AN EXTENSIVE STUDY ON GENERALIZED ROUGH CLOSED SETS IN ROUGH TOPOLOGICAL SPACES

Abstract

This study explores the properties and characterizations of generalized rough closed sets within rough topological spaces to enhance understanding of their structure and applications. Employing theoretical analysis, the research introduces the concept of generalized rough closed sets and investigates their fundamental attributes, including their relationships with rough open and closed sets. Key findings demonstrate that every rough closed set qualifies as a generalized rough closed set, while the union of such sets remains within the same class. The work further characterizes rough spaces where every generalized rough closed set is also a rough closed set, termed Rough- space, establishing conditions for their equivalence. These insights contribute to the development of refined models in data analysis and digital topology, offering potential for improved techniques in image processing and machine learning. The findings advance the mathematical framework of rough set theory, fostering its practical application in complex data systems.