Fuzzy Algebraic Structures on JU-Algebra

Selamawit, Hunie

dc.contributor.author	Selamawit, Hunie
dc.date.accessioned	2026-08-17T07:19:20Z
dc.date.available	2026-08-17T07:19:20Z
dc.date.issued	2025-11
dc.identifier.uri	http://ir.bdu.edu.et/handle/123456789/16978
dc.description.abstract	Fuzzy set theory provides a mathematical framework for handling uncertainty and partial truth, ex tending classical set theory by allowing elements to have degrees of membership. This study aimed to introduce a new class of algebraic structures in fuzzy sets, including Q-fuzzy sets, T-fuzzy sets, and interval-valued fuzzy sets. The concepts of fuzzy JU-subalgebras and fuzzy JU-ideals have been introduced for JU-algebras, and their properties have been duly characterized. Also, we estab lish the relation between fuzzy JU-subalgebra and fuzzy JU-ideal on JU-algebra. This study begins with foundational concepts of fuzzy sets, Q-fuzzy sets, doubt Q-fuzzy sets, T-fuzzy sets, interval valued fuzzy sets, and anti-fuzzy sets. It also introduces key algebraic systems such as BCK algebras, BCI-algebras, UP-algebras, PS-algebras, B-algebras, BG-algebras, and KU-algebras to establish the necessary theoretical background for the development of JU-algebraic theory. In this dissertation, we investigate fuzzy subalgebras and fuzzy ideals in JU-algebras, with empha sis on prime fuzzy sets and p-multiplicative relations. Their behavior under homomorphisms and Cartesian products is rigorously analyzed. The theory is extended to Q-fuzzy and doubt Q-fuzzy structures, incorporating normality and doubt relations, and exploring their level subsets. Further, we studied T-fuzzy structures, characterized by chain conditions and Cartesian product. Interval valued fuzzy structures, including (˜ E, ˜ F)-based models, are introduced to represent uncertainty more precisely, with analysis of their properties under mappings, level set, and product opera tions. The study also explores anti-fuzzy structures, presenting complementary notions through anti-fuzzy subalgebras and ideals, and investigating their relational dynamics. Overall, this disser tation contributes to the advancement of fuzzy algebraic theory by extending fuzzy set concepts to JU-algebras and providing a unified framework for analyzing their structural behavior	en_US
dc.language.iso	en	en_US
dc.subject	Mathematics	en_US
dc.title	Fuzzy Algebraic Structures on JU-Algebra	en_US
dc.type	Dissartation	en_US