Abstract
In this study, we define the concept of an omega-fuzzy set omega-fuzzy subring and show that the intersection of two omega-fuzzy subrings is also an omega-fuzzy subring of a given ring. Moreover, we give the notion of an omega-fuzzy ideal and investigate different fundamental results of this phenomenon. We extend this ideology to propose the notion of an omega-fuzzy coset and develop a quotient ring with respect to this particular fuzzy ideal analog into a classical quotient ring. Additionally, we found an omega-fuzzy quotient subring. We also define the idea of a support set of an omega-fuzzy set and prove various important characteristics of this phenomenon. Further, we describe omega-fuzzy homomorphism and omega-fuzzy isomorphism. We establish an omega-fuzzy homomorphism between an omega-fuzzy subring of the quotient ring and an omega-fuzzy subring of this ring. We constitute a significant relationship between two omega-fuzzy subrings of quotient rings under the given omega-fuzzy surjective homomorphism and prove some more fundamental theorems of omega-fuzzy homomorphism for these specific fuzzy subrings. Finally, we present three fundamental theorems of omega-fuzzy isomorphism.