Idealistic Vague Soft Rings and Vague Soft Ring Homomorphism

Soft set theory, proposed by Molodtsov has been regarded as an effective mathematical tool to deal with uncertainties. Vague set is a set of objects, each of which has a grade of membership whose value is a continuous subinterval of [0, 1]. Such a set is characterized by a truth-membership function and a falsemembership function. Thus, a vague set is actually a form of fuzzy set, albeit a more accurate form of fuzzy set. Hence the concept of vague soft sets were introduced as an extension to the notion of soft sets, as a means to overcome the problem of assigning a suitable value for the grade of membership of an element in a set since the exact grade of membership may be unknown. Hence using the concept of vague soft sets, we are able to ascertain that the grade of membership of an element lies within a certain closed interval which can help to overcome the problems faced when using ordinary soft sets or fuzzy soft sets. In this paper, we introduce the novel concept of idealistic vague soft rings and vague soft ring homomorphism in Rosenfeld’s sense. The notion of idealistic vague soft rings is an extension to the concept of vague soft rings and vague soft ideals of a ring. The basic properties and structural characteristics of these concepts are also studied and discussed. 1276 G. Selvachandran and A. R. Salleh