The paper analyses the concept of poverty through a multidimensional approach that uses multiple indicators to define a condition of poverty and allows to denote territorial areas and/or population subgroups characterized by situations of hardship or severe social exclusion. This study responds to need of defining and constructing indicators that are capable of estimating poverty in small areas. The complexity of the poverty phenomenon thus poses the need to identify analytical techniques that allow poverty to be framed in a broader context, to improve knowledge of the problem and deal with it through specific economic and social interventions. The data analysed in this paper allowed the construction of three sets of indicators referring to three areas of poverty: economic, social, and housing. The data refer to one Italian region: Apulia. Two methodologies were adopted to study the data. The first based on the Fuzzy approach that uses the technique of Fuzzy Sets to synthesize and measure the incidence of relative poverty in the considered population starting from the statistical information provided by a plurality of indicators. The second, based on a cluster analysis algorithm: the DBSCAN method for identifying dense areas from the fuzzy values processed by the first methodology.