We present the theory of a new class of logical algebras, known as K-algebras, which was built on a group G by adjoining the induced binary operation on G. We introduce the notion of fuzzy K-ideals of K- algebras and present some interesting properties. We describe fuzzy isomorphism theorems of K-algebras. We discuss a new generalized fuzzy ideal of a K-algebra and present some of its properties. We explain the concept of interval- valued fuzzy ideals of K-algebras and discuss some of their results. We explain the notion of bifuzzy ideals of K-algebras and investigate several interesting properties. We also talk about the concept of bifuzzy topological K-algebras.