Pythagorean fuzzy set is a reliable technique for soft computing because of its ability to curb indeterminate data when compare to intuitionistic fuzzy set. Among the several measuring tools in Pythagorean fuzzy environment, correlation coefficient is very vital since it has the capacity to measureinterdependency and interrelationship between any two arbitrary Pythagorean fuzzy sets (PFSs). In Pythagorean fuzzy correlation coefficient, some techniques of calculating correlation coefficient of PFSs (CCPFSs) via statistical perspective have been proposed, however, with some limitations namely; (i) failure to incorporate all parameters of PFSs which lead to information loss, (ii) imprecise results, and (iii) less performance indexes. Sequel, this paper introduces some new statistical techniques of computing CCPFSs by using Pythagorean fuzzy variance and covariance which resolve the limitations with better performance indexes. The new techniques incorporate the three parameters of PFSs and defined within the range [-1, 1] to show the power of correlation between the PFSs and to indicate whether the PFSs under consideration are negatively or positively related. The validity of the new statistical techniques of computing CCPFSs is tested by considering some numerical examples, wherein the new techniques show superior performance indexes in contrast to the similar existing ones. To demonstrate the applicability of the new statistical techniques of computing CCPFSs, some multi-criteria decision-making problems (MCDM) involving medical diagnosis and pattern recognition problems are determined via the new techniques.

中文翻译：

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一些基于统计观点的勾股模糊相关技术及其在决策中的应用

毕达哥拉斯模糊集是一种可靠的软计算技术，因为与直觉模糊集相比，它具有抑制不确定数据的能力。在毕达哥拉斯模糊环境中的几种测量工具中，相关系数非常重要，因为它具有测量任意两个任意毕达哥拉斯模糊集（PFS）之间的相互依赖性和相互关系的能力。在毕达哥拉斯的模糊相关系数中，提出了一些从统计角度来计算PFS（CCPFS）的相关系数的技术，但是有一定的局限性。（i）未能纳入PFS的所有参数，这会导致信息丢失；（ii）结果不准确；（iii）性能指标降低。续集，本文介绍了一些利用勾股模糊方差和协方差来计算CCPFS的新统计技术，这些技术解决了性能指标更好的局限性。新技术结合了PFS的三个参数，并定义在[-1，1]范围内，以显示PFS之间的相关能力并指示所考虑的PFS是负相关还是正相关。通过考虑一些数值示例来测试计算CCPFS的新统计技术的有效性，其中新技术与类似的现有技术相比显示出更高的性能指标。为了证明计算CCPFS的新统计技术的适用性，