In this paper, a Pythagorean fuzzy decision-making method based on overall entropy is presented. First, a new definition is proposed for fuzzy entropy for any given Pythagorean fuzzy set (PFS). The proposed definition is based on the relationship between the fuzziness contained in the given PFS and the distance from a point to a line on a projection plane. Some related properties are introduced. Second, the overall entropy of the PFS is determined based on fuzzy entropy and the degree of hesitancy; proofs are presented to formalize some related properties. Third, an entropy weight formula is provided that is based on overall entropy, and a Pythagorean fuzzy decision-making method is developed on this basis. Finally, the effectiveness and practicability of the proposed methods are illustrated by an example and three comparative analyses.

中文翻译：

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勾股模糊熵及其在多准则决策中的应用

提出了一种基于整体熵的勾股模糊决策方法。首先，对于任何给定的勾股模糊集（PFS），提出了一种新的模糊熵定义。提议的定义基于给定PFS中包含的模糊性与投影平面上从点到线的距离之间的关系。介绍了一些相关的属性。其次，基于模糊熵和犹豫程度确定PFS的总体熵。提供证明以规范化一些相关属性。第三，提供了基于整体熵的熵权公式，并在此基础上发展了勾股模糊决策方法。最后，通过实例和三个对比分析说明了所提方法的有效性和实用性。