Hesitant fuzzy linguistic preference relations (HFLPRs) can be used to represent cognitive complex information in a situation in which people hesitate among several possible linguistic terms for the preference degrees of pairwise comparisons over alternatives. HFLPRs have attracted growing attention owing to their efficiency in dealing with increasingly cognitive complex decision-making problems. Due to the emergence of various studies on HFLPRs, it is necessary to make a comprehensive overview of the theory of HFLPRs and their applications. In this paper, we first review different types of linguistic representation models, including the hesitant fuzzy linguistic term set, hesitant 2-tuple fuzzy linguistic term set, probabilistic linguistic term set, and double-hierarchy hesitant fuzzy linguistic term set. The reasons for proposing these models are discussed in detail. Then, the hesitant linguistic preference relation models associated with the aforementioned linguistic representation models are addressed one by one. An overview is then provided in terms of their consistency properties, inconsistency-repairing processes, priority vector derivation methods, consensus measures, applications, and future directions. Basically, we try to answer to two questions: where we stand and what is next? The preference relations and consistency properties are discussed in detail. The inconsistency-repairing processes for those preference relations that are not acceptably consistent are summarized. Methods to derive the priorities from the HFLPRs and their extensions are further reviewed. The consensus measures and consensus-reaching processes for group decision making with HFLPRs and their extensions are discussed. The applications of HFLPRs and their extensions in different areas are highlighted. The future research directions regarding HFLPRs are given from different perspectives. This paper provides a comprehensive overview of the development and research status of HFLPRs for representing cognitive complex information. It can help researchers to identify the frontier of cognitive complex preference relation theory in the realm of decision analysis. Since the research on HFLPRs is still at its initial stage, this review has guiding significance for the later stage of study on this topic. Furthermore, this paper can engage further research or extend the research interests of scholars.

中文翻译：

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代表认知复杂信息的犹豫性语言偏好关系概述：我们的立场和下一步是什么

犹豫的模糊语言偏好关系（HFLPR）可用于表示认知复杂信息，在这种情况下，人们对几种可能的语言术语犹豫不决，成对比较的偏好程度高于其他选择。HFLPRs在处理日益增加的认知复杂决策问题方面的效率引起了越来越多的关注。由于对HFLPRs的各种研究的兴起，有必要对HFLPRs的理论及其应用进行全面的概述。在本文中，我们首先回顾不同类型的语言表示模型，包括犹豫的模糊语言术语集，犹豫的2元组模糊语言术语集，概率语言术语集和双层次犹豫的模糊语言术语集。提出这些模型的原因已详细讨论。然后，与上述语言表示模型相关联的犹豫的语言偏好关系模型被一一解决。然后根据它们的一致性属性，不一致性修复过程，优先级向量推导方法，共识性度量，应用程序和未来方向提供概述。基本上，我们尝试回答两个问题：我们的立场和下一步是什么？详细讨论了偏好关系和一致性属性。总结了那些不可接受的一致性的偏好关系的不一致修​​复过程。进一步审查了从HFLPR及其扩展中得出优先级的方法。讨论了使用HFLPR进行群体决策的共识措施和达成共识的过程及其扩展。重点介绍了HFLPRs的应用及其扩展。从不同的角度给出了有关HFLPRs的未来研究方向。本文提供了用于代表认知复杂信息的HFLPRs的发展和研究现状的全面概述。它可以帮助研究人员在决策分析领域识别认知复杂偏好关系理论的前沿领域。由于对HFLPRs的研究仍处于起步阶段，因此本综述对于该主题的后期研究具有指导意义。此外，本文可以进行进一步的研究或扩展学者的研究兴趣。