Abstract: Pythagorean fuzzy sets can describe uncertain and inconsistent information in complex problems more comprehensively and effectively than intuitionistic fuzzy sets, and the Pythagorean fuzzy sets have been extensively studied. Aiming at the problem of Pythagorean fuzzy Multi-Attribute Decision Making（MADM） with completely unknown attribute weights, a novel MADM model is investigated, which is based on the proposed Pythagorean fuzzy information measures. This model first uses logarithmic function to design a new information entropy of Pythagorean fuzzy numbers. Then, we present a concept of Pythagorean fuzzy similarity, and a similarity measure for Pythagorean fuzzy numbers is designed based on logarithmic function. In addition, the internal relationship between information entropy and similarity of Pythagorean fuzzy numbers is excavated. Finally, with the help of the proposed Pythagorean fuzzy entropy and similarity measures, a new multi-attribute decision-making model is built and applied. The experimental results show that the proposed model is effective and extends the scope of application of the model.

Key words: Pythagorean fuzzy set, information entropy, similarity measure, closeness degree, decision-making model

摘要： 相对于直觉模糊集，勾股模糊集能够更为全面和有效地表达描述复杂问题中的不确定和非一致信息，使其受到了广泛研究。对于属性评价值为勾股模糊数并且属性指标权重信息数据完全未知的多属性决策问题，以提出的勾股模糊信息测度为基础，设计了新的多属性决策模型。该模型运用对数函数设计了一种新的勾股模糊数信息熵计算方法；引入了勾股模糊相似度概念，并结合对数行数提出勾股模糊数相似度的衡量方法，随后挖掘出勾股模糊数的信息熵和相似度之间的内在联系；运用提出的勾股模糊熵和相似度计算方法，构建新的多属性决策模型，并进行应用研究。实验结果表明，提出的模型合理有效，同时拓展了模型的使用范围。

关键词: 勾股模糊集, 信息熵, 相似度, 贴近度, 决策模型