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Fuzzy lower partial moment and Mean-risk Dominance: An application for poverty Measurement

Author

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  • Christian Deffo Tassak

    (UY1 - Université de Yaoundé I)

  • Louis Aimé Fono

    (Université de Douala)

  • Jules Sadefo-Kamdem

    (LAMETA - Laboratoire Montpelliérain d'Économie Théorique et Appliquée - UM1 - Université Montpellier 1 - UPVM - Université Paul-Valéry - Montpellier 3 - INRA - Institut National de la Recherche Agronomique - Montpellier SupAgro - Centre international d'études supérieures en sciences agronomiques - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier, UG - Université de Guyane, MRE - Montpellier Recherche en Economie - UM - Université de Montpellier)

Abstract

A more general concept of risk in economics consists on the chance of getting an income or a return less than a threshold one. Risk has been studied and generalized more earlier by Fishburn [8] through Mean Partial Lower Moment specially when income can be described by a random variable. In this paper, we present a new concept of partial moment, namely Fuzzy Lower Partial Moment (FLPM) based on credibility measure, to quantify risk of getting a return described by a fuzzy variable and we study its properties. Based on FLPM, we introduce mean risk dominance for fuzzy variables, we characterize the dominance for some specific cases and we determine some of its properties. Furthermore, we study the consistency of mean-risk models with respect to first and second order dominances. We display one application of FLPM by introducing a new poverty index for poverty measurement in the context of fuzzy environment and we examine some of its properties.

Suggested Citation

  • Christian Deffo Tassak & Louis Aimé Fono & Jules Sadefo-Kamdem, 2019. "Fuzzy lower partial moment and Mean-risk Dominance: An application for poverty Measurement," Working Papers hal-02433422, HAL.
    • Handle: RePEc:hal:wpaper:hal-02433422
    Note: View the original document on HAL open archive server: https://hal.umontpellier.fr/hal-02433422
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    References listed on IDEAS

    as
    1. Satya R. Chakravarty, 2019. "An Axiomatic Approach to Multidimensional Poverty Measurement via Fuzzy Sets," Themes in Economics, in: Satya R. Chakravarty (ed.), Poverty, Social Exclusion and Stochastic Dominance, pages 123-141, Springer.
    2. Hagenaars, Aldi J M, 1987. "A Class of Poverty Indices," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(3), pages 583-607, October.
    3. Christian Deffo Tassak & Jules Sadefo Kamdem & Louis Aimé Fono & Nicolas Gabriel Andjiga, 2017. "Characterization of order dominances on fuzzy variables for portfolio selection with fuzzy returns," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(12), pages 1491-1502, December.
    4. Mauricio Gallardo, 2018. "Identifying Vulnerability To Poverty: A Critical Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 32(4), pages 1074-1105, September.
    5. Sadefo Kamdem, Jules & Tassak Deffo, Christian & Fono, Louis Aimé, 2012. "Moments and semi-moments for fuzzy portfolio selection," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 517-530.
    6. Mozaffar Qizilbash, 2006. "Philosophical Accounts of Vagueness, Fuzzy Poverty Measures and Multidimensionality," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Achille Lemmi & Gianni Betti (ed.), Fuzzy Set Approach to Multidimensional Poverty Measurement, chapter 1, pages 9-28, Springer.
    7. Sen, Amartya K, 1976. "Poverty: An Ordinal Approach to Measurement," Econometrica, Econometric Society, vol. 44(2), pages 219-231, March.
    8. Fishburn, Peter C, 1977. "Mean-Risk Analysis with Risk Associated with Below-Target Returns," American Economic Review, American Economic Association, vol. 67(2), pages 116-126, March.
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    Keywords

    Credibility measure; Fuzzy variable; Fuzzy lower partial mo-ment; Mean-Risk dominance; Poverty index;
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