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

$$Ori=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{11 \times11}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10 &F11\\ \hline F1 &0 &0 &0 &0 &1 &0 &1 &1 &2 &2 &1\\ \hline F2 &0 &0 &0 &0 &0 &0 &1 &1 &2 &3 &1\\ \hline F3 &0 &0 &0 &0 &0 &1 &2 &1 &1 &1 &3\\ \hline F4 &1 &2 &2 &0 &0 &0 &1 &0 &0 &0 &1\\ \hline F5 &0 &3 &3 &0 &0 &0 &1 &0 &0 &0 &1\\ \hline F6 &1 &0 &0 &0 &0 &0 &2 &2 &3 &2 &2\\ \hline F7 &0 &0 &0 &0 &0 &0 &0 &2 &3 &3 &2\\ \hline F8 &0 &0 &0 &0 &0 &0 &0 &0 &3 &3 &3\\ \hline F9 &3 &0 &3 &0 &0 &0 &1 &0 &0 &3 &2\\ \hline F10 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline F11 &3 &0 &0 &4 &0 &0 &0 &0 &0 &1 &0\\ \hline \end{array} $$

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

$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{11 \times11}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10 &F11\\ \hline F1 &0 &0 &0 &0 &0.046 &0 &0.046 &0.046 &0.092 &0.092 &0.046\\ \hline F2 &0 &0 &0 &0 &0 &0 &0.046 &0.046 &0.092 &0.139 &0.046\\ \hline F3 &0 &0 &0 &0 &0 &0.046 &0.092 &0.046 &0.046 &0.046 &0.139\\ \hline F4 &0.046 &0.092 &0.092 &0 &0 &0 &0.046 &0 &0 &0 &0.046\\ \hline F5 &0 &0.139 &0.139 &0 &0 &0 &0.046 &0 &0 &0 &0.046\\ \hline F6 &0.046 &0 &0 &0 &0 &0 &0.092 &0.092 &0.139 &0.092 &0.092\\ \hline F7 &0 &0 &0 &0 &0 &0 &0 &0.092 &0.139 &0.139 &0.092\\ \hline F8 &0 &0 &0 &0 &0 &0 &0 &0 &0.139 &0.139 &0.139\\ \hline F9 &0.139 &0 &0.139 &0 &0 &0 &0.046 &0 &0 &0.139 &0.092\\ \hline F10 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline F11 &0.139 &0 &0 &0.185 &0 &0 &0 &0 &0 &0.046 &0\\ \hline \end{array} $$

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

　　综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{11 \times11}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10 &F11\\ \hline F1 &0.027 &0.008 &0.024 &0.014 &0.047 &0.001 &0.058 &0.054 &0.113 &0.132 &0.077\\ \hline F2 &0.026 &0.001 &0.017 &0.014 &0.001 &0.001 &0.055 &0.053 &0.111 &0.176 &0.073\\ \hline F3 &0.039 &0.003 &0.014 &0.032 &0.002 &0.047 &0.105 &0.063 &0.081 &0.098 &0.174\\ \hline F4 &0.063 &0.094 &0.099 &0.015 &0.003 &0.005 &0.065 &0.018 &0.031 &0.043 &0.08\\ \hline F5 &0.018 &0.14 &0.145 &0.016 &0.001 &0.007 &0.07 &0.021 &0.035 &0.05 &0.088\\ \hline F6 &0.092 &0.003 &0.028 &0.027 &0.004 &0.001 &0.109 &0.108 &0.179 &0.164 &0.144\\ \hline F7 &0.041 &0.002 &0.025 &0.024 &0.002 &0.001 &0.013 &0.097 &0.159 &0.187 &0.129\\ \hline F8 &0.044 &0.003 &0.023 &0.03 &0.002 &0.001 &0.013 &0.005 &0.147 &0.175 &0.161\\ \hline F9 &0.164 &0.003 &0.147 &0.025 &0.008 &0.007 &0.071 &0.022 &0.036 &0.186 &0.136\\ \hline F10 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline F11 &0.154 &0.019 &0.021 &0.19 &0.007 &0.001 &0.02 &0.011 &0.021 &0.073 &0.025\\ \hline \end{array} $$

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$

$$\tilde B=\begin{array} {c|c|c}{M_{11 \times11}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10 &F11\\ \hline F1 &1 &0.0079 &0.0235 &0.0143 &0.0475 &0.0011 &0.0582 &0.0544 &0.1125 &0.132 &0.0774\\ \hline F2 &0.0262 &1 &0.0168 &0.0136 &0.0012 &0.0008 &0.0549 &0.0534 &0.1109 &0.1759 &0.0733\\ \hline F3 &0.039 &0.0032 &1 &0.0323 &0.0018 &0.0469 &0.1054 &0.0629 &0.0806 &0.0979 &0.1745\\ \hline F4 &0.0625 &0.0942 &0.0986 &1 &0.0029 &0.0046 &0.0653 &0.0183 &0.0313 &0.0434 &0.0798\\ \hline F5 &0.0181 &0.1403 &0.1451 &0.0162 &1 &0.0067 &0.07 &0.0211 &0.0349 &0.05 &0.0877\\ \hline F6 &0.0923 &0.0031 &0.0279 &0.0266 &0.0043 &1 &0.1093 &0.1084 &0.1791 &0.1645 &0.144\\ \hline F7 &0.0411 &0.0025 &0.0245 &0.0238 &0.0019 &0.0011 &1 &0.0969 &0.1592 &0.1873 &0.1285\\ \hline F8 &0.0441 &0.003 &0.0234 &0.0298 &0.002 &0.0011 &0.0127 &1 &0.1467 &0.1745 &0.161\\ \hline F9 &0.164 &0.0034 &0.1471 &0.0251 &0.0076 &0.0068 &0.0714 &0.0218 &1 &0.1859 &0.1357\\ \hline F10 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1 &0\\ \hline F11 &0.154 &0.0185 &0.0215 &0.1896 &0.0071 &0.001 &0.0201 &0.0109 &0.0214 &0.0726 &1\\ \hline \end{array} $$

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。

$$\tilde R=\begin{array} {c|c|c}{M_{11 \times11}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10 &F11\\ \hline F1 &1 &0.0942 &0.1125 &0.1125 &0.0475 &0.0469 &0.1054 &0.0969 &0.1125 &0.132 &0.1125\\ \hline F2 &0.1109 &1 &0.1109 &0.1109 &0.0475 &0.0469 &0.1054 &0.0969 &0.1109 &0.1759 &0.1109\\ \hline F3 &0.154 &0.0942 &1 &0.1745 &0.0475 &0.0469 &0.1054 &0.0969 &0.1125 &0.132 &0.1745\\ \hline F4 &0.0986 &0.0942 &0.0986 &1 &0.0475 &0.0469 &0.0986 &0.0969 &0.0986 &0.0986 &0.0986\\ \hline F5 &0.1451 &0.1403 &0.1451 &0.1451 &1 &0.0469 &0.1054 &0.0969 &0.1125 &0.1403 &0.1451\\ \hline F6 &0.164 &0.0942 &0.1471 &0.1471 &0.0475 &1 &0.1093 &0.1084 &0.1791 &0.1791 &0.1471\\ \hline F7 &0.1592 &0.0942 &0.1471 &0.1471 &0.0475 &0.0469 &1 &0.0969 &0.1592 &0.1873 &0.1471\\ \hline F8 &0.154 &0.0942 &0.1467 &0.161 &0.0475 &0.0469 &0.1054 &1 &0.1467 &0.1745 &0.161\\ \hline F9 &0.164 &0.0942 &0.1471 &0.1471 &0.0475 &0.0469 &0.1054 &0.0969 &1 &0.1859 &0.1471\\ \hline F10 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1 &0\\ \hline F11 &0.154 &0.0942 &0.1125 &0.1896 &0.0475 &0.0469 &0.1054 &0.0969 &0.1125 &0.132 &1\\ \hline \end{array} $$

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	0.046891	总共9个	$2^{9}$	异构体个数太多，超过$2^7$，超出算力范围！
2	0.047475	总共9个	$2^{9}$	异构体个数太多，超过$2^7$，超出算力范围！
3	0.094215	总共8个	$2^{8}$	异构体个数太多，超过$2^7$，超出算力范围！
4	0.096896	总共8个	$2^{8}$	异构体个数太多，超过$2^7$，超出算力范围！
5	0.09855	总共6个	$2^{6}$
6	0.105374	总共7个	$2^{7}$
7	0.108369	总共1个	$2^{1}$	异构体个数太少，不需要计算
8	0.109265	总共1个	$2^{1}$	异构体个数太少，不需要计算
9	0.110917	总共5个	$2^{5}$
10	0.112531	总共8个	$2^{8}$	异构体个数太多，超过$2^7$，超出算力范围！
11	0.132028	总共3个	$2^{3}$
12	0.14029	总共2个	$2^{2}$
13	0.145132	总共4个	$2^{4}$
14	0.14665	总共2个	$2^{2}$
15	0.147055	总共9个	$2^{9}$	异构体个数太多，超过$2^7$，超出算力范围！
16	0.153986	总共3个	$2^{3}$
17	0.159219	总共2个	$2^{2}$
18	0.161024	总共2个	$2^{2}$
19	0.163973	总共2个	$2^{2}$
20	0.17446	总共2个	$2^{2}$
21	0.174521	总共1个	$2^{1}$	异构体个数太少，不需要计算
22	0.175943	总共1个	$2^{1}$	异构体个数太少，不需要计算
23	0.179141	总共2个	$2^{2}$
24	0.185923	总共1个	$2^{1}$	异构体个数太少，不需要计算
25	0.187301	总共1个	$2^{1}$	异构体个数太少，不需要计算
26	0.189613	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

$$\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{11 \times4}} &Di &Ci &Mi &Ri\\ \hline F1 &0.556 &0.668 &1.224 &-0.112\\ \hline F2 &0.529 &0.278 &0.806 &0.251\\ \hline F3 &0.659 &0.543 &1.202 &0.116\\ \hline F4 &0.516 &0.386 &0.901 &0.13\\ \hline F5 &0.591 &0.077 &0.668 &0.514\\ \hline F6 &0.861 &0.071 &0.932 &0.789\\ \hline F7 &0.68 &0.58 &1.26 &0.1\\ \hline F8 &0.603 &0.453 &1.055 &0.15\\ \hline F9 &0.805 &0.913 &1.717 &-0.108\\ \hline F10 &0 &1.284 &1.284 &-1.284\\ \hline F11 &0.542 &1.087 &1.63 &-0.545\\ \hline \end{array} $$

基于综合影响矩阵T特征截距

DEMATEL-UISM联用方法