Abstract
When applying rough set theory to rule learning, one commonly associates equivalence relations or partitions to a complete information table and tolerance relations or coverings to an incomplete table. Such associations are sometimes misleading. We argue that Pawlak three-step approach for data analysis indeed uses both partitions and coverings for a complete information table. A slightly different formulation of Pawlak approach is given based on the notions of attribute reducts of a classification table, attribute reducts of objects and rule reducts. Variations of Pawlak approach are examined.
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Blaszczynski, J., Slowinski, R., Szelag, M.: Sequential covering rule induction algorithm for variable consistency rough set approaches. Information Sciences 181, 987–1002 (2011)
Cendrowska, J.: PRISM: An algorithm for inducing modular rules. International Journal of Man-Machine Studies 27, 349–370 (1987)
Fürnkranz, J.: Separate-and-conquer rule learning. Artificial Intelligence Review 13, 3–54 (1999)
Grzymala-Busse, J.: LERS - A system for learning from examples based on rough sets. In: Slowinski, R. (ed.) Intelligent Decision Support: Handbook of Applications and Advances of the Rough Sets Theory, pp. 3–18. Kluwer Academic Publishers, Dordrecht (1992)
Grzymala-Busse, J., Rzasa, W.: Approximation space and LEM2-like algorithms for computing local coverings. Fundamenta Informaticae 85, 205–217 (2008)
Mi, J.S., Leung, Y., Wu, W.Z.: Dependence-space-based attribute reduction in consistent decision tables. Soft Computing 15, 261–268 (2011)
Pawlak, Z.: Rough sets: Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishers, Dordrecht (1991)
Pawlak, Z., Skowron, A.: Rough sets and Boolean reasoning. Information Sciences 177, 41–73 (2007)
Quinlin, J.R.: Induction of decision tree. Machine Learning 1, 81–106 (1986)
Van Mechelen, I., Hampton, J., Michalski, R.S., Theuns, P. (eds.): Categories and Concepts: Theoretical Views and Inductive Data Analysis. Academic Press, New York (1993)
Yao, Y.Y.: Interpreting concept learning in cognitive informatics and granular computing. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 39, 855–866 (2009)
Yao, Y.Y., Deng, X.F.: A granular computing paradigm for concept learning (2011) (manuscript)
Yao, Y., Zhao, Y., Wang, J.: On reduct construction algorithms. In: Wang, G.-Y., Peters, J.F., Skowron, A., Yao, Y. (eds.) RSKT 2006. LNCS (LNAI), vol. 4062, pp. 297–304. Springer, Heidelberg (2006)
Zhao, Y., Yao, Y.Y., Yao, J.T.: Level construction of decision trees for classification. International Journal Software Engineering and Knowledge Engineering 16, 103–126 (2006)
Zhu, W., Wang, F.Y.: Reduction and axiomization of covering generalized rough sets. Information Sciences 152, 217–230 (2003)
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Yao, Y., Fu, R. (2011). Partitions, Coverings, Reducts and Rule Learning in Rough Set Theory. In: Yao, J., Ramanna, S., Wang, G., Suraj, Z. (eds) Rough Sets and Knowledge Technology. RSKT 2011. Lecture Notes in Computer Science(), vol 6954. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24425-4_16
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DOI: https://doi.org/10.1007/978-3-642-24425-4_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24424-7
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