Rough Set Approach to Incomplete Data
In this paper incomplete data are assumed to be decision tables with missing attribute values. We discuss two main cases of missing attribute values: lost values (a value was recorded but it is unavailable) and “do not care” conditions (the original values were irrelevant). Through the entire paper the same calculus, based on computations of blocks of attribute-value pairs, is used. Complete data are characterized by the indiscernibility relations, a basic idea of rough set theory. Incomplete data are characterized by characteristic relations. Using characteristic relations, lower and upper approximations are generalized for incomplete data. Finally, from three definitions of such approximations certain and possible rule sets may be induced.
KeywordsIncomplete Data Characteristic Relation Decision Table Rule Induction Entire Paper
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- 1.Grzymala-Busse, J.W.: On the unknown attribute values in learning from examples. In: Raś, Z.W., Zemankova, M. (eds.) ISMIS 1991. LNCS, vol. 542, pp. 368–377. Springer, Heidelberg (1991)Google Scholar
- 2.Grzymala-Busse, J.W.: 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)Google Scholar
- 3.Grzymala-Busse, J.W.: MLEM2: A new algorithm for rule induction from imperfect data. In: Proceedings of the 9th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2002, Annecy, France, July 1-5, pp. 243–250 (2002)Google Scholar
- 4.Grzymala-Busse, J.W.: Rough set strategies to data with missing attribute values. In: Workshop Notes, Foundations and New Directions of Data Mining, the 3-rd International Conference on Data Mining, Melbourne, FL, USA, November 19–22, pp. 56–63 (2003)Google Scholar
- 5.Grzymala-Busse, J.W., Wang, A.Y.: Modified algorithms LEM1 and LEM2 for rule induction from data with missing attribute values. In: Proc. of the Fifth International Workshop on Rough Sets and Soft Computing (RSSC 1997) at the Third Joint Conference on Information Sciences (JCIS 1997), Research Triangle Park, NC, March 2-5, pp. 69–72 (1997)Google Scholar
- 6.Kryszkiewicz, M.: Rough set approach to incomplete information systems. In: Proceedings of the Second Annual Joint Conference on Information Sciences, Wrightsville Beach, NC, September 28–October 1, pp. 194–197 (1995)Google Scholar