Q-fuzzy structure on JU-algebra

Résumé

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.

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