Abstract: Weighted hesitant fuzzy set is a generalized hesitant fuzzy set, which can more accurate and comprehensive describe decision information. The Frank norm operations can mine the relationship between multiple input parameter values. Based on the Frank norm, this paper develops a weighted hesitant fuzzy group decision making model based on the weighted hesitant Frank geometric average operator. Firstly, the new weighted hesitant fuzzy basic operations are introduced by using Frank norm, and a novel score function is constructed. Then, the Weighted Hesitant Frank Geometric Average（WHFGA） operator is proposed, and the related properties of WHFGA operator with respect to parameter r are studied. Finally, based on the WHFGA operator, a weighted hesitant fuzzy multi-attribute group decision making model is designed, and an example is provided to illustrate that the WHFGA operator has excellent internal consistency.

Key words: probabilistic hesitant fuzzy sets, Frank norm, weighted hesitant Frank geometric average operator, decision making model

摘要： 加权犹豫模糊集是一种广义的犹豫模糊集，其可以更准确和全面地刻画决策信息。而Frank三角模运算能够挖掘多个输入参数值间的相互关系。基于Frank三角模思想，在加权犹豫模糊环境下，提出了一种加权犹豫Frank几何平均算法的群决策模型。首先，运用Frank三角模定义了加权犹豫模糊基本运算法则，并构建了新的得分函数；接着，提出了加权犹豫Frank几何平均（WHFGA）算子，分析了WHFGA算子关于参数[r]的相关性质；最后，基于提出的WHFGA算子，建立了加权犹豫模糊多属性决策模型，并通过算例进行分析。实验结果表明，WHFGA算子具有良好的内在一致性。

关键词: 加权犹豫模糊集, Frank三角模, 加权犹豫Frank几何平均算子, 决策模型