A new similarity function for Pythagorean fuzzy sets with application in football analysis

The idea of Pythagorean fuzzy sets (PFSs) has been extensively applied in various decision-making scenarios. Many of the applications of PFSs were carried out based on similarity functions. Some methods of similarity functions for PFSs (SFPFSs) cannot be trusted for a reliable interpretations in practical cases due to some of their setbacks. In this work, a new method of SFPFSs is developed with the capacity to outsmart the efficiency of the extant SFPFSs in terms of precise results and appropriately satisfying the rules of SFs. The new method is described with some results to validate the properties of SFs. In terms of practical application, we use the newly developed method of SFPFSs to discuss the relationship between the players of the Liverpool Football Club (FC) in the 2022/2023 English Premier League (EPL) season to assess their performances in their resurgent moments within the season. Using data from BBC Sport analysis (BBCSA) on the players' rating per match in a Pythagorean fuzzy setting, we establish the players' interactions, communications, passing, contributions, and performances to ascertain the high ranking players based on performances. Similarly, a comparative analyses are presented in tables to undoubtedly express the superiority of the newly developed method of SFPFSs. Due to the flexibility of the newly developed method of SFPFSs, it can be used for clustering analysis. In addition, the new method of SFPFSs can be extended to other uncertain environments other than PFSs.