Application of New Neutrosophic Open Set via Neutrosophic Topological Spaces

We introduce a new class of open sets in neutrosophic topological spaces, called neutrosophic Iopen (NI-open) sets, together with their dual NI-closed sets, defined via neutrosophic δ-interior and δ-closure operators. We establish basic stability (arbitrary unions of NI-open sets and arbitrary intersections of NI-closed sets), give characterizations in terms of the associated interior/closure operators, and prove a decomposition formula expressing every NI-open set as the union of its NδS-interior and Nδβ-interior. We further locate NIopenness within the existing landscape by showing that NδS-open, NδP-open, N-eopen, and Ne∗-open sets are, in general, contained in NI-open sets, while the converses may fail; illustrative examples are provided. Finally, we present a neutrosophic multi-criteria assessment for supplier selection that combines the neutrosophic score with its negative counterpart to rank alternatives under ambiguity and indeterminacy, including a worked example with per-strategy rankings and an assignment rule.