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In order to involve user knowledge in determining equality of sets, which maynot be equal in the mathematical sense, three types of approximate (rough)equalities were introduced by Novotny and Pawlak ([8, 9, 10]). These notionswere generalized by Tripathy, Mitra and Ojha ([13]), who introduced theconcepts of approximate (rough) equivalences of sets. Rough equivalencescapture equality of sets at a higher level than rough equalities. Moreproperties of these concepts were established in [14]. Combining the conditionsfor the two types of approximate equalities, two more approximate equalitieswere introduced by Tripathy [12] and a comparative analysis of their relativeefficiency was provided. In [15], the four types of approximate equalities wereextended by considering rough fuzzy sets instead of only rough sets. In factthe concepts of leveled approximate equalities were introduced and propertieswere studied. In this paper we proceed further by introducing and studying theapproximate equalities based on rough intuitionistic fuzzy sets instead ofrough fuzzy sets. That is we introduce the concepts of approximate(rough)equalities of intuitionistic fuzzy sets and study their properties. Weprovide some real life examples to show the applications of rough equalities offuzzy sets and rough equalities of intuitionistic fuzzy sets.

Approximate Equalities on Rough Intuitionistic Fuzzy Sets and an Analysis of Approximate Equalities