Q-fuzzy structure on JU-algebra [version 1; peer review: 1 approved, 2 approved with reservations] - Birhanu Assaye Alaba; Mihret Alamneh Taye; Selamawit Hunie Gelaw (F1000Research)
Background JU-algebras, an important class in abstract algebra, are extended here by incorporating fuzzy set theory to handle uncertainty in algebraic structures. In this study, we apply the concept of Q-fuzzy sets to JU-subalgebras and JU-ideals in JU-algebra. Method The study defines Q-fuzzy JU-subalgebras and Q-fuzzy JU-ideals as subsets of a JU-algebra. It also explores lower and upper level subsets of these fuzzy structures to analyze their properties. Additionally, the concepts of Doubt and Normal Q-fuzzy JU-subalgebras and Q-fuzzy JU-ideals are introduced, offering a way to deal with varying degrees of uncertainty and regularity in these algebraic structures. Supportive concepts relevant to this study are presented, along with illustrative examples. Conclusion The study introduces and defines new types of fuzzy structures in JU-algebras, such as Q-fuzzy JU-subalgebras and Q-fuzzy JU-ideals, enhancing classical JU-algebra theory. It also examines key properties of these structures, including their lower and upper level subsets, and investigates specific cases like Doubt and Normal Q-fuzzy structures, paving the way for further exploration of fuzzy algebra in mathematical and applied contexts.