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Due to the increasing size and complexity of construction projects, construction engineering and management involves the coordination of many complex and dynamic processes and relies on the analysis of uncertain, imprecise and incomplete information, including subjective and linguistically expressed information. Various modelling and computing techniques have been used by construction researchers and applied to practical construction problems in order to overcome these challenges, including fuzzy hybrid techniques. Fuzzy hybrid techniques combine the human-like reasoning capabilities of fuzzy logic with the capabilities of other techniques, such as optimization, machine learning, multi-criteria decision-making (MCDM) and simulation, to capitalise on their strengths and overcome their limitations. Based on a review of construction literature, this chapter identifies the most common types of fuzzy hybrid techniques applied to construction problems and reviews selected papers in each category of fuzzy hybrid technique to illustrate their capabilities for addressing construction challenges. Finally, this chapter discusses areas for future development of fuzzy hybrid techniques that will increase their capabilities for solving construction-related problems. The contributions of this chapter are threefold: (1) the limitations of some standard techniques for solving construction problems are discussed, as are the ways that fuzzy methods have been hybridized with these techniques in order to address their limitations; (2) a review of existing applications of fuzzy hybrid techniques in construction is provided in order to illustrate the capabilities of these techniques for solving a variety of construction problems and (3) potential improvements in each category of fuzzy hybrid technique in construction are provided, as areas for future research.

Platform-based enterprises, as micro-entities in the platform economy, have the potential to effectively promote the low-carbon development of both supply and demand sides in the supply chain. Therefore, this paper aims to provide a multi-criteria decision-making method in a probabilistic hesitant fuzzy environment to assist platform-type companies in selecting cooperative suppliers for carbon reduction in green supply chains.

This paper combines the advantages of probabilistic hesitant fuzzy sets (PHFS) to address uncertainty issues and proposes an improved multi-criteria decision-making method called PHFS-DNMEREC-MABAC for aiding platform-based enterprises in selecting carbon emission reduction collaboration suppliers in green supply chains. Within this decision-making method, we enhance the standardization process of both the DNMEREC and MABAC methods by directly standardizing probabilistic hesitant fuzzy elements. Additionally, a probability splitting algorithm is introduced to handle probabilistic hesitant fuzzy elements of varying lengths, mitigating information bias that traditional approaches tend to introduce when adding values based on risk preferences.

In this paper, we apply the proposed method to a case study involving the selection of carbon emission reduction collaboration suppliers for Tmall Mart and compare it with the latest existing decision-making methods. The results demonstrate the applicability of the proposed method and the effectiveness of the introduced probability splitting algorithm in avoiding information bias.

Firstly, this paper proposes a new multi-criteria decision making method for aiding platform-based enterprises in selecting carbon emission reduction collaboration suppliers in green supply chains. Secondly, in this method, we provided a new standard method to process probability hesitant fuzzy decision making information. Finally, the probability splitting algorithm was introduced to avoid information bias in the process of dealing with inconsistent lengths of probabilistic hesitant fuzzy elements.

With numerous and ambiguous sets of information and often conflicting requirements, construction management is a complex process involving much uncertainty. Decision makers may be challenged with satisfying multiple criteria using vague information. Fuzzy multi-criteria decision-making (FMCDM) provides an innovative approach for addressing complex problems featuring diverse decision makers’ interests, conflicting objectives and numerous but uncertain bits of information. FMCDM has therefore been widely applied in construction management. With the increase in information complexity, extensions of fuzzy set (FS) theory have been generated and adopted to improve its capacity to address this complexity. Examples include hesitant FSs (HFSs), intuitionistic FSs (IFSs) and type-2 FSs (T2FSs). This chapter introduces commonly used FMCDM methods, examines their applications in construction management and discusses trends in future research and application. The chapter first introduces the MCDM process as well as FS theory and its three main extensions, namely, HFSs, IFSs and T2FSs. The chapter then explores the linkage between FS theory and its extensions and MCDM approaches. In total, 17 FMCDM methods are reviewed and two FMCDM methods (i.e. T2FS-TOPSIS and T2FS-PROMETHEE) are further improved based on the literature. These 19 FMCDM methods with their corresponding applications in construction management are discussed in a systematic manner. This review and development of FS theory and its extensions should help both researchers and practitioners better understand and handle information uncertainty in complex decision problems.

The main purpose of this study is to provide a comprehensive review and critical insights of the application of fuzzy methods in modeling, assessing and understanding the various aspects of green and sustainable supply chains (SSCs).

The present study conducts a systematic literature review (SLR) and bibliometric analysis of 252 research articles. This study employs various tools such as VOSviewer version 1.6.10, Publish or Perish, Mendeley and Excel that aid in descriptive analysis, bibliometric analysis and network visualization. These tools have been used for performing citation analysis, top authors' analysis, co-occurrence of keywords, cluster and content analysis.

The authors have divided the literature into seven application areas and discussed detailed insights. This study has observed that research in the social sustainability area, including various issues like health and safety, labor rights, discrimination, etc. is scarce. Integration of the Industry 4.0 technologies like blockchain, big data analytics, Internet of Things (IoT) with the sustainable and green supply chain (GSC) is a promising field for future research.

The authors' contribution primarily lies in providing the integrated framework which shows the changing trends in the use of fuzzy methods in the sustainability area classifying and consolidating green and sustainable supply chain management (SSCM) literature in seven major areas where fuzzy methods are predominantly applied. These areas have been obtained after the analysis of clusters and content analysis of the literature presenting key insights from the past and developing the conceptual framework for future research studies.

The decision-making to outsource and select the most suitable global manufacturing outsourcing partner (MOP) is complex and uncertain due to multiple conflicting qualitative and quantitative criteria as well as multiple alternatives. Vagueness and variability exist in ratings of criteria and alternatives by group of decision-makers (DMs). The paper provides a novel Stochastic Fuzzy (SF) method for evaluation and selection of agile and sustainable global MOP in uncertain and volatile business environment.

Four main selection criteria for global MOP selection were identified such as economic, agile, environmental and social criteria. Total 16 sub-criteria were selected. To consider the vagueness and variability in ratings by group of DMs, SF method using t-distribution or z-distribution was adopted. The criteria weights were determined using the Stochastic Fuzzy-CRiteria Importance Through Intercriteria Correlation (SF-CRITIC), while MOP selection was carried out using Stochastic Fuzzy-VIseKriterijumskaOptimizacija I KompromisnoResenje (SF-VIKOR) in the case study of footwear industry. Sensitivity analysis was performed to test the robustness of the proposed model. A comparative analysis of SF-VIKOR and VIKOR was made.

The worker’s wages and welfare, product price, product quality, green manufacturing process and collaboration with partners are the most important criteria for MOP selection. The MOP3 was found to be the best agile and sustainable global MOP for the footwear company. In sensitivity analysis, significance level is found to have important role in MOP ranking. Hence, the study concluded that integrated SF-CRITIC and SF-VIKOR is an improved method for MOP selection problem.

In a group decision-making, ambiguity, impreciseness and variability are found in relative ratings. Fuzzy variant Multi-Criteria Decision-Making methods cover impreciseness in ratings but not the variability. On the other hand, deterministic models do not cover either. Hence, the stochastic method based on the probability theory combining fuzzy theory is proposed to deal with decision-making problems in imprecise and uncertain environments. Most notably, the proposed model has novelty as it captures and reveals both the stochastic perspective and the fuzziness perspective in rating by group of DMs.

The proposed multi-criteria group decision-making model contributes to the sustainable and agile footwear supply chain management and will help the policymakers in selecting the best global MOP.

To the best of the authors’ knowledge, SF method has not been used to select MOP in the existing literature. For the first time, integrated SF-CRITIC and SF-VIKOR method were applied to select the best agile and sustainable MOP under uncertainty. Unlike other studies, this study considered agile criteria along with triple bottom line sustainable criteria for MOP selection. The novel method of SF assessment contributes to the literature and put forward the managerial implication for improving agility and sustainability of global manufacturing outsourcing in footwear industry.

The aim of this paper is to present a fuzzy centroid‐based method to ranking customer requirements with competition consideration. The proposed method not only focuses on normal fuzzy numbers, but also considers non‐normal fuzzy numbers to capture the true customer requirements.

This paper proposes a new customer requirements ranking method using QFD that not only focuses on the voice of the customer, but also considers the competitive environment. The method uses fuzzy mathematics instead of crisp numbers; this is known as the fuzzy centroid‐based method.

A numerical example demonstrates that if the fuzzy numbers are non‐normal, previous ranking methods were shown to be incorrect and to have led to some misapplications. To avoid possible further misapplications or spread in the future, the correct centroid formula used for fuzzy numbers is derived and their simplified expressions for non‐normal fuzzy numbers are given.

Various methods have been developed to rate and rank customer needs; however, few methods consider the competitive environment. In addition, in real applications, fuzzy mathematics are usually more appropriate than crisp models. Many previous methods are misleading and have led to some misapplications if the fuzzy numbers are non‐normal. The paper contributes to theory and practice by explaining the reasons for using the fuzzy centroid‐based method.

The control charts are used in many production areas because they give an idea about the quality characteristic(s) of a product. The control limits are calculated and the data are examined whether the quality characteristic(s) is/are within these limits. At this point, it may be confusing to comment, especially if it is slightly below or above the limit values. In order to overcome this situation, it is suitable to use fuzzy numbers instead of crisp numbers. The purpose of this paper is to demonstrate how to create control limits of X ¯ -R control charts for a specified data set of interval type-2 fuzzy sets.

There are methods in the literature, such as defuzzification, distance, ranking and likelihood, which may be applicable for interval type-2 fuzzy set. This study is the first that these methods are adapted to the X ¯ -R control charts. This methodology enables interval type-2 fuzzy sets to be used in X ¯ -R control charts.

It is demonstrated that the methods – such as defuzzification, distance, ranking and likelihood for interval type-2 fuzzy sets – could be applied to the X ¯ -R control charts. The fuzzy control charts created using the methods provide similar results in terms of in/out control situations. On the other hand, the sample points depicted on charts show similar pattern, even though the calculations are different based on their own structures. Finally, the control charts obtained with interval type-2 fuzzy sets and the control charts obtained with crisp numbers are compared.

Based on the related literature, research works on interval type-2 fuzzy control charts seem to be very limited. This study shows the applicability of different interval type-2 fuzzy methods on X ¯ -R control charts. For the future study, different interval type-2 fuzzy methods may be considered for X ¯ -R control charts.

The unique contribution of this research to the relevant literature is that interval type-2 fuzzy numbers for quantitative control charts, such as X ¯ -R control charts, is used for the first time in this context. Since the research is the first adaptation of interval type-2 fuzzy sets on X ¯ -R control charts, the authors believe that this study will lead and encourage the people who work on this topic.

In the past decades, artificial intelligence (AI)-based hybrid methods have been increasingly applied in construction risk management practices. The purpose of this paper is to review and compile the current AI methods used for cost-risk assessment in the construction management domain in order to capture complexity and risk interdependencies under high uncertainty.

This paper makes a content analysis, based on a comprehensive literature review of articles published in high-quality journals from the years 2008 to 2018. Fuzzy hybrid methods, such as fuzzy-analytical network processing, fuzzy-artificial neural network and fuzzy-simulation, have been widely used and dominated in the literature due to their ability to measure the complexity and uncertainty of the system.

The findings of this review article suggest that due to the limitation of subjective risk data and complex computation, the applications of these AI methods are limited in order to address cost overrun issues under high uncertainty. It is suggested that a hybrid approach of fuzzy logic and extended form of Bayesian belief network (BBN) can be applied in cost-risk assessment to better capture complexity-risk interdependencies under uncertainty.

This study only focuses on the subjective risk assessment methods applied in construction management to overcome cost overrun problem. Therefore, future research can be extended to interpret the input data required to deal with uncertainties, rather than relying solely on subjective judgments in risk assessment analysis.

These results may assist in the management of cost overrun while addressing complexity and uncertainty to avoid chaos in a project. In addition, project managers, experts and practitioners should address the interrelationship between key complexity and risk factors in order to plan risk impact on project cost. The proposed hybrid method of fuzzy logic and BBN can better support the management implications in recent construction risk management practice.

This study addresses the applications of AI-based methods in complex construction projects. A proposed hybrid approach could better address the complexity-risk interdependencies which increase cost uncertainty in project.

In this paper, the four popular multiple-criteria decision-making (MCDM) methods in fuzzy environment are utilized to reflect the vagueness and uncertainty on the judgments of decision-makers (DMs), because the crisp pairwise comparison in these conventional MCDM methods seems to be insufficient and imprecise to capture the right judgments of DMs. Of these methods, as Fuzzy analytic hierarchy process (F-AHP) is used to calculate criteria weights, the other methods; Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (F-TOPSIS), Fuzzy Grey relational analysis (F-GRA) and Fuzzy Preference Ranking Organization METhod for Enrichment of Evaluations (F- PROMETHEE II) are used to rank alternatives in the three different ways for a comparative study.

The demand for green products has dramatically increased because the importance and public awareness of the preservation of natural environment was taken into consideration much more in the last two decades. As a result of this, especially manufacturing companies have been forced to design more green products, resulting in a problem of how they incorporate environmental issues into their design and evaluate concept options. The need for the practical decision-making tools to address this problem is rapidly evolving since the problem turns into an MCDM problem in the presence of a set of green concept alternatives and criteria.

The incorporation of fuzzy set theory into these methods is discussed on a real-life case study, and a comparative analysis is done by using its numerical results in which the three fuzzy-based methods reveal the same outcomes (or rankings), while F-GRA requires less computational steps. Moreover, more detailed analyses on the numerical results of the case study are completed on the normalization methods, distance metrics, aggregation functions, defuzzification methods and other issues.

The designing and manufacturing environmental-friendly products in a product design process has been a vital issue for many companies which take care of reflecting environmental issues into their product design and meeting standards of recent green guidelines. These companies have utilized these guidelines by following special procedures at the design phase. Along the design process consisting of various steps, the environmental issues have been considered an important factor in the end-of-life of products since it can reduce the impact on the nature. In the stage of developing a new product with the aim of environmental-friendly design, the green thinking should be incorporated as early as possible in the process.

The case study was inspired from the previous work of the author, which was realized in a hot runner systems manufacturer, used in injection molding systems in a Canada. In a new product development process, the back- and front-ends of development efforts mainly determine the following criteria: cost, risk, quality and green used in this paper. The case study showed that the three fuzzy MCDM methods come to the same ranking outcomes. F-GRA has a better time complexity compared to the other two methods and uses a smaller number of computational steps. Moreover, a comparative analysis of the three F-MCDM methods; F-PROMETHEE II, F-TOPSIS and F-GRA used in ranking for green concept alternatives using the numerical results of the case study. For the case study; as seen in table 20, the three F-MCDM methods produced the numerical results on the rankings of the green concept alternatives as follows; {Concept A-Concept C–Concept B–Concept D}.

Inclusion of environmental-related criteria into concept selection problem has been gaining increasing importance in the last decade. Therefore, to facilitate necessary calculations in applying each method especially with its fuzzy extension, it can be developed a knowledge-based (KB) or an expert system (ES) to help the DMs make the required calculations of each method, and interpret its results with detailed analysis.

The objective of the research was to propose a F-AHP based F-MCDM approach to green concept selection problem through F-PROMETHEE II, F-TOPSIS and F-GRA methods. As the F-AHP is used to weight evaluation criteria, the other methods are respectively used for ranking the concept alternatives and determine the best concept alternative.

Risk assessment is a very important step toward managing risks in various organizations and industries. One of the most extensively applied risk assessment techniques is failure mode and effects analysis (FMEA). In this paper, a novel fuzzy multiple-criteria decision-making (MCDM)-based FMEA model is proposed for assessing the risks of different failure modes more accurately.

In this model, the weight of each failure mode is considered instead of risk priority number (RPN). Additionally, three criteria of time, cost and profit are added to the three previous risk factors of occurrence (O), severity (S) and detection (D). Furthermore, the weights of the mentioned criteria and the priority weights of the decision-makers calculated by modified fuzzy AHP and fuzzy weighted MULTIMOORA methods, respectively, are considered in the proposed model. A new ranking method of fuzzy numbers is also utilized in both proposed fuzzy MCDM methods.

To show the capability and usefulness of the suggested fuzzy MCDM-based FMEA model, Kerman Steel Industries Factory is considered as a case study. Moreover, a sensitivity analysis is conducted for validating the achieved results. Findings indicate that the proposed model is a beneficial and applicable tool for risk assessment.

To the best of authors’ knowledge, no research has considered the weights of failure modes, the weights of risk factors and the priority weights of decision-makers simultaneously in the FMEA method.