Definable and rough sets in covering-based approximation spaces

Authors:
Arun Kumar;Mohua Banerjee
Affiliations:
Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur, India;Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur, India
Venue:
RSKT'12 Proceedings of the 7th international conference on Rough Sets and Knowledge Technology
Year:
2012

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Abstract

This article explores the notion of definable sets in approximation spaces based on coverings, and presents properties of algebraic structures obtained from the collection of all definable sets. A granule-based definition of lower and upper approximations of sets, is then investigated. A rough set is defined in the usual way, viz. as a pair of the lower and upper approximations of a set, and we investigate the algebraic structure of the collection of all rough sets.