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Hasse diagrams, poset theory and fuzzy poverty measure


  • Marco Fattore


In recent years, it has become evident that pure monetary measures cannot represent the poverty phenomenon faithfully. Poverty involves many different aspects of life that can be hardly condensed in a single monetary indicator. People can be poor in different ways, at different degrees and from several points of view. In this perspective, fuzzy multidimensional indicators have been proposed to measure material deprivation and the degree of membership of an individual to the set of poor. Actually, the statistical procedures used to build membership functions do not seem to be fully consistent. In this paper, we suggest that partially ordered set theory can provide new tools to develop fuzzy poverty measures on a sound basis. Particularly, we show how multidimensional poverty data can be modelled as a partially ordered set, whose linear extensions can provide consistent criteria in view of membership functions definition.

Suggested Citation

  • Marco Fattore, 2007. "Hasse diagrams, poset theory and fuzzy poverty measure," Working Papers 20071104, Università degli Studi di Milano-Bicocca, Dipartimento di Statistica, revised Nov 2007.
  • Handle: RePEc:mis:wpaper:20071104

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    References listed on IDEAS

    1. Marco Fattore, 2006. "Finite groups in Axiomatic Index Number Theory," Working Papers 20070101, Università degli Studi di Milano-Bicocca, Dipartimento di Statistica.
    2. Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, vol. 4(2), pages 115-145, May.
    3. Hill, Robert J., 2006. "Superlative index numbers: not all of them are super," Journal of Econometrics, Elsevier, vol. 130(1), pages 25-43, January.
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    Cited by:

    1. 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.

    More about this item


    Price index; Poverty; Fuzzy poverty measures; Poset theory; Partial order;

    JEL classification:

    • I3 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty

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