Consensus Reaching Process Research Articles

The classification-based consensus in multi-attribute group decision-making

In multi-attribute group decision-making problem (MAGDM), the existing consensus reaching process (CRP) is to obtain a consensus ranking of alternatives. However, these CRPs contradict some real-life MAGDM problems in which decision-makers do not need to rank alternatives and hope to classify the alternatives into several groups instead. Thus, in this paper we propose a new CRP in MAGDM, called the classification-based consensus reaching process (CCRP). First, we present a feedback method with minimum adjustments to generate the optimal adjusted individual matrices via a 0–1 mixed linear programming model for CCRP. Subsequently, we develop the interactive consensus reaching process based on the feedback method with minimum adjustments in CCRP. Finally, a practical example from China Undergraduate Mathematical Contest in Modeling and a simulation analysis are conducted to demonstrate the validity of the proposed CCRP.

Sustainable building material selection: A QFD- and ELECTRE III-embedded hybrid MCGDM approach with consensus building

Industrialization and urbanization have led to the rapid development of the building industry. To alleviate the adverse impact on the environment, natural resources, health and comfort of inhabitants, sustainable principles have been incorporated into the design, construction, decoration, operation, and maintenance of buildings. Among all these endeavors, sustainable building material selection is diffusely regarded as the simplest and most essential way of achieving sustainability. To this end, this paper develops a novel hybrid multi-criteria group decision making model for sustainable building material selection under uncertainty. The information representation construction used for alternative-criteria assessments in this model is a brand-new notion called Basic Uncertain Linguistic Information, which is capable of handling the qualitative performance estimates as well as its partial reliability. Multiple stakeholders are usually responsible for sustainable building material selection, and therefore, the fact that multiple perspectives are involved in the collective decision-making efforts is revealed by a Consensus Reaching Process to reach a decision reflecting at least a majority-based agreement among them. The Quality Function Deployment-based approach to determining comprehensive importance ratings of assessment criteria is further proposed to take into account diversifying sustainable building material requirements from different stakeholders. Subsequently, the ELECTRE III methodology, which models the heterogeneity and non-compensation among assessment criteria as well as their qualitative essence, is introduced to determine the ultimate priorities of alternative sustainable building materials. Finally, sensitive and comparative analyses are performed to verify the advantages of the proposed model in comparison with several existing methodologies.

Defective alternatives detection-based multi-attribute intuitionistic fuzzy large-scale decision making model

This paper focuses on multi-attribute intuitionistic fuzzy large-scale decision making (LSDM) scenarios. The alternatives are described by attributes in the LSDM model. The decision failure may be caused by unqualified alternative being the final decision. To avoid this, we propose a Defective Alternative Detection-based multi-attribute intuitionistic fuzzy LSDM (DAD-LSDM) model. The model consists of two stages: the Defective Alternatives Detection (DAD) stage and the corresponding Intuitionistic Fuzzy Consensus Reaching Process (IF-CRP) stage. In the DAD stage, it is easy to recognize the defective alternatives by calculating the attributes’ scores and to accordingly improve them with the attributes against the corresponding alternatives. In the IF-CRP stage, by utilizing an intuitionistic fuzzy clustering method and similarity calculation, we detect and manage the potential non-cooperative decision makers to increase the consensus degree of the LSDM event. By implementing the DAD stage before the IF-CRP stage, we can avoid those excessively defective alternatives to be chosen and can also improve the quality of slightly defective alternatives. It not only decreases the risk of decision failure and improves the feasibility of the provided alternatives, but also guarantees the validity and scientificity of the following IF-CRP stage. With a numerical example, we show the DAD-LSDM model can well detect and classify the defective alternatives as well as improve the slightly defective alternatives. The decision makers finally reach a high consensus with detecting and managing the non-cooperative decision makers. The DAD-LSDM model is feasible and efficient in practice for the intuitionistic fuzzy LSDM scenarios.

A dynamic expert contribution-based consensus model for hesitant fuzzy group decision making with an application to water resources allocation selection

This research focuses on group decision making (GDM) under hesitant fuzzy condition. All experts (decision makers) are allowed to use hesitant fuzzy preference relations (HFPRs) to express their opinions. Subsequently, a dynamically expert contribution-based consensus model is developed for GDM with HFPRs. In the proposed method, a combination of a weight update model and a preference adjustment model is applied to consensus reaching processes (CRPs). In the weight update model, we propose to dynamically update experts’ weights according to their contributions in the CRPs. In the preference adjustment model, only the preferences which are far away from the expected values are modified, aiming to retain the experts’ original information as much as possible. Finally, the proposed model is applied to water resources allocation selection to show how it works in practice. And some comparisons and discussions are given to show the advantages of the proposed method.

Modeling the Social Influence in Consensus Reaching Process with Interval Fuzzy Preference Relations

Consensus process plays a prominent role in decision-making problems. In traditional way, experts with low consensus degree are asked to modify their opinions according to the given advices. However, in fact, experts neither simply adopt nor completely ignore the opinions of others. In general, experts will refer to other experts’ opinions to a certain extent and their opinions will evolve due to their interactions. The aim of this paper, therefore, is to propose a consensus model based on uncertain opinion evolution to model the influence between experts during the negotiation and communication process. Firstly, we construct an influence network among experts by taking both objective similarity degree and some subjective psychological traits into consideration. Secondly, a consensus model based on opinion evolution with interval fuzzy preference relations (IFPRs) is proposed. After identifying the incompatible preference with lower consensus degree, experts will modify their preferences according to the preference evolution under the influence network. Then, we prove that the reciprocity property maintains through the dynamic consensus reaching process, and a sufficient condition guaranteeing that the consensus can be reached in the influence network is derived. Furthermore, two nonlinear programming models are proposed to justify whether the IFPR satisfies the acceptable consistency and to calculate the priority vector of the IFPR, respectively. Finally, a case study and comparative analysis are made to illustrate the effectiveness of the proposed model.

Consensus evolution networks: A consensus reaching tool for managing consensus thresholds in group decision making

The consensus reaching process (CRP) is a critical part of group decision making (GDM). In order to explore the evolution of consensus, a new CRP tool is proposed based on consensus evolution networks (CENs). The CENs are built based on the consensus degrees among decision makers (DMs) and allow us to manage the consensus thresholds and its evolution. A new consensus index is introduced based on the structured and numerical aspects of the CENs. The new consensus index can not only deeply analyze the constitution of consensus, but also determine the weights of DMs. According to the clustering coefficient, the sensitive consensus threshold is identified and the sensitive consensus evolution network (SCEN) is built. Based on the complementary SCEN, a pairwise feedback adjustment method is proposed to improve consensus. Besides, the sparsity of the CENs can act as a reference to determine the agreed consensus thresholds, which is considered an important issue in traditional models. A numerical example is used to verify the usefulness of the proposed CRP tool. The numerical results show that the evolution of consensus can be clearly found based on CENs and the pairwise method can improve consensus in only four rounds.

Flexible Linguistic Expressions and Consensus Reaching With Accurate Constraints in Group Decision-Making.

Various linguistic expressions have been presented to model the flexibility of linguistic preference expressions and to support the consensus reaching in linguistic group decision-making (GDM). In this paper, we propose the concept of flexible linguistic expressions (FLEs) as a general linguistic preference expression format to improve the flexibility of the construction of complex linguistic expressions and the elicitation of linguistic preferences and, then, we develop a new linguistic GDM model with FLEs, referred to as FLE-based GDM (FLEGDM). In the FLEGDM, an FLE aggregation process with accurate constraints is developed to improve the quality (i.e., accuracy) of the collective result as well as guarantee the principle of minimum preference-loss through a mixed 0-1 linear programming model. Meanwhile, the consensus rules with minimum preference-loss are designed to support the consensus reaching process (CRS) in the FLEGDM. Finally, we present the detailed comparative analysis involving different linguistic GDM models to show the advantages of the FLEGDM.

A hybrid group decision making framework for achieving agreed solutions based on stable opinions

Polarization in a group’s opinions drives to disagreements and dissent among individuals, which make it harder to achieve group satisfactory decisions. Within Group Decision Making (GDM) problems to soften disagreements, lots of consensus reaching processes (CRPs) have been proposed to converge opinions but rarely consider the existing dynamic relationships among the experts. Meanwhile, Opinion Dynamics studies the evolution of opinions based on the relationships existing among the group members by using Social Network Analysis (SNA). In real-world GDM problems the application of CRPs alone may not be enough to achieve the desired level of agreement when there is too much dissent among experts. In this paper, a novel framework is proposed that hybridizes both the process of making closer opinions realized by CRPs and the evolving relationships among experts based on SNA. This new framework addresses when it might be impossible to achieve the agreement through CRPs, which tries to achieve a potential consensus considering that if opinions are too polarized, maybe different stable opinions states are still suitable and easier to achieve by applying a SNA together with the CRP. This framework is further analyzed through simulation experiments for demonstrating its validity and some properties.

Aggregation-Based Framework for Construction Risk Assessment with Heterogeneous Groups of Experts

Construction companies continuously seek to improve risk analysis techniques to determine the contingency of projects. Construction risk assessment relies on a group decision-making (GDM) process, in which a heterogeneous group of experts provides their opinions to determine the probabilities and impacts of project risks. In this paper, risk probabilities and impacts are expressed as linguistic terms, which are then represented by fuzzy sets to account for the uncertainty in these assessments. Current GDM processes help experts to obtain collective agreement through the use of a consensus-reaching process, which has several limitations, such as being a time-consuming procedure. The main contributions of this paper are to introduce a list of criteria and a set of metrics to evaluate risk-assessment expertise. Additionally, this paper discusses the development of a method for weighting the importance of experts’ opinions according to their expertise levels. This research will also serve to improve GDM processes in construction risk assessment by introducing a structured framework that combines assessments from a heterogeneous group of experts through aggregation.

Revisiting the Role of Hesitant Multiplicative Preference Relations in Group Decision Making With Novel Consistency Improving and Consensus Reaching Processes

In recent years, hesitant multiplicative preference relation (HMPR) has been a powerful means to represent the evaluation information of decision makers during the pairwise comparison concerning alternatives. As the important parts of group decision making (GDM) issues with HMPRs, the consistency improving and consensus reaching processes have been researched by many scholars; however, the existing approaches present several limitations, including defining the consistency index depend on the other HMPR instead of the original HMPR, improving the consistency and consensus levels of HMPRs independently, and that the high computational complexity of the existing iterative algorithms. To overcome these drawbacks, this paper proposes a mathematical programming model to improve the consistency and consensus levels of HMPRs, simultaneously. First, a consistency index according to multiplicative consistency is put forward to compute the consistency degree of normalized HMPR (NHMPR) after the normalization procedure. Second, a programming model by minimizing the difference between the original NHMPR and the revised NHMPR is developed to obtain the acceptably consistent NHMPR; then, a consistency-based method is constructed to solve the decision making problems with an HMPR. Third, considering the GDM issues, a consistency- and consensus-based programming model is established to obtain the acceptably consistent and consensus NHMPRs, in which the original evaluation information can remain as much as possible. Fourth, the normalized hesitant multiplicative weighted geometric operator is introduced to fuse the revised NHMPRs and an algorithm for GDM is proposed with novel consistency improving and consensus reaching processes. Finally, two numerical examples are applied to show the practicality and advantages of the proposed approaches.

A Self-Management Mechanism for Noncooperative Behaviors in Large-Scale Group Consensus Reaching Processes

In large-scale group decision making (GDM), noncooperative behavior in the consensus reaching process (CRP) is not unusual. For example, some individuals might form a small alliance with the aim to refuse attempts to modify their preferences or even to move them against consensus to foster the alliance's own interests. In this paper, we propose a novel framework based on a self-management mechanism for noncooperative behaviors in large-scale CRPs (LCRPs). In the proposed consensus reaching framework, experts are classified into different subgroups using a clustering method, and experts provide their evaluation information, i.e., the multicriteria mutual evaluation matrices (MCMEMs), regarding the subgroups based on subgroups’ performance (e.g., professional skills, cooperation, and fairness). The subgroups’ weights are dynamically generated from the MCMEMs, which are in turn employed to update the individual experts’ weights. This self-management mechanism in the LCRP allows penalizing the weights of the experts with noncooperative behaviors. Detailed simulation experiments and comparison analysis are presented to verify the validity of the proposed framework for managing noncooperative behaviors in the LCRP.

Consensus efficiency in group decision making: A comprehensive comparative study and its optimal design

Consensus reaching processes (CRPs) aim to help decision-makers achieve agreement regarding the solution to a common decision problem, and consequently play an increasingly important role in the resolution of group decision making (GDM) problems. To date, a large number of CRPs have been reported. However, there is a lack of a general framework and criteria to evaluate the efficiency of the different CRPs. This paper aims to fill this gap in the research literature on CRPs. To achieve this goal, firstly, a comprehensive review regarding the different approaches to CRP is reported, and a series of CRPs as the comparison objects are presented. Secondly, the following comparison criteria for measuring the efficiency of CPRs are proposed: the number of adjusted decision-makers, the number of adjusted alternatives, the number of adjusted preference values, the distance between the original and the adjusted preference information (adjustment cost), and the number of negotiation rounds required to reach consensus. Following this, a detailed simulation experiment is designed to analyze the efficiency of different CRPs under the mentioned different comparison criteria. Furthermore, new multi-stage optimization-based CRPs are also developed, which the simulation experiment shows to have better comprehensive consensus efficiency in different GDM settings.

Expertise-based consensus building for MCGDM with hesitant fuzzy linguistic information

The integration of a consensus reaching process (CRP) becomes paramount to make highly accepted group decisions in complex real-life multi-criteria group decision making (MCGDM) problems. Notwithstanding, existing CRPs for MCGDM do neither exhaustively analyse the diversity in decision makers’ expertise levels, nor they consider that (because of such diversity) individuals might exhibit distinct perceptions on the relative importance of evaluation criteria. In this study, we present a novel expertise-based consensus building model for MCGDM under a hesitant fuzzy linguistic setting. Firstly, an expertise identification approach is devised to objectively determine the expertise degree of each decision maker based on multiple features. The proposed approach allows to dynamically assigning importance weights to the decision makers’ opinions based on their expertise, as well as intelligently combining their individually elicited subjective and objective criteria weights into meaningful expertise-dependent combinative weights. Then, a CRP for MCGDM problems is introduced based on an improved consensus measurement process and an expertise-based feedback mechanism that provides a highly tailored, personalised means of direction rules to guide decision makers during the consensus building process. A numerical example is provided to illustrate the application of the CRP, and a detailed comparison analysis is presented to verify the validity and accuracy of this study’s proposal.

A Method Adjusting Consistency and Consensus for Group Decision-Making Problems with Hesitant Fuzzy Linguistic Preference Relations Based on Discrete Fuzzy Numbers

In each hesitant fuzzy linguistic preference relation, experts may express their opinions through comparison linguistic information combined with a discrete fuzzy number. In this paper, a hesitant fuzzy linguistic computational model based on discrete fuzzy numbers whose support is a subset of consecutive natural numbers is proposed, which enriches the flexibility of group decision-making. First, some main concepts related to discrete fuzzy numbers and an aggregation function of individual subjective linguistic preference relations are introduced. Then, a consistency measure is presented to check and improve the consistency in a given matrix. Further, in order to achieve the predefined degree of consensus and to arrive at the final result, a consensus-reaching process based on the interactive feedback mechanism is defined. Meanwhile, a revised formula is introduced to calculate the consistency and the degree of consensus in a preference relation matrix. Besides, an illustrative example and comparative analysis are conducted through the proposed calculation process and the optimization algorithm. Finally, the analysis on the threshold values is made to help the decision-maker determine critical consensus level. The proposed method can address both consistency and consensus, and the results confirmed the effectiveness of the proposed method and its potential use in the qualitative decision-making problems.

Consensus reaching in social network group decision making: Research paradigms and challenges

In social network group decision making (SNGDM), the consensus reaching process (CRP) is used to help decision makers with social relationships reach consensus. Many CRP studies have been conducted in SNGDM until now. This paper provides a review of CRPs in SNGDM, and as a result it classifies them into two paradigms: (i) the CRP paradigm based on trust relationships, and (ii) the CRP paradigm based on opinion evolution. Furthermore, identified research challenges are put forward to advance this area of research.

A large scale consensus reaching process managing group hesitation

Nowadays due to the social networks and the technological development, large-scale group decision making (LS-GDM) problems are fairly common and decisions that may affect to lots of people or even the society are better accepted and more appreciated if they agreed. For this reason, consensus reaching processes (CRPs) have attracted researchers attention. Although, CRPs have been usually applied to GDM problems with a few experts, they are even more important for LS-GDM, because differences among a big number of experts are higher and achieving agreed solutions is much more complex. Therefore, it is necessary to face some challenges in LS-GDM. This paper presents a new adaptive CRP model to deal with LS-GDM which includes: (i) a clustering process to weight experts’ sub-groups taking into account their size and cohesion, (ii) it uses hesitant fuzzy sets to fuse expert’s sub-group preferences to keep as much information as possible and (iii) it defines an adaptive feedback process that generates advice depending on the consensus level achieved to reduce the time and supervision costs of the CRP. Additionally, the proposed model is implemented and integrated in an intelligent CRP support system, so-called AFRYCA 2.0 to carry out this new CRP on a case study and compare it with existing models.

A novel consensus model for multi-attribute large-scale group decision making based on comprehensive behavior classification and adaptive weight updating

Consensus reaching process (CRP) has received increasing attention in recent years, as the demand for decision results with mutual agreement has greatly grown. With the current tendency to introduce e-democracy and public participation into decision making for public issues, decision makers from various backgrounds are more likely to encounter conflict when attempting to reach a consensus, especially under a multi-attribute large-scale group decision making framework. In order to improve the efficiency of the CRPs, different consensus models have been proposed. Specific patterns of behaviors presented by decision makers, such as non-cooperative behaviors and minority opinions, are also strictly supervised in these models. However, not every type of behaviors is specifically defined and given directed treatment, this includes the behavior of highly-weighted clusters, which may seriously bias group consensus. In this paper, we present a novel CRP model named uninorm-based comprehensive behavior classification (UBCBC) model with enhanced efficiency and rationality. First, a behavior classification model based on the calculation of a cooperative index and a non-cooperative index is proposed to classify three kinds of modification behaviors. Second, decision weights in the next iteration of the CRP are updated using a uninorm aggregation operator to reward or penalize the behaviors of clusters. Furthermore, a floating neutral element is introduced into the uninorm aggregation operator to lay stricter supervision upon highly-weighted clusters. Finally, an illustrative example and a numerical simulation are implemented to prove that this model is of high efficiency and feasibility.

A group decision support model based on incomplete hesitant fuzzy linguistic preference relations for mine disaster rescue

Owing to the uncertainty and complexity of decision-making environments, it is more suitable for decision makers (DMs) to express their preferences by means of hesitant fuzzy linguistic preference relation (HFLPR). Furthermore, incomplete assessments usually exist in complex decision-making problems because DMs lack knowledge related to the problem domain. This paper proposes a group decision-making (GDM) model based on incomplete HFLPRs. First, we review the additive consistency of HFLPR and introduce the concept of incomplete HFLPR. Second, two proposals are developed to supplement the missing elements of incomplete HFLPR. Third, an HFLPR is improved and developed into an additive HFLPR to obtain a rational result. Moreover, a consensus-reaching process is established to solve a GDM on the basis of the obtained consistent HFLPRs. Finally, to demonstrate the effectiveness of the results, the proposed model is applied to a mining disaster rescue attempt.

Failure Mode and Effects Analysis Considering Consensus and Preferences Interdependence

Failure mode and effects analysis is an effective and powerful risk evaluation technique in the field of risk management, and it has been extensively used in various industries for identifying and decreasing known and potential failure modes in systems, processes, products, and services. Traditionally, a risk priority number is applied to capture the ranking order of failure modes in failure mode and effects analysis. However, this method has several drawbacks and deficiencies, which need to be improved for enhancing its application capability. For instance, this method ignores the consensus-reaching process and the correlations among the experts’ preferences. Therefore, the aim of this study was to present a new risk priority method to determine the risk priority of failure modes under an interval-valued Pythagorean fuzzy environment, which combines the extended Geometric Bonferroni mean operator, a consensus-reaching process, and an improved Multi-Attributive Border Approximation area Comparison approach. Finally, a case study concerning product development is described to demonstrate the feasibility and effectiveness of the proposed method. The results show that the risk priority of failure modes obtained by the proposed method is more reasonable in practical application compared with other failure mode and effects analysis methods.

Consensus-reaching methods for hesitant fuzzy multiple criteria group decision making with hesitant fuzzy decision making matrices

Group decision making plays an important role in various fields of management decision and economics. In this paper, we develop two methods for hesitant fuzzy multiple criteria group decision making with group consensus in which all the experts use hesitant fuzzy decision matrices (HFDMs) to express their preferences. The aim of this paper is to present two novel consensus models applied in different group decision making situations, which are composed of consensus checking processes, consensus-reaching processes, and selection processes. All the experts make their own judgments on each alternative over multiple criteria by hesitant fuzzy sets, and then the aggregation of each hesitant fuzzy set under each criterion is calculated by the aggregation operators. Furthermore, we can calculate the distance between any two aggregations of hesitant fuzzy sets, based on which the deviation between any two experts is yielded. After introducing the consensus measure, we develop two kinds of consensus-reaching procedures and then propose two step-by-step algorithms for hesitant fuzzy multiple criteria group decision making. A numerical example concerning the selection of selling ways about ‘Trade-Ins’ for Apple Inc. is provided to illustrate and verify the developed approaches. In this example, the methods which aim to reach a high consensus of all the experts before the selection process can avoid some experts’ preference values being too high or too low. After modifying the previous preference information by using our consensus measures, the result of the selection process is much more reasonable.