Abstract: For the Multi-Attribute Group Decision Making（MAGDM） problem under the hesitant fuzzy linguistic environment, based on Hesitant Linguistic Geometric Bonferroni Mean（HLGBM） operator, a novel MAGDM model is developed, which is considering the importance of each attribute and the interrelationships among them. Firstly, based on the hesitant linguistic operational laws with Archimedean T-norm and S-norm, this paper proposes the HLGBM operator, which is followed by the discussion of its desirable properties. Then, some special cases of the HLGBM operator are studied in detail and the hesitant linguistic weighted geometric Bonferroni mean（HLWGBM） operator is presented. Finally, a new model for MAGDM is investigated based on the HLWGBM operator, and applies the example for the selection of database to demonstrate the model’s practicality and effectiveness.

Key words: hesitant fuzzy linguistic set, Archimedean norm, geometric Bonferroni mean, multi-attribute group decision making

摘要： 针对犹豫模糊语言环境下的多属性群决策问题，建立了一种基于犹豫语言几何Bonferroni平均（HLGBM）算子的多属性群决策模型，该模型不仅充分考虑了每种属性的重要性，而且能够有效捕获属性间的内在联系。首先利用基于Archimedean T-范数和S-范数的犹豫语言运算法则，提出了一种新的HLGBM算子，并研究该算子的四种基本性质；其次，探讨了HLGBM算子的几类特殊形式，并提出了犹豫语言加权几何Bonferroni加权（HLWGBM）算子；最后基于HLWGBM算子构建了一种新的犹豫语言多属性群决策模型，并通过数据库选择实例验证决策模型是可行和有效的。

关键词: 犹豫模糊语言集, Archimedean范数, 几何Bonferroni平均, 多属性群决策