DEMATEL-ISM中特征突变结构的在线计算

特征结构的计算与说明

原始矩阵（直接影响矩阵）为

$$Ori=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{11 \times11}} &A1 &A2 &B1 &B2 &C1 &C2 &C3 &C4 &D1 &D2 &D3\\ \hline A1 &0 &50 &12 &46 &43 &34 &38 &24 &45 &23 &40\\ \hline A2 &51 &0 &17 &34 &21 &30 &47 &16 &12 &4 &7\\ \hline B1 &18 &23 &0 &39 &51 &34 &32 &19 &36 &42 &29\\ \hline B2 &24 &16 &16 &0 &45 &45 &24 &30 &36 &28 &33\\ \hline C1 &25 &20 &18 &21 &0 &36 &16 &21 &33 &25 &31\\ \hline C2 &19 &15 &45 &30 &32 &0 &14 &18 &23 &29 &25\\ \hline C3 &21 &13 &25 &37 &29 &27 &0 &28 &36 &32 &32\\ \hline C4 &32 &22 &21 &38 &31 &31 &36 &0 &31 &28 &27\\ \hline D1 &18 &11 &50 &21 &35 &50 &26 &33 &0 &31 &30\\ \hline D2 &14 &17 &27 &24 &23 &27 &36 &19 &35 &0 &17\\ \hline D3 &20 &16 &26 &15 &20 &23 &27 &15 &22 &29 &0\\ \hline \end{array} $$

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

$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{11 \times11}} &A1 &A2 &B1 &B2 &C1 &C2 &C3 &C4 &D1 &D2 &D3\\ \hline A1 &0 &0.102 &0.025 &0.094 &0.088 &0.069 &0.078 &0.049 &0.092 &0.047 &0.082\\ \hline A2 &0.104 &0 &0.035 &0.069 &0.043 &0.061 &0.096 &0.033 &0.025 &0.008 &0.014\\ \hline B1 &0.037 &0.047 &0 &0.08 &0.104 &0.069 &0.065 &0.039 &0.074 &0.086 &0.059\\ \hline B2 &0.049 &0.033 &0.033 &0 &0.092 &0.092 &0.049 &0.061 &0.074 &0.057 &0.067\\ \hline C1 &0.051 &0.041 &0.037 &0.043 &0 &0.074 &0.033 &0.043 &0.067 &0.051 &0.063\\ \hline C2 &0.039 &0.031 &0.092 &0.061 &0.065 &0 &0.029 &0.037 &0.047 &0.059 &0.051\\ \hline C3 &0.043 &0.027 &0.051 &0.076 &0.059 &0.055 &0 &0.057 &0.074 &0.065 &0.065\\ \hline C4 &0.065 &0.045 &0.043 &0.078 &0.063 &0.063 &0.074 &0 &0.063 &0.057 &0.055\\ \hline D1 &0.037 &0.022 &0.102 &0.043 &0.072 &0.102 &0.053 &0.067 &0 &0.063 &0.061\\ \hline D2 &0.029 &0.035 &0.055 &0.049 &0.047 &0.055 &0.074 &0.039 &0.072 &0 &0.035\\ \hline D3 &0.041 &0.033 &0.053 &0.031 &0.041 &0.047 &0.055 &0.031 &0.045 &0.059 &0\\ \hline \end{array} $$

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

　　综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{11 \times11}} &A1 &A2 &B1 &B2 &C1 &C2 &C3 &C4 &D1 &D2 &D3\\ \hline A1 &0.077 &0.157 &0.108 &0.18 &0.183 &0.171 &0.162 &0.119 &0.18 &0.129 &0.162\\ \hline A2 &0.151 &0.048 &0.09 &0.135 &0.117 &0.133 &0.153 &0.084 &0.095 &0.071 &0.079\\ \hline B1 &0.102 &0.101 &0.077 &0.158 &0.19 &0.162 &0.142 &0.103 &0.158 &0.159 &0.135\\ \hline B2 &0.109 &0.084 &0.104 &0.078 &0.171 &0.175 &0.12 &0.118 &0.15 &0.128 &0.137\\ \hline C1 &0.101 &0.084 &0.096 &0.107 &0.073 &0.144 &0.095 &0.092 &0.131 &0.11 &0.121\\ \hline C2 &0.09 &0.076 &0.146 &0.125 &0.138 &0.077 &0.093 &0.087 &0.116 &0.12 &0.111\\ \hline C3 &0.1 &0.076 &0.117 &0.145 &0.139 &0.138 &0.071 &0.112 &0.147 &0.132 &0.132\\ \hline C4 &0.125 &0.097 &0.112 &0.153 &0.148 &0.15 &0.145 &0.062 &0.143 &0.128 &0.127\\ \hline D1 &0.098 &0.077 &0.169 &0.123 &0.158 &0.186 &0.127 &0.125 &0.085 &0.138 &0.133\\ \hline D2 &0.079 &0.076 &0.112 &0.112 &0.117 &0.126 &0.131 &0.088 &0.135 &0.061 &0.094\\ \hline D3 &0.084 &0.071 &0.103 &0.088 &0.103 &0.11 &0.108 &0.074 &0.104 &0.11 &0.053\\ \hline \end{array} $$

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$

$$\tilde B=\begin{array} {c|c|c}{M_{11 \times11}} &A1 &A2 &B1 &B2 &C1 &C2 &C3 &C4 &D1 &D2 &D3\\ \hline A1 &1 &0.1571 &0.1077 &0.1796 &0.183 &0.1715 &0.1622 &0.1187 &0.1803 &0.1293 &0.1618\\ \hline A2 &0.1511 &1 &0.0903 &0.1354 &0.1165 &0.1331 &0.1533 &0.0837 &0.0955 &0.0705 &0.0789\\ \hline B1 &0.1025 &0.1008 &1 &0.1579 &0.1898 &0.1621 &0.1417 &0.1029 &0.1575 &0.1595 &0.1347\\ \hline B2 &0.1086 &0.0844 &0.104 &1 &0.1714 &0.1746 &0.1204 &0.1181 &0.1503 &0.1277 &0.1367\\ \hline C1 &0.1009 &0.0839 &0.0962 &0.1068 &1 &0.1438 &0.0951 &0.0915 &0.1314 &0.11 &0.1208\\ \hline C2 &0.0902 &0.0756 &0.1459 &0.1253 &0.1378 &1 &0.0928 &0.087 &0.1159 &0.1204 &0.1114\\ \hline C3 &0.0997 &0.076 &0.1165 &0.1449 &0.1392 &0.138 &1 &0.1122 &0.1474 &0.1325 &0.1316\\ \hline C4 &0.1248 &0.097 &0.1121 &0.1527 &0.1479 &0.1502 &0.1451 &1 &0.1431 &0.1283 &0.1268\\ \hline D1 &0.0984 &0.0767 &0.1693 &0.1229 &0.158 &0.1858 &0.1269 &0.1249 &1 &0.1379 &0.1334\\ \hline D2 &0.0789 &0.076 &0.1119 &0.1118 &0.117 &0.1263 &0.1305 &0.0878 &0.1347 &1 &0.0941\\ \hline D3 &0.0845 &0.0707 &0.1026 &0.0882 &0.1032 &0.1098 &0.1081 &0.074 &0.1035 &0.1104 &1\\ \hline \end{array} $$

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。

$$\tilde R=\begin{array} {c|c|c}{M_{11 \times11}} &A1 &A2 &B1 &B2 &C1 &C2 &C3 &C4 &D1 &D2 &D3\\ \hline A1 &1 &0.1571 &0.1693 &0.1796 &0.183 &0.1803 &0.1622 &0.1249 &0.1803 &0.1595 &0.1618\\ \hline A2 &0.1511 &1 &0.1511 &0.1511 &0.1511 &0.1511 &0.1533 &0.1249 &0.1511 &0.1511 &0.1511\\ \hline B1 &0.1248 &0.1248 &1 &0.1579 &0.1898 &0.1621 &0.1417 &0.1249 &0.1575 &0.1595 &0.1367\\ \hline B2 &0.1248 &0.1248 &0.1503 &1 &0.1714 &0.1746 &0.1417 &0.1249 &0.1503 &0.1503 &0.1367\\ \hline C1 &0.1248 &0.1248 &0.1438 &0.1438 &1 &0.1438 &0.1417 &0.1249 &0.1438 &0.1438 &0.1367\\ \hline C2 &0.1248 &0.1248 &0.1459 &0.1459 &0.1459 &1 &0.1417 &0.1249 &0.1459 &0.1459 &0.1367\\ \hline C3 &0.1248 &0.1248 &0.1474 &0.1474 &0.1474 &0.1474 &1 &0.1249 &0.1474 &0.1474 &0.1367\\ \hline C4 &0.1248 &0.1248 &0.1503 &0.1527 &0.1527 &0.1527 &0.1451 &1 &0.1503 &0.1503 &0.1367\\ \hline D1 &0.1248 &0.1248 &0.1693 &0.1579 &0.1693 &0.1858 &0.1417 &0.1249 &1 &0.1595 &0.1367\\ \hline D2 &0.1248 &0.1248 &0.1347 &0.1347 &0.1347 &0.1347 &0.1347 &0.1249 &0.1347 &1 &0.1347\\ \hline D3 &0.1104 &0.1104 &0.1104 &0.1104 &0.1104 &0.1104 &0.1104 &0.1104 &0.1104 &0.1104 &1\\ \hline \end{array} $$

由阈值集合$\ddot \Delta $　得出综合影响矩阵$T$对应 30个结构。

序号	阈值集合中——特征阈值	聚类特征-对应截距$\lambda $数值区段
1	0.11045	0<$\lambda$<0.11045
2	0.12485	0.11045<$\lambda$<0.12485
3	0.1249	0.12485<$\lambda$<0.1249
4	0.13467	0.1249<$\lambda$<0.13467
5	0.1367	0.13467<$\lambda$<0.1367
6	0.14171	0.1367<$\lambda$<0.14171
7	0.14375	0.14171<$\lambda$<0.14375
8	0.14507	0.14375<$\lambda$<0.14507
9	0.14589	0.14507<$\lambda$<0.14589
10	0.14741	0.14589<$\lambda$<0.14741
11	0.15033	0.14741<$\lambda$<0.15033
12	0.15107	0.15033<$\lambda$<0.15107
13	0.15266	0.15107<$\lambda$<0.15266
14	0.15328	0.15266<$\lambda$<0.15328
15	0.15713	0.15328<$\lambda$<0.15713
16	0.15751	0.15713<$\lambda$<0.15751
17	0.15791	0.15751<$\lambda$<0.15791
18	0.15947	0.15791<$\lambda$<0.15947
19	0.16177	0.15947<$\lambda$<0.16177
20	0.16212	0.16177<$\lambda$<0.16212
21	0.16216	0.16212<$\lambda$<0.16216
22	0.16935	0.16216<$\lambda$<0.16935
23	0.17143	0.16935<$\lambda$<0.17143
24	0.17456	0.17143<$\lambda$<0.17456
25	0.17956	0.17456<$\lambda$<0.17956
26	0.18033	0.17956<$\lambda$<0.18033
27	0.18298	0.18033<$\lambda$<0.18298
28	0.18583	0.18298<$\lambda$<0.18583
29	0.18981	0.18583<$\lambda$<0.18981
30	1	0.18981<$\lambda$<1

特征结构

截距范围：0.151067164<$\lambda$<0.152660123

$$A=\begin{array} {c|c|c|c|c|c|c|c}{M_{11 \times11}} &A1 &A2 &B1 &B2 &C1 &C2 &C3 &C4 &D1 &D2 &D3\\ \hline A1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1\\ \hline A2 & &1 & & & & &1 & & & & \\ \hline B1 & & &1 &1 &1 &1 & & &1 &1 & \\ \hline B2 & & & &1 &1 &1 & & & & & \\ \hline C1 & & & & &1 & & & & & & \\ \hline C2 & & & & & &1 & & & & & \\ \hline C3 & & & & & & &1 & & & & \\ \hline C4 & & & &1 &1 &1 & &1 & & & \\ \hline D1 & & &1 &1 &1 &1 & & &1 &1 & \\ \hline D2 & & & & & & & & & &1 & \\ \hline D3 & & & & & & & & & & &1\\ \hline \end{array} $$

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

$$\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{11 \times4}} &Di &Ci &Mi &Ri\\ \hline A1 &1.628 &1.116 &2.744 &0.512\\ \hline A2 &1.156 &0.946 &2.103 &0.21\\ \hline B1 &1.486 &1.233 &2.72 &0.253\\ \hline B2 &1.374 &1.403 &2.777 &-0.029\\ \hline C1 &1.153 &1.537 &2.69 &-0.384\\ \hline C2 &1.179 &1.572 &2.752 &-0.393\\ \hline C3 &1.309 &1.347 &2.657 &-0.038\\ \hline C4 &1.39 &1.063 &2.452 &0.327\\ \hline D1 &1.419 &1.445 &2.864 &-0.025\\ \hline D2 &1.13 &1.288 &2.418 &-0.158\\ \hline D3 &1.009 &1.284 &2.292 &-0.275\\ \hline \end{array} $$

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

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

绘制中心度与原因度建构的散点图图表

DEMATEL-FISM流程图如下：