The Fuzzy Set Approach to Multidimensional Poverty: the Case of Italy in the 1990s

Most of the methods designed for the analysis of poverty share two main limitations: (i) they are unidimensional, i.e. refer to only one proxy of poverty such as low income or consumption expenditure; (ii) they need to dichotomize the population into the poor and the non-poor by means of the so-called poverty line. Nowadays many authors recognize that poverty is a complex phenomenon that cannot be reduced to the sole monetary dimension. This leads to the need for a multidimensional approach that consists in extending the analysis to a variety of non-monetary indicators of living conditions. Such a multidimensional analysis has indeed become increasingly feasible as more information has become available, and this in turn has induced many countries to launch surveys covering the various aspects of living conditions. In this chapter we present a survey of the research on the fuzzy approach to poverty measurement which was launched by the contribution of Cerioli and Zani (1990). We emphasized elements which a fuzzy approach takes into account and which are ignored by the conventional analysis of poverty. We note that in the fuzzy approach, choices have to be made concerning at least two additional aspects: Membership functions. I t is necessary to give a quantitative specification to the propensity to poverty and deprivation of each individual in the population, given the level and distribution of income and other indicators of living standards. Rules for manipulation of the resulting fuzzy sets. This issue concerns in particular the definition of complements and the intersection, union and aggregation of sets. A major objective of this chapter is to make clear that these choices must meet some basic logical and substantive requirements to be meaningful. We discussed and proposed measures reflecting the multidimensional aspects of deprivation, in particular measures of the degree of overlap between monetary and non-monetary deprivation, and also developed a number of fuzzy measures of the degree of persistence of poverty over time.