Bonferroni means with induced ordered weighted average operators

Blanco‐Mesa, Fabio; León‐Castro, Ernesto; Merigó, José M.; Zhang, Xu

doi:10.1002/int.22033

Cited by 35 publications

(18 citation statements)

References 52 publications

(79 reference statements)

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“…The OWA operator has been widely used in many fields, such as decision-making (Yager, 1993;Cutello & Montero, 1994), expert systems (O'Hagan, 1998), and market research (Yager et al, 1994). The OWA operator can obtain the optimal ordering of the alternatives according to the reordering steps of weighted vectors in the decision process of aggregation as follows (Chang & Cheng, 2011;Blanco-Mesa et al, 2019):…”

Section: Owamentioning

confidence: 99%

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Evaluation of Group Decision Making Based on Group Preferences Under a Multi-Criteria Environment

Zhang

Kou

2020

Technological and Economic Development of Economy

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Arrow’s impossibility theorem stated that no single group decision making (GDM) method is perfect, in other words, different GDM methods can produce different or even conflicting rankings. So, 1) how to evaluate GDM methods and 2) how to reconcile different or even conflicting rankings are two important and difficult problems in GDM process, which have not been fully studied. This paper aims to develop and propose a group decision-making consensus recognition model, named GDMCRM, to address these two problems in the evaluation of GDM methods under a multi-criteria environment in order to identify and achieve optimal group consensus. In this model, the ordinal and cardinal GDM methods are both implemented and studied in the process of evaluating the GDM methods. What’s more, this proposed model can reconcile different or even conflicting rankings generated by the eight GDM methods, based on empirical research on two real-life datasets: financial data of 12 urban commercial banks and annual report data of seven listed oil companies. The results indicate the proposed model not only can largely satisfy the group preferences of multiple stakeholders, but can also identify the best compromise solution from the opinion of all the participants involved in the group decision process.

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Section: Owamentioning

confidence: 99%

“…Definition 1: An n dimension OWA operator (Yager, 1988;Blanco-Mesa et al, 2019) can be a mapping : n F R R → , which has an associated n weighting vector…”

Section: Owamentioning

confidence: 99%

Evaluation of Group Decision Making Based on Group Preferences Under a Multi-Criteria Environment

Zhang

Kou

2020

Technological and Economic Development of Economy

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“…This operator has generated great interest in the scientific community, which has led to the development of various extensions where other methods are combined with the operator BON-OWA and Bonferroni means. Among these are the operators that combine distance measures Blanco-Mesa & Merigo-Lindahl, 2016;Blanco-Mesa, Merigó, & Kacprzyk, 2016;Merigó, Palacios-Marqués, & Soto-Acosta, 2017), linguistic variables (Dutta & Guha, 2015;Jiang & Wei, 2014;Liu, Rong, Chu, & Li, 2014), induced variables (Blanco-Mesa, León-Castro, & Merigó, 2018a;Blanco-Mesa, León-Castro, Merigó, & Xu, 2018b)uncertainty variables (Wei, Zhao, Lin, & Wang, 2013;Xu, 2012), intuitionisticmembership and non-membership functions- (Dutta & Guha, 2013;Y. He & Z.…”

Section: Uncertainty and Decision Makingmentioning

confidence: 99%

The Importance of Enterprise Risk Management in Large Companies in Colombia

Blanco‐Mesa

Rivera-Rubiano

Patiño-Hernandez

et al. 2019

Technological and Economic Development of Economy

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The main aim of this paper is to establish that essential aspects are determinant in the enterprise risk identification (ERI) and the existing interrelationship between each corporate risk goals, in the large companies of Colombia. Study proposes a parametric analysis and a non-parametric. The first uses correlation matrices for statistical analysis, a multiple linear regression statistical tools to identify that essential aspects are determinant in the (ERI). The second proposes a new aggregation called the Bonferroni Induced Ordered Weighted Average Adequacy Coefficient (BON-IHOWAAC) operator and Bonferroni Induced Ordered Weighted Average the Maximum and Minimum level (BON-IHOWAIMAM) to establish the existing interrelationship between each corporate risk goals using the risk management information and manager perception. Of the results obtained is highlighted that for all economic sectors; first, control measures are highlighted in the (ERI) and second, the goal with the greatest interrelationship for the other ones to be achieved is protect people. Finally, the study concludes with a holistic analysis of the importance that executive team gives to the management of risks from the prioritization of objectives and the use of tools for the treatment of information to improve the process of decisions-making in uncertain contexts.

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“…The BON‐IOWA operator is an operator that combines the function that captures the interrelationship between arguments of the Bonferroni means and the induced weighted vector of the IOWA operator. The definition is as follows.…”

Section: Owa and Iowa Operatormentioning

confidence: 99%

“…From Bonferroni means, has been proposed a great deal of extensions to solve multicriteria decision‐making, multiple criteria decision‐making, multiple attribute decision‐making, and group decision‐making . Consequently, within these propositions are introduced extensions in combination with the OWA operator, which are focused on linguistic variables, induced variables, distance measures, hybrid weighted distance and immediate weighted distance, and logarithmic . All these extensions have contributed to create new hybrid methods that configures an aggregation operator family.…”

Section: Introductionmentioning

confidence: 99%

Variances with Bonferroni means and ordered weighted averages

et al. 2019

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The variance is a statistical measure frequently used for analysis of dispersion in the data. This paper presents new types of variances that use Bonferroni means and ordered weighted averages in the aggregation process of the variance. The main advantage of this approach is that we can underestimate or overestimate the variance according to the attitudinal character of the decisionmaker. The work considers several particular cases including the minimum and the maximum variance and presents some numerical examples. The article also develops some extensions and generalizations by using induced aggregation operators and generalized and quasi-arithmetic means. These approaches provide a more general framework that can consider a lot of other particular cases and a complex attitudinal character that could be affected by a wide range of variables. The study ends with an application of the new approach in a business decision-making problem regarding strategic analysis in enterprise risk management. K E Y W O R D S asymmetric information, Bonferroni means, OWA operator, strategy decision-making, varianceStatistics is a science that collects, organizes, presents, analyzes, and interprets data to provide information to make decisions more effectively. Among its diverse applications is statistics applied to business and the economy, in which studies focus on descriptive statistics and statistical inference. On the one hand, descriptive statistics allows organizing, summarizing, and presenting data in an informative manner. On the other hand, statistical inference uses methods to describe or determine a specific property of a population based on a sample of it. For both approaches, it is important to highlight the origin of the data, which must be measurable and countable to be treated with different methods, allowing filtering to obtain objective information. Thus, statistics allows obtaining specific measures and conjectures about these. Among the most used procedures and measures are the frequency distribution (to organize the data), the average (the central location of a group of numeric data), measures of central tendency and dispersion (to observe the proximity of a set of data around the average) and other more complex measures related to probability and test statistics.However, statistics, although quite useful to describe, explain, and verify various phenomena within business and economic studies, is not able to capture nonnumerical aspects, such as semantics, linguistic meaning, approximate reasoning, intuition, and attitude. This is because these types of data do not follow formal patterns and largely respond to human behavior and subjectivity, which makes them more complex to measure. 1 Perhaps, this is the first difficulty in their mathematical treatment, as they try to measure with high-precision, data that in their nature have a high degree of complexity. According to Zadeh 2 human reasoning is related to possibility and uncertainty, which is different from probability, that is, high complexity is incompatibl...

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Bonferroni means with induced ordered weighted average operators

Cited by 35 publications

References 52 publications

Evaluation of Group Decision Making Based on Group Preferences Under a Multi-Criteria Environment

Evaluation of Group Decision Making Based on Group Preferences Under a Multi-Criteria Environment

The Importance of Enterprise Risk Management in Large Companies in Colombia

Variances with Bonferroni means and ordered weighted averages

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