Fuzzy Algebraic Structures on Pseudo-UP Algebra

Amaneh, Alachew

dc.contributor.author	Amaneh, Alachew
dc.date.accessioned	2025-06-19T12:33:51Z
dc.date.available	2025-06-19T12:33:51Z
dc.date.issued	2025-03
dc.identifier.uri	http://ir.bdu.edu.et/handle/123456789/16741
dc.description.abstract	Fuzzy set theories offered well-defined mathematical frameworks for analyze vague phenomena. Core mathematical theories, including algebra, topology, lattice theory and analysis are subject to fuzzification. Many researchers explored the fuzzification of subalgebras, ideals, Cartesian prod ucts, homomorphisms, congruence relation and other related concepts. In this study, an attempt has been made to introduce a new class of algebraic structures in fuzzy set, bipolar fuzzy set and Q-fuzzy set. The concepts of fuzzy pseudo-UP subalgebras and fuzzy pseudo-UP ideals have been introduced for pseudo-UP algebra and their properties have been duly characterized. The relation between fuzzy pseudo-UP subalgebra and fuzzy pseudo-UP ideal on pseudo-UP algebra has been established. In the study, an introduction has been given to develop the ideas of fuzzy pseudo-UP subalgebra and fuzzy pseudo-UP ideal of pseudo-UP algebra, while also comparing fuzzy pseudo-UP subal gebra and fuzzy pseudo-UP ideal to that of the crisp pseudo-UP algebra. The study also described the relationship between fuzzy pseudo-UP subalgebras and fuzzy pseudo-UP ideals of pseudo-UP algebra and their level-cuts and the image and pre-image of fuzzy pseudo-UP subalgebras, and fuzzy pseudo-UP ideals of pseudo-UP algebras under homomorphism have been analyzed. The notion of Cartesian products of two fuzzy pseudo-UP subalgebras and two fuzzy pseudo-UP ide als of two pseudo-UP algebras have also been discussed, and some related properties have been investigated. The concept of the strongest fuzzy relations on a fuzzy pseudo-UP subalgebra and a fuzzy pseudo-UP ideal of a pseudo-UP algebra have been addressed. The relationships between the strongest fuzzy relations and the fuzzy pseudo-UP subalgebras, fuzzy pseudo-UP ideals have been studied. On the other hand, the study deal with fuzzy congruence relations and their classes called fuzzy congruence classes in pseudo-UP algebra. Fuzzy congruence relations have been characterized using fuzzy pseudo-UP ideals. Additionally, we have used their level set to define the fuzzy con gruence relation. The Cartesian product of two fuzzy congruences and the intersection of two fuzzy congruences have been discussed. The study also provided the connection between the collection of fuzzy pseudo-UP ideals and the collection of fuzzy congruence relations in pseudo-UP algebra. The study demonstrated that there exists an associated algebra that is a pseudo-UP algebra for each fuzzy pseudo-UP ideal and fuzzy congruence generated by a fuzzy pseudo-UP ideal. vi Again, the concept of an extreme fuzzy pseudo-UP ideal was introduced and described. A fuzzy uniform structure studied on a pseudo-UP algebra. The notion of a fuzzy uniform topological pseudo-UP algebra was explored. This notion is a pseudo-UP algebra equipped with a specific type of fuzzy topology that ensures the two binary operations are topologically fuzzy continuous. This concept extends the notion of fuzzy uniform topological pseudo UP- algebra. Consequently, many properties of fuzzy topological pseudo-UP algebra have been derived. Further, concepts of a bipolar fuzzy pseudo-UP sub-algebra and a bipolar fuzzy pseudo-UP ideal of pseudo-UP algebra have been explained. Then, the intersection of bipolar fuzzy pseudo-UP subalgebras and the intersection of bipolar fuzzy pseudo-UP ideals have been proved. As a result, they became bipolar fuzzy pseudo-UP sub-algebra and bipolar fuzzy pseudo-UP ideal respectively. They are proved under their arbitrary intersections. Thus, it has been shown that every bipolar fuzzy pseudo-UP ideal is a bipolar fuzzy pseudo-UP subalgebra, and that the converse need not be necessarily true. In the study, it has also been stated that the homomorphic images and inverse im ages of bipolar fuzzy pseudo-UP subalgebra and bipolar fuzzy pseudo-UP ideal are again bipolar fuzzy pseudo-UP sub-algebra and bipolar fuzzy pseudo-UP ideal respectively. Cartesian products of fuzzy pseudo-UP algebras have been studied. In this study, a Q-fuzzy pseudo-UP sub-algebra and a Q-fuzzy pseudo-UP ideal have been con ceptualized. It has also been portrayed that the Q-fuzzy pseudo-UP ideal is a Q-fuzzy pseudo-UP subalgebra of a pseudo-UP algebra. Moreover, characterizations of Q-fuzzy pseudo-UP ideals of pseudo-UP algebra in terms of their level sets have been given. It has also been stated that the ho momorphic image and inverse image of a Q- fuzzy pseudo-UP subalgebra and a Q-fuzzy pseudo UP ideal are again Q-fuzzy pseudo-UP subalgebra and Q-fuzzy pseudo-UP ideal of a pseudo-UP algebra respectively.	en_US
dc.language.iso	en	en_US
dc.subject	Mathematics	en_US
dc.title	Fuzzy Algebraic Structures on Pseudo-UP Algebra	en_US
dc.type	Dissartation	en_US