K-L divergence-based distance measure for Pythagorean fuzzy sets with various applications

The Pythagorean fuzzy sets have achieved remarkable success in curbing uncertainty in real-world problems. Distance measures are widely used to handle uncertainty and discriminate between two objects in a Pythagorean fuzzy environment. The literature suggests that many of the existing distance functions need to meet the circumstances of metric conditions. In addition to that, the calculation via some measures is error-prone as well as gives unreasonable results. To overcome such drawbacks, in this paper, we determine a new metric for Pythagorean fuzzy sets using the assistance of the K-L divergence measure. Many mathematical properties of the introduced measure are discussed. Furthermore, geometrical representation is provided. A comparative study of the proposed and existing distance measures is carried out to establish the superiority of the new measure. Numerical examples provided here have successfully assessed the efficiency and feasibility of the introduced measure in pattern recognition, medical diagnosis, and decision-making problem.