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Variances and Logarithmic Aggregation Operators: Extended Tools for Decision-Making Processes

Author

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  • Rodrigo Gómez Monge

    (Facultad de Economía “Vasco de Quiroga”, Universidad Michoacana de San Nicolás de Hidalgo, Morelia 58030, Mexico)

  • Evaristo Galeana Figueroa

    (Facultad de Contaduría y Ciencias Administrativas, Universidad Michoacana de San Nicolás de Hidalgo, Morelia 58030, Mexico)

  • Víctor G. Alfaro-García

    (Facultad de Contaduría y Ciencias Administrativas, Universidad Michoacana de San Nicolás de Hidalgo, Morelia 58030, Mexico)

  • José M. Merigó

    (School of Information, Systems and Modelling, University of Technology Sydney, Utimo, NSW 2007, Australia)

  • Ronald R. Yager

    (Machine Intelligence Institute, Iona College, New Rochelle, NY 10801, USA)

Abstract

Variance, as a measurement of dispersion, is a basic component of decision-making processes. Recent advances in intelligent systems have included the concept of variance in information fusion techniques for decision-making under uncertainty. These dispersion measures broaden the spectrum of decision makers by extending the toolset for the analysis and modeling of problems. This paper introduces some variance logarithmic averaging operators, including the variance generalized ordered weighted averaging (Var-GOWLA) operator and the induced variance generalized ordered weighted averaging (Var-IGOWLA) operator. Moreover, this paper analyzes some properties, families and particular cases of the proposed operators. Finally, an illustrative example of the characteristic design of the operators is proposed using real-world information retrieved from financial markets. The objective of this paper is to analyze the performance of some equities based on the expected payoff and the dispersion of its elements. Results show that the equity payoff results present diverse rankings combined with the proposed operators, and the introduced variance measures aid decision-making by offering new tools for information analysis. These results are particularly interesting when selecting logarithmic averaging operators for decision-making processes. The approach presented in this paper extends the available tools for decision-making under ignorance, uncertainty, and subjective environments.

Suggested Citation

  • Rodrigo Gómez Monge & Evaristo Galeana Figueroa & Víctor G. Alfaro-García & José M. Merigó & Ronald R. Yager, 2021. "Variances and Logarithmic Aggregation Operators: Extended Tools for Decision-Making Processes," Mathematics, MDPI, vol. 9(16), pages 1-19, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1892-:d:611131
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    References listed on IDEAS

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    Cited by:

    1. Victor G. Alfaro-Garcia & Fabio Blanco-Mesa & Ernesto León-Castro & Jose M. Merigo, 2022. "Bonferroni Weighted Logarithmic Averaging Distance Operator Applied to Investment Selection Decision Making," Mathematics, MDPI, vol. 10(12), pages 1-13, June.

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