Hesitant fuzzy linguistic preference relation (HFLPR) as a new preference relation is introduced to express the decision makers’ (DMs’) hesitant preference information for each pairwise comparison between different alternatives or criteria. In this paper, the priority vector and consistency of HFLPR are discussed based on a two-stage optimization and multiplicative consistency. Based on the original hesitant preference information, the multiplicative consistency index of an HFLPR is defined to measure the consistency level of the HFLPR. For an unacceptable multiplicative consistent HFLPR, a goal programming model, which is an integer optimization model, is developed to derive an acceptable, multiplicative, consistent HFLPR. According to probability sampling, a linguistic preference relation (LPR) with the best consistency level and an LPR with the worst consistency level with regard to an HFLPR are defined. Combining the two LPRs, a two-stage optimization framework is constructed to obtain the HFLPR’s priority vector, which considers the DM’s risk preference. A multi-stage optimization approach is proposed to solve decision-making problems by integrating the goal programming model and the two-stage optimization framework. Two real life problems are analyzed to show the feasibility of the proposed approach.

中文翻译：

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带有犹豫模糊语言偏好关系的犹豫定性决策的多阶段优化模型

引入犹豫模糊语言偏好关系（HFLPR）作为新的偏好关系，以表达决策者（DMs）的犹豫偏好信息，用于不同选择或准则之间的每个成对比较。本文基于两阶段优化和乘性一致性，讨论了HFLPR的优先级向量和一致性。基于原始犹豫偏好信息，定义了HFLPR的乘法一致性指标，以测量HFLPR的一致性级别。对于不可接受的乘法一致HFLPR，开发了一个目标规划模型，它是一个整数优化模型，以得出可接受的，乘法一致的HFLPR。根据概率抽样，对于HFLPR，定义了具有最佳一致性级别的语言偏好关系（LPR）和具有最差一致性级别的LPR。结合两个LPR，构建了一个两阶段的优化框架来获得HFLPR的优先级向量，该向量考虑了DM的风险偏好。提出了一种多阶段优化方法，通过集成目标规划模型和两阶段优化框架来解决决策问题。分析了两个现实生活中的问题，以证明该方法的可行性。提出了一种多阶段优化方法，通过集成目标规划模型和两阶段优化框架来解决决策问题。分析了两个现实生活中的问题，以证明该方法的可行性。提出了一种多阶段优化方法，通过集成目标规划模型和两阶段优化框架来解决决策问题。分析了两个现实生活中的问题，以证明该方法的可行性。