Probabilistic dual hesitant fuzzy sets (PDHFSs) have good flexibility and integrity in expressing fuzzy and uncertain information. However, some crucial problems related to PDHFSs remain unsolved, such as how to define probabilistic dual hesitant fuzzy preference relations (PDHFPRs) and solve groupdecision-making (GDM) problems with PDHFPRs. This paper establishes the concept of PDHFPRs and investigates consensus-based GDM methods with PDHFPRs. First, a new distance measure is proposed to quantify the difference between two PDHFPRs, which does not increase the virtual elements of membership and non-membership degrees, and can contain all distance combination of membership and non-membership elements. Therefore, the distance calculation results are not affected by the subjectivity of decision-makers (DMs). Second, the consensus measures for PDHFPRs are proposed, which are effective tool to measure the consensus level among DMs. Moreover, two consensus-based GDM methods are proposed, which can improve the group consensus level for PDHFPRs by changing the PDHFPR with the worst consensus level or modifying the weights of DMs. Finally, the proposed methods are applied to the location selection of large-scale industrial solid waste treatment facilities. The comparison with existing methods illustrates the validity and feasibility of the proposed methods.

中文翻译：

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具有概率双犹豫模糊偏好关系的基于共识的群决策方法及其应用

概率对偶犹豫模糊集（PDHFSs）在表达模糊和不确定信息方面具有良好的灵活性和完整性。然而，与 PDHFS 相关的一些关键问题仍未解决，例如如何定义概率对偶犹豫模糊偏好关系 (PDHFPR) 和使用 PDHFPR 解决群体决策 (GDM) 问题。本文建立了 PDHFPR 的概念，并研究了基于共识的 GDM 方法与 PDHFPR。首先，提出了一种新的距离度量来量化两个PDHFPR之间的差异，该度量不增加隶属度和非隶属度的虚拟元素，并且可以包含隶属和非隶属元素的所有距离组合。因此，距离计算结果不受决策者（DM）主观性的影响。第二，提出了PDHFPRs的共识措施，这是衡量DMs共识水平的有效工具。此外，提出了两种基于共识的 GDM 方法，它们可以通过改变具有最差共识水平的 PDHFPR 或修改 DM 的权重来提高 PDHFPR 的群体共识水平。最后，将所提出的方法应用于大型工业固废处理设施的选址。与现有方法的比较说明了所提出方法的有效性和可行性。所提出的方法应用于大型工业固体废物处理设施的选址。与现有方法的比较说明了所提出方法的有效性和可行性。所提出的方法应用于大型工业固体废物处理设施的选址。与现有方法的比较说明了所提出方法的有效性和可行性。