As the development and extension of hesitant fuzzy linguistic term sets (HFLTSs), free double hierarchy hesitant fuzzy linguistic term sets (FDHHFLTSs) can describe the evaluation information in more detail. In addition, in practical multiple attribute decision-making (MADM) problems, priority relations and interaction relations usually exist among attributes, and the prioritized interactive Choquet (PIC) operator based on generalized prioritized measure-guided aggregation (GPMGA) operator and Choquet integral (CI) operator is an effective tool for dealing with decision-making problems with priority relations and interaction relations. Under the above contexts, we improve the PIC operator and propose the FDHHFLPIC operator which can aggregate the evaluation information under free double hesitant fuzzy linguistic environment and take both priority and interaction relations into account. Furthermore, we propose an approach based on the FDHHFLPIC operators to address the real MADM problem, and the proposed method considering the different relations between attributes in decision-making process. Finally, two numerical examples are given to demonstrate the effectiveness and advantages of the proposed method which can consider priority relations and interaction relations under the FDHHFLTSs.

中文翻译：

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一种考虑优先交互属性的基于自由双层次犹豫模糊语言信息的多属性决策方法

作为犹豫模糊语言术语集（HFLTSs）的发展和扩展，免费的双层次犹豫模糊语言术语集（FDHHFLTSs）可以更详细地描述评价信息。此外，在实际的多属性决策（MADM）问题中，属性之间通常存在优先级关系和交互关系，基于广义优先度量引导聚合（GPMGA）算子和Choquet积分的优先交互Choquet（PIC）算子（ CI)算子是处理具有优先关系和交互关系的决策问题的有效工具。在上述情况下，我们改进了PIC算子，提出了FDHHFLPIC算子，可以在自由双犹豫模糊语言环境下聚合评价信息，同时兼顾优先级和交互关系。此外，我们提出了一种基于 FDHHFLPIC 算子的方法来解决真正的 MADM 问题，并且提出的方法考虑了决策过程中属性之间的不同关系。最后，通过两个数值例子证明了该方法的有效性和优势，该方法可以考虑FDHHFLTSs下的优先关系和交互关系。并提出了考虑决策过程中属性之间不同关系的方法。最后，通过两个数值例子证明了该方法的有效性和优势，该方法可以考虑FDHHFLTSs下的优先关系和交互关系。并提出了考虑决策过程中属性之间不同关系的方法。最后，通过两个数值例子证明了该方法的有效性和优势，该方法可以考虑FDHHFLTSs下的优先关系和交互关系。