## 3 Materials and Methods
### Multi-Criteria Decision-Making Method  
The optimal solar design (dimensioning and selection) of the presented GTCs (Figure 1) is determined using three groups of indicators: geometric (mass \(m\) [kg], surface occupation \(SO\) [m\({}^{2}\)], total surface occupation \(TSO\) [m\({}^{2}\)], volume occupation \(VO\) [m\({}^{3}\)]), economic (manufacturing cost \(CM\) [EUR] and exploitation cost \(CE\) [EUR]), and ecological (embodied energy \(E_{emb}\) [kWh] and greenhouse gas emissions \(e_{CO2}\) [kg]). A multidisciplinary evaluation of GTC performance can be conducted using various multi-criteria analysis (MCA) methods [47]. Due to its simplicity and accuracy, the multi-criteria decision-making (MCDM) method with simple additive weighting (SAW) was chosen for this paper [48; 49]. The MCDM method assigns a specific percentage criterion of importance, i.e., weight of significance (\(w_{c}\) [%] and \(w_{sc}\) [%]), to all indicators used (Table 2). By defining \(w_{c}\) and \(w_{sc}\) values, all included indicators (in this case, eight of them, as shown in Table 2) are normalized to a dimensionless level. Only then can their classification in descending or ascending order, depending on the desired objective (the objective function), be performed. In this case, the objective function is minimizing heat losses in GTCs. The following figure (Figure 8) illustrates the procedure for selecting the mentioned objective function. In the first two steps, numerous values of all sub-criteria, i.e., indicators (\(k_{1}\) values: \(m\), \(SO\), \(TSO\), \(VO\), \(CM\), \(CE\), \(E_{emb}\), and \(e_{CO2}\)) and specific indicators (\(k_{2}\) values: \(Q_{loss}/m\), \(Q_{loss}/SO\), \(Q_{loss}/TSO\), \(Q_{loss}/VO\), \(Q_{loss}/CM\), \(Q_{loss}/CE\), \(Q_{loss}/E_{emb}\), and \(Q_{loss}/e_{CO2}\)), are defined for all GTC types. In the third step, \(k_{3}\) values are calculated as in Equation (13), while in the fifth step, values \(k_{5}\) are a function of \(k_{2},k_{3}\), and \(k_{4}\), as shown Figure 8.  
\[k_{3}=\left(\frac{Q_{loss}}{m}\right)_{SGTCa}+\left(\frac{Q_{loss}}{m}\right) _{SGTCa}+\left(\frac{Q_{loss}}{m}\right)_{DGTCa}+\left(\frac{Q_{loss}}{m} \right)_{DGTCa} \tag{13}\] \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Criterion** & & \multicolumn{2}{c}{**Geometric**} & \multicolumn{2}{c}{**Economic**} & \multicolumn{2}{c}{**Ecological**} & \multicolumn{1}{c}{**C-sum**} \\ \hline \(w_{c}\) & & \multicolumn{2}{c}{14} & \multicolumn{2}{c}{50} & \multicolumn{2}{c}{36} & 100 \\ \hline
**Sub-criterion** & \(m\) & \(SO\) & \(TSO\) & \(VO\) & \(CM\) & \(CE\) & \(E_{emb}\) & \(e_{CO2}\) & **SC-sum** \\ \hline \(w_{sc}\) & 5 & 5 & 2 & 2 & 35 & 15 & 18 & 18 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The weight of importance to all used indicators. Figure 8: Multi-criteria decision-making method with simple additive weighting in the function of selecting GTC type. Equation (13) represents the sum of \(Q_{loss}/m\) specific indicators for an SGTC with an air layer, SGTC with a vacuum layer, DGTC with an air layer, and DGTC with a vacuum layer. Based on this equation, the remaining seven equations can also be developed (for the other specific indicators). Determining the \(k_{5}\) values in the fifth step is shown in the example of the SGTC with an air layer taking into account specific indicator \(Q_{loss}/m\) (Equation (14)):  
\[k_{5}=k_{4}\frac{k_{2}}{k_{3}}=0.05\frac{\left(\frac{Q_{loss}}{m}\right)_{SGTCa }}{\left(\frac{Q_{loss}}{m}\right)_{SGTCa}+\left(\frac{Q_{loss}}{m}\right)_{ SGTCa}+\left(\frac{Q_{loss}}{m}\right)_{DGTCa}+\left(\frac{Q_{loss}}{m}\right)_{DGTCb}} \tag{14}\]  
In the final stage, the values obtained from the fifth step are classified (sixth step, \(k_{6}\) values) to identify the minimum value, which represents the objective function. This process concludes the calculation. The subsequent table (Table 3) presents the adopted geometric indicators (as per the data in Table 1), along with the economic and ecological indicators.