Prospects for Applied Mathematics and Data Analysis PAMDA 2836-4449 10.54216/PAMDA https://www.americaspg.com/journals/show/3986 2022 2022 Independent Researcher, Shinjuku, Shinjuku-ku, Tokyo, Japan Takaaki Takaaki Department of Mathematics, Institute of Numerical Sciences, Gomal University, Dera Ismail Khan 29050, KPK, Pakistan Arif Mehmood Khattak Department of Information Technology, Management Technical College, Southern Technical University, Basrah, 61004, Iraq Arkan A. Ghaib Uncertainty-handling frameworks such as fuzzy sets, rough sets, intuitionistic fuzzy sets, neutrosophic sets, Picture Fuzzy Sets, hyperneutrosophic sets, and plithogenic sets have attracted sustained research interest. These frameworks have been widely applied across various mathematical disciplines, including graph theory, topology, algebra, and group theory. More recently, the concept of the offset has emerged as a powerful and promising generalization of conventional uncertainty models. In this paper, we introduce a novel algebraic structure called the Fuzzy Off-Group and conduct an in-depth study of its fundamental mathematical properties. We hope that this framework will further advance research in group theory and uncertainty modeling with offsets, and that it will open up new avenues for application. 2025 2025 01 11 10.54216/PAMDA.050101 https://www.americaspg.com/articleinfo/34/show/3986