The axiomatic distance-based method is a powerful tool to aggregate individual preferences, and the extant axiomatic distance-based aggregation methods are with regard to individual numerical preferences. However, in some real-world decision problems with qualitative aspects, it is more convenient and natural for individuals to express their preferences through linguistic terms rather than through numerical values. Therefore, in this paper, we propose axiomatic distance in the linguistic context based on ordered linguistic term sets to aggregate individual linguistic preferences. Specifically, we provide some natural axioms on the distance measure among linguistic preferences. We then prove that there exists a unique distance function that satisfies all the proposed axioms. Based on the axiomatic distance function, we aggregate individual linguistic preferences into the group linguistic preference, which minimizes the total distance among individual linguistic preferences. Furthermore, we present a novel consensus measure based on the unique axiomatic distance and develop a minimum cost consensus model to obtain the optimal adjusted linguistic preference, which serves as a reference for the moderator to persuade individuals to modify their linguistic preferences.

基于公理距离的方法是汇总个人偏好的强大工具，而现存的基于公理距离的汇总方法是针对个人数字偏好。但是，在某些具有定性方面的现实决策问题中，个人通过语言而不是数值来表达自己的偏好更为方便自然。因此，在本文中，我们提出了基于有序语言术语集的语言环境中的公理距离，以汇总各个语言偏好。具体来说，我们提供了语言偏好之间距离度量的一些自然公​​理。然后，我们证明存在一个满足所有提出的公理的唯一距离函数。根据公理距离函数，我们将个人语言偏好汇总到组语言偏好中，从而使各个语言偏好之间的总距离最小化。此外，我们提出了一种基于唯一公理距离的新颖共识方法，并开发了一种最小成本共识模型来获得最优的调整后的语言偏好，这可为主持人说服个人修改其语言偏好提供参考。