Variable Precision Rough Set Model in Information Tables with Missing Values

Yoshifumi Kusunoki; Masahiro Inuiguchi

doi:10.20965/jaciii.2011.p0110

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JACIII Vol.15 No.1 pp. 110-116

doi: 10.20965/jaciii.2011.p0110

(2011)

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Variable Precision Rough Set Model in Information Tables with Missing Values

Yoshifumi Kusunoki and Masahiro Inuiguchi

Department of Systems Innovation, Graduate School of Engineering Sciences, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan

Received:

March 9, 2010

Accepted:

April 22, 2010

Published:

January 20, 2011

Keywords:

rough sets, missing values, variable precision rough set model, lower and upper rough membership functions

Abstract

In this paper, we study rough set models in information tables with missing values. The variable precision rough set model proposed by Ziarko tolerates misclassification error using a membership function in complete information tables. We generalize the variable precision rough set in information tables with missing values. Because of incompleteness, the membership degree of each objects becomes an interval value. We define six different approximate regions using the lower and upper bounds of membership functions. The properties of the proposed rough set model are investigated. Moreover we show that the proposed model is a generalization of rough set models based on similarity relations.

Cite this article as:

Y. Kusunoki and M. Inuiguchi, “Variable Precision Rough Set Model in Information Tables with Missing Values,” J. Adv. Comput. Intell. Intell. Inform., Vol.15, No.1, pp. 110-116, 2011.

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References

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[12] P. J. Lingras and Y. Y. Yao, “Data mining using extensions of the rough set model,” J. Am. Soc. Inform. Sci., Vol.49, No.5, pp. 415-422, 1998.
[13] J. W. Grzymala-Busse and W. J. Grzymala-Busse, “An experimental comparison of three rough set approaches to missing attribute values,” In J. F. Peters et al. (Eds.), Trans. on Rough Sets VI, LNCS 4374, Springer-Verlag, Berlin Heidelberg, pp. 31-50, 2007.
[14] R. Słowiński and J. Stefanowski, “Rough classification in incomplete information systems,” Math. Comput. Modelling, Vol.12(10/11), pp. 1347-1357, 1989.
[15] Y. Leung, W. Z. Wu, and W. X. Zhang, “Knowledge acquisition in incomplete information systems: A rough set approach,” Euro. J. Oper. Res., Vol.168, pp. 164-180, 2006.
[16] M. Nakata and H. Sakai, “Applying rough sets to data tables containing imprecise information under probabilistic interpretation,” In S. Greco et al. (Eds.), RSCTC 2006, LNAI 4259, Springer-Verlag Berlin Heidelberg, pp. 213-223, 2006.
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[18] Y. Leung and D. Li, “Maximal consistent block technique for rule acquisition in incomplete information systems,” Inf. Sci., Vol.153, pp. 85-106, 2003.
[19] W. Ziarko, “Variable precision rough set model,” J. Comput. Sys. Sci., Vol.46, pp. 39-59, 1993.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] Z. Pawlak, “Rough sets,” Int. J. Inf. Comput. Sci., Vol.11, No.5, pp. 341-356, 1982.

[2] [2] Z. Pawlak and A. Skowron, “Rudiments of rough sets,” Inf. Sci., Vol.177, pp. 3-27, 2007.

[3] [3] I. Düntsch, G. Gediga, and E. Orlowska, “Relational attribute systems,” Int. J. Hum.-Comput. Studies, Vol.55, pp. 293-309, 2001.

[4] [4] J. W. Grzymala-Busse, “Characteristic relations for incomplete data: A generalization of the indiscernibility relation,” In J. F. Peters and A. Skowron (Eds.), Trans. on Rough Sets IV, LNCS, 3700, Springer-Verlag, Berlin Heidelberg, pp. 58-68, 2005.

[5] [5] J. Stefanowski and A. Tsoukiàs, “Incomplete information tables and rough classification,” Comput. Intell., Vol.17, No.3, pp. 545-566, 2001.

[6] [6] J. R. Quinlan, “Induction of decision trees,” Mach. Learn., Vol.1, pp. 81-106, 1986.

[7] [7] M. R. Chmieliwski, J. W. Grzymala-Busse, N. W. Peterson, and S. Than, “The rule induction system LERS – A version for personal computers,” Found. Comput. Decis. Sci., Vol.18, pp. 181-212, 1993.

[8] [8] M. Kryszkiewicz, “Rules in incomplete information systems,” Inf. Sci., Vol.113, pp. 271-292, 1999.

[9] [9] H. Sakai, R. Ishibashi, and M. Nakata, “Lower and upper approximations of rules in non-deterministic information systems,”C.-C. Chen et al. (Eds.), RSCTC 2008, LNAI 5306, Springer-Verlag, Heidelberg, pp. 299-309, 2008.

[10] [10] H. Sakai, K. Hayashi, H. Kimura, and M. Nakata, “An aspect of decision making in rough non-deterministic information analysis,” K. Nakamatsu et al. (Eds.), New Advan. in Intel. Decision Techno., SCI 199, Springer-Verlag Berlin Heidelberg, pp. 527-536, 2009.

[11] [11] M. Kryszkiewicz, “Rough set approach to incomplete information systems,” Inf. Sci., Vol.112, pp. 39-49, 1998.

[12] [12] P. J. Lingras and Y. Y. Yao, “Data mining using extensions of the rough set model,” J. Am. Soc. Inform. Sci., Vol.49, No.5, pp. 415-422, 1998.

[13] [13] J. W. Grzymala-Busse and W. J. Grzymala-Busse, “An experimental comparison of three rough set approaches to missing attribute values,” In J. F. Peters et al. (Eds.), Trans. on Rough Sets VI, LNCS 4374, Springer-Verlag, Berlin Heidelberg, pp. 31-50, 2007.

[14] [14] R. Słowiński and J. Stefanowski, “Rough classification in incomplete information systems,” Math. Comput. Modelling, Vol.12(10/11), pp. 1347-1357, 1989.

[15] [15] Y. Leung, W. Z. Wu, and W. X. Zhang, “Knowledge acquisition in incomplete information systems: A rough set approach,” Euro. J. Oper. Res., Vol.168, pp. 164-180, 2006.

[16] [16] M. Nakata and H. Sakai, “Applying rough sets to data tables containing imprecise information under probabilistic interpretation,” In S. Greco et al. (Eds.), RSCTC 2006, LNAI 4259, Springer-Verlag Berlin Heidelberg, pp. 213-223, 2006.

[17] [17] M. Nakata and H. Sakai, “Rough sets approximations in data tables containing missing values,” IEEE Int. Conf. on Fuzzy Syst., art. No.4630442, pp. 673-680, 2008.

[18] [18] Y. Leung and D. Li, “Maximal consistent block technique for rule acquisition in incomplete information systems,” Inf. Sci., Vol.153, pp. 85-106, 2003.

[19] [19] W. Ziarko, “Variable precision rough set model,” J. Comput. Sys. Sci., Vol.46, pp. 39-59, 1993.