Journal of Neutrosophic and Fuzzy Systems JNFS 2771-6449 2771-6430 10.54216/JNFS https://www.americaspg.com/journals/show/2624 2021 2021 Tishreen University, Department of Mathematics, Latakia, Syria Mohammad Mohammad This paper is dedicated to studying the algebraic structure generated from the fusion of two-fold algebras with the standard fuzzy number theoretical system, where the novel fuzzy algebraic structure will be defined with a well-defined binary operation, and then its substructures will be studied concerning the corresponding operation such as hyperunder ideals, and two-fold fuzzy homomorphisms. Also, many examples will be illustrated to clarify the validity of our work. 2023 2023 24 29 10.54216/JNFS.070202 https://www.americaspg.com/articleinfo/24/show/2624