关键词: 勾股模糊集, 信息熵, 相似度, 贴近度, 决策模型

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