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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.

For some specific multi-criteria decision-making (MCDM) problems, especially in emergency situations, because of the feature of criteria and other fuzzy factors, it is more appropriate that values of different criteria are expressed in their correspondingly appropriate value types. The purpose of this paper is to build a multi-criteria group decision-making (MCGDM) model dealing with heterogeneous information based on distance-based VIKOR to solve emergency supplier selection in practice appropriately and flexibly, where a compromise solution is more acceptable and suitable.

This paper extends the classical VIKOR to a generalized distance-based VIKOR to handle heterogeneous information containing crisp number, interval number, intuitionistic fuzzy number and hesitant fuzzy linguistic value, and develops an MCGDM model based on the distance-based VIKOR to handle the multi-criteria heterogeneous information in practice. This paper also introduces a parameter called non-fuzzy degree for each type of heterogeneous value to moderate the computation on aggregating heterogeneous hybrid distances.

The proposed distance-based model can handle the heterogeneous information appropriately and flexibly because the computational process is directly operated on the heterogeneous information based on generalized distance without a transformation process, which can improve the decision-making efficiency and reduce information loss. An example of emergency supplier selection is given to illustrate the proposed method.

This paper develops an MCGDM model based on the distance-based VIKOR to handle heterogeneous information appropriately and flexibly. In emergency supplier selection situations, the proposed decision-making model allows the decision-makers to express their judgments on criteria in their appropriate value types.

A problem of handling fuzzy quantities in a process of knowledge acquisition and deriving an inference mechanism by means of fuzzy relation equations is studied in extensive way. It is clearly pointed out that both of them are closely related and correspond to various types of fuzzy relation equations that are considered. Their relevance to the form of knowledge collected is also indicated. A problem of dimension reduction of a knowledge base is considered as well. Two modes of the use of the knowledge base (goal‐, and data‐driven) are also studied.

Accuracy is only part of the planner's mission; the other is knowing what to forecast in the first place. The best way to improve some forecasts, it seems, is to eliminate them.

This study aims to propose a framework for designing appropriate triangular fuzzy numbers in a fuzzy analytic hierarchy process (FAHP) for selecting a road freight transport route and investigate the appropriate fuzzy numbers determined from a reliable consensus among participating experts based on the Delphi method.

The fundamental nine-point scale was investigated and separated into nonfuzzy intervals for importance assessment. A total of 17 individual experts participated in this study, and their consensus was that appropriate fuzzy numbers could be obtained using a three-round Delphi process. Moreover, the appropriate fuzzy numbers were used instead of the primary fuzzy numbers to calculate the relative weights of the decision criteria for road freight route selection.

The results confirmed that the Delphi method can be easily and rigorously applied to define appropriate fuzzy numbers. Further, this framework can serve as a guideline for a situation wherein the input of other fuzzy multiple criteria decision-making tools must be provided.

The FAHP has been widely used to address the imprecise assessments of decision-makers. However, most existing studies on the incorporation of such techniques have not defined fuzzy numbers, which are relevant to the problem of interest. This study contributes by incorporating the Delphi method that can design an appropriate fuzzy number for road freight route selection.

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.

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.

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.