Preference ordering structures are useful and popular tools to represent experts’ preferences in the decision making process. In the existing preference orderings, they lack the research on the precise relationship between any two adjacent alternatives in the preference orderings, and the decision making methods are unreasonable. To overcome these issues, this paper establishes a novel concept of linguistic preference ordering (LPO) in which the ordering of alternatives and the relationships between two adjacent alternatives should be fused well, and develops two transformation models to transform each LPO into the corresponding double hierarchy linguistic preference relation with complete consistency. Additionally, to fully respect the experts’ expression habits and provide more refined solutions to experts, this paper establishes a multi-stage consensus optimization model by considering the suggested preferences represented in both the continuous scale and the discrete scale, and develops a multi-stage interactive consensus reaching algorithm to deal with multi-expert decision making problem with LPOs. Furthermore, some numerical examples are presented to illustrate the developed methods and models. Finally, some comparative analyses between the proposed methods and models and some existing methods have been made to show the advantages of the proposed methods and models.

中文翻译：

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通过具有语言偏好顺序和双层次语言偏好的多阶段优化模型管理共识

偏好排序结构是在决策过程中代表专家偏好的有用且流行的工具。在现有的偏好排序中，缺乏对偏好排序中任意两个相邻选项之间精确关系的研究，决策方法不合理。为了克服这些问题，本文建立了语言偏好排序 (LPO) 的新概念，其中选项的排序和两个相邻选项之间的关系应该很好地融合，并开发了两种转换模型将每个 LPO 转换为相应的双层次结构。完全一致的语言偏好关系。此外，为了充分尊重专家的表达习惯，为专家提供更精细化的解决方案，本文通过考虑连续尺度和离散尺度所代表的建议偏好建立了多阶段共识优化模型，并开发了多阶段交互式共识达成算法来处理 LPO 的多专家决策问题。此外，还提供了一些数值例子来说明所开发的方法和模型。最后，对所提出的方法和模型与一些现有方法进行了一些比较分析，以展示所提出的方法和模型的优点。提供了一些数值例子来说明开发的方法和模型。最后，对所提出的方法和模型与一些现有方法进行了一些比较分析，以展示所提出的方法和模型的优点。提供了一些数值例子来说明开发的方法和模型。最后，对所提出的方法和模型与一些现有方法进行了一些比较分析，以展示所提出的方法和模型的优点。