  In order to involve user knowledge in determining equality of sets, which may
not be equal in the mathematical sense, three types of approximate (rough)
equalities were introduced by Novotny and Pawlak ([8, 9, 10]). These notions
were generalized by Tripathy, Mitra and Ojha ([13]), who introduced the
concepts of approximate (rough) equivalences of sets. Rough equivalences
capture equality of sets at a higher level than rough equalities. More
properties of these concepts were established in [14]. Combining the conditions
for the two types of approximate equalities, two more approximate equalities
were introduced by Tripathy [12] and a comparative analysis of their relative
efficiency was provided. In [15], the four types of approximate equalities were
extended by considering rough fuzzy sets instead of only rough sets. In fact
the concepts of leveled approximate equalities were introduced and properties
were studied. In this paper we proceed further by introducing and studying the
approximate equalities based on rough intuitionistic fuzzy sets instead of
rough fuzzy sets. That is we introduce the concepts of approximate
(rough)equalities of intuitionistic fuzzy sets and study their properties. We
provide some real life examples to show the applications of rough equalities of
fuzzy sets and rough equalities of intuitionistic fuzzy sets.
