IDEAS home Printed from
   My bibliography  Save this book chapter

Multidimensional and Longitudinal Poverty: an Integrated Fuzzy Approach

In: Fuzzy Set Approach to Multidimensional Poverty Measurement


  • Gianni Betti

    (University of Siena)

  • Bruno Cheli

    (University of Siena)

  • Achille Lemmi

    (University of Siena)

  • Vijay Verma

    (University of Pisa)


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.

Suggested Citation

  • Gianni Betti & Bruno Cheli & Achille Lemmi & Vijay Verma, 2006. "Multidimensional and Longitudinal Poverty: an Integrated Fuzzy Approach," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Achille Lemmi & Gianni Betti (ed.), Fuzzy Set Approach to Multidimensional Poverty Measurement, chapter 6, pages 115-137, Springer.
  • Handle: RePEc:spr:esichp:978-0-387-34251-1_7
    DOI: 10.1007/978-0-387-34251-1_7

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Belhadj, Besma & Limam, Mohamed, 2012. "Unidimensional and multidimensional fuzzy poverty measures: New approach," Economic Modelling, Elsevier, vol. 29(4), pages 995-1002.
    2. Tavares, Fernando Flores & Betti, Gianni, 2021. "The pandemic of poverty, vulnerability, and COVID-19: Evidence from a fuzzy multidimensional analysis of deprivations in Brazil," World Development, Elsevier, vol. 139(C).
    3. Gianni Betti & Francesca Gagliardi & Salvucci Vincenzo, 2014. "Multidimensional And Fuzzy Measures Of Poverty At Regional Level In Mozambique," Economy of region, Centre for Economic Security, Institute of Economics of Ural Branch of Russian Academy of Sciences, vol. 1(4), pages 114-128.
    4. Oula Ben Hassine & Hela Bouras, 2022. "Fuzzy Measures of Monetary and Non-monetary Deprivations in Tunisia," International Journal of Economics and Financial Issues, Econjournals, vol. 12(4), pages 65-71, July.
    5. Valérie Berenger & Cuauhtémoc Calderón Villarreal & Franck Celestini, 2009. "Modelling the Distribution of Multidimensional Poverty Scores: Evidence from Mexico," Estudios Económicos, El Colegio de México, Centro de Estudios Económicos, vol. 24(1), pages 3-34.
    6. Molina, Isabel, 2022. "Disaggregating data in household surveys: Using small area estimation methodologies," Estudios Estadísticos 48107, Naciones Unidas Comisión Económica para América Latina y el Caribe (CEPAL).
    7. Ayala, Luis & Bárcena-Martín, Elena & Cantó, Olga & Navarro, Carolina, 2022. "COVID-19 lockdown and housing deprivation across European countries," Social Science & Medicine, Elsevier, vol. 298(C).
    8. Gianni Betti & Francesca Gagliardi & Laura Neri, 2021. "The Heavy Burden of “Dependent Children”: An Italian Story," Sustainability, MDPI, vol. 13(17), pages 1-12, September.
    9. Burhan Can Karahasan & Fırat Bilgel, 2021. "The Topography and Sources of Multidimensional Poverty in Turkey," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 154(2), pages 413-445, April.
    10. Francesco Schirripa Spagnolo & Antonella D’Agostino & Nicola Salvati, 2018. "Measuring differences in economic standard of living between immigrant communities in Italy," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(4), pages 1643-1667, July.
    11. Anh Thu Quang Pham & Pundarik Mukhopadhaya & Ha Vu, 2021. "Estimating poverty and vulnerability to monetary and non-monetary poverty: the case of Vietnam," Empirical Economics, Springer, vol. 61(6), pages 3125-3177, December.
    12. Antonella D’agostino & Giovanni De Luca & Dominique Guégan, 2023. "Estimating Lower Tail Dependence Between Pairs of Poverty Dimensions in Europe," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 69(2), pages 419-442, June.
    13. Bruno Cheli & Achille Lemmi & Nicoletta Pannuzi & Andrea Regoli, 2019. "From the TFR to the IFR approach for the multidimensional analysis of poverty and living conditions," Discussion Papers 2019/252, Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy.
    14. Vincenzo Salvucci & Gianni Betti & Francesca Gagliardi, 2012. "Multidimensional and Fuzzy Measures of Poverty and Inequality at National and Regional Level in Mozambique," Department of Economics University of Siena 649, Department of Economics, University of Siena.
    15. Sen, Sugata, 2019. "Decomposition of intra-household disparity sensitive fuzzy multi-dimensional poverty index: A study of vulnerability through Machine Learning," MPRA Paper 93550, University Library of Munich, Germany.
    16. Hanna Dudek & Wiesław Szczesny, 2021. "Multidimensional material deprivation in Poland: a focus on changes in 2015–2017," Quality & Quantity: International Journal of Methodology, Springer, vol. 55(2), pages 741-763, April.


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:esichp:978-0-387-34251-1_7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.