关键词: 区间直觉模糊集, 连续交叉熵, 连续有序加权平均（COWA）算子, 多属性决策

Abstract: This paper presents the concept of the interval-valued intuitionistic fuzzy continuous cross-entropy under the interval-valued intuitionistic fuzzy environment, which is based on the COWA operator. The continuous cross-entropy distance between two interval-valued intuitionistic fuzzy values is proposed by using the concept of the interval-valued intuitionistic fuzzy continuous cross-entropy. It obtains the weighted distance degree values between every alternative and ideal alternative depending on the Technique for Order Preference by Similarity to an Ideal Solution（TOPSIS） method, and calculates the relative closeness for each alternative with respect to ideal alternative. It can select the best alternative in accordance with the relative closeness. On the one hand, a programming model based on the principle of maximum cross-entropy is proposed to calculate the attribute weights aiming at the decision making problem with binding attribute weight conditions. On the other hand, it develops a method to obtain the attribute weights in accordance with the cross-entropy theory, aiming that the information about attribute weights is completely unknown. A practical example shows the feasibility and validity of the proposed decision making method.

Key words: interval-valued intuitionistic fuzzy sets, continuous cross-entropy, Continuous Ordered Weighted Average（COWA） operator, multi-criteria decision making