Prioritized induced probabilistic operator and its application in group decision making

Pérez-Arellano, Luis Alessandri; León‐Castro, Ernesto; Avilés‐Ochoa, Ezequiel; Merigó, José M.

doi:10.1007/s13042-017-0724-2

Cited by 23 publications

(16 citation statements)

References 58 publications

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“…Among the aggregation operators, a common one that can obtain the maximum and minimum operator is the OWA operator devolved by Yager . Since it was developed, many extensions have been done, such as moving averages, induced operators, prioritized operators, distance operators, and many more. The definition is as follows.…”

Section: Owa and Iowa Operatormentioning

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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Section: Owa and Iowa Operatormentioning

confidence: 99%

Variances with Bonferroni means and ordered weighted averages

et al. 2019

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“…This operator is useful in group decision-making problems, where it considers prioritized criteria among the decision makers, a probability vector and an induced-ordered weighting vector. The definition is as follows [34]: Definition 3. A prioritized induced probabilistic OWA (PIPOWA) operator of dimension n is a mapping of IPOWA : R n xR n → R that has an associated weight vector w of dimension n, where w j ∈ [0, 1] and n j=1 w j = 1, so that…”

Section: Owa Operator and Main Extensionsmentioning

confidence: 99%

“…The aim of this paper is to present some new aggregation operators based on the Prioritized Induced Probabilistic Ordered Weighted Average Distance (PIPOWAD) operator. It is a new aggregation operator that introduces the Hamming distance into the PIPOWA operator [34]. The primary advantage of this new operator is that one formulation combines four different operators: 1) the Prioritized OWA (PrOWA) operator [39], that has developed different extension such as intuitionistic fuzzy prioritized OWA operator [37], hesitant fuzzy prioritized operators [5] and so on.…”

Section: Introductionmentioning

confidence: 99%

Government transparency measurement through prioritized distance operators

Avilés‐Ochoa

León‐Castro

Pérez-Arellano

et al. 2018

IFS

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The prioritized induced probabilistic ordered weighted average distance (PIPOWAD) has been developed. This new operator is an extension of the ordered weighted average (OWA) operator that can be used in cases where we have two sets of data that want to be compared. Some of the main characteristics of this new operator are: 1) Not all the decision makers are equally important, so the information needs to be prioritized, 2) The information has a probability to occur and 3) The decision makers can change the importance of the information based in an induced variable. Additionally, characteristics and families of the PIPOWAD operator are presented. Finally, an application of the PIPOWAD operator in order to measure government transparency in Mexico is presented.

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“…With economic and social development, the growth of data has become increasingly faster, and the decision-making process has become increasingly more complex owing to great concern about multiple criteria, objectives or targets of a conflicting nature. GDM under a multi-criteria environment aims to address this GDM problem, and supports preferential decision to select the most satisfactory alternatives which have multiple conflicting goals or criteria in a group (Ma et al, 2010;Pérez-Arellano et al, 2019).…”

Section: Introductionmentioning

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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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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Prioritized induced probabilistic operator and its application in group decision making

Cited by 23 publications

References 58 publications

Variances with Bonferroni means and ordered weighted averages

Variances with Bonferroni means and ordered weighted averages

Government transparency measurement through prioritized distance operators

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

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