Multidimensional and Longitudinal Poverty: an Integrated Fuzzy Approach

Gianni Betti, Bruno Cheli, Achille Lemmi and Vijay Verma
Additional contact information
Bruno Cheli: University of Siena
Achille Lemmi: University of Siena
Vijay Verma: University of Pisa

Chapter 6 in Fuzzy Set Approach to Multidimensional Poverty Measurement, 2006, pp 115-137 from Springer

Abstract: Concluding Remarks When poverty is viewed as a matter of degree in contrast to the conventional poor/non-poor dichotomy, that is, as a fuzzy state, two additional aspects are introduced into the analysis. (i) The choice of membership functions i.e. quantitative specification of individuals’ or households’ degrees of poverty and deprivation. (ii) And the choice of rules for the manipulation of the resulting fuzzy sets, rules defining their complements, intersections, union and aggregation. Specifically, for longitudinal analysis of poverty using the fuzzy set approach, we need joint membership functions covering more than one time period, which have to be constructed on the basis of the series of cross-sectional membership functions over those time periods. This Chapter has discussed approaches and procedures for constructing fuzzy measures of income poverty and of combining them with similarly constructed measures of non-monetary deprivation using the fuzzy set approach. In fact, the procedures for combining fuzzy measures in multiple dimensions at a given time are identical, in formal terms, to the procedures for combining fuzzy cross-sectional measures over multiple time periods. We have proposed a general rule for the construction of fuzzy set intersections, that is, for the construction of a longitudinal poverty measure from a sequence of cross-sectional measures under fuzzy conceptualization. This general rule is meant to be applicable to any sequence of “poor” and “non-poor” sets, and it satisfies all the marginal constraints. On the basis of the results obtained, various fuzzy poverty measures over time can be constructed as consistent generalizations of the corresponding conventional (dichotomous) measures. Numerical results of these procedures applied to measures of multidimensional poverty and deprivation, and to combinations of such measures have been presented elsewhere.

Keywords: Membership Function; Lorenz Curve; Poverty Measure; Fuzzy Measure; Income Poverty (search for similar items in EconPapers)
Date: 2006
References: Add references at CitEc
Citations: View citations in EconPapers (17)

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:esichp:978-0-387-34251-1_7

Ordering information: This item can be ordered from
http://www.springer.com/9780387342511

DOI: 10.1007/978-0-387-34251-1_7

Access Statistics for this chapter

More chapters in Economic Studies in Inequality, Social Exclusion, and Well-Being from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().