Abstract
The presentation introduces the basic ideas and investigates the stochastic approach to rough set theory. The major aspects of the stochastic approach to rough set theory to be explored during the presentation are: the probabilistic view of the approximation space, the probabilistic approximations of sets, as expressed via variable precision and Bayesian rough set models, and probabilistic dependencies between sets and multi-valued attributes, as expressed by the absolute certainty gain and expected certainty gain measures, respectively. The measures allow for more comprehensive evaluation of rules computed from data and for computation of attribute reduct, core and significance factors in probabilistic decision tables.
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
Pawlak, Z.: Rough sets. Intl. Journal of Computer and Information Science 11, 341–356 (1982)
Pawlak, Z.: Rough sets - Theoretical Aspects of Reasoning About Data. Kluwer, Dordrecht (1991)
Ziarko, W.: Variable precision rough sets model. Journal of Computer and Systems Sciences 46(1), 39–59 (1993)
Yao, Y.Y., Wong, S.K.M.: A decision theoretic framework for approximating concepts. Intl. Journal of Man-Machine Studies 37, 793–809 (1992)
Wong, S.K.M., Ziarko, W.: Comparison of the probabilistic approximate classification and the fuzzy set model. Intl. Journal for Fuzzy Sets and Systems 21, 357–362 (1986)
Wei, L., Zhang, W.: Probabilistic rough sets characterized by fuzzy sets. In: Wang, G., Liu, Q., Yao, Y., Skowron, A. (eds.) RSFDGrC 2003. LNCS (LNAI), vol. 2639, pp. 173–180. Springer, Heidelberg (2003)
Greco, S., Matarazzo, B., Słowiński, R.: Rough Membership and Bayesian Confirmation Measures for Parameterized Rough Sets. In: Ślęzak, D., Wang, G., Szczuka, M.S., Düntsch, I., Yao, Y. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3641, pp. 314–324. Springer, Heidelberg (2005)
Zhong, N., Dong, J., Ohsuga, S.: Data mining: a probabilistic rough set approach. In: Polkowski, L., Skowron, A. (eds.) Rough Sets and Knowledge Discovery, pp. 127–146. Physica Verlag (1998)
Inuiguchi, M., Miyajima, T.: Variable precision rough set approach to multiple decision tables. In: Ślęzak, D., Wang, G., Szczuka, M., Düntsch, I., Yao, Y. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3641, pp. 304–313. Springer, Heidelberg (2005)
Muto, Y., Kudo, M.: Discernibility-Based Variable Granularity and Kansei Representations. In: Ślęzak, D., Wang, G., Szczuka, M.S., Düntsch, I., Yao, Y. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3641, pp. 692–700. Springer, Heidelberg (2005)
Yao, Y.: Probabilistic approaches to rough sets. Expert Systems 20(5), 287–291 (2003)
Slezak, D., Ziarko, W.: The Investigation of the Bayesian rough set model. Intl. Journal of Approximate Reasoning 40, 81–91 (2005)
Ziarko, W.: Set approximation quality measures in the variable precision rough set model. In: Soft Computing Systems, pp. 442–452. IOS Press, Amsterdam (2001)
Ziarko, W.: Probabilistic rough sets. In: Ślęzak, D., Wang, G., Szczuka, M.S., Düntsch, I., Yao, Y. (eds.) RSFDGrC 2005. LNCS, vol. 3641, pp. 283–293. Springer, Heidelberg (2005)
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
Ziarko, W. (2006). Stochastic Approach to Rough Set Theory. In: Greco, S., et al. Rough Sets and Current Trends in Computing. RSCTC 2006. Lecture Notes in Computer Science(), vol 4259. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11908029_5
Download citation
DOI: https://doi.org/10.1007/11908029_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-47693-1
Online ISBN: 978-3-540-49842-1
eBook Packages: Computer ScienceComputer Science (R0)