 &0.228\\ \hline S6 &0.188 &0.23 &0.209 &0.192 &0.215 &0.148 &0.213 &0.082 &0.092 &0.203 &0.166 &0.167 &0.151 &0.139 &0.189 &0.14 &0.179 &0.208\\ \hline S7 &0.207 &0.241 &0.228 &0.191 &0.238 &0.239 &0.169 &0.09 &0.102 &0.226 &0.175 &0.24 &0.214 &0.191 &0.235 &0.158 &0.205 &0.27\\ \hline S8 &0.166 &0.231 &0.166 &0.187 &0.159 &0.196 &0.16 &0.064 &0.113 &0.165 &0.132 &0.23 &0.14 &0.184 &0.24 &0.132 &0.199 &0.245\\ \hline S9 &0.117 &0.159 &0.121 &0.109 &0.128 &0.129 &0.127 &0.117 &0.057 &0.182 &0.125 &0.185 &0.111 &0.114 &0.201 &0.111 &0.13 &0.203\\ \hline S10 &0.14 &0.187 &0.162 &0.128 &0.186 &0.169 &0.172 &0.076 &0.088 &0.136 &0.144 &0.218 &0.149 &0.148 &0.209 &0.143 &0.2 &0.228\\ \hline S11 &0.159 &0.147 &0.16 &0.115 &0.138 &0.151 &0.167 &0.067 &0.074 &0.171 &0.096 &0.149 &0.135 &0.109 &0.147 &0.163 &0.126 &0.15\\ \hline S12 &0.125 &0.196 &0.126 &0.111 &0.136 &0.137 &0.139 &0.068 &0.076 &0.167 &0.114 &0.116 &0.116 &0.151 &0.22 &0.111 &0.166 &0.218\\ \hline S13 &0.137 &0.162 &0.126 &0.11 &0.15 &0.147 &0.181 &0.067 &0.073 &0.15 &0.124 &0.183 &0.096 &0.112 &0.169 &0.107 &0.143 &0.188\\ \hline S14 &0.157 &0.214 &0.143 &0.125 &0.15 &0.152 &0.17 &0.076 &0.099 &0.156 &0.125 &0.202 &0.166 &0.108 &0.231 &0.158 &0.197 &0.229\\ \hline S15 &0.105 &0.146 &0.11 &0.097 &0.146 &0.113 &0.116 &0.06 &0.068 &0.136 &0.096 &0.147 &0.118 &0.133 &0.114 &0.099 &0.13 &0.15\\ \hline S16 &0.206 &0.229 &0.212 &0.178 &0.219 &0.201 &0.215 &0.081 &0.091 &0.205 &0.192 &0.166 &0.148 &0.138 &0.188 &0.123 &0.16 &0.193\\ \hline S17 &0.178 &0.217 &0.197 &0.136 &0.176 &0.209 &0.205 &0.076 &0.086 &0.174 &0.145 &0.151 &0.137 &0.131 &0.19 &0.129 &0.131 &0.225\\ \hline S18 &0.165 &0.19 &0.184 &0.134 &0.193 &0.209 &0.209 &0.078 &0.102 &0.178 &0.162 &0.157 &0.154 &0.148 &0.208 &0.146 &0.202 &0.163\\ \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 &0.2711 &0.2527 &0.1921 &0.2609 &0.2491 &0.2372 &0.0986 &0.1091 &0.2561 &0.2328 &0.2391 &0.2416 &0.1969 &0.2938 &0.2216 &0.1971 &0.2331\\ \hline S2 &0.2065 &1 &0.1862 &0.2132 &0.1945 &0.2246 &0.2069 &0.0894 &0.0961 &0.197 &0.1455 &0.1784 &0.1574 &0.1639 &0.2442 &0.173 &0.2023 &0.2492\\ \hline S3 &0.2619 &0.2506 &1 &0.2288 &0.2824 &0.2788 &0.2472 &0.1027 &0.1438 &0.27 &0.2291 &0.2159 &0.2357 &0.1752 &0.2891 &0.2409 &0.239 &0.2891\\ \hline S4 &0.1511 &0.2322 &0.1535 &1 &0.1671 &0.1657 &0.1654 &0.0845 &0.0942 &0.2157 &0.1323 &0.2315 &0.1889 &0.1905 &0.2418 &0.1358 &0.2166 &0.2618\\ \hline S5 &0.17 &0.1997 &0.2045 &0.1733 &1 &0.183 &0.1807 &0.0811 &0.0933 &0.2034 &0.1387 &0.2009 &0.1645 &0.1734 &0.239 &0.17 &0.1978 &0.2277\\ \hline S6 &0.1877 &0.2297 &0.2085 &0.1922 &0.2155 &1 &0.2127 &0.0823 &0.092 &0.2029 &0.1664 &0.1672 &0.1512 &0.1393 &0.1891 &0.14 &0.1791 &0.2077\\ \hline S7 &0.2069 &0.2412 &0.2278 &0.191 &0.2376 &0.2387 &1 &0.0904 &0.1023 &0.2263 &0.1747 &0.2397 &0.2141 &0.1909 &0.2352 &0.1585 &0.2046 &0.2702\\ \hline S8 &0.1657 &0.2312 &0.166 &0.1867 &0.1588 &0.1958 &0.1595 &1 &0.1128 &0.1648 &0.1316 &0.2303 &0.1399 &0.1841 &0.2399 &0.1317 &0.1988 &0.2445\\ \hline S9 &0.1168 &0.1591 &0.1211 &0.1086 &0.1276 &0.1288 &0.1269 &0.1174 &1 &0.1815 &0.1252 &0.1848 &0.1106 &0.1143 &0.2011 &0.1113 &0.1301 &0.2034\\ \hline S10 &0.1398 &0.1869 &0.162 &0.1282 &0.1863 &0.169 &0.1725 &0.0758 &0.0881 &1 &0.1438 &0.218 &0.1487 &0.1478 &0.2088 &0.1432 &0.2002 &0.2282\\ \hline S11 &0.1586 &0.1471 &0.1601 &0.1146 &0.1384 &0.1514 &0.1675 &0.0666 &0.0739 &0.1711 &1 &0.1491 &0.1349 &0.1088 &0.1473 &0.1634 &0.1258 &0.1495\\ \hline S12 &0.1255 &0.196 &0.126 &0.1114 &0.1363 &0.1373 &0.1385 &0.0681 &0.076 &0.1672 &0.1144 &1 &0.1155 &0.1507 &0.2202 &0.1105 &0.1656 &0.2179\\ \hline S13 &0.1368 &0.1615 &0.1259 &0.1102 &0.1495 &0.1467 &0.1808 &0.0666 &0.0735 &0.1503 &0.1239 &0.1826 &1 &0.1115 &0.1693 &0.1074 &0.1433 &0.1876\\ \hline S14 &0.157 &0.2145 &0.1429 &0.1254 &0.1501 &0.1516 &0.1701 &0.076 &0.0989 &0.1556 &0.1248 &0.2016 &0.166 &1 &0.2308 &0.1578 &0.1972 &0.229\\ \hline S15 &0.1051 &0.1458 &0.1101 &0.0966 &0.1465 &0.1134 &0.1157 &0.06 &0.068 &0.1361 &0.0959 &0.1475 &0.1184 &0.1334 &1 &0.0993 &0.1296 &0.15\\ \hline S16 &0.2056 &0.2294 &0.2119 &0.178 &0.2186 &0.2014 &0.215 &0.0812 &0.0907 &0.2054 &0.1916 &0.1662 &0.1478 &0.1378 &0.1877 &1 &0.1598 &0.193\\ \hline S17 &0.1782 &0.2169 &0.1971 &0.1356 &0.1762 &0.2086 &0.2054 &0.0762 &0.0857 &0.1742 &0.1451 &0.151 &0.1375 &0.1305 &0.19 &0.1292 &1 &0.2248\\ \hline S18 &0.1654 &0.1899 &0.1836 &0.1341 &0.1928 &0.2093 &0.2086 &0.0784 &0.1022 &0.1776 &0.1619 &0.1566 &0.1542 &0.148 &0.2076 &0.1457 &0.2019 &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 &0.2711 &0.2527 &0.2288 &0.2609 &0.2527 &0.2472 &0.1174 &0.1438 &0.2561 &0.2328 &0.2397 &0.2416 &0.1969 &0.2938 &0.2409 &0.239 &0.2527\\ \hline S2 &0.2127 &1 &0.2127 &0.2132 &0.2155 &0.2246 &0.2127 &0.1174 &0.1438 &0.2132 &0.2127 &0.2132 &0.2127 &0.1969 &0.2442 &0.2127 &0.2132 &0.2492\\ \hline S3 &0.2619 &0.2619 &1 &0.2288 &0.2824 &0.2788 &0.2472 &0.1174 &0.1438 &0.27 &0.2328 &0.2397 &0.2416 &0.1969 &0.2891 &0.2409 &0.239 &0.2891\\ \hline S4 &0.2127 &0.2322 &0.2127 &1 &0.2155 &0.2246 &0.2127 &0.1174 &0.1438 &0.2157 &0.2127 &0.2315 &0.2127 &0.1969 &0.2418 &0.2127 &0.2166 &0.2618\\ \hline S5 &0.2093 &0.2093 &0.2093 &0.2093 &1 &0.2093 &0.2093 &0.1174 &0.1438 &0.2093 &0.2093 &0.2093 &0.2093 &0.1969 &0.239 &0.2093 &0.2093 &0.2277\\ \hline S6 &0.2127 &0.2297 &0.2127 &0.2132 &0.2155 &1 &0.2127 &0.1174 &0.1438 &0.2132 &0.2127 &0.2132 &0.2127 &0.1969 &0.2297 &0.2127 &0.2132 &0.2297\\ \hline S7 &0.2278 &0.2412 &0.2278 &0.2278 &0.2376 &0.2387 &1 &0.1174 &0.1438 &0.2278 &0.2278 &0.2397 &0.2278 &0.1969 &0.2412 &0.2278 &0.2278 &0.2702\\ \hline S8 &0.2127 &0.2312 &0.2127 &0.2132 &0.2155 &0.2246 &0.2127 &1 &0.1438 &0.2132 &0.2127 &0.2303 &0.2127 &0.1969 &0.2399 &0.2127 &0.2132 &0.2445\\ \hline S9 &0.2034 &0.2034 &0.2034 &0.2034 &0.2034 &0.2034 &0.2034 &0.1174 &1 &0.2034 &0.2034 &0.2034 &0.2034 &0.1969 &0.2034 &0.2034 &0.2034 &0.2034\\ \hline S10 &0.2093 &0.2093 &0.2093 &0.2093 &0.2093 &0.2093 &0.2093 &0.1174 &0.1438 &1 &0.2093 &0.218 &0.2093 &0.1969 &0.218 &0.2093 &0.2093 &0.2282\\ \hline S11 &0.1711 &0.1711 &0.1711 &0.1711 &0.1711 &0.1711 &0.1711 &0.1174 &0.1438 &0.1711 &1 &0.1711 &0.1711 &0.1711 &0.1711 &0.1711 &0.1711 &0.1711\\ \hline S12 &0.2093 &0.2093 &0.2093 &0.2093 &0.2093 &0.2093 &0.2093 &0.1174 &0.1438 &0.2093 &0.2093 &1 &0.2093 &0.1969 &0.2202 &0.2093 &0.2093 &0.2179\\ \hline S13 &0.1876 &0.1876 &0.1876 &0.1876 &0.1876 &0.1876 &0.1876 &0.1174 &0.1438 &0.1876 &0.1876 &0.1876 &1 &0.1876 &0.1876 &0.1876 &0.1876 &0.1876\\ \hline S14 &0.2127 &0.2145 &0.2127 &0.2132 &0.2145 &0.2145 &0.2127 &0.1174 &0.1438 &0.2132 &0.2127 &0.2132 &0.2127 &1 &0.2308 &0.2127 &0.2132 &0.229\\ \hline S15 &0.15 &0.15 &0.15 &0.15 &0.15 &0.15 &0.15 &0.1174 &0.1438 &0.15 &0.15 &0.15 &0.15 &0.15 &1 &0.15 &0.15 &0.15\\ \hline S16 &0.215 &0.2294 &0.215 &0.215 &0.2186 &0.2246 &0.215 &0.1174 &0.1438 &0.215 &0.215 &0.215 &0.215 &0.1969 &0.2294 &1 &0.215 &0.2294\\ \hline S17 &0.2127 &0.2169 &0.2127 &0.2132 &0.2155 &0.2169 &0.2127 &0.1174 &0.1438 &0.2132 &0.2127 &0.2132 &0.2127 &0.1969 &0.2169 &0.2127 &1 &0.2248\\ \hline S18 &0.2093 &0.2093 &0.2093 &0.2093 &0.2093 &0.2093 &0.2093 &0.1174 &0.1438 &0.2093 &0.2093 &0.2093 &0.2093 &0.1969 &0.2093 &0.2093 &0.2093 &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 $区段	该结构的数目	互不连通区域数目	层级数	系统包含几个回路	最大回路要素数目
1	0.11739	0<$\lambda$<0.11739	17	1	1	1	18
2	0.14384	0.11739<$\lambda$<0.14384	17	1	2	1	17
3	0.15001	0.14384<$\lambda$<0.15001	15	1	2	1	16
4	0.17107	0.15001<$\lambda$<0.17107	15	1	3	1	15
5	0.18761	0.17107<$\lambda$<0.18761	15	1	3	1	14
6	0.19689	0.18761<$\lambda$<0.19689	14	1	3	1	13
7	0.20337	0.19689<$\lambda$<0.20337	15	1	3	1	12
8	0.20934	0.20337<$\lambda$<0.20934	49	2	3	1	12
9	0.21272	0.20934<$\lambda$<0.21272	36	2	5	1	8
10	0.21322	0.21272<$\lambda$<0.21322	18	2	5	2	4
11	0.21449	0.21322<$\lambda$<0.21449	3	2	6	2	4
12	0.21505	0.21449<$\lambda$<0.21505	9	2	6	2	4
13	0.21548	0.21505<$\lambda$<0.21548	5	2	6	2	3
14	0.21568	0.21548<$\lambda$<0.21568	1	2	5	2	3
15	0.21663	0.21568<$\lambda$<0.21663	1	2	5	2	3
16	0.21688	0.21663<$\lambda$<0.21688	3	2	4	2	3
17	0.21793	0.21688<$\lambda$<0.21793	1	2	4	2	3
18	0.21796	0.21793<$\lambda$<0.21796	2	2	4	2	3
19	0.21855	0.21796<$\lambda$<0.21855	1	2	4	2	3
20	0.22021	0.21855<$\lambda$<0.22021	1	2	4	2	3
21	0.22459	0.22021<$\lambda$<0.22459	4	2	4	2	3
22	0.22481	0.22459<$\lambda$<0.22481	1	2	4	1	3
23	0.22771	0.22481<$\lambda$<0.22771	1	2	4	1	3
24	0.22783	0.22771<$\lambda$<0.22783	8	2	4	1	3
25	0.22819	0.22783<$\lambda$<0.22819	1	2	5	1	2
26	0.22885	0.22819<$\lambda$<0.22885	2	2	5	1	2
27	0.22902	0.22885<$\lambda$<0.22902	1	2	5	1	2
28	0.22945	0.22902<$\lambda$<0.22945	3	2	5	1	2
29	0.22965	0.22945<$\lambda$<0.22965	3	2	5	1	2
30	0.23033	0.22965<$\lambda$<0.23033	1	2	4	1	2
31	0.23078	0.23033<$\lambda$<0.23078	1	2	4	1	2
32	0.23116	0.23078<$\lambda$<0.23116	1	3	4	1	2
33	0.23147	0.23116<$\lambda$<0.23147	1	3	4	1	2
34	0.23216	0.23147<$\lambda$<0.23216	1	3	4	1	2
35	0.23284	0.23216<$\lambda$<0.23284	2	3	4	1	2
36	0.23755	0.23284<$\lambda$<0.23755	1	4	4	1	2
37	0.2387	0.23755<$\lambda$<0.2387	1	4	4	1	2
38	0.23901	0.2387<$\lambda$<0.23901	1	4	4	1	2
39	0.23902	0.23901<$\lambda$<0.23902	2	4	4	1	2
40	0.23967	0.23902<$\lambda$<0.23967	3	5	4	1	2
41	0.2399	0.23967<$\lambda$<0.2399	1	6	4	1	2
42	0.24092	0.2399<$\lambda$<0.24092	2	6	4	1	2
43	0.24122	0.24092<$\lambda$<0.24122	2	7	4	1	2
44	0.24165	0.24122<$\lambda$<0.24165	2	7	3	1	2
45	0.24178	0.24165<$\lambda$<0.24178	1	8	3	1	2
46	0.24425	0.24178<$\lambda$<0.24425	1	8	3	1	2
47	0.24454	0.24425<$\lambda$<0.24454	1	8	3	1	2
48	0.24722	0.24454<$\lambda$<0.24722	2	9	3	1	2
49	0.24919	0.24722<$\lambda$<0.24919	1	9	3	1	2
50	0.25268	0.24919<$\lambda$<0.25268	3	9	2	1	2
51	0.25612	0.25268<$\lambda$<0.25612	1	9	3	0	1
52	0.26086	0.25612<$\lambda$<0.26086	1	9	3	0	1
53	0.26184	0.26086<$\lambda$<0.26184	1	9	3	0	1
54	0.26194	0.26184<$\lambda$<0.26194	2	10	3	0	1
55	0.26997	0.26194<$\lambda$<0.26997	1	10	2	0	1
56	0.27015	0.26997<$\lambda$<0.27015	1	11	2	0	1
57	0.27113	0.27015<$\lambda$<0.27113	1	12	2	0	1
58	0.2788	0.27113<$\lambda$<0.2788	1	13	2	0	1
59	0.28236	0.2788<$\lambda$<0.28236	1	14	2	0	1
60	0.28908	0.28236<$\lambda$<0.28908	1	15	2	0	1
61	0.28909	0.28908<$\lambda$<0.28909	1	16	2	0	1
62	0.2938	0.28909<$\lambda$<0.2938	1	17	2	0	1
63	1	0.2938<$\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 $区段	该结构的数目	互不连通区域数目	层级数	包含回路数目	最大回路要素数目
13	0.21505<$\lambda$<0.21548	5	2	6	2	3
12	0.21449<$\lambda$<0.21505	9	2	6	2	4
11	0.21322<$\lambda$<0.21449	3	2	6	2	4
14	0.21548<$\lambda$<0.21568	1	2	5	2	3
15	0.21568<$\lambda$<0.21663	1	2	5	2	3

T-AISM

前置流程图说明

DEMATEL-T-AISM流程图与说明