Abstract: In view of the Multi-Attribute Group Decision Making（MAGDM） problem in which the attribute values are in the form of hesitant fuzzy linguistic information and attribute arguments are associated with each other, a MAGDM model based on the Hesitant Linguistic Heronian Geometric（HLHG） operator is developed. Firstly, some new hesitant fuzzy linguistic operation laws are defined on the basis of Archimedean norm. Then, the HLHG operator is proposed, and the properties of the HLHG operator are discussed. Some special cases of the HLHG operator are studied and the Hesitant Linguistic Heronian Weighted Geometric（HLHWG） operator is introduced. In addition, based on HLHWG operator, a novel hesitant fuzzy linguistic MAGDM model is investigated, which can capture the relationship among the input decision making information and enable decision maker to select different parameters to make decision with their preference. In the end, the presented method is applied to select the information security systems to demonstrate its practicality and effectiveness.

Key words: Multi-Attribute Group Decision Making（MAGDM）, hesitant fuzzy linguistic set, Heronian geometric mean, Archimedean norm, information security system

摘要： 针对属性值为犹豫模糊语言信息且属性输入变量之间存在相互联系的多属性群决策问题，提出了一种基于犹豫语言Heronian几何算子的多属性群决策模型。基于Archimedean范数定义了新的犹豫模糊语言运算法则，并提出了犹豫语言Heronian几何（HLHG）算子；探讨了HLHG算子的一些优良性质，研究了HLHG算子的几种常见形式，引入了犹豫语言Heronian加权几何（HLHWG）算子；基于HLHWG算子构建了一种新的犹豫模糊语言多属性群决策模型，该群决策模型不仅考虑到了输入决策信息之间的相互联系，而且使得决策者能够依据自身偏好选择不同参数进行决策。结合信息安全系统选择实例验证了提出的群决策模型是可行的和有效的。

关键词: 多属性群决策, 犹豫模糊语言集, Heronian几何平均, Archimedean范数, 信息安全系统