Exploring Quantum and Binary Soft í µí»¼–Open Sets:Practical Applications through Soft Topologies

Abstract

This paper presents an exploration of Quantum and Binary Soft 𝛼 –Open Sets, focusing on their practical applications within the framework of soft topologies. In the binary soft topological spaces, binary soft 𝛼-closures, binary soft 𝛼-interiors and binary soft 𝛼-open (closed) sets are defined and study many of their properties along with how these concepts are connected to other soft open (closed) sets via theorems and propositions. The non-coincidence of these soft set theory concepts are proven via the use of counter examples. Further we look into the idea of binary soft 𝛼-continuous function which is described on family of binary soft 𝛼-open (closed) sets referred to as soft class over two starting universes with parameters, as well as their links to other soft continuous and weaker sections of soft continuous functions. The findings of this study represent the beginning of a new soft structure that will work as theoretical base for topological applications on soft sets, and will also act as a springboard for the extension of information systems and other engineering disciplines. Additionally, we demonstrate how binary soft set concept can be applied in medical information system. AMS Subject Classifications: 54A05, 54C08, 54A99