Application of New Neutrosophic Open Set via Neutrosophic Topological Spaces

S.R. Yaseen; Qays Hatem Imran; Giorgio Nordo

Authors

S.R. Yaseen Department of Mathematics, College of Education for Pure Science, Tikrit University, Tikrit, Iraq;
Qays Hatem Imran Department of Mathematics, College of Education for Pure Science, Al-Muthanna University, Samawah, Iraq;
Giorgio Nordo MIFT Department, University of Messina, Viale Ferdinando Stagno d’Alcontres, 31– 98166 Messina, Italy;

Keywords:

Supplier selection, Neutrosophic scoring function, Neutrosophic β-open sets

Abstract

We introduce a new class of open sets in neutrosophic topological spaces, called neutrosophic I
open (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 NI
openness 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.

DOI 10.5281/zenodo.19209686