## 2 Fuzzy Clustering Method  
A fuzzy matrix is constructed by the fuzzy clustering method based on the structure and changing characteristics of the data, and they are classified and divided according to the transfer closure method. A finite theoretical domain \(U\) with \(n\) samples and a fuzzy assessment set \(V\) with \(m\) assessment values are assumed. Here, \(U\) and \(V\) can be expressed by Equations (1) and (2) [27; 28], as follows:  
\[U=\{u_{1},u_{2},\cdots,u_{n}\}, \tag{1}\]  
\[V=\{v_{1},v_{2},\cdots,v_{m}\}. \tag{2}\]  
The original data matrix \(Z\) is built up according to \(U\) and \(V\). Here, \(Z\) is defined as follows:  
\[Z=\begin{pmatrix}z_{11}&\cdots&z_{1m}\\ \vdots&\ddots&\vdots\\ z_{n1}&\cdots&z_{mm}\end{pmatrix}, \tag{3}\]  
where \(z_{nm}\) is the value of the \(m\)-th assessment indicator for the \(n\)-th sample. Based on the raw data obtained, the three steps of the fuzzy clustering method are executed as follows:  
Step 1. Standardisation of the original data matrix \(Z\). The original data matrix \(Z\) was standardised by the following Equation (4):  
\[{z^{\prime}}_{ik}=\frac{z_{ik}-\frac{1}{n}\sum\limits_{l=1}^{n}z_{ik}}{\sqrt{ \frac{1}{n}\sum\limits_{l=1}^{n}\left(z_{ik}-\frac{1}{n}\sum\limits_{l=1}^{n} z_{ik}\right)^{2}}}, \tag{4}\]  
and the following Equation (5) [29; 30]:  
\[z_{ik}^{\prime\prime}=\frac{z_{ik}^{\prime}-min\ z_{ik}^{\prime}}{max\ z_{ik}^ {\prime}-min\ z_{ik}^{\prime}}. \tag{5}\]  
The standardisation matrix \(Z^{\prime\prime}\) was obtained, which could be expressed as follows:  
\[Z^{\prime\prime}=\begin{pmatrix}z_{11}^{\prime\prime}&\cdots&z_{1n}^{\prime \prime}\\ \vdots&\ddots&\vdots\\ z_{m1}^{\prime\prime}&\cdots&z_{mm}^{\prime\prime}\end{pmatrix};\;(i=1,2, \cdots,n;k=1,2,\cdots,m). \tag{6}\]  
Step 2. Construction of fuzzy similarity matrix. The fuzzy similarity matrix \(C=\left[c_{ij}\right]_{nm}\) was obtained from the above \(Z^{\prime\prime}\) using the following Equation (7):  
\[\left\{\begin{array}{l}c_{ij}=1-\sum\limits_{k=1}^{m}\left|z_{ik}^{\prime \prime}-z_{jk}^{\prime\prime}\right|\\ c_{ij}=c_{ji}\\ c_{ii}=1\end{array}\right.. \tag{7}\]  
According to the squared self-synthesis method, the matrix \(C\) was squared by the following:  
\[\left\{\begin{array}{l}C^{\sigma}\circ C^{\sigma}=C^{2\sigma}(\sigma=1,2, \cdots\cdots)\\ c^{2}_{ij}=\vee_{k=1}^{m}\left(c_{ik}\wedge c_{jk}\right)\end{array}\right.. \tag{8}\]  
to obtain the fuzzy equivalence matrix \(C^{*}=\left[c_{ij}^{*}\right]_{nm}\), where \(\vee_{k=1}^{m}\) represented the selection of the item with the largest value among the m numbers; \(\wedge\) represented the selection of the one with the smallest value among the m numbers; \(\sigma\) was a natural number. When\(C^{2k}=C^{2(k+1)}\), \(C^{2k}\) was already transmissible, at which point \(C^{*}=t(C)=C^{2k}\) was satisfied. Then, the fuzzy equivalence matrix \(\mathrm{C}\) was identified.  
Step 3. Cluster analysis. There existed a similarity index \(\lambda\) as a threshold for sample similarity classification, by which the samples could be classified into several classes.  
The classification criteria in this paper were simplified based on the criteria proposed by [PERSON] et al. [31]. When \(\lambda\in[0,1]\), the value of \(\lambda\) would directly affect the accuracy of the classification. If \(\lambda>0.6\), the samples were considered correlated. Furthermore, if \(0.3\ll\lambda\ll 0.6\), they were considered to be weakly correlated with each other. Then, if \(\lambda<0.3\), they were considered uncorrelated.