Abstract
In this paper, we consider a rough set analysis of non-ordinal and ordinal classification data with missing attribute values. We show how this problem can be addressed by several variants of Indiscernibility-based Rough Set Approach (IRSA) and Dominance-based Rough Set Approach (DRSA). We propose some desirable properties that a rough set approach being able to handle missing attribute values should possess. Then, we analyze which of these properties are satisfied by the considered variants of IRSA and DRSA.
References
Błaszczyński, J., Słowiński, R., Szeląg, M.: Induction of ordinal classification rules from incomplete data. In: Yao, J.T., Yang, Y., Słowiński, R., Greco, S., Li, H., Mitra, S., Polkowski, L. (eds.) RSCTC 2012. LNCS (LNAI), vol. 7413, pp. 56–65. Springer, Heidelberg (2012). doi:10.1007/978-3-642-32115-3_6
Błaszczyński, J., Greco, S., Słowiński, R., Szeląg, M.: Monotonic variable consistency rough set approaches. In: Yao, J.T., Lingras, P., Wu, W.-Z., Szczuka, M., Cercone, N.J., Ślezak, D. (eds.) RSKT 2007. LNCS (LNAI), vol. 4481, pp. 126–133. Springer, Heidelberg (2007). doi:10.1007/978-3-540-72458-2_15
Błaszczyński, J., Greco, S., Słowiński, R., Szeląg, M.: Monotonic variable consistency rough set approaches. Int. J. Approximate Reason. 50(7), 979–999 (2009)
Błaszczyński, J., Słowiński, R., Szeląg, M.: Rough set approach to classification of incomplete data. Research Report RA-22/2013, Poznań University of Technology (2013)
Dembczyński, K., Greco, S., Słowiński, R.: Rough set approach to multiple criteria classification with imprecise evaluations and assignments. Eur. J. Oper. Res. 198(2), 626–636 (2009)
Greco, S., Matarazzo, B., Słowinski, R.: Handling missing values in rough set analysis of multi-attribute and multi-criteria decision problems. In: Zhong, N., Skowron, A., Ohsuga, S. (eds.) RSFDGrC 1999. LNCS (LNAI), vol. 1711, pp. 146–157. Springer, Heidelberg (1999). doi:10.1007/978-3-540-48061-7_19
Greco, S., Matarazzo, B., Słowiński, R.: Dealing with missing data in rough set analysis of multi-attribute and multi-criteria decision problems. In: Zanakis, S., et al. (eds.) Decision Making: Recent Developments and Worldwide Applications, pp. 295–316. Kluwer, Dordrecht (2000)
Greco, S., Matarazzo, B., Słowiński, R.: Rough sets theory for multicriteria decision analysis. Eur. J. Oper. Res. 129(1), 1–47 (2001)
Greco, S., Matarazzo, B., Słowiński, R.: Granular computing for reasoning about ordered data: the dominance-based rough set approach. In: Pedrycz, W., et al. (eds.) Handbook of Granular Computing, Chap. 15. Wiley, Chichester (2008)
Grzymala-Busse, J.W., Hu, M.: A comaprison of several approaches in missing attribute values in data mining. In: Ziarko, W., Yao, Y. (eds.) RSCTC 2000. LNAI, vol. 2005, pp. 378–385. Springer, Berlin (2001). doi:10.1007/3-540-45554-X_46
Grzymala-Busse, J.W.: Mining incomplete data - a rough set approach. In: Yao, J.T., et al. (eds.) RSKT 2011. LNCS, vol. 6954, pp. 1–7. Springer, Berlin (2011). doi:10.1007/978-3-642-24425-4_1
Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning. Springer, Berlin (2009)
Hu, M.L., Liu, S.F.: A rough analysis method of multi-attribute decision making for handling decision system with incomplete information. In: Proceedings of 2007 IEEE International Conference on Grey Systems and Intelligent Services, 18–20, November 2007, Nanjing, China (2007)
Kryszkiewicz, M.: Rough set approach to incomplete information systems. Inf. Sci. 112, 39–49 (1998)
Liang, D., Yang, S.X., Jiang, C., Zheng, X., Liu, D.: A new extended dominance relation approach based on probabilistic rough set theory. In: Yu, J., Greco, S., Lingras, P., Wang, G., Skowron, A. (eds.) RSKT 2010. LNCS (LNAI), vol. 6401, pp. 175–180. Springer, Heidelberg (2010). doi:10.1007/978-3-642-16248-0_28
Pawlak, Z.: Rough Sets. Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)
Słowiński, R., Greco, S., Matarazzo, B.: Rough set methodology for decision aiding. In: Kacprzyk, J., Pedrycz, W. (eds.) Handbook of Computational Intelligence, Chap. 22, pp. 349–370. Springer, Berlin (2015). doi:10.1007/978-3-662-43505-2_22
Słowiński, R., Vanderpooten, D.: A generalized definition of rough approximations based on similarity. IEEE Trans. Knowl. Data Eng. 12(2), 331–336 (2000)
Stefanowski, J., Tsoukias, A.: Incomplete information tables and rough classification. Comput. Intell. 17(3), 545–566 (2001)
Yang, X., Yang, J., Wu, C., Yu, D.: Dominance-based rough set approach and knowledge reductions in incomplete ordered information system. Inf. Sci. 178(4), 1219–1234 (2008)
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The first author acknowledges financial support from the Poznań University of Technology, grant no. 09/91/DSMK/0609.
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Szeląg, M., Błaszczyński, J., Słowiński, R. (2017). Rough Set Analysis of Classification Data with Missing Values. In: Polkowski, L., et al. Rough Sets. IJCRS 2017. Lecture Notes in Computer Science(), vol 10313. Springer, Cham. https://doi.org/10.1007/978-3-319-60837-2_44
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