## 2 Materials and Methods
### ACU Automation Rule Generation Using Rough Set Theory  
The decision table (see Table 6) provides examples representing the real-time datasets acquired for the first half of 2024, all defined by 8 conditional attributes--namely room occupancy (\(A_{1}\)), indoor dry bulb temperature (\(A_{2}\)), indoor relative humidity (\(A_{3}\)), outdoor heat index (\(A_{4}\)), carbon dioxide level (\(A_{5}\)), carbon monoxide level (\(A_{6}\)), total volatile organic compound (TVOC) level (\(A_{7}\)), and ACU room authorization conditions (\(A_{8}\))--and 1 decision (\(D_{1}\)). Room occupancy is represented by the occupants' average clothing insulation (_clo_) and metabolic rate (_met_) as personal parameters that affect thermal comfort. In this study, clothing insulation was assumed to have an average value of 0.40 clo, while metabolic rate was set at 1.0 met. The ACU setpoint decision, \(D_{1}\), is defined in Equations (2) and (3) for instructional rooms. \[A_{8}=\left\{\begin{array}{ll}\text{``}Y\text{''},&\text{if }(T\text{$\tau$}>0\text{ and }A_{1}\
eq 0)  
For office spaces, \(A_{1}\) is omitted from the analysis, while \(A_{8}\) and \(D_{1}\) are defined as in Equation (6) and Equation (7), respectively. \[A_{8}=\left\{ \begin{array}{ll}\text{``}Y\text{''},&\text{if }08:00\leq\text{ Timestamp }\leq 18:00\text{ and }\text{Datestamp }=\text{Weekday}\\ \text{``}N\text{''},&\text{otherwise}\end{array} \right. \tag{6}\]  
\[D_{1}=\left\{\begin{array}{ll}\text{``}\text{OFF''},&\text{if }A_{8}>\text{``}N\text{''} \\ &23,&\text{if }A_{4}\in\{\  
will pre-determine the ACU control decisions, such as turned off, manual operation, and specific setpoints of 22 \({}^{\circ}\)C, 23 \({}^{\circ}\)C, 24 \({}^{\circ}\)C, or 25 \({}^{\circ}\)C.  
The histograms illustrated in Figure 1 show the distributions of various environmental and occupancy variables that could be used within the dataset for a fuzzy logic system. Taking room occupancy as an example, the spread ranges between 0 and approximately 44, with peaks at 16 and 28. This non-uniform distribution pattern suggests variable occupancy levels reflecting low, moderate, high, and full capacity scenarios. Multiple peaks in the data show that varied scenarios are covered, potentially reflecting fluctuations over time or different settings when the rooms were occupied. Regarding indoor temperature, the histogram is right-skewed, with most values ranging between 20 \({}^{\circ}\)C and 35 \({}^{\circ}\)C. The highest frequency is observed around 28 \({}^{\circ}\)C to 29 \({}^{\circ}\)C. Indoor humidity is relatively well-distributed within a range of 40% to 80%, with a frequency peak at around 61% to 65%, which is generally considered a slightly humid level for indoor conditions. This indicates that, while the dataset covers a wide range of humidity conditions, it primarily focuses on levels that are conducive to comfort. For the outdoor heat index, the distribution spans from 30 \({}^{\circ}\)C to 48 \({}^{\circ}\)C, with a high concentration at around 42 \({}^{\circ}\)C. This suggests that outdoor conditions were predominantly warm to hot, as around 67% of the data were collected during the hot and dry season (March 2024 to June 2024). The values concentrated around 40 \({}^{\circ}\)C might be representative of specific weather conditions or regions in the dataset. This FIS for office spaces includes 550 rules, with various input membership functions linked by AND relationships. Four inputs are considered for the FIS--indoor temperature (\(A_{2}\)), indoor humidity (\(A_{3}\)), outdoor heat index (\(A_{4}\)), and authorization condition (\(A_{8}\))--and there is one output (\(D_{1}\)) representing the ACU control condition. The modeling of the system was performed using a Mamdani-type fuzzy system. As shown in Figure 2, the frequency distributions of the input variables provide insights into the occurrence of certain values in this dataset. This helps to outline the prevailing environmental conditions that influence the outputs of the FIS.