# Hierarchical Fuzzy MCDA Multi-Risk Model for Detecting Critical Urban Areas in Climate Scenarios
###### Abstract
This model is particularly suited to dealing with complex urban features. Each criterion is broken down into sub-criteria, and each node of the criteria tree is assigned a fuzzy set built starting from the fuzzy sets in the child nodes and considering the preferences assigned to them, built using the Saaty comparison matrix. The alternatives of the model are represented by the subzones into which the area of study is divided; the alternative that most adheres to the set of criteria is the one with the greatest degree of membership in the resulting fuzzy set, a combination of the fuzzy sets in the root nodes of the criteria. In [7], this model is tested to determine which districts in the city of Naples (Italy) were most vulnerable to heatwave scenarios. The results were consistent with expert assessments. To evaluate which were the most critical subzones in the presence of both types of climatic hazards, we used this fuzzy MCDA model, considering as the main criteria of the hierarchy four criteria given by the vulnerabilities of the two subsystems to heatwave and pluvial flooding phenomena. The root node of the hierarchy provides the assessment of the criticality of the subzone, determined starting from the four criteria. The main advantage of the proposed model is its adaptability to deal with independent climatic hazards. In fact, the vulnerabilities of an urban subsystem to the two phenomena are assessed separately. Furthermore, it is easily portable as it requires a limited number of characteristics for each subsystem. In addition, the model has the advantage, on the one hand, of providing a computationally fast tool for detecting the most critical areas and, on the other, of allowing the criticalities of an urban area to be evaluated in a natural way in the presence of multiple types of independent hazards. Related Works  
In the last decade, several models have been implemented to assess the damage caused by independent hazards. Some examples are HAZUS [8], developed by the Federal Emergency Management Agency (FEMA) and implemented in the tool GIS ArcGIS to evaluate separately the risks produced by earthquakes, floods, and hurricanes, and the CAPRA Probabilistic Risk Assessment Program ([[https://oasishub.co/organization/about/capra](https://oasishub.co/organization/about/capra)]([https://oasishub.co/organization/about/capra](https://oasishub.co/organization/about/capra)) accessed on 1 March 2024), a tool that uses probabilistic models to assess separately the risks caused by earthquakes, hurricanes, extreme rainfall, and volcanic hazards. These models, in addition to assessing the physical damage and social impacts that can be produced by multiple hazards, also carry out an assessment of the resilient effects and costs of mitigation or adaptation strategies. Their main flaw is the need to find detailed local information on the urban fabric under study to provide accurate results. An increasingly relevant attention caused by the negative effects of climate change today is directed towards the multi-risk analysis generated by independent different climate hazard scenarios. Following the Intergovernmental Panel on Climate Change (IPCC) Sixth Assessment Report (AR6) [9], the impacts/risks generated by a climate phenomenon on exposed elements in a geographical area are assessed in terms of the vulnerability of the analyzed area, the intensity of the hazard scenario, and the value of the elements exposed to risk. In order to accurately evaluate the impacts produced by climate phenomena, it is essential to comprehensively model the vulnerability of the analyzed ecosystem to climate hazards, i.e., its propensity to be damaged by the occurrence of the extreme climate phenomenon. Urban settlements are particularly vulnerable to climate hazards due to the presence of anthropogenic elements and activities, which have increased the ecosystem's propensity to be damaged by extreme climatic events.