## 2 Theory and Methods
### Improved Attribute Recognition Model  
The attribute recognition model consists of three parts: single-indicator attribute measure analysis, multi-indicator attribute measure analysis, and attribute recognition analysis [21]. Assuming there is an evaluation space \(X\), m indicators \(X=\{x_{1},\cdots,x_{i},\cdots,x_{n}\}\) on the evaluation object Xi are evaluated, corresponding to the \(K\) evaluation levels \(Ck\). The measurement value \(tj\) of the \(j\)th indicator for the evaluation object \(X\) has the corresponding single index attribute measure function under different levels \(Ck\). The classification of the single indicator level is shown in Table 2.  
After calculating the single indicator attribute measures of each indicator, the comprehensive attribute measures of the object to be evaluated \(Xi\) are determined by combining the indicator weights. The comprehensive evaluation is realized. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Index**} & \multicolumn{5}{c}{**Level**} \\ \cline{2-6}  & \(\mathbf{C_{1}}\) & \(\mathbf{C_{2}}\) & \(\ldots\) & \(\mathbf{C_{M-1}}\) & \(\mathbf{C_{M}}\) \\ \hline \(I_{1}\) & \(h_{10}\)–\(h_{11}\) & \(h_{11}\)–\(h_{12}\) & \(\ldots\) & \(h_{1M\)-\(2}\)–\(h_{1M\)-\(1}\) & \(h_{1M\)-\(1}\)–\(h_{1M}\) \\ \(I_{2}\) & \(h_{20}\)–\(h_{21}\) & \(h_{21}\)–\(h_{22}\) & \(\ldots\) & \(h_{2M\)-\(2}\)–\(h_{2M\)-\(1}\) & \(h_{2M\)-\(1}\)–\(h_{2M}\) \\ \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) \\ \(l_{w}\) & \(h_{w0}\)–\(h_{w1}\) & \(h_{w1}\)–\(h_{w2}\) & \(\ldots\) & \(h_{w0M\)-\(2}\)–\(h_{w0M\)-\(1}\) & \(h_{w0M\)-\(1}\)–\(h_{w0M}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Classification of single index grades. Figure 5: State variable weight vector. There are two disadvantages for traditional attribute measurement functions. Firstly, the function is linear; however, the measured values vary non-linearly in actual engineering. Secondly, the traditional function curve has several mutation points, which will lead to an error from the actual situation. Therefore, this paper uses trigonometric functions to improve the linear attribute measurement functions and to establish a non-linear single indicator attribute measurement function. The details are as follows. If \(\mathrm{h_{q0}}<\mathrm{h_{q1}}\cdots<\mathrm{h_{qm}}\), the attribute measure functions \(\mu_{\mathrm{xqm}}(t)\) are expressed as:  
\[\mu_{\mathrm{xq1}}(t)=\left\{ \begin{array}{l}1\qquad\qquad\mathrm{t<h_{q1}- P_{q1}}\\ \frac{1}{2}\cos(\pi\cdot\frac{\mathrm{t-h_{q1}-P_{q1}}}{2P_{q1}})+\frac{1}{2} \qquad\mathrm{h_{q1}-P_{q1}}\leq\mathrm{t}\leq\mathrm{h_{q1}}+P_{q1}\\ 0\qquad\qquad\mathrm{t>h_{q1}+P_{q1}}\end{array} \right. \tag{16}\]  
\[\mu_{\mathrm{xqm}}(t)=\left\{ \begin{array}{l}0\qquad\qquad\mathrm{t<h_{q(m-1 )}-P_{q(m-1)}}\\ \frac{1}{2}\sin(\pi\cdot\frac{\mathrm{t-h_{q(m-1)}}}{2P_{q(m-1)}})+\frac{1}{2} \qquad\mathrm{h_{q(m-1)}-P_{q(m-1)}}\leq\mathrm{t}\leq\mathrm{h_{q(m-1)}+P_{q( m-1)}}\\ 1\qquad\qquad\mathrm{h_{q(m-1)}+P_{q(m-1)}<t<h_{qm}-P_{qm}}\\ -\frac{1}{2}\cos(\pi\cdot\frac{\mathrm{t-h_{qm}}}{2P_{qm}})+\frac{1}{2}\qquad \mathrm{h_{qm}-P_{qm}}\leq\mathrm{t}\leq\mathrm{h_{q(m-1)}+P_{q(m-1)}}\\ 0\qquad\qquad\mathrm{t>h_{q(m-1)}+P_{q(m-1)}}\end{array} \right. \tag{17}\]  
\[\mu_{\mathrm{xqM}}(t)=\left\{ \begin{array}{l}0\qquad\qquad\mathrm{t<h_{q(M- 1)}-P_{q(M-1)}}\\ \frac{1}{2}\sin(\pi\cdot\frac{\mathrm{t-h_{q(M-1)}}}{2P_{q(M-1)}})+\frac{1}{2} \qquad\mathrm{h_{q(M-1)}-P_{q(M-1)}}\leq\mathrm{t}\leq\mathrm{h_{q(M-1)}+P_{q( M-1)}}\\ 1\qquad\qquad\mathrm{t>h_{q(M-1)}+P_{q(M-1)}}\end{array} \right. \tag{18}\]  
The symbol definition is the same as before. If \(\mathrm{h_{q0}}>\mathrm{h_{q1}}\cdots>\mathrm{h_{qm}}\), the attribute measure functions \(\mu_{\mathrm{xqm}}(t)\) are expressed as:  
\[\mu_{\mathrm{xq1}}(t)=\left\{