# Hierarchical Fuzzy MCDA Multi-Risk Model for Detecting Critical Urban Areas in Climate Scenarios
## 3 Results and Discussion
The reason for this is linked to the high volume of residential buildings located in these subzones; this connotation is typical of the areas of the historic center, present to the west of our study area, which have an extremely low presence of open spaces. Conversely, the medium density pattern records an exceptionally low value for subzones classified with high criticality; this is inferable from the presence of open spaces mainly of permeable type and an overall lower built volume. This type of pattern can be found in the areas to the east and south-east of the study area that constitute the most peripheral districts of the city of Naples; these districts are characterized by green spaces and residential buildings with smaller volumes compared to those of the historic center and different types of construction. About 27% of subzones belonging to the low-built pattern are classified as having high criticality; the reason for that is the high presence of waterproof open spaces, typical of the industrial areas present in the center-north of the study area. In fact, despite being residential, in these subzones there are industrial complexes that, despite having a low volume of buildings, have large open spaces that are completely waterproof. In summary, the most critical areas are concentrated as follows:  
* in the western area, corresponding to the historic city center and corresponding to areas with a high-built density and an absence of permeable open spaces;
* in the industrial areas to the north-east of the urban area of study, which, despite being characterized by a low building density, are poor in permeable open spaces and equipped with large permeable open space surfaces, which affect the vulnerability to hazard scenarios of heat waves and pluvial flooding. In order to verify the performance of the model, the results were compared with those obtained by applying the heatwave and pluvial flooding vulnerability assessment model [5] described in previously. To carry out the comparative tests, the model proposed in [5] was implemented by building the hierarchical structure of the indicators necessary to evaluate the vulnerabilities of the building and open space subsystems to the two phenomena, which are divided into five classes: 1--high, 2--medium-high, 3--medium, 4--medium-low, 5--low. To compare the results obtained in the two models for each of the two phenomena and for each of the two physical subsystems, a statistical analysis was carried out aimed at verifying the congruence of the spatial distribution of the vulnerabilities obtained with the two models. For all the subzones belonging to a specific vulnerability class according to the model [5], the average and standard deviation values of the membership degrees to the fuzzy set of the corresponding criterion in the proposed model were calculated. Table 12 shows the number of subzones belonging to each vulnerability class and the average and standard deviation of the membership degree value. \begin{table}
\begin{tabular}{c c c c c} \hline
**Type of Pattern** & **Number of Subzones** & **High Criticality** & **Medium Criticality** & **Low Criticality** \\ \hline High built density & 471 & 37\% (174) & 14\% (65) & 49\% (232) \\ Medium built density & 275 & 1\% (25) & 52\% (144) & 47\% (106) \\ Low built density & 327 & 27\% (89) & 47\% (154) & 26\% (84) \\ \hline \end{tabular}
\end{table} 
Table 11: Frequencies of subzones grouped by pattern and classified with low, medium, and high criticality. The results in Table 12 show that, in all four cases, as the vulnerability of the subzones increases, the average value of the membership degree to the fuzzy set that models the criterion increases. Furthermore, the values of the standard deviations are in all cases smaller than the mean values, and the ratio between the measured standard deviation and the mean is always less than 0.4.