## 1 Introduction
Among these decision-making methods, the traditional overall ranking technique PROMETHEE attaches much importance to the evaluation information provided by experts and works on different types of criteria simultaneously, can be qualitative and quantitative, and needs much less inputs. What's more, among the whole PROMETHEE family, the PROMETHEE II ([PERSON] et al., 2017) has the capability of obtaining the complete ranking concerning several alternatives. Compared with other methods, the outstanding superiority of PROMETHEE II in the process of calculation lies in the simplicity of its comparative technique. Moreover, the PROMETHEE II has not been utilized in selecting green agricultural product supplier under q-ROF environment. By recognizing this, the PROMETHEE II was utilized to rank the feasible suppliers in this paper, then the enterprises could reasonably evaluate and choose the optimal supplier to cooperate. In the MCDM process, it is indispensable to determine each criterion weight, which also denotes the degree of relative importance. During the past few decades, fruitful efforts have focused on the introduction of deriving the criteria weights by means of different techniques. AHP was originally developed in [PERSON] (2018), which can be viewed as one of the most popular and common methods to determine the criteria weights. The method has the capability to solve subjective judgments and include multiple DMs in the decision-making situation. However, if the preference degree of option A to B cannot be properly depicted, abnormal phenomena will occur in the process of gaining the weights. In addition, among \(n\) criteria, normally \(n(n-1)/2\) comparisons are required to calculate the final weightings. That is, when the number of criteria increases dramatically, the calculation process will be tedious, as well as time consuming. Recently, aiming at the insufficiency in AHP, [PERSON] (2018) provided us a novel best-worst method (BWM), which only utilizes \(2n-3\) pairwise comparisons and has the capability to greatly improve the consistency of comparisons. The prominent characteristic of BWM is that the best and worst criterion should be identified before the process of comparison, and then we need to determine the preference degree of the most desirable criterion over others, as well as all other criteria over the least desirable criterion, and finally the weights concerning each criterion can be obtained by means of the model defined in [24]. Due to the simplicity of the method and the dependability of the obtained results, abundant studies have paid attention to utilize the BWM to derive each criterion weights, meanwhile, combining with other existing methods to rank the feasible alternatives or applying in the practical application. In [PERSON] [25], a BWM framework was presented for medical tourism development in Iran. However, the application of the above-mentioned technique ignores the significance of multiple DMs towards the evaluation results and cannot play the role of group decision making (GDM). Therefore, motivated by [PERSON] et al. [26], we constructed the group best-worst method (GBWM) under the q-ROF context with the comprehensive model by taking the DMs' weights into account to obtain the reasonable criteria weights for supplier selection. The motivation of this paper was to deal with the selection of green agricultural product supplier effectively by integrating GBWM method with the PROMETHEE II, which can obtain reasonable rankings of agricultural material suppliers, as well as consider the significance of different experts. Meanwhile, the PROMETHEE II was improved by combining the generalized p-norm knowledge measure of q-ROFS, which provides a comprehensive distance measure of q-ROFSs. Then, the detailed study was further developed by the following aspects:  
1. Based on the background of supplier selection in green agricultural industry, the q-ROFSs were utilized to express the assessment values of DMs, for the sake of giving DMs more flexibility and freedom.