**1. Introduction**

Nowadays, with the increasingly global awareness of environmental responsibility, green production has already become the development orientation of industrial production for most manufacturing firms. Growing environmental concerns mean that it is necessary for manufacturing companies to be more concerned about green supply chain managemen<sup>t</sup> (GSCM) to reduce environmental pollution from industrial sectors [1]. The green supplier selection (GSS) is a critical link of GSCM, which can directly affect the sustainable development and performance of manufacturing enterprises [2]. GSS can be regarded as a multiple criteria group decision making (MCGDM) problem that involves many conflicting assessment criteria [3], such as cost, materials, recycling capacity, green competencies, green technology, and green certification. Essentially, the act of decision making is more complicated than in the traditional supplier selection since some environmental criteria need to be considered, and these criteria are qualitative in nature and the weights cannot be provided in advance [3,4]. Therefore, how to choose a suitable green supplier in GSCM has become a key strategic consideration.

Researchers have come up with and applied a range of multi-criteria decision making (MCDM) approaches for green supplier decision making problems [5,6]. To synthesize multiple qualitative or quantitative environmental criteria and obtain a clear evaluation result, some MCDM approaches based on precise information are used in green supplier decision making. Handfield et al. [7] evaluated the

environmental standards of green suppliers by using the analytic hierarchy process(AHP). Likewise, Lu et al. [8] used AHP to evaluate and coordinate green suppliers. Hsu and Hu [9] applied the the analytic network process(ANP) for GSS. Kuo et al. [10] integrated artificial neural network and MCDM approaches to GSS. Bai and Sarkis [11] came up with an analytical evaluation on the basis of rough set theory. Yeh and Chuang [12] introduced an optimal mathematical planning approach for selecting a green supplier. The ANP and radial basis function neural network approaches of choosing green suppliers for China chemical industries was proposed by Zhou et al [13]. Kuo et al. [14] integrated ANP with the data envelopment analysis (DEA) to evaluate green suppliers. A mathematical model based on DEA for choosing green suppliers was proposed by Jauhar et al. [15]. Dobos and Vörösmarty [16] used a DEA approach towards environmental issues. Freeman and Chen [17] designed an approach for GSS by combining technique for order preferenceby similarity to ideal solution (TOPSIS), the AHP model, and entropy approach. Hashemi et al. [18] combined the GSS approach with the ANP method. Yazdani et al. [19] recommended a novel integrated MCDM basis of selecting most suitable green suppliers. Liu et al. [20] expanded a linguistic group decision-making method in assessing big projects.

The major issue obstructing the ability to determine the right mathematical method for choosing a green supplier is the absence of the ability to handle uncertain and inadequate information which mostly happens in real-life conditions. In the practical problems of GSS, a grea<sup>t</sup> number of assessment detailed information is unknown, and additionally, several criteria are affected by uncertainty. Meanwhile, decision makers (DMs) usually cannot make completely reasonable judgements due to uncertain and ambiguous information. DMs judgments are usually uncertain and difficult to measure by exact numerical values, so a fuzzy set theory proposed by Zadeh [21] has become essential for solving the complications characterized by vagueness and imprecision. Recently, several studies have applied the typical MCDM methods to a range of fuzzy environments [22–25]. Chiou et al. [26] applied a fuzzy AHP for GSS in China electronic industries. Lee et al. [27] extended a fuzzy AHP decision model to identify GSS for high-tech industries. Tsai and Huang [28] came up with a fuzzy goal programming technique for GSS. Tuzkaya et al. [29] developed a hybrid fuzzy MCDM model, and Büyüközkan and Cifci [30] recommended a unique hybrid MCDM method to evaluate green suppliers base on reference [29]. Datta et al. [31] presented a VlseKriterijuska Optimizacija I Komoromisno Resenje (VIKOR) method together with the interval valued fuzzy set to choose the best green supplier. Shen et al. [32] presented a fuzzy MCDM as basis for selecting green supplier with linguistic preference. Wang and Chan [33] proposed the hierarchical fuzzy TOPSIS model to choose the green supplier. Cao et al. [34] presented a unique intuitionistic fuzzy judgment matrix integrated with the TOPSIS approach to define the subjective and objective weights in green supplier assessment and selection. Kannan et al. [35] utilized a fuzzy axiomatic design method to choose the most suitable green supplier. Hamdan and Cheaitou [36] proposed fuzzy TOPSIS and AHP methods to define preference weights of respective supplier and criterion. Guo et al. [37] developed a fuzzy MCDM method to solve the GSS in apparel manufacturing.

GSS is known as a MCGDM problem that involves both several interrelated evaluation criteria and several DMs behavior characters. Moreover, the complexity of MCGDM problems is increased when several DMs might be considered in assessment of the problems [38]. Tsui et al. [39] came up with a hybrid MCGDM method based on entropy and AHP to assess GSS problems in manufacturing enterprise. Based on group decision analysis, Darabi and Heydari [40] presented an interval-valued hesitant fuzzy ranking method for selecting green suppliers. Gitinavard et al. [41] developed a unique interval-valued hesitant fuzzy group outranking method for choosing green suppliers. Qin et al. [42] recommended a comprehensive MCGDM approach for GSS in interval type-2 fuzzy sets. Tang [43] employed the hesitant fuzzy Hamacher power weighted average operator to solve the GSS complexities with hesitant fuzzy information.

As evidently shown in the above reviewed literature, various MCDM methods for GSS have been extended to intuitionistic fuzzy sets [44], linguistic fuzzy sets [32], interval-valued fuzzy sets, and type-2 fuzzy sets [31,42]. However, little study has been done on GSS by using a hesitant fuzzy set (HFS), which was first introduced by Torra [45,46]. As a generalization of fuzzy sets, HFS can describe the situations that permit the expert's preference judgment for a particular criterion that have few different values, which is a very suitable method for tackling uncertain information and for expressing DMs' hesitancy in real group decision making [47–49]. Nowadays, to be able to solve the MCGDM problems, varieties of extensions of the HFS have been proposed by scholars, such as generalized HFS, dual hesitant fuzzy sets, hesitant fuzzy linguistic term sets, the higher order HFS, and NaP-HFS [50–56].

However, the HFS method has its own shortcomings, because it only expresses the expert's judgment as several probable values lack considerations of their importance. In several applied MCGDM problems, especially in GSS, experts usually come from the same field, and might often make the same judgments on a given criterion. Thus, the possible value repeated many times is more significant than that displayed only one time. For this reason, Zhang and Wu [57] developed the model of weighted hesitant fuzzy set (WHFS), in which the importance of possible values provided by DMs has been considered. Farhadinia and Xu [58] modified the definition of WHFS and proposed a new extension of HFS as the ordered weighted hesitant fuzzy set (OWHFS), in which the importance of DMs' judgments is defined as the repetition rate of the possible values. Therefore, OWHFS can not only express the experts' judgments as several possible values but also give the importance of each possible value.

Besides the importance of DMs' judgments, the priority relationship among criteria of GSS selection for OWHFS is one of the most critical research topics at present. To be able to aggregate the evaluation values of criteria for an alternative, Yager [59] first presented a prioritized scoring operator and prioritized average (PA) operator. Recently, several studies have concentrated on aggregation operators for HFS and their application in MCDM. Xia and Xu [60] investigated a series of aggregation operators for hesitant fuzzy information. Wei [61] developed hesitant fuzzy prioritized operators. Qua et al. [62] examined induced generalized dual hesitant fuzzy Shapley hybrid operators. Wei et al. [63] utilized Pythagorean hesitant fuzzy Hamacher aggregation operators. Farhadinia and Xu [58] first presented several aggregation operators for OWHFS and used them for MCDM. However, as far as we know, the priority relationship among criteria for OWHFS has rarely been investigated.

Moreover, by reviewing the existing literature, the criteria of GSS can usually be classified into two categories: General and green criteria [64,65]. Generally, organizations consider criteria such as cost, quality, and delivery performance when evaluating supplier performance. However, due to enterprises facing double pressures of environmental laws and regulations and the increasing demands of environmental protection, environmental performance is considered by many enterprises in selecting suppliers. To solve the complexity of GSS problems in practice, the criteria of green supplier evaluation were studied by scholars. For instance, Lee et al. [27] mentioned that quality, technology capability, environment management, and green competencies are the most commonly referred criteria in green supplier evaluation literature. Yeh and Chuang [12] developed assessment criteria for GSS such as green image, product recycling, green design, green supply chain management, pollution treatment cost, and environment performance assessment criteria. A summary of the most critical standards for GSS are shown in Table 1.

In summary, the concept of GSS is a typical MCGDM problem, of which there are two critical issues of concern. The first issue depicts the importance of DMs' judgments. Another is mathematically expressing the priority relationship among criteria. The focus of this study is to develop a novel group decision making approach with ordered weighted hesitant fuzzy information for GSS that addresses both of the above problems.

The remainder of this study is established as follows: Section 2 briefly introduces the basic principles of OWHFS and the PA operator. Section 3 develops the generalized ordered weighted hesitant fuzzy prioritized weighted average (GOWHFPWA) operator and investigates its desirable properties. Section 4 proposes a novel MCGDM method for GSS with a GOWHFPWA operator. Section 5 presents a numerical example of GSS to demonstrate the superiority and effectiveness of the

proposed approach. Section 6 provides performance analysis and comparison, including sensitivity and validity analysis of the proposed approach. Finally, conclusions and recommendations are discussed in Section 7.


**Table 1.** Key criteria for green supplier selection.
