Title: Approximate equalities using topological space

Authors: Alka Tripathi; Kanchan Tyagi

Addresses: Department of Mathematics, Jaypee Institute of Information Technology, A-10, Sector-62, Noida (Uttar Pradesh), 201307, India ' Jaypee Institute of Information Technology, A-10, Sector-62, Noida-201307 (U.P.), 201307, India

Abstract: Rough equivalence of sets generalises the concept of rough approximate equalities. Two sets may not be rough equal but may be rough equivalent. This leads to study of approximate equality in higher level. In this paper, we have studied rough set from topological point of view. Here, we have proposed definitions of rough equality, rough equivalence, approximate rough equality and approximate rough equivalence of two sets with the help of interior and closure. Some properties related to proposed equalities are proved topologically (with the help of interior and closure). Real life example is given to understand the rough equivalence situations.

Keywords: rough sets; approximate equalities; topological space; rough topology; rough equality; rough equivalence.

DOI: 10.1504/IJGCRSIS.2014.068024

International Journal of Granular Computing, Rough Sets and Intelligent Systems, 2014 Vol.3 No.4, pp.272 - 291

Received: 01 Oct 2013
Accepted: 28 Mar 2014

Published online: 10 Mar 2015 *

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