Covariances with OWA operators and Bonferroni means
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METHODOLOGIES AND APPLICATION
Covariances with OWA operators and Bonferroni means Fabio Blanco-Mesa1
•
Ernesto Leo´n-Castro2 • Jose´ M. Merigo´3
Ó Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The covariance is a statistical technique that is widely used to measure the dispersion between two sets of elements. This work develops new covariance measures by using the ordered weighted average (OWA) operator and Bonferroni means. Thus, this work presents the Bonferroni covariance OWA operator. The main advantage of this approach is that the decision maker can underestimate or overestimate the covariance according to his or her attitudes. The article further generalizes this formulation by using generalized and quasi-arithmetic means to obtain a wide range of particular types of covariances, including the quadratic Bonferroni covariance and the cubic Bonferroni covariance. The paper also considers some other extensions by using induced aggregation operators in order to use complex reordering processes in the analysis. The work ends by studying the applicability of these new techniques to real-world problems and presents an illustrative example of a research and development (R&D) investment problem. Keywords Variance Covariance Bonferroni means OWA operator
1 Introduction In decision-making problems, it is common to use statistics and probabilistic measures to treat and analyze data and to obtain valid information about the data. These tools allow one to organize and condense the data set and to determine a specific property of a population based on a population sample. The use of these tools ensures that the measurement
Communicated by V. Loia. & Fabio Blanco-Mesa [email protected] Ernesto Leo´n-Castro [email protected] Jose´ M. Merigo´ [email protected] 1
Facultad de Ciencias Econo´micas y Administrativas, Escuela de Administracio´n de Empresas, Universidad Pedago´gica y Tecnolo´gica de Colombia, Av. Central del Norte, 39-115, Tunja 150001, Colombia
2
Faculty of Economics and Business Administration, Universidad Cato´lica de la Santı´sima Concepcio´n, Av. Alonso de Ribera 2850, 4070129 Concepcio´n, Chile
3
Department of Management Control and Information Systems, School of Economics and Business, University of Chile, Av. Diagonal Paraguay 257, 8330015 Santiago, Chile
and accounting data provide objective information. Among the most used procedures and measures are the frequency distribution; the average; measures of the central tendency, dispersion and others related to the probability; and test statistics with greater complexity. Nonetheless, statistics have limitations when capturing and explaining meaning of the information, as they include semantics, linguistic meanings, approximate reasoning, intuition and attitudes. These limitations occur because this sort of data does not support formal patterns and has a broad relationship with human behavior and subjectivity (Blanco-Mesa et al. 2017). Feasibly, measuring th
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