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F-FOD: Fuzzy First Order Dominance Analysis and Populations Ranking Over Ordinal Multi-Indicator Systems

Author

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  • Marco Fattore

    (University of Milano-Bicocca)

  • Alberto Arcagni

    (University of Milano-Bicocca)

Abstract

In this paper, we develop a new statistical procedure for the comparison of frequency distributions on systems of ordinal indicators, based on a multidimensional fuzzy extension of the first order dominance (FOD) criterion. The procedure, named fuzzy-first order dominance (F-FOD), employs concepts and tools from partially ordered set theory and from fuzzy relational calculus and is designed to overcome the main limitations of previously developed algorithms for FOD analysis. In particular, F-FOD produces full pairwise comparison matrices, allows for partial orderings and rankings of the statistical units to be derived from the input data, is computationally sufficiently light to be applied in most cases of practical interest and is freely available in the R package PARSEC. To illustrate its effectiveness, we also show F-FOD in action on two real datasets concerning health in Denmark and child well-being in the Democratic Republic of Congo.

Suggested Citation

  • Marco Fattore & Alberto Arcagni, 2019. "F-FOD: Fuzzy First Order Dominance Analysis and Populations Ranking Over Ordinal Multi-Indicator Systems," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 144(1), pages 1-29, July.
    • Handle: RePEc:spr:soinre:v:144:y:2019:i:1:d:10.1007_s11205-018-2049-2
    DOI: 10.1007/s11205-018-2049-2
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    1. Channing Arndt & Vincent Leyaro & Kristi Mahrt, 2014. "Multi-dimensional Poverty Analysis for Tanzania: First Order Dominance Approach with Discrete Indicators," WIDER Working Paper Series wp-2014-146, World Institute for Development Economic Research (UNU-WIDER).
    2. Arndt, Channing & Tarp, Finn (ed.), 2016. "Measuring Poverty and Wellbeing in Developing Countries," OUP Catalogue, Oxford University Press, number 9780198744818.
    3. Udaya S. Mishra & Vachaspati Shukla, 2016. "Welfare Comparisons with Multidimensional Well-Being Indicators: An Indian Illustration," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 129(2), pages 505-525, November.
    4. Arndt, Channing & Distante, Roberta & Hussain, M. Azhar & Østerdal, Lars Peter & Huong, Pham Lan & Ibraimo, Maimuna, 2012. "Ordinal Welfare Comparisons with Multiple Discrete Indicators: A First Order Dominance Approach and Application to Child Poverty," World Development, Elsevier, vol. 40(11), pages 2290-2301.
    5. M. Azhar Hussain & Mette Møller Jørgensen & Lars Peter Østerdal, 2016. "Refining Population Health Comparisons: A Multidimensional First Order Dominance Approach," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 129(2), pages 739-759, November.
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    7. Arndt, Channing & Distante, Roberta & Hussain, M. Azhar & Østerdal, Lars Peter & Huong, Pham Lan & Ibraimo, Maimuna, 2012. "Ordinal Welfare Comparisons with Multiple Discrete Indicators: A First Order Dominance Approach and Application to Child Poverty," World Development, Elsevier, vol. 40(11), pages 2290-2301.
    8. Arndt, Channing & Leyaro, Vincent & Mahrt, Kristi, 2014. "Multi-dimensional poverty analysis for Tanzania: First order dominance approach with discrete indicators," WIDER Working Paper Series 146, World Institute for Development Economic Research (UNU-WIDER).
    9. Olu Ajakaiye & Afeikhena T. Jerome & Olanrewaju Olaniyan & Kristi Mahrt & Olufunke A. Alaba, 2014. "Multidimensional Poverty in Nigeria: First Order Dominance Approach," WIDER Working Paper Series wp-2014-143, World Institute for Development Economic Research (UNU-WIDER).
    10. Nanivazo, Malokele, 2014. "First order dominance analysis: Child wellbeing in the Democratic Republic of Congo," WIDER Working Paper Series 025, World Institute for Development Economic Research (UNU-WIDER).
    11. Marco Fattore, 2016. "Partially Ordered Sets and the Measurement of Multidimensional Ordinal Deprivation," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 128(2), pages 835-858, September.
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    13. Paola Annoni & Marco Fattore & Rainer Brüggemann, 2008. "A multi-criteria fuzzy approach for analyzing poverty structure," UNIMI - Research Papers in Economics, Business, and Statistics unimi-1072, Universitá degli Studi di Milano.
    14. Malokele Nanivazo, 2015. "First Order Dominance Analysis: Child Wellbeing in the Democratic Republic of Congo," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 122(1), pages 235-255, May.
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    2. Arcagni, Alberto & Avellone, Alessandro & Fattore, Marco, 2022. "Complexity reduction and approximation of multidomain systems of partially ordered data," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    3. Stefania M. L. Rimoldi & Alberto Arcagni & Marco Fattore & Elisa Barbiano di Belgiojoso, 2021. "Targeting Policies for Multidimensional Poverty and Social Fragility Relief Among Migrants in Italy, Using F-FOD Analysis," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 157(1), pages 57-75, August.
    4. Filippo Damiani & Paula Rodríguez-Modroño, 2024. "Measuring the digital inclusion of women: a poset-based approach to the women in digital scoreboard," Quality & Quantity: International Journal of Methodology, Springer, vol. 58(1), pages 705-722, February.
    5. Desirée Campagna & Giulio Caperna & Valentina Montalto, 2020. "Does Culture Make a Better Citizen? Exploring the Relationship Between Cultural and Civic Participation in Italy," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 149(2), pages 657-686, June.
    6. Nita Handastya & Gianni Betti, 2023. "The ‘Double Fuzzy Set’ Approach to Multidimensional Poverty Measurement: With a Focus on the Health Dimension," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 166(1), pages 201-217, February.

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