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

$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &D1 &D2 &D3 &D4 &D5 &D6 &D7 &D8 &D9 &D10\\ \hline D1 &0 &0.07 &0.07 &0.103 &0.124 &0.119 &0.065 &0.07 &0.065 &0.141\\ \hline D2 &0.114 &0 &0.027 &0.114 &0.086 &0.065 &0.081 &0.065 &0.103 &0.135\\ \hline D3 &0.108 &0.043 &0 &0.076 &0.07 &0.054 &0.07 &0.086 &0.13 &0.114\\ \hline D4 &0.178 &0.054 &0.027 &0 &0.086 &0.103 &0.103 &0.103 &0.103 &0.108\\ \hline D5 &0.178 &0.054 &0.108 &0.054 &0 &0.146 &0.092 &0.108 &0.135 &0.124\\ \hline D6 &0.108 &0.135 &0.07 &0.114 &0.011 &0 &0.124 &0.119 &0.114 &0.114\\ \hline D7 &0.119 &0.168 &0.054 &0.054 &0.135 &0.097 &0 &0.13 &0.108 &0.103\\ \hline D8 &0.054 &0.07 &0.07 &0.059 &0.141 &0.135 &0.114 &0 &0.108 &0.13\\ \hline D9 &0.108 &0.059 &0.114 &0.054 &0.054 &0.146 &0.119 &0.114 &0 &0.168\\ \hline D10 &0.054 &0.108 &0.076 &0.054 &0.114 &0.114 &0.119 &0.114 &0.059 &0\\ \hline \end{array} $$

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

　　综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &D1 &D2 &D3 &D4 &D5 &D6 &D7 &D8 &D9 &D10\\ \hline D1 &0.664 &0.605 &0.503 &0.563 &0.674 &0.775 &0.67 &0.685 &0.671 &0.875\\ \hline D2 &0.738 &0.517 &0.446 &0.552 &0.623 &0.704 &0.658 &0.654 &0.674 &0.842\\ \hline D3 &0.7 &0.533 &0.402 &0.496 &0.582 &0.665 &0.621 &0.644 &0.671 &0.791\\ \hline D4 &0.849 &0.619 &0.487 &0.492 &0.674 &0.797 &0.73 &0.741 &0.728 &0.887\\ \hline D5 &0.938 &0.693 &0.62 &0.61 &0.668 &0.924 &0.806 &0.832 &0.842 &1.006\\ \hline D6 &0.808 &0.706 &0.532 &0.61 &0.627 &0.718 &0.767 &0.773 &0.757 &0.914\\ \hline D7 &0.872 &0.771 &0.557 &0.596 &0.774 &0.862 &0.702 &0.828 &0.803 &0.965\\ \hline D8 &0.762 &0.648 &0.537 &0.557 &0.727 &0.838 &0.756 &0.666 &0.753 &0.921\\ \hline D9 &0.826 &0.661 &0.588 &0.573 &0.679 &0.87 &0.784 &0.791 &0.676 &0.981\\ \hline D10 &0.706 &0.634 &0.501 &0.515 &0.66 &0.761 &0.707 &0.713 &0.661 &0.742\\ \hline \end{array} $$

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$

$$\tilde B=\begin{array} {c|c|c}{M_{10 \times10}} &D1 &D2 &D3 &D4 &D5 &D6 &D7 &D8 &D9 &D10\\ \hline D1 &1 &0.6052 &0.5026 &0.5626 &0.674 &0.7755 &0.6701 &0.685 &0.6707 &0.8754\\ \hline D2 &0.7382 &1 &0.4464 &0.5519 &0.6226 &0.7043 &0.6583 &0.6542 &0.6743 &0.8419\\ \hline D3 &0.7002 &0.5327 &1 &0.4963 &0.5823 &0.6648 &0.6212 &0.6445 &0.6709 &0.7908\\ \hline D4 &0.8489 &0.619 &0.4868 &1 &0.6737 &0.797 &0.7298 &0.7408 &0.7282 &0.8868\\ \hline D5 &0.9383 &0.6931 &0.6202 &0.61 &1 &0.9242 &0.8057 &0.8318 &0.8424 &1\\ \hline D6 &0.8084 &0.7056 &0.5318 &0.6101 &0.6272 &1 &0.7674 &0.7727 &0.7572 &0.9142\\ \hline D7 &0.8716 &0.7714 &0.5569 &0.5958 &0.7744 &0.8623 &1 &0.8284 &0.8027 &0.9653\\ \hline D8 &0.7625 &0.6476 &0.5368 &0.5573 &0.7274 &0.8382 &0.7562 &1 &0.7529 &0.9214\\ \hline D9 &0.8264 &0.6615 &0.5885 &0.573 &0.6794 &0.8702 &0.7839 &0.791 &1 &0.9815\\ \hline D10 &0.7062 &0.6339 &0.5007 &0.515 &0.6599 &0.7608 &0.7073 &0.7133 &0.6614 &1\\ \hline \end{array} $$

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。

$$\tilde R=\begin{array} {c|c|c}{M_{10 \times10}} &D1 &D2 &D3 &D4 &D5 &D6 &D7 &D8 &D9 &D10\\ \hline D1 &1 &0.7674 &0.6202 &0.6101 &0.7674 &0.7755 &0.7674 &0.7727 &0.7674 &0.8754\\ \hline D2 &0.7608 &1 &0.6202 &0.6101 &0.7608 &0.7608 &0.7608 &0.7608 &0.7608 &0.8419\\ \hline D3 &0.7608 &0.7608 &1 &0.6101 &0.7608 &0.7608 &0.7608 &0.7608 &0.7608 &0.7908\\ \hline D4 &0.8489 &0.7674 &0.6202 &1 &0.7674 &0.797 &0.7674 &0.7727 &0.7674 &0.8868\\ \hline D5 &0.9383 &0.7714 &0.6202 &0.6101 &1 &0.9242 &0.8057 &0.8318 &0.8424 &1\\ \hline D6 &0.8084 &0.7674 &0.6202 &0.6101 &0.7674 &1 &0.7674 &0.7727 &0.7674 &0.9142\\ \hline D7 &0.8716 &0.7714 &0.6202 &0.6101 &0.7744 &0.8623 &1 &0.8284 &0.8027 &0.9653\\ \hline D8 &0.8084 &0.7674 &0.6202 &0.6101 &0.7674 &0.8382 &0.7674 &1 &0.7674 &0.9214\\ \hline D9 &0.8264 &0.7714 &0.6202 &0.6101 &0.7744 &0.8702 &0.7839 &0.791 &1 &0.9815\\ \hline D10 &0.7608 &0.7608 &0.6202 &0.6101 &0.7608 &0.7608 &0.7608 &0.7608 &0.7608 &1\\ \hline \end{array} $$

由阈值集合$\ddot \Delta $　得出综合影响矩阵$T$对应 33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	0.610084	总共9个	$2^{9}$	异构体个数太多，超过$2^7$，超出算力范围！
2	0.620221	总共9个	$2^{9}$	异构体个数太多，超过$2^7$，超出算力范围！
3	0.760829	总共20个	$2^{20}$	异构体个数太多，超过$2^7$，超出算力范围！
4	0.767405	总共16个	$2^{16}$	异构体个数太多，超过$2^7$，超出算力范围！
5	0.771422	总共3个	$2^{3}$
6	0.772654	总共3个	$2^{3}$
7	0.774449	总共2个	$2^{2}$
8	0.775492	总共1个	$2^{1}$	异构体个数太少，不需要计算
9	0.783862	总共1个	$2^{1}$	异构体个数太少，不需要计算
10	0.79084	总共1个	$2^{1}$	异构体个数太少，不需要计算
11	0.790997	总共1个	$2^{1}$	异构体个数太少，不需要计算
12	0.797029	总共1个	$2^{1}$	异构体个数太少，不需要计算
13	0.802689	总共1个	$2^{1}$	异构体个数太少，不需要计算
14	0.805732	总共1个	$2^{1}$	异构体个数太少，不需要计算
15	0.80836	总共2个	$2^{2}$
16	0.826392	总共1个	$2^{1}$	异构体个数太少，不需要计算
17	0.828399	总共1个	$2^{1}$	异构体个数太少，不需要计算
18	0.831798	总共1个	$2^{1}$	异构体个数太少，不需要计算
19	0.838242	总共1个	$2^{1}$	异构体个数太少，不需要计算
20	0.841941	总共1个	$2^{1}$	异构体个数太少，不需要计算
21	0.842372	总共1个	$2^{1}$	异构体个数太少，不需要计算
22	0.848864	总共1个	$2^{1}$	异构体个数太少，不需要计算
23	0.862277	总共1个	$2^{1}$	异构体个数太少，不需要计算
24	0.870163	总共1个	$2^{1}$	异构体个数太少，不需要计算
25	0.871552	总共1个	$2^{1}$	异构体个数太少，不需要计算
26	0.875432	总共1个	$2^{1}$	异构体个数太少，不需要计算
27	0.886819	总共1个	$2^{1}$	异构体个数太少，不需要计算
28	0.914245	总共1个	$2^{1}$	异构体个数太少，不需要计算
29	0.92137	总共1个	$2^{1}$	异构体个数太少，不需要计算
30	0.924154	总共1个	$2^{1}$	异构体个数太少，不需要计算
31	0.938285	总共1个	$2^{1}$	异构体个数太少，不需要计算
32	0.965302	总共1个	$2^{1}$	异构体个数太少，不需要计算
33	0.981478	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

$$\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times4}} &Di &Ci &Mi &Ri\\ \hline D1 &6.685 &7.865 &14.55 &-1.179\\ \hline D2 &6.409 &6.387 &12.797 &0.022\\ \hline D3 &6.105 &5.172 &11.278 &0.933\\ \hline D4 &7.003 &5.564 &12.567 &1.439\\ \hline D5 &7.94 &6.689 &14.63 &1.251\\ \hline D6 &7.213 &7.915 &15.128 &-0.703\\ \hline D7 &7.731 &7.202 &14.933 &0.529\\ \hline D8 &7.166 &7.327 &14.493 &-0.161\\ \hline D9 &7.431 &7.237 &14.668 &0.194\\ \hline D10 &6.6 &8.925 &15.526 &-2.325\\ \hline \end{array} $$

基于综合影响矩阵T特征截距

DEMATEL-UISM联用方法