An Analysis of Approximate Equalities based on Rough Set Theory

Abstract

Three types of rough equalities were introduced by Novotny and Pawlak ([1, 2, 3]), which take care of approximate equalities of sets. These sets may not be equal in the usual sense. These notions were generalized by Tripathy, Mitra and Ojha ([10]), who introduced the concepts of rough equivalences of sets. These approximate equalities of sets capture equality of the concerned sets at a higher level than their corresponding rough equalities. Some more properties were proved in [11]. In this paper, we introduce two other types of approximate equalities of sets, called the approximate rough equivalences and approximate rough equality. We study some properties of these four types of approximate equalities and analyse their relevance from the application point of view.