## 3 Results and Discussion
### Estimation of Mass and Volume  
The actual mass (\(M_{acc}\)) and the actual volume (\(V_{acc}\)) of all samples were determined and used to calculate the slope (\(k\)) and intercept (\(b\)) in Equation (5). By linear fitting analysis, \(k\) and \(b\) were determined as 2.1076 and \(-\)490.6325, respectively, with a coefficient of determination (R\({}^{2}\)) of 0.9048, as shown in Figure 8. The R\({}^{2}\) value was close to 1, indicating a high correlation, with a high coefficient of determination between \(M_{acc}\) and \(V_{acc}\). Based on IIAS, \(V\) can be calculated by Equations (3) and (4). According to \(k\), \(b\), and \(V\), \(M\) can be obtained by the application of Equation (6). The maximum, minimum, mean, and standard error values of mass (\(M_{acc}\) and \(M\)) and volume (\(V_{acc}\) and \(V\)) are displayed in Table 2.  
Figure 8: Linear fitting analysis of the actual mass (\(Macc\)) as weighed with a balance and the actual volume (\(Vacc\)) as measured using WDM. Figure 7: Visible and near-infrared transmittance spectra of samples: (**a,c**) raw spectra; (**b,d**) mean spectra for different granulation levels. A paired \(t\)-test was used for further comparison (Table 3). The obtained \(p\)-values for \(M_{acc}\) and \(M\) and \(V_{acc}\) and \(V\) were 0.2702 and 0.3022, respectively. These results showed \(M_{acc}\) and \(V_{acc}\) were not significantly different from \(M\) and \(V\), respectively (\(p>0.05\)). Therefore, the size of the pomelo did not affect the accuracy of the estimated values (\(p>0.05\)) [21]. The corresponding standard deviations for the mass and volume differences were 14.9130 g and 73.4712 cm\({}^{3}\), respectively. In 1978, [PERSON] introduced rough sets theory, where the actual values and estimated values have an equivalence relation [54]. The equivalence relation can be interpreted as a linear equation by linear fitting analysis, as shown in Figure 9A,B. In Figure 9A, for \(M_{acc}\) and \(M\), the R\({}^{2}\) value was 0.9859. For \(V_{acc}\) and \(V\), the R\({}^{2}\) value was 0.9879 (Figure 9B). The R\({}^{2}\) values can be interpreted as the proportion of the variance in the estimated data attributable to the variance in the actual data [21]. Higher R\({}^{2}\) values indicate that the estimated data are closer to the actual data. The IIAS method gave at least 98% accuracy for the estimation of mass and volume. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Mass (g)**} & \multicolumn{2}{c}{**Volume (cm\({}^{3}\))**} & \multirow{2}{*}{\(\mathbf{k}\)} & \multirow{2}{*}{\(\mathbf{b}\)} \\ \cline{2-2} \cline{5-6}  & \(\mathbf{M_{acc}}\) & & & & \\ \hline Maximum & 2735.12 & 2720.72 & 5660.00 & 5243.56 & \\ \hline Minimum & 893.89 & 885.39 & 1440.00 & 1375.42 & 2.1076 & \(-\)490.6325 \\ \hline Mean & 1316.96 & 1252.89 & 2285.00 & 2149.96 & \\ \hline Standard error & 423.35 & 386.97 & 924.60 & 902.99 & 0.0419 & 63.4135 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of measured and estimated values for mass and volume. Figure 9: (**A,B**) Linear fitting analysis of mass (\(M\) and \(M_{acc}\)) and volume (\(V\) and \(V_{acc}\)), respectively; (**C,D**) Bland–Altman plot of mass (\(M\) and \(M_{acc}\)) and volume (\(V\) and \(V_{acc}\)), respectively. Figure 9C,D show the Bland-Altman plots of the differences between the actual and estimated value of samples [55]. The 95% limits of agreement of the differences are designated by \(\mathrm{d}-1.96\) SD and \(\mathrm{d}+1.96\) SD, as indicated by the outer lines, and the center line represents the 95% confidence interval for the mean differences. The percentage of mean differences (\(M_{acc}\)-\(M\)/mean) was 1.84 at the 95% limits of agreement for 0.89 and 2.78 (Figure 9C). The percentage of mean difference (\(V_{acc}\)-\(V\)/mean) was 7.2 at the 95% limits of agreement for 4.4 and 9.9 (Figure 9D). The results showed that \(V\) may be less than \(V_{acc}\) by 4.4% to 9.9%, and \(M\) may be lower than \(M_{acc}\) by 0.89% to 2.78%.