On reduction of morphological covering rough sets

Authors:
Tingquan Deng;Yanmei Chen
Affiliations:
College of Science, Harbin Engineering University, Harbin, P.R. China;Department of Mathematics, Harbin Institute of Technology, Harbin, P.R. China
Venue:
FSKD'06 Proceedings of the Third international conference on Fuzzy Systems and Knowledge Discovery
Year:
2006

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Abstract

Both rough set theory and mathematical morphology originated from the classical set theory, and are characterized by using dual operators sharing similar properties. In this paper, a notion of morphological covering rough set is introduced by means of combining rough set with fundamental morphological operators. The focus of this paper is on constructing a covering and a pair of morphological rough approximation operators. The issue on reduction of a morphological covering is explored and the procedure for generating the reduction is presented. Necessary and sufficient conditions on characterization of the reduction are proved.