The First Moments and Semi-Moments of Fuzzy Variables Based on an Optimism-Pessimism Measure with Application for Portfolio Selection

Justin Dzuche, Christian Deffo Tassak, Jules Sadefo Kamdem and Louis Aimé Fono
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Justin Dzuche: Laboratory of Mathematics and Computer Science – Faculty of Sciences, University of Douala, B. P. 24157 Douala Cameroon
Christian Deffo Tassak: Laboratory of Mathematics and Computer Science – Faculty of Sciences, University of Douala, B. P. 24157 Douala Cameroon
Louis Aimé Fono: Laboratory of Mathematics and Computer Science – Faculty of Sciences, University of Douala, B. P. 24157 Douala Cameroon

New Mathematics and Natural Computation (NMNC), 2020, vol. 16, issue 02, 271-290

Abstract: Possibility, necessity and credibility measures are used in the literature in order to deal with imprecision. Recently, Yang and Iwamura [L. Yang and K. Iwamura, Applied Mathematical Science 2(46) (2008) 2271–2288] introduced a new measure as convex linear combination of possibility and necessity measures and they determined some of its axioms. In this paper, we introduce characteristics (parameters) of a fuzzy variable based on that measure, namely, expected value, variance, semi-variance, skewness, kurtosis and semi-kurtosis. We determine some properties of these characteristics and we compute them for trapezoidal and triangular fuzzy variables. We display their application for the determination of optimal portfolios when assets returns are described by triangular or trapezoidal fuzzy variables.

Keywords: Fuzzy measure; fuzzy variable; expected value; variance and semi-variance; skewness; kurtosis and semi-kurtosis; optimal portfolios (search for similar items in EconPapers)
Date: 2020
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Working Paper: The First Moments and Semi-Moments of Fuzzy Variables Based on an Optimism-Pessimism Measure with Application for Portfolio Selection (2020)
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DOI: 10.1142/S1793005720500167

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