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

$$Ori=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &C1 &C2 &C3 &C4 &C5 &C6 &C7 &C8 &C9 &C10\\ \hline C1 &0 &27 &13 &19 &23 &22 &22 &3 &12 &26\\ \hline C2 &21 &0 &5 &21 &16 &12 &15 &12 &19 &25\\ \hline C3 &20 &8 &0 &14 &13 &10 &13 &16 &24 &21\\ \hline C4 &33 &10 &5 &0 &16 &19 &19 &19 &19 &20\\ \hline C5 &33 &10 &20 &10 &0 &27 &17 &20 &25 &23\\ \hline C6 &20 &25 &13 &21 &2 &0 &23 &22 &21 &21\\ \hline C7 &22 &31 &10 &10 &25 &18 &0 &24 &20 &10\\ \hline C8 &10 &13 &13 &11 &26 &25 &21 &0 &20 &24\\ \hline C9 &20 &11 &21 &10 &9 &7 &22 &21 &0 &31\\ \hline C10 &10 &20 &14 &10 &21 &21 &22 &21 &11 &0\\ \hline \end{array} $$

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

$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &C1 &C2 &C3 &C4 &C5 &C6 &C7 &C8 &C9 &C10\\ \hline C1 &0 &0.099 &0.048 &0.07 &0.084 &0.081 &0.081 &0.011 &0.044 &0.095\\ \hline C2 &0.077 &0 &0.018 &0.077 &0.059 &0.044 &0.055 &0.044 &0.07 &0.092\\ \hline C3 &0.073 &0.029 &0 &0.051 &0.048 &0.037 &0.048 &0.059 &0.088 &0.077\\ \hline C4 &0.121 &0.037 &0.018 &0 &0.059 &0.07 &0.07 &0.07 &0.07 &0.073\\ \hline C5 &0.121 &0.037 &0.073 &0.037 &0 &0.099 &0.062 &0.073 &0.092 &0.084\\ \hline C6 &0.073 &0.092 &0.048 &0.077 &0.007 &0 &0.084 &0.081 &0.077 &0.077\\ \hline C7 &0.081 &0.113 &0.037 &0.037 &0.092 &0.066 &0 &0.088 &0.073 &0.037\\ \hline C8 &0.037 &0.048 &0.048 &0.04 &0.095 &0.092 &0.077 &0 &0.073 &0.088\\ \hline C9 &0.073 &0.04 &0.077 &0.037 &0.033 &0.026 &0.081 &0.077 &0 &0.113\\ \hline C10 &0.037 &0.073 &0.051 &0.037 &0.077 &0.077 &0.081 &0.077 &0.04 &0\\ \hline \end{array} $$

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

　　综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &C1 &C2 &C3 &C4 &C5 &C6 &C7 &C8 &C9 &C10\\ \hline C1 &0.106 &0.183 &0.11 &0.138 &0.164 &0.166 &0.173 &0.103 &0.137 &0.198\\ \hline C2 &0.163 &0.08 &0.077 &0.135 &0.133 &0.124 &0.14 &0.121 &0.147 &0.183\\ \hline C3 &0.154 &0.104 &0.057 &0.108 &0.119 &0.112 &0.129 &0.13 &0.159 &0.166\\ \hline C4 &0.21 &0.126 &0.084 &0.07 &0.141 &0.156 &0.162 &0.15 &0.155 &0.177\\ \hline C5 &0.222 &0.137 &0.143 &0.115 &0.095 &0.192 &0.169 &0.165 &0.187 &0.202\\ \hline C6 &0.169 &0.176 &0.109 &0.144 &0.097 &0.09 &0.177 &0.163 &0.164 &0.183\\ \hline C7 &0.181 &0.196 &0.103 &0.11 &0.173 &0.156 &0.1 &0.171 &0.165 &0.152\\ \hline C8 &0.138 &0.135 &0.112 &0.108 &0.172 &0.175 &0.169 &0.09 &0.162 &0.19\\ \hline C9 &0.159 &0.122 &0.132 &0.099 &0.114 &0.109 &0.164 &0.152 &0.084 &0.204\\ \hline C10 &0.13 &0.151 &0.109 &0.101 &0.15 &0.156 &0.164 &0.154 &0.126 &0.1\\ \hline \end{array} $$

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$

$$\tilde B=\begin{array} {c|c|c}{M_{10 \times10}} &C1 &C2 &C3 &C4 &C5 &C6 &C7 &C8 &C9 &C10\\ \hline C1 &1 &0.1833 &0.1103 &0.1381 &0.1637 &0.1664 &0.173 &0.1026 &0.1365 &0.198\\ \hline C2 &0.1632 &1 &0.0772 &0.1348 &0.1327 &0.124 &0.1401 &0.1205 &0.1466 &0.1833\\ \hline C3 &0.1538 &0.1041 &1 &0.1077 &0.1186 &0.1121 &0.1289 &0.1297 &0.1594 &0.1661\\ \hline C4 &0.2098 &0.1265 &0.0836 &1 &0.1406 &0.1558 &0.1623 &0.1497 &0.1546 &0.1767\\ \hline C5 &0.222 &0.1373 &0.1432 &0.1152 &1 &0.1919 &0.1686 &0.1652 &0.1874 &0.202\\ \hline C6 &0.1694 &0.1763 &0.1091 &0.144 &0.0974 &1 &0.1768 &0.1631 &0.1642 &0.1826\\ \hline C7 &0.1808 &0.1963 &0.1032 &0.11 &0.1733 &0.1558 &1 &0.1706 &0.1653 &0.1517\\ \hline C8 &0.1375 &0.1347 &0.1121 &0.1084 &0.1716 &0.1753 &0.1689 &1 &0.1618 &0.1902\\ \hline C9 &0.1585 &0.1219 &0.1323 &0.0991 &0.1144 &0.1094 &0.1644 &0.1524 &1 &0.2042\\ \hline C10 &0.1296 &0.151 &0.1086 &0.1007 &0.1503 &0.1556 &0.1639 &0.1536 &0.126 &1\\ \hline \end{array} $$

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。

$$\tilde R=\begin{array} {c|c|c}{M_{10 \times10}} &C1 &C2 &C3 &C4 &C5 &C6 &C7 &C8 &C9 &C10\\ \hline C1 &1 &0.1833 &0.1432 &0.144 &0.173 &0.173 &0.173 &0.1706 &0.173 &0.198\\ \hline C2 &0.1639 &1 &0.1432 &0.144 &0.1639 &0.1639 &0.1639 &0.1639 &0.1639 &0.1833\\ \hline C3 &0.1639 &0.1639 &1 &0.144 &0.1639 &0.1639 &0.1639 &0.1639 &0.1639 &0.1661\\ \hline C4 &0.2098 &0.1833 &0.1432 &1 &0.173 &0.173 &0.173 &0.1706 &0.173 &0.198\\ \hline C5 &0.222 &0.1833 &0.1432 &0.144 &1 &0.1919 &0.1768 &0.1706 &0.1874 &0.202\\ \hline C6 &0.1768 &0.1768 &0.1432 &0.144 &0.1733 &1 &0.1768 &0.1706 &0.1733 &0.1826\\ \hline C7 &0.1808 &0.1963 &0.1432 &0.144 &0.1733 &0.1733 &1 &0.1706 &0.1733 &0.1833\\ \hline C8 &0.1753 &0.1753 &0.1432 &0.144 &0.1733 &0.1753 &0.1753 &1 &0.1733 &0.1902\\ \hline C9 &0.1644 &0.1644 &0.1432 &0.144 &0.1644 &0.1644 &0.1644 &0.1644 &1 &0.2042\\ \hline C10 &0.1639 &0.1639 &0.1432 &0.144 &0.1639 &0.1639 &0.1639 &0.1639 &0.1639 &1\\ \hline \end{array} $$

由阈值集合$\ddot \Delta $　得出综合影响矩阵$T$对应 23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	0.143243	总共9个	$2^{9}$	异构体个数太多，超过$2^7$，超出算力范围！
2	0.144012	总共9个	$2^{9}$	异构体个数太多，超过$2^7$，超出算力范围！
3	0.163916	总共20个	$2^{20}$	异构体个数太多，超过$2^7$，超出算力范围！
4	0.164449	总共6个	$2^{6}$
5	0.166099	总共1个	$2^{1}$	异构体个数太少，不需要计算
6	0.170586	总共5个	$2^{5}$
7	0.173	总共8个	$2^{8}$	异构体个数太多，超过$2^7$，超出算力范围！
8	0.173269	总共7个	$2^{7}$
9	0.175256	总共4个	$2^{4}$
10	0.176824	总共4个	$2^{4}$
11	0.180794	总共1个	$2^{1}$	异构体个数太少，不需要计算
12	0.18261	总共1个	$2^{1}$	异构体个数太少，不需要计算
13	0.183281	总共2个	$2^{2}$
14	0.183308	总共3个	$2^{3}$
15	0.187393	总共1个	$2^{1}$	异构体个数太少，不需要计算
16	0.190206	总共1个	$2^{1}$	异构体个数太少，不需要计算
17	0.191906	总共1个	$2^{1}$	异构体个数太少，不需要计算
18	0.196277	总共1个	$2^{1}$	异构体个数太少，不需要计算
19	0.198023	总共2个	$2^{2}$
20	0.201998	总共1个	$2^{1}$	异构体个数太少，不需要计算
21	0.204151	总共1个	$2^{1}$	异构体个数太少，不需要计算
22	0.209803	总共1个	$2^{1}$	异构体个数太少，不需要计算
23	0.221973	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

$$\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times4}} &Di &Ci &Mi &Ri\\ \hline C1 &1.478 &1.63 &3.108 &-0.153\\ \hline C2 &1.303 &1.412 &2.715 &-0.109\\ \hline C3 &1.237 &1.036 &2.274 &0.201\\ \hline C4 &1.429 &1.128 &2.557 &0.301\\ \hline C5 &1.627 &1.357 &2.985 &0.27\\ \hline C6 &1.473 &1.436 &2.909 &0.037\\ \hline C7 &1.507 &1.547 &3.055 &-0.04\\ \hline C8 &1.451 &1.398 &2.848 &0.053\\ \hline C9 &1.341 &1.486 &2.827 &-0.145\\ \hline C10 &1.34 &1.755 &3.095 &-0.416\\ \hline \end{array} $$

基于综合影响矩阵T特征截距

DEMATEL-UISM联用方法