Fuzzy cluster and validity indices in a socio-economic context

The numerous concepts of socio-economic hardship are, furthermore, attributable to a traditional distinction between absolute and relative conditions of hardship. The options of scientific research were therefore oriented towards the establishment of a multi-dimensional approach, sometimes abandoning dichotomous logic in order to arrive at fuzzy classifications in which each unit belongs and, at the same time, does not belong, to a category. The cluster analysis allows to identify the profiles families who meet certain descriptive characteristics, not defined a priori. The approach used in this work to synthesize and measure the conditions of the hardship of a population is based on a clustering procedure which is known as Fuzzy clustering by Local Approximation of Membership (FLAME) worked by defining the neighborhood of each object and identifying cluster supporting objects. This clustering method allows a set of data to belong not only to a main cluster but also to two or more clusters with “fuzzy profiles”.