International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3258 2020 2020 Department of Mathematics. College of Education-Tuzkhurmatu. Tikrit University. Iraq Ibrahim Ibrahim Department of Mathematics and Computer Applications. College of Science. Al – Nahrain University. Iraq Ali Al Al-Fayadh Department of Mathematics. College of Computer Science and Mathematics. Tikrit University. Iraq Hassan H. Ebrahim Department of Mathematics. College of Computer Science and Mathematics. Tikrit University. Iraq Luma S. Abdalbaqi 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 2025 187 193 10.54216/IJNS.250317 https://www.americaspg.com/articleinfo/21/show/3258