A New Type of Nano Generalized Closed Sets in Nano Topological Spaces with Applications to Attribute Reduction in Student Dropout Risk

Abstract

This research study focuses on the notion of -closed sets, which play a significant role in the structural analysis of nano topological spaces and the development of generalized topological concepts. The -closed sets is introduced as a new class of nano generalized closed sets formulated within the framework of nano topology. In this study, the concept of -closed sets is defined and investigated through its fundamental properties and characteristic features. The relationships between -closed sets and several existing classes of nano closed sets are also established and analyzed. Moreover, the notions of -interior and -closure are characterized using -closed sets, highlighting their structural behavior and topological significance within nano topological spaces. Further, the concept is applied to attribute reduction in student dropout risk analysis in higher education. By using nano topological bases, the key attributes affecting dropout risk are identified. The study shows that the proposed method can be effectively used for decision-making problems.