Abstract
In the paper, we consider the notions of exact and approximate decision reducts for binary decision tables. We present upper bounds on minimum cardinality of exact and approximate reducts depending on the number of rows (objects) in the decision table. We show that the bound for exact reducts is unimprovable in the general case, and the bound for approximate reducts is almost unimprovable in the general case.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Moshkov, M., Piliszczuk, M., Zielosko, B.: Universal attribute reduction problem. In: Kryszkiewicz, M., Peters, J.F., Rybiński, H., Skowron, A. (eds.) RSEISP 2007. LNCS (LNAI), vol. 4585, pp. 417–426. Springer, Heidelberg (2007)
Moshkov, M., Piliszczuk, M., Zielosko, B.: Partial Covers, Reducts and Decision Rules in Rough Sets: Theory and Applications. Springer book series Studies in Computational Intelligence, vol. 145. Springer, Heidelberg (2008)
Nguyen, H.S., Ślȩzak, D.: Approximate reducts and association rules – correspondence and complexity results. In: Zhong, N., Skowron, A., Ohsuga, S. (eds.) RSFDGrC 1999. LNCS (LNAI), vol. 1711, pp. 137–145. Springer, Heidelberg (1999)
Pawlak, Z.: Rough sets. International J. Comp. Inform. Science 11, 341–356 (1982)
Pawlak, Z.: Rough Sets – Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)
Pawlak, Z., Skowron, A.: Rudiments of rough sets. Information Sciences 177(1), 3–27 (2007); Rough sets: Some extensions. Information Sciences 177(1), 28–40 (2007); Rough sets and boolean reasoning. Information Sciences 177(1) 41–73 (2007)
Skowron, A.: Rough sets in KDD. In: Proceedings of the 16th World Computer Congress (IFIP 2000), Beijing, China, pp. 1–14 (2000)
Skowron, A., Rauszer, C.: The discernibility matrices and functions in information systems. In: Slowinski, R. (ed.) Intelligent Decision Support. Handbook of Applications and Advances of the Rough Set Theory, pp. 331–362. Kluwer Academic Publishers, Dordrecht (1992)
Ślȩzak, D.: Approximate entropy reducts. Fundamenta Informaticae 53, 365–390 (2002)
Ślȩzak, D., Wróblewski, J.: Order-based genetic algorithms for the search of approximate entropy reducts. In: Wang, G., Liu, Q., Yao, Y., Skowron, A. (eds.) RSFDGrC 2003. LNCS (LNAI), vol. 2639, pp. 308–311. Springer, Heidelberg (2003)
Wróblewski, J.: Ensembles of classifiers based on approximate reducts. Fundamenta Informaticae 47, 351–360 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chikalov, I., Moshkov, M., Zielosko, B. (2010). Upper Bounds on Minimum Cardinality of Exact and Approximate Reducts. In: Szczuka, M., Kryszkiewicz, M., Ramanna, S., Jensen, R., Hu, Q. (eds) Rough Sets and Current Trends in Computing. RSCTC 2010. Lecture Notes in Computer Science(), vol 6086. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13529-3_44
Download citation
DOI: https://doi.org/10.1007/978-3-642-13529-3_44
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13528-6
Online ISBN: 978-3-642-13529-3
eBook Packages: Computer ScienceComputer Science (R0)