Abstract: Considering the advantages of Pythagorean Fuzzy Set（PFS）, a new approach is developed to solve Multicriteria Decision Making（MCDM） problems under the Pythagorean fuzzy environment. Firstly, based on the TOPSIS method, the positive ideal solution and the negative ideal solution are determined under the Pythagorean fuzzy environment. The cross entropy measures for PFS are defined simultaneously, and the related properties are also proved. Furthermore, the cross entropy between alternatives to the positive ideal solution and the negative solution is calculated. Moreover, the optimal ranking order of alternatives is determined under the closeness index. Finally, a practical example for coping with green supplier selection is used to demonstrate the effectiveness and practicality.

Key words: Pythagorean fuzzy set, cross entropy, TOPSIS, multicriteria decision making

摘要： 考虑到Pythagorean模糊集（Pythagorean Fuzzy Set，PFS）具有的优势，提出了一个Pythagorean模糊环境下解决多准则决策（Multicriteria Decision Making，MCDM）问题的新方法。根据TOPSIS理论计算Pythagorean模糊环境下的正、负理想解，同时提出两个Pythagorean模糊集之间的交叉熵定义，并对其性质给予证明。计算每个方案各自和正、负理想解之间的交叉熵，再根据相对贴近度对所有方案进行排序。通过一个在绿色环境下的供应商选择的算例验证了有效性和实用性。

关键词: Pythagorean模糊集, 交叉熵, TOPSIS, 多准则决策