Rainer Brüggemann

Applied Statistics is certainly devoted to extract information from any kind of data. Data which characterize objects of interest. Ranking, i.e. finding a complete order among objects, belongs to the tasks of Applied Statistics. Not anticipating a historical research, it seems, however, as if the task of ranking in terms of the theory of partially ordered sets does not play that role in statistics which it should do, taking into account the enormous multitude, diversity and popularity of ranking studies. The idea is simple, not to say trivial. Let objects x1, …, xn be characterized by m data, attributes, say qj(j = l, …, m), then xi1 < xi2 if and only if qj (xi1) = qj (xi2) for all j, and with at least one qj* with a strict inequality. It can be easily seen that this definition (being the basis of the ‘‘Hasse diagram technique’’ (HDT)) does not guarantee that every object is in a

Poverty is a fuzzy and complex phenomenon which is intrinsically multidimensional. First attempts of tackling poverty with multidimensional measures trace back to the seventies with the conceptual writings on income poverty by Amartya Sen (1976). Since then much research has been devoted to answer questions of the type: (i) Who is poor? (ii) How poor is a poor? The measure of poverty and social exclusion is certainly a key point in poverty description. While much effort has been put in the last decades to the measurement of poverty, less attention has been paid to find relations among different poverty aspects. In this paper, we start from a classical definition of the population of the poor and we employ Fuzzy Multi-Criteria Analysis to provide an attempt to relate poverty aspects to one another, which we call a ‘structural representation of poverty’. Our focus is on the pattern of implications existing among different descriptors characterizing poverty aspects. We show how fuzzy relation theory and partially ordered set techniques are effective in representing complex relational structures and provide new insights into multidimensional poverty. As simple test cases the method is applied to data concerning two Italian regions based on EU-SILC database 2004. Keywords: Multidimensional Poverty, Multi-criteria Analysis, Poverty Structure, Ordinal Variables, Posets, Fuzzy Quasi-order Relations.