aspg-21-2658-1791468728 20261008141208 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2024 24 1 Jos´e Sanabria Departamento de Matem´aticas, Facultad de Educaci´on y Ciencias, Universidad de Sucre, Sincelejo, Colombia Carlos Granados Doctorado en Matem´aticas, Universidad de Antioquia, Medell´ın, Colombia Carlos Carpintero Facultad de Ciencias B´asicas, Ingenier´ıas y Arquitectura, Corporaci´on Universitaria del Caribe-CECAR, Sincelejo, Colombia In this article, we use the notion of neutrosophic local function to introduce a new neutrosophic operator in the context of a neutrosophic topological space equipped with a neutrosophic ideal. Also, we introduce and study some new classes of neutrosophic sets defined in terms of the neutrosophic local function and the new notion of neutrosophic operator given. 2024 186 195 2658 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.240117 https://www.americaspg.com/journal/21/article/2658 https://www.americaspg.com/storage/01712552410.pdf