## 1 Introduction
Later, to depict the preference and evaluation information in a more comprehensive and accurate way, the extended form of FSs, namely IFSs and PFSs, have been proposed to deal with complicated decision-making information with fewer restrictions. However, the range of IFSs and PFSs is narrowed by the membership grades. Thus, DMs cannot flexibly depict their true evaluation or preference on the supplier selection. Recently, by combining the notion of the IFS with the q-rung negation, a novel information form of orthopair fuzzy sets (OFSs) with the name of q-rung OFSs (q-ROFSs) was proposed by [PERSON] [14]. Different from the existing IFSs and PFSs, the space of the MD and NMD of the q-ROFSs is larger and wider, as well as satisfying the restriction that the result summed by \(q\) power of the MD and NMD is equal or less than one [15]. We can easily find that as \(q\) gets larger, the practicable membership grade range also increases. Moreover, when the values of \(q\) are assigned by the number of one or two, respectively, the q-ROFSs degenerate to the ordinary IFSs or PFSs. That is, q-ROFSs is viewed as the generalized form  
Figure 1: The core operations of agricultural supply chain (ASC) [4]. of diverse existing OFSs. Therefore, as a general and forceful technique, the q-ROFSs have the capability of allowing the experts to depict their actual opinions and assessment information in a more flexible way with larger feasible MD and NMD under complicated decision-making cases. At the same time, many studies have focused on the application of q-ROFSs from various fields and multiple perspectives, including information measure, aggregation operators, decision-making methods, etc. For example, [PERSON] and [PERSON] (2016) presented us two aggregation operators, respectively based on averaging operator as well as geometric operator to tackle the q-ROF decision-making. Additionally, [PERSON] et al. (2015) provided us a q-ROFSs decision-making method based on another aggregation operator--Heronian mean operator, which can consider the interrelation among different criteria. Nevertheless, the q-ROFSs have not been studied in green agricultural product supplier selection, which largely limits the expression of DMs. Hence, for green agricultural product supplier selection issues, the q-ROFSs are utilized to depict the evaluation information by DMs, which ensures that the experts are more flexible and have fewer restrictions in describing their true opinions. In addition, in this paper, we found that both the commonly used score function and some improved forms to address q-ROFSs may result in some undesirable results. Then, as a feasible comparison solution to this issue, we propose a novel score function based on the notion of p-norm knowledge-based measure. As we all know, the MCDM method is widely applied in diverse fields ([PERSON] et al., 2017). Up to now, many classical decision-making techniques have studied tackling the supplier selection. For example, the technique of order preference by similarity of ideal solution (TOPSIS) ([PERSON] et al., 2017), preference ranking organization methods for enrichment evaluation (PROMETHEE) ([PERSON] et al., 2017), as well as some popular combined methods, such as the VIKOR based on DS theory ([PERSON] et al., 2017), and the integrated AHP and GRA ([PERSON] et al., 2017). In detail, the TOPSIS method ([PERSON] et al., 2017) considers the distance between each alternative and the positive and the negative ideal points comprehensively. Meanwhile, the PROMETHEE method ([PERSON] et al., 2017) is simplified and the calculation process is easy to understand. However, from the extensive literature on classical supplier assessment and selection, only comparatively few studies have focused on the green agricultural industry ([PERSON] et al., 2017).