Distribution linguistic preference relations (DLPRs) that model linguistic expressions with the aid of probabilistic distributions of multiple linguistic terms provide an effective tool to accurately elicit the preferences of decision makers (DMs) in linguistic decisions. Meanwhile, numerical scale models have been suitable choices for DMs to handle computing with words when solving linguistic decision problems. This study focuses on improving the group decision making (GDM) with DLPRs via the help of numerical scale models by filling the following gap. It is obvious that words might exhibit different meanings for different people. DMs may have a varying understanding of a given linguistic term in real-world fuzzy linguistic GDM. Setting personalized semantics of the linguistic terms for each DM becomes a critical task in GDM with DLPRs. To do this, we first define an improved numerical scale model to facilitate the linkages between DLPRs and numerical fuzzy preference relations. Then an additive consistency and a multiplicative consistency of DLPRs are analyzed, and the corresponding consistency indices are provided to measure the consistency levels of DLPRs. Based on them, we develop two consistency-driven optimization models to personalize numerical scales for linguistic terms with individual DLPRs. Next, we develop an approach for addressing GDM with DLPRs. In the proposed approach, a dissimilarity-based consensus measure is designed. To determine a group numerical scale for the linguistic terms with the corresponding group DLPR, two consistency and consensus-driven optimization models are constructed. Finally, illustrative examples are analyzed using the proposed approach to demonstrate its applicability and validity.

借助多种语言术语的概率分布对语言表达进行建模的分布语言偏好关系（DLPR）提供了一种有效的工具，可以准确地得出语言决策中决策者（DM）的偏好。同时，在解决语言决策问题时，数字比例模型已成为DM处理单词的合适选择。这项研究的重点是通过弥合以下差距，借助数字比例尺模型借助DLPR改善群体决策（GDM）。显然，单词对不同的人可能表现出不同的含义。DM对现实世界中的模糊语言GDM中的给定语言术语可能会有不同的理解。在具有DLPR的GDM中，为每个DM设置语言术语的个性化语义成为一项关键任务。为此，我们首先定义一个改进的数字比例模型，以促进DLPR与数字模糊偏好关系之间的联系。然后分析了DLPR的加性一致性和乘法一致性，并提供了相应的一致性指标来衡量DLPR的一致性水平。基于它们，我们开发了两个一致性驱动的优化模型，以使用单个DLPR来个性化语言术语的数字量表。接下来，我们开发一种使用DLPR解决GDM的方法。在提出的方法中，设计了一种基于差异的共识度量。为了确定具有相应组DLPR的语言术语的组数字量表，构建了两个一致性和共识驱动的优化模型。最后，