Abstract
We consider different variants of Variable Consistency Dominance-based Rough Set Approach (VC-DRSA). These variants produce more general (extended) lower approximations than those computed by Dominance-based Rough Set Approach (DRSA), (i.e., lower approximations that are supersets of those computed by DRSA). They define lower approximations that contain objects characterized by a strong but not necessarily certain relation with approximated sets. This is achieved by introduction of parameters that control consistency of objects included in lower approximations. We show that lower approximations generalized in this way enable us to observe dependencies that remain undiscovered by DRSA. Extended lower approximations are also a better basis for rule generation. In the paper, we focus our considerations on different definitions of generalized lower approximations. We also show definitions of VC-DRSA decision rules, as well as their application to classification/sorting and ranking/choice problems.
This is a preview of subscription content, log in via an institution to check access.
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
Błaszczyński, J., Słowiński, R.: Incremental Induction of Decision Rules from Dominance-based Rough Approximations. Electronic Notes in Theoretical Computer Science 82, 4 (2003)
Dembczyński, K., Pindur, R., Susmaga, R.: Generation of Exhaustive Set of Rules within Dominance-based Rough Set Approach. Electronic Notes in Theoretical Computer Science 82, 4 (2003)
Fortemps, P., Greco, S., Słowiński, R.: Multicriteria decision support using rules that represent rough-graded preference relations (submitted, 2005)
Greco, S., Matarazzo, B., Słowiński, R.: Rough sets theory for multicriteria decision analysis. European Journal of Operational Research 129(1), 1–47 (2001)
Greco, S., Matarazzo, B., Słowiński, R., Stefanowski, J.: Variable Consistency Model of Dominance-Based Rough Sets Approach. In: Ziarko, W.P., Yao, Y. (eds.) RSCTC 2000. LNCS (LNAI), vol. 2005, pp. 170–181. Springer, Heidelberg (2001)
Greco, S., Matarazzo, B., Słowiński, R., Stefanowski, J.: An algorithm for induction of decision rules consistent with the dominance principle. In: Ziarko, W.P., Yao, Y. (eds.) RSCTC 2000. LNCS (LNAI), vol. 2005, pp. 304–313. Springer, Heidelberg (2001)
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, vol. 3641, pp. 314–324. Springer, Heidelberg (2005)
Grzymala-Busse, J.W.: LERS - A system for learning from examples based on rough sets. In: Słowiński, R. (ed.) Intelligent Decision Support. Handbook of Applications and Advances of the Rough sets Theory, pp. 3–18. Kluwer Academic Publishers, Dordrecht (1992)
Pawlak, Z.: Rough sets. International Journal of Information & Computer Sciences 11, 341–356 (1982)
Pawlak, Z., Skowron, A.: Rough membership functions. In: Yaeger, R.R., Fedrizzi, M., Kacprzyk, J. (eds.) Advances in the Dempster Shafer Theory of Evidence, pp. 251–271. John Wiley & Sons, Inc., Chichester (1994)
Ślęzak, D.: Rough Sets and Bayes Factor. Transactions on Rough Sets III, 202–229 (2005)
Ślęzak, D., Ziarko, W.: The investigation of the Bayesian rough set model. International Journal of Approximate Reasoning 40, 81–91 (2005)
Słowiński, R., Stefanowski, J.: RoughDAS and RoughClass software implementations of rough sets approach. In: Słowiński, R. (ed.) Intelligent Decision Support. Handbook of Applications and Advances of the Rough Sets Theory, pp. 445–456. Kluwer Academic Publishers, Dordrecht (1992)
Słowiński, R., Greco, S., Matarazzo, B.: Mining decision-rule preference model from rough approximation of preference relation. In: Proc. 26th IEEE Annual International Conference on Computer Software & Applications, Oxford, England, pp. 1129–1134 (2002)
Słowiński, R., Greco, S.: Inducing Robust Decision Rules from Rough Approximations of a Preference Relation. In: Rutkowski, L., Siekmann, J.H., Tadeusiewicz, R., Zadeh, L.A. (eds.) ICAISC 2004. LNCS (LNAI), vol. 3070, pp. 118–132. Springer, Heidelberg (2004)
Słowiński, R., Greco, S., Matarazzo, B.: Rough Set Based Decision Support. In: Burke, E., Kendall, G. (eds.) Introductory Tutorials on Optimization, Search and Decision Support Methodologies, ch. 16. Kluwer Academic Publishers, Boston (2005)
Skowron, A.: Boolean Reasoning for Decision Rules Generation. In: Komorowski, J., Raś, Z.W. (eds.) ISMIS 1993. LNCS, vol. 689, pp. 295–305. Springer, Heidelberg (1993)
Stefanowski, J.: On rough set based approaches to induction of decision rules. In: Polkowski, L., Skowron, A. (eds.) Rough Sets in Data Mining and Knowledge Discovery, vol. 1, pp. 500–529. Physica-Verlag, Heidelberg (1998)
Ziarko, W.: Variable Precision Rough Set Model. J. Comput. Syst. Sci. 46(1), 39–59 (1993)
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
Błaszczyński, J., Greco, S., Słowiński, R., Szeląg, M. (2006). On Variable Consistency Dominance-Based Rough Set Approaches. 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_22
Download citation
DOI: https://doi.org/10.1007/11908029_22
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)