## 4 Simulation Results and Discussions
### Analysis of Decision Rules Obtained from the Proposed Algorithm
\begin{table}
\begin{tabular}{c c} \hline \hline
**No.** & **Rules** \\ \hline
**1** & When PM2.5 \(<\) 49.5 and PM10 \(<\) 35.5, the air quality rating is 1. It means, data required to start the test from the root node PM2.5 \(<\) 49.5. According to different data attributes, it moves to the sub node PM10 \(<\) 35.5, finally reaches the leaf node of the air quality level 1. \\ \hline
**2** & When PM2.5 \(<\) 49.5 and PM10 \(\geq\) 35.5, the air quality rating is 2. It means, data required to start the test from node PM2.5 \(<\) 49.5. According to different data attributes, it moves to the sub node PM10 \(\geq\) 35.5, finally reaches the leaf node of the air quality level 2. \\ \hline
**3** & When PM2.5 \(\geq\) 49.5, PM10 \(<\) 74.5 and PM2.5 \(<\) 150.5, the air quality rating is 2. It means, data required to start the test from the root node PM2.5 \(\geq\) 49.5. According to different data attributes, it moves to the sub node PM10 \(<\) 74.5, then recursively moves to another sub node PM2.5 \(<\) 150.5, finally reaches the leaf node of the air quality level 2. \\ \hline
**4** & When PM2.5 \(\geq\) 49.5, PM10 \(<\) 74.5 and PM10 \(\geq\) 150.5, the air quality rating is 3. It means, data required to start the test from the root node PM2.5 \(\geq\) 49.5. According to different data attributes, it moves to the sub node PM10 \(<\) 74.5, then recursively moves to another sub node PM2.5 \(\geq\) 49.5. Accordingly to different data attributes, it moves to the sub node PM10 \(<\) 74.5, then recursively moves to another sub node PM2.5 \(\geq\) 150.5, finally reaches the leaf node of the air quality level 3. \\ \hline
**5** & When PM2.5 \(\geq\) 49.5, PM10 \(\geq\) 74.5 and PM10 \(<\) 114.5, the air quality evaluation level is 3. It means, data required to start the test from the root node PM2.5 \(\geq\) 49.5. According to different data attributes, it moves to the sub node PM10 \(\geq\) 74.5, then recursively moves to another sub node PM10 \(<\) 114.5, finally reaches the leaf node of the air quality level 3. \\ \hline
**6** & When PM2.5 \(\geq\) 49.5, PM10 \(\geq\) 74.5 and PM10 \(\geq\) 114.5, then recursively moves to another sub node PM10 \(\geq\) 74.5, then recursively moves to another sub node PM10 \(>\) 149.5, finally reaches the leaf node of the air quality level 4. \\ \hline
**7** & When PM2.5 \(\geq\) 49.5, PM10 \(\geq\) 74.5 and PM10 \(\geq\) 114.5, further judging that when PM10 \(<\) 149.5, the air quality rating is 5. It means, data required to start the test from the root node PM2.5 \(\geq\) 49.5. According to different data attributes, it moves to the sub node PM10 \(\geq\) 74.5, then recursively moves to another sub node PM10 \(\geq\) 114.5, then recursively moves to another sub node PM10 \(\geq\) 114.5, then recursively moves to another sub node PM10 \(<\) 249.5, finally reaches the leaf node of the air quality 5. \\ \hline
**8** & When PM2.5 \(\geq\) 49.5, PM10 \(\geq\) 74.5 and PM10 \(\geq\) 114.5, it is further judged that when PM10 \(\geq\) 149.5 and PM10 \(\geq\) 249.5, the air quality rating is 6. It means, data required to start the test from the root node PM2.5 \(\geq\) 49.5. According to different data attributes, it moves to the sub node PM10 \(\geq\) 74.5, then recursively moves to another sub node PM10 \(\geq\) 149.5, then recursively moves to another sub node PM10 \(\geq\) 249.5, finally reaches the leaf node of the air quality 6. \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Decision rules obtained from the proposed algorithm.