An algebraic framework for fuzzy soft subrings, cosets, and ring homomorphisms

This paper constructs a general algebraic framework for fuzzy soft structures in the context of ring theory. Building upon fuzzy soft set theory, the study introduces and investigates fuzzy soft subrings and fuzzy soft ideals over rings. Characterizations are established through fuzzy soft level subsets, yielding necessary and sufficient conditions that associate fuzzy soft ideals with classical ring ideals. Moreover, fuzzy soft cosets associated with fuzzy soft subrings and ideals are defined and shown to form a ring under properly defined operations. Quotient constructions are further discussed and a fuzzy soft analogue of the classical ring homomorphism theorem is presented. The results extend some classical algebraic notions to the fuzzy soft setting which enriches the theoretical foundation of fuzzy algebra.