基于综合影响矩阵的对抗解释结构模型联合分析法

规范化方法选择（参数选择）：

原始矩阵（直接影响矩阵）为

$$Ori=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{18 \times18}} &S1 &S2 &S3 &S4 &S5 &S6 &S7 &S8 &S9 &S10 &S11 &S12 &S13 &S14 &S15 &S16 &S17 &S18\\ \hline S1 &0 &41 &46 &22 &44 &39 &31 &11 &10 &39 &49 &31 &49 &28 &49 &41 &11 &10\\ \hline S2 &39 &0 &22 &50 &22 &41 &31 &13 &11 &22 &11 &13 &13 &21 &39 &29 &30 &40\\ \hline S3 &50 &21 &0 &40 &50 &50 &30 &10 &28 &40 &40 &11 &40 &10 &40 &49 &31 &38\\ \hline S4 &12 &41 &11 &0 &14 &12 &11 &12 &12 &41 &10 &49 &39 &41 &41 &12 &41 &50\\ \hline S5 &21 &21 &39 &31 &0 &21 &20 &10 &11 &31 &11 &31 &22 &31 &40 &30 &31 &31\\ \hline S6 &31 &41 &40 &40 &40 &0 &40 &11 &11 &30 &28 &11 &13 &11 &11 &11 &21 &20\\ \hline S7 &31 &32 &40 &30 &40 &41 &0 &10 &10 &31 &22 &41 &40 &31 &22 &12 &22 &41\\ \hline S8 &21 &40 &19 &40 &10 &31 &10 &0 &23 &10 &10 &50 &10 &37 &40 &10 &32 &41\\ \hline S9 &10 &20 &10 &10 &10 &10 &10 &39 &0 &40 &21 &40 &10 &11 &40 &13 &10 &40\\ \hline S10 &10 &22 &20 &11 &31 &20 &22 &10 &12 &0 &21 &50 &21 &22 &31 &21 &40 &40\\ \hline S11 &31 &12 &29 &11 &12 &21 &31 &10 &10 &31 &0 &20 &21 &10 &10 &41 &10 &10\\ \hline S12 &12 &40 &10 &10 &12 &12 &13 &10 &10 &30 &13 &0 &10 &32 &50 &10 &29 &47\\ \hline S13 &20 &21 &10 &10 &21 &19 &40 &10 &10 &20 &19 &40 &0 &10 &22 &10 &19 &31\\ \hline S14 &21 &39 &10 &10 &10 &10 &21 &10 &19 &12 &10 &41 &32 &0 &45 &31 &40 &42\\ \hline S15 &10 &22 &11 &10 &30 &10 &11 &10 &11 &22 &11 &28 &21 &31 &0 &12 &19 &19\\ \hline S16 &40 &40 &40 &30 &40 &30 &40 &10 &10 &30 &41 &10 &10 &10 &10 &0 &10 &12\\ \hline S17 &30 &40 &38 &11 &21 &40 &40 &10 &10 &20 &19 &10 &11 &12 &20 &10 &0 &39\\ \hline S18 &21 &21 &28 &10 &30 &40 &40 &10 &19 &20 &28 &10 &20 &21 &29 &19 &40 &0\\ \hline \end{array} $$

规范直接关系矩阵求解过程

$$\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 &0.051 &0.058 &0.028 &0.055 &0.049 &0.039 &0.014 &0.013 &0.049 &0.061 &0.039 &0.061 &0.035 &0.061 &0.051 &0.014 &0.013\\ \hline S2 &0.049 &0 &0.028 &0.063 &0.028 &0.051 &0.039 &0.016 &0.014 &0.028 &0.014 &0.016 &0.016 &0.026 &0.049 &0.036 &0.038 &0.05\\ \hline S3 &0.063 &0.026 &0 &0.05 &0.063 &0.063 &0.038 &0.013 &0.035 &0.05 &0.05 &0.014 &0.05 &0.013 &0.05 &0.061 &0.039 &0.048\\ \hline S4 &0.015 &0.051 &0.014 &0 &0.018 &0.015 &0.014 &0.015 &0.015 &0.051 &0.013 &0.061 &0.049 &0.051 &0.051 &0.015 &0.051 &0.063\\ \hline S5 &0.026 &0.026 &0.049 &0.039 &0 &0.026 &0.025 &0.013 &0.014 &0.039 &0.014 &0.039 &0.028 &0.039 &0.05 &0.038 &0.039 &0.039\\ \hline S6 &0.039 &0.051 &0.05 &0.05 &0.05 &0 &0.05 &0.014 &0.014 &0.038 &0.035 &0.014 &0.016 &0.014 &0.014 &0.014 &0.026 &0.025\\ \hline S7 &0.039 &0.04 &0.05 &0.038 &0.05 &0.051 &0 &0.013 &0.013 &0.039 &0.028 &0.051 &0.05 &0.039 &0.028 &0.015 &0.028 &0.051\\ \hline S8 &0.026 &0.05 &0.024 &0.05 &0.013 &0.039 &0.013 &0 &0.029 &0.013 &0.013 &0.063 &0.013 &0.046 &0.05 &0.013 &0.04 &0.051\\ \hline S9 &0.013 &0.025 &0.013 &0.013 &0.013 &0.013 &0.013 &0.049 &0 &0.05 &0.026 &0.05 &0.013 &0.014 &0.05 &0.016 &0.013 &0.05\\ \hline S10 &0.013 &0.028 &0.025 &0.014 &0.039 &0.025 &0.028 &0.013 &0.015 &0 &0.026 &0.063 &0.026 &0.028 &0.039 &0.026 &0.05 &0.05\\ \hline S11 &0.039 &0.015 &0.036 &0.014 &0.015 &0.026 &0.039 &0.013 &0.013 &0.039 &0 &0.025 &0.026 &0.013 &0.013 &0.051 &0.013 &0.013\\ \hline S12 &0.015 &0.05 &0.013 &0.013 &0.015 &0.015 &0.016 &0.013 &0.013 &0.038 &0.016 &0 &0.013 &0.04 &0.063 &0.013 &0.036 &0.059\\ \hline S13 &0.025 &0.026 &0.013 &0.013 &0.026 &0.024 &0.05 &0.013 &0.013 &0.025 &0.024 &0.05 &0 &0.013 &0.028 &0.013 &0.024 &0.039\\ \hline S14 &0.026 &0.049 &0.013 &0.013 &0.013 &0.013 &0.026 &0.013 &0.024 &0.015 &0.013 &0.051 &0.04 &0 &0.056 &0.039 &0.05 &0.053\\ \hline S15 &0.013 &0.028 &0.014 &0.013 &0.038 &0.013 &0.014 &0.013 &0.014 &0.028 &0.014 &0.035 &0.026 &0.039 &0 &0.015 &0.024 &0.024\\ \hline S16 &0.05 &0.05 &0.05 &0.038 &0.05 &0.038 &0.05 &0.013 &0.013 &0.038 &0.051 &0.013 &0.013 &0.013 &0.013 &0 &0.013 &0.015\\ \hline S17 &0.038 &0.05 &0.048 &0.014 &0.026 &0.05 &0.05 &0.013 &0.013 &0.025 &0.024 &0.013 &0.014 &0.015 &0.025 &0.013 &0 &0.049\\ \hline S18 &0.026 &0.026 &0.035 &0.013 &0.038 &0.05 &0.05 &0.013 &0.024 &0.025 &0.035 &0.013 &0.025 &0.026 &0.036 &0.024 &0.05 &0\\ \hline \end{array} $$

综合影响矩阵求解过程

　　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 &0.043 &0.099 &0.099 &0.066 &0.1 &0.092 &0.084 &0.033 &0.035 &0.095 &0.096 &0.084 &0.098 &0.071 &0.111 &0.088 &0.058 &0.066\\ \hline S2 &0.081 &0.044 &0.064 &0.092 &0.066 &0.088 &0.076 &0.032 &0.032 &0.067 &0.045 &0.055 &0.05 &0.058 &0.091 &0.065 &0.074 &0.093\\ \hline S3 &0.104 &0.079 &0.048 &0.088 &0.11 &0.108 &0.086 &0.034 &0.057 &0.099 &0.089 &0.063 &0.09 &0.051 &0.102 &0.098 &0.083 &0.101\\ \hline S4 &0.047 &0.09 &0.046 &0.028 &0.052 &0.051 &0.05 &0.031 &0.033 &0.085 &0.04 &0.096 &0.077 &0.08 &0.093 &0.043 &0.087 &0.106\\ \hline S5 &0.059 &0.067 &0.081 &0.067 &0.037 &0.062 &0.061 &0.028 &0.032 &0.075 &0.043 &0.074 &0.058 &0.067 &0.091 &0.066 &0.074 &0.081\\ \hline S6 &0.071 &0.088 &0.083 &0.08 &0.085 &0.037 &0.084 &0.029 &0.031 &0.074 &0.063 &0.05 &0.049 &0.043 &0.056 &0.044 &0.061 &0.068\\ \hline S7 &0.076 &0.085 &0.088 &0.071 &0.09 &0.091 &0.042 &0.03 &0.033 &0.081 &0.061 &0.092 &0.085 &0.072 &0.076 &0.049 &0.069 &0.1\\ \hline S8 &0.057 &0.09 &0.055 &0.077 &0.047 &0.073 &0.047 &0.016 &0.046 &0.049 &0.04 &0.096 &0.043 &0.075 &0.092 &0.04 &0.075 &0.094\\ \hline S9 &0.036 &0.056 &0.037 &0.035 &0.039 &0.04 &0.039 &0.06 &0.014 &0.076 &0.047 &0.078 &0.035 &0.038 &0.082 &0.038 &0.041 &0.082\\ \hline S10 &0.043 &0.064 &0.056 &0.04 &0.07 &0.058 &0.06 &0.027 &0.031 &0.034 &0.052 &0.093 &0.053 &0.054 &0.077 &0.052 &0.081 &0.089\\ \hline S11 &0.064 &0.046 &0.063 &0.037 &0.045 &0.054 &0.066 &0.024 &0.026 &0.067 &0.025 &0.053 &0.05 &0.034 &0.044 &0.073 &0.038 &0.045\\ \hline S12 &0.041 &0.08 &0.039 &0.035 &0.043 &0.044 &0.045 &0.025 &0.027 &0.065 &0.038 &0.029 &0.036 &0.063 &0.094 &0.035 &0.065 &0.091\\ \hline S13 &0.05 &0.057 &0.039 &0.035 &0.054 &0.052 &0.076 &0.024 &0.026 &0.053 &0.046 &0.077 &0.024 &0.036 &0.06 &0.034 &0.051 &0.071\\ \hline S14 &0.056 &0.084 &0.043 &0.039 &0.045 &0.046 &0.059 &0.027 &0.039 &0.048 &0.039 &0.082 &0.066 &0.027 &0.093 &0.063 &0.08 &0.09\\ \hline S15 &0.034 &0.054 &0.036 &0.032 &0.059 &0.036 &0.037 &0.023 &0.026 &0.051 &0.032 &0.059 &0.046 &0.058 &0.029 &0.034 &0.048 &0.053\\ \hline S16 &0.083 &0.088 &0.084 &0.069 &0.086 &0.074 &0.084 &0.028 &0.03 &0.075 &0.08 &0.049 &0.045 &0.042 &0.054 &0.032 &0.047 &0.057\\ \hline S17 &0.068 &0.085 &0.079 &0.043 &0.061 &0.084 &0.082 &0.027 &0.029 &0.059 &0.051 &0.045 &0.043 &0.041 &0.062 &0.04 &0.032 &0.086\\ \hline S18 &0.058 &0.064 &0.068 &0.042 &0.072 &0.084 &0.083 &0.027 &0.04 &0.06 &0.062 &0.047 &0.054 &0.053 &0.074 &0.051 &0.081 &0.04\\ \hline \end{array} $$

模糊可达矩阵FR的求解

FR：模糊可达矩阵的求解
$FB= T +I$
$FB^{(k-1)}≠FB^{k}=FB^{(k+1)}= FR$
$FR 为模糊可达矩阵$
$FB 为模糊相乘矩阵$
$FB 主对角线为1$
$FB= \begin{array} {c|c|c|c|c|c|c|c}{ FB_{n \times n}} &1 &2 &{\cdots} &n \\ \hline 1 & \color{blue}{1}&{b_{12}}&{\cdots}&{b_{1n}}\\ \hline 2 & {b_{21}}&\color{blue}{1}&{\cdots}&{b_{2n}}\\ \hline {\vdots} &{\vdots}&{\vdots}&\color{blue}{1}&{\vdots}\\ \hline n & {b_{n1}}&{b_{n2}}&{\cdots}&\color{blue}{1}\\ \hline \end{array}$
$FB 主对角线为1$
$ 设FC =FB \times FB \quad FC=\left[ c_{ij} \right]_{n \times n} \quad FB=\left[ b_{ij} \right]_{n \times n}$
$ \begin{equation}\begin{split} c_{ij}&=\sum_{k=1}^n b_{ik}\odot b_{kj} \\ &=(b_{i1} \odot b_{1j}) \oplus (b_{i2} \odot b_{2j}) \oplus (b_{i3} \odot b_{3j}) \cdots \oplus \cdots(b_{in} \odot b_{nj})\\ \end{split}\end{equation}$
模糊算子采用查德算子，即最大最小算子，格式如下。
$ \begin{equation}\begin{split} c_{ij}&=\sum_{k=1}^n b_{ik} \land b_{kj} \\ &=(b_{i1} \land b_{1j}) \vee (b_{i2} \land b_{2j}) \vee (b_{i3} \land b_{3j}) \cdots \vee \cdots(b_{in} \land b_{nj})\\ \end{split}\end{equation}$

模糊相乘矩阵求解 FB=T+I即综合影响矩阵中主对角线全部变成1

$$FB=\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 &0.0991 &0.0986 &0.0657 &0.0996 &0.0921 &0.0835 &0.0331 &0.035 &0.0946 &0.0962 &0.0842 &0.0984 &0.0706 &0.1109 &0.0878 &0.0576 &0.0659\\ \hline S2 &0.0815 &1 &0.0639 &0.092 &0.0661 &0.0878 &0.0756 &0.0323 &0.0325 &0.0666 &0.0452 &0.0548 &0.05 &0.0576 &0.091 &0.0653 &0.0738 &0.0929\\ \hline S3 &0.104 &0.0791 &1 &0.0881 &0.1098 &0.1081 &0.0856 &0.0336 &0.0573 &0.0992 &0.089 &0.063 &0.0901 &0.0514 &0.1024 &0.0982 &0.0829 &0.1006\\ \hline S4 &0.0467 &0.0903 &0.0461 &1 &0.0521 &0.0507 &0.0504 &0.0306 &0.0331 &0.0851 &0.0403 &0.0964 &0.077 &0.0798 &0.0933 &0.0429 &0.0871 &0.1055\\ \hline S5 &0.0588 &0.0666 &0.0809 &0.0671 &1 &0.062 &0.0606 &0.028 &0.0321 &0.0749 &0.0434 &0.0743 &0.0584 &0.0674 &0.091 &0.0657 &0.0738 &0.0813\\ \hline S6 &0.0711 &0.0885 &0.0832 &0.0796 &0.0847 &1 &0.0836 &0.029 &0.0314 &0.0742 &0.0631 &0.0505 &0.0486 &0.0434 &0.0559 &0.0441 &0.061 &0.0675\\ \hline S7 &0.0757 &0.0851 &0.0876 &0.071 &0.0903 &0.0912 &1 &0.0302 &0.0335 &0.0807 &0.0607 &0.0916 &0.0847 &0.0717 &0.0765 &0.0493 &0.0687 &0.0995\\ \hline S8 &0.0573 &0.0897 &0.0554 &0.0775 &0.0468 &0.0726 &0.0473 &1 &0.0463 &0.0491 &0.0402 &0.0963 &0.0426 &0.0753 &0.0922 &0.0403 &0.0753 &0.094\\ \hline S9 &0.0364 &0.0556 &0.0375 &0.0347 &0.0393 &0.0398 &0.039 &0.06 &1 &0.0761 &0.0473 &0.0782 &0.0349 &0.038 &0.0821 &0.0376 &0.0411 &0.0825\\ \hline S10 &0.0428 &0.0642 &0.0561 &0.0402 &0.0703 &0.0579 &0.0605 &0.0267 &0.0314 &1 &0.052 &0.0928 &0.053 &0.0542 &0.0765 &0.0518 &0.0813 &0.0885\\ \hline S11 &0.0639 &0.0462 &0.0628 &0.0374 &0.0446 &0.0543 &0.0659 &0.0243 &0.0261 &0.067 &1 &0.0527 &0.0502 &0.0345 &0.0441 &0.0727 &0.0385 &0.0445\\ \hline S12 &0.0406 &0.08 &0.039 &0.0353 &0.0433 &0.0439 &0.0449 &0.0249 &0.027 &0.0645 &0.0383 &1 &0.0365 &0.0628 &0.0941 &0.0354 &0.0646 &0.0912\\ \hline S13 &0.0495 &0.0568 &0.0395 &0.0352 &0.0536 &0.0516 &0.076 &0.0244 &0.026 &0.0532 &0.0456 &0.0767 &1 &0.0361 &0.0596 &0.0343 &0.0506 &0.0712\\ \hline S14 &0.0556 &0.0843 &0.0434 &0.0388 &0.0453 &0.0461 &0.0593 &0.027 &0.0395 &0.0482 &0.0391 &0.0818 &0.0657 &1 &0.0928 &0.0629 &0.0802 &0.0901\\ \hline S15 &0.0339 &0.0537 &0.0358 &0.0317 &0.0593 &0.0358 &0.0374 &0.0229 &0.0256 &0.0509 &0.0321 &0.0591 &0.0457 &0.0576 &1 &0.0342 &0.0476 &0.0529\\ \hline S16 &0.0827 &0.0876 &0.0844 &0.0686 &0.0858 &0.0739 &0.0843 &0.0278 &0.0302 &0.075 &0.0798 &0.0492 &0.0454 &0.042 &0.0544 &1 &0.0471 &0.0569\\ \hline S17 &0.0683 &0.0846 &0.0791 &0.0432 &0.061 &0.0839 &0.0824 &0.0266 &0.0292 &0.059 &0.0513 &0.0446 &0.0431 &0.0415 &0.0625 &0.0404 &1 &0.0857\\ \hline S18 &0.0581 &0.0637 &0.0683 &0.0416 &0.0717 &0.0835 &0.0834 &0.0274 &0.0402 &0.06 &0.0623 &0.0467 &0.0541 &0.0528 &0.0736 &0.0512 &0.0808 &1\\ \hline \end{array} $$

模糊可达矩阵FR

$$FR=\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 &0.0991 &0.0986 &0.092 &0.0996 &0.0986 &0.0856 &0.0573 &0.0573 &0.0986 &0.0962 &0.0928 &0.0984 &0.0798 &0.1109 &0.0982 &0.0871 &0.0986\\ \hline S2 &0.0836 &1 &0.0836 &0.092 &0.0847 &0.0878 &0.0836 &0.0573 &0.0573 &0.0851 &0.0836 &0.092 &0.0836 &0.0798 &0.092 &0.0836 &0.0871 &0.0929\\ \hline S3 &0.104 &0.0991 &1 &0.092 &0.1098 &0.1081 &0.0856 &0.0573 &0.0573 &0.0992 &0.0962 &0.0928 &0.0984 &0.0798 &0.104 &0.0982 &0.0871 &0.1006\\ \hline S4 &0.0836 &0.0903 &0.0836 &1 &0.0847 &0.0878 &0.0836 &0.0573 &0.0573 &0.0851 &0.0836 &0.0964 &0.0836 &0.0798 &0.0941 &0.0836 &0.0871 &0.1055\\ \hline S5 &0.0813 &0.0813 &0.0813 &0.0813 &1 &0.0813 &0.0813 &0.0573 &0.0573 &0.0813 &0.0813 &0.0813 &0.0813 &0.0798 &0.091 &0.0813 &0.0813 &0.0813\\ \hline S6 &0.0836 &0.0885 &0.0836 &0.0885 &0.0847 &1 &0.0836 &0.0573 &0.0573 &0.0851 &0.0836 &0.0885 &0.0836 &0.0798 &0.0885 &0.0836 &0.0871 &0.0885\\ \hline S7 &0.0876 &0.0885 &0.0876 &0.0885 &0.0903 &0.0912 &1 &0.0573 &0.0573 &0.0876 &0.0876 &0.0916 &0.0876 &0.0798 &0.0916 &0.0876 &0.0871 &0.0995\\ \hline S8 &0.0836 &0.0897 &0.0836 &0.0897 &0.0847 &0.0878 &0.0836 &1 &0.0573 &0.0851 &0.0836 &0.0963 &0.0836 &0.0798 &0.0941 &0.0836 &0.0871 &0.094\\ \hline S9 &0.0825 &0.0825 &0.0825 &0.0825 &0.0825 &0.0825 &0.0825 &0.06 &1 &0.0825 &0.0825 &0.0825 &0.0825 &0.0798 &0.0825 &0.0825 &0.0825 &0.0825\\ \hline S10 &0.0835 &0.0835 &0.0835 &0.0835 &0.0835 &0.0835 &0.0835 &0.0573 &0.0573 &1 &0.0835 &0.0928 &0.0835 &0.0798 &0.0928 &0.0835 &0.0835 &0.0912\\ \hline S11 &0.0727 &0.0727 &0.0727 &0.0727 &0.0727 &0.0727 &0.0727 &0.0573 &0.0573 &0.0727 &1 &0.0727 &0.0727 &0.0727 &0.0727 &0.0727 &0.0727 &0.0727\\ \hline S12 &0.0835 &0.0835 &0.0835 &0.0835 &0.0835 &0.0835 &0.0835 &0.0573 &0.0573 &0.0835 &0.0835 &1 &0.0835 &0.0798 &0.0941 &0.0835 &0.0835 &0.0912\\ \hline S13 &0.0767 &0.0767 &0.0767 &0.0767 &0.0767 &0.0767 &0.0767 &0.0573 &0.0573 &0.0767 &0.0767 &0.0767 &1 &0.0767 &0.0767 &0.0767 &0.0767 &0.0767\\ \hline S14 &0.0836 &0.0843 &0.0836 &0.0843 &0.0843 &0.0843 &0.0836 &0.0573 &0.0573 &0.0843 &0.0836 &0.0843 &0.0836 &1 &0.0928 &0.0836 &0.0843 &0.0901\\ \hline S15 &0.0593 &0.0593 &0.0593 &0.0593 &0.0593 &0.0593 &0.0593 &0.0573 &0.0573 &0.0593 &0.0593 &0.0593 &0.0593 &0.0593 &1 &0.0593 &0.0593 &0.0593\\ \hline S16 &0.0844 &0.0876 &0.0844 &0.0876 &0.0858 &0.0876 &0.0844 &0.0573 &0.0573 &0.0851 &0.0844 &0.0876 &0.0844 &0.0798 &0.0876 &1 &0.0871 &0.0876\\ \hline S17 &0.0836 &0.0846 &0.0836 &0.0846 &0.0846 &0.0846 &0.0836 &0.0573 &0.0573 &0.0846 &0.0836 &0.0846 &0.0836 &0.0798 &0.0846 &0.0836 &1 &0.0857\\ \hline S18 &0.0835 &0.0835 &0.0835 &0.0835 &0.0835 &0.0835 &0.0835 &0.0573 &0.0573 &0.0835 &0.0835 &0.0835 &0.0835 &0.0798 &0.0835 &0.0835 &0.0835 &1\\ \hline \end{array} $$

模糊可达矩阵FR中阈值集合分析

模糊可达矩阵FR中除数字0外不重复的值作为元素构成的集合称为阈值集合。

54个结构数量分布图（瀑布图）

特征结构分析

由模糊可达矩阵的阈值集合$\ddot \Delta $ 元素的数目得出在(0,1]的截距值范围内得到 54个结构。

其中模糊可达矩阵(0,1]的截距值范围内取截距，得到的截矩阵为可达矩阵

设截距值为$\lambda $ ，$T$的截距阵为 $A$ ,$R$为 $A$的可达矩阵。

$R$即为模糊可达矩阵 $FR$ 的　$\lambda $ 　截距阵

序号	特征阈值	聚类对应截距$\lambda $区段	该结构的数目	互不连通区域数目	层级数	系统包含几个回路	最大回路要素数目
1	0.05732	0<$\lambda$<0.05732	33	1	1	1	18
2	0.05931	0.05732<$\lambda$<0.05931	15	1	3	1	16
3	0.05995	0.05931<$\lambda$<0.05995	1	1	4	1	15
4	0.07271	0.05995<$\lambda$<0.07271	15	1	3	1	15
5	0.07673	0.07271<$\lambda$<0.07673	15	1	3	1	14
6	0.07983	0.07673<$\lambda$<0.07983	14	1	3	1	13
7	0.08131	0.07983<$\lambda$<0.08131	13	1	3	1	12
8	0.0825	0.08131<$\lambda$<0.0825	15	1	4	1	11
9	0.08353	0.0825<$\lambda$<0.08353	37	2	4	1	11
10	0.08356	0.08353<$\lambda$<0.08356	36	2	5	1	8
11	0.08426	0.08356<$\lambda$<0.08426	7	2	5	2	4
12	0.08442	0.08426<$\lambda$<0.08442	5	2	5	2	4
13	0.08458	0.08442<$\lambda$<0.08458	7	2	6	2	4
14	0.08471	0.08458<$\lambda$<0.08471	4	2	6	2	3
15	0.0851	0.08471<$\lambda$<0.0851	5	2	6	2	3
16	0.0856	0.0851<$\lambda$<0.0856	2	2	5	2	3
17	0.08568	0.0856<$\lambda$<0.08568	1	2	6	2	3
18	0.08578	0.08568<$\lambda$<0.08578	1	2	6	2	3
19	0.08712	0.08578<$\lambda$<0.08712	8	2	6	2	3
20	0.08757	0.08712<$\lambda$<0.08757	6	3	6	2	3
21	0.08762	0.08757<$\lambda$<0.08762	6	3	5	2	3
22	0.08776	0.08762<$\lambda$<0.08776	3	3	4	2	3
23	0.08849	0.08776<$\lambda$<0.08849	7	3	5	2	2
24	0.08967	0.08849<$\lambda$<0.08967	2	3	4	2	2
25	0.09009	0.08967<$\lambda$<0.09009	1	3	4	2	2
26	0.09025	0.09009<$\lambda$<0.09025	1	3	4	2	2
27	0.0903	0.09025<$\lambda$<0.0903	1	3	4	2	2
28	0.09096	0.0903<$\lambda$<0.09096	1	3	5	1	2
29	0.09121	0.09096<$\lambda$<0.09121	2	3	5	1	2
30	0.09124	0.09121<$\lambda$<0.09124	1	3	5	1	2
31	0.09163	0.09124<$\lambda$<0.09163	2	3	5	1	2
32	0.09196	0.09163<$\lambda$<0.09196	5	3	5	1	2
33	0.09276	0.09196<$\lambda$<0.09276	4	3	4	1	2
34	0.0928	0.09276<$\lambda$<0.0928	1	3	3	1	2
35	0.09288	0.0928<$\lambda$<0.09288	1	4	3	1	2
36	0.09397	0.09288<$\lambda$<0.09397	1	4	3	1	2
37	0.09409	0.09397<$\lambda$<0.09409	3	4	3	1	2
38	0.09616	0.09409<$\lambda$<0.09616	2	4	2	1	2
39	0.09633	0.09616<$\lambda$<0.09633	1	5	2	1	2
40	0.09638	0.09633<$\lambda$<0.09638	1	6	2	1	2
41	0.09816	0.09638<$\lambda$<0.09816	2	7	2	1	2
42	0.09839	0.09816<$\lambda$<0.09839	2	8	2	1	2
43	0.09861	0.09839<$\lambda$<0.09861	4	9	2	1	2
44	0.09911	0.09861<$\lambda$<0.09911	2	9	3	0	1
45	0.09918	0.09911<$\lambda$<0.09918	1	10	3	0	1
46	0.09952	0.09918<$\lambda$<0.09952	1	11	3	0	1
47	0.09958	0.09952<$\lambda$<0.09958	1	12	3	0	1
48	0.10057	0.09958<$\lambda$<0.10057	1	12	3	0	1
49	0.10403	0.10057<$\lambda$<0.10403	2	13	3	0	1
50	0.10551	0.10403<$\lambda$<0.10551	1	14	2	0	1
51	0.10811	0.10551<$\lambda$<0.10811	1	15	2	0	1
52	0.10979	0.10811<$\lambda$<0.10979	1	16	2	0	1
53	0.11088	0.10979<$\lambda$<0.11088	1	17	2	0	1
54	1	0.11088<$\lambda$<1	18	18	1	0	1

选择特征结构的原则

第一、层级数最多的，理由越能体现要素之间的因果关系

层级数目与随着截距值的增加，总体趋势是逐渐增多，随后变少。

第二、孤立系统少的。比如独立区块等于要素的数目这种就没有意义。

独立区域的数目与随着截距值的增加，是单调的递增关系。

第三、系统包含的回路数目，回路数目越多越好

回路数目与截距值的关系是，随着截距值的增加，总体趋势是逐渐增多，随后减少。

第四、没有大回路的，比如最大回路中含5个以上的要素属于大回路

如果存在回路，所有回路中所含的要素数目的最大值，随着截距值的增加，是单调的递减关系。

第五、在瀑布图中，数目大的，即结构数量多的。

某个结构的数目，同截距值的大小，没有必然的联系。

上面五项原则会发现，对于T矩阵来说，截距通常是在平均数+标准差附近；对于模糊可达矩阵FR来说，截距通常是FR（去掉主对角线的值）的平均数附近

按照上述原则选取其中排名最靠前的五个结构

序号	聚类对应截距$\lambda $区段	该结构的数目	互不连通区域数目	层级数	包含回路数目	最大回路要素数目
19	0.08578<$\lambda$<0.08712	8	2	6	2	3
15	0.08471<$\lambda$<0.0851	5	2	6	2	3
14	0.08458<$\lambda$<0.08471	4	2	6	2	3
17	0.0856<$\lambda$<0.08568	1	2	6	2	3
18	0.08568<$\lambda$<0.08578	1	2	6	2	3

T-AISM

前置流程图说明

DEMATEL-T-AISM流程图与说明