决策与实验室-不确定性解释结构模型在线计算，DEMATEL-UISM

原始矩阵（直接影响矩阵）为

$$Ori=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &D1 &D2 &D3 &D4 &D5 &D6 &D7 &D8 &D9 &D10\\ \hline D1 &0 &13 &13 &19 &23 &22 &12 &13 &12 &26\\ \hline D2 &21 &0 &5 &21 &16 &12 &15 &12 &19 &25\\ \hline D3 &20 &8 &0 &14 &13 &10 &13 &16 &24 &21\\ \hline D4 &33 &10 &5 &0 &16 &19 &19 &19 &19 &20\\ \hline D5 &33 &10 &20 &10 &0 &27 &17 &20 &25 &23\\ \hline D6 &20 &25 &13 &21 &2 &0 &23 &22 &21 &21\\ \hline D7 &22 &31 &10 &10 &25 &18 &0 &24 &20 &19\\ \hline D8 &10 &13 &13 &11 &26 &25 &21 &0 &20 &24\\ \hline D9 &20 &11 &21 &10 &10 &27 &22 &21 &0 &31\\ \hline D10 &10 &20 &14 &10 &21 &21 &22 &21 &11 &0\\ \hline \end{array} $$

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

$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &D1 &D2 &D3 &D4 &D5 &D6 &D7 &D8 &D9 &D10\\ \hline D1 &0 &0.05 &0.05 &0.074 &0.089 &0.085 &0.046 &0.05 &0.046 &0.101\\ \hline D2 &0.081 &0 &0.019 &0.081 &0.062 &0.046 &0.058 &0.046 &0.074 &0.097\\ \hline D3 &0.077 &0.031 &0 &0.054 &0.05 &0.039 &0.05 &0.062 &0.093 &0.081\\ \hline D4 &0.128 &0.039 &0.019 &0 &0.062 &0.074 &0.074 &0.074 &0.074 &0.077\\ \hline D5 &0.128 &0.039 &0.077 &0.039 &0 &0.105 &0.066 &0.077 &0.097 &0.089\\ \hline D6 &0.077 &0.097 &0.05 &0.081 &0.008 &0 &0.089 &0.085 &0.081 &0.081\\ \hline D7 &0.085 &0.12 &0.039 &0.039 &0.097 &0.07 &0 &0.093 &0.077 &0.074\\ \hline D8 &0.039 &0.05 &0.05 &0.043 &0.101 &0.097 &0.081 &0 &0.077 &0.093\\ \hline D9 &0.077 &0.043 &0.081 &0.039 &0.039 &0.105 &0.085 &0.081 &0 &0.12\\ \hline D10 &0.039 &0.077 &0.054 &0.039 &0.081 &0.081 &0.085 &0.081 &0.043 &0\\ \hline \end{array} $$

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

　　综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &D1 &D2 &D3 &D4 &D5 &D6 &D7 &D8 &D9 &D10\\ \hline D1 &0.118 &0.142 &0.124 &0.151 &0.18 &0.197 &0.152 &0.157 &0.152 &0.224\\ \hline D2 &0.188 &0.09 &0.093 &0.154 &0.154 &0.159 &0.157 &0.149 &0.17 &0.217\\ \hline D3 &0.178 &0.115 &0.071 &0.125 &0.139 &0.146 &0.146 &0.158 &0.183 &0.198\\ \hline D4 &0.238 &0.137 &0.1 &0.086 &0.164 &0.194 &0.18 &0.182 &0.179 &0.212\\ \hline D5 &0.254 &0.15 &0.165 &0.136 &0.117 &0.237 &0.189 &0.202 &0.216 &0.242\\ \hline D6 &0.197 &0.193 &0.128 &0.165 &0.119 &0.126 &0.198 &0.196 &0.19 &0.22\\ \hline D7 &0.214 &0.219 &0.126 &0.134 &0.205 &0.202 &0.123 &0.21 &0.197 &0.224\\ \hline D8 &0.164 &0.151 &0.131 &0.128 &0.197 &0.216 &0.191 &0.118 &0.188 &0.227\\ \hline D9 &0.199 &0.149 &0.161 &0.129 &0.148 &0.226 &0.199 &0.198 &0.119 &0.257\\ \hline D10 &0.154 &0.167 &0.126 &0.118 &0.173 &0.191 &0.184 &0.183 &0.149 &0.13\\ \hline \end{array} $$

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$

$$\tilde B=\begin{array} {c|c|c}{M_{10 \times10}} &D1 &D2 &D3 &D4 &D5 &D6 &D7 &D8 &D9 &D10\\ \hline D1 &1 &0.1421 &0.1243 &0.1508 &0.1803 &0.1967 &0.1519 &0.1573 &0.1521 &0.2244\\ \hline D2 &0.1883 &1 &0.0927 &0.1539 &0.1542 &0.1586 &0.1574 &0.1488 &0.1698 &0.2165\\ \hline D3 &0.1778 &0.1151 &1 &0.1249 &0.1389 &0.1464 &0.1455 &0.1576 &0.1828 &0.1975\\ \hline D4 &0.2383 &0.1372 &0.1004 &1 &0.1637 &0.1939 &0.1803 &0.1824 &0.1793 &0.2118\\ \hline D5 &0.2537 &0.1502 &0.165 &0.1361 &1 &0.2369 &0.189 &0.2016 &0.2163 &0.2416\\ \hline D6 &0.197 &0.1928 &0.1278 &0.1653 &0.1191 &1 &0.1981 &0.196 &0.1905 &0.2196\\ \hline D7 &0.2143 &0.2187 &0.126 &0.1336 &0.2047 &0.2021 &1 &0.2104 &0.1968 &0.224\\ \hline D8 &0.1637 &0.1507 &0.1312 &0.1278 &0.1971 &0.2159 &0.191 &1 &0.1881 &0.2274\\ \hline D9 &0.1989 &0.1491 &0.1609 &0.1291 &0.1482 &0.2261 &0.1988 &0.1976 &1 &0.2566\\ \hline D10 &0.1535 &0.1667 &0.1261 &0.1184 &0.1732 &0.1907 &0.1843 &0.1829 &0.1488 &1\\ \hline \end{array} $$

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。

$$\tilde R=\begin{array} {c|c|c}{M_{10 \times10}} &D1 &D2 &D3 &D4 &D5 &D6 &D7 &D8 &D9 &D10\\ \hline D1 &1 &0.1967 &0.165 &0.1653 &0.1967 &0.1967 &0.1967 &0.1967 &0.1967 &0.2244\\ \hline D2 &0.1907 &1 &0.165 &0.1653 &0.1907 &0.1907 &0.1907 &0.1907 &0.1907 &0.2165\\ \hline D3 &0.1907 &0.1907 &1 &0.1653 &0.1907 &0.1907 &0.1907 &0.1907 &0.1907 &0.1975\\ \hline D4 &0.2383 &0.1967 &0.165 &1 &0.1967 &0.1967 &0.1967 &0.1967 &0.1967 &0.2244\\ \hline D5 &0.2537 &0.1988 &0.165 &0.1653 &1 &0.2369 &0.1988 &0.2016 &0.2163 &0.2416\\ \hline D6 &0.1981 &0.1981 &0.165 &0.1653 &0.1981 &1 &0.1981 &0.1981 &0.1981 &0.2196\\ \hline D7 &0.2143 &0.2187 &0.165 &0.1653 &0.2047 &0.2104 &1 &0.2104 &0.2047 &0.224\\ \hline D8 &0.1981 &0.1981 &0.165 &0.1653 &0.1981 &0.2159 &0.1981 &1 &0.1981 &0.2274\\ \hline D9 &0.1989 &0.1988 &0.165 &0.1653 &0.1988 &0.2261 &0.1988 &0.1988 &1 &0.2566\\ \hline D10 &0.1907 &0.1907 &0.165 &0.1653 &0.1907 &0.1907 &0.1907 &0.1907 &0.1907 &1\\ \hline \end{array} $$

由阈值集合$\ddot \Delta $　得出综合影响矩阵$T$对应 26个特征阈值。

序号	阈值	模糊可达矩阵中该数值的个数	特征值对应的子矩阵个数	UISM运算过程
1	0.165023	总共9个	$2^{9}$	异构体个数太多，超过$2^7$，超出算力范围！
2	0.165275	总共9个	$2^{9}$	异构体个数太多，超过$2^7$，超出算力范围！
3	0.190703	总共20个	$2^{20}$	异构体个数太多，超过$2^7$，超出算力范围！
4	0.196737	总共12个	$2^{12}$	异构体个数太多，超过$2^7$，超出算力范围！
5	0.197513	总共1个	$2^{1}$	异构体个数太少，不需要计算
6	0.198069	总共11个	$2^{11}$	异构体个数太多，超过$2^7$，超出算力范围！
7	0.198803	总共6个	$2^{6}$
8	0.198869	总共1个	$2^{1}$	异构体个数太少，不需要计算
9	0.201621	总共1个	$2^{1}$	异构体个数太少，不需要计算
10	0.204729	总共2个	$2^{2}$
11	0.210419	总共2个	$2^{2}$
12	0.214332	总共1个	$2^{1}$	异构体个数太少，不需要计算
13	0.215897	总共1个	$2^{1}$	异构体个数太少，不需要计算
14	0.21629	总共1个	$2^{1}$	异构体个数太少，不需要计算
15	0.216514	总共1个	$2^{1}$	异构体个数太少，不需要计算
16	0.21868	总共1个	$2^{1}$	异构体个数太少，不需要计算
17	0.219646	总共1个	$2^{1}$	异构体个数太少，不需要计算
18	0.223991	总共1个	$2^{1}$	异构体个数太少，不需要计算
19	0.224402	总共2个	$2^{2}$
20	0.226116	总共1个	$2^{1}$	异构体个数太少，不需要计算
21	0.227442	总共1个	$2^{1}$	异构体个数太少，不需要计算
22	0.236905	总共1个	$2^{1}$	异构体个数太少，不需要计算
23	0.238345	总共1个	$2^{1}$	异构体个数太少，不需要计算
24	0.241572	总共1个	$2^{1}$	异构体个数太少，不需要计算
25	0.253673	总共1个	$2^{1}$	异构体个数太少，不需要计算
26	0.256637	总共1个	$2^{1}$	异构体个数太少，不需要计算

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

$$\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times4}} &Di &Ci &Mi &Ri\\ \hline D1 &1.598 &1.904 &3.502 &-0.306\\ \hline D2 &1.53 &1.513 &3.043 &0.018\\ \hline D3 &1.458 &1.225 &2.683 &0.232\\ \hline D4 &1.674 &1.326 &3 &0.347\\ \hline D5 &1.908 &1.597 &3.504 &0.311\\ \hline D6 &1.732 &1.893 &3.625 &-0.161\\ \hline D7 &1.854 &1.72 &3.574 &0.134\\ \hline D8 &1.711 &1.753 &3.464 &-0.042\\ \hline D9 &1.785 &1.744 &3.528 &0.041\\ \hline D10 &1.575 &2.15 &3.725 &-0.575\\ \hline \end{array} $$

基于综合影响矩阵T特征截距

DEMATEL-UISM联用方法