A Novel Framework of Pythagorean Fuzzy Dominance-Based Rough Sets and Analysis of Knowledge Reductions

Abstract

The dominance-based rough set approach is crucial to the advancement of rough set theory. It gives a more thorough and adaptable framework for knowledge acquisition, information analysis, and DM. It is a means of expressing discrepancies resulting from the examination of the domains with specified preference rankings of the characteristics. This work seeks to extend the Rough set approach utilizing dominance relationships to a Pythagorean fuzzy setting. The lower and upper approximations of Pythagorean fuzzy dominance-based rough set are determined by using the constructive technique. Next, we examine the basic characteristics for the rough estimations relying on the Pythagorean fuzzy dominance. By combining Approximate Distribution Reductions with a Pythagorean fuzzy dominance-based rough set, reductions are prescribed in four distinct manners. Additionally, the discernibility matrices and theorems connected to these reductions are produced. Such findings are all Pythagorean fuzzy generalizations or extensions of the conventional rough set method relying on dominance. Finally, the conceptual ideas are supported with a numerical example.

Keywords

• Dominance–based rough set approach
• dominance–based fuzzy rough set approach
• Pythagorean fuzzy dominance–based rough set approach
• approximate distribution reduct
• approximate distribution consistent set