Extensions and intentions in the rough set theory

The approach to rough set theory proposed in this paper is based on the mutual correspondence of the concepts of extension and intension. It is different from the well-known approaches in the literature in that the upper approximations and the lower approximations of ‘unknown’ sets are considered as...

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Bibliographic Details
Published in:Information sciences 1998-06, Vol.107 (1), p.149-167
Main Authors: Bonikowski, Zbigniew, Bryniarski, Edward, Wybraniec-Skardowska, Urszula
Format: Article
Language:English
Subjects:
Approximation spaces
Operations on rough sets
Representative approximation spaces
Rough set inclusion
Rough sets
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Summary:The approach to rough set theory proposed in this paper is based on the mutual correspondence of the concepts of extension and intension. It is different from the well-known approaches in the literature in that the upper approximations and the lower approximations of ‘unknown’ sets are considered as certain families of ‘known’ sets. This approach makes it possible to formulate necessary and sufficient conditions for the existence of operations on rough sets, which are analogous to classical operations on sets. The basic results presented in this paper, based on certain ideas of the second author, were formulated by the first author in his doctoral dissertation prepared under the supervision of the third author.
ISSN:0020-0255
1872-6291
DOI:10.1016/S0020-0255(97)10046-9