Intuitionistic Fuzzy Structures on Pms-Algebras

Lamesgin, Beza

dc.contributor.author	Lamesgin, Beza
dc.date.accessioned	2023-06-21T08:24:47Z
dc.date.available	2023-06-21T08:24:47Z
dc.date.issued	2023-06
dc.identifier.uri	http://ir.bdu.edu.et/handle/123456789/15419
dc.description.abstract	This research aims at developing intuitionistic fuzzy structures in PMS-algebra. In this con text, we introduce the notion of intuitionistic fuzzy structures of PMS-subalgebra, intuitionistic fuzzy structures of PMS-ideal of PMS-algebra, and establish the relation between intuitionistic fuzzy PMS-subalgebra and intuitionistic fuzzy PMS-ideal. A condition for an intuitionistic fuzzy set in a PMS-algebra to be an intuitionistic fuzzy PMS-subalgebra and an intuitionis tic fuzzy PMS-ideal is given. The relation between level subsets, intuitionistic fuzzy PMS subalgebras, and intuitionistic fuzzy PMS-ideals of PMS-algebra is obtained. Homomorphism and Cartesian products of intuitionistic fuzzy PMS-subalgebras and intuitionistic fuzzy PMS ideals are studied in detail. The concept of the strongest intuitionistic fuzzy relations on an intuitionistic fuzzy PMS-subalgebra and an intuitionistic fuzzy PMS-ideal of a PMS-algebra is addressed, and the relationships between the strongest intuitionistic fuzzy relations and the intuitionistic fuzzy PMS-subalgebras are studied. The notions of intuitionistic Q-fuzzy PMS-subalgebras and intuitionistic Q-fuzzy PMS-ideals of PMS-algebra are described, and the interrelation is established between intuitionistic Q-fuzzy PMS-subalgebra and intuitionistic Q-fuzzy PMS-ideal of PMS algebra. A condition for an intuitionistic Q-fuzzy set in a PMS algebra to be an intuitionistic Q-fuzzy PMS-subalgebra and an intuitionistic Q-fuzzy PMS-ideal of a PMS-algebra has been established. Characterizations of intuitionistic Q-fuzzy PMS-ideals of PMS-algebras in terms of their level sets are given. The intuitionistic Q-fuzzy characteristic PMS-ideal and the characteristic PMS-ideal in a PMS-algebra are defined, and related findings are derived. The relationships between an intuitionistic Q-fuzzy characteristic PMS-ideal and the characteristic upper and lower level ideals of a PMS-algebra are addressed. The homo morphism and Cartesian products of intuitionistic Q-fuzzy PMS-algebras are studied. The strongest Q-fuzzy relations in intuitionistic Q-fuzzy PMS-algebra are considered, and relations between the strongest intuitionistic Q-fuzzy relation and the intuitionistic Q-fuzzy PMS-ideal are explored. The notions of t-intuitionistic fuzzy PMS-subalgebra and t-intuitionistic fuzzy PMS-ideal of PMS-algebra are introduced. The relationships between a t-intuitionistic fuzzy PMS-ideal and a t-intuitionistic fuzzy PMS-subalgebra of a PMS-algebra, as well as the re lationships between an intuitionistic fuzzy PMS-ideal and a t-intuitionistic fuzzy PMS-ideal, are discussed in detail. A condition for an intuitionistic fuzzy set to be a t-intuitionistic fuzzy PMS-subalgebra and a t-intuitionistic fuzzy PMS-ideal is provided. The t-intuitionistic fuzzy PMS-subalgebras and t-intuitionistic fuzzy PMS-ideals of PMS-algebra are described v using their (α, β) level cuts. The homomorphism and Cartesian products of t-intuitionistic fuzzy PMS-subalgebra and t-intuitionistic fuzzy PMS-ideal of PMS-algebra are discussed, and some related results are derived. The Cartesian products of the t-intuitionistic fuzzy PMS subalgebras and t-intuitionistic fuzzy PMS-ideals are also characterized using their (α, β) level cuts. The strongest t-intuitionistic fuzzy PMS-relation in a PMS-algebra is defined, and the re lationships between the strongest t-intuitionistic fuzzy PMS-relation and t-intuitionistic fuzzy PMS-ideal are studied.	en_US
dc.language.iso	en_US	en_US
dc.subject	Mathematics	en_US
dc.title	Intuitionistic Fuzzy Structures on Pms-Algebras	en_US
dc.type	Dissartation	en_US