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Multidimensional and Longitudinal Poverty: an Integrated Fuzzy Approach

  • Gianni Betti
  • Bruno Cheli
  • Achille Lemmi
  • Vijay Verma
Part of the Economic Studies in Inequality, Social Exclusion and Well-Being book series (EIAP, volume 3)

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.
  1. (i)

    The choice of membership functions i.e. quantitative specification of individuals’ or households’ degrees of poverty and deprivation.

     
  2. (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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Betti G, Cheli B, Cambini R (2004) A statistical model for the dynamics between two fuzzy states: theory and an application to poverty analysis. Metron 62:391–411.MathSciNetGoogle Scholar
  2. Betti G, Cheli B, Lemmi A, Verma V (2005a) On the construction of fuzzy measures for the analysis of poverty and social exclusion. Presented at the International Conference in Memory of two Eminent Social Scientists: C. Gini and M.O. Lorenz, Siena, Italy, May 2005Google Scholar
  3. Betti G, Cheli B, Lemmi A, Verma V (2005b) On longitudinal analysis of poverty conceptualised as a fuzzy state. Presented at the First Meeting of the Society for the Study of Economic Inequality (ECINEQ), Palma de Mallorca, Spain, July 2005Google Scholar
  4. Betti G, Verma V (1999) Measuring the degree of poverty in a dynamic and comparative context: a multi-dimensional approach using fuzzy set theory. Proceedings ICCS-VI, Vol. 11, pp. 289–301, Lahore, PakistanGoogle Scholar
  5. Betti G, Verma V (2002) Non-monetary or Lifestyle Deprivation. In: Eurostat, European Social Statistics: Income, Poverty and Social Exclusion: 2nd Report, Luxembourg: Office for Official Publications of the European Communities, pp 76–92.Google Scholar
  6. Betti G, Verma V (2004) A methodology for the study of multi-dimensional and longitudinal aspects of poverty and deprivation. Universitá di Siena, Dipartimento di Metodi Quantitativi, Working Paper 49Google Scholar
  7. Cerioli A, Zani S (1990) A Fuzzy Approach to the Measurement of Poverty. In: Dagum C, Zenga M (eds) Income and Wealth Distribution, Inequality and Poverty, Studies in Contemporary Economics, Springer Verlag, Berlin, pp 272–284.Google Scholar
  8. Cheli B (1995) Totally Fuzzy and Relative Measures in Dynamics Context. Metron 53:183–205.zbMATHGoogle Scholar
  9. Cheli B, Betti G (1999) Fuzzy Analysis of Poverty Dynamics on an Italian Pseudo Panel, 1985–1994. Metron 57:83–103.zbMATHMathSciNetGoogle Scholar
  10. Cheli B, Lemmi A (1995) A “Totally” Fuzzy and Relative Approach to the Multi-dimensional Analysis of Poverty. Economic Notes 24:115–134.Google Scholar
  11. Chiappero-Martinetti E (2000) A multidimensional assessment of well-being based on Sen’s functioning approach. Rivista Internazionale di Scienze Sociali 108:207–239.Google Scholar
  12. Clark D, Qizilbash M (2002) Core poverty and extreme vulnerability in South Africa. The Economics Research Centre, School of Economic and Social Studies, University of East Anglia, Discussion Paper 2002/3Google Scholar
  13. Eurostat (2002) European Social Statistics: Income, Poverty and Social Exclusion: 2nd Report. Luxembourg: Office for Official Publications of the European CommunitiesGoogle Scholar
  14. Hagenaars AJM (1986) The Perception of Poverty. North Holland, AmsterdamGoogle Scholar
  15. Klir G J, Yuan B (1995) Fuzzy Sets and Fuzzy Logic. Prentice Hall, New JerseyzbMATHGoogle Scholar
  16. Lelli S (2001) Factor Analysis vs. Fuzzy Sets Theory: Assessing the Influence of Different Techniques on Sen’s Functioning Approach. Discussion Paper Series DPS 01.21, November 2001, Center for Economic Studies, Catholic University of LouvainGoogle Scholar
  17. Maasoumi E, Nickelsburg G (1988) Multivariate measures of well-being and ananalysis of inequality in the Michigan data. Journal of Business & Economic Statistics 6:326–334.CrossRefGoogle Scholar
  18. Nolan B, Whelan CT (1996) Resources, deprivation and poverty. Clarendon Press, OxfordGoogle Scholar
  19. Ram R (1982) Composite indices of physical quality of life, basic needs fulfillment and income. A principal component representation. Journal of Development Economics 11:227–248.CrossRefGoogle Scholar
  20. Verma V, Betti G (2002) Longitudinal measures of income poverty and life-style deprivation. Universith degli Studi di Padova, Dipartimento di Scienze di Statistiche, Working Paper 50Google Scholar
  21. Whelan CT, Layte R, Maitre B, Nolan B (2001) Income, deprivation and economic strain: an analysis of the European Community Household Panel. European Sociological Review 17:357–372.CrossRefGoogle Scholar
  22. Zadeh LA (1965) Fuzzy sets. Information and Control 8:338–353.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  • Gianni Betti
    • 1
  • Bruno Cheli
    • 1
  • Achille Lemmi
    • 1
  • Vijay Verma
    • 2
  1. 1.Dipartimento di Metodi QuantitativiUniversity of SienaItaly
  2. 2.Dipartimento di Statistica e Matematica applicata all’EconomiaUniversity of PisaItaly

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