# Hierarchical Fuzzy MCDA Multi-Risk Model for Detecting Critical Urban Areas in Climate Scenarios
## 4 Conclusions and Future Works  
We propose a novel GIS-based fuzzy hierarchical MCDA model applied to assess the vulnerability of physical components of urban settlements in the presence of climatic independent multi-hazard scenarios. The model allows us to evaluate the propensity of physical components to vulnerability to multi-hazard heatwave and pluvial flooding scenarios. Following [5], the urban settlement is partitioned into the building and open space subsystems and the model is applied to evaluate a multi-hazard vulnerability index given by the criticality of urban subzones in the presence of both phenomena. The model was tested on the central-eastern area of the municipality of Naples, in Italy. The results highlighted the presence of a critical region to the north-east of the area of study in which there is a high predisposition of open spaces to be vulnerable to heatwave scenarios and of buildings to be vulnerable to pluvial flooding scenarios. \begin{table}
\begin{tabular}{c c c c c} \hline
**Criterion** & **Vulnerability Class** & **Number of Subzones** & **Mean Membership Degree** & **Standard Deviation** \\ \hline \multirow{4}{*}{Heatwave residential building vulnerability} & 1—High & 0 & & \\  & 2—Medium-high & 15 & 0.349 & 0.056 \\  & 3—Medium & 383 & 0.322 & 0.088 \\  & 4—Medium-low & 566 & 0.041 & 0.015 \\  & 5—Low & 109 & 0.003 & 0.001 \\ \hline \multirow{4}{*}{Heatwave open space vulnerability} & 1—High & 0 & & \\  & 2—Medium-high & 370 & 0.224 & 0.076 \\  & 3—Medium & 698 & 0.045 & 0.017 \\  & 4—Medium-low & 5 & 0.002 & 0.001 \\  & 5—Low & 0 & & \\ \hline \multirow{4}{*}{Pluvial flooding building vulnerability} & 1—High & 15 & 0.536 & 0.084 \\  & 2—Medium-high & 432 & 0.411 & 0.095 \\  & 3—Medium & 402 & 0.091 & 0.032 \\  & 4—Medium-low & 44 & 0.016 & 0.006 \\  & 5—Low & 3 & 0.009 & 0.002 \\ \hline \multirow{4}{*}{Pluvial flooding open space vulnerability} & 1—High & 0 & & \\  & 2—Medium-high & 230 & 0.334 & 0.072 \\  & 3—Medium & 489 & 0.270 & 0.083 \\  & 4—Medium-low & 214 & 0.050 & 0.018 \\  & 5—Low & 0 & & \\ \hline \end{tabular}
\end{table} 
Table 12: Average and standard deviation of the membership degrees to the fuzzy sets of the four vulnerability criteria of the subzones belonging to each vulnerability class. Comparison tests have shown that the results are compatible with those obtained using the vulnerability assessment model of buildings and open spaces to heatwave and pluvial flooding phenomena proposed in [5]. Compared to other multi-risk models based on multi-criteria approaches, the proposed model has the advantage of defining the subsystems of an urban settlement in a more natural way. In fact, it uses a hierarchical fuzzy-based MCDA model in which each sub-criterion node corresponds to a fuzzy set automatically constructed starting from the fuzzy sets of the sub-nodes that compose it. The degree of criticality is determined in the root node of the hierarchical tree of criteria, assigning a degree of preference to the vulnerabilities of the two subsystems, buildings, and open spaces, based on the built density in the subzone. The main critical point of this model is that it was built taking into consideration only the set of characteristics determined in [5] for the assessment of the vulnerabilities to heatwaves and pluvial flooding of the two urban subsystems. However, the hierarchical structure of the fuzzy MCDA model used may allow in the future to refine the model by taking into consideration a larger number of characteristics of an urban subsystem that impact its vulnerability. Furthermore, [PERSON]'s pairwise comparison matrix for each criterion was constructed taking into consideration the weights of the intermediate indicators assigned in [5] for the determination of the vulnerability indicators.