Hasse diagrams, poset theory and fuzzy poverty measure

In recent years, it has become evident that pure monetary measures cannot represent the poverty phenomenon faithfully. Poverty involves many different aspects of life that can be hardly condensed in a single monetary indicator. People can be poor in different ways, at different degrees and from several points of view. In this perspective, fuzzy multidimensional indicators have been proposed to measure material deprivation and the degree of membership of an individual to the set of poor. Actually, the statistical procedures used to build membership functions do not seem to be fully consistent. In this paper, we suggest that partially ordered set theory can provide new tools to develop fuzzy poverty measures on a sound basis. Particularly, we show how multidimensional poverty data can be modelled as a partially ordered set, whose linear extensions can provide consistent criteria in view of membership functions definition.