Abstract
A probabilistic approximation is a generalization of the standard idea of lower and upper approximations, defined for equivalence relations. Recently probabilistic approximations were additionally generalized to an arbitrary binary relation so that probabilistic approximations may be applied for incomplete data. We discuss two ways to induce rules from incomplete data using probabilistic approximations, by applying true MLEM2 algorithm and an emulated MLEM2 algorithm. In this paper we report novel research on a comparison of both approaches: new results of experiments on incomplete data with three interpretations of missing attribute values. Our results show that both approaches do not differ much.
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Clark, P.G., Grzymala-Busse, J.W.: Experiments on probabilistic approximations. In: Proceedings of the 2011 IEEE International Conference on Granular Computing, pp. 144–149 (2011)
Clark, P.G., Grzymala-Busse, J.W.: Rule induction using probabilistic approximations and data with missing attribute values. In: Proceedings of the 15-th IASTED International Conference on Artificial Intelligence and Soft Computing, ASC 2012, pp. 235–242 (2012)
Grzymala-Busse, J.W.: A new version of the rule induction system LERS. Fundamenta Informaticae 31, 27–39 (1997)
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, pp. 243–250 (2002)
Grzymala-Busse, J.W.: Rough set strategies to data with missing attribute values. In: Workshop Notes, Foundations and New Directions of Data Mining, in Conjunction with the 3rd International Conference on Data Mining, pp. 56–63 (2003)
Grzymala-Busse, J.W.: Data with missing attribute values: Generalization of indiscernibility relation and rule induction. Transactions on Rough Sets 1, 78–95 (2004)
Grzymala-Busse, J.W.: Three approaches to missing attribute values—a rough set perspective. In: Proceedings of the Workshop on Foundation of Data Mining, in Conjunction with the Fourth IEEE International Conference on Data Mining, pp. 55–62 (2004)
Grzymała-Busse, J.W.: Generalized parameterized approximations. In: Yao, J., Ramanna, S., Wang, G., Suraj, Z. (eds.) RSKT 2011. LNCS, vol. 6954, pp. 136–145. Springer, Heidelberg (2011)
Grzymala-Busse, J.W.: Generalized probabilistic approximations. Transactions on Rough Sets 16, 1–16 (2013)
Grzymala-Busse, J.W., Rzasa, W.: Local and global approximations for incomplete data. In: Greco, S., Hata, Y., Hirano, S., Inuiguchi, M., Miyamoto, S., Nguyen, H.S., Słowiński, R. (eds.) RSCTC 2006. LNCS (LNAI), vol. 4259, pp. 244–253. Springer, Heidelberg (2006)
Grzymala-Busse, J.W., Ziarko, W.: Data mining based on rough sets. In: Wang, J. (ed.) Data Mining: Opportunities and Challenges, pp. 142–173. Idea Group Publ., Hershey (2003)
Lin, T.Y.: Topological and fuzzy rough sets. In: Slowinski, R. (ed.) Intelligent Decision Support. Handbook of Applications and Advances of the Rough Sets Theory, pp. 287–304. Kluwer Academic Publishers, Dordrecht (1992)
Pawlak, Z., Skowron, A.: Rough sets: Some extensions. Information Sciences 177, 28–40 (2007)
Pawlak, Z., Wong, S.K.M., Ziarko, W.: Rough sets: probabilistic versus deterministic approach. International Journal of Man-Machine Studies 29, 81–95 (1988)
Ślęzak, D., Ziarko, W.: The investigation of the bayesian rough set model. International Journal of Approximate Reasoning 40, 81–91 (2005)
Wong, S.K.M., Ziarko, W.: INFER—an adaptive decision support system based on the probabilistic approximate classification. In: Proceedings of the 6-th International Workshop on Expert Systems and their Applications, pp. 713–726 (1986)
Yao, Y.Y.: Probabilistic rough set approximations. International Journal of Approximate Reasoning 49, 255–271 (2008)
Yao, Y.Y., Wong, S.K.M.: A decision theoretic framework for approximate concepts. International Journal of Man-Machine Studies 37, 793–809 (1992)
Ziarko, W.: Variable precision rough set model. Journal of Computer and System Sciences 46(1), 39–59 (1993)
Ziarko, W.: Probabilistic approach to rough sets. International Journal of Approximate Reasoning 49, 272–284 (2008)
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Clark, P.G., Grzymala-Busse, J.W. (2014). A Comparison of Two Versions of the MLEM2 Rule Induction Algorithm Extended to Probabilistic Approximations. In: Cornelis, C., Kryszkiewicz, M., Ślȩzak, D., Ruiz, E.M., Bello, R., Shang, L. (eds) Rough Sets and Current Trends in Computing. RSCTC 2014. Lecture Notes in Computer Science(), vol 8536. Springer, Cham. https://doi.org/10.1007/978-3-319-08644-6_11
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DOI: https://doi.org/10.1007/978-3-319-08644-6_11
Publisher Name: Springer, Cham
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