Neutrosophic Vague Hypersoft Open and Closed Mappings

Abstract

In this paper, we introduce and formalize the concepts of Interval-Valued Neutrosophic Hypersoft (IVNHS) open mappings and IVNHS-closed mappings within the framework of IVNHS-topological spaces. We establish necessary and sufficient conditions for these mappings using the fundamental topological operators of interior and closure. Furthermore, we extensively investigate the behavior of these mappings under composition. Specifically, we prove that the composition of two IVNHS-open (or closed) mappings preserves their respective properties. We also derive the structural conditions under which the component mappings inherit openness or closedness from their composite forms, utilizing the auxiliary conditions of injectivity, surjectivity, and continuity. These findings enrich the structural theory of interval-valued neutrosophic hypersoft topology and pave the way for deeper geometric and algebraic mappings within multi-attribute decision-making environments.