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A cubic set is a hybrid structure involving an interval-valued fuzzy set and a fuzzy set. A cubic soft set is a parameterized family of cubic sets. It is yet another hybrid structure obtained by combining cubic sets with soft sets. A generalized interval-valued intuitionistic fuzzy soft set is a further generalization of a cubic soft set where instead of interval component of cubic sets, we consider interval-valued intuitionistic fuzzy sets. This book is the outcome of the research work carried out by us towards finding the application of soft sets, cubic soft sets, Neutrosophic cubic soft sets and Generalized interval-valued intuitionistic fuzzy soft sets.