Abstract: In this paper, it investigates the hesitant fuzzy information aggregation operators and their application to multi-attribute group decision making with the condition of attribute weight information completely known. The hesitant fuzzy Einstein sum, hesitant fuzzy Einstein product and hesitant fuzzy Einstein exponentiation are defined and it analyzes some relations of these operations. Four new kinds of hesitant fuzzy aggregation operators are proposed, such as the Hesitant Fuzzy Einstein Weighted Geometric （HFEWG） operator, Hesitant Fuzzy Einstein Ordered Weighted Geometric （HFEOWG） operator, Hesitant Fuzzy Einstein Hybrid Geometric （HFEHG） operator and Hesitant Fuzzy Einstein Induced Ordered Weighted Geometric （HFEIOWG） operator, whose desirable properties are studied in detail. An approach to hesitant fuzzy multi-attribute group decision making based on the HFEIOWG operator is developed, and it applies the developed method to select the financial products and demonstrate its practicality and effectiveness.

Key words: multi-attribute group decision making, hesitant fuzzy sets, Einstein operations, geometric averaging aggregation operators

摘要： 研究了属性权重信息已知条件下的犹豫模糊信息集结算子及其在多属性群决策问题中的应用。基于Einstein运算定义了犹豫模糊Einstein和、犹豫模糊Einstein积以及犹豫模糊Einstein幂运算，并且研究了犹豫模糊Einstein运算法则间的关系。提出了四种犹豫模糊信息集结算子，即犹豫模糊Einstein加权几何（HFEWG）算子、犹豫模糊Einstein有序加权几何（HFEOWG）算子、犹豫模糊Einstein混合几何（HFEHG）算子和犹豫模糊Einstein诱导有序加权几何（HFEIOWG）算子，并分析了这些算子的性质。给出了基于HFEIOWG算子的犹豫模糊多属性决策方法，并结合投资公司对金融产品的选择来验证提出的决策方法是可行有效的。

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