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

$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &D1 &D2 &D3 &D4 &D5 &D6 &D7 &D8 &D9 &D10\\ \hline D1 &0 &0.062 &0.062 &0.09 &0.11 &0.105 &0.057 &0.062 &0.057 &0.124\\ \hline D2 &0.1 &0 &0.024 &0.1 &0.076 &0.057 &0.071 &0.057 &0.09 &0.119\\ \hline D3 &0.095 &0.038 &0 &0.067 &0.062 &0.048 &0.062 &0.076 &0.114 &0.1\\ \hline D4 &0.157 &0.048 &0.024 &0 &0.076 &0.09 &0.09 &0.09 &0.09 &0.095\\ \hline D5 &0.157 &0.048 &0.095 &0.048 &0 &0.129 &0.081 &0.095 &0.119 &0.11\\ \hline D6 &0.095 &0.119 &0.062 &0.1 &0.01 &0 &0.11 &0.105 &0.1 &0.1\\ \hline D7 &0.105 &0.148 &0.048 &0.048 &0.119 &0.086 &0 &0.114 &0.095 &0.09\\ \hline D8 &0.048 &0.062 &0.062 &0.052 &0.124 &0.119 &0.1 &0 &0.095 &0.114\\ \hline D9 &0.095 &0.052 &0.1 &0.048 &0.048 &0.129 &0.105 &0.1 &0 &0.148\\ \hline D10 &0.048 &0.095 &0.067 &0.048 &0.1 &0.1 &0.105 &0.1 &0.052 &0\\ \hline \end{array} $$

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

　　综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &D1 &D2 &D3 &D4 &D5 &D6 &D7 &D8 &D9 &D10\\ \hline D1 &0.285 &0.288 &0.244 &0.283 &0.338 &0.381 &0.314 &0.323 &0.315 &0.432\\ \hline D2 &0.363 &0.22 &0.202 &0.282 &0.303 &0.329 &0.315 &0.307 &0.33 &0.416\\ \hline D3 &0.344 &0.245 &0.172 &0.243 &0.279 &0.308 &0.295 &0.312 &0.34 &0.386\\ \hline D4 &0.436 &0.288 &0.22 &0.209 &0.325 &0.385 &0.354 &0.359 &0.353 &0.425\\ \hline D5 &0.473 &0.319 &0.311 &0.284 &0.285 &0.456 &0.383 &0.401 &0.416 &0.483\\ \hline D6 &0.39 &0.358 &0.255 &0.308 &0.275 &0.306 &0.38 &0.379 &0.37 &0.439\\ \hline D7 &0.422 &0.397 &0.261 &0.278 &0.387 &0.41 &0.299 &0.407 &0.389 &0.457\\ \hline D8 &0.35 &0.307 &0.26 &0.262 &0.367 &0.414 &0.371 &0.285 &0.367 &0.447\\ \hline D9 &0.397 &0.31 &0.298 &0.268 &0.314 &0.431 &0.385 &0.386 &0.289 &0.488\\ \hline D10 &0.326 &0.316 &0.245 &0.243 &0.329 &0.371 &0.351 &0.352 &0.309 &0.316\\ \hline \end{array} $$

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$

$$\tilde B=\begin{array} {c|c|c}{M_{10 \times10}} &D1 &D2 &D3 &D4 &D5 &D6 &D7 &D8 &D9 &D10\\ \hline D1 &1 &0.2877 &0.2441 &0.2829 &0.3384 &0.3807 &0.3142 &0.3228 &0.3145 &0.4315\\ \hline D2 &0.3634 &1 &0.2022 &0.2823 &0.3027 &0.3294 &0.3153 &0.3071 &0.3298 &0.4157\\ \hline D3 &0.3438 &0.2448 &1 &0.2427 &0.2787 &0.3082 &0.2951 &0.3116 &0.3396 &0.3858\\ \hline D4 &0.4355 &0.2876 &0.2201 &1 &0.3249 &0.3847 &0.3543 &0.3591 &0.3528 &0.4246\\ \hline D5 &0.4732 &0.3192 &0.311 &0.2842 &1 &0.4557 &0.3829 &0.4006 &0.4156 &0.4828\\ \hline D6 &0.3901 &0.3578 &0.2549 &0.3082 &0.2753 &1 &0.3795 &0.3792 &0.3703 &0.4388\\ \hline D7 &0.4224 &0.3974 &0.2608 &0.2782 &0.387 &0.4097 &1 &0.4067 &0.3885 &0.4569\\ \hline D8 &0.35 &0.3069 &0.2595 &0.2623 &0.3671 &0.4142 &0.3706 &1 &0.3674 &0.447\\ \hline D9 &0.3965 &0.3097 &0.2985 &0.268 &0.3138 &0.4314 &0.3849 &0.3859 &1 &0.488\\ \hline D10 &0.3258 &0.3161 &0.245 &0.2428 &0.3287 &0.3715 &0.3511 &0.3518 &0.3094 &1\\ \hline \end{array} $$

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。

$$\tilde R=\begin{array} {c|c|c}{M_{10 \times10}} &D1 &D2 &D3 &D4 &D5 &D6 &D7 &D8 &D9 &D10\\ \hline D1 &1 &0.3795 &0.311 &0.3082 &0.3795 &0.3807 &0.3795 &0.3795 &0.3795 &0.4315\\ \hline D2 &0.3715 &1 &0.311 &0.3082 &0.3715 &0.3715 &0.3715 &0.3715 &0.3715 &0.4157\\ \hline D3 &0.3715 &0.3715 &1 &0.3082 &0.3715 &0.3715 &0.3715 &0.3715 &0.3715 &0.3858\\ \hline D4 &0.4355 &0.3795 &0.311 &1 &0.3795 &0.3847 &0.3795 &0.3795 &0.3795 &0.4315\\ \hline D5 &0.4732 &0.3849 &0.311 &0.3082 &1 &0.4557 &0.3849 &0.4006 &0.4156 &0.4828\\ \hline D6 &0.3901 &0.3795 &0.311 &0.3082 &0.3795 &1 &0.3795 &0.3795 &0.3795 &0.4388\\ \hline D7 &0.4224 &0.3974 &0.311 &0.3082 &0.387 &0.4097 &1 &0.4067 &0.3885 &0.4569\\ \hline D8 &0.3901 &0.3795 &0.311 &0.3082 &0.3795 &0.4142 &0.3795 &1 &0.3795 &0.447\\ \hline D9 &0.3965 &0.3849 &0.311 &0.3082 &0.3849 &0.4314 &0.3849 &0.3859 &1 &0.488\\ \hline D10 &0.3715 &0.3715 &0.311 &0.3082 &0.3715 &0.3715 &0.3715 &0.3715 &0.3715 &1\\ \hline \end{array} $$

由阈值集合$\ddot \Delta $　得出综合影响矩阵$T$对应 31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	0.308243	总共9个	$2^{9}$	异构体个数太多，超过$2^7$，超出算力范围！
2	0.311009	总共9个	$2^{9}$	异构体个数太多，超过$2^7$，超出算力范围！
3	0.371473	总共20个	$2^{20}$	异构体个数太多，超过$2^7$，超出算力范围！
4	0.379529	总共19个	$2^{19}$	异构体个数太多，超过$2^7$，超出算力范围！
5	0.3807	总共1个	$2^{1}$	异构体个数太少，不需要计算
6	0.384682	总共1个	$2^{1}$	异构体个数太少，不需要计算
7	0.384856	总共5个	$2^{5}$
8	0.385778	总共1个	$2^{1}$	异构体个数太少，不需要计算
9	0.385943	总共1个	$2^{1}$	异构体个数太少，不需要计算
10	0.387001	总共1个	$2^{1}$	异构体个数太少，不需要计算
11	0.388517	总共1个	$2^{1}$	异构体个数太少，不需要计算
12	0.390121	总共2个	$2^{2}$
13	0.396548	总共1个	$2^{1}$	异构体个数太少，不需要计算
14	0.397377	总共1个	$2^{1}$	异构体个数太少，不需要计算
15	0.400643	总共1个	$2^{1}$	异构体个数太少，不需要计算
16	0.406708	总共1个	$2^{1}$	异构体个数太少，不需要计算
17	0.409728	总共1个	$2^{1}$	异构体个数太少，不需要计算
18	0.41416	总共1个	$2^{1}$	异构体个数太少，不需要计算
19	0.415605	总共1个	$2^{1}$	异构体个数太少，不需要计算
20	0.415704	总共1个	$2^{1}$	异构体个数太少，不需要计算
21	0.422368	总共1个	$2^{1}$	异构体个数太少，不需要计算
22	0.431434	总共1个	$2^{1}$	异构体个数太少，不需要计算
23	0.431533	总共2个	$2^{2}$
24	0.435515	总共1个	$2^{1}$	异构体个数太少，不需要计算
25	0.438837	总共1个	$2^{1}$	异构体个数太少，不需要计算
26	0.447035	总共1个	$2^{1}$	异构体个数太少，不需要计算
27	0.455745	总共1个	$2^{1}$	异构体个数太少，不需要计算
28	0.45692	总共1个	$2^{1}$	异构体个数太少，不需要计算
29	0.473246	总共1个	$2^{1}$	异构体个数太少，不需要计算
30	0.482819	总共1个	$2^{1}$	异构体个数太少，不需要计算
31	0.487976	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

$$\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times4}} &Di &Ci &Mi &Ri\\ \hline D1 &3.201 &3.786 &6.987 &-0.584\\ \hline D2 &3.068 &3.047 &6.115 &0.021\\ \hline D3 &2.922 &2.468 &5.39 &0.454\\ \hline D4 &3.353 &2.661 &6.014 &0.692\\ \hline D5 &3.81 &3.201 &7.011 &0.609\\ \hline D6 &3.46 &3.791 &7.252 &-0.331\\ \hline D7 &3.707 &3.447 &7.154 &0.26\\ \hline D8 &3.43 &3.51 &6.94 &-0.08\\ \hline D9 &3.565 &3.476 &7.042 &0.089\\ \hline D10 &3.158 &4.288 &7.446 &-1.129\\ \hline \end{array} $$

基于综合影响矩阵T特征截距

DEMATEL-UISM联用方法