Akram, Muhammad (2010) On Bifuzzy K-algebras. PhD thesis, PMAS-Arid Agriculture University, Rawalpindi.
In this thesis we introduce a new class of logical algebras: K-algebras on a group G with identity element e by adjoining the induced binary operations on a group G, if G is not an elementary abelian 2-group. A K-algebra is non-commutative and non-associative with right identity element e. We characterize K-algebras by using their left and right mappings. Homomorphism of K-algebras is studied. Isomorphism theorems are given. We introduce the notion of fuzzy K-ideals of K-algebras and give connection between fuzzy ideals and fuzzy K-ideals of K-algebras. Fuzzy isomorphism theorems are given. We discuss a new kind of fuzzy ideal of a K-algebra called, an (ε,ε Vq)- fuzzy ideal. We introduce the notion of interval-valued fuzzy ideals of K-algebras and investigate some of their properties. Using interval-valued fuzzy ideals, characterizations of Noetherian K-algebras are established. A new generalized fuzzy K-subalgebra is introduced. We introduce the notion of bifuzzy ideals of K-algebras and investigate some interesting properties. We also introduce the notion of bifuzzy topological K-algebras and investigate some of their properties.
|Item Type:||Thesis (PhD)|
|Uncontrolled Keywords:||Bifuzzy, K-algebras, logical, left, right, mappings, topological|
|Subjects:||Physical Sciences (f) > Mathematics(f5)|
|Deposited By:||Mr. Javed Memon|
|Deposited On:||01 Jun 2010 12:35|
|Last Modified:||21 Mar 2015 15:38|
Repository Staff Only: item control page