特征结构的计算与说明

原始矩阵（直接影响矩阵）为

$$Ori=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{18 \times18}} &S1 &S2 &S3 &S4 &S5 &S6 &S7 &S8 &S9 &S10 &S11 &S12 &S13 &S14 &S15 &S16 &S17 &S18\\ \hline S1 &0 &8 &0 &8 &8 &8 &5 &0 &8 &5 &11 &8 &5 &5 &5 &3 &3 &9\\ \hline S2 &0 &0 &0 &5 &8 &8 &6 &11 &6 &3 &3 &5 &5 &0 &0 &3 &3 &9\\ \hline S3 &0 &8 &0 &11 &0 &0 &6 &11 &3 &0 &3 &3 &5 &3 &0 &5 &0 &11\\ \hline S4 &3 &3 &3 &0 &6 &6 &0 &0 &0 &0 &0 &0 &0 &8 &8 &6 &6 &6\\ \hline S5 &3 &6 &0 &6 &0 &0 &6 &5 &8 &9 &9 &6 &9 &6 &9 &0 &0 &6\\ \hline S6 &6 &6 &9 &0 &3 &0 &0 &8 &8 &8 &8 &3 &6 &9 &6 &3 &3 &3\\ \hline S7 &6 &3 &9 &6 &3 &6 &0 &12 &0 &0 &0 &0 &9 &9 &9 &6 &6 &12\\ \hline S8 &0 &12 &12 &0 &6 &10 &12 &0 &12 &4 &4 &9 &9 &9 &3 &3 &3 &3\\ \hline S9 &10 &6 &3 &3 &9 &9 &0 &12 &0 &6 &7 &3 &6 &7 &3 &3 &0 &6\\ \hline S10 &7 &2 &0 &6 &10 &6 &0 &3 &7 &0 &0 &6 &3 &0 &4 &0 &3 &0\\ \hline S11 &9 &3 &3 &3 &0 &9 &0 &3 &3 &0 &0 &3 &9 &12 &6 &6 &6 &12\\ \hline S12 &9 &6 &3 &6 &6 &3 &0 &9 &3 &6 &3 &0 &3 &3 &6 &3 &12 &3\\ \hline S13 &6 &6 &6 &6 &6 &9 &3 &9 &6 &0 &12 &3 &0 &9 &12 &9 &12 &12\\ \hline S14 &6 &0 &3 &8 &5 &7 &7 &7 &5 &0 &9 &4 &9 &0 &9 &6 &9 &3\\ \hline S15 &6 &0 &0 &9 &9 &6 &9 &3 &3 &0 &6 &6 &9 &3 &0 &0 &0 &0\\ \hline S16 &3 &3 &0 &0 &0 &3 &3 &3 &3 &0 &3 &3 &3 &0 &0 &0 &0 &3\\ \hline S17 &3 &0 &7 &7 &3 &3 &3 &7 &8 &6 &6 &7 &6 &6 &6 &6 &0 &8\\ \hline S18 &3 &0 &6 &3 &6 &3 &3 &3 &6 &0 &6 &3 &6 &3 &0 &3 &9 &0\\ \hline \end{array} $$

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_{18 \times18}} &S1 &S2 &S3 &S4 &S5 &S6 &S7 &S8 &S9 &S10 &S11 &S12 &S13 &S14 &S15 &S16 &S17 &S18\\ \hline S1 &0 &0.049 &0 &0.049 &0.049 &0.049 &0.03 &0 &0.049 &0.03 &0.067 &0.049 &0.03 &0.03 &0.03 &0.018 &0.018 &0.055\\ \hline S2 &0 &0 &0 &0.03 &0.049 &0.049 &0.036 &0.067 &0.036 &0.018 &0.018 &0.03 &0.03 &0 &0 &0.018 &0.018 &0.055\\ \hline S3 &0 &0.049 &0 &0.067 &0 &0 &0.036 &0.067 &0.018 &0 &0.018 &0.018 &0.03 &0.018 &0 &0.03 &0 &0.067\\ \hline S4 &0.018 &0.018 &0.018 &0 &0.036 &0.036 &0 &0 &0 &0 &0 &0 &0 &0.049 &0.049 &0.036 &0.036 &0.036\\ \hline S5 &0.018 &0.036 &0 &0.036 &0 &0 &0.036 &0.03 &0.049 &0.055 &0.055 &0.036 &0.055 &0.036 &0.055 &0 &0 &0.036\\ \hline S6 &0.036 &0.036 &0.055 &0 &0.018 &0 &0 &0.049 &0.049 &0.049 &0.049 &0.018 &0.036 &0.055 &0.036 &0.018 &0.018 &0.018\\ \hline S7 &0.036 &0.018 &0.055 &0.036 &0.018 &0.036 &0 &0.073 &0 &0 &0 &0 &0.055 &0.055 &0.055 &0.036 &0.036 &0.073\\ \hline S8 &0 &0.073 &0.073 &0 &0.036 &0.061 &0.073 &0 &0.073 &0.024 &0.024 &0.055 &0.055 &0.055 &0.018 &0.018 &0.018 &0.018\\ \hline S9 &0.061 &0.036 &0.018 &0.018 &0.055 &0.055 &0 &0.073 &0 &0.036 &0.043 &0.018 &0.036 &0.043 &0.018 &0.018 &0 &0.036\\ \hline S10 &0.043 &0.012 &0 &0.036 &0.061 &0.036 &0 &0.018 &0.043 &0 &0 &0.036 &0.018 &0 &0.024 &0 &0.018 &0\\ \hline S11 &0.055 &0.018 &0.018 &0.018 &0 &0.055 &0 &0.018 &0.018 &0 &0 &0.018 &0.055 &0.073 &0.036 &0.036 &0.036 &0.073\\ \hline S12 &0.055 &0.036 &0.018 &0.036 &0.036 &0.018 &0 &0.055 &0.018 &0.036 &0.018 &0 &0.018 &0.018 &0.036 &0.018 &0.073 &0.018\\ \hline S13 &0.036 &0.036 &0.036 &0.036 &0.036 &0.055 &0.018 &0.055 &0.036 &0 &0.073 &0.018 &0 &0.055 &0.073 &0.055 &0.073 &0.073\\ \hline S14 &0.036 &0 &0.018 &0.049 &0.03 &0.043 &0.043 &0.043 &0.03 &0 &0.055 &0.024 &0.055 &0 &0.055 &0.036 &0.055 &0.018\\ \hline S15 &0.036 &0 &0 &0.055 &0.055 &0.036 &0.055 &0.018 &0.018 &0 &0.036 &0.036 &0.055 &0.018 &0 &0 &0 &0\\ \hline S16 &0.018 &0.018 &0 &0 &0 &0.018 &0.018 &0.018 &0.018 &0 &0.018 &0.018 &0.018 &0 &0 &0 &0 &0.018\\ \hline S17 &0.018 &0 &0.043 &0.043 &0.018 &0.018 &0.018 &0.043 &0.049 &0.036 &0.036 &0.043 &0.036 &0.036 &0.036 &0.036 &0 &0.049\\ \hline S18 &0.018 &0 &0.036 &0.018 &0.036 &0.018 &0.018 &0.018 &0.036 &0 &0.036 &0.018 &0.036 &0.018 &0 &0.018 &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_{18 \times18}} &S1 &S2 &S3 &S4 &S5 &S6 &S7 &S8 &S9 &S10 &S11 &S12 &S13 &S14 &S15 &S16 &S17 &S18\\ \hline S1 &0.036 &0.075 &0.027 &0.081 &0.084 &0.088 &0.053 &0.044 &0.083 &0.05 &0.104 &0.076 &0.072 &0.07 &0.067 &0.045 &0.052 &0.097\\ \hline S2 &0.026 &0.026 &0.027 &0.053 &0.076 &0.079 &0.056 &0.1 &0.067 &0.036 &0.048 &0.053 &0.064 &0.034 &0.029 &0.039 &0.044 &0.086\\ \hline S3 &0.02 &0.069 &0.023 &0.086 &0.026 &0.03 &0.056 &0.095 &0.043 &0.011 &0.042 &0.037 &0.058 &0.046 &0.024 &0.051 &0.026 &0.096\\ \hline S4 &0.035 &0.032 &0.032 &0.02 &0.055 &0.055 &0.017 &0.022 &0.021 &0.011 &0.024 &0.017 &0.025 &0.067 &0.066 &0.05 &0.051 &0.057\\ \hline S5 &0.052 &0.062 &0.025 &0.068 &0.037 &0.041 &0.06 &0.069 &0.08 &0.069 &0.088 &0.063 &0.093 &0.073 &0.088 &0.026 &0.033 &0.075\\ \hline S6 &0.067 &0.065 &0.078 &0.034 &0.053 &0.04 &0.027 &0.088 &0.084 &0.065 &0.084 &0.048 &0.076 &0.089 &0.068 &0.043 &0.047 &0.058\\ \hline S7 &0.064 &0.048 &0.084 &0.071 &0.053 &0.075 &0.032 &0.112 &0.039 &0.017 &0.041 &0.031 &0.096 &0.092 &0.088 &0.064 &0.068 &0.113\\ \hline S8 &0.04 &0.107 &0.105 &0.042 &0.077 &0.105 &0.102 &0.06 &0.113 &0.047 &0.069 &0.086 &0.104 &0.099 &0.06 &0.051 &0.056 &0.072\\ \hline S9 &0.09 &0.068 &0.046 &0.051 &0.09 &0.094 &0.029 &0.11 &0.041 &0.057 &0.082 &0.05 &0.079 &0.081 &0.054 &0.044 &0.032 &0.077\\ \hline S10 &0.063 &0.032 &0.015 &0.057 &0.083 &0.059 &0.016 &0.043 &0.065 &0.017 &0.026 &0.055 &0.043 &0.025 &0.048 &0.015 &0.036 &0.025\\ \hline S11 &0.083 &0.043 &0.044 &0.05 &0.033 &0.09 &0.025 &0.055 &0.053 &0.017 &0.04 &0.045 &0.092 &0.106 &0.068 &0.062 &0.068 &0.109\\ \hline S12 &0.08 &0.062 &0.042 &0.067 &0.069 &0.053 &0.025 &0.088 &0.053 &0.055 &0.052 &0.029 &0.055 &0.052 &0.066 &0.041 &0.096 &0.055\\ \hline S13 &0.077 &0.072 &0.072 &0.079 &0.08 &0.104 &0.054 &0.106 &0.084 &0.025 &0.121 &0.057 &0.057 &0.104 &0.115 &0.088 &0.11 &0.125\\ \hline S14 &0.07 &0.031 &0.048 &0.082 &0.065 &0.083 &0.069 &0.084 &0.067 &0.02 &0.094 &0.054 &0.097 &0.044 &0.092 &0.065 &0.086 &0.064\\ \hline S15 &0.062 &0.024 &0.022 &0.079 &0.08 &0.066 &0.072 &0.05 &0.044 &0.016 &0.066 &0.056 &0.085 &0.052 &0.033 &0.022 &0.027 &0.036\\ \hline S16 &0.029 &0.029 &0.011 &0.01 &0.012 &0.032 &0.026 &0.033 &0.031 &0.007 &0.031 &0.028 &0.032 &0.014 &0.012 &0.009 &0.012 &0.033\\ \hline S17 &0.05 &0.029 &0.068 &0.074 &0.052 &0.056 &0.042 &0.081 &0.081 &0.053 &0.071 &0.069 &0.075 &0.072 &0.069 &0.061 &0.031 &0.086\\ \hline S18 &0.04 &0.021 &0.056 &0.042 &0.057 &0.044 &0.035 &0.048 &0.061 &0.014 &0.063 &0.038 &0.064 &0.047 &0.026 &0.038 &0.075 &0.032\\ \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_{18 \times18}} &S1 &S2 &S3 &S4 &S5 &S6 &S7 &S8 &S9 &S10 &S11 &S12 &S13 &S14 &S15 &S16 &S17 &S18\\ \hline S1 &1 &0.0753 &0.0268 &0.0812 &0.0844 &0.0879 &0.053 &0.0435 &0.0834 &0.0505 &0.1038 &0.0757 &0.0725 &0.0704 &0.0672 &0.0452 &0.0522 &0.0968\\ \hline S2 &0.0262 &1 &0.0267 &0.0534 &0.0759 &0.0789 &0.0565 &0.0996 &0.0672 &0.0359 &0.0482 &0.0532 &0.0639 &0.034 &0.0292 &0.0391 &0.044 &0.0864\\ \hline S3 &0.0204 &0.0691 &1 &0.0862 &0.0257 &0.0302 &0.0557 &0.0948 &0.0433 &0.0109 &0.042 &0.0372 &0.0584 &0.0461 &0.0237 &0.0507 &0.0256 &0.0962\\ \hline S4 &0.0348 &0.0315 &0.0316 &1 &0.0545 &0.055 &0.0168 &0.0224 &0.0212 &0.0111 &0.0236 &0.0173 &0.0248 &0.0667 &0.0664 &0.0496 &0.0513 &0.0568\\ \hline S5 &0.0515 &0.0618 &0.0248 &0.0683 &1 &0.041 &0.0595 &0.0687 &0.0803 &0.0694 &0.0882 &0.0626 &0.0927 &0.0726 &0.0881 &0.0256 &0.0326 &0.0751\\ \hline S6 &0.0667 &0.065 &0.0778 &0.0343 &0.0527 &1 &0.0271 &0.0881 &0.0836 &0.0652 &0.0845 &0.0476 &0.0763 &0.0889 &0.0676 &0.0432 &0.0465 &0.0584\\ \hline S7 &0.0642 &0.0483 &0.0841 &0.0707 &0.053 &0.0748 &1 &0.1118 &0.0393 &0.0171 &0.0412 &0.0309 &0.0963 &0.0921 &0.0877 &0.0641 &0.0679 &0.113\\ \hline S8 &0.0398 &0.1073 &0.1047 &0.0424 &0.0769 &0.1053 &0.1016 &1 &0.1128 &0.0475 &0.0686 &0.0858 &0.1037 &0.0987 &0.06 &0.051 &0.0556 &0.0717\\ \hline S9 &0.0904 &0.0684 &0.0456 &0.0507 &0.0896 &0.0942 &0.0288 &0.1104 &1 &0.057 &0.0823 &0.0498 &0.0786 &0.081 &0.0536 &0.0436 &0.0316 &0.077\\ \hline S10 &0.0625 &0.0325 &0.0154 &0.0567 &0.0834 &0.0595 &0.0157 &0.0431 &0.0654 &1 &0.0261 &0.0549 &0.0431 &0.0251 &0.0477 &0.0149 &0.0356 &0.0252\\ \hline S11 &0.083 &0.0433 &0.0441 &0.0497 &0.0331 &0.0898 &0.0252 &0.0554 &0.0531 &0.0169 &1 &0.0453 &0.0917 &0.1059 &0.0683 &0.062 &0.0676 &0.1089\\ \hline S12 &0.0798 &0.0622 &0.0416 &0.0666 &0.0687 &0.0532 &0.0254 &0.0878 &0.0534 &0.055 &0.0522 &1 &0.0547 &0.0515 &0.0664 &0.0408 &0.0962 &0.0547\\ \hline S13 &0.0769 &0.0718 &0.0722 &0.0791 &0.0795 &0.104 &0.0541 &0.1058 &0.0839 &0.0248 &0.1214 &0.057 &1 &0.1044 &0.1146 &0.0884 &0.11 &0.1253\\ \hline S14 &0.07 &0.031 &0.0483 &0.0821 &0.0647 &0.0829 &0.0686 &0.0835 &0.0668 &0.0198 &0.0937 &0.0538 &0.097 &1 &0.0923 &0.0651 &0.0857 &0.0638\\ \hline S15 &0.0622 &0.0244 &0.0222 &0.0793 &0.0798 &0.0665 &0.0719 &0.0497 &0.0445 &0.0158 &0.0661 &0.0563 &0.0853 &0.0522 &1 &0.0223 &0.027 &0.0357\\ \hline S16 &0.0292 &0.029 &0.0106 &0.0104 &0.0122 &0.0323 &0.0262 &0.033 &0.0306 &0.007 &0.0311 &0.0276 &0.032 &0.0141 &0.0117 &1 &0.0118 &0.0332\\ \hline S17 &0.05 &0.0289 &0.0676 &0.0738 &0.052 &0.0556 &0.0425 &0.0806 &0.0811 &0.0526 &0.071 &0.0687 &0.0746 &0.0723 &0.0686 &0.0614 &1 &0.0863\\ \hline S18 &0.0404 &0.0212 &0.0555 &0.0419 &0.0574 &0.044 &0.0351 &0.0481 &0.0608 &0.0144 &0.063 &0.0379 &0.0645 &0.0467 &0.0259 &0.0381 &0.0746 &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_{18 \times18}} &S1 &S2 &S3 &S4 &S5 &S6 &S7 &S8 &S9 &S10 &S11 &S12 &S13 &S14 &S15 &S16 &S17 &S18\\ \hline S1 &1 &0.097 &0.097 &0.0862 &0.0896 &0.097 &0.097 &0.097 &0.097 &0.0694 &0.1038 &0.0858 &0.097 &0.1038 &0.097 &0.0884 &0.097 &0.1038\\ \hline S2 &0.0904 &1 &0.0996 &0.0862 &0.0896 &0.0996 &0.0996 &0.0996 &0.0996 &0.0694 &0.0996 &0.0858 &0.0996 &0.0996 &0.0996 &0.0884 &0.0996 &0.0996\\ \hline S3 &0.0904 &0.0948 &1 &0.0862 &0.0896 &0.0948 &0.0948 &0.0948 &0.0948 &0.0694 &0.0948 &0.0858 &0.0948 &0.0948 &0.0948 &0.0884 &0.0948 &0.0962\\ \hline S4 &0.0667 &0.0667 &0.0667 &1 &0.0667 &0.0667 &0.0667 &0.0667 &0.0667 &0.0667 &0.0667 &0.0667 &0.0667 &0.0667 &0.0667 &0.0667 &0.0667 &0.0667\\ \hline S5 &0.0904 &0.0927 &0.0927 &0.0862 &1 &0.0927 &0.0927 &0.0927 &0.0927 &0.0694 &0.0927 &0.0858 &0.0927 &0.0927 &0.0927 &0.0884 &0.0927 &0.0927\\ \hline S6 &0.0889 &0.0889 &0.0889 &0.0862 &0.0889 &1 &0.0889 &0.0889 &0.0889 &0.0694 &0.0889 &0.0858 &0.0889 &0.0889 &0.0889 &0.0884 &0.0889 &0.0889\\ \hline S7 &0.0904 &0.1073 &0.1047 &0.0862 &0.0896 &0.1053 &1 &0.1118 &0.1118 &0.0694 &0.1037 &0.0858 &0.1037 &0.1037 &0.1037 &0.0884 &0.1037 &0.113\\ \hline S8 &0.0904 &0.1073 &0.1047 &0.0862 &0.0896 &0.1053 &0.1016 &1 &0.1128 &0.0694 &0.1037 &0.0858 &0.1037 &0.1037 &0.1037 &0.0884 &0.1037 &0.1037\\ \hline S9 &0.0904 &0.1073 &0.1047 &0.0862 &0.0896 &0.1053 &0.1016 &0.1104 &1 &0.0694 &0.1037 &0.0858 &0.1037 &0.1037 &0.1037 &0.0884 &0.1037 &0.1037\\ \hline S10 &0.0834 &0.0834 &0.0834 &0.0834 &0.0834 &0.0834 &0.0834 &0.0834 &0.0834 &1 &0.0834 &0.0834 &0.0834 &0.0834 &0.0834 &0.0834 &0.0834 &0.0834\\ \hline S11 &0.0904 &0.097 &0.097 &0.0862 &0.0896 &0.097 &0.097 &0.097 &0.097 &0.0694 &1 &0.0858 &0.097 &0.1059 &0.097 &0.0884 &0.097 &0.1089\\ \hline S12 &0.0878 &0.0878 &0.0878 &0.0862 &0.0878 &0.0878 &0.0878 &0.0878 &0.0878 &0.0694 &0.0878 &1 &0.0878 &0.0878 &0.0878 &0.0878 &0.0962 &0.0878\\ \hline S13 &0.0904 &0.1058 &0.1047 &0.0862 &0.0896 &0.1053 &0.1016 &0.1058 &0.1058 &0.0694 &0.1214 &0.0858 &1 &0.1059 &0.1146 &0.0884 &0.11 &0.1253\\ \hline S14 &0.0904 &0.097 &0.097 &0.0862 &0.0896 &0.097 &0.097 &0.097 &0.097 &0.0694 &0.097 &0.0858 &0.097 &1 &0.097 &0.0884 &0.097 &0.097\\ \hline S15 &0.0853 &0.0853 &0.0853 &0.0853 &0.0853 &0.0853 &0.0853 &0.0853 &0.0853 &0.0694 &0.0853 &0.0853 &0.0853 &0.0853 &1 &0.0853 &0.0853 &0.0853\\ \hline S16 &0.0332 &0.0332 &0.0332 &0.0332 &0.0332 &0.0332 &0.0332 &0.0332 &0.0332 &0.0332 &0.0332 &0.0332 &0.0332 &0.0332 &0.0332 &1 &0.0332 &0.0332\\ \hline S17 &0.0811 &0.0811 &0.0811 &0.0811 &0.0811 &0.0811 &0.0811 &0.0811 &0.0811 &0.0694 &0.0811 &0.0811 &0.0811 &0.0811 &0.0811 &0.0811 &1 &0.0863\\ \hline S18 &0.0746 &0.0746 &0.0746 &0.0746 &0.0746 &0.0746 &0.0746 &0.0746 &0.0746 &0.0694 &0.0746 &0.0746 &0.0746 &0.0746 &0.0746 &0.0746 &0.0746 &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 $数值区段
1	0.03324	0<$\lambda$<0.03324
2	0.06674	0.03324<$\lambda$<0.06674
3	0.06943	0.06674<$\lambda$<0.06943
4	0.0746	0.06943<$\lambda$<0.0746
5	0.0811	0.0746<$\lambda$<0.0811
6	0.08344	0.0811<$\lambda$<0.08344
7	0.0853	0.08344<$\lambda$<0.0853
8	0.08585	0.0853<$\lambda$<0.08585
9	0.08621	0.08585<$\lambda$<0.08621
10	0.08632	0.08621<$\lambda$<0.08632
11	0.08778	0.08632<$\lambda$<0.08778
12	0.08844	0.08778<$\lambda$<0.08844
13	0.08889	0.08844<$\lambda$<0.08889
14	0.08964	0.08889<$\lambda$<0.08964
15	0.09044	0.08964<$\lambda$<0.09044
16	0.09271	0.09044<$\lambda$<0.09271
17	0.09477	0.09271<$\lambda$<0.09477
18	0.09622	0.09477<$\lambda$<0.09622
19	0.09623	0.09622<$\lambda$<0.09623
20	0.09705	0.09623<$\lambda$<0.09705
21	0.09955	0.09705<$\lambda$<0.09955
22	0.10157	0.09955<$\lambda$<0.10157
23	0.10369	0.10157<$\lambda$<0.10369
24	0.1038	0.10369<$\lambda$<0.1038
25	0.10472	0.1038<$\lambda$<0.10472
26	0.10525	0.10472<$\lambda$<0.10525
27	0.10579	0.10525<$\lambda$<0.10579
28	0.10585	0.10579<$\lambda$<0.10585
29	0.10728	0.10585<$\lambda$<0.10728
30	0.10894	0.10728<$\lambda$<0.10894
31	0.11	0.10894<$\lambda$<0.11
32	0.11039	0.11<$\lambda$<0.11039
33	0.11179	0.11039<$\lambda$<0.11179
34	0.11277	0.11179<$\lambda$<0.11277
35	0.11303	0.11277<$\lambda$<0.11303
36	0.11457	0.11303<$\lambda$<0.11457
37	0.12143	0.11457<$\lambda$<0.12143
38	0.12533	0.12143<$\lambda$<0.12533
39	1	0.12533<$\lambda$<1

特征结构——不含孤立子系统

截距范围：0.081104902<$\lambda$<0.083444699

$$A_t=\begin{array} {c|c|c|c|c|c|c|c}{M_{18 \times18}} &S1 &S2 &S3 &S4 &S5 &S6 &S7 &S8 &S9 &S10 &S11 &S12 &S13 &S14 &S15 &S16 &S17 &S18\\ \hline S1 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S2 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S3 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S4 & & & &1 & & & & & & & & & & & & & & \\ \hline S5 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S6 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S7 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S8 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S9 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S10 &1 &1 &1 &1 &1 &1 &1 &1 &1 &1 &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S11 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S12 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S13 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S14 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S15 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S16 & & & & & & & & & & & & & & & &1 & & \\ \hline S17 & & & & & & & & & & & & & & & & &1 &1\\ \hline S18 & & & & & & & & & & & & & & & & & &1\\ \hline \end{array} $$

$$WS_t=\begin{array}{c|c|c|c|c|c|c}{M_{18 \times18}} &S1 &S2 &S3 &S4 &S5 &S6 &S7 &S8 &S9 &S10 &S11 &S12 &S13 &S14 &S15 &S16 &S17 &S18\\ \hline S1 &0 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &0 &0.0968\\ \hline S2 &1 &0 &1 &0 &1 &1 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &0 &0.0864\\ \hline S3 &1 &1 &0 &0.0862 &1 &1 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &0 &0.0962\\ \hline S4 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline S5 &1 &1 &1 &0 &0 &1 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &0 &0\\ \hline S6 &1 &1 &1 &0 &1 &0 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &0 &0\\ \hline S7 &1 &1 &1 &0 &1 &1 &0 &1 &1 &0 &1 &1 &1 &1 &1 &0 &0 &0.113\\ \hline S8 &1 &1 &1 &0 &1 &1 &1 &0 &1 &0 &1 &1 &1 &1 &1 &0 &0 &0\\ \hline S9 &1 &1 &1 &0 &1 &1 &1 &1 &0 &0 &1 &1 &1 &1 &1 &0 &0 &0\\ \hline S10 &0 &0 &0 &0 &0.0834 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline S11 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &0 &1 &1 &1 &1 &0 &0 &0.1089\\ \hline S12 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &0 &1 &1 &1 &0 &0.0962 &0\\ \hline S13 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &1 &0 &1 &1 &0.0884 &0.11 &0.1253\\ \hline S14 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &1 &1 &0 &1 &0 &0.0857 &0\\ \hline S15 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &1 &1 &1 &0 &0 &0 &0\\ \hline S16 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline S17 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.0863\\ \hline S18 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline \end{array} $$

含孤立子系统的特征结构

截距范围：0.083444699<$\lambda$<0.085298092

$$A_s=\begin{array} {c|c|c|c|c|c|c|c}{M_{18 \times18}} &S1 &S2 &S3 &S4 &S5 &S6 &S7 &S8 &S9 &S10 &S11 &S12 &S13 &S14 &S15 &S16 &S17 &S18\\ \hline S1 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S2 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S3 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S4 & & & &1 & & & & & & & & & & & & & & \\ \hline S5 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S6 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S7 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S8 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S9 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S10 & & & & & & & & & &1 & & & & & & & & \\ \hline S11 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S12 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S13 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S14 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S15 &1 &1 &1 &1 &1 &1 &1 &1 &1 & &1 &1 &1 &1 &1 &1 &1 &1\\ \hline S16 & & & & & & & & & & & & & & & &1 & & \\ \hline S17 & & & & & & & & & & & & & & & & &1 &1\\ \hline S18 & & & & & & & & & & & & & & & & & &1\\ \hline \end{array} $$

$$WS_s=\begin{array}{c|c|c|c|c|c|c}{M_{18 \times18}} &S1 &S2 &S3 &S4 &S5 &S6 &S7 &S8 &S9 &S10 &S11 &S12 &S13 &S14 &S15 &S16 &S17 &S18\\ \hline S1 &0 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &0 &0.0968\\ \hline S2 &1 &0 &1 &0 &1 &1 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &0 &0.0864\\ \hline S3 &1 &1 &0 &0.0862 &1 &1 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &0 &0.0962\\ \hline S4 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline S5 &1 &1 &1 &0 &0 &1 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &0 &0\\ \hline S6 &1 &1 &1 &0 &1 &0 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &0 &0\\ \hline S7 &1 &1 &1 &0 &1 &1 &0 &1 &1 &0 &1 &1 &1 &1 &1 &0 &0 &0.113\\ \hline S8 &1 &1 &1 &0 &1 &1 &1 &0 &1 &0 &1 &1 &1 &1 &1 &0 &0 &0\\ \hline S9 &1 &1 &1 &0 &1 &1 &1 &1 &0 &0 &1 &1 &1 &1 &1 &0 &0 &0\\ \hline S10 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline S11 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &0 &1 &1 &1 &1 &0 &0 &0.1089\\ \hline S12 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &0 &1 &1 &1 &0 &0.0962 &0\\ \hline S13 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &1 &0 &1 &1 &0.0884 &0.11 &0.1253\\ \hline S14 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &1 &1 &0 &1 &0 &0.0857 &0\\ \hline S15 &1 &1 &1 &0 &1 &1 &1 &1 &1 &0 &1 &1 &1 &1 &0 &0 &0 &0\\ \hline S16 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline S17 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.0863\\ \hline S18 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline \end{array} $$

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

$$\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{18 \times4}} &Di &Ci &Mi &Ri\\ \hline S1 &1.206 &0.984 &2.191 &0.222\\ \hline S2 &0.944 &0.897 &1.842 &0.047\\ \hline S3 &0.839 &0.823 &1.662 &0.017\\ \hline S4 &0.656 &1.047 &1.703 &-0.391\\ \hline S5 &1.1 &1.081 &2.181 &0.019\\ \hline S6 &1.113 &1.194 &2.307 &-0.081\\ \hline S7 &1.188 &0.795 &1.984 &0.393\\ \hline S8 &1.393 &1.286 &2.679 &0.107\\ \hline S9 &1.174 &1.112 &2.285 &0.062\\ \hline S10 &0.723 &0.587 &1.311 &0.136\\ \hline S11 &1.083 &1.147 &2.231 &-0.064\\ \hline S12 &1.039 &0.891 &1.93 &0.149\\ \hline S13 &1.53 &1.267 &2.797 &0.263\\ \hline S14 &1.213 &1.167 &2.38 &0.046\\ \hline S15 &0.894 &1.072 &1.966 &-0.178\\ \hline S16 &0.391 &0.815 &1.206 &-0.423\\ \hline S17 &1.118 &0.947 &2.065 &0.172\\ \hline S18 &0.802 &1.297 &2.099 &-0.495\\ \hline \end{array} $$

无孤立系统的中心度、原因度坐标体系综合影响关系特征结构图表

有孤立系统的中心度、原因度坐标体系综合影响关系特征结构图表

特征结构论文写作相关注意事项

数据来源即直接影响矩阵$O$的详细说明。直接影响矩阵O是整个流程中的输入。

参数选择。规范化（归一化）方法需要重点说明，采用不同的归一化方法会导致不同的结果。

输出结果为，1、带影响值的对抗层级拓扑图。2、带影响值的M,R直角坐标图

模糊可达矩阵，及阈值集合是一个重点。即综合影响矩阵$T$与对抗层级拓扑图是1对多的关系。

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——不含孤立子系统

含孤立子系统的特征结构

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

无孤立系统的中心度、原因度坐标体系综合影响关系特征结构图表

有孤立系统的中心度、原因度坐标体系综合影响关系特征结构图表

特征结构论文写作相关注意事项