Abstract: Considering that there may exist some interactions between membership function and non-membership function of different intuitionistic fuzzy sets，this paper generalizes the Power operator to intuitionistic fuzzy environment and presents the intuitionistic fuzzy power interaction average operator.The properties of the operator are investigated.An example is illustrated to show the feasibility and validity of the new operator in the application of group decision making problems. It makes a comparison on stability between the proposed operator and the existing intuitionistic fuzzy power averaging operator.

Key words: intuitionistic fuzzy set, Power interaction averaging operator, validity, group decision making

摘要： 将Power算子推广到直觉模糊环境中，提出了直觉模糊Power交叉影响平均算子，考虑了不同直觉模糊集的隶属度与非隶属度之间可能存在的交叉影响，根据数学归纳法得到了其具体计算公式，并研究了其性质。实例说明了新的集成算子在多属性群决策应用中的有效性。将提出的算子与现存的直觉模糊Power平均算子做了稳定性比较。

关键词: 直觉模糊集, Power交叉影响平均算子, 有效性, 群决策