Abstract: Hesitant fuzzy information aggregation plays an important part in hesitant fuzzy set theory, which has emerged to be a new research direction receiving more and more attention in recent years. Some operations on hesitant fuzzy elements are defined, such as Einstein sum, Einstein product and Einstein exponentiation. Three new kinds of Einstein arithmetic averaging aggregation operators are proposed, such as Hesitant Fuzzy Einstein Weighted Averaging（HFEWA） operator, Hesitant Fuzzy Einstein Ordered Weighted Averaging（HFEOWA） operator and Hesitant Fuzzy Einstein Hybrid Averaging（HFEHA） operator. According to these new kinds of Einstein arithmetic average aggregation operators, a new approach for hesitant fuzzy multi-attribute decision-making problems is developed, and an illustrative example is given to verify the developed method and to demonstrate its practicality and effectiveness.

Key words: hesitant fuzzy sets, Einstein operation, arithmetic averaging aggregation operators, multi-attribute decision making

摘要： 犹豫模糊信息集结是犹豫模糊集理论中的重要组成部分，近年来由于其越来越受到关注，已成为一个新的研究方向。基于Einstein运算定义了犹豫模糊元间的运算法则，比如：Einstein和、Einstein积以及Einstein幂运算。提出了三种新的Einstein算术平均集结算子，即犹豫模糊Einstein加权平均（HFEWA）算子、犹豫模糊Einstein有序加权平均（HFEOWA）算子以及犹豫模糊Einstein混合平均（HFEHA）算子。基于新的Einstein算术平均集结算子给出一种新的处理犹豫模糊环境下多属性决策问题的方法，并结合实例对决策方法的可行性与有效性进行检验。

关键词: 犹豫模糊集, Einstein运算, 算术平均集结算子, 多属性决策