Abstract: The interval-valued intuitionistic fuzzy cross-entropy is proposed, which considers membership, non-membership and hesitancy degree of Interval-Valued Intuitionistic Fuzzy Set（IVIFS）. Then the axiomatic principles of the entropy of IVIFS are constructed and based on the proposed cross-entropy formula, the interval-valued intuitionistic fuzzy entropy measure is showed. The proposed entropy formula is applied to multiple attributes decision-making with unknown information of attribute weights by using the weighted correlation coefficient between IVIFSs.

Key words: interval-valued intuitionistic fuzzy set, interval-valued intuitionistic fuzzy cross-entropy, interval-valued intuitionistic fuzzy entropy, weighted correlation coefficient, multiple attributes decision making

摘要： 提出了区间值直觉模糊集的区间直觉模糊交叉熵，这种交叉熵充分考虑了区间值直觉模糊集的隶属度，非隶属度以及犹豫度。给出一种区间值直觉模糊集的区间直觉模糊熵的公理化体系，并且基于直觉模糊交叉熵公式给出一种区间直觉模糊熵的具体测度公式。利用区间值直觉模糊集的加权相关系数，将提出的熵公式应用于解决属性权重完全未知的区间直觉模糊多属性决策问题。

关键词: 区间值直觉模糊集, 区间直觉模糊交叉熵, 区间直觉模糊熵, 加权的相关系数, 多属性决策