Abstract: To deal with Multi-Attribute Decision Making（MADM） problems when the attribute values are in the form of hesitant fuzzy information and the input arguments are associated with each other, a novel Hesitant Fuzzy Heronian Mean（HFHM） operator is proposed on the basis of Archimedean norm and Heronian mean. Then, the properties of the HFHM operator are studied in detail. Furthermore, some special cases of the HFHM operator are discussed and the Hesitant Fuzzy Weighted Heronian Mean（HFWHM） operator is presented. In addition, a new hesitant fuzzy MADM method based on HFWHM operator is developed, which can capture the interrelationships among the input arguments and enable decision maker to make decision with different parameters in accordance with their own risk preference attitude. In the end, a numerical example about traffic flow model selection is provided to illustrate the effectiveness of the proposed method.

Key words: hesitant fuzzy set, Heronian mean, Archimedean norm, multi-attribute decision making, traffic flow model

摘要： 针对输入变量之间存在相互影响和联系以及属性值为犹豫模糊信息的多属性决策问题，基于阿基米德范数和Heronian平均，提出一种新的犹豫模糊Heronian平均（HFHM）算子；详细研究了HFHM算子的一些基本性质，包括幂等性、单调性和有界性；探讨了HFHM算子的一些特例，并提出了犹豫模糊加权Heronian平均（HFWHM）算子；进一步，基于HFWHM算子建立了一种新的犹豫模糊多属性决策方法，该决策方法不仅能够有效地捕获输入变量之间的相互联系，还使得决策者能够依据自身的风险偏好态度选择不同的参数进行决策。最后，通过交通流模型的选择实例对提出的决策方法进行了有效性验证。

关键词: 犹豫模糊集, Heronian平均, 阿基米德范数, 多属性决策, 交通流模型