Abstract The hesitant fuzzy element (HFE), as an extension of fuzzy numbers, has received much attention and the occurrence probabilities of each membership in the HFEs are assumed to be equal, i.e., the decision makers (DMs) share the same preference for each membership. Anecdotal observations suggest otherwise. To address this issue, the hesitant probabilistic fuzzy set (HPFS) is proposed, which is more suitable for depicting the DMs’ preferences in decision making. Research reports that psychological behavior matters in the decision-making process. Consequently, this paper proposes a multi-attribute group decision making method under a hesitant probabilistic fuzzy environment that considers the DMs’ psychological state in the decision-making process. A weights determination model is constructed, incorporating objective decision-making information and the subjective preferences of the DMs based on a score function and the minimum relative entropy principle. Finally, an established case example is applied to validate the applicability of the proposed method, and comparative analysis is also completed to verify the validity of the proposed method.

中文翻译：

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犹豫概率模糊环境下基于前景理论的多属性群决策方法

摘要 犹豫模糊元（HFE）作为模糊数的扩展受到了广泛关注，假设 HFE 中每个成员的出现概率相等，即决策者（DM）对每个成员具有相同的偏好。会员资格。轶事观察表明并非如此。为了解决这个问题，提出了犹豫概率模糊集（HPFS），它更适合描述决策者在决策中的偏好。研究报告说，心理行为在决策过程中很重要。为此，本文提出了一种在犹豫概率模糊环境下考虑决策者心理状态的多属性群决策方法。构建权重确定模型，基于评分函数和最小相对熵原理，结合客观决策信息和 DM 的主观偏好。最后,通过一个已建立的实例验证了所提方法的适用性,并通过对比分析来验证所提方法的有效性。