DEMATEL-ISM中特征突变结构的在线计算

特征结构的计算与说明

原始矩阵（直接影响矩阵）为

$$Ori=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{11 \times11}} &A1 &A2 &B1 &B2 &C1 &C2 &C3 &C4 &D1 &D2 &D3\\ \hline A1 &0 &50 &12 &46 &43 &34 &38 &24 &45 &23 &40\\ \hline A2 &51 &0 &17 &34 &21 &30 &47 &16 &12 &4 &7\\ \hline B1 &18 &23 &0 &39 &51 &34 &32 &19 &36 &42 &29\\ \hline B2 &24 &16 &16 &0 &45 &45 &24 &30 &36 &28 &33\\ \hline C1 &25 &20 &18 &21 &0 &36 &16 &21 &33 &25 &31\\ \hline C2 &19 &15 &45 &30 &32 &0 &14 &18 &23 &29 &25\\ \hline C3 &21 &13 &25 &37 &29 &27 &0 &28 &36 &32 &32\\ \hline C4 &32 &22 &21 &38 &31 &31 &36 &0 &31 &28 &27\\ \hline D1 &18 &11 &50 &21 &35 &50 &26 &33 &0 &31 &30\\ \hline D2 &14 &17 &27 &24 &23 &27 &36 &19 &35 &0 &17\\ \hline D3 &20 &16 &26 &15 &20 &23 &27 &15 &22 &29 &0\\ \hline \end{array} $$

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

$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{11 \times11}} &A1 &A2 &B1 &B2 &C1 &C2 &C3 &C4 &D1 &D2 &D3\\ \hline A1 &0 &0.141 &0.034 &0.13 &0.121 &0.096 &0.107 &0.068 &0.127 &0.065 &0.113\\ \hline A2 &0.144 &0 &0.048 &0.096 &0.059 &0.085 &0.132 &0.045 &0.034 &0.011 &0.02\\ \hline B1 &0.051 &0.065 &0 &0.11 &0.144 &0.096 &0.09 &0.054 &0.101 &0.118 &0.082\\ \hline B2 &0.068 &0.045 &0.045 &0 &0.127 &0.127 &0.068 &0.085 &0.101 &0.079 &0.093\\ \hline C1 &0.07 &0.056 &0.051 &0.059 &0 &0.101 &0.045 &0.059 &0.093 &0.07 &0.087\\ \hline C2 &0.054 &0.042 &0.127 &0.085 &0.09 &0 &0.039 &0.051 &0.065 &0.082 &0.07\\ \hline C3 &0.059 &0.037 &0.07 &0.104 &0.082 &0.076 &0 &0.079 &0.101 &0.09 &0.09\\ \hline C4 &0.09 &0.062 &0.059 &0.107 &0.087 &0.087 &0.101 &0 &0.087 &0.079 &0.076\\ \hline D1 &0.051 &0.031 &0.141 &0.059 &0.099 &0.141 &0.073 &0.093 &0 &0.087 &0.085\\ \hline D2 &0.039 &0.048 &0.076 &0.068 &0.065 &0.076 &0.101 &0.054 &0.099 &0 &0.048\\ \hline D3 &0.056 &0.045 &0.073 &0.042 &0.056 &0.065 &0.076 &0.042 &0.062 &0.082 &0\\ \hline \end{array} $$

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

　　综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{11 \times11}} &A1 &A2 &B1 &B2 &C1 &C2 &C3 &C4 &D1 &D2 &D3\\ \hline A1 &0.273 &0.355 &0.337 &0.452 &0.479 &0.47 &0.42 &0.324 &0.462 &0.372 &0.414\\ \hline A2 &0.327 &0.171 &0.26 &0.338 &0.329 &0.354 &0.354 &0.233 &0.291 &0.24 &0.252\\ \hline B1 &0.292 &0.267 &0.278 &0.405 &0.468 &0.437 &0.375 &0.289 &0.413 &0.396 &0.361\\ \hline B2 &0.289 &0.236 &0.303 &0.283 &0.428 &0.437 &0.333 &0.298 &0.389 &0.34 &0.351\\ \hline C1 &0.257 &0.216 &0.268 &0.296 &0.265 &0.365 &0.273 &0.241 &0.334 &0.291 &0.304\\ \hline C2 &0.245 &0.208 &0.336 &0.324 &0.358 &0.28 &0.274 &0.238 &0.318 &0.309 &0.295\\ \hline C3 &0.271 &0.219 &0.313 &0.366 &0.377 &0.381 &0.26 &0.284 &0.377 &0.34 &0.338\\ \hline C4 &0.313 &0.255 &0.316 &0.388 &0.401 &0.409 &0.369 &0.224 &0.383 &0.344 &0.341\\ \hline D1 &0.28 &0.23 &0.396 &0.352 &0.418 &0.459 &0.348 &0.311 &0.308 &0.361 &0.353\\ \hline D2 &0.225 &0.204 &0.286 &0.3 &0.323 &0.339 &0.318 &0.234 &0.337 &0.223 &0.266\\ \hline D3 &0.22 &0.186 &0.259 &0.253 &0.287 &0.299 &0.273 &0.203 &0.279 &0.274 &0.196\\ \hline \end{array} $$

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$

$$\tilde B=\begin{array} {c|c|c}{M_{11 \times11}} &A1 &A2 &B1 &B2 &C1 &C2 &C3 &C4 &D1 &D2 &D3\\ \hline A1 &1 &0.3545 &0.3366 &0.4523 &0.4788 &0.4703 &0.4201 &0.3239 &0.4615 &0.3717 &0.4142\\ \hline A2 &0.3267 &1 &0.2603 &0.3383 &0.3287 &0.3542 &0.3536 &0.2332 &0.2907 &0.2402 &0.2519\\ \hline B1 &0.292 &0.2667 &1 &0.4049 &0.4681 &0.4371 &0.3747 &0.2887 &0.4132 &0.3959 &0.3615\\ \hline B2 &0.2889 &0.2356 &0.3034 &1 &0.4279 &0.4373 &0.3326 &0.2977 &0.3886 &0.3404 &0.3512\\ \hline C1 &0.2566 &0.2164 &0.2677 &0.2955 &1 &0.3649 &0.2731 &0.2407 &0.3344 &0.2905 &0.3038\\ \hline C2 &0.2451 &0.2079 &0.3365 &0.3241 &0.3579 &1 &0.2738 &0.2376 &0.3185 &0.3087 &0.2951\\ \hline C3 &0.2708 &0.2192 &0.3128 &0.3662 &0.3774 &0.3806 &1 &0.2844 &0.3774 &0.3401 &0.3375\\ \hline C4 &0.3134 &0.2551 &0.3159 &0.3879 &0.4008 &0.4088 &0.3692 &1 &0.3829 &0.3439 &0.3412\\ \hline D1 &0.2799 &0.2296 &0.3961 &0.3516 &0.4181 &0.4592 &0.3476 &0.3114 &1 &0.3612 &0.3528\\ \hline D2 &0.2252 &0.2035 &0.2865 &0.3 &0.323 &0.3394 &0.3178 &0.2345 &0.3367 &1 &0.2663\\ \hline D3 &0.2199 &0.1862 &0.2591 &0.2528 &0.2865 &0.2988 &0.2731 &0.2032 &0.2787 &0.2742 &1\\ \hline \end{array} $$

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。

$$\tilde R=\begin{array} {c|c|c}{M_{11 \times11}} &A1 &A2 &B1 &B2 &C1 &C2 &C3 &C4 &D1 &D2 &D3\\ \hline A1 &1 &0.3545 &0.3961 &0.4523 &0.4788 &0.4703 &0.4201 &0.3239 &0.4615 &0.3959 &0.4142\\ \hline A2 &0.3267 &1 &0.3536 &0.3536 &0.3542 &0.3542 &0.3536 &0.3239 &0.3536 &0.3536 &0.3536\\ \hline B1 &0.3114 &0.3114 &1 &0.4049 &0.4681 &0.4371 &0.3747 &0.3114 &0.4132 &0.3959 &0.3615\\ \hline B2 &0.3114 &0.3114 &0.3886 &1 &0.4279 &0.4373 &0.3747 &0.3114 &0.3886 &0.3886 &0.3615\\ \hline C1 &0.3114 &0.3114 &0.3365 &0.3365 &1 &0.3649 &0.3365 &0.3114 &0.3365 &0.3365 &0.3365\\ \hline C2 &0.3114 &0.3114 &0.3365 &0.3365 &0.3579 &1 &0.3365 &0.3114 &0.3365 &0.3365 &0.3365\\ \hline C3 &0.3114 &0.3114 &0.3774 &0.3774 &0.3774 &0.3806 &1 &0.3114 &0.3774 &0.3774 &0.3615\\ \hline C4 &0.3134 &0.3134 &0.3879 &0.3879 &0.4008 &0.4088 &0.3747 &1 &0.3879 &0.3879 &0.3615\\ \hline D1 &0.3114 &0.3114 &0.3961 &0.3961 &0.4181 &0.4592 &0.3747 &0.3114 &1 &0.3959 &0.3615\\ \hline D2 &0.3114 &0.3114 &0.3367 &0.3367 &0.3394 &0.3394 &0.3367 &0.3114 &0.3367 &1 &0.3367\\ \hline D3 &0.2988 &0.2988 &0.2988 &0.2988 &0.2988 &0.2988 &0.2988 &0.2988 &0.2988 &0.2988 &1\\ \hline \end{array} $$

由阈值集合$\ddot \Delta $　得出综合影响矩阵$T$对应 39个结构。

序号	阈值集合中——特征阈值	聚类特征-对应截距$\lambda $数值区段
1	0.29883	0<$\lambda$<0.29883
2	0.31141	0.29883<$\lambda$<0.31141
3	0.31339	0.31141<$\lambda$<0.31339
4	0.32387	0.31339<$\lambda$<0.32387
5	0.32672	0.32387<$\lambda$<0.32672
6	0.33648	0.32672<$\lambda$<0.33648
7	0.33673	0.33648<$\lambda$<0.33673
8	0.33936	0.33673<$\lambda$<0.33936
9	0.35356	0.33936<$\lambda$<0.35356
10	0.35417	0.35356<$\lambda$<0.35417
11	0.35455	0.35417<$\lambda$<0.35455
12	0.35789	0.35455<$\lambda$<0.35789
13	0.36148	0.35789<$\lambda$<0.36148
14	0.3649	0.36148<$\lambda$<0.3649
15	0.37467	0.3649<$\lambda$<0.37467
16	0.37736	0.37467<$\lambda$<0.37736
17	0.37743	0.37736<$\lambda$<0.37743
18	0.38063	0.37743<$\lambda$<0.38063
19	0.38786	0.38063<$\lambda$<0.38786
20	0.38861	0.38786<$\lambda$<0.38861
21	0.39591	0.38861<$\lambda$<0.39591
22	0.39609	0.39591<$\lambda$<0.39609
23	0.40078	0.39609<$\lambda$<0.40078
24	0.40487	0.40078<$\lambda$<0.40487
25	0.40882	0.40487<$\lambda$<0.40882
26	0.41318	0.40882<$\lambda$<0.41318
27	0.41419	0.41318<$\lambda$<0.41419
28	0.41813	0.41419<$\lambda$<0.41813
29	0.42008	0.41813<$\lambda$<0.42008
30	0.42789	0.42008<$\lambda$<0.42789
31	0.43714	0.42789<$\lambda$<0.43714
32	0.43733	0.43714<$\lambda$<0.43733
33	0.45233	0.43733<$\lambda$<0.45233
34	0.45924	0.45233<$\lambda$<0.45924
35	0.46152	0.45924<$\lambda$<0.46152
36	0.46807	0.46152<$\lambda$<0.46807
37	0.47034	0.46807<$\lambda$<0.47034
38	0.47877	0.47034<$\lambda$<0.47877
39	1	0.47877<$\lambda$<1

特征结构

截距范围：0.35417371<$\lambda$<0.354546649

$$A=\begin{array} {c|c|c|c|c|c|c|c}{M_{11 \times11}} &A1 &A2 &B1 &B2 &C1 &C2 &C3 &C4 &D1 &D2 &D3\\ \hline A1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1\\ \hline A2 & &1 & & & & & & & & & \\ \hline B1 & & &1 &1 &1 &1 &1 & &1 &1 &1\\ \hline B2 & & &1 &1 &1 &1 &1 & &1 &1 &1\\ \hline C1 & & & & &1 &1 & & & & & \\ \hline C2 & & & & &1 &1 & & & & & \\ \hline C3 & & &1 &1 &1 &1 &1 & &1 &1 &1\\ \hline C4 & & &1 &1 &1 &1 &1 &1 &1 &1 &1\\ \hline D1 & & &1 &1 &1 &1 &1 & &1 &1 &1\\ \hline D2 & & & & & & & & & &1 & \\ \hline D3 & & & & & & & & & & &1\\ \hline \end{array} $$

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

$$\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{11 \times4}} &Di &Ci &Mi &Ri\\ \hline A1 &4.357 &2.991 &7.348 &1.365\\ \hline A2 &3.149 &2.546 &5.694 &0.603\\ \hline B1 &3.981 &3.353 &7.334 &0.628\\ \hline B2 &3.687 &3.757 &7.443 &-0.07\\ \hline C1 &3.109 &4.132 &7.241 &-1.024\\ \hline C2 &3.185 &4.23 &7.415 &-1.046\\ \hline C3 &3.526 &3.595 &7.121 &-0.069\\ \hline C4 &3.743 &2.88 &6.623 &0.864\\ \hline D1 &3.815 &3.89 &7.705 &-0.075\\ \hline D2 &3.056 &3.49 &6.546 &-0.434\\ \hline D3 &2.729 &3.471 &6.2 &-0.743\\ \hline \end{array} $$

DEMATEL-ISM联用中特征突变结构的计算

特征结构的计算与说明

原始矩阵（直接影响矩阵）为

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

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

从综合影响矩阵$T$到ISM的处理过程简介

特征结构

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}

求解原理

结果

绘制中心度与原因度建构的散点图图表

DEMATEL-FISM流程图如下：