# Hierarchical Fuzzy MCDA Multi-Risk Model for Detecting Critical Urban Areas in Climate Scenarios
## 2 Materials and Methods
### The Case Study Area  
The model has been tested on an urban area of study given by the central-eastern districts of the city of Naples (Italy); it extends from the districts of the city center, such as San Lorenzo and Vicaria, to the coastal and eastern districts, such as San Giovanni a Teduccio and Ponticelli.  
The availability of many fabrics with different built-in densities is a key component in the choice of this area of study. Three different patterns may really be distinguished: a high-built density, a medium-built density, and a low-built density.  
The high-built density pattern can be traced back to the subzones in the historic center, in the district of San Lorenzo to the east of the area of study; the surface of these subzones is mainly covered by residential buildings, with almost little open space present. The medium built density pattern is found in the sections to the east, near the district of Ponticelli, and to the south-east, in correspondence of the districts of Barra and San Giovanni to Teduccio; in these subzones there is a more equal distribution of the surface between open spaces and buildings. The low-built density pattern can be traced back to the subzones of the center and center-north, in correspondence with the district of Poggioerale; the surface of these areas has a less residential character in favor of wider open spaces that occupy more area of the Census area.  
Figure 4 shows the area of study and the subzones located in it. Non-residential subzones are highlighted in gray; they were excluded from the test as they lack urban settlements.  
We have implemented our model on a GIS platform built using the ESRI ArcGIS Pro Tool GIS suite and the ESRI ArcPy Python libraries for ArcGIS Pro 3.2.  
To test the GIS platform in the area of study, it was partitioned into subzones consisting of the census areas included in it. The reason for this is that the census areas constitute the  
Figure 4: The area of study: the central-eastern area of the city of Naples.  
homogeneous areas in terms of territorial and urban characteristics into which the area of study is divided. The data containing the characteristics of the census areas were extracted from the latest population and building heritage census carried out by ISTAT, the Italian national institute of statistics. The area of study is partitioned into 1328 subzones, of which 1073 are residential subzones.  
To build the dataset of the characteristics of the subzones, the dataset of the characteristics of buildings and open spaces created in [5] was used. All the building indices were calculated as a weighted average of the values of the indices assigned to the buildings located in the subzone, where the weight is given by the volume of the building. The open space indices were calculated considering the weighted average of the values of the indices assigned to the open spaces located in the subzone, where the weight is given by the area covered by the open space in the subzone.  
After building the hierarchical model of the criteria schematized in Figure 2, each subzone was assigned to a built density class based on the classification in Table 7, after calculating the density of the built environment in the subzone.  
To execute the model all the numerical indices calculated for the subzone were normalized and assigned to the leaf nodes; then, they were fuzzified using the sub-criteria fuzzy set shown in Figure 3b. The model is executed using all the pairwise comparison matrices in Tables 3-6. Based on the built density class to which the subzone is assigned, one of the three pairwise comparison matrices in the radix node shown, respectively, in Tables 8-10 is used.