The pythagorean fuzzy set (PFS) which is developed based on intuitionistic fuzzy set, is more efficient in elaborating and disposing uncertainties in indeterminate situations, which is a very reason of that PFS is applied in various kinds of fields. How to measure the distance between two pythagorean fuzzy sets is still an open issue. Mnay kinds of methods have been proposed to present the of the question in former reaserches. However, not all of existing methods can accurately manifest differences among pythagorean fuzzy sets and satisfy the property of similarity. And some other kinds of methods neglect the relationship among three variables of pythagorean fuzzy set. To addrees the proplem, a new method of measuring distance is proposed which meets the requirements of axiom of distance measurement and is able to indicate the degree of distinction of PFSs well. Then some numerical examples are offered to to verify that the method of measuring distances can avoid the situation that some counter? intuitive and irrational results are produced and is more effective, reasonable and advanced than other similar methods. Besides, the proposed method of measuring distances between PFSs is applied in a real environment of application which is the medical diagnosis and is compared with other previous methods to demonstrate its superiority and efficiency. And the feasibility of the proposed method in handling uncertainties in practice is also proved at the same time.

翻译：毕达哥拉斯模糊集（PFS）是在直觉模糊集基础上发展而来的，在阐述和处理不确定情境中的模糊性方面更为有效，这使其被广泛应用于诸多领域。如何度量两个毕达哥拉斯模糊集之间的距离仍是一个开放性问题。先前研究已提出多种方法以呈现该问题的解决方案，然而并非所有现有方法都能准确体现毕达哥拉斯模糊集之间的差异并满足相似性性质，且某些方法忽略了毕达哥拉斯模糊集三个变量间的关联性。为解决此问题，本文提出一种新的距离度量方法，该方法满足距离度量的公理要求，并能有效表征PFS间的区分程度。通过数值算例验证，该距离度量方法可避免产生反直觉或不合理的结果，相较于同类方法更具效度、合理性与先进性。此外，将所提出的PFS间距离度量方法应用于医学诊断这一实际场景，并与既有方法进行比较，证明了其优越性与实效性，同时验证了该方法在处理实际不确定性问题中的可行性。