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. (2011). Experiments on probabilistic approximations. In Proceedings of the 2011 IEEE International Conference on Granular Computing (pp. 144–149).
Clark, P.G., & Grzymala-Busse, J.W. (2012). 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).
Clark, P.G., & Grzymala-Busse, J.W. (2014a). A comparison of two versions of the MLEM2 rule induction algorithm extended to probabilistic approximations. In Proceedings of the 9-th International Conference on Rough Sets and Current Trends in Computing (pp. 109–119).
Clark, P.G., & Grzymala-Busse, J.W. (2014b). Mining incomplete data with attribute-concept values and “do not care” conditions. In Proceedings of the 9th International Conference on Hybrid Artificial Intelligence Systems (pp. 146–167).
Clark, P.G., & Grzymala-Busse, J.W. (2014c). Mining incomplete data with lost values and attribute-concept values. In Proceedings of the 2014 IEEE International Conference on Granular Computing (pp. 49–54).
Grzymala-Busse, J.W. (1997). A new version of the rule induction system LERS. Fundamenta Informaticae, 31, 27–39.
Grzymala-Busse, J.W. (2002). 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).
Grzymala-Busse, J.W. (2003). Rough set strategies to data with missing attribute values. In Notes of the Workshop on Foundations and New Directions of Data Mining, in conjunction with the Third International Conference on Data Mining (pp. 56–63).
Grzymala-Busse, J.W. (2004a). Data with missing attribute values: Generalization of indiscernibility relation and rule induction. Transactions on Rough Sets, 1, 78–95.
Grzymala-Busse, J.W. (2004b). 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).
Grzymala-Busse, J.W. (2011). Generalized parameterized approximations. In Proceedings of the 6-th International Conference on Rough Sets and Knowledge Technology (pp. 136–145).
Grzymala-Busse, J.W. (2013). Generalized probabilistic approximations. Transactions on Rough Sets, 16, 1–16.
Grzymala-Busse, J.W., & Rzasa, W. (2006). Local and global approximations for incomplete data. In Proceedings of the Fifth International Conference on Rough Sets and Current Trends in Computing (pp. 244–253).
Grzymala-Busse, J.W., & Rzasa, W. (2008). Local and global approximations for incomplete data. Transactions on Rough Sets, 8, 21–34.
Grzymala-Busse, J.W., & Ziarko, W. (2003). Datamining based on rough sets. In J. Wang (Ed.), Data Mining: Opportunities and Challenges (pp. 142–173). Hershey: Idea Group Publ.
Lin, T.Y. (1992). Topological and fuzzy rough sets. In R. Slowinski (Ed.), Intelligent Decision Support. Handbook of Applications and Advances of the Rough Sets Theory (pp. 287–304). Dordrecht: Kluwer Academic Publishers.
Pawlak, Z., & Skowron, A. (2007). Rough sets: Some extensions. Information Sciences, 177, 28–40.
Pawlak, Z., Wong, S.K.M., & Ziarko, W. (1988). Rough sets: probabilistic versus deterministic approach. International Journal of Man-Machine Studies, 29, 81–95.
Ślȩzak, D., & Ziarko, W. (2005). The investigation of the bayesian rough set model. International Journal of Approximate Reasoning, 40, 81–91.
Wong, S.K.M., & Ziarko, W. (1986). 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).
Yao, Y.Y. (2008). Probabilistic rough set approximations. International Journal of Approximate Reasoning, 49, 255–271.
Yao, Y.Y., & Wong, S.K.M. (1992). A decision theoretic framework for approximate concepts. International Journal of Man-Machine Studies, 37, 793–809.
Ziarko, W. (1993). Variable precision rough set model. Journal of Computer and System Sciences, 46 (1), 39–59.
Ziarko, W. (2008). Probabilistic approach to rough sets. International Journal of Approximate Reasoning, 49, 272–284.
Acknowledgments
This work was partially supported by the Polish National Science Centre grant DEC-2013/09/B/ST6/01568 and by the Centre for Innovation and Transfer of Natural Sciences and Engineering Knowledge of University of Rzeszow, Poland.
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Clark, P.G., Grzymala-Busse, J.W. & Rzasa, W. A comparison of two MLEM2 rule induction algorithms extended to probabilistic approximations. J Intell Inf Syst 47, 515–529 (2016). https://doi.org/10.1007/s10844-015-0385-0
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DOI: https://doi.org/10.1007/s10844-015-0385-0