Title of Thesis

On Bifuzzy K-algebras

Author(s)

 Muhammad Akram

Abstract
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.

1

1.1 Literature Survey

2.1 K-algebras

2.2 Ideals of K-algebras
2.3 Characterization of K-algebras using self maps

3.1 K-homomorphisms of K-algebras

3.2 Structure of homomorphisms of K-algebras

4.1 Fuzzy K-ideals of K-algebras

4.2 (ε,ε Vq)- fuzzy ideals

5.1 Interval-valued fuzzy ideals

5.2 New fuzzy K-subalgebras

6.1 Bifuzzy ideals of K-algebras

6.2 Bifuzzy topological K-algebras

7.1 Conclusions

7.2 Applications

7.3 Future Work

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