On Two Dominances of Fuzzy Variables based on a Parametric Fuzzy Measure and Application to Portfolio Selection with Fuzzy Return

Justin Dzuche, Christian Deffo Tassak, Jules Sadefo-Kamdem and Louis Aimé Fono ()
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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
Authors registered in the RePEc Author Service: Jules SADEFO KAMDEM

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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.

Keywords: Fuzzy variable; Parametric fuzzy measure; Generalized Firstorder dominance; Optiminism Dominance; Set of best portfolios (search for similar items in EconPapers)
Date: 2019
New Economics Papers: this item is included in nep-rmg and nep-upt
Note: View the original document on HAL open archive server: https://hal.umontpellier.fr/hal-02433438v1
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Published in [Research Report] WP MRE 2019.3, MRE - Montpellier Recherche en Economie. 2019

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