aspg-24-2672-1791482519 20261008180159 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Journal of Neutrosophic and Fuzzy Systems JNFS 2771-6430 2771-6449 2023 7 2 Ahmed Hatip Gaziantep University, Department of Mathematics, Gaziantep, Turkey Necati Olgun Gaziantep University, Department of Mathematics, Gaziantep, Turkey The concept of two-fold algebras is generated by merging some special sets such as fuzzy sets, neutrosophic sets or plithogenic sets with various algebraic structures. The main objective of this research paper is to provide a strict mathematical definition and a general study of two-fold fuzzy vector spaces defined over the real numbers and also two-fold fuzzy vector spaces defined over the complex numbers, as well as two-fold fuzzy algebraic modules defined over commutative rings with unity. The elementary properties and algebraic operations of those structures will be explained through many theorems and mathematical proofs. 2023 46 52 2672 https://creativecommons.org/licenses/by/4.0/ 10.54216/JNFS.070205 https://www.americaspg.com/journal/24/article/2672 https://www.americaspg.com/storage/81714352981.pdf