Journal of Neutrosophic and Fuzzy Systems JNFS 2771-6449 2771-6430 10.54216/JNFS https://www.americaspg.com/journals/show/2672 2021 2021 Gaziantep University, Department of Mathematics, Gaziantep, Turkey Ahmed Ahmed Gaziantep University, Department of Mathematics, Gaziantep, Turkey Necati Olgun 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 2023 46 52 10.54216/JNFS.070205 https://www.americaspg.com/articleinfo/24/show/2672