## 4 Research Methodology  
The collection of human perspectives is the first step for implementing any MCDM. The survey was distributed with the explanation of the purpose of the study. Participants were asked to participate in quantitative judgment using the linguistic scale, shown in Figure 2, to assess the importance of criteria and the performance of alternatives (interventions) for UHS mitigation. The experts belonged to academics in the field of urban climate.  
The collected questionnaires were checked, and assessments that contained inconsistencies were discarded and not used for further analysis. After this quality check, it was observed that 25 ratings could be useful. These judgments were aggregated using geometric means and then MCDMs, such as ELECTRE-NS, ELECTRE-NI, MOORA, PROMETHE, TOPSIS, VIKOR, WPM, and WSM, were applied to prioritize the UHS mitigation alternatives (A1, A2... ). These methods were implemented in two ways: stand-alone, where direct criteria weights were used, and coupled with AHP (criteria weights calculated by AHP using the judgment matrix shown in Table 3). Seven different normalization methods were used for the simple application of MCDMs (stand-alone). The research methodology is shown in Figure 3.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**Normalization**} & **Abbreviation** & **Beneficial** & **Non-Beneficial** \\ \hline \multirow{6}{*}{Linear} & \(\text{L}_{\text{N-i}}\) & \(\overline{X}_{ij}=\frac{X_{ij}}{X_{ij}^{\text{min}}}\) & \(\overline{X}_{ij}=1-\frac{X_{ij}}{X_{ij}^{\text{min}}}\) \\ \cline{2-4}  & \(\text{L}_{\text{N-ii}}\) & \(\overline{X}_{ij}=\frac{X_{ij}}{X_{ij}^{\text{min}}}\) & \(\overline{X}_{ij}=\frac{X_{ij}^{\text{min}}}{X_{ij}^{\text{min}}}\) \\ \cline{2-4}  & \(\text{L}_{\text{N-max-min}}\) & \(\overline{X}_{ij}=\frac{X_{ij}-X_{ij}^{\text{min}}}{X_{ij}^{\text{min}}-X_{ ij}^{\text{min}}}\) & \(\overline{X}_{ij}=\frac{X_{ij}^{\text{min}}}{X_{ij}^{\text{min}}-X_{ij}^{\text{ min}}}\) \\ \cline{2-4}  & \(\text{L}_{\text{N-Sum}}\) & \(\overline{X}_{ij}=\frac{X_{ij}}{\sum_{i=1}^{n}X_{ij}}\) & \(\overline{X}_{ij}=\frac{\frac{1}{X_{ij}}}{\sum_{i=1}^{n}(\frac{1}{X_{ij}})}\) \\ \hline Enhanced accuracy & \(\text{E}_{\text{AN}}\) & \(\overline{X}_{ij}=1-\frac{X_{ij}^{\text{min}}-X_{ij}}{\sum_{i=1}^{n}(X_{ij}^{ \text{min}}-X_{ij})}\) & \(\overline{X}_{ij}=1-\frac{X_{ij}-X_{ij}^{\text{min}}}{\sum_{i=1}^{n}(X_{ij}-X_ {ij}^{\text{min}})}\) \\ \hline Logarithmic & \(\text{L}_{\text{nN}}\) & \(\overline{X}_{ij}=\frac{\text{ln}X_{ij}}{\text{ln}(\text{ln}(\text{ln}_{\text{ ln}_{\text{ln}_{\text{ln}_{\text{ln}_{\text{ln}_{\text{ln}_{\text{ln}_{\text{ln}}_{ \text{\text{ln}}}}}}}}}})}\) & \(\overline{X}_{ij}=1-\frac{\frac{\text{ln}X_{ij}}{\text{ln}(\text{ln}_{\text{ln} _{\text{ln}}}})}{\text{ln}-1}\) \\ \hline Vector & \(\text{V}_{\text{N}}\) & \(\overline{X}_{ij}=\frac{X_{ij}}{\sqrt{\sum_{i=1}^{n}X_{ij}^{\text{min}}}}\) & \(\overline{X}_{ij}=1-\frac{X_{ij}}{\sqrt{\sum_{i=1}^{n}X_{ij}^{\text{min}}}}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Mathematical formulas of different normalization methods.  
Figure 2: Linguistic scale for rating the importance of criteria and performance of alternatives.  
The inputs for criteria and alternatives using the linguistic scale 1-10 was used, where high value of scale represents the high importance; for example, cost is a non-beneficial criterion, and in the case of shades the score was 8, which means it is very expensive, but the durability score was 5, which means that sometimes shades require maintenance after windstorms. All inputs were formulated in the decision matrix shown in Table 4, where criteria weights are given by direct method for the stand-alone application, and criteria weights are calculated by AHP for the combined approach by using the related formulas in Table 1.