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

$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{11 \times11}} &A1 &A2 &B1 &B2 &C1 &C2 &C3 &C4 &D1 &D2 &D3\\ \hline A1 &0 &0.148 &0.036 &0.136 &0.128 &0.101 &0.113 &0.071 &0.134 &0.068 &0.119\\ \hline A2 &0.151 &0 &0.05 &0.101 &0.062 &0.089 &0.139 &0.047 &0.036 &0.012 &0.021\\ \hline B1 &0.053 &0.068 &0 &0.116 &0.151 &0.101 &0.095 &0.056 &0.107 &0.125 &0.086\\ \hline B2 &0.071 &0.047 &0.047 &0 &0.134 &0.134 &0.071 &0.089 &0.107 &0.083 &0.098\\ \hline C1 &0.074 &0.059 &0.053 &0.062 &0 &0.107 &0.047 &0.062 &0.098 &0.074 &0.092\\ \hline C2 &0.056 &0.045 &0.134 &0.089 &0.095 &0 &0.042 &0.053 &0.068 &0.086 &0.074\\ \hline C3 &0.062 &0.039 &0.074 &0.11 &0.086 &0.08 &0 &0.083 &0.107 &0.095 &0.095\\ \hline C4 &0.095 &0.065 &0.062 &0.113 &0.092 &0.092 &0.107 &0 &0.092 &0.083 &0.08\\ \hline D1 &0.053 &0.033 &0.148 &0.062 &0.104 &0.148 &0.077 &0.098 &0 &0.092 &0.089\\ \hline D2 &0.042 &0.05 &0.08 &0.071 &0.068 &0.08 &0.107 &0.056 &0.104 &0 &0.05\\ \hline D3 &0.059 &0.047 &0.077 &0.045 &0.059 &0.068 &0.08 &0.045 &0.065 &0.086 &0\\ \hline \end{array} $$

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

　　综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{11 \times11}} &A1 &A2 &B1 &B2 &C1 &C2 &C3 &C4 &D1 &D2 &D3\\ \hline A1 &0.369 &0.442 &0.447 &0.577 &0.616 &0.61 &0.539 &0.42 &0.591 &0.487 &0.53\\ \hline A2 &0.403 &0.231 &0.341 &0.431 &0.428 &0.457 &0.443 &0.303 &0.384 &0.323 &0.335\\ \hline B1 &0.381 &0.344 &0.377 &0.519 &0.595 &0.565 &0.483 &0.376 &0.531 &0.504 &0.467\\ \hline B2 &0.373 &0.307 &0.398 &0.384 &0.545 &0.558 &0.432 &0.38 &0.499 &0.439 &0.45\\ \hline C1 &0.328 &0.277 &0.348 &0.384 &0.36 &0.466 &0.357 &0.31 &0.428 &0.374 &0.388\\ \hline C2 &0.318 &0.27 &0.422 &0.416 &0.459 &0.379 &0.36 &0.308 &0.413 &0.395 &0.38\\ \hline C3 &0.351 &0.287 &0.404 &0.468 &0.489 &0.494 &0.352 &0.363 &0.483 &0.436 &0.432\\ \hline C4 &0.4 &0.328 &0.412 &0.496 &0.519 &0.53 &0.472 &0.304 &0.494 &0.444 &0.441\\ \hline D1 &0.366 &0.303 &0.498 &0.459 &0.539 &0.584 &0.451 &0.397 &0.417 &0.464 &0.455\\ \hline D2 &0.294 &0.263 &0.367 &0.388 &0.419 &0.439 &0.403 &0.303 &0.429 &0.303 &0.347\\ \hline D3 &0.283 &0.24 &0.331 &0.33 &0.373 &0.387 &0.349 &0.264 &0.36 &0.349 &0.266\\ \hline \end{array} $$

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$

$$\tilde B=\begin{array} {c|c|c}{M_{11 \times11}} &A1 &A2 &B1 &B2 &C1 &C2 &C3 &C4 &D1 &D2 &D3\\ \hline A1 &1 &0.4419 &0.4465 &0.5773 &0.6158 &0.61 &0.539 &0.4197 &0.5911 &0.4865 &0.5304\\ \hline A2 &0.4029 &1 &0.3412 &0.4307 &0.4285 &0.457 &0.4429 &0.3033 &0.3839 &0.3229 &0.3351\\ \hline B1 &0.3813 &0.3438 &1 &0.5187 &0.5949 &0.5652 &0.4828 &0.3759 &0.5315 &0.5038 &0.467\\ \hline B2 &0.3727 &0.3066 &0.3976 &1 &0.5452 &0.5575 &0.4322 &0.38 &0.4986 &0.4392 &0.4499\\ \hline C1 &0.3281 &0.2774 &0.348 &0.384 &1 &0.4664 &0.3571 &0.3099 &0.4277 &0.3743 &0.3876\\ \hline C2 &0.3175 &0.2697 &0.4216 &0.4158 &0.4594 &1 &0.3597 &0.3081 &0.4132 &0.3952 &0.3804\\ \hline C3 &0.3508 &0.287 &0.4042 &0.4678 &0.4885 &0.4942 &1 &0.3633 &0.4831 &0.4356 &0.4323\\ \hline C4 &0.3996 &0.3282 &0.412 &0.4958 &0.5188 &0.5296 &0.4722 &1 &0.4943 &0.4444 &0.441\\ \hline D1 &0.3657 &0.3025 &0.4975 &0.4594 &0.5387 &0.584 &0.4509 &0.3967 &1 &0.4642 &0.4545\\ \hline D2 &0.2943 &0.263 &0.3667 &0.3877 &0.4195 &0.4386 &0.4029 &0.3026 &0.4291 &1 &0.3475\\ \hline D3 &0.2826 &0.2397 &0.3308 &0.3304 &0.3726 &0.3872 &0.3487 &0.2637 &0.3602 &0.3489 &1\\ \hline \end{array} $$

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。

$$\tilde R=\begin{array} {c|c|c}{M_{11 \times11}} &A1 &A2 &B1 &B2 &C1 &C2 &C3 &C4 &D1 &D2 &D3\\ \hline A1 &1 &0.4419 &0.4975 &0.5773 &0.6158 &0.61 &0.539 &0.4197 &0.5911 &0.4975 &0.5304\\ \hline A2 &0.4029 &1 &0.4429 &0.4429 &0.457 &0.457 &0.4429 &0.4029 &0.4429 &0.4429 &0.4429\\ \hline B1 &0.3967 &0.3967 &1 &0.5187 &0.5949 &0.5652 &0.4828 &0.3967 &0.5315 &0.5038 &0.467\\ \hline B2 &0.3967 &0.3967 &0.4975 &1 &0.5452 &0.5575 &0.4828 &0.3967 &0.4986 &0.4975 &0.467\\ \hline C1 &0.3967 &0.3967 &0.4277 &0.4277 &1 &0.4664 &0.4277 &0.3967 &0.4277 &0.4277 &0.4277\\ \hline C2 &0.3967 &0.3967 &0.4277 &0.4277 &0.4594 &1 &0.4277 &0.3967 &0.4277 &0.4277 &0.4277\\ \hline C3 &0.3967 &0.3967 &0.4831 &0.4831 &0.4885 &0.4942 &1 &0.3967 &0.4831 &0.4831 &0.467\\ \hline C4 &0.3996 &0.3996 &0.4958 &0.4958 &0.5188 &0.5296 &0.4828 &1 &0.4958 &0.4958 &0.467\\ \hline D1 &0.3967 &0.3967 &0.4975 &0.4975 &0.5387 &0.584 &0.4828 &0.3967 &1 &0.4975 &0.467\\ \hline D2 &0.3967 &0.3967 &0.4291 &0.4291 &0.4386 &0.4386 &0.4291 &0.3967 &0.4291 &1 &0.4291\\ \hline D3 &0.3872 &0.3872 &0.3872 &0.3872 &0.3872 &0.3872 &0.3872 &0.3872 &0.3872 &0.3872 &1\\ \hline \end{array} $$

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 $数值区段
1	0.38717	0<$\lambda$<0.38717
2	0.39673	0.38717<$\lambda$<0.39673
3	0.39965	0.39673<$\lambda$<0.39965
4	0.40295	0.39965<$\lambda$<0.40295
5	0.41968	0.40295<$\lambda$<0.41968
6	0.4277	0.41968<$\lambda$<0.4277
7	0.42912	0.4277<$\lambda$<0.42912
8	0.43856	0.42912<$\lambda$<0.43856
9	0.44185	0.43856<$\lambda$<0.44185
10	0.44288	0.44185<$\lambda$<0.44288
11	0.45704	0.44288<$\lambda$<0.45704
12	0.45936	0.45704<$\lambda$<0.45936
13	0.46644	0.45936<$\lambda$<0.46644
14	0.46704	0.46644<$\lambda$<0.46704
15	0.48277	0.46704<$\lambda$<0.48277
16	0.48311	0.48277<$\lambda$<0.48311
17	0.48855	0.48311<$\lambda$<0.48855
18	0.49422	0.48855<$\lambda$<0.49422
19	0.49582	0.49422<$\lambda$<0.49582
20	0.49751	0.49582<$\lambda$<0.49751
21	0.49856	0.49751<$\lambda$<0.49856
22	0.50377	0.49856<$\lambda$<0.50377
23	0.51868	0.50377<$\lambda$<0.51868
24	0.51876	0.51868<$\lambda$<0.51876
25	0.5296	0.51876<$\lambda$<0.5296
26	0.53045	0.5296<$\lambda$<0.53045
27	0.53148	0.53045<$\lambda$<0.53148
28	0.53871	0.53148<$\lambda$<0.53871
29	0.53895	0.53871<$\lambda$<0.53895
30	0.54519	0.53895<$\lambda$<0.54519
31	0.55751	0.54519<$\lambda$<0.55751
32	0.56518	0.55751<$\lambda$<0.56518
33	0.57734	0.56518<$\lambda$<0.57734
34	0.58397	0.57734<$\lambda$<0.58397
35	0.59113	0.58397<$\lambda$<0.59113
36	0.59485	0.59113<$\lambda$<0.59485
37	0.61001	0.59485<$\lambda$<0.61001
38	0.61582	0.61001<$\lambda$<0.61582
39	1	0.61582<$\lambda$<1

特征结构

截距范围：0.442883662<$\lambda$<0.457035728

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

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

$$\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{11 \times4}} &Di &Ci &Mi &Ri\\ \hline A1 &5.627 &3.864 &9.491 &1.763\\ \hline A2 &4.08 &3.291 &7.37 &0.789\\ \hline B1 &5.142 &4.343 &9.485 &0.799\\ \hline B2 &4.763 &4.852 &9.615 &-0.088\\ \hline C1 &4.02 &5.341 &9.362 &-1.321\\ \hline C2 &4.12 &5.469 &9.589 &-1.349\\ \hline C3 &4.559 &4.641 &9.2 &-0.081\\ \hline C4 &4.84 &3.728 &8.568 &1.113\\ \hline D1 &4.931 &5.03 &9.961 &-0.099\\ \hline D2 &3.955 &4.518 &8.472 &-0.563\\ \hline D3 &3.531 &4.492 &8.023 &-0.961\\ \hline \end{array} $$

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：