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Hasse Diagrams, Poset Theory and Fuzzy Poverty Measures

Author

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  • Marco Fattore

    (Department of Statistics, University of Milano)

Abstract

It is generally agreed that poverty cannot be faithfully represented by a single monetary measure. Poverty involves many different aspects of life, and people can be poor in different ways, to different degrees and from several points of view. For this reason, fuzzy multidimensional indicators have been proposed to measure material deprivation. However, the statistical procedures used to build such indicators do not seem to be fully consistent. In this paper we show how partially ordered set theory can help overcome such consistency problems, providing a sound basis for a multidimensional and fuzzy analysis of poverty. In particular, we propose new criteria for defining fuzzy poverty membership functions and give a fuzzy generalization of the notion of quantile, which may prove useful when analyzing and comparing poverty data.

Suggested Citation

  • Marco Fattore, 2008. "Hasse Diagrams, Poset Theory and Fuzzy Poverty Measures," Rivista Internazionale di Scienze Sociali, Vita e Pensiero, Pubblicazioni dell'Universita' Cattolica del Sacro Cuore, vol. 116(1), pages 63-75.
    • Handle: RePEc:vep:journl:y:2008:v:116:i:1:p:63-75
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    Citations

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    Cited by:

    1. Enrico Ivaldi & Andrea Ciacci & Riccardo Soliani, 2020. "Urban deprivation in Argentina: A POSET analysis," Papers in Regional Science, Wiley Blackwell, vol. 99(6), pages 1723-1747, December.
    2. Rainer Bruggemann & Lars Carlsen, 2015. "Incomparable: what now II? Absorption of incomparabilities by a cluster method," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(4), pages 1633-1645, July.
    3. Frauke Fuhrmann & Margit Scholl & Rainer Bruggemann, 2018. "How Can the Empowerment of Employees with Intellectual Disabilities Be Supported?," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 136(3), pages 1269-1285, April.
    4. Flavio Comim, 2021. "A Poset-Generalizability Method for Human Development Indicators," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 158(3), pages 1179-1198, December.
    5. Jan W. Owsiński, 2018. "Is There Any ‘Law of Requisite Variety’ in Construction of Indices for Complex Systems?," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 136(3), pages 1125-1137, April.
    6. Marco Fattore & Filomena Maggino, 2018. "Some Considerations on Well-Being Evaluation Procedures, Taking the Cue from “Exploring Multidimensional Well-Being in Switzerland: Comparing Three Synthesizing Approaches”," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 137(1), pages 83-91, May.

    More about this item

    Keywords

    Multidimensional poverty measurement; Fuzzy approach; Partially ordered sets;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • I32 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - Measurement and Analysis of Poverty

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