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

$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{11 \times11}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10 &F11\\ \hline F1 &0 &0 &0 &0 &0.054 &0 &0.054 &0.054 &0.108 &0.108 &0.054\\ \hline F2 &0 &0 &0 &0 &0 &0 &0.054 &0.054 &0.108 &0.163 &0.054\\ \hline F3 &0 &0 &0 &0 &0 &0.054 &0.108 &0.054 &0.054 &0.054 &0.163\\ \hline F4 &0.054 &0.108 &0.108 &0 &0 &0 &0.054 &0 &0 &0 &0.054\\ \hline F5 &0 &0.163 &0.163 &0 &0 &0 &0.054 &0 &0 &0 &0.054\\ \hline F6 &0.054 &0 &0 &0 &0 &0 &0.108 &0.108 &0.163 &0.108 &0.108\\ \hline F7 &0 &0 &0 &0 &0 &0 &0 &0.108 &0.163 &0.163 &0.108\\ \hline F8 &0 &0 &0 &0 &0 &0 &0 &0 &0.163 &0.163 &0.163\\ \hline F9 &0.163 &0 &0.163 &0 &0 &0 &0.054 &0 &0 &0.163 &0.108\\ \hline F10 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline F11 &0.163 &0 &0 &0.217 &0 &0 &0 &0 &0 &0.054 &0\\ \hline \end{array} $$

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

　　综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{11 \times11}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10 &F11\\ \hline F1 &0.04 &0.012 &0.034 &0.022 &0.056 &0.002 &0.073 &0.067 &0.139 &0.168 &0.101\\ \hline F2 &0.039 &0.003 &0.025 &0.021 &0.002 &0.001 &0.068 &0.065 &0.136 &0.218 &0.095\\ \hline F3 &0.058 &0.006 &0.023 &0.047 &0.003 &0.055 &0.129 &0.079 &0.105 &0.131 &0.217\\ \hline F4 &0.08 &0.112 &0.119 &0.023 &0.004 &0.006 &0.082 &0.026 &0.046 &0.065 &0.104\\ \hline F5 &0.029 &0.166 &0.174 &0.025 &0.002 &0.009 &0.089 &0.031 &0.052 &0.075 &0.116\\ \hline F6 &0.123 &0.005 &0.042 &0.04 &0.007 &0.002 &0.135 &0.133 &0.223 &0.215 &0.185\\ \hline F7 &0.06 &0.004 &0.036 &0.035 &0.003 &0.002 &0.02 &0.116 &0.194 &0.235 &0.162\\ \hline F8 &0.063 &0.005 &0.034 &0.043 &0.003 &0.002 &0.02 &0.008 &0.177 &0.216 &0.197\\ \hline F9 &0.202 &0.006 &0.177 &0.038 &0.011 &0.01 &0.091 &0.032 &0.054 &0.234 &0.173\\ \hline F10 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline F11 &0.187 &0.026 &0.031 &0.225 &0.01 &0.002 &0.03 &0.017 &0.033 &0.096 &0.039\\ \hline \end{array} $$

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$

$$\tilde B=\begin{array} {c|c|c}{M_{11 \times11}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10 &F11\\ \hline F1 &1 &0.0116 &0.0342 &0.0219 &0.0564 &0.0019 &0.0727 &0.067 &0.139 &0.1676 &0.1009\\ \hline F2 &0.0387 &1 &0.0247 &0.0205 &0.0021 &0.0013 &0.0679 &0.0653 &0.1362 &0.2178 &0.0946\\ \hline F3 &0.0579 &0.0056 &1 &0.047 &0.0031 &0.0555 &0.1288 &0.0789 &0.1052 &0.1313 &0.2168\\ \hline F4 &0.0803 &0.1116 &0.1191 &1 &0.0044 &0.0065 &0.0822 &0.0265 &0.046 &0.0649 &0.1044\\ \hline F5 &0.0291 &0.1657 &0.1741 &0.0251 &1 &0.0094 &0.0889 &0.0307 &0.0516 &0.0747 &0.1158\\ \hline F6 &0.1229 &0.0054 &0.0417 &0.0402 &0.0067 &1 &0.1348 &0.1326 &0.2228 &0.215 &0.1853\\ \hline F7 &0.06 &0.0043 &0.0359 &0.0352 &0.0033 &0.0019 &1 &0.1163 &0.1942 &0.2347 &0.1623\\ \hline F8 &0.0633 &0.0052 &0.034 &0.0428 &0.0034 &0.0018 &0.0197 &1 &0.1768 &0.2164 &0.1972\\ \hline F9 &0.2022 &0.0059 &0.1773 &0.0376 &0.011 &0.0096 &0.0913 &0.0318 &1 &0.2344 &0.1732\\ \hline F10 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1 &0\\ \hline F11 &0.1867 &0.0261 &0.0314 &0.2254 &0.0101 &0.0017 &0.0297 &0.0166 &0.0326 &0.0956 &1\\ \hline \end{array} $$

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。

$$\tilde R=\begin{array} {c|c|c}{M_{11 \times11}} &F1 &F2 &F3 &F4 &F5 &F6 &F7 &F8 &F9 &F10 &F11\\ \hline F1 &1 &0.1116 &0.139 &0.139 &0.0564 &0.0555 &0.1288 &0.1163 &0.139 &0.1676 &0.139\\ \hline F2 &0.1362 &1 &0.1362 &0.1362 &0.0564 &0.0555 &0.1288 &0.1163 &0.1362 &0.2178 &0.1362\\ \hline F3 &0.1867 &0.1116 &1 &0.2168 &0.0564 &0.0555 &0.1288 &0.1163 &0.139 &0.1676 &0.2168\\ \hline F4 &0.1191 &0.1116 &0.1191 &1 &0.0564 &0.0555 &0.1191 &0.1163 &0.1191 &0.1191 &0.1191\\ \hline F5 &0.1741 &0.1657 &0.1741 &0.1741 &1 &0.0555 &0.1288 &0.1163 &0.139 &0.1676 &0.1741\\ \hline F6 &0.2022 &0.1116 &0.1773 &0.1853 &0.0564 &1 &0.1348 &0.1326 &0.2228 &0.2228 &0.1853\\ \hline F7 &0.1942 &0.1116 &0.1773 &0.1773 &0.0564 &0.0555 &1 &0.1163 &0.1942 &0.2347 &0.1773\\ \hline F8 &0.1867 &0.1116 &0.1768 &0.1972 &0.0564 &0.0555 &0.1288 &1 &0.1768 &0.2164 &0.1972\\ \hline F9 &0.2022 &0.1116 &0.1773 &0.1773 &0.0564 &0.0555 &0.1288 &0.1163 &1 &0.2344 &0.1773\\ \hline F10 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1 &0\\ \hline F11 &0.1867 &0.1116 &0.139 &0.2254 &0.0564 &0.0555 &0.1288 &0.1163 &0.139 &0.1676 &1\\ \hline \end{array} $$

由阈值集合$\ddot \Delta $　得出综合影响矩阵$T$对应 27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	0.055465	总共9个	$2^{9}$	异构体个数太多，超过$2^7$，超出算力范围！
2	0.05642	总共9个	$2^{9}$	异构体个数太多，超过$2^7$，超出算力范围！
3	0.11163	总共8个	$2^{8}$	异构体个数太多，超过$2^7$，超出算力范围！
4	0.116308	总共8个	$2^{8}$	异构体个数太多，超过$2^7$，超出算力范围！
5	0.119116	总共6个	$2^{6}$
6	0.128818	总共7个	$2^{7}$
7	0.132556	总共1个	$2^{1}$	异构体个数太少，不需要计算
8	0.134817	总共1个	$2^{1}$	异构体个数太少，不需要计算
9	0.136182	总共5个	$2^{5}$
10	0.138979	总共8个	$2^{8}$	异构体个数太多，超过$2^7$，超出算力范围！
11	0.16568	总共1个	$2^{1}$	异构体个数太少，不需要计算
12	0.16759	总共4个	$2^{4}$
13	0.17407	总共4个	$2^{4}$
14	0.176752	总共2个	$2^{2}$
15	0.177308	总共7个	$2^{7}$
16	0.185348	总共2个	$2^{2}$
17	0.186674	总共3个	$2^{3}$
18	0.194156	总共2个	$2^{2}$
19	0.197233	总共2个	$2^{2}$
20	0.202187	总共2个	$2^{2}$
21	0.216388	总共1个	$2^{1}$	异构体个数太少，不需要计算
22	0.216796	总共2个	$2^{2}$
23	0.217771	总共1个	$2^{1}$	异构体个数太少，不需要计算
24	0.222752	总共2个	$2^{2}$
25	0.225405	总共1个	$2^{1}$	异构体个数太少，不需要计算
26	0.234427	总共1个	$2^{1}$	异构体个数太少，不需要计算
27	0.234675	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

$$\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{11 \times4}} &Di &Ci &Mi &Ri\\ \hline F1 &0.713 &0.881 &1.595 &-0.168\\ \hline F2 &0.672 &0.344 &1.016 &0.328\\ \hline F3 &0.853 &0.695 &1.548 &0.158\\ \hline F4 &0.668 &0.518 &1.187 &0.15\\ \hline F5 &0.767 &0.102 &0.869 &0.665\\ \hline F6 &1.11 &0.092 &1.202 &1.018\\ \hline F7 &0.868 &0.736 &1.605 &0.132\\ \hline F8 &0.768 &0.574 &1.342 &0.195\\ \hline F9 &1.028 &1.158 &2.186 &-0.13\\ \hline F10 &0 &1.652 &1.652 &-1.652\\ \hline F11 &0.695 &1.39 &2.085 &-0.695\\ \hline \end{array} $$

基于综合影响矩阵T特征截距

DEMATEL-UISM联用方法