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Most decision-making problems in construction are complex and difficult to solve, as they involve multiple criteria and multiple decision makers in addition to subjective uncertainties, imprecisions and vagueness surrounding the decision-making process. In many instances, the decision-making process is based on linguistic terms rather than numerical values. Hence, structured fuzzy consensus-reaching processes and fuzzy aggregation methods are instrumental in multi-criteria group decision-making (MCGDM) problems for capturing the point of view of a group of experts. This chapter outlines different fuzzy consensus-reaching processes and fuzzy aggregation methods. It presents the background of the basic theory and formulation of these processes and methods, as well as numerical examples that illustrate their theory and formulation. Application areas of fuzzy consensus reaching and fuzzy aggregation in the construction domain are identified, and an overview of previously developed frameworks for fuzzy consensus reaching and fuzzy aggregation is provided. Finally, areas for future work are presented that highlight emerging trends and the imminent needs of fuzzy consensus reaching and fuzzy aggregation in the construction domain.

The purpose of this paper is to construct an optimal resource reallocation model of the limited resource by a moderator for reaching the greatest consensus, and show how to reallocate the limited resources by using optimization methodology once the consensus opinion is reached. Moreover, this paper also devotes to theoretically exploring when or what is the condition that the group decision-making (GDM) system is stable; and when new opinions enter into the GDM, how the level of consensus changes.

By minimizing the differences between the individuals’ opinions and the collective consensus opinion, this paper constructs a consensus optimization model and shows that the objective weights of the individuals are actually the optimal solution to this model.

If all individual deviations of the decision makers (DMs) from the consensus balance each other out, the information entropy theorem shows this GDM is most stable, and economically each individual DM gets the same optimal unit of compensation. Once the consensus opinion is determined and each individual opinion of the DMs is under an acceptable consensus level, the consensus is still acceptable even if additional DMs are added, and the moderator’s cost is still no more than a fixed upper limitation.

The optimization model based on acceptable consensus is constructed in this paper, and its economic significance, including the theoretical and practical significance, is emphatically analyzed: it is shown that the weight information of the optimization model carries important economic significance. Besides, some properties of the proposed model are discussed by analyzing its particular solutions: the stability of the consensus system is explored by introducing information entropy theory and variance distribution; in addition, the effect of adding new DMs on the stability of the acceptable consensus system is discussed by analyzing the convergence of consensus level: it is also built up the condition that once the consensus opinion is determined, the consensus degree will not decrease even when additional DMs are added to the GDM.

The purpose of this paper is to propose a consensus method for multi-attribute group decision-making (MAGDM) problems based on preference-approval structure and regret theory, which can improve the efficiency of decision-making and promote the consensus level among individuals.

First, a new method to obtain the reference points based on regret theory and expert weighting method is proposed. Second, a consensus reaching method based on preference-approval structure is proposed. Then, an adjustment mechanism to further improve the consensus level between individuals is designed. Finally, an example of the assessment of elderly care institutions is used to illustrate the feasibility and effectiveness of the proposed method.

The feasibility and validity of the proposed method are verified by comparing with the advanced two-stage minimum adjustment method. The compared results show that the proposed method is more consistent with the actual situation.

This paper presents a consensus reaching method for MAGDM based on preference-approval structure, which considers the avoidance behaviors of individuals and reference points. Decision makers (DMs) can use this approach to rank and categorize alternatives while further increasing the level of consensus among them. This can further help determine the optimal alternative more efficiently.

A new MAGDM problem based on the combination of regret theory and individual reference points is proposed. Besides, a new method of obtaining experts' weights and a consensus reaching method for MAGDM based on preference-approval structure are designed.

The existing consensus reaching mechanisms ignore the influence of social triangle structure on the decision-makers’ (DMs') weights, and the consensus reaching process (CRP) fails to fully reflect the DMs' subjectivity and can be time consuming and costly. To solve these issues, a novel CRP for multi-criteria group decision-making (MCGDM) problems with intuitionistic grey linguistic numbers (IGLNs) is proposed in this paper.

First, a weight calculation method is proposed by analysing the triangle structure of DMs' social network and scale of adjacent nodes. Then, a consensus degree index based on three-level polygon area is defined and applied to identify the inconsistent DMs. Finally, the feedback mechanism based on particle swarm optimisation (PSO) algorithm under grey linguistic environment is developed, where subjective trust relationships in social network is utilised to determine the adjustment coefficient.

The advantages of the proposed method are highlighted by two practical applications of the evaluation of tunnel construction method and the selection of a hotel for the centralised isolation. Comparision analysis and numerical simulation are performed to reveal the effectiveness and applicability of the method.

The proposed model can not only reflect the effect of triangle structure in social network on DMs' weights, but also reduce the time and cost of decision-making.

The main contribution of this paper is to propose a new MCGDM model based on intuitionistic grey linguistic numbers, which can handle the problem of inconsistency of information more effectively.

The consensus opinion helps with the achievement of fairness of the decision process, especially when the new decision makers (DMs) are added into the group decision making (GDM). This paper aims to show by constructing consensus models that when some conditions are met, the consensus level does not decrease even when new DMs are invited to join the GDM (new opinions are added to the GDM).

This paper first constructs a deviation which is the difference between each two individual opinions. The smaller these differences are, the higher consensus degree (level) of the group. Then, a consensus optimization model based on individual differences (IDCO) is constructed by minimizing the aggregated deviations. Lastly, based on the optimization model, the condition of reaching a high level of consensus when new DMs are added into the GDM is discussed.

The discussion on the properties of the IDCO indicates that once the consensus with all DMs reaching an acceptable level, the consensus deviation degree decreases as the number of DMs increases when certain conditions are met, and the consensus level does not decrease even when new DMs join the GDM.

Practically, high-level consensus needs to be reached no matter how difficult it is when the new opinions are added into the GDM. To see how this end could be achieved, this paper takes the fuzzy preference relations as particular instances to investigate the conditions of consensus under which new DMs (opinions) are added into the GDM. The rather holistic analysis leads us to such a conclusion that the authors can replace this particular kind of preference, as used in the discussion, in many other cases by, for instance, multiplicative preference relation, linguistic preference relation, etc.

The purpose of this study is to build a consensus model of social network group decision-making (SNGDM) based on improved PageRank algorithm. By objectively and fairly measuring the evaluation ability of participants in the decision-making process, the authors can improve the fairness and authenticity of the weight solution of decision-makers (DM) in the decision-making process. This ensures the reliability of the final group consensus results.

This study mainly includes six parts: preference expression, calculation of DM's weight, preference aggregation, consensus measurement, opinion adjustment and alternative selection. First, Pythagorean fuzzy expression is introduced to express the preference of DMs, which expands the scope of preference expression of DMs. Second, based on the social network structure among DMs, the process of “mutual judgment” among DMs is increased to measure the evaluation ability of DMs. On this basis, the PageRank algorithm is improved to calculate the weight of DMs. This makes the process of reaching consensus more objective and fair. Third, in order to minimize the evaluation difference between groups and individuals, a preference aggregation model based on plant growth simulation algorithm (PGSA) is proposed to aggregate group preferences. Fourth, the consensus index of DMs is calculated from three levels to judge whether the consensus degree reaches the preset value. Fifth, considering the interaction of DMs in the social network, the evaluation value to achieve the required consensus degree is adjusted according to the DeGroot model to obtain the overall consensus. Finally, taking the group preference as the reference, the ranking of alternatives is determined by using the Pythagorean fuzzy score function.

This paper proposes a consensus model of SNGDM based on improved PageRank algorithm to aggregate expert preference information. A numerical case of product evaluation is introduced, and the feasibility and effectiveness of the model are explained through sensitivity analysis and comparative analysis. The results show that this method can solve the problem of reaching consensus in SNGDM.

Different DMs may have different judgment criteria for the same decision-making problem, and the angle and depth of considering the problem will also be different. By increasing the process of mutual evaluation of DMs, the evaluation ability of each DM is judged only from the decision-making problem itself. In this way, the evaluation opinions recognized by most DMs will form the mainstream of opinions, and the influence of corresponding DMs will increase. Therefore, in order to improve the fairness and reliability of the consensus process, this study measures the real evaluation ability of DMs by increasing the “mutual judgment” process. On this basis, the defect of equal treatment of PageRank algorithm in calculating the weight of DMs is improved. This ensures the authenticity and objectivity of the weight of DMs. That is to improve the effectiveness of the whole evaluation mechanism. This method considers both the influence of DMs in the social network and their own evaluation level. The weight of DMs is calculated from two aspects: sociality and professionalism. It provides a new method and perspective for the calculation of DM’s weight in SNGDM.

The purpose of this paper is to explore the conversation activities of design teams to negotiate task conflict and reach consensus.

Four case studies were conducted to analyse the conversation activities that teams use in the course of design projects.

The conversation activities that teams used to negotiate conflict and bring about consensus were identified. These conversation activities are associated with collaboration, communication and social skills enabling teams to engage in the high level of information exchange and negotiation that is required to manage task conflict. How they were used to negotiate conflict and help reach consensus is also discussed.

The findings from this research are based on a small number of participants; hence, it cannot be generalised without further study with larger groups. However, the questions this paper has raised can be generalised to other design tasks and groups.

The findings have implications for the management of design teams and teams working on complex unstructured problems both in industry and education. They highlight how conflict can be constructively managed to bring about consensus that integrates the knowledge and perspective of all team members.

The benefits of task conflict have been disputed in the literature. This research has identified the conversation activities that facilitate the constructive management of task conflict to bring about consensus that integrates the perspectives and knowledge of a team.

This study aims to construct a Weber point-based model to complete the visualization of preference aggregation in group decision-making problem, in which decision-makers are associated with trust relationship.

This study mainly comprises four parts: trust propagation, preference aggregation, opinion adjustment and alternative selection. Firstly, the incomplete trust between decision-makers is completed with trust transfer operators and propagation probability in trust propagation process. Secondly, a preference aggregation model based on Weber point is proposed to aggregate the group preference visually. Thirdly, opinions are adjusted to reach a consensus. Finally, the ranking of alternatives is determined by the correlation coefficient with the group preference as a reference.

The Weber point-based model proposed in this study can minimize the gap in the preference of alternatives between the group and all decision-makers, and realize the visualization of aggregation result. A case of plan selection is introduced to illustrate the feasibility and effectiveness of the proposed model.

By comparing the result with the weighted average-based preference aggregation method, the Weber point-based model proposed in this study can show the result of preference aggregation intuitively and improve group consensus.

The development of social networks enhances the interaction between people, which brings new challenges to the research of group decision-making (GDM). This study aims at the problem that the synergy and redundancy due to interaction among decision-makers are ignored in the previous GDM, a trust-enhanced consensus reaching model based on interaction among decision-makers with incomplete preferences is proposed.

Firstly, confidence level is introduced to improve the hesitation phenomenon that should be considered when calculating trust degree; Secondly, a new trust propagation operator is developed to deal with indirect trust relationships; Thirdly, trust degree is transformed into interaction index to quantify the synergy and redundancy in decision-making. Fuzzy capacities of decision-makers are used to replace traditional weights, and the final scores of alternatives are obtained through Choquet integral.

The proposed model using fuzzy capacity can reflect the synergy or redundancy among decision-makers and improve the accuracy of final ranking result and reduce the loss of information.

This study proposes a trust-enhanced consensus reaching model, which develops a new trust propagation operator to ensure the continuous attenuation of trust in propagation process. And the proposed model uses fuzzy capacity to improve the enhancement or attenuation on the scores of alternatives.

A successful process of design concept evaluation has positive influence on subsequent processes. This study aims to consider the evaluation information at multiple stages and the interaction among evaluators and improve the credibility of evaluation results.

This paper proposes a multi-stage approach for design concept evaluation based on complex network and bounded confidence. First, a network is constructed according to the evaluation data. Depending on the consensus degree of evaluation opinions, the number of evaluation rounds is determined. Then, bounded confidence rules are applied for the modification of preference information. Last, a planning function is constructed to calculate the weight of each stage and aggregate information at multiple evaluation stages.

The results indicate that the opinions of the evaluators tend to be consistent after multiple stages of interactive adjustment, and the ordering of design concept alternatives tends to be stable with the progress of the evaluation.

Updating preferences according to the bounded confidence rules, only the opinions within the trust threshold are considered. The attribute information of the node itself is inadequately considered.

This method addresses the need for considering the evaluation information at each stage and minimizes the impact of disagreements within the evaluation group on the evaluation results.