## 4 Results and Discussion
### Multiple-Criteria Decision-Making Model Results  
As described in Section 3.2, the MCDM matrix for a particular eco-material is composed of a set of submatrices associated with the different SWOT factors. For the particular case of rammed earth, the resulting MCDM matrix is described as follows:  
\[\mathbf{X}_{m_{1}}=\left[ \begin{array}{c}\mathbf{X}_{m_{1}}^{(S)}\\ \mathbf{X}_{m_{1}}^{(W)}\\ \mathbf{X}_{m_{1}}^{(O)}\\ \mathbf{X}_{m_{1}}^{(T)}\end{array} \right] \tag{22}\]  
where \(m_{1}\) denotes the selected eco-material (rammed earth), and the submatrices \(\mathbf{X}_{m_{1}}^{(S)},\mathbf{X}_{m_{1}}^{(W)}\), \(\mathbf{X}_{m_{1}}^{(O)}\) and \(\mathbf{X}_{m_{1}}^{(T)}\) contain the scores given by the 15 experts (by columns) for the \(M\) SWOT items (by rows), as follows:  
\[\mathbf{X}_{m_{1}}^{(S)}=\left[ \begin{array}{cccccccccccccccc}9&6&9&9&9&8&8&9& 0&7&5&7&2&9&6\\ 6&5&0&5&9&5&9&7&3&6&9&8&2&9&6\\ 7&7&0&8&9&6&8&7&5&7&5&7&6&9&8\\ 9&7&0&7&9&0&9&9&8&8&7&7&6&9&6\end{array} \right] \tag{23}\]  
\[\mathbf{X}_{m_{1}}^{(W)}=\left[ \begin{array}{cccccccccccccccc}6&8&0&7&3&7&6& 8&2&9&8&7&8&5&8\\ 6&4&0&8&3&8&8&9&7&8&6&8&9&2&8\\ 6&6&0&6&0&7&4&9&9&8&6&7&9&8&8\\ 6&5&0&6&3&8&6&9&4&5&2&7&9&1&8\\ 6&7&0&8&5&6&7&9&2&7&5&2&9&1&6\end{array} \right] \tag{24}\]  
\[\mathbf{X}_{m_{1}}^{(O)}=\left[ \begin{array}{cccccccccccccccc}8&7&9&8&8&8&2&9 &4&9&7&6&7&9&8\\ 8&3&7&9&7&6&9&9&4&5&6&6&8&9&6\end{array} \right] \tag{25}\] \begin{table}
\begin{tabular}{p{142.3 pt} p{142.3 pt}} \hline \hline
**Strengths** & **Weaknesses** \\ \hline \(x_{1}^{(S)}\)—Ferrock production depends on the reaction between iron dust with carbon dioxide and rust, so it is considered a CO2-negative material and has low environmental impacts, in line with SDG 13 [73; 74]. \\ \(x_{2}^{(S)}\)—Economical operation through the use of recycled waste iron in landfills, in line with SDG 12 (target 12.5) [74]. \\ \(x_{3}^{(S)}\)—Ferrock is stronger than Portland cement and uses less energy, in line with SDG 7 (target 7.3) [76]. \\ \(x_{4}^{(S)}\)—It uses less water for curing compared with cement, so the time required for curing is also shorter, in line with SDG 6 (target 6.4) and SDG 12 (target 12.2) [76]. \\ \hline
**Opportunities** & **Therats** \\ \hline \(x_{1}^{(T)}\)—Ferrock could be used for maritime constructions, due to the contact with water, which enhances the rusting operation [73; 74]. \\ \(x_{2}^{(O)}\)—Ferrock concrete has good fire and thermal resistance [74]. \\ \(x_{3}^{(O)}\)—Ferrock has tensile properties due to iron dust, which enhances the durability and compressive strength of concrete [74]. \\ \(x_{4}^{(O)}\)—It is resistant to rotting, corrosion, and UV radiation [77]. \\ \hline \hline \end{tabular}
\end{table} 
Table 4: SWOT analysis of ferrock. \[\mathbf{X}_{m_{1}}^{(T)}=\left[ \begin{array}{cccccccccccccccc}6&2&0&8&1&9&6&5&6&8&2&4&9&0&6 \\ 6&3&0&6&1&8&2&3&6&5&5&4&8&5&7\\ 2&4&0&4&0&5&3&3&6&6&7&0&8&1&6\\ 6&8&0&7&0&7&3&9&8&7&3&0&8&1&7\end{array} \right] \tag{26}\]  
In this example, the scores range from 0 to 9, with 0 denoting \"unsure\", 1 denoting \"not relevant\", and 9 \"completely relevant\". Similar submatrices can be easily obtained for the rest of the candidate eco-materials using the survey data detailed in Appendix A. To account for the heterogeneity of the expertise in the group of respondents, a weight of 0.6 is applied to the responses coming from academics and 0.4 to those coming from engineering practitioners. The weighted scores were statistically re-sampled and Gaussian probability models were fit to the resampled data. Tables 5-7 present the probabilistic response models obtained for each SWOT item (third column), which corresponds to Equation (3) in the proposed methodology, specifically \(p(\bar{x}_{i_{e}}^{(k)})\). The probabilistic response models for the \(k\)-_th_ SWOT factor \(p(\bar{x}_{m}^{(k)})\) are subsequently obtained according to Equation (4). Results are shown in the fourth columns of Tables 5-7 for rammed-earth, hempcrete, and ferrock, respectively.