Distance measure for Pythagorean fuzzy sets with varied applications

Distance measure is one of the research hotspot in Pythagorean fuzzy environment due to its quantitative ability of distinguishing Pythagorean fuzzy sets (PFSs). Various distance functions for PFSs are introduced in the literature and have their own pros and cons. The common thread of incompetency for these existing distance functions is their inability to distinguish highly uncertain PFSs distinctly. To tackle this point, we introduce a novel distance measure for PFSs. An added advantage of the measure is its simple mathematical form. Moreover, superiority and reasonability of the prescribed definition are demonstrated through proper numerical examples. Boundedness and nonlinear behaviour of the distance measure is established and verified via suitable illustrations. In the current scenario, selecting an antivirus face-mask as a preventive measure in the COVID-19 pandemic and choosing the best school in private sector for children are some of the burning issues of a modern society. These issues are addressed here as multi-attribute decision-making problems and feasible solutions are obtained using the introduced definition. Applicability of the distance measure is further extended in the areas of pattern recognition and medical diagnosis.