On Rough Equalities and Rough Equivalences of Sets

Authors:
Bala Krushna Tripathy;Anirban Mitra;Jaladhar Ojha
Affiliations:
School of Computing Sciences, V.I.T. University, Vellore, India 632 014;Department of Computer Science, Berhampur University, Berhampur, India 760 007;Department of Mathematics, Khallikote College, Berhampur, India 760001
Venue:
RSCTC '08 Proceedings of the 6th International Conference on Rough Sets and Current Trends in Computing
Year:
2008

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Abstract

The different types of rough equalities [4,5,6] of sets deal with approximate equalities of sets which may not be equal in the usual sense of classical set theory. In this article, we make further study of the properties of rough equalities. A more general kind of equality of sets (we call it rough equivalence) shall be introduced, which captures equalities of sets at a higher level than rough equalities. Many properties of this new notion and its comparison with rough equalities shall be dealt with. We shall make use of the concepts of rough inclusions of sets in this sequel.