Vague soft gamma rings and idealistic vague soft gamma rings

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]. This set is characterized by a truth-membership function and a false-membership function. Thus, a vague set is actually more accurate form of fuzzy set. Hence the concept of vague soft sets were introduced as an extension to the notion of soft sets. 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 ordinariy soft set or fuzzy soft sets. In this thesis, using the vague soft set's concepts which were introduced by Rosenfeld's approach, vague soft gamma rings, vague soft gamma ideals of a gamma ring, the vague soft gamma ideal of a vague soft gamma ring, idealistic vague soft gamma ring and vague soft gamma ring homomorphism are studied.