# Hierarchical Fuzzy MCDA Multi-Risk Model for Detecting Critical Urban Areas in Climate Scenarios
## 3 Results and Discussion  
This section shows and discusses the results of the test performed on the study area. Figures 5 and 6 show the thematic maps of the criteria heatwave residential building vulnerability and heatwave open space vulnerability, respectively, where the distribution of the membership degree to the correspondent fuzzy set is displayed. As can be seen from the thematic map in Figure 6, a large central area of the area of study has a greater propensity of open spaces to heatwave vulnerability, mainly because it is predominantly of an industrial nature with open spaces that are almost totally impervious. Even the western area of the area of study in the historic city center shows a propensity of open spaces to heatwave vulnerability; this is due to the presence in this area of exclusively waterproof open spaces. Conversely, the low propensity of open spaces to heatwave vulnerability in two zones to the south and south-east of the area of study is mainly due to the fact that in this area there are permeable surfaces of different types of soil, which prevent the achievement of negative or low values of the NDVI index. Figures 7 and 8 show the thematic maps of the criteria pluvial flooding residential building vulnerability and pluvial flooding open space vulnerability, respectively. Figure 7 shows an exceptionally large area located mainly to the west and center of the area of study, with buildings more likely to be vulnerable to pluvial flooding scenarios; this is mainly due to the prevalence of multiple activities on the ground floors in this area. On the contrary, in the eastern area of the city, there are much fewer buildings with activities on the ground floors. Figure 6: Thematic map of the heatwave open space vulnerability criterion. Figure 7: Thematic map of the pluvial flooding residential building vulnerability criterion. The thematic map in Figure 8 shows that in almost all the subzones of the area of study, the open spaces have a not negligible propensity to be vulnerable to pluvial flooding scenarios. This result is due to the presence in the area of study of drainage and rainwater disposal systems that are ineffective in managing the wastewater load. To set the two criticality thresholds, \(\theta_{\mathrm{L}}\) and \(\theta_{\mathrm{H}}\), the help of a domain expert was used. He identified in a set of urban settlements, based on his own experience, which areas were most vulnerable to both phenomena (hot spots) and which ones were the least critical (cold spots). After running the model in these areas, the minimum criticality value determined in the hot spot areas was set as the \(\theta_{\mathrm{H}}\) threshold, and the maximum value determined in the cold spot areas was set as the \(\theta_{\mathrm{L}}\) threshold. These values are fixed to \(\theta_{\mathrm{H}}\) = 0.1 and \(\theta_{\mathrm{L}}\) = 0.01. Figure 9 shows the thematic map of criticality, in which the subzones are classified as having low, medium, and high criticality. The most critical subzones are mainly concentrated to the west and north-east of the area of study. In them, the propensity for vulnerability of buildings and open spaces to both phenomena is high or not negligible. On the contrary, in the south and south-eastern areas, low criticality prevails in most subzones, mainly due to a low propensity of open  
Figure 8: Thematic map of the pluvial flooding open space vulnerability criterion. Figure 9: Final criticality map of the area of study. spaces to be vulnerable to heatwave scenarios and to a low propensity of buildings to be vulnerable to pluvial flooding scenarios. Table 11 shows the percentages of subzones of the three patterns belonging to the three classes of criticality. In Table 11, the high-built density pattern records the greatest presence of subzones classified as having high criticality.