aspg-21-3258-1791472122 20261008150842 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2025 25 3 Ibrahim S. Ahmed Department of Mathematics. College of Education-Tuzkhurmatu. Tikrit University. Iraq Ali Al-Fayadh Department of Mathematics and Computer Applications. College of Science. Al – Nahrain University. Iraq Hassan H. Ebrahim Department of Mathematics. College of Computer Science and Mathematics. Tikrit University. Iraq Luma S. Abdalbaqi Department of Mathematics. College of Computer Science and Mathematics. Tikrit University. Iraq The generalization for interval fuzzy set name as neutrosophic set employed to construct a measurable space in this work. The measurable space with respect to a ring of sets that is closed under difference and union, is studied. The objective of this study is to extend the notion of a ring of sets by using neutrosophic sets. Neutrosophic set concept has gained popularity in various fields of mathematics, probability, and other sciences due to its many uses, especially when dealing with uncertainties. Several different properties of neutrosophic ring are studied. Examples and characterizations to the proposed extension are given. 2025 187 193 3258 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.250317 https://www.americaspg.com/journal/21/article/3258 https://www.americaspg.com/storage/51729686559.pdf