Rough approximations of similarity measures under Pythagorean fuzzy information: a novel approach to decision-making

Rough sets offer an efficient mathematical framework to formalize the process of data analysis and knowledge discovery in the presence of incomplete or uncertain information. The hybridization of rough sets with other mathematical structures is a significant tool to tackle ambiguity and obscurity as compared to a single mathematical approach. The integration of rough sets with other extensions of fuzzy sets provides a way to deal with the complexity and uncertainty of real-world decision-making problems. Similarity measures can be discussed more accurately when lower and upper approximate values of a crisp set are to be dealt with Pythagorean fuzzy information. In this research, a hybrid model is developed by assimilating the concept of rough approximations with various similarity measures under Pythagorean fuzzy information. Upper and lower approximation operators for a Pythagorean fuzzy set are defined. Several types of similarity measures between Pythagorean fuzzy rough sets including, cotangent, cosine, sine and tangent similarity measures and their important properties are discussed in detail. The similarity measures are also extended using different configuration parameters. We exhibit the efficiency of the suggested similarity measures using various measurement parameters. Different types of weighted similarity measures are defined using Pythagorean fuzzy rough sets. Comparison between all similarity measures is discussed to notice which similarity measure provides more precise results. The significance of the presented similarity measures is studied with an application to recognize the pattern of COVID-19 spread and its impacts in different countries. A comparative analysis of the impact of COVID-19 spread in ten different countries with existing techniques is given and explained using numerical tables and graphs. The main advantages and out-performance of the suggested approaches are highlighted in detail.