A Pythagorean fuzzy set (PFS) is an extension of an intuitionistic FS that can be extended by relaxing the restriction on the grades of satisfaction and dissatisfaction. PFS is a powerful tool for dealing with uncertainty and vagueness. Correlation analysis of PFSs is a hot research topic in Pythagorean fuzzy (PF) theory and has practical applications in many areas, such as decision‐making, pattern recognition, medical diagnosis, engineering, and so forth. In this communication, we introduce some novel correlation coefficients in the PF‐environment satisfying the condition that the correlation coefficient of two PFSs is one if and only if the two sets are equal. We discuss the properties and applications of the proposed measures in pattern recognition, medical diagnosis, multicriteria decision‐making, and clustering analysis. Furthermore, the superiority of our proposed correlation coefficients over some existing ones is also established. We also extend the correlation coefficients to interval‐valued PFSs.

中文翻译：

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毕达哥拉斯模糊环境中的一些相关系数及其应用

毕达哥拉斯模糊集 (PFS) 是直觉 FS 的扩展，可以通过放宽对满意和不满意等级的限制来扩展。PFS 是处理不确定性和模糊性的强大工具。PFS 的相关分析是勾股模糊 (PF) 理论中的一个热门研究课题，在决策、模式识别、医学诊断、工程等许多领域都有实际应用。在这次交流中，我们在满足两个 PFS 的相关系数为 1 的条件的 PF 环境中引入了一些新的相关系数，当且仅当这两个集合相等。我们讨论了所提出的措施在模式识别、医学诊断、多标准决策和聚类分析中的特性和应用。此外，我们提出的相关系数优于一些现有的相关系数也得到了证实。我们还将相关系数扩展到区间值 PFS。