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

$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &C1 &C2 &C3 &C4 &C5 &C6 &C7 &C8 &C9 &C10\\ \hline C1 &0 &0.134 &0.065 &0.095 &0.114 &0.109 &0.109 &0.015 &0.06 &0.129\\ \hline C2 &0.104 &0 &0.025 &0.104 &0.08 &0.06 &0.075 &0.06 &0.095 &0.124\\ \hline C3 &0.1 &0.04 &0 &0.07 &0.065 &0.05 &0.065 &0.08 &0.119 &0.104\\ \hline C4 &0.164 &0.05 &0.025 &0 &0.08 &0.095 &0.095 &0.095 &0.095 &0.1\\ \hline C5 &0.164 &0.05 &0.1 &0.05 &0 &0.134 &0.085 &0.1 &0.124 &0.114\\ \hline C6 &0.1 &0.124 &0.065 &0.104 &0.01 &0 &0.114 &0.109 &0.104 &0.104\\ \hline C7 &0.109 &0.154 &0.05 &0.05 &0.124 &0.09 &0 &0.119 &0.1 &0.05\\ \hline C8 &0.05 &0.065 &0.065 &0.055 &0.129 &0.124 &0.104 &0 &0.1 &0.119\\ \hline C9 &0.1 &0.055 &0.104 &0.05 &0.045 &0.035 &0.109 &0.104 &0 &0.154\\ \hline C10 &0.05 &0.1 &0.07 &0.05 &0.104 &0.104 &0.109 &0.104 &0.055 &0\\ \hline \end{array} $$

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

　　综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &C1 &C2 &C3 &C4 &C5 &C6 &C7 &C8 &C9 &C10\\ \hline C1 &0.384 &0.459 &0.304 &0.355 &0.423 &0.438 &0.463 &0.348 &0.404 &0.524\\ \hline C2 &0.431 &0.298 &0.243 &0.33 &0.359 &0.358 &0.393 &0.347 &0.39 &0.475\\ \hline C3 &0.407 &0.32 &0.209 &0.286 &0.331 &0.332 &0.368 &0.349 &0.397 &0.441\\ \hline C4 &0.513 &0.38 &0.266 &0.259 &0.388 &0.419 &0.443 &0.403 &0.42 &0.49\\ \hline C5 &0.559 &0.42 &0.364 &0.341 &0.351 &0.492 &0.481 &0.45 &0.491 &0.556\\ \hline C6 &0.465 &0.448 &0.301 &0.361 &0.335 &0.334 &0.466 &0.425 &0.438 &0.502\\ \hline C7 &0.487 &0.48 &0.299 &0.322 &0.44 &0.429 &0.372 &0.44 &0.446 &0.471\\ \hline C8 &0.422 &0.392 &0.306 &0.312 &0.429 &0.446 &0.454 &0.328 &0.433 &0.51\\ \hline C9 &0.429 &0.358 &0.319 &0.286 &0.34 &0.343 &0.43 &0.393 &0.312 &0.507\\ \hline C10 &0.393 &0.397 &0.288 &0.29 &0.387 &0.404 &0.43 &0.396 &0.37 &0.372\\ \hline \end{array} $$

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$

$$\tilde B=\begin{array} {c|c|c}{M_{10 \times10}} &C1 &C2 &C3 &C4 &C5 &C6 &C7 &C8 &C9 &C10\\ \hline C1 &1 &0.4592 &0.3043 &0.3549 &0.4226 &0.4378 &0.4627 &0.348 &0.4035 &0.5241\\ \hline C2 &0.4315 &1 &0.2432 &0.3303 &0.3592 &0.3579 &0.3934 &0.3469 &0.3905 &0.4753\\ \hline C3 &0.4072 &0.3197 &1 &0.2863 &0.3311 &0.3316 &0.3679 &0.3492 &0.3973 &0.441\\ \hline C4 &0.5127 &0.3795 &0.2656 &1 &0.3876 &0.4186 &0.443 &0.4028 &0.4201 &0.4896\\ \hline C5 &0.5586 &0.4204 &0.3644 &0.3414 &1 &0.4923 &0.4806 &0.4499 &0.4914 &0.556\\ \hline C6 &0.4646 &0.4483 &0.3012 &0.361 &0.3354 &1 &0.4663 &0.4251 &0.4375 &0.5025\\ \hline C7 &0.4874 &0.4799 &0.2991 &0.3217 &0.4399 &0.4287 &1 &0.4404 &0.4461 &0.4707\\ \hline C8 &0.4217 &0.3916 &0.3056 &0.3122 &0.4294 &0.4461 &0.454 &1 &0.4334 &0.51\\ \hline C9 &0.4286 &0.3581 &0.3191 &0.2864 &0.3405 &0.343 &0.4296 &0.3931 &1 &0.5073\\ \hline C10 &0.3934 &0.397 &0.2884 &0.29 &0.387 &0.4045 &0.4298 &0.396 &0.3705 &1\\ \hline \end{array} $$

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。

$$\tilde R=\begin{array} {c|c|c}{M_{10 \times10}} &C1 &C2 &C3 &C4 &C5 &C6 &C7 &C8 &C9 &C10\\ \hline C1 &1 &0.4627 &0.3644 &0.361 &0.4399 &0.4404 &0.4627 &0.4404 &0.4461 &0.5241\\ \hline C2 &0.4315 &1 &0.3644 &0.361 &0.4315 &0.4315 &0.4315 &0.4315 &0.4315 &0.4753\\ \hline C3 &0.4298 &0.4298 &1 &0.361 &0.4298 &0.4298 &0.4298 &0.4298 &0.4298 &0.441\\ \hline C4 &0.5127 &0.4627 &0.3644 &1 &0.4399 &0.4404 &0.4627 &0.4404 &0.4461 &0.5127\\ \hline C5 &0.5586 &0.4799 &0.3644 &0.361 &1 &0.4923 &0.4806 &0.4499 &0.4914 &0.556\\ \hline C6 &0.4663 &0.4663 &0.3644 &0.361 &0.4399 &1 &0.4663 &0.4404 &0.4461 &0.5025\\ \hline C7 &0.4874 &0.4799 &0.3644 &0.361 &0.4399 &0.4404 &1 &0.4404 &0.4461 &0.4874\\ \hline C8 &0.454 &0.454 &0.3644 &0.361 &0.4399 &0.4461 &0.454 &1 &0.4461 &0.51\\ \hline C9 &0.4298 &0.4298 &0.3644 &0.361 &0.4298 &0.4298 &0.4298 &0.4298 &1 &0.5073\\ \hline C10 &0.4298 &0.4298 &0.3644 &0.361 &0.4298 &0.4298 &0.4298 &0.4298 &0.4298 &1\\ \hline \end{array} $$

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	0.361044	总共9个	$2^{9}$	异构体个数太多，超过$2^7$，超出算力范围！
2	0.364429	总共9个	$2^{9}$	异构体个数太多，超过$2^7$，超出算力范围！
3	0.429815	总共20个	$2^{20}$	异构体个数太多，超过$2^7$，超出算力范围！
4	0.431464	总共6个	$2^{6}$
5	0.439895	总共5个	$2^{5}$
6	0.440383	总共7个	$2^{7}$
7	0.441047	总共1个	$2^{1}$	异构体个数太少，不需要计算
8	0.446127	总共5个	$2^{5}$
9	0.44613	总共1个	$2^{1}$	异构体个数太少，不需要计算
10	0.449857	总共1个	$2^{1}$	异构体个数太少，不需要计算
11	0.454022	总共3个	$2^{3}$
12	0.462679	总共4个	$2^{4}$
13	0.466252	总共3个	$2^{3}$
14	0.475267	总共1个	$2^{1}$	异构体个数太少，不需要计算
15	0.479851	总共2个	$2^{2}$
16	0.480604	总共1个	$2^{1}$	异构体个数太少，不需要计算
17	0.487417	总共2个	$2^{2}$
18	0.49137	总共1个	$2^{1}$	异构体个数太少，不需要计算
19	0.492327	总共1个	$2^{1}$	异构体个数太少，不需要计算
20	0.502462	总共1个	$2^{1}$	异构体个数太少，不需要计算
21	0.507338	总共1个	$2^{1}$	异构体个数太少，不需要计算
22	0.509987	总共1个	$2^{1}$	异构体个数太少，不需要计算
23	0.512746	总共2个	$2^{2}$
24	0.52411	总共1个	$2^{1}$	异构体个数太少，不需要计算
25	0.556038	总共1个	$2^{1}$	异构体个数太少，不需要计算
26	0.558585	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

$$\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times4}} &Di &Ci &Mi &Ri\\ \hline C1 &4.101 &4.489 &8.59 &-0.389\\ \hline C2 &3.626 &3.952 &7.578 &-0.326\\ \hline C3 &3.44 &2.9 &6.34 &0.54\\ \hline C4 &3.978 &3.143 &7.122 &0.835\\ \hline C5 &4.506 &3.784 &8.29 &0.722\\ \hline C6 &4.076 &3.995 &8.071 &0.081\\ \hline C7 &4.185 &4.299 &8.484 &-0.113\\ \hline C8 &4.032 &3.879 &7.911 &0.153\\ \hline C9 &3.718 &4.103 &7.821 &-0.385\\ \hline C10 &3.728 &4.848 &8.576 &-1.12\\ \hline \end{array} $$

基于综合影响矩阵T特征截距

DEMATEL-UISM联用方法