On Neutrosophic Axial Interior, Exterior, and Confused Sets via Neutrosophic Axial Topological Spaces

In this paper, we introduce and systematically investigate a novel class of neutrosophic sets, designated as neutrosophic axial sets (NA-sets). We analyze their foundational and algebraic properties, along with the newly defined operations of neutrosophic axial intersection and union. Furthermore, we introduce neutrosophic axial topological spaces and establish the concepts of NA-interior, NA-exterior, and NA-confused sets, exploring their core characteristics and interplay. Specifically, we prove that NA-sets are closed under NA-intersection and NA-union, establish the relevant De Morgan and lattice laws, and delineate the fundamental properties of the associated topological operators. Finally, counterexamples are provided for set inclusions that fail to hold as equalities.