区间直觉模糊连续交叉熵及其多属性决策方法

Interval-valued intuitionistic fuzzy continuous cross-entropy and its application in multi-attribute decisionmaking

在区间直觉模糊(IVIF)环境下,利用连续有序加权平均(COWA)算子定义了一种新的区间直觉模糊数间的交叉熵,即区间直觉模糊连续交叉熵。依据提出的区间直觉模糊连续交叉熵定义了直觉模糊数间的连续交叉熵距离。基于TOPSIS的思想得到备选方案与理想方案的加权距离,并且计算备选方案与理想方案的相对贴近度,依据相对贴近度选择最优方案。其中,针对属性权重信息不完全确定条件下的决策问题,提出了以区间直觉模糊连续交叉熵最大为准则的规划模型;针对属性权重信息完全未知的情况,根据交叉熵理论确定属性权重向量。实验结果验证了新的决策方法的可行性和有效性。

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 contin- uous 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 makin~ method.