## 4 Case Application
### Method Comparison  
Different methods are used to evaluate the performance of science and technology talents and the evaluation results are different.  
Method A: the method used in this paper. The evaluation value is represented by interval grey number and multiple 'dominant-implicit' reference points are considered. The deviation method is used to optimize the indicator weight and the ball grey target method is used to solve the reference point weight.  
Method B: on the basis of method A, only dominant reference points are considered.  
Method C: on the basis of method A, only implicit reference points are considered.  
Method D: on the basis of method A, the weights of indicators and reference points are given in advance. \(\mathrm{e}_{\mathrm{i}}^{(\mathrm{P})}=0.2\), \(\mathrm{\omega}^{(\mathrm{P})}=0.25\).  
Method E: according to the grey incidence degree theory in reference [35], first normalize the data and find the optimal target center, \(\underline{a_{\mathrm{ij}}}^{\prime}=\underline{a_{\mathrm{ij}}}/\sum_{i=1}^ {\mathrm{m}}\bar{a_{\mathrm{ij}}}\), \(\overline{a_{\mathrm{ij}}}^{\prime}=\overline{a_{\mathrm{ij}}}/\sum_{i=1}^ {\mathrm{m}}\underline{a_{\mathrm{ij}}}\), \(\mathrm{a_{\mathrm{ij}}}=\max\{(\underline{a_{\mathrm{ij}}}+\overline{a_{ \mathrm{ij}}})/2\,|\mathrm{i}=1,2,\ldots,\mathrm{m}\}\), then calculate the target center distance \(\Delta\) and the degree of interval grey number incidence \(\pi\), \(\Delta_{\mathrm{ij}}=\frac{\sqrt{(\underline{a_{\mathrm{ij}}}^{\prime}- \underline{a_{\mathrm{ij}}})^{2}+(\overline{a_{\mathrm{ij}}}^{\prime}- \overline{a_{\mathrm{ij}}})^{2}}}{\sqrt{2}}\), \(\pi_{\mathrm{i}}=\frac{\mathrm{minmin}\Delta+0.5\mathrm{maxmax}\Delta}{ \Delta+0.5\mathrm{maxmax}\Delta}\). Finally, calculate the comprehensive value, \(\mathrm{S_{i}}=\mathrm{h}*\pi_{\mathrm{i}(\mathrm{input})}+(1-\mathrm{h})*\pi_ {\mathrm{i}(\mathrm{output})}\).  
Method F: the kernel of the interval grey number is used to replace the interval grey number; first normalize the data, \(\underline{a_{\mathrm{ij}}}^{\prime}=\underline{a_{\mathrm{ij}}}/\sum_{i=1}^ {\mathrm{m}}\overline{a_{\mathrm{ij}}}\), \(\overline{a_{\mathrm{ij}}}^{\prime}=\overline{a_{\mathrm{ij}}}/\sum_{i=1}^ {\mathrm{m}}\underline{a_{\mathrm{ij}}}\), then the kernel value is calculated, \(\hat{\otimes}=\frac{1}{2}(\underline{a}+\overline{a})\). Finally, calculate the comprehensive value, \(\mathrm{S_{i}}=\mathrm{h}*\sum_{j=1}^{\mathrm{k_{i}}}\bigl{(}\mathrm{e_{j}}* \hat{\otimes}_{\mathrm{input}}\bigr{)}+1-\mathrm{h}*\sum_{j=1}^{\mathrm{k_{2}}} \bigl{(}\mathrm{e_{j}}*\hat{\otimes}_{\mathrm{output}}\bigr{)}\).  
In the above methods, the weight h of input indicators is 0.5 and the comprehensive values under different methods are obtained, as shown in Table 8.  
The comprehensive values of different methods are not the same and the order is not exactly the same. The target rate of the method in this paper is 80%. The method that this paper uses does not only consider dominant-implicit multiple reference points, but also uses Interval Grey Number Analysis and Grey Target Theory. Given indicator weight and optimized indicator weight, the evaluation results of science and technology talents are inconsistent. The paper's method emphasizes operability and practicability, and it provides a new way to solve multi-attribute decision-making problems associated with multiple reference points and has a closer resemblance to reality.