Binary Hypersoft Sets: Operations and Topoloy

Abstract

This paper introduces a novel extension of hypersoft sets, termed binary hypersoft sets (BnHySSs), representing an advanced generalization of binary soft sets over two universal sets and a parameter set. It presents fundamental operations of BnHySSs such as subset, superset, equality, complement, null and absolute sets, extended union/intersection, union, intersection, difference, AND, and OR operations. We also examine foundational properties and provide a comparative analysis of BnHySSs, HySSs, and BnSSs. Building on this foundation, we introduce the notion of binary hypersoft topology and its corresponding subspace concept. Further, we explore topological notions within this framework, including limit points, neighborhoods, closure, interior, exterior, and boundary in the context of BnHySSs.