Dominances on fuzzy variables based on credibility measure

Christian Tassak (), Jules Sadefo-Kamdem and Louis Aimé Fono ()
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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 - 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
Louis Aimé Fono: MASS - Laboratoire de Mathématiques appliquées aux Sciences Sociales - Université de Douala
Authors registered in the RePEc Author Service: Jules SADEFO KAMDEM

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Abstract: 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.

Keywords: Credibility measure; Fuzzy variable; Fuzzy Lower partial moment; Fuzzy mean-Risk dominance; First credibilistic dominance; Second credibilistic dominance; crossing points.; crossing points (search for similar items in EconPapers)
Date: 2012-08-01
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