The fuzzy aggregation information plays an important role in the group decision support system under the interval-valued hesitant fuzzy information and interval-valued probabilistic hesitant fuzzy information. Therefore, in this paper, we develop a new approach of the interval-valued hesitant fuzzy Frank aggregation (IVHFFA) and interval-valued probabilistic hesitant fuzzy aggregation (IVPHFFA) operators. First, we define some operational laws of IVHEs and IVPHFEs by using Frank t-norm and t-conorm. Furthermore, we develop a series of IVHFFA and IVPHFFA operators based on these operational laws under the IVHF and IVPHF information. Also, discuss some fundamental properties and relations of the proposed aggregation operators for IVHF and IVPHF information. In order to implement the proposed aggregation operators of IVHF and IVPHF information in group decision-making problem, we construct general algorithms for multi-attribute group decision-making problem based on the proposed IVHFFA and IVPHFFA. Finally, from the comparative and sensitivity analysis, the proposed fuzzy decision-making model is more effective and reliable as compared with existing method.

在区间值犹豫模糊信息和区间值概率犹豫模糊信息下，模糊聚集信息在群体决策支持系统中起着重要作用。因此，在本文中，我们开发了一种区间值犹豫模糊弗兰克聚集（IVHFFA）和区间值概率犹豫模糊聚集（IVPHFFA）算子的新方法。首先，我们通过使用Frank t范数和t-conorm定义IVHE和IVPHFE的一些操作定律。此外，我们根据IVHF和IVPHF信息下的这些运营法律，开发了一系列IVHFFA和IVPHFFA运营商。此外，讨论IVHF和IVPHF信息的拟议聚合算子的一些基本性质和关系。为了在群体决策问题中实现IVHF和IVVPF信息的聚合算子，我们在IVHFFA和IVPHFFA的基础上构造了多属性群体决策问题的通用算法。最后，通过比较和敏感性分析，提出的模糊决策模型与现有方法相比更加有效，可靠。