The Dynamics of Consensus in Group Decision Making: Investigating the Pairwise Interactions between Fuzzy Preferences

Fedrizzi, Mario; Pereira, Ricardo Alberto Marques; Brunelli, Matteo

doi:10.1007/978-3-642-15976-3_10

Cited by 12 publications

(4 citation statements)

References 63 publications

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“…The case when experts' opinions are expressed by means of linguistic assessments has been extensively studied and it is worth mentioning the works of Ben-Arieh and Chen [12], Cabrerizo, Alonso and Herrera-Viedma [14], García-Lapresta, Pérez-Román [30], Herrera, Herrera-Viedma and Verdegay [36], Herrera-Viedma, et al [40], Pérez-Asurmendi and Chiclana [53] and Wu, Chiclana and Herrera-Viedma [65]. Finally, models to reach consensus where experts assess their preferences using different preference representation structures (preference orderings, utility functions, multiplicative preference relations and fuzzy preference relations) have also been studied and proposed by Dong and Zhang [23], Fedrizzi et al [26] and Herrera-Viedma, Herrera and Chiclana [39]. The problem of measuring and reaching consensus with intuitionistic fuzzy preference relations and triangular fuzzy complementary preference relations have also been covered in detail by Wu and Chiclana in [62,64].…”

Section: Consensus Measurement In the Literaturementioning

confidence: 99%

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

González-Arteaga

Calle

Chiclana

2016

Knowledge-Based Systems

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The achievement of a 'consensual' solution in a group decision making problem depends on experts' ideas, principles, knowledge, experience, etc. The measurement of consensus has been widely studied from the point of view of different research areas, and consequently different consensus measures have been formulated, although a common characteristic of most of them is that they are driven by the implementation of either distance or similarity functions. In the present work though, and within the framework of experts' opinions modelled via reciprocal preference relations, a different approach to the measurement of consensus based on the Pearson correlation coefficient is studied. The new correlation consensus degree measures the concordance between the intensities of preference for pairs of alternatives as expressed by the experts. Although a detailed study of the formal properties of the new correlation consensus degree shows that it verifies important properties that are common either to distance or to similarity functions between intensities of preferences, it is also proved that it is different to traditional consensus measures. In order to emphasise novelty, two applications of the proposed methodology are also included. The first one is used to illustrate the computation process and discussion of the results, while the second one covers a real life application that makes use of data from Clinical Decision-Making.

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Section: Consensus Measurement In the Literaturementioning

confidence: 99%

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

González-Arteaga

Calle

Chiclana

2016

Knowledge-Based Systems

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“…The endogenous definition of the interaction coefficients can be done in various ways. In the soft consensus model for the multiagent context-see Fedrizzi et al (1999Fedrizzi et al ( , 2007, and Fedrizzi et al (2008Fedrizzi et al ( , 2010)-the interaction coefficients v i j , with i = j, are defined by filtering the square difference values (x i − x j ) 2 with a decreasing sigmoid function σ (t) = 1/(1+e β (t−α) ). As a result, agents with similar opinions ((x i −x j ) 2 < α) interact strongly, whereas agents with dissimilar opinions ((x i − x j ) 2 > α) interact weakly.…”

Section: Introductionmentioning

confidence: 99%

Shapley and superShapley aggregation emerging from consensus dynamics in the multicriteria Choquet framework

Bortot

Pereira

Stamatopoulou

2020

Decisions Econ Finan

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We investigate a negotiation model for the progressive aggregation of interacting multicriteria evaluations. The model is based on a network of interacting criteria and combines the Choquet aggregation framework with the classical DeGroot's model of consensus linear dynamics. We consider a set N = {1, . . . , n} of interacting criteria whose single evaluations are expressed in some domain D ⊆ R. The pairwise interaction among the criteria is described by a complete graph with edge values in the open unit interval. In the Choquet framework, the interacting network structure is the basis for the construction of a consensus capacity μ, whose Shapley indices are proportional to the average degree of interaction between criterion i ∈ N and the remaining criteria j = i ∈ N . We discuss three types of linear consensus dynamics, each of which represents a progressive aggregation process towards a consensual multicriteria evaluation corresponding to some form of mean of the original multicriteria evaluations. All three models refer significantly to the notion of multicriteria context evaluation. In one model, the progressive aggregation converges simply to the plain mean of the original multicriteria evaluations, while another model converges to the Shapley mean of those original multicriteria evaluations. The third model, instead, converges to an emphasized form of Shapley mean, which we call superShapley mean. The interesting relation between Shapley and superShapley aggregation is investigated.

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“…The endogenous definition of the interaction coefficients can be done in various ways. For instance, in the soft consensus model -see Fedrizzi, Fedrizzi, and Marques Pereira [28,29], and Fedrizzi, Fedrizzi, Marques Pereira, and Brunelli [30,31] -the interaction coefficients v ij , with i = j, are defined by filtering the square difference values (x i − x j ) 2 with a decreasing sigmoid function σ(t) = 1/(1+e β(t−α) ). As a result, agents with similar opinions ((x i −x j ) 2 < α) interact strongly, whereas agents with dissimilar opinions ((x i − x j ) 2 > α) interact weakly.…”

Section: Introductionmentioning

confidence: 99%

Consensus dynamics, network interaction, and Shapley indices in the Choquet framework

2019

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We consider a set N = {1, ..., n} of interacting agents whose individual opinions are denoted by x i , i ∈ N in some domain D ⊆ R. The interaction among the agents is expressed by a symmetric interaction matrix with null diagonal and off-diagonal coefficients in the open unit interval. The interacting network structure is thus that of a complete graph with edge values in (0, 1).In the Choquet framework, the interacting network structure is the basis for the construction of a consensus capacity µ, where the capacity value µ(S) of a coalition of agents S ⊆ N is defined to be proportional to the sum of the edge interaction values contained in the subgraph associated to S. The capacity µ is obtained in terms of its 2-additive Möbius transform m µ , and the corresponding Shapley power and interaction indices are identified.We then discuss two types of consensus dynamics, both of which refer significantly to the notion of context opinion. The second type converges simply the plain mean, whereas the first type produces the Shapley mean as the asymptotic consensual opinion. In this way it provides a dynamical realization of Shapley aggregation.

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The Dynamics of Consensus in Group Decision Making: Investigating the Pairwise Interactions between Fuzzy Preferences

Cited by 12 publications

References 63 publications

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

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

Shapley and superShapley aggregation emerging from consensus dynamics in the multicriteria Choquet framework

Consensus dynamics, network interaction, and Shapley indices in the Choquet framework

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