Abstract:

 For the network public opinion prediction model selection problems in which 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 geometric mean (HFHGM) operator is proposed on the basis of Archimedean norm and Heronian geometric mean, whose properties are studied in detail. Then, some special cases of the HFHGM operator are discussed and the hesitant fuzzy weighted Heronian geometric mean (HFWHGM) operator is introduced. In addition, a new hesitant fuzzy multi-attribute decision making method based on HFWHGM operator is developed, which can capture the interrelationships among the input arguments and enable decision maker to select different parameters to make decision in accordance with their own risk preferences attitude. Finally, a numerical example about the network public opinion prediction model selection is provided to illustrate the effectiveness of the developed method.

Key words: Hesitant fuzzy set, Heronian geometric mean, Archimedean norm, multi-attribute decision making, network public opinion prediction model

摘要： 针对属性值为犹豫模糊信息且输入变量之间存在相互影响和联系的网络舆情预测模型选择决策问题，首先基于阿基米德范数和Heronian几何平均，提出一种新的犹豫模糊Heronian几何平均（HFHGM）算子，并详细研究了HFHGM算子的一些基本性质；其次，探讨了HFHGM算子的一些特例，并引入了犹豫模糊加权Heronian几何平均（HFWHGM）算子；进一步，基于HFWHGM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，通过网络舆情预测模型的选择实例验证提出的决策方法是可行的和有效的。

关键词: 犹豫模糊集, Heronian几何平均, 阿基米德范数, 多属性决策, 网络舆情预测模型