Variances and Logarithmic Aggregation Operators: Extended Tools for Decision-Making Processes
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...
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MDPI AG
2021-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/16/1892 |
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| author | Rodrigo Gómez Monge Evaristo Galeana Figueroa Víctor G. Alfaro-García José M. Merigó Ronald R. Yager |
| author_facet | Rodrigo Gómez Monge Evaristo Galeana Figueroa Víctor G. Alfaro-García José M. Merigó Ronald R. Yager |
| author_sort | Rodrigo Gómez Monge |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T08:37:24Z |
| format | Article |
| id | doaj.art-baf55e0e9198455eadcd2f6c1b97db0f |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T08:37:24Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-baf55e0e9198455eadcd2f6c1b97db0f2023-11-22T08:33:29ZengMDPI AGMathematics2227-73902021-08-01916189210.3390/math9161892Variances and Logarithmic Aggregation Operators: Extended Tools for Decision-Making ProcessesRodrigo Gómez Monge0Evaristo Galeana Figueroa1Víctor G. Alfaro-García2José M. Merigó3Ronald R. Yager4Facultad de Economía “Vasco de Quiroga”, Universidad Michoacana de San Nicolás de Hidalgo, Morelia 58030, MexicoFacultad de Contaduría y Ciencias Administrativas, Universidad Michoacana de San Nicolás de Hidalgo, Morelia 58030, MexicoFacultad de Contaduría y Ciencias Administrativas, Universidad Michoacana de San Nicolás de Hidalgo, Morelia 58030, MexicoSchool of Information, Systems and Modelling, University of Technology Sydney, Utimo, NSW 2007, AustraliaMachine Intelligence Institute, Iona College, New Rochelle, NY 10801, USAVariance, 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.https://www.mdpi.com/2227-7390/9/16/1892OWA operatorGOWLA operatorvariance measuresvariance OWA |
| spellingShingle | Rodrigo Gómez Monge Evaristo Galeana Figueroa Víctor G. Alfaro-García José M. Merigó Ronald R. Yager Variances and Logarithmic Aggregation Operators: Extended Tools for Decision-Making Processes Mathematics OWA operator GOWLA operator variance measures variance OWA |
| title | Variances and Logarithmic Aggregation Operators: Extended Tools for Decision-Making Processes |
| title_full | Variances and Logarithmic Aggregation Operators: Extended Tools for Decision-Making Processes |
| title_fullStr | Variances and Logarithmic Aggregation Operators: Extended Tools for Decision-Making Processes |
| title_full_unstemmed | Variances and Logarithmic Aggregation Operators: Extended Tools for Decision-Making Processes |
| title_short | Variances and Logarithmic Aggregation Operators: Extended Tools for Decision-Making Processes |
| title_sort | variances and logarithmic aggregation operators extended tools for decision making processes |
| topic | OWA operator GOWLA operator variance measures variance OWA |
| url | https://www.mdpi.com/2227-7390/9/16/1892 |
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