## 4 Results and Discussion
### Assignment to the Classes
Comparing AHP weights and entropy weights, it is obvious that a significant improvement in the use of combined methods in the proposed model could reduce possible weighting biases. Figure 8: Impact of the weighting methods on the core assignment results. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{\(a_{s}\)} & \multicolumn{3}{c}{\(\sigma_{s}^{j}=\sum\limits_{m=1}^{R}f(X_{r})\cdot\eta_{r}\)} & \multicolumn{3}{c}{**Maximum**} \\  & \multicolumn{3}{c}{**Coefficient Value**} & **Grey Class** \\ \cline{2-6}  & \(j=1\) & \(j=2\) & \(j=3\) & \(\sigma_{s}^{j}=max_{1\leq j\leq 3}[\sigma_{s}^{j}]\) & \\ \hline \(a_{1}\) & 0.6672 & 0.6014 & **0.7040** & 0.7040 & \(j^{*}=3\) \\ \(a_{2}\) & 0.6600 & **0.7350** & 0.6850 & 0.7350 & \(j^{*}=2\) \\ \(a_{3}\) & **0.7400** & 0.5150 & 0.5490 & 0.7400 & \(j^{*}=1\) \\ \(a_{4}\) & **0.7260** & 0.5300 & 0.4780 & 0.7260 & \(j^{*}=1\) \\ \(a_{5}\) & **0.7020** & 0.5590 & 0.6530 & 0.7020 & \(j^{*}=1\) \\ \(a_{6}\) & 0.6740 & **0.6990** & 0.6965 & 0.6990 & \(j^{*}=2\) \\ \(a_{7}\) & 0.5760 & **0.6820** & 0.6556 & 0.6820 & \(j^{*}=2\) \\ \(a_{8}\) & **0.7900** & 0.4670 & 0.6460 & 0.7900 & \(j^{*}=1\) \\ \(a_{9}\) & **0.7620** & 0.4915 & 0.4735 & 0.7620 & \(j^{*}=2\) \\ \hline \hline \end{tabular}
\end{table} 
Table 18: Grey fixed weight cluster coefficients for each class \(\left(c_{s}^{j}\right)\) based on combined weights. Further results showed that this research has been successfully conducted in order to assess the importance of the quality levels of used products for heavy-duty equipment in terms of considering them with grey classes. One interesting finding is that assessment formulae can be obtained both qualitatively and quantitatively. Another important finding is that the grey quality classes of incoming cores can be found by combining the AHP-entropy weights and a grey clustering model. In summary, these results show the effectiveness of the proposed model to handle uncertainty in quality sorting problems for incoming cores in remanufacturing systems. The model considers limited data and is a novel sorting model for solving quality uncertainty problems in core acquisition management. The findings of this work have some managerial implications. First, these findings have significant practical implications for the management of remanufacturing companies regarding the understanding of how to manage uncertain quality. The evidence from this study suggests that sorting problems should be solved by applying AHP-entropy weights and grey clustering as a short-term quality control, rather than a probability statistics approach as a solution for incomplete data obstacles. Second, this study has revealed that, in general, physical, technical, and usage conditions are important criteria for sorting of incoming core quality. In other words, visual inspection and sorting can be performed simultaneously based on the physical condition. Another implication of the current study is that it supports strong recommendations to focus on multiple-criteria decision-making for the quality sorting of incoming cores based on the expert knowledge. Third, the results seem to indicate that the combination of weights provides some support for the conceptual premise that possible biases in weighting will be reduced. In summary, these results show that the proposed model could be applied without difficulty in order to handle uncertain core quality with limited data. This study strengthens the idea that sorting incoming cores into three classes in heavy-duty remanufacturing is a practical option. This is certainly true in the case of the three quality levels for incoming cores of reuse, repair, and scrapping. Like other works, this research has its limitations. For example, the scope of this study was limited in terms of quality. The model could be extended by applying sustainability and remanufacturability as evaluation criteria. In addition, this model considers one-way relationships between criteria and sub-criteria.