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 $$ \require{cancel} \require{AMScd} \begin{CD} O @>>>N \\ \end{CD} $$

$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{11 \times11}} &A1 &A2 &B1 &B2 &C1 &C2 &C3 &C4 &D1 &D2 &D3\\ \hline A1 &0 &0.115 &0.028 &0.106 &0.099 &0.078 &0.088 &0.055 &0.104 &0.053 &0.092\\ \hline A2 &0.117 &0 &0.039 &0.078 &0.048 &0.069 &0.108 &0.037 &0.028 &0.009 &0.016\\ \hline B1 &0.041 &0.053 &0 &0.09 &0.117 &0.078 &0.074 &0.044 &0.083 &0.097 &0.067\\ \hline B2 &0.055 &0.037 &0.037 &0 &0.104 &0.104 &0.055 &0.069 &0.083 &0.064 &0.076\\ \hline C1 &0.058 &0.046 &0.041 &0.048 &0 &0.083 &0.037 &0.048 &0.076 &0.058 &0.071\\ \hline C2 &0.044 &0.035 &0.104 &0.069 &0.074 &0 &0.032 &0.041 &0.053 &0.067 &0.058\\ \hline C3 &0.048 &0.03 &0.058 &0.085 &0.067 &0.062 &0 &0.064 &0.083 &0.074 &0.074\\ \hline C4 &0.074 &0.051 &0.048 &0.088 &0.071 &0.071 &0.083 &0 &0.071 &0.064 &0.062\\ \hline D1 &0.041 &0.025 &0.115 &0.048 &0.081 &0.115 &0.06 &0.076 &0 &0.071 &0.069\\ \hline D2 &0.032 &0.039 &0.062 &0.055 &0.053 &0.062 &0.083 &0.044 &0.081 &0 &0.039\\ \hline D3 &0.046 &0.037 &0.06 &0.035 &0.046 &0.053 &0.062 &0.035 &0.051 &0.067 &0\\ \hline \end{array} $$

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

　　综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{11 \times11}} &A1 &A2 &B1 &B2 &C1 &C2 &C3 &C4 &D1 &D2 &D3\\ \hline A1 &0.115 &0.2 &0.153 &0.237 &0.244 &0.233 &0.216 &0.161 &0.239 &0.178 &0.214\\ \hline A2 &0.19 &0.072 &0.125 &0.178 &0.16 &0.179 &0.197 &0.114 &0.135 &0.104 &0.113\\ \hline B1 &0.141 &0.135 &0.116 &0.209 &0.249 &0.219 &0.19 &0.141 &0.211 &0.209 &0.181\\ \hline B2 &0.146 &0.115 &0.144 &0.117 &0.225 &0.23 &0.164 &0.156 &0.2 &0.172 &0.181\\ \hline C1 &0.133 &0.112 &0.131 &0.145 &0.11 &0.19 &0.131 &0.122 &0.174 &0.147 &0.159\\ \hline C2 &0.122 &0.103 &0.187 &0.167 &0.184 &0.116 &0.129 &0.118 &0.157 &0.16 &0.149\\ \hline C3 &0.135 &0.105 &0.157 &0.191 &0.188 &0.188 &0.108 &0.148 &0.195 &0.176 &0.175\\ \hline C4 &0.164 &0.13 &0.154 &0.202 &0.2 &0.203 &0.192 &0.093 &0.193 &0.173 &0.171\\ \hline D1 &0.135 &0.107 &0.218 &0.169 &0.212 &0.243 &0.172 &0.164 &0.128 &0.184 &0.179\\ \hline D2 &0.109 &0.102 &0.148 &0.151 &0.159 &0.17 &0.17 &0.118 &0.177 &0.093 &0.129\\ \hline D3 &0.113 &0.095 &0.135 &0.122 &0.141 &0.149 &0.143 &0.101 &0.14 &0.145 &0.081\\ \hline \end{array} $$

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$

$$\tilde B=\begin{array} {c|c|c}{M_{11 \times11}} &A1 &A2 &B1 &B2 &C1 &C2 &C3 &C4 &D1 &D2 &D3\\ \hline A1 &1 &0.2001 &0.1533 &0.2368 &0.2443 &0.2328 &0.2159 &0.1609 &0.239 &0.1783 &0.2145\\ \hline A2 &0.19 &1 &0.1245 &0.1782 &0.1598 &0.1787 &0.1965 &0.1143 &0.1346 &0.1037 &0.1133\\ \hline B1 &0.141 &0.1351 &1 &0.2094 &0.2486 &0.2188 &0.1899 &0.1408 &0.2106 &0.2093 &0.1815\\ \hline B2 &0.1459 &0.1152 &0.1444 &1 &0.2254 &0.2298 &0.1638 &0.1558 &0.2 &0.1717 &0.1815\\ \hline C1 &0.1335 &0.1115 &0.1313 &0.1454 &1 &0.1901 &0.1312 &0.1225 &0.1739 &0.1474 &0.1592\\ \hline C2 &0.122 &0.1027 &0.187 &0.1667 &0.1837 &1 &0.1293 &0.1179 &0.1575 &0.1597 &0.1494\\ \hline C3 &0.1348 &0.105 &0.157 &0.1913 &0.1882 &0.1877 &1 &0.1483 &0.1955 &0.1758 &0.1746\\ \hline C4 &0.1645 &0.1298 &0.1535 &0.2019 &0.1999 &0.2034 &0.192 &1 &0.1926 &0.1727 &0.171\\ \hline D1 &0.1352 &0.1074 &0.2181 &0.1694 &0.2119 &0.2435 &0.1721 &0.1641 &1 &0.1844 &0.1788\\ \hline D2 &0.1086 &0.1022 &0.1484 &0.1506 &0.1592 &0.1702 &0.1702 &0.1181 &0.1772 &1 &0.1291\\ \hline D3 &0.1126 &0.0947 &0.1354 &0.1217 &0.1406 &0.1486 &0.1427 &0.1005 &0.1396 &0.145 &1\\ \hline \end{array} $$

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。

$$\tilde R=\begin{array} {c|c|c}{M_{11 \times11}} &A1 &A2 &B1 &B2 &C1 &C2 &C3 &C4 &D1 &D2 &D3\\ \hline A1 &1 &0.2001 &0.2181 &0.2368 &0.2443 &0.239 &0.2159 &0.1641 &0.239 &0.2093 &0.2145\\ \hline A2 &0.19 &1 &0.1955 &0.1955 &0.1955 &0.1955 &0.1965 &0.1641 &0.1955 &0.1955 &0.19\\ \hline B1 &0.1641 &0.1641 &1 &0.2094 &0.2486 &0.2188 &0.1899 &0.1641 &0.2106 &0.2093 &0.1815\\ \hline B2 &0.1641 &0.1641 &0.2 &1 &0.2254 &0.2298 &0.1899 &0.1641 &0.2 &0.2 &0.1815\\ \hline C1 &0.1641 &0.1641 &0.187 &0.187 &1 &0.1901 &0.187 &0.1641 &0.187 &0.187 &0.1815\\ \hline C2 &0.1641 &0.1641 &0.187 &0.187 &0.187 &1 &0.187 &0.1641 &0.187 &0.187 &0.1815\\ \hline C3 &0.1641 &0.1641 &0.1955 &0.1955 &0.1955 &0.1955 &1 &0.1641 &0.1955 &0.1955 &0.1815\\ \hline C4 &0.1645 &0.1645 &0.2 &0.2019 &0.2019 &0.2034 &0.192 &1 &0.2 &0.2 &0.1815\\ \hline D1 &0.1641 &0.1641 &0.2181 &0.2094 &0.2181 &0.2435 &0.1899 &0.1641 &1 &0.2093 &0.1815\\ \hline D2 &0.1641 &0.1641 &0.1772 &0.1772 &0.1772 &0.1772 &0.1772 &0.1641 &0.1772 &1 &0.1772\\ \hline D3 &0.1486 &0.1486 &0.1486 &0.1486 &0.1486 &0.1486 &0.1486 &0.1486 &0.1486 &0.1486 &1\\ \hline \end{array} $$

由阈值集合$\ddot \Delta $　得出综合影响矩阵$T$对应 31个结构。

序号	阈值集合中——特征阈值	聚类特征-对应截距$\lambda $数值区段
1	0.14865	0<$\lambda$<0.14865
2	0.16411	0.14865<$\lambda$<0.16411
3	0.16448	0.16411<$\lambda$<0.16448
4	0.17717	0.16448<$\lambda$<0.17717
5	0.18148	0.17717<$\lambda$<0.18148
6	0.18701	0.18148<$\lambda$<0.18701
7	0.18993	0.18701<$\lambda$<0.18993
8	0.19002	0.18993<$\lambda$<0.19002
9	0.19006	0.19002<$\lambda$<0.19006
10	0.19198	0.19006<$\lambda$<0.19198
11	0.19547	0.19198<$\lambda$<0.19547
12	0.19652	0.19547<$\lambda$<0.19652
13	0.19996	0.19652<$\lambda$<0.19996
14	0.20011	0.19996<$\lambda$<0.20011
15	0.20192	0.20011<$\lambda$<0.20192
16	0.20335	0.20192<$\lambda$<0.20335
17	0.20932	0.20335<$\lambda$<0.20932
18	0.20943	0.20932<$\lambda$<0.20943
19	0.21059	0.20943<$\lambda$<0.21059
20	0.21445	0.21059<$\lambda$<0.21445
21	0.21592	0.21445<$\lambda$<0.21592
22	0.21814	0.21592<$\lambda$<0.21814
23	0.21882	0.21814<$\lambda$<0.21882
24	0.22536	0.21882<$\lambda$<0.22536
25	0.2298	0.22536<$\lambda$<0.2298
26	0.23679	0.2298<$\lambda$<0.23679
27	0.23898	0.23679<$\lambda$<0.23898
28	0.24349	0.23898<$\lambda$<0.24349
29	0.24432	0.24349<$\lambda$<0.24432
30	0.24856	0.24432<$\lambda$<0.24856
31	1	0.24856<$\lambda$<1

特征结构

截距范围：0.199958809<$\lambda$<0.200111672

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

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

$$\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{11 \times4}} &Di &Ci &Mi &Ri\\ \hline A1 &2.191 &1.503 &3.694 &0.688\\ \hline A2 &1.566 &1.276 &2.841 &0.29\\ \hline B1 &2.001 &1.669 &3.67 &0.332\\ \hline B2 &1.851 &1.889 &3.739 &-0.038\\ \hline C1 &1.556 &2.071 &3.627 &-0.516\\ \hline C2 &1.592 &2.12 &3.712 &-0.528\\ \hline C3 &1.766 &1.811 &3.577 &-0.045\\ \hline C4 &1.875 &1.436 &3.311 &0.438\\ \hline D1 &1.913 &1.948 &3.861 &-0.035\\ \hline D2 &1.527 &1.741 &3.267 &-0.214\\ \hline D3 &1.362 &1.734 &3.096 &-0.371\\ \hline \end{array} $$

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：