## 3 Results
### Results for theIAQ\({}_{\text{index}}\) and IEQ\({}_{\text{index}}\) Prediction
However, formaldehyde is an unusual pollutant because, although it belongs to VOC\({}_{\text{-odorous}}\) compounds, the concentrations found in buildings are many times lower than the HCHO threshold \(c_{th}\) = 300 \(\mu\)g/m\({}^{3}\) according to the WHO [7] and lower than the threshold concentrations of HCHO from 60 \(\mu\)g/m\({}^{3}\) to 70 \(\mu\)g/m\({}^{3}\) issued in 2013 by the American Industrial Hygiene Association [44]. The permissible value of \(c_{ref}\) = 100 \(\mu\)g/m\({}^{3}\) is also higher than the formaldehyde concentration found in buildings, according to Reference [5] and the standard EN16798-1:2019 [10]. Therefore, the authors propose that in such a case (to avoid a negative value of \(\Delta c_{j}\)), the value modelling the reference should be taken as zero. Then, the form of the adjusted \(W_{HCHO}\) weight in the model described by Equation (11) for air with three pollutants, would be as follows. \[W_{HCHO}=\frac{\Delta c_{j}}{\sum\limits_{j=2\dots 3}\Delta c_{2\dots 3}}= \frac{(c_{HCHO}-0)}{(c_{TVOC}-c_{ELV})+(c_{HCHO}-0)} \tag{23}\]  
The results of the weights assessment for the two variants of the \(\sum\)IAQ\({}_{\text{quality}}\) model are presented in Table 6.  
According to the diagram of the model \(\sum\)IAQ from Figure 5 and Equation (8), we proposed sensory equations for the percentage of persons dissatisfied \(\%PD^{\star}\) in two variants. The submodel \(\sum\)IAQ's first variant includes the following:  
1. The IAQ submodels used so far in References [22; 33] for CO\({}_{2}\) and TVOC pollutants, as shown in Table 5;
2. The IAQ submodel for formaldehyde, using two types of equations depending on the range of HCHO concentrations measured in the building. Formaldehyde concentrations in the air with values above the threshold concentration, \(c_{th}\), for its odor, i.e., above 60 or even 300 \(\mu\)g/m\({}^{3}\), can be used to create IAQ submodels for rooms with volatile and aromatic VOC compounds as well as for the HCHO equation [50]. \[PD_{HCHO}=\frac{\exp\ (2.14\cdot\text{OI}-3.81)}{\exp\ (2.14\cdot\text{OI}-3.81)+1}\] (24)  
However, in the case study building, the maximum concentration of HCHO was 18 \(\mu\)g/m\({}^{3}\) and, therefore, its concentration in the air was several times lower than the concentration of the odor threshold, \(c_{th}\)[44]. The intensity of the formaldehyde odor was undetectable under these conditions, and the sensory equation \(PD\) = f(_OI_), which is appropriate for sensory detection of IEQ, is not applicable for odors below the threshold. Therefore, for small concentrations, we proposed the use of the equation \begin{table}
\begin{tabular}{c c c c c} \hline
**Sub-Index** & **Input Value cj** & **Input 1 Value cref** & \
\begin{tabular}{c} **Excess** \\ **Concentration \(\Delta\mathbf{c_{j}}\)** \\ \end{tabular} &
\begin{tabular}{c} **Wj** \\ **Wj** \\ \end{tabular} \\ \hline IAQ(TVOC) & 787 \(\mu\)g/m\({}^{3}\) & 300 \(\mu\)g/m\({}^{3}\) & 487 \(\mu\)g/m\({}^{3}\) & 0.96 \\ \hline IAQ(HCHO) & 18 \(\mu\)g/m\({}^{3}\) & 0 & 18 \(\mu\)g/m\({}^{3}\) & 0.04 \\ \hline \end{tabular}  
* EN 16798-1:2019 for a very low-pollution building.  
\end{table} 
Table 6: Calculation of the weights of the \(W_{TVOC}\) and \(W_{HCHO}\) values for the two sub-indices of the combined IAQ(VOC) model. taken from the work of [PERSON] and [PERSON] [47] based on the analysis of \"health effects on the human body\", derived from \"indoor air quality comfort evaluation experiments and the literature\". \[PMV_{HCHO}=2 log\frac{c_{HCHO}}{0.01} \tag{25}\]  
This equation links the value of the new unit \"the effect of formaldehyde on human comfort\", called PMV\({}_{\text{HCHO}}\), with its \(c_{\text{HCHO}}\) concentration (\(\upmu\)g/m\({}^{3}\)) in the air.