Abstract
As a classical problem of Rough Sets, the reduct problem still attracts research interests recently. Many existing works on the reduct problem are devoted into finding optimal reducts where the optimal metrics is the number of attributes. In reality, however, this optimal metrics is not fair since some attributes may have much larger domains than others, and they tend to have better discernibility thus more likely to be included in optimal reducts. To cope with this fairness problem, in this paper we propose the concept of average discernibility which takes into consideration the cardinality of the attribute domain. Attribute reduction based on average discernibility can be implemented through assigning each attribute an appropriate weight in the reduction process to adjust attribute significance. We point out further that some human experts knowledge can also be expressed by the weight vector formed by weights of all attributes. Then we propose a weighted reduction algorithm based on discernibility, and analyze the usefulness the weight vector along with its setting policies. This algorithm is consistent with the existing reduction algorithm based on discernibility in that the former contains the latter as a special case when all elements of the weight vector are equal and non-zero. Experiment results of the Bridges dataset in the UCI library validate the usefulness of our algorithm.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Pawlak, Z.: Rough sets. International Journal of Computer and Information Sciences 11, 341–356 (1982)
Wang, G., Yu, H., Yang, D.: Decision table reduction based on conditional information entropy. Chinese Journal of Computers 25(7), 1–8 (2002)
Zhang, W., Mi, J., Wu, W.: Knowledge reductions in inconsistent information systems. Chinese Journal of Computers 26(1), 12–18 (2003)
Xu, Y., Peng, H., Wang, Z.: Reduction algorithm based on discernibility and its applications. Chinese Journal of Computers 26(1), 97–103 (2003)
Min, F., Bai, Z., He, M., Liu, Q.: The reduct problem with specified attributes. In: Rough Sets and Soft Computing in Intelligent Agent and Web Technology, International Workshop at WI-IAT 2005, pp. 36–42 (2005)
Wong, S.K.M., Ziarko, W.: On optimal decision rules in decision tables. Bulletin of polish academy of sciences 33, 693–696 (1985)
Wróblewski, J.: Finding minimal reducts using genetic algorithms. In: Wang, P.P. (ed.) JCIS 1995, Wrightsville Beach, North Carolina, pp. 186–189 (1995)
Pawlak, Z.: Some issues on rough sets. In: Peters, J.F., Skowron, A., Grzymała-Busse, J.W., Kostek, B.z., Świniarski, R.W., Szczuka, M. (eds.) Transactions on Rough Sets I. LNCS, vol. 3100, pp. 1–58. Springer, Heidelberg (2004)
Nguyen, S.H.: Regularity Analysis And Its Application. In Data Mining. PhD thesis, Warsaw University, Warsaw, Poland (1999)
Blake, C.L., Merz, C.J.: UCI repository of machine learning databases (1998), http://www.ics.uci.edu/~mlearn/mlrepository.html
Bazan, J., Szczuka, M.: The RSES homepage (1994–2005), http://alfa.mimuw.edu.pl/~rses
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Xu, C., Min, F. (2006). Weighted Reduction for Decision Tables. In: Wang, L., Jiao, L., Shi, G., Li, X., Liu, J. (eds) Fuzzy Systems and Knowledge Discovery. FSKD 2006. Lecture Notes in Computer Science(), vol 4223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11881599_28
Download citation
DOI: https://doi.org/10.1007/11881599_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-45916-3
Online ISBN: 978-3-540-45917-0
eBook Packages: Computer ScienceComputer Science (R0)