Consensus In Group Decision-making Research Articles

Effect of three-stage cascade of opinion dynamics models in coupled networks

Information technology has contributed to the spread of public opinion across multiple coupled networks, and the scope of information spread has expanded. Owing to the impact of personal subjective cognition, information attenuation occurs during the process of opinion transmission in social networks, particularly in multi-layer social networks. In this paper, we construct a three-stage cascade opinion dynamics model, based on the Hegselmann–Krause (HK) model, to analyze the effect of information dissemination attenuation on group decision behavior in coupled social networks. This model considers three-stage cascade information transmission and two competitive opinion leader subgroups in two different social network environments, and can describe a public opinion dissemination environment more closely. The results show that the combination of the network structure and the level of trust of the public can effectively guide the spread of public opinion, which provides valuable insights into the role of social media in shaping public opinion and its impact on various fields. These findings can be useful for advertisers and policymakers to control public opinion and reach a consensus in group decision-making.

Humans strategically avoid connecting to others who agree and avert the emergence of network polarization in a coordination task

Clusters of like-minded individuals can impede consensus in group decision-making. We implemented an online color coordination task to investigate whether control over communication links creates clusters impeding group consensus. In 244 6-member networks, individuals were incentivized to reach a consensus by agreeing on a color, but had conflicting incentives for which color to choose. We varied (1) if communication links were static, changed randomly over time, or were player-controlled; (2) whether links determined who was observed or addressed; and (3) whether a majority existed or equally many individuals preferred each color. We found that individuals preferentially selected links to previously unobserved and disagreeing others, avoiding links with agreeing others. This prevented cluster formation, sped up consensus formation rather than impeding it, and increased the probability that the group agreed on the majority incentive. Overall, participants with a consensus goal avoided clusters by applying strategies that resolved uncertainty about others.

A Fuzzy-set based formulation for minimum cost consensus models

Minimum Cost Consensus (MCC) models are a popular approach to obtaining consensus in Group Decision-Making (GDM) problems, but previous extensions of these models have not been thoroughly analyzed in terms of their relationships and generalizability, which limits the practical application of these models. This paper presents a reformulation of MCC models for GDM problems using the Fuzzy Set Theory. The proposed fuzzy-based MCC (FZZ-MCC) framework offers a clearer understanding of MCC models and their extensions, as well as a rigorous and flexible methodology for addressing various types of GDM problems. The applicability of the FZZ-MCC framework is demonstrated through three practical examples related to e-democracy, personnel selection, and green supplier selection.

Consensus modeling with interactive utility and partial preorder of decision-makers, involving fairness and tolerant behavior

Reaching consensus in group decision-making (GDM) is usually achieved by minimizing opinion deviation (distance) or maximizing the utility of the group in traditional mathematical modeling. While the former ignores the preferences (individual values) of decision-makers (DMs), the latter is most often based on the implicit assumption that DMs are mutually independent, which results in the loss of a large amount of decision-making information about the actual interactions between DMs. Moreover, numerous studies on GDM did not pay enough attention to individual participation and satisfaction in the decision-making process. To overcome these defects, in this paper, we construct a new kind of consensus models for group utility optimization. We employ 2-additive Choquet integral to aggregate the utilities of individual DMs interacting pairwise. Linear programming is used to learn fuzzy measures (weights) that are consistent with a partial preorder of DMs. Moreover, we describe the coordinator's fairness preference and tolerant behavior with the help of Gini coefficient and orness operator, thus exploring the impacts of coordinator's psychological behaviors on consensus reaching. The orness operator of the Choquet integral is generalized to a particularly useful 2-additive form with Möbius representation. Finally, a comparative and parametric analysis is performed to illustrate and validate the proposed models on a case study concerning the price negotiation of medical insurance drugs.

Robust minimum cost consensus models with aggregation operators under individual opinion uncertainty

Individual opinion is one of the vital factors influencing the consensus in group decision-making, and is often uncertain. The previous studies mostly used probability distribution, interval distribution or uncertainty distribution function to describe the uncertainty of individual opinions. However, this requires an accurate understanding of the individual opinions distribution, which is often difficult to satisfy in real life. In order to overcome this shortcoming, this paper uses a robust optimization method to construct three uncertain sets to better characterize the uncertainty of individual initial opinions. In addition, we used three different aggregation operators to obtain collective opinions instead of using fixed values. Furthermore, we applied the numerical simulations on flood disaster assessment in south China so as to evaluate the robustness of the solutions obtained by the robust consensus models that we proposed. The results showed that the proposed models are more robust than the previous models. Finally, the sensitivity analysis of uncertain parameters was discussed and compared, and the characteristics of the proposed models were revealed.

Large-scale peer-to-peer loan consensus based on minimum cost consensus

Large-scale decision-making, which involves a large number of participants, is common in practical applications. While cost is a crucial factor in large- scale decision-making, research on minimum cost consensus in group decision-making are mainly focused on a small number of experts. The goal of this paper is to expand the application of minimum cost consensus models to large-scale decision-making problems, and provide an approach for modeling and optimizing the cost in large-scale decision-making. This paper randomly collected a sample of 103 loans from one of the leading U.S. peer-to-peer loan platforms-Lending Club, and constructed several loan consensuses models. The minimum cost of loan consensus and changes of borrowers’ group opinions under such scenarios were studied. In addition, we discussed the effects of different loan consensus levels on the adjustments of interest rates and the consensus costs. The results showed that the proposed models can help Lending Club improve the efficiency of loan consensus reaching, and increase the rate of return of lenders. The proposed models provide a new way to coordinate the funds supply and demand of large-scale peer-to-peer lending, and help lenders and borrowers to reach a certain level of consensus on interest rates.

Group decision support model based on sequential additive complementary pairwise comparisons

In group decision support systems, it is important on how to process and manage individual decision information. In the paper, a sequential model is proposed to manage individual judgements with additively reciprocal property over paired alternatives. The process of realizing additive complementary pairwise comparisons (ACPCs) is captured. A real-time feedback mechanism is constructed to address the irrational behavior of individuals. An optimization model is established and solved by using the particle swarm optimization (PSO) algorithm, such that the consistency of individual judgements can be improved fast yet effectively. For the aggregation of individual decision information in group decision making (GDM), the weighted averaging operator is used. It is found that when all individual judgements are acceptably additively consistent, the collective matrix is with acceptable additive consistency. Under the control of individual consistency degrees, the approach of reaching consensus in GDM is further proposed. By comparing with some existing models, the observations reveal that the sequential model of originating additive complementary pairwise comparisons possesses the ability to rationally manage individual decision information.

An optimisation-based method to conduct consistency and consensus in group decision making under probabilistic uncertain linguistic preference relations

The use of probabilistic uncertain linguistic preference relations (PULPRs) enriches the flexibility of decision makers (DMs) in group decision making (GDM). However, the GDM models under PULPRs are mainly focussed on the consensus reaching process rather than the individual consistent improvement. The goal of this paper is to manage the consistency and consensus in GDM based on PULPRs, and provide a feasible method for minimising the preference information loss by optimisation model. First, according to DMs’ psychological preferences (optimistic, pessimistic, and neutral characteristics), we proposed a conversion function to fit uncertain linguistic terms in PULPRs, which may be transformed into probabilistic linguistic preference relations. Second, to preserve as much as possible the original preference information of DMs, a consensus model based on optimisation is established, which not only obtains the acceptable group consensus but also guarantees that the consistency level of individuals is acceptable. Finally, we validated the proposed method through a case study of an investment project selection for central enterprises’ poverty alleviation fund. The proposed method provides a new way to deal with GDM problems under PULPRs, and help DMs to reach a certain level of consensus on basis of acceptable consistent level of individuals.

Iterative Algorithms to Manage the Consistency and Consensus for Group Decision-Making With Hesitant Multiplicative Preference Relations

In this article, we study how to manage the consistency and consensus in group decision-making (GDM) with hesitant multiplicative preference relations (HMPRs). First, an approach to develop the priority weight vector of an HMPR is presented. Then, the consistency index of an HMPR is defined for its consistency checking. Subsequently, we define an acceptable consistent HMPR and propose an iterative procedure to improve the consistency of an unacceptable consistent HMPR. As to the GDM with HMPRs, distance measures and proximity degrees are defined to derive the weights of the decision makers (DMs). Moreover, a consensus index is proposed for measuring the agreement degree of different DMs’ judgments, and an iterative approach is offered to implement the consensus reaching process. In the sequel, an algorithm to GDM with HMPRs is put forward. Two numerical examples are covered to highlight the merits of the proposed algorithms.

An Additive-Consistency- and Consensus-Based Approach for Uncertain Group Decision Making With Linguistic Preference Relations

Linguistic preference relations (LPRs) can indicate the decision makers (DMs)’ qualitative pairwise judgments regarding a set of alternatives in uncertain multicriteria decision-making problems. This paper examines several goal programming models for managing the additive consistency and consensus of LPRs and then develops an additive-consistency- and consensus-based method for group decision making (GDM) with LPRs. First, this paper offers a consistency index to quantify the consistency level for LPRs and define acceptable consistent LPRs. For an LPR that is unacceptably additive consistent, several additive-consistency-based programming models are developed to address the inconsistency and to establish an acceptably consistent LPR. Then, an additive-consistency-based procedure to generate the priority weight vector from the LPR is offered. An additive-consistency-based algorithm for decision making with an LPR is presented. Subsequently, considering the consensus in GDM, a consensus index is proposed for gauging the agreement degree among individual LPRs. Regarding individual LPRs that do not exhibit acceptably additive consistency or acceptable consensus, several goal programming models to derive new LPRs with acceptable consistency and consensus are provided. Afterward, the DMs’ weights are determined objectively, and individual LPRs are integrated into a collective LPR. An additive-consistency- and consensus-based GDM method with a group of LPRs is developed. Finally, two practical numerical examples are offered, and a comparative analysis is presented.

Soft consensus cost models for group decision making and economic interpretations

In a group decision-making (GDM) process, experts reach a consensus after discussion and persuasion, which requires a moderator to spend time and resource to persuade experts to change their original opinions. Since a unanimous agreement is hard to achieve and costly, a consensus degree or soft consensus was used and various approaches have been proposed to measure the level of consensus in GDM. Though cost is an important factor in GDM, few works have calculated consensus cost occurred during the process. Moreover, the degree of consensus was not considered in the minimum cost consensus study. The objective of this paper is to propose consensus models under a certain degree of consensus, which considers both consensus degree and cost in GDM. To do this, we develop a generalized soft cost consensus model under a certain degree of consensus, which is built by defining a consensus level function and a generalized aggregation operator. A soft minimum cost consensus model is constructed based on arithmetic weighted average operator (AWAO), and the maximum return model is constructed through its dual model. The cost (compensation) is studied from both the perspectives of a moderator and individual experts. The relationships between the two soft consensus cost models are analyzed, and the economic significance of the models are also discussed. Numerical examples are used to explain the proposed models. In addition, to show the usability of the proposed models in real-world context, we apply the proposed models to a loan consensus scenario using data from an online peer-to-peer lending platform.

Goal Programming Approaches to Managing Consistency and Consensus for Intuitionistic Multiplicative Preference Relations in Group Decision Making

Intuitionistic multiplicative preference relations (IMPRs), as an extension of multiplicative preference relations (MPRs), are suitable to capture hesitation and indeterminacy of the experts’ judgments. This paper aims to build several goal programming models to manage consistency and consensus of IMPRs and develop a consistency and consensus-based approach for dealing with group decision making (GDM) with IMPRs. First, the study offers a consistency index to quantify the consistency level for IMPRs as well as to define acceptably consistent IMPRs. For an IMPR, which is unacceptably consistent, several consistency-based programming models are developed to deal with the inconsistency and to establish an acceptable consistent IMPR. A consistency-based method to decision making with an IMPR is presented. Subsequently, considering the consensus in GDM, a consensus index is proposed for gauging the agreement degree among individual IMPRs. As to the individual IMPRs, which do not exhibit acceptable consistency or acceptable consensus, several goal programming models to derive new IMPRs with acceptable consistency and consensus are provided. Afterward, individual IMPRs are fused into a group IMPR by an aggregation operator that can guarantee the consistency of the obtained group IMPR. A consistency and consensus-based GDM method with a group of IMPRs is developed. Finally, two practical numerical examples are offered and a comparative analysis is presented.

Evaluation of a Third-Party Logistics (3PL) Provider Using a Rough SWARA–WASPAS Model Based on a New Rough Dombi Agregator

For companies active in various sectors, the implementation of transport services and other logistics activities has become one of the key factors of efficiency in the total supply chain. Logistics outsourcing is becoming more and more important, and there is an increasing number of third party logistics providers. In this paper, logistics providers were evaluated using the Rough SWARA (Step-Wise Weight Assessment Ratio Analysis) and Rough WASPAS (Weighted Aggregated Sum Product Assessment) models. The significance of the eight criteria on the basis of which evaluation was carried out was determined using the Rough SWARA method. In order to allow for a more precise consensus in group decision-making, the Rough Dombi aggregator was developed in order to determine the initial rough matrix of multi-criteria decision-making. A total of 10 logistics providers dealing with the transport of dangerous goods for chemical industry companies were evaluated using the Rough WASPAS approach. The obtained results demonstrate that the first logistics provider is also the best one, a conclusion confirmed by a sensitivity analysis comprised of three parts. In the first part, parameter ρ was altered through 10 scenarios in which only alternatives four and five change their ranks. In the second part of the sensitivity analysis, a calculation was performed using the following approaches: Rough SAW (Simple Additive Weighting), Rough EDAS (Evaluation Based on Distance from Average Solution), Rough MABAC (MultiAttributive Border Approximation Area Comparison), and Rough TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution). They showed a high correlation of ranks determined by applying Spearman’s correlation coefficient in the third part of the sensitivity analysis.

Consistency and consensus models for group decision-making with uncertain 2-tuple linguistic preference relations

Due to the uncertainty of the decision environment and the lack of knowledge, decision-makers may use uncertain linguistic preference relations to express their preferences over alternatives and criteria. For group decision-making problems with preference relations, it is important to consider the individual consistency and the group consensus before aggregating the preference information. In this paper, consistency and consensus models for group decision-making with uncertain 2-tuple linguistic preference relations (U2TLPRs) are investigated. First of all, a formula which can construct a consistent U2TLPR from the original preference relation is presented. Based on the consistent preference relation, the individual consistency index for a U2TLPR is defined. An iterative algorithm is then developed to improve the individual consistency of a U2TLPR. To help decision-makers reach consensus in group decision-making under uncertain linguistic environment, the individual consensus and group consensus indices for group decision-making with U2TLPRs are defined. Based on the two indices, an algorithm for consensus reaching in group decision-making with U2TLPRs is also developed. Finally, two examples are provided to illustrate the effectiveness of the proposed algorithms.

Analyzing Consensus Measures in Group Decision Making

Abstract In Group Decision Making (GDM) problems before to obtain a solution a high level of consensus among experts is required. Consensus measures are usually built using similarity functions measuring how close experts’ opinions or preferences are. Similarity functions are defined based on the use of a metric describing the distance between experts’ opinions or preferences. In the literature, die rent distance functions have been proposed to implement consensus measures. This paper presents analyzes the effect of the application of some die rent distance functions for measuring consensus in GDM. By using the nonparametric Wilcoxon matched-pairs signed-ranks test, it is concluded that die rent distance functions can produce significantly die rent results. Moreover, it is also shown that their application also has a significant elect on the speed of achieving consensus. Finally, these results are analyzed and used to derive decision support rules, based on a convergent criterion, that can be used to control the convergence speed of the consensus process using the compared distance functions.

A statistical comparative study of different similarity measures of consensus in group decision making

An essential aim in group decision making (GDM) problems is to achieve a high level of consensus among experts. Consensus is defined as general or widespread agreement, and it is usually modelled mathematically via a similarity function measuring how close experts’ opinions or preferences are. Similarity functions are defined based on the use of a metric describing the distance between experts’ opinions or preferences. In the literature, different metrics or distance functions have been proposed to implement in consensus models, but no study has been carried out to analyse the influence the use of different distance functions can have in the GDM process.This paper presents a comparative study of the effect of the application of some different distance functions for measuring consensus in GDM. By using the nonparametric Wilcoxon matched-pairs signed-ranks test, it is concluded that different distance functions can produce significantly different results. Moreover, it is also shown that their application also has a significant effect on the speed of achieving consensus. Finally, these results are analysed and used to derive decision support rules, based on a convergent criterion, that can be used to control the convergence speed of the consensus process using the compared distance functions.