Volume 5 • Issue 1 • PP: 01–07 • 2025
A Brief Study on Fuzzy Off-Group Theory
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© 2025 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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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.
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