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On Two Dominances of Fuzzy Variables based on a Parametric 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, 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)

  • Louis Aimé Fono

    (Université de Douala)

Abstract

Iwamura [18] introduced a new parametric fuzzy measure as a convex linear combination of possibility and necessity measures. This measure generalizes the credibility measure and the parameter of the possibility measure is considered as the decision making (investors) optimism's level. In this paper, we introduce by means of that mea-sure two new dominances (binary relations) on fuzzy variables. The first one generalizes the first order dominance introduced recently by Tassak et al. [17] and the second one, based on optimism's level and called optimisnism dominance, is stronger than the first one. We study properties of these dominances on trapezoidal fuzzy numbers and we characterize them. We implement the optiminism dominance in a nu-merical example to display that its set of efficient portfolios enlarges the set of efficient portfolios obtained by Tassak et al. [17] through their first order dominance.

Suggested Citation

  • Justin Dzuche & Christian Deffo Tassak & Jules Sadefo-Kamdem & Louis Aimé Fono, 2019. "On Two Dominances of Fuzzy Variables based on a Parametric Fuzzy Measure and Application to Portfolio Selection with Fuzzy Return," Working Papers hal-02433438, HAL.
    • Handle: RePEc:hal:wpaper:hal-02433438
    Note: View the original document on HAL open archive server: https://hal.umontpellier.fr/hal-02433438
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    References listed on IDEAS

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    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. 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.
    4. 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.
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    Keywords

    Fuzzy variable; Parametric fuzzy measure; Generalized Firstorder dominance; Optiminism Dominance; Set of best portfolios;
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