## 3 Results  
### Results for theIAQ\({}_{\text{index}}\) and IEQ\({}_{\text{index}}\) Prediction  
A previous publication of ours [22] reported on IEQ and IAQ building assessments for a larger number of BREEAM buildings, where IEQ was assessed without calculating the combined \(\sum\)IAQ index. The combined model of the \(\sum\)IAQ\({}_{\text{index}}\) presented in this paper had not yet been previously developed, and we were limited in determining the IEQ\({}_{\text{index}}\), thus we only took into account two of the most well-known pollutants (i.e., CO\({}_{2}\) and TVOC) separately. The assessment of the IEQ index was made by adaptation of the measured parameters (complying with the draft EN 16798-1:2019 standard for indoor environments) as the input values for the submodels of the IEQ\({}_{\rm{index}}\). The input values for the case study are presented in Table 5, which provides the input data for determining the IEQ\({}_{\rm{index}}\) sub-indices of thermal comfort (TC\({}_{\rm{index}}\)), indoor air quality (IAQ\({}_{\rm{index}}\)), acoustics (AC\({}_{\rm{index}}\)), and lighting quality (L\({}_{\rm{index}}\)) for an office building (47 th floor) three days after completion of the finishing work before users were allowed in the building (i.e., pre-occupancy stage). Results for the \(\Sigma\)IAQ\({}_{\rm{index}}\) and IEQ\({}_{\rm{index}}\) Assessment Including Identified Pollutants (CO\({}_{2}\), TVOC, and HCHO)  
The example of a modified calculation of the collective submodel \(\Sigma\)IAQ\({}_{\rm{Quality}}\) for three basic pollutants, as a component of the IEQ model for determining one project value for this indicator, is provided in two variants. The first variant uses sub-indices of IAQ for two pollutants, CO\({}_{2}\) and TVOC, which are described in Table 5, as well the sub-index of the third pollutant, HCHO (according to Reference [47]), where these differences in the approaches mean one must combine them into one submodel \(\Sigma\)IAQ in order to be used in IEQ calculation. The second variant uses submodels of IAQ for TVOC and HCHO pollutants based on the IAQI system [30] and then converts them into percentages of persons dissatisfied PD* in %. According to the diagram of the model \(\Sigma\)IAQ from Figure 5 and using Equation (12) of the \(\Sigma\)IAQ\({}_{\rm{Quality}}\) model, the submodel weights are calculated as follows. W\({}_{\rm{CO_{2}}}\) for the submodel IAQ(CO\({}_{2}\)) = 0.5 is a component of the polynomial:  
\[\sum\
olimits_{\rm{IAQ}_{\rm{quality}}}=0.5\mbox{-}{\rm{IAQ}}({\rm{CO_{2}}})+0. 5\mbox{-}{\rm{IAQ}}({\rm{VOC}}) \tag{21}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sub-Index** & **Sub-Index \(PD(SI_{d})\) Models** & **Input Values** & **Sub-Index (Satisfied) and \(\pm\)SD** \\ \hline \multirow{6}{*}{TC\({}_{\rm{index}}\)} & \multirow{6}{*}{ \begin{tabular}{c} PMV (Fanger-CBE-ISO 7730) \\ _PMV_ = \(\{t_{a},\,t_{r},\,v_{a},\,p_{a},\,M,\,l_{cl}\}\), \\ _PDTC_ = \(\{\rm{t}(PMV)\}\) \\ \end{tabular}  } & \multirow{6}{*}{ \begin{tabular}{c} \(I_{cl}\) 0.55 clo \\ \(t_{a}\) 24.0 \({}^{\circ}\)C \\ \(t\) 24.5 \({}^{\circ}\)C \\ _v\({}_{a}\) 0.15 m/s \\ RH 45\% \\ \(M\) 1.1 met \\ \end{tabular}  } & \multirow{6}{*}{\ \begin{tabular}{c} \(90\%\pm 3.2\%\) \\ \(M\) 1.1 met \\ \end{tabular}  } \\ \hline \multirow{6}{*}{IAQ\({}_{\rm{index}}\)} & \(PD_{IAQ(CO_{2})}\) = & \multirow{6}{*}{
\begin{tabular}{c} \(450\) ppm \\ \(T_{a}\)24.0 \({}^{\circ}\)C \\ \(t\) 24.5 \({}^{\circ}\)C \\ \(t\) 24. \(W_{VOC}\) for submodel IAQ(VOC) = 0.5 is a weight for combined submodel of the polynomial:  
\[\text{IAQ(VOC)}=W_{TVOC}\text{-IAQ(TVOC)}+W_{HCHO}\text{-IAQ(HCHO)} \tag{22}\]  
with the terms W\({}_{TVOC}\) and W\({}_{HCHO}\) calculated from Equation (14) using the measured values \(c_{j}\) (actual concentration of TVOC and HCHO) and the reference values \(c_{ref}\) (Table 6). In our case study, the value of the submodel IAQ weight for the model (HCHO) ought to also be calculated from the measured value and the reference value \(c_{ref}\).