In this paper, two fuzzy clustering methods for spatial interval-valued data are proposed, i.e. the fuzzy $C$-Medoids clustering of spatial interval-valued data with and without entropy regularization. Both methods are based on the Partitioning Around Medoids (PAM) algorithm, inheriting the great advantage of obtaining non-fictitious representative units for each cluster.

In both methods, the units are endowed with a relation of contiguity, represented by a symmetric binary matrix. This can be intended both as contiguity in a physical space and as a more abstract notion of contiguity. The performances of the methods are proved by simulation, testing the methods with different contiguity matrices associated to natural clusters of units. In order to show the effectiveness of the methods in empirical studies, three applications are presented: the clustering of municipalities based on interval-valued pollutants levels, the clustering of European fact-checkers based on interval-valued data on the average number of impressions received by their tweets and the clustering of the residential zones of the city of Rome based on the interval of price values.

本文提出了两种空间区间值数据的模糊聚类方法，即模糊聚类方法。$C$-带或不带熵正则化的空间区间值数据的 Medoids 聚类。这两种方法都基于围绕中心点分区（PAM）算法，继承了为每个簇获取非虚构代表单元的巨大优势。

在这两种方法中，单元都被赋予了由对称二进制矩阵表示的连续关系。这既可以作为物理空间中的连续性，也可以作为更抽象的连续性概念。这些方法的性能通过仿真得到了证明，并用与自然单元簇相关的不同邻接矩阵测试了该方法。为了证明这些方法在实证研究中的有效性，提出了三种应用：基于区间值污染物水平的城市聚类、基于收到的平均印象数区间值数据的欧洲事实检查器聚类通过他们的推文以及基于价格区间的罗马市住宅区的聚类。