特征结构的计算与说明

原始矩阵（直接影响矩阵）为

$$Ori=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{13 \times13}} &A1 &A2 &B1 &B2 &C1 &C2 &C3 &C4 &D1 &D2 &D3 &E1 &E2\\ \hline A1 &0 &31 &12 &46 &43 &34 &38 &24 &45 &23 &40 &30 &18\\ \hline A2 &25 &0 &19 &18 &38 &27 &27 &17 &36 &22 &44 &20 &9\\ \hline B1 &18 &38 &0 &39 &51 &34 &32 &19 &36 &42 &29 &34 &16\\ \hline B2 &24 &14 &16 &0 &45 &45 &24 &30 &36 &28 &33 &36 &22\\ \hline C1 &25 &26 &18 &21 &0 &36 &16 &21 &33 &25 &31 &36 &28\\ \hline C2 &19 &23 &45 &30 &32 &0 &14 &18 &23 &29 &25 &36 &34\\ \hline C3 &21 &24 &25 &37 &29 &27 &0 &28 &36 &32 &32 &27 &30\\ \hline C4 &32 &30 &21 &38 &31 &31 &36 &0 &31 &28 &27 &26 &26\\ \hline D1 &18 &29 &50 &21 &35 &50 &26 &33 &0 &31 &30 &42 &31\\ \hline D2 &14 &24 &27 &24 &23 &27 &36 &19 &35 &0 &17 &18 &35\\ \hline D3 &20 &19 &26 &15 &20 &23 &27 &15 &22 &29 &0 &28 &27\\ \hline E1 &30 &30 &34 &34 &43 &34 &29 &34 &28 &32 &43 &0 &41\\ \hline E2 &10 &15 &21 &12 &22 &10 &18 &20 &12 &28 &18 &16 &0\\ \hline \end{array} $$

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

$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{13 \times13}} &A1 &A2 &B1 &B2 &C1 &C2 &C3 &C4 &D1 &D2 &D3 &E1 &E2\\ \hline A1 &0 &0.053 &0.021 &0.079 &0.074 &0.058 &0.065 &0.041 &0.077 &0.039 &0.069 &0.051 &0.031\\ \hline A2 &0.043 &0 &0.033 &0.031 &0.065 &0.046 &0.046 &0.029 &0.062 &0.038 &0.076 &0.034 &0.015\\ \hline B1 &0.031 &0.065 &0 &0.067 &0.088 &0.058 &0.055 &0.033 &0.062 &0.072 &0.05 &0.058 &0.027\\ \hline B2 &0.041 &0.024 &0.027 &0 &0.077 &0.077 &0.041 &0.051 &0.062 &0.048 &0.057 &0.062 &0.038\\ \hline C1 &0.043 &0.045 &0.031 &0.036 &0 &0.062 &0.027 &0.036 &0.057 &0.043 &0.053 &0.062 &0.048\\ \hline C2 &0.033 &0.039 &0.077 &0.051 &0.055 &0 &0.024 &0.031 &0.039 &0.05 &0.043 &0.062 &0.058\\ \hline C3 &0.036 &0.041 &0.043 &0.064 &0.05 &0.046 &0 &0.048 &0.062 &0.055 &0.055 &0.046 &0.051\\ \hline C4 &0.055 &0.051 &0.036 &0.065 &0.053 &0.053 &0.062 &0 &0.053 &0.048 &0.046 &0.045 &0.045\\ \hline D1 &0.031 &0.05 &0.086 &0.036 &0.06 &0.086 &0.045 &0.057 &0 &0.053 &0.051 &0.072 &0.053\\ \hline D2 &0.024 &0.041 &0.046 &0.041 &0.039 &0.046 &0.062 &0.033 &0.06 &0 &0.029 &0.031 &0.06\\ \hline D3 &0.034 &0.033 &0.045 &0.026 &0.034 &0.039 &0.046 &0.026 &0.038 &0.05 &0 &0.048 &0.046\\ \hline E1 &0.051 &0.051 &0.058 &0.058 &0.074 &0.058 &0.05 &0.058 &0.048 &0.055 &0.074 &0 &0.07\\ \hline E2 &0.017 &0.026 &0.036 &0.021 &0.038 &0.017 &0.031 &0.034 &0.021 &0.048 &0.031 &0.027 &0\\ \hline \end{array} $$

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

　　综合影响矩阵如下

$T=\mathcal{N}(I-\mathcal{N})^{-1}$

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{13 \times13}} &A1 &A2 &B1 &B2 &C1 &C2 &C3 &C4 &D1 &D2 &D3 &E1 &E2\\ \hline A1 &0.055 &0.114 &0.089 &0.143 &0.154 &0.136 &0.128 &0.099 &0.15 &0.111 &0.142 &0.124 &0.099\\ \hline A2 &0.084 &0.051 &0.086 &0.085 &0.129 &0.108 &0.097 &0.075 &0.12 &0.095 &0.133 &0.093 &0.07\\ \hline B1 &0.085 &0.126 &0.069 &0.132 &0.168 &0.137 &0.119 &0.091 &0.137 &0.142 &0.125 &0.131 &0.096\\ \hline B2 &0.09 &0.083 &0.091 &0.064 &0.15 &0.146 &0.101 &0.104 &0.129 &0.114 &0.124 &0.128 &0.101\\ \hline C1 &0.086 &0.095 &0.087 &0.092 &0.07 &0.124 &0.082 &0.084 &0.117 &0.102 &0.114 &0.12 &0.103\\ \hline C2 &0.078 &0.093 &0.13 &0.108 &0.126 &0.068 &0.081 &0.08 &0.104 &0.111 &0.107 &0.122 &0.113\\ \hline C3 &0.084 &0.097 &0.103 &0.122 &0.124 &0.117 &0.061 &0.1 &0.128 &0.119 &0.121 &0.111 &0.111\\ \hline C4 &0.103 &0.108 &0.097 &0.126 &0.13 &0.125 &0.121 &0.055 &0.123 &0.114 &0.116 &0.112 &0.106\\ \hline D1 &0.086 &0.114 &0.151 &0.107 &0.145 &0.162 &0.111 &0.114 &0.079 &0.127 &0.128 &0.144 &0.121\\ \hline D2 &0.065 &0.089 &0.098 &0.093 &0.104 &0.106 &0.11 &0.078 &0.117 &0.058 &0.088 &0.088 &0.11\\ \hline D3 &0.071 &0.077 &0.091 &0.075 &0.094 &0.094 &0.092 &0.067 &0.091 &0.1 &0.054 &0.098 &0.093\\ \hline E1 &0.106 &0.116 &0.126 &0.128 &0.159 &0.138 &0.118 &0.117 &0.127 &0.13 &0.15 &0.078 &0.138\\ \hline E2 &0.046 &0.059 &0.07 &0.057 &0.081 &0.059 &0.066 &0.064 &0.062 &0.085 &0.07 &0.066 &0.036\\ \hline \end{array} $$

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$

$$\tilde B=\begin{array} {c|c|c}{M_{13 \times13}} &A1 &A2 &B1 &B2 &C1 &C2 &C3 &C4 &D1 &D2 &D3 &E1 &E2\\ \hline A1 &1 &0.1137 &0.0889 &0.1429 &0.1544 &0.1364 &0.1279 &0.0994 &0.1502 &0.1111 &0.1424 &0.1244 &0.0986\\ \hline A2 &0.0844 &1 &0.0861 &0.0847 &0.1286 &0.1082 &0.0973 &0.0751 &0.1202 &0.0946 &0.1325 &0.093 &0.07\\ \hline B1 &0.0852 &0.1259 &1 &0.1324 &0.168 &0.1367 &0.1192 &0.0914 &0.1372 &0.1418 &0.1254 &0.1306 &0.096\\ \hline B2 &0.09 &0.0826 &0.0907 &1 &0.1504 &0.1464 &0.1006 &0.1038 &0.1292 &0.1135 &0.1243 &0.1277 &0.1007\\ \hline C1 &0.086 &0.0953 &0.0871 &0.0916 &1 &0.124 &0.082 &0.0836 &0.1169 &0.1017 &0.1143 &0.1196 &0.1026\\ \hline C2 &0.0778 &0.0929 &0.1304 &0.1082 &0.1261 &1 &0.0811 &0.0804 &0.104 &0.111 &0.1068 &0.1218 &0.1134\\ \hline C3 &0.0838 &0.0969 &0.1026 &0.1222 &0.1244 &0.1166 &1 &0.0995 &0.1282 &0.1187 &0.1213 &0.1114 &0.1108\\ \hline C4 &0.1029 &0.108 &0.0974 &0.1264 &0.1301 &0.125 &0.1208 &1 &0.1232 &0.114 &0.1162 &0.1118 &0.1058\\ \hline D1 &0.086 &0.114 &0.1512 &0.1068 &0.1452 &0.1616 &0.1113 &0.114 &1 &0.1271 &0.1278 &0.1441 &0.1209\\ \hline D2 &0.0653 &0.0891 &0.0978 &0.0932 &0.1042 &0.106 &0.1102 &0.0779 &0.1167 &1 &0.0879 &0.0878 &0.1099\\ \hline D3 &0.0714 &0.0772 &0.0912 &0.0748 &0.0937 &0.0939 &0.0922 &0.0672 &0.0913 &0.1001 &1 &0.098 &0.0931\\ \hline E1 &0.1062 &0.1159 &0.1258 &0.1279 &0.1586 &0.1384 &0.1179 &0.117 &0.1271 &0.1296 &0.1499 &1 &0.1377\\ \hline E2 &0.0459 &0.0593 &0.0703 &0.0572 &0.0812 &0.0591 &0.0661 &0.0643 &0.0618 &0.0852 &0.0704 &0.0656 &1\\ \hline \end{array} $$

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。

$$\tilde R=\begin{array} {c|c|c}{M_{13 \times13}} &A1 &A2 &B1 &B2 &C1 &C2 &C3 &C4 &D1 &D2 &D3 &E1 &E2\\ \hline A1 &1 &0.1259 &0.1502 &0.1429 &0.1544 &0.1502 &0.1279 &0.117 &0.1502 &0.1418 &0.1441 &0.1441 &0.1377\\ \hline A2 &0.1062 &1 &0.124 &0.124 &0.1286 &0.124 &0.1192 &0.117 &0.124 &0.124 &0.1325 &0.124 &0.124\\ \hline B1 &0.1062 &0.1259 &1 &0.1324 &0.168 &0.1372 &0.1192 &0.117 &0.1372 &0.1418 &0.1372 &0.1372 &0.1372\\ \hline B2 &0.1062 &0.1259 &0.1304 &1 &0.1504 &0.1464 &0.1192 &0.117 &0.1304 &0.1304 &0.1304 &0.1304 &0.1304\\ \hline C1 &0.1062 &0.124 &0.124 &0.124 &1 &0.124 &0.1192 &0.117 &0.124 &0.124 &0.124 &0.124 &0.124\\ \hline C2 &0.1062 &0.1259 &0.1304 &0.1304 &0.1304 &1 &0.1192 &0.117 &0.1304 &0.1304 &0.1304 &0.1304 &0.1304\\ \hline C3 &0.1062 &0.1259 &0.1282 &0.1282 &0.1282 &0.1282 &1 &0.117 &0.1282 &0.1282 &0.1282 &0.1282 &0.1282\\ \hline C4 &0.1062 &0.1259 &0.1264 &0.1264 &0.1301 &0.1264 &0.1208 &1 &0.1264 &0.1264 &0.1264 &0.1264 &0.1264\\ \hline D1 &0.1062 &0.1259 &0.1512 &0.1324 &0.1512 &0.1616 &0.1192 &0.117 &1 &0.1418 &0.1441 &0.1441 &0.1377\\ \hline D2 &0.1062 &0.1167 &0.1167 &0.1167 &0.1167 &0.1167 &0.1167 &0.1167 &0.1167 &1 &0.1167 &0.1167 &0.1167\\ \hline D3 &0.1001 &0.1001 &0.1001 &0.1001 &0.1001 &0.1001 &0.1001 &0.1001 &0.1001 &0.1001 &1 &0.1001 &0.1001\\ \hline E1 &0.1062 &0.1259 &0.1304 &0.1304 &0.1586 &0.1384 &0.1192 &0.117 &0.1304 &0.1304 &0.1499 &1 &0.1377\\ \hline E2 &0.0852 &0.0852 &0.0852 &0.0852 &0.0852 &0.0852 &0.0852 &0.0852 &0.0852 &0.0852 &0.0852 &0.0852 &1\\ \hline \end{array} $$

由阈值集合$\ddot \Delta $　得出综合影响矩阵$T$对应 33个结构。

序号	阈值集合中——特征阈值	聚类特征-对应截距$\lambda $数值区段
1	0.08521	0<$\lambda$<0.08521
2	0.10008	0.08521<$\lambda$<0.10008
3	0.10617	0.10008<$\lambda$<0.10617
4	0.11672	0.10617<$\lambda$<0.11672
5	0.11701	0.11672<$\lambda$<0.11701
6	0.11924	0.11701<$\lambda$<0.11924
7	0.12081	0.11924<$\lambda$<0.12081
8	0.12396	0.12081<$\lambda$<0.12396
9	0.12588	0.12396<$\lambda$<0.12588
10	0.12643	0.12588<$\lambda$<0.12643
11	0.1279	0.12643<$\lambda$<0.1279
12	0.12817	0.1279<$\lambda$<0.12817
13	0.12864	0.12817<$\lambda$<0.12864
14	0.13009	0.12864<$\lambda$<0.13009
15	0.13039	0.13009<$\lambda$<0.13039
16	0.13239	0.13039<$\lambda$<0.13239
17	0.13252	0.13239<$\lambda$<0.13252
18	0.13721	0.13252<$\lambda$<0.13721
19	0.13768	0.13721<$\lambda$<0.13768
20	0.13836	0.13768<$\lambda$<0.13836
21	0.1418	0.13836<$\lambda$<0.1418
22	0.14289	0.1418<$\lambda$<0.14289
23	0.14413	0.14289<$\lambda$<0.14413
24	0.14645	0.14413<$\lambda$<0.14645
25	0.14995	0.14645<$\lambda$<0.14995
26	0.1502	0.14995<$\lambda$<0.1502
27	0.15044	0.1502<$\lambda$<0.15044
28	0.15123	0.15044<$\lambda$<0.15123
29	0.15443	0.15123<$\lambda$<0.15443
30	0.15862	0.15443<$\lambda$<0.15862
31	0.16158	0.15862<$\lambda$<0.16158
32	0.16798	0.16158<$\lambda$<0.16798
33	1	0.16798<$\lambda$<1

特征结构——不含孤立子系统

截距范围：0.127902658<$\lambda$<0.128170075

$$A_t=\begin{array} {c|c|c|c|c|c|c|c}{M_{13 \times13}} &A1 &A2 &B1 &B2 &C1 &C2 &C3 &C4 &D1 &D2 &D3 &E1 &E2\\ \hline A1 &1 & &1 &1 &1 &1 & & &1 &1 &1 &1 &1\\ \hline A2 & &1 & & &1 & & & & & &1 & & \\ \hline B1 & & &1 &1 &1 &1 & & &1 &1 &1 &1 &1\\ \hline B2 & & &1 &1 &1 &1 & & &1 &1 &1 &1 &1\\ \hline C1 & & & & &1 & & & & & & & & \\ \hline C2 & & &1 &1 &1 &1 & & &1 &1 &1 &1 &1\\ \hline C3 & & &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1\\ \hline C4 & & & & &1 & & &1 & & & & & \\ \hline D1 & & &1 &1 &1 &1 & & &1 &1 &1 &1 &1\\ \hline D2 & & & & & & & & & &1 & & & \\ \hline D3 & & & & & & & & & & &1 & & \\ \hline E1 & & &1 &1 &1 &1 & & &1 &1 &1 &1 &1\\ \hline E2 & & & & & & & & & & & & &1\\ \hline \end{array} $$

$$WS_t=\begin{array}{c|c|c|c|c|c|c}{M_{13 \times13}} &A1 &A2 &B1 &B2 &C1 &C2 &C3 &C4 &D1 &D2 &D3 &E1 &E2\\ \hline A1 &0 &0 &0 &0.1429 &0.1544 &0.1364 &0 &0 &0.1502 &0 &0.1424 &0 &0\\ \hline A2 &0 &0 &0 &0 &0.1286 &0 &0 &0 &0 &0 &0.1325 &0 &0\\ \hline B1 &0 &0 &0 &1 &0.168 &1 &0 &0 &1 &0.1418 &0 &1 &0\\ \hline B2 &0 &0 &1 &0 &0.1504 &1 &0 &0 &1 &0 &0 &1 &0\\ \hline C1 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline C2 &0 &0 &1 &1 &0 &0 &0 &0 &1 &0 &0 &1 &0\\ \hline C3 &0 &0 &0 &0 &0 &0 &0 &0 &0.1282 &0 &0 &0 &0\\ \hline C4 &0 &0 &0 &0 &0.1301 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline D1 &0 &0 &1 &1 &0.1452 &1 &0 &0 &0 &0 &0 &1 &0\\ \hline D2 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline D3 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline E1 &0 &0 &1 &1 &0.1586 &1 &0 &0 &1 &0.1296 &0.1499 &0 &0.1377\\ \hline E2 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline \end{array} $$

含孤立子系统的特征结构

截距范围：0.128170075<$\lambda$<0.128640173

$$A_s=\begin{array} {c|c|c|c|c|c|c|c}{M_{13 \times13}} &A1 &A2 &B1 &B2 &C1 &C2 &C3 &C4 &D1 &D2 &D3 &E1 &E2\\ \hline A1 &1 & &1 &1 &1 &1 & & &1 &1 &1 &1 &1\\ \hline A2 & &1 & & &1 & & & & & &1 & & \\ \hline B1 & & &1 &1 &1 &1 & & &1 &1 &1 &1 &1\\ \hline B2 & & &1 &1 &1 &1 & & &1 &1 &1 &1 &1\\ \hline C1 & & & & &1 & & & & & & & & \\ \hline C2 & & &1 &1 &1 &1 & & &1 &1 &1 &1 &1\\ \hline C3 & & & & & & &1 & & & & & & \\ \hline C4 & & & & &1 & & &1 & & & & & \\ \hline D1 & & &1 &1 &1 &1 & & &1 &1 &1 &1 &1\\ \hline D2 & & & & & & & & & &1 & & & \\ \hline D3 & & & & & & & & & & &1 & & \\ \hline E1 & & &1 &1 &1 &1 & & &1 &1 &1 &1 &1\\ \hline E2 & & & & & & & & & & & & &1\\ \hline \end{array} $$

$$WS_s=\begin{array}{c|c|c|c|c|c|c}{M_{13 \times13}} &A1 &A2 &B1 &B2 &C1 &C2 &C3 &C4 &D1 &D2 &D3 &E1 &E2\\ \hline A1 &0 &0 &0 &0.1429 &0.1544 &0.1364 &0 &0 &0.1502 &0 &0.1424 &0 &0\\ \hline A2 &0 &0 &0 &0 &0.1286 &0 &0 &0 &0 &0 &0.1325 &0 &0\\ \hline B1 &0 &0 &0 &1 &0.168 &1 &0 &0 &1 &0.1418 &0 &1 &0\\ \hline B2 &0 &0 &1 &0 &0.1504 &1 &0 &0 &1 &0 &0 &1 &0\\ \hline C1 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline C2 &0 &0 &1 &1 &0 &0 &0 &0 &1 &0 &0 &1 &0\\ \hline C3 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline C4 &0 &0 &0 &0 &0.1301 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline D1 &0 &0 &1 &1 &0.1452 &1 &0 &0 &0 &0 &0 &1 &0\\ \hline D2 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline D3 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline E1 &0 &0 &1 &1 &0.1586 &1 &0 &0 &1 &0.1296 &0.1499 &0 &0.1377\\ \hline E2 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline \end{array} $$

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

$$\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{13 \times4}} &Di &Ci &Mi &Ri\\ \hline A1 &1.545 &1.04 &2.585 &0.505\\ \hline A2 &1.226 &1.222 &2.447 &0.004\\ \hline B1 &1.559 &1.288 &2.847 &0.27\\ \hline B2 &1.424 &1.332 &2.756 &0.092\\ \hline C1 &1.275 &1.635 &2.91 &-0.36\\ \hline C2 &1.322 &1.52 &2.842 &-0.198\\ \hline C3 &1.397 &1.287 &2.684 &0.11\\ \hline C4 &1.437 &1.129 &2.566 &0.308\\ \hline D1 &1.589 &1.485 &3.074 &0.104\\ \hline D2 &1.204 &1.406 &2.61 &-0.202\\ \hline D3 &1.098 &1.474 &2.572 &-0.375\\ \hline E1 &1.63 &1.414 &3.044 &0.216\\ \hline E2 &0.823 &1.296 &2.119 &-0.473\\ \hline \end{array} $$

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