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Methodology and Axiomatic Characterization of a Multidimensional and Fuzzy Measure of Deprivation

Author

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  • Dipesh Gangopadhyay

    (University of Georgia
    National Statistical Office, Government of India)

  • Robert B. Nielsen

    (University of Georgia
    The University of Alabama)

  • Velma Zahirovic-Herbert

    (University of Georgia
    Department of Financial Planning, Housing, and Consumer Economics)

Abstract

This article proposes a general methodology to measure multidimensional deprivation in a fuzzy setup. Each dimension comprises multiple dimensional attributes. The methodology is developed in a flexible manner to incorporate any theoretical construct of wellbeing. The new fuzzy membership functions proposed in the method combines the absolute and relative notions of deprivation and take the functional form of normalized and weighted deprivation gaps. A new weight structure is proposed for aggregations within and across the dimensions. Three forms of deprivation indices are discussed: the headcount ratio, the adjusted deprivation index, and the deprivation index. A unified axiomatic framework is discussed for the multidimensional and fuzzy measures of deprivation. Various desired axiomatic properties of the fuzzy membership functions are included as precursory axioms in the framework. The proposed measure satisfies a majority of the desirable axioms.

Suggested Citation

  • Dipesh Gangopadhyay & Robert B. Nielsen & Velma Zahirovic-Herbert, 2021. "Methodology and Axiomatic Characterization of a Multidimensional and Fuzzy Measure of Deprivation," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 153(1), pages 1-37, January.
    • Handle: RePEc:spr:soinre:v:153:y:2021:i:1:d:10.1007_s11205-020-02486-6
    DOI: 10.1007/s11205-020-02486-6
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    More about this item

    Keywords

    Deprivation measure; Multidimensional; Absolute and relative; Fuzzy; Distribution sensitive; Axioms;
    All these keywords.

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • I30 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - General
    • I32 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - Measurement and Analysis of Poverty

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