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On two dominances of fuzzy variables based on a parametrized fuzzy measure and application to portfolio selection with fuzzy return

Author

Listed:
  • Justin Dzuche

    (Université de Douala)

  • Christian Deffo Tassak

    (UY1 - Université de Yaoundé I)

  • Jules Sadefo-Kamdem

    (MRE - Montpellier Recherche en Economie - UM - Université de Montpellier)

  • Louis Aimé Fono

    (Université de Douala)

Abstract

Yang and Iwamura (Appl Math Sci 46:2271–2288, 2008) introduced a new fuzzy measure as a convex linear combination of possibility and necessity measures. This measure generalizes the credibility measure and the real parameter associated to the possibility measure is considered as the decision making's optimism level. In this paper, we introduce by means of that measure, two new dominances as binary relations on fuzzy variables. The first one generalizes the first order dominance based on credibility measure and introduced recently by Tassak et al. (J Oper Res Soc 68:1491–1502, 2017) and the second one, based on the investor's optimism level, is more stronger than the other. Moreover, we study some properties of those dominances and characterize them on the particular family of trapezoidal fuzzy numbers. We implement the second dominance in a numerical example to illustrate the impact of the investor's attitude through the set of best portfolios.

Suggested Citation

  • Justin Dzuche & Christian Deffo Tassak & Jules Sadefo-Kamdem & Louis Aimé Fono, 2020. "On two dominances of fuzzy variables based on a parametrized fuzzy measure and application to portfolio selection with fuzzy return," Post-Print hal-03010279, HAL.
    • Handle: RePEc:hal:journl:hal-03010279
    DOI: 10.1007/s10479-020-03873-5
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    References listed on IDEAS

    as
    1. 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.
    2. Sharpe, William F., 1971. "A Linear Programming Approximation for the General Portfolio Analysis Problem," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 6(5), pages 1263-1275, December.
    3. Ogryczak, Wlodzimierz & Ruszczynski, Andrzej, 1999. "From stochastic dominance to mean-risk models: Semideviations as risk measures," European Journal of Operational Research, Elsevier, vol. 116(1), pages 33-50, July.
    4. 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.
    5. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    6. Li, Xiang & Qin, Zhongfeng & Kar, Samarjit, 2010. "Mean-variance-skewness model for portfolio selection with fuzzy returns," European Journal of Operational Research, Elsevier, vol. 202(1), pages 239-247, April.
    7. Stone, Bernell K., 1973. "A Linear Programming Formulation of the General Portfolio Selection Problem†," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 8(4), pages 621-636, September.
    8. Anderson, Robert M, 1978. "An Elementary Core Equivalence Theorem," Econometrica, Econometric Society, vol. 46(6), pages 1483-1487, November.
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    Cited by:

    1. Alfred Mbairadjim Moussa & Jules Sadefo Kamdem, 2022. "A fuzzy multifactor asset pricing model," Annals of Operations Research, Springer, vol. 313(2), pages 1221-1241, June.

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