## 4 Results and Discussion
### Assignment to the Classes
Interestingly, there were also slightly different subjective weights in the results between the combined methods; however, multiple life cycles, disassembblability, and the damage level were still the three most important sub-criteria for the combined weighting methods. Altogether, we found that the values of the subjective weights more fluctuated than objective weights. The overall values of the grey fixed weight cluster coefficients based on the Shannon entropy weight method are reported in Table 17. From this table, we can see that the clustering weights using the Shannon entropy method resulted in the highest of coefficient values for cores a5, a6, a8 in the best class; a2, a4, a9 into the middle class; and a1, a3, a7 into the worst class. These results indicate that the use of the Shannon entropy weight and grey clustering methods presumably acquired greater balance in the assignment process into overall quality classes. Nevertheless, the maximum grey clustering coefficient values based on combined weights were distinct between subjective and objective weighting. Therefore, these may have contributed to the changes in core assignment within classes as can be seen in Table 18. It is listed in the table that the number of the assigned cores within the worst class was minor. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{\(\mathbf{a_{s}}\)} & \multicolumn{3}{c}{\(\mathbf{\sigma_{s}^{j}}=\sum\limits_{r=1}^{R}\mathbf{f_{r}(X_{r})}\cdot\mathbf{\eta_{r}}\)} & \multicolumn{3}{c}{**Maximum**} \\  & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & **Coefficient Value** & **Grey Class** \\ \cline{2-6}  & \(j=1\) & \(j=2\) & \(j=3\) & \(\mathbf{\sigma_{s}^{j}}=\mathbf{max_{1\leq j\leq 3}}\{\mathbf{\sigma_{s}^{j}}\}\) & \\ \hline \(a_{1}\) & 0.6503 & 0.6184 & **0.8032** & 0.8032 & \(j^{*}=3\) \\ \(a_{2}\) & 0.6877 & **0.7170** & 0.6590 & 0.7170 & \(j^{*}=2\) \\ \(a_{3}\) & 0.6957 & 0.6368 & **0.7076** & 0.7076 & \(j^{*}=3\) \\ \(a_{4}\) & 0.6455 & **0.6885** & 0.5569 & 0.6885 & \(j^{*}=2\) \\ \(a_{5}\) & **0.6988** & 0.6097 & 0.6790 & 0.6988 & \(j^{*}=1\) \\ \(a_{6}\) & **0.7172** & 0.6571 & 0.6249 & 0.7172 & \(j^{*}=1\) \\ \(a_{7}\) & 0.6719 & 0.6419 & **0.7087** & 0.7087 & \(j^{*}=3\) \\ \(a_{8}\) & **0.7082** & 0.6233 & 0.6262 & 0.7082 & \(j^{*}=1\) \\ \(a_{9}\) & 0.6053 & **0.6950** & 0.6698 & 0.6950 & \(j^{*}=2\) \\ \hline \hline \end{tabular}
\end{table} 
Table 17: Grey fixed weight cluster coefficients for each class \(\left(\sigma_{s}^{j}\right)\) based on entropy weight. Figure 7: Comparison of the weighted results of the methods. As mentioned previously, this work aimed to propose a multi-criteria quality sorting model based on an AHP and entropy weights coupled with grey clustering to handle quality uncertainty for incoming cores. The clustering weights of the model could be acquired through subjective and objective methods. By comparing subjective and objective weighting, it was obvious that the output of the model produced significantly different results for the majority of cores assigned into pre-determined classes. It is evident from the results that the model with subjective weights gave significant results when classifying the qualities of incoming cores into two classes. By contrast, the model with objective weights gave significant results when classifying the qualities of incoming cores into three classes. We found that weighting methods may have a great influence on the assignment of classified cores. Figure 8 reveals a clustered column chart that was used to compare the results and the proportion of assigned cores across the quality classes when using the three weighting methods. What is striking in this chart is the phenomenon arising from the use of the subjective AHP pairwise comparison weighting method in terms of the proposed model, which gives a result where core assignment results tend to be dominant in certain classes. The use of objective entropy weighting produced results that were more balanced in terms of assigning cores into overall classes.