Abstract: Aiming at multi-criteria group decision making (MCGDM) problems where criteria values are hesitant fuzzy information and criterions are associated with each other, a generalized hesitant fuzzy geometric Bonferroni mean (GHFGBM) operator is proposed on the basis of Archimedean T-norm and S-norm, and then a novel computer network system selection model is designed. The advantages of the developed method are not only its capability to capture the interrelationship among the input variables, it also enables the model method to be applied to other fields. Some desirable properties of the GHFGBM operator are discussed, including Permutation invariance, monotonicity, boundedness and idempotence and so on. Some special cases are obtained if the parameter and additive operator takes different values and functions. In the end, a numerical example about update alternative of computer network system selection to illustrate the rationality and effectiveness of the proposed model.

Key words: Multi-criteria group decision making, hesitant fuzzy set (HFS), Bonferroni mean, geometric mean, Archimedean norm

摘要： 针对决策信息为犹豫模糊信息且准则之间存在相互关系的多准则群决策问题，提出了一种基于阿基米德T-范数和S-范数的广义的犹豫模糊信息几何B-平均（GHFGBM）集成算法，构建一种新的计算机网络系统选择决策模型，提出的GHFGBM不仅在信息集结的过程中能够考虑到输入变量之间的相互联系，还能够使得该模型方法应用于其他领域。在此过程中，研究了GHFGBM算法的几种基本特性，比如置换不变性、单调性、有界性和幂等性等等。紧接着，分别对参数和加性算子赋予不同的数值和函数，详细分析了GHFGBM算法的一系列常用算子表示。最后结合对计算机网络系统更新方案的选择实验，验证了提出的选择决策模型是合理的且是有效的。

关键词: 多准则群决策, 犹豫模糊集, Bonferroni平均, 几何平均, 阿基米德范数