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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.

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.

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.

Pharmaceutical supply chains (PSCs) need a well-operating and faultless logistics system to successfully store and distribute their medicines. Hospitals, health institutes, and pharmacies must maintain extra stock to respond requirements of the patients. Nevertheless, there is an inverse correlation between the level of medicine stock and logistics service level. The high stock level held by health institutions indicates that we have not sufficiently excellent logistics systems presently. As such, selecting appropriate logistics service providers (drug distributors) is crucial and strategic for PSCs. However, this is difficult for decision-makers, as highly complex situations and conflicting criteria influence such evaluation processes. So, a robust, applicable, and strong methodological frame is required to solve these decision-making problems.

To achieve this challenging issue, the authors develop and apply an integrated entropy-WASPAS methodology with Fermatean fuzzy sets for the first time in the literature. The evaluation process takes place in two stages, as in traditional multi-criteria problems. In the first stage, the importance levels of the criteria are determined by the FF-entropy method. Afterwards, the FF-WASPAS approach ranks the alternatives.

The feasibility of the proposed model is also supported by a case study where six companies are evaluated comprehensively regarding ten criteria. Herewith, total warehouse capacity, number of refrigerated vehicles, and personnel are the top three criteria that significantly influence the evaluation of pharmaceutical distribution and warehousing companies. Further, a comprehensive sensitivity analysis proves the robustness and effectiveness of the proposed approach.

The proposed multi-attribute decision model quantitatively aids managers in selecting logistics service providers considering imprecisions in the multi-criteria decision-making process.

A new model has been developed to present a sound mathematical model for selecting logistics service providers consisting of Fermatean fuzzy entropy and WASPAS methods. The paper's main contribution is presenting a comprehensive and more robust model for the ex ante evaluation and ranking of providers.

The objective of this paper is to present the employment of the new hierarchical fuzzy technique for order preference by similarity to ideal solution (TOPSIS) approach to evaluate the most suitable business process outsourcing (BPO) decision.

The paper explains the importance of selection criteria for evaluation of BPO. It then describes briefly the fuzzy hierarchical TOPSIS methodology. There then follows a discussion of the application of the fuzzy hierarchical TOPSIS with some sensitivity analysis to the BPO evaluation problem. Finally, some concluding remarks and perspectives are offered.

Use of the hierarchical fuzzy TOPSIS methodology offers a number of benefits. It is a more systematic method than the other fuzzy multi‐criteria decision‐making (FMCDM) methods and it is more capable of capturing a human's appraisal of ambiguity when complex multi‐criteria decision‐making problems are considered. The hierarchical fuzzy TOPSIS is superior to the other FMCDM methods, such as fuzzy analytic hierarchy process (FAHP) and classical fuzzy TOPSIS methods, since the hierarchical structure without making pairwise comparisons among criteria, sub‐criteria, and alternatives is considered. Hierarchical fuzzy TOPSIS is an excellent tool to handle qualitative assessments about BPO evaluation problems, and its calculations are faster than FAHP. Also, hierarchical fuzzy TOPSIS makes it possible to take into account the hierarchical structure in the evaluation model. However, there are drawbacks. The classical fuzzy TOPSIS is a highly complex methodology and requires more numerical calculations in assessing the ranking order of the alternatives than the hierarchical fuzzy TOPSIS methodology and hence it increases the effort, thus limiting its applicability to real world problems.

The proposed model will be very useful to managers in the manufacturing sector, as this method makes decision making easier, systematic, efficient and effective.

Supplier selection in the supply chain network (SCN) has strategic importance and involves multiple factors. The multi-criteria nature of the problem coupled with environmental uncertainty requires several procedures and considerations. The issue of decision-making in selecting the best among various qualified suppliers remains the major challenge in the pharmaceutical industry. This study investigated the multi-criteria multi-supplier decision-making process and proposed a model for supplier selection problems based on mixed-integer linear programming.

The concept of principal component analysis (PCA) was used to reduce data dimensionality, and the four best criteria have been considered and selected. The result is subjected to decision-makers’ (DMs’) reliability test using the concept of a triangular fuzzy number (TFN). The importance of each supplier to each measure is established using fuzzy technique for order preference by similarity to an ideal solution approach, and the suppliers have ranked accordingly.

This study proposes a mixed integer linear programming model for supplier selection in a pharmaceutical company. The effectiveness of the proposed model has been demonstrated using a numerical example. The solution shows the model's applicability in making a sound decision in pharmaceutical companies in the space of reality. The model proposed is simple. Readily commercial packages such as LINDO/LINGO and GAMS can solve the model.

This research contributed to the systematic manner of supplier selection considering DMs’ value judgement under a fuzzy environment and is limited to the case study area. However, interested researchers can apply the study in other related manufacturing industries. However, the criteria have to be revisited to suit that system and might require varying ratings based on the experts' opinions in that field.

This work suggests more insights practically by considering a realistic and precise investigation based on a real-life case study of pharmaceutical companies with six primary criteria and twenty-four sub-criteria. The study outcome will assist organizations and managers in conducting the best decision objectively by selecting the best suppliers with their various standards and terms among many available contenders in the manufacturing industry.

In this paper, the authors attempted to identify the most critical attributes to be preserved by the top managers (DMs) while selecting suppliers in pharmaceutical companies. The study proposed an MILP model for supplier selection in the pharmaceutical company using fuzzy TOPSIS.

The problem of evaluating potential suppliers has always been based on finding an optimal tradeoff between supplier’s performance consistently meeting firms’ needs and acceptable cost. The purpose of this paper is to propose a hybrid multi-criteria decision framework to quantify this qualitative judgment and reduce ambiguity in selection of suppliers in the era of Industry 4.0.

A hybrid intuitionistic fuzzy entropy weight-based multi-criteria decision model with TOPSIS is proposed. The authors make use of the intuitionistic fuzzy weighted approach operator for aggregating individual decision maker’s opinions regarding each alternative over every criterion. Additionally, the authors employ the concept of Shannon’s entropy to calculate the criteria weights.

Results obtained on the basis of the proposed hybrid methodology are analyzed against two more cases wherein the authors try to showcase the relevance of using IFS and entropy-based decision framework and find out the uniqueness of the proposed framework in supplier selection process.

The proposed model is apposite to solve management problem of supplier selection in two ways: aggregating individual decision maker’s opinion for each of the predefined criteria along with individual decision maker’s importance and ranking the suppliers based on both positive and negative ideal solutions using TOPSIS.

A robust framework incorporates not only suppliers’ performance but also provides weightage to key decision makers. Especially in the context of MCDMs wherein both qualitative and quantitative data is evaluated simultaneously, the proposed framework is unique in its practical implementation of reducing ambiguity in the supplier selection process.

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.

Project selection is a critical decision for any organization seeking to commission a large-scale construction project. Project selection is a complex multi-criteria decision-making problem with significant uncertainty and high risks. Fuzzy set theory has been used to address various aspects of project uncertainty, but with key practical limitations. This study aims to develop and apply a novel Pythagorean fuzzy sets (PFSs) approach that overcomes these key limitations.

The study is particular to complex project selection in the context of increasing interest in resilience as a key project selection criterion. Project resilience is proposed and considered in the specific situation of a large-scale construction project selection case study. The case study develops and applies a PFS approach to manage project uncertainty. The case study is presented to demonstrate how PFS is applied to a practical problem of realistic complexity. Working through the case study highlights some of the key benefits of the PFS approach for practicing project managers and decision-makers in general.

The PFSs approach proposed in this study is shown to be scalable, efficient, generalizable and practical. The results confirm that the inclusion of last aggregation and last defuzzification avoids the potentially critical information loss and relative lack of transparency. Most especially, the developed PFS is able to accommodate and manage domain expert expressions of uncertainty that are realistic and practical.

The main novelty of this study is to address project resilience in the form of multi-criteria evaluation and decision-making under PFS uncertainty. The approach is defined mathematically and presented as a six-step approach to decision-making. The PFS approach is given to allow multiple domain experts to focus more clearly on accurate expressions of their agreement and disagreement. PFS is shown to be an important new direction in practical multi-criteria decision-making methods for the project management practitioner.