In this study, ?-interval valued set is defined whose elements are closed sub-intervals including ? of unit interval that is I = [0, 1]. With different order relation on this set, the properties of ?-interval valued set are examined. By the help of this order relation, it is shown that ?-interval valued set is complete lattice. Negation function on ?-interval valued set is given in order to study the theoretical properties of this set. By means of discussions on ?-interval valued set, the fundamental features of ?-interval valued set are studied. By the help of ?-interval valued set, ?-interval valued fuzzy sets are defined. The fundamental algebraic properties of these sets are examined. The level subsets of ?-interval valued fuzzy sets are defined to give the relations between ?-interval valued sets and crisp sets. With the help of this definition, some propositions and examples are given.