## 1 Introduction
Both approaches rely on remotely sensed datasets, such as LST raster data, and normalized difference vegetation index (NDVI) data obtained from satellite imagery (e.g., Landsat or MODIS), as well as meteorological data such as air temperature collected from ground stations or sensing campaigns. These techniques have several limitations that can impact their accuracy, scalability, and adaptability to different urban settlements. Machine learning (ML) and deep learning (DL) methods, while effective, depend on carefully labeled datasets, substantial computational resources, and expert knowledge. Moreover, data collection and management can be resource-intensive and error-prone, particularly in complex urban environments, limiting the scalability and efficiency of supervised techniques in UHI studies. We propose an unsupervised UHI detection method based on the fuzzy C-means (FCM) fuzzy clustering algorithm. FCM is applied to detect urban heat islands from satellite-derived LST and NDVI data acquired during heatwaves. Additionally, the method assesses the spatial reliability of the detected urban heat islands based on the membership degree of datapoints within the clusters. This represents an advantage over other methods, which do not allow for reliability estimation. In response to the limitations of traditional methods, unsupervised AI-based UHI detection techniques offer a more detailed and adaptive approach to UHI detection. In addition, unlike AI-based supervised techniques, the proposed unsupervised UHI detection technique based on FCM does not require large, accurately labeled datasets, which are often difficult and costly to obtain. FCM identifies clusters directly from the data, assigning each data point a membership degree across multiple clusters. This flexibility allows the proposed FCM-based UHI detection method to better capture the continuous and heterogeneous nature of UHIs, providing a robust framework for accurately mapping and understanding UHI patterns. Furthermore, to overcome the limitations of FCM in assigning the number of clusters a priori, the proposed method adopts a preprocessing phase in which validity indices such as Xie-Beni, Fukuyama-Sugeno, and Davies-Bouldin [14] are measured in order to determine the optimal number of clusters. These indices determine the optimal number of clusters by measuring the similarity between data points of each cluster and the dissimilarities between clusters. Additionally, the proposed method has the advantage of estimating the reliability of the localization of the detected UHIs. This estimate is performed by measuring the average degree of belonging to the corresponding cluster of the data points that fall within the UHI. The higher this value is, within a range from 0 to 1, the more reliable the zoning and the extension of the detected UHI. This provides more detailed information for the decision maker to identify the urban areas most at risk during heat waves. This feature makes the proposed UHI detection method a robust and efficient tool for an accurate and reliable detection of urban heat islands. In a nutshell, the proposed FCM-based UHI detection framework addresses key limitations of traditional supervised methods and offers unique advantages, including the following:  
* Rather than being fixed a priori, the optimal number of clusters is determined using cluster validity indices. Their use allows for the assignment of the most appropriate number of clusters, ensuring that the result of the detection process accurately reflects the spatial patterns of UHIs. * The unsupervised nature of FCM eliminates the need for extensive labeled datasets, significantly reducing computational requirements and preparation time compared to supervised methods. * The flexibility of the proposed method allows it to adapt to various urban settings and dataset configurations, making it a versatile tool applicable across different geographical and environmental contexts.