Abstract:
I n 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. Homomor-
phism of K-algebras is studied. Isomorphism theorems are given. We intro-
duce 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
(∈, ∈ ∨q)- 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 investi-
gate some of their properties.
