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Dominances on fuzzy variables based on credibility measure


  • Christian Tassak

    () (MASS - Laboratoire de Mathématiques appliquées aux Sciences Sociales - Université de Douala)

  • Jules Sadefo Kamdem

    (LAMETA - Laboratoire Montpelliérain d'Économie Théorique et Appliquée - UM1 - Université Montpellier 1 - UM3 - Université Paul-Valéry - Montpellier 3 - Montpellier SupAgro - Centre international d'études supérieures en sciences agronomiques - INRA Montpellier - Institut national de la recherche agronomique [Montpellier] - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier)

  • Louis Aimé Fono

    () (MASS - Laboratoire de Mathématiques appliquées aux Sciences Sociales - Université de Douala)


This paper studies three notions of fuzzy dominance based on credibility measure, namely, the fuzzy mean-risk dominance, the rst credibilistic dominance and the second credibilistic dominance. More precisely, we introduce and examine some properties of the Fuzzy Lower Partial Moments (FLPM) of a fuzzy variable and, we deduce the Fuzzy Kappa index (FK) of a fuzzy variable, that is, a risk-adjusted performance measure of an asset or a portfolio with fuzzy return. Based on the aforementioned notion, we introduce the fuzzy mean-risk dominance of two fuzzy variables and we characterize it in three speci c and interesting cases. We recall the rst credibilistic dominance and the second credibilistic dominance for fuzzy variables introduced earlier by Peng et al. [20]. We characterize the rst credibilistic dominance and determine some of its properties. We introduce and characterize the notion of crossing points of distributions of two fuzzy numbers and use them to characterize the second credibilistic dominance for fuzzy numbers. We justify that the rst credibilistic dominance is stronger than the fuzzy mean-risk dominance and the second credibilistic dominance, and neither of these two later implies the other.

Suggested Citation

  • Christian Tassak & Jules Sadefo Kamdem & Louis Aimé Fono, 2012. "Dominances on fuzzy variables based on credibility measure," Working Papers hal-00796215, HAL.
  • Handle: RePEc:hal:wpaper:hal-00796215
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    References listed on IDEAS

    1. 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.
    2. 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.
    3. Huang, Dashan & Zhu, Shushang & Fabozzi, Frank J. & Fukushima, Masao, 2010. "Portfolio selection under distributional uncertainty: A relative robust CVaR approach," European Journal of Operational Research, Elsevier, vol. 203(1), pages 185-194, May.
    4. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
    5. Bawa, Vijay S., 1975. "Optimal rules for ordering uncertain prospects," Journal of Financial Economics, Elsevier, vol. 2(1), pages 95-121, March.
    6. Darinka Dentcheva & Andrzej Ruszczynski, 2004. "Optimization Under First Order Stochastic Dominance Constraints," GE, Growth, Math methods 0403002, University Library of Munich, Germany, revised 07 Aug 2005.
    7. S. M. Sunoj & S. S. Maya, 2008. "The role of lower partial moments in stochastic modeling," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 223-242.
    8. Brogan, Anita J. & Stidham Jr., Shaler, 2008. "Non-separation in the mean-lower-partial-moment portfolio optimization problem," European Journal of Operational Research, Elsevier, vol. 184(2), pages 701-710, January.
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