Rings and ideals in a vague soft set setting

In this paper, we present a more accurate definition of the concepts pertaining to the theory of vague soft rings. We redefine the notion of vague soft rings and other concepts related to this concept such as vague soft ideals, idealistic vague soft rings and vague soft ring homomorphism in a manner which better reflects the characteristics of the concept of vague soft sets that were used to construct these concepts. The fundamental properties and structural characteristics of these concepts are then studied and discussed. The relationship between the concepts introduced here and the corresponding concepts in soft ring theory and classical ring theory are investigated. Lastly, we prove that the vague soft ring homomorphism introduced here preserves vague soft rings.