A new measure of consensus with reciprocal preference relations: The correlation consensus degree

González-Arteaga, Teresa; Calle, Rocío de Andrés; Chiclana, Francisco

doi:10.1016/j.knosys.2016.06.002

Cited by 66 publications

(33 citation statements)

References 65 publications

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“…Consensus degrees, which are based on distance functions, measure the actual agreement level in group decision making process [58], [59]. In general, consensus degrees can be divide into two categories [18]: (i) based on distances to the aggregated group/collective preference [60]; and (ii) based on pairwise distances between decision makers' preferences.…”

Section: A Determining the Consensus Degree At Three Levelsmentioning

confidence: 99%

A Personalized Consensus Feedback Mechanism Based on Maximum Harmony Degree

Cao

Chiclana

et al. 2021

IEEE Trans. Syst. Man Cybern, Syst.

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This article proposes a framework of personalized feedback mechanism to help multiple inconsistent experts to reach consensus in group decision making by allowing to select different feedback parameters according to individual consensus degree. The general harmony degree (GHD) is defined to determine the before/after feedback difference between the original and revised opinions. It is proved that the GHD index is monotonically decreasing with respect to the feedback parameter, which means that higher parameters values will result in higher changes of opinions. An optimisation model is built with the GHD as the objective function and the consensus thresholds as constraints, with solution being personalized feedback advices to the inconsistent experts that keep a balance between consensus (group aim) and independence (individual aim). This approach is, therefore, more reasonable than the unpersonalized feedback mechanisms in which the inconsistent experts are forced to adopt feedback generated with only consensus target without considering the extent of the changes acceptable by individual experts. Furthermore, the following interesting theoretical results are also proved: (1) the personalized feedback mechanism guarantees that the increase of consensus level after feedback advices are implemented; (2) the GHD by the personalized feedback mechanism is higher than that of the unpersonalized one; and (3) the personalized feedback mechanism generalises the unpersonalized one as it is proved the latter is a particular type of the former. Finally, a numerical example is provided to model the feedback process and to corroborates these results when comparing both feedback mechanism approaches.

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Section: A Determining the Consensus Degree At Three Levelsmentioning

confidence: 99%

A Personalized Consensus Feedback Mechanism Based on Maximum Harmony Degree

Cao

Chiclana

et al. 2021

IEEE Trans. Syst. Man Cybern, Syst.

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“…In Ref. , the Spearman's correlation coefficient is introduced as a measure of consensus in GDM problems modeled with FPRs. Following that results, with the aim of taking fuzzy separators into account when computing the similarity between fuzzy rankings, we introduce the Spearman's correlation coefficient for fuzzy rankings as an extension of the homonymous correlation coefficient for ordinal rankings defined in Ref.…”

Section: Similarity Between Fuzzy Rankingsmentioning

confidence: 99%

“…In fact the preference gap between 4 and 5 is wide in 1 and thin in 3 while the preference gap between 2 and 3 is thin in 1 and wide in 3 16. In Ref 40,. the Spearman's correlation coefficient is introduced as a measure of consensus in GDM problems modeled with FPRs.…”

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confidence: 94%

Fuzzy rankings for preferences modeling in group decision making

Capuano

Chiclana

Herrera‐Viedma

et al. 2018

Int. J. Intell. Syst.

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Although fuzzy preference relations (FPRs) are among the most commonly used preference models in group decision making (GDM), they are not free from drawbacks. First of all, especially when dealing with many alternatives, the definition of FPRs becomes complex and time consuming. Moreover, they allow to focus on only two options at a time. This facilitates the expression of preferences but let experts lose the global perception of the problem with the risk of introducing inconsistencies that impact negatively on the whole decision process. For these reasons, different preference models are often adopted in real GDM settings and, if necessary, transformation functions are applied to obtain equivalent FPRs. In this paper, we propose fuzzy rankings, a new approximate preference model that offers a higher level of user‐friendliness with respect to FPRs while trying to maintain an adequate level of expressiveness. Fuzzy rankings allow experts to focus on two alternatives at a time without losing the global picture so reducing inconsistencies. Conversion algorithms from fuzzy rankings to FPRs and backward are defined as well as similarity measures, useful when evaluating the concordance between experts’ opinion. A comparison of the proposed model with related works is reported as well as several explicative examples.

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“…Indeed, some researchers believe that coming to consensus plays a key role in group decision-making [1,2].…”

Section: Introductionmentioning

confidence: 99%

Using a Computational Approach for Generalizing a Consensus Measure to Likert Scales of Any Size n

Rahem

Darrah

2018

International Journal of Mathematics and Mathematical Sciences

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There are many consensus measures that can be computed using Likert data. Although these measures should work with any number n of choices on the Likert scale, the measurements have been most widely studied and demonstrated for n = 5. One measure of consensus introduced by Akiyama et al. for n = 5 and theoretically generalized to all n depends on both the mean and variance and gives results that can differentiate between some group consensus behavior patterns better than other measures that rely on either just the mean or just the variance separately. However, this measure is more complicated and not easy to apply and understand. This paper addresses these two common problems by introducing a new computational method to find the measure of consensus that works for any number of Likert item choices. The novelty of the approach is that it uses computational methods in -dimensional space. Numerical examples in three-dimensional (for n=6) and four-dimensional (for n=7) spaces are provided in this paper to assure the agreement of the computational and theoretical approach outputs.

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A new measure of consensus with reciprocal preference relations: The correlation consensus degree

Cited by 66 publications

References 65 publications

A Personalized Consensus Feedback Mechanism Based on Maximum Harmony Degree

A Personalized Consensus Feedback Mechanism Based on Maximum Harmony Degree

Fuzzy rankings for preferences modeling in group decision making

Using a Computational Approach for Generalizing a Consensus Measure to Likert Scales of Any Size n

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