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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 attributes that influence the selection of applicants and the relevant crediting decisions are naturally distinguished by interactions and interdependencies. A new method of possibilistic discrimination analysis (MPDA) was developed for the second stage to address this phenomenon. The method generates positive and negative discrimination measures for each alternative applicant in relation to a particular attribute. The obtained discrimination pair reflects the interaction of attributes and represents intuitionistic fuzzy numbers (IFNs). For the aggregation of applicant's discrimination intuitionistic fuzzy assessments (with respect to attributes), new intuitionistic aggregation operators, such as AsP-IFOWA and AsP-IFOWG, are defined and studied. The new operators are certain extensions of the well-known Choquet integral and Yager OWA operators. The extensions, in contrast to the Choquet aggregation, take into account all possible interactions of the attributes by introducing associated probabilities of a fuzzy measure.

For optimal planning of investments distribution and decreasing of credit risks, it is crucial to have selected projects ranked within deeply detailed investment model. To achieve this, a new approach developed in this article involves three stages. The first stage is to reduce a possibly large number of applicants for credit, and here, the method of expertons is used. At the second stage, a model of improved decisions is built, which reduces the risks of decision making. In this model, as it is in multi-attribute decision-making (MADM) + multi-objective decision-making (MODM), expert evaluations are presented in terms of utility, gain, and more. At the third stage, the authors construct the bi-criteria discrete intuitionistic fuzzy optimization problem for making the most profitable investment portfolio with new criterion: 1) Maximization of total ranking index of selected applicants' group and classical criterion and 2) Maximization of total profit of selected applicants' group.

The example gives the Pareto fronts obtained by both new operators, the Choquet integral and Yager OWA operators also well-known TOPSIS approach, for selecting applicants and awarding credits. For a fuzzy measure, the possibility measure defined on the expert evaluations of attributes is taken.

The comparative analysis identifies the applicants who will receive the funding sequentially based on crediting resources and their requirements. It has become apparent that the use of the new criterion has given more credibility to applicants in making optimal credit decisions in the environment of extended new operators, where the phenomenon of interaction of all attributes was also taken into account.

The purpose of this paper is to present some dynamic hesitant fuzzy aggregation operators to tackle with the multi-period decision-making problems where all decision information is provided by decision makers in hesitant fuzzy information from different periods.

First, the notions and operational laws of the hesitant fuzzy variable are defined. Then, some dynamic hesitant fuzzy aggregation operators involve the dynamic hesitant fuzzy weighted averaging (DHFWA) operator, the dynamic hesitant fuzzy weighted geometric (DHFWG) operator, and their generalized versions are presented. Some desirable properties of these proposed operators are established. Furthermore, two linguistic quantifier-based methods are introduced to determine the weights of periods. Next, the paper extends the results to the interval-valued hesitant fuzzy situation. Furthermore, the authors develop an approach to solve the multi-period multiple criteria decision making (MPMCDM) problems. Finally, an illustrative example is given.

The presented hesitant fuzzy aggregation operators are very suitable for aggregating the hesitant fuzzy information collected at different periods. The developed approach can solve the MPMCDM problems where all decision information takes the form of hesitant fuzzy information collected at different periods.

The presented hesitant fuzzy aggregation operators and decision-making approach can widely apply to dynamic decision analysis, multi-stage decision analysis in real life.

The paper presents the useful way to aggregate the hesitant fuzzy information collected at different periods in MPMCDM situations.

The purpose of the development of the paper is to construct probabilistic interval-valued hesitant fuzzy Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) model and to improve some preliminary aggregation operators such as probabilistic interval-valued hesitant fuzzy averaging (PIVHFA) operator, probabilistic interval-valued hesitant fuzzy geometric (PIVHFG) operator, probabilistic interval-valued hesitant fuzzy weighted averaging (PIVHFWA) operator, probabilistic interval-valued hesitant fuzzy ordered weighted averaging (PIVHFOWA) operator, probabilistic interval-valued hesitant fuzzy weighted geometric (PIVHFWG) operator and probabilistic interval-valued hesitant fuzzy ordered weighted geometric (PIVHFOWG) operator to cope with multicriteria group decision-making (MCGDM) problems in an efficient manner.

(1) To design probabilistic interval-valued hesitant fuzzy TOPSIS model. (2) To improve some of the existing aggregation operators. (3) To propose the Hamming distance, Euclidean distance, Hausdorff distance and generalized distance between probabilistic interval-valued hesitant fuzzy sets (PIVHFSs).

The results of the proposed model are discussed in comparison with the aggregation-based method from the related literature and found the effectiveness of the proposed model and improved aggregation operators.

A case study concerning the healthcare facilities in public hospital is addressed.

The notion of the proposed distance measure is used as rational tool to extend TOPSIS model for probabilistic interval-valued hesitant fuzzy setting.

The purpose of this paper is to develop a new decision making method based on distance measures that uses the probabilistic weighted averaging (PWA) operator. The paper introduces the PWA distance (PWAD) operator. It is a new aggregation operator that uses probabilities, weighted averages (WAs) and distance measures. Some of its main properties and particular cases are studied such as the arithmetic weighted Hamming distance and the arithmetic probabilistic Hamming distance. An application in a group decision making problem concerning the selection of investment strategies is also presented.

The paper follows the aggregation operator literature by designing new aggregation operators based on the use of distance measures. Also an application in investment selection is developed.

The PWAD operator is presented. It permits to use distance measures with probabilities and WAs in the same formulation. Moreover, the paper also finds the PWA norm aggregation and implements them in a group decision making problem.

The PWAD operator can be applied in a wide range of problems including statistics, economics and engineering. The paper focuses on a multi‐person decision making application concerning the selection of the optimal investment strategies.

New aggregation operators by using distance measures are presented. Their main advantage is that they unify the WA with the probability. Thus, the paper considers distance measures that include subjective and objective information in the same formulation.

A flexible and realistic linguistic assessment approach is developed to provide a mathematical tool for synthesis and evaluation analysis of nuclear safeguards indicator information. This symbolic approach, which acts by the direct computation on linguistic terms, is established based on fuzzy set theory. More specifically, a lattice‐valued linguistic algebra model, which is based on a logical algebraic structure of the lattice implication algebra, is applied to represent imprecise information and to deal with both comparable and incomparable linguistic terms (i.e. non‐ordered linguistic values). Within this framework, some weighted aggregation functions introduced by Yager are analyzed and extended to treat these kinds of lattice‐value linguistic information. The application of these linguistic aggregation operators for managing nuclear safeguards indicator information is successfully demonstrated.

Single-valued neutrosophic sets (SVNSs) are efficient models to address the complexity issues potentially with three components, namely indeterminacy, truthness and falsity. Taking advantage of SVNSs, this paper introduces some new aggregation operators (AOs) for information fusion of single-valued neutrosophic numbers (SVNNs) to meet multi-criteria group decision-making (MCGDM) challenges.

Einstein operators are well-known AOs for smooth approximation, and prioritized operators are suitable to take advantage of prioritized relationships among multiple criteria. Motivated by the features of these operators, new hybrid aggregation operators are proposed named as “single-valued neutrosophic Einstein prioritized weighted average (SVNEPWA) operator” and “single-valued neutrosophic Einstein prioritized weighted geometric (SVNEPWG) operators.” These hybrid aggregation operators are more efficient and reliable for information aggregation.

A robust approach for MCGDM problems is developed to take advantage of newly developed hybrid operators. The effectiveness of the proposed MCGDM method is demonstrated by numerical examples. Moreover, a comparative analysis and authenticity analysis of the suggested MCGDM approach with existing approaches are offered to examine the practicality, validity and superiority of the proposed operators.

The study reveals that by choosing a suitable AO as per the choice of the expert, it will provide a wide range of compromise solutions for the decision-maker.

The purpose of this paper is to develop some 2-tuple linguistic aggregation operators based on Muirhead mean (MM), which is combined with multiple attribute group decision making (MAGDM) and applied the proposed MAGDM model for supplier selection under 2-tuple linguistic environment.

The supplier selection problem can be regarded as a typical MAGDM problem, in which the decision information should be aggregated. In this paper, the authors investigate the MAGDM problems with 2-tuple linguistic information based on traditional MM operator. The MM operator is a well-known mean type aggregation operator, which has some particular advantages for aggregating multi-dimension arguments. The prominent characteristic of the MM operator is that it can capture the whole interrelationship among the multi-input arguments. Motivated by this idea, in this paper, the authors develop the 2-tuple linguistic Muirhead mean (2TLMM) operator and the 2-tuple linguistic dual Muirhead mean (2TLDMM) operator for aggregating the 2-tuple linguistic information, respectively. Some desirable properties and special cases are discussed in detail. Based on which, two approaches to deal with MAGDM problems under 2-tuple linguistic information environment are developed. Finally, a numerical example concerns the supplier selection problem is provided to illustrate the effectiveness and feasibility of the proposed methods.

The results show that the proposed can solve the MAGDM problems within the context of 2-tuple linguistic information, in which the attributes are existing interaction phenomenon. Some 2-tuple aggregation operators based on MM have been developed. A case study of supplier selection is provided to illustrate the effectiveness and feasibility of the proposed methods. The results show that the proposed methods are useful to aggregate the linguistic decision information in which the attributes are not independent so as to select the most suitable supplier.

The proposed methods can solve the 2-tuple linguistic MAGDM problem, in which the interactions exist among the attributes. Therefore, it can be used to supplier selection problems and other similar management decision problems.

The paper develop some 2-tuple aggregation operators based on MM, and further present two methods based on the proposed operators for solving MAGDM problems. It is useful to deal with multiple attribute interaction decision-making problems and suitable to solve a variety of management decision-making applications.

The aim of this study as to find out an approach for emergency program selection.

The authors have generated six aggregation operators (AOs), namely picture fuzzy Yager weighted average (PFYWA), picture fuzzy Yager ordered weighted average, picture fuzzy Yager hybrid weighted average, picture fuzzy Yager weighted geometric (PFYWG), picture fuzzy Yager ordered weighted geometric and picture fuzzy Yager hybrid weighted geometric aggregations operators.

First of all, the authors defined the score and accuracy function for picture fuzzy set (FS), and some fundamental operational laws for picture FS using the Yager aggregation operation. After that, using the developed operational laws, developed some AOs, namely PFYWA, picture fuzzy Yager ordered weighted average, picture fuzzy Yager hybrid weighted average, PFYWG, picture fuzzy Yager ordered weighted geometric and picture fuzzy Yager hybrid weighted geometric aggregations operators, have been proposed along with their desirable properties. A decision-making (DM) approach based on these operators has also been presented. An illustrative example has been given for demonstrating the approach. Finally, discussed the comparison of the proposed method with the other existing methods and write the conclusion of the article.

To find the best alternative for emergency program selection.

This paper is focused on developing an integrated algorithmic approach named as data envelopment analysis and multicriteria decision-making (DEA-MCDM) for ranking decision-making units (DMUs) based on cross-efficiency technique and subjective preference(s) of the decision maker.

Self-evaluation in data envelopment analysis (DEA) lacks in discrimination power among DMUs. To fix this, a cross-efficiency technique has been introduced that ranks DMUs based on peer-evaluation. Different cross-efficiency formulations such as aggressive and benevolent and neutral are available in the literature. The existing ranking approaches fail to incorporate subjective preference of “one” or “some” or “all” or “most” of the cross-efficiency evaluation formulations. Therefore, the integrated framework in this paper, based on DEA and multicriteria decision-making (MCDM), aims to present a ranking approach to incorporate different cross-efficiency formulations as well as subjective preference(s) of decision maker.

The proposed approach has an advantage that each of the aggressive, benevolent and neutral cross-efficiency formulations contribute to select the best alternative among the DMUs in a MCDM problem. Ordered weighted averaging (OWA) aggregation is applied to aggregate final cross-efficiencies and to achieve complete ranking of the DMUs. This new approach is further illustrated and compared with existing MCDM approaches like simple additive weighting (SAW) and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) to prove its validity in real situations.

The choice of cross-efficiency formulation(s) as per subjective preference of the decision maker and different orness levels lead to different aggregated scores and thus ranking of the DMUs accordingly. The proposed ranking approach is highly useful in real applications like R and D projects, flexible manufacturing systems, electricity distribution sector, banking industry, labor assignment and the economic environmental performances for ranking and benchmarking.

To prove the practical applicability and robustness of the proposed integrated DEA-MCDM approach, it is applied to top twelve Indian banks in terms of three inputs and two outputs for the period 2018–2019. The findings of the study (1) ensure the impact of non-performing assets (NPAs) on the ranking of the selected banks and (2) are enormously valuable for the bank experts and policy makers to consider the impact of peer-evaluation and subjective preference(s) in formulating appropriate policies to improve performance and ranks of underperformed banks in competitive scenario.

To the best of the authors’ knowledge, this is the first study that has integrated both DEA and MCDM via OWA aggregation to present a ranking approach that can incorporate different cross-efficiency formulations and subjective preference(s) of the decision maker for ranking DMUs.