Abstract
The standard rough set theory has been introduced in 1982 [5]. In this paper we use a topological concepts to investigate a new definitions for the lower and upper approximation operators. This approach is a generalization for Pawlak approach and the generalizations in [2, 7, 10, 12, 13, 14, 15, 16]. Properties of the suggested concepts are obtained. Also comparison between our approach and previous approaches are given. In this case, we show that the generalized approximation space is a topological space for any reflexive relation.
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References
Allam, A.A., Bakeir, M.Y., Abo-Tabl, E.A.: A relational view to some basic topological concepts (submitted)
Kim, D.: Data classification based on tolerant rough set. Pattern Recognition 34, 1613–1624 (2001)
Bloch, I.: On links between mathematical morphology and rough sets. Pattern Recognition 33, 1487–1496 (2000)
Kortelainen, J.: On relationship between modified sets, topological spaces and rough sets. Fuzzy sets and systems 61, 91–95 (1994)
Pawlak, Z.: Rough sets. International Journal of Information and Computer Sciences 11, 341–356 (1982)
Pawlak, Z.: Rough sets. In: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)
Pomykala, J.A.: Approximation operations in approximation space. Bulletin of the Polish Academy of Sciences, Mathematics 35, 653–662 (1987)
Rasiowa, H.: An algebraic approach to non-classical logics. North-Holland, Amsterdam (1974)
Slowinski, R., Vanderpooten, D.: A Generalized Definition of Rough Approximations Based on Similarity. IEEE Transactions on Knowledge and Data Engineering 12(2), 331–336 (2000)
Wybraniec-Skardowska, U.: On a generalization of approximation space. Bulletin of the Polish Academy of Sciences, Mathematics 37, 51–61 (1989)
Yao, Y.Y.: Two views of the theory of rough sets in finite universes. International Journal of Approximation Reasoning 15, 291–317 (1996)
Yao, Y.Y.: Constructive and algebraic methods of the theory of rough sets. Information Sciences 109, 21–47 (1998)
Yao, Y.Y.: Generalized rough set models. In: Polkowski, L., Skowron, A. (eds.) Rough Sets in Knowledge Discovery, pp. 286–318. Physica, Heidelberg (1998)
Yao, Y.Y.: Relational interpretations of neighborhood operators and rough set approximation operators. Information Sciences 111, 239–259 (1998)
Yao, Y.Y., Lin, T.Y.: Generalized of rough sets using model logic. Intelligent Automation and Soft Computing 2, 103–120 (1996)
Yao, Y.Y., Wong, S.K.M., Lin, T.Y.: A review of rough set models. In: Lin, T.Y., Cercone, N. (eds.) Rough Sets and Data Mining: Analysis for Imprecise Data, pp. 47–75. Kluwer Academic Publishers, Boston (1997)
Electronic Bulletin of Rough Set Community, http://www.cs.uregina.ca/~roughset
Rough Set Database System, http://rsds.wsiz.rzeszow.pl/rsds.php
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© 2005 Springer-Verlag Berlin Heidelberg
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Allam, A.A., Bakeir, M.Y., Abo-Tabl, E.A. (2005). New Approach for Basic Rough Set Concepts. In: Ślęzak, D., Wang, G., Szczuka, M., Düntsch, I., Yao, Y. (eds) Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. RSFDGrC 2005. Lecture Notes in Computer Science(), vol 3641. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11548669_7
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DOI: https://doi.org/10.1007/11548669_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28653-0
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