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

Author

Listed:
  • 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)

  • Jules Sadefo Kamdem

    (#x2020;MRE EA 7491 (Université de Montpellier, France) and DFR SJE (Université de Guyane), Site Richter Avenue Raymond Dugrand, CS 79606, 34960 Montpellier Cedex 2, France)

  • Louis Aimé Fono

    (Laboratory of Mathematics and Computer Science – Faculty of Sciences, University of Douala, B. P. 24157 Douala Cameroon)

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.

Suggested Citation

  • Justin Dzuche & Christian Deffo Tassak & Jules Sadefo Kamdem & Louis Aimé Fono, 2020. "The First Moments and Semi-Moments of Fuzzy Variables Based on an Optimism-Pessimism Measure with Application for Portfolio Selection," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 16(02), pages 271-290, July.
    • Handle: RePEc:wsi:nmncxx:v:16:y:2020:i:02:n:s1793005720500167
    DOI: 10.1142/S1793005720500167
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