## 3 Experimental Results
### Model Evaluation  
This study used performance metrics of accuracy, precision, recall, and F1-score, which are defined as follows:  
\[Accuracy=\frac{TP+TN}{TP+TN+FP+FN} \tag{10}\]  
\[Recall=\frac{TP}{TP+FP} \tag{11}\]  
\[Precision=\frac{TP}{TP+FN} \tag{12}\]  
\[F1\text{-}score=\frac{2\times Recall\times Precision}{Recall+Precision} \tag{13}\]  
where \(TP\), \(TN\), \(FP\), and \(FN\) are the numbers of true positives, false positives, true negatives, and false negatives, respectively. Figure 4a shows the MCCFNN confusion matrix. Although the model performed poorly in predicting N1, it performed well in predicting W, N2, N3, and REM in terms of accuracy. Figure 4b indicates that the use of T-MCCFNN parameter optimization in the Taguchi experiment yielded improvements in the model's predictions of W, N3, and REM by 3.02%, 2.98%, and 8.54%, respectively, in terms of accuracy. The comparison results of the proposed T-MCCFNN with other FNNs are shown in Table 6. In Table 6, MCCFNN uses a multi-scale convolution kernel and a fully connected network. A Mamdani-type MCFNN and TSK-type MCFNN use a multi-scale convolution kernel and Mamdani-type and TSK-type FNNs. In Table 6, the accuracy of MCCFNN with TSK-type is 84.4%, which is better than 84.1% of Mamdani-type MCCFNN. After parameter optimization through the Taguchi experiment, T-MCCFNN can increase the accuracy by 0.9% compared to TSK-type MCCFNN, and it is better than other FNNs and fully connected network models. In Table 6, the standard deviation of the accuracy of the proposed T-MCCFNN is 0.0321, which means that the proposed T-MCCFNN model has good robustness and universality in terms of accuracy. Figure 4: Confusion matrix of (**a**) MCCFNN and (**b**) T-MCCFNN. In order to verify that the compensatory FNN has a better convergence speed, this study uses MCCFNN to compare it with MCFNN without the compensatory fuzzy set. It can be observed from Figure 5 that MCCFNN tends to converge after nearly 15 epochs. However, MCFNN slowly converges at 25 epochs. The experimental results indicate that the MCCFNN with the compensatory fuzzy set has a better convergence speed than the MCFNN without the compensatory fuzzy set. In this paper, we use cross-entropy as the loss function, which is defined as follows:  
\[CE=-\sum_{i}y_{i}log\,\hat{y}_{i} \tag{14}\]  
where \(CE\) represents cross-entropy; \(y\) and \(\hat{y}\) represent our model's prediction and ground truth. In addition, this study compares the performance of the multi-scale convolution kernel (T-MCCFNN) and the single-scale convolution kernel (T-SSCFNN), as shown in Table 7. In Table 7, the accuracy, recall, precision, and F1-score of T-MCCFNN with multi-scale convolution kernels have higher performance than T-SSCFNN with single-scale convolution kernels. In particular, there is a 1.1% increase in the accuracy of T-MCCFNN. Table 8 illustrates the comparison of T-MCCFNN with other deep learning methods. [PERSON] et al. [29] proposed the DeepSleepNet network architecture. This architecture \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Methods** & **Accuracy** & **Recall** & **Precision** & **F1-Score** & **Standard Deviation of Accuracy** \\ \hline MCCFNN & 84.2\% & 81.2\% & 87.5\% & 84.2\% & 0.0559 \\ Mamdani-type & 84.3\% & 82.1\% & 86.7\% & 84.3\% & 0.0298 \\ MCFNN & 84.2\% & 80.8\% & 87.4\% & 84.0\% & 0.0282 \\ Mamdani-type & 84.1\% & 82.5\% & 86.0\% & 84.2\% & 0.0966 \\ MCCFNN & 84.4\% & 82.4\% & 86.8\% & 84.5\% & 0.0397 \\ T-MCCFNN & 85.3\% & 83.3\% & 87.3\% & 85.3\% & 0.0321 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of results of the proposed T-MCCFNN with other fuzzy neural networks. Figure 5: Comparison of learning curves of MCCFNN and MCFNN. (**a**) Accuracy (**b**) Cross-entropy. uses a two-branched convolutional layer to extract features from the raw EEG signal, and a two-layer bi-directional long short-term memory (Bi-LSTM) as a classifier. [PERSON] et al. [30] improved the architecture of DeepSleepNet and proposed a DeepSleepNet-lite network architecture.