Compared to the intuitionistic fuzzy sets, the Pythagorean fuzzy sets (PFSs) can provide the decision makers with more freedom to express their evaluation information. There exist some research results on the correlation coefficient between PFSs, but sometimes they fail to deal with the problems of disease diagnosis and cluster analysis. To tackle the drawbacks of the existing correlation coefficients between PFSs, some novel directional correlation coefficients are put forward to compute the relationship between two PFSs by taking four parameters of the PFSs into consideration, which are the membership degree, non-membership degree, strength of commitment, and direction of commitment. Afterwards, two practical examples are given to show the application of the proposed directional correlation coefficient in the disease diagnosis, and the application of the proposed weighted directional correlation coefficient in the cluster analysis. Finally, they are compared with the previous correlation coefficients that have been developed for PFSs.

与直觉模糊集相比，勾股模糊集（PFS）可以为决策者提供更多表达其评估信息的自由。关于PFS之间的相关系数已有一些研究结果，但有时它们未能解决疾病诊断和聚类分析的问题。针对PFS之间现有相关系数存在的弊端，提出了一些新颖的方向相关系数，通过考虑PFS的隶属度，非隶属度，强度等四个参数来计算两个PFS之间的关系。承诺和承诺方向。随后，通过两个实际示例来说明所提出的方向相关系数在疾病诊断中的应用，提出的加权方向相关系数在聚类分析中的应用。最后，将它们与为PFS开发的先前相关系数进行比较。