Abstract
We introduce a pair of rough set approximations in formal concept analysis. The proposed approximation operators are defined based on both lattice-theoretic and set-theoretic operators. The properties of the approximation operators are examined. Algorithms for attribute reduction and object reduction in concept lattices are presented.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Pawlak, Z.: Rough sets. International Journal of Computer and Information Science 11, 341–356 (1982)
Pawlak, Z.: Rough Sets Theory and It’s Application to Data Analysis [J]. Cybernetics Systems, An International Journal 29, 661–688 (1998)
Kryszkiewicz, M.: Rough set approach to incomplete systems. Information Sciences 112, 39–49 (1998)
Ziarko, W.: Variable precision rough set model. Journal of Computer and System Sciences 46, 39–59 (1993)
Tsumoto, S.: Automated extraction of medical expert system rules from clinical databases based on rough set theory. Information Sciences 112, 67–84 (1998)
Greco, S., Matarazzo, B., Slowinski, R.: A New Rough Set Approach to Multicriteria and Multiattribute Classification. In: Polkowski, L., Skowron, A. (eds.) RSCTC 1998. LNCS (LNAI), vol. 1424, pp. 60–67. Springer, Heidelberg (1998)
Lin, T.Y., Liu, Q.: Rough approximate operators: axiomatic rough set theory. In: Ziarko, W. (ed.) Rough Sets, Fuzzy Sets and Knowledge Discovery, pp. 256–260. Springer, Berlin (1994)
Quafafou, M.: α-RST: a generalization of rough set theory. Information Science 124, 301–316 (2000)
Slowinski, R., Vanderpooten, D.: Similarity relation as a basis for rough approximations. In: Paul, P. (ed.) Advances in Machine Intelligence and Soft-Computing. Department of Electrical Engineering, pp. 17–33. Duke University, Durham (1997)
Yao, Y.Y., Lin, T.Y.: Generalization of rough sets using modal logic. Intelligent Automation and Soft Computing, An International Journal 2, 103–120 (1996)
Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered Sets, pp. 445–470. Reidel, Dordrecht (1982)
Gediga, G., Wille, R.: Formal Concept Analysis. In: Mathematic Foundations, Springer, Berlin (1999)
Chaudron, L., Maille, N.: Generalized formal concept analysis. In: Ganter, B., Mineau, G.W. (eds.) ICCS 2000. LNCS, vol. 1867, pp. 357–370. Springer, Heidelberg (2000)
Deogun, J.S., Saqer, J.: Monotone concepts for formal concept analysis. Discrete Applied Mathematics 144, 70–78 (2004)
Yao, Y.Y.: Concept lattices in rough set theory. In: Proceedings of 2004 Annual Meeting of the North American Fuzzy Information Processing Society, pp. 796–801 (2004)
Gediga, G., Duentsch, I.: Modal-style operators in qualitative data analysis. In: Rroceedings of the 2002 IEEE International Conference on Data Mining, pp. 155–162 (2002)
Yao, Y.Y.: A comparative study of formal concept analysis and rough set theory in Data analysis. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 59–68. Springer, Heidelberg (2004)
Hu, K., Sui, Y., Lu, Y., Wang, J., Shi, C.: Concept approximation in concept lattice. In: Cheung, D., Williams, G.J., Li, Q. (eds.) PAKDD 2001. LNCS (LNAI), vol. 2035, pp. 167–173. Springer, Heidelberg (2001)
Kent, R.E.: Rough concept analysis: a synthesis of rough sets and formal concept analysis. Fundamenta Informaticae 27, 169–181 (1996)
Saquer, J., Deogun, J.S.: Formal rough concept analysis. In: Zhong, N., Skowron, A., Ohsuga, S. (eds.) RSFDGrC 1999. LNCS (LNAI), vol. 1711, pp. 91–99. Springer, Heidelberg (1999)
Wolff, K.E.: A conceptual view of knowledge bases in rough set theory. In: Ziarko, W.P., Yao, Y. (eds.) RSCTC 2000. LNCS (LNAI), vol. 2005, pp. 220–228. Springer, Heidelberg (2001)
Shao, M.-W., Zhang, W.-X.: The reduction of concept lattices in rough set theory (2004) (manuscript)
Skowron, A., Rauszer, C.: The discernibility matrices and functions in information systems. In: Slowinski, R. (ed.) Intelligent Decision Support: Handbook of Applications and Advances of Rough Sets Theory, pp. 331–362. Kluwer Academic Publishers, Dordrecht (1992)
Yao, Y.Y., Chen, Y.: Rough set approximations in formal concept analysis. In: Proceedings of 2004 Annual Meeting of the North American Fuzzy Information Processing Society, pp. 73–78 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Shao, MW., Zhang, WX. (2005). Approximation in Formal Concept Analysis. In: Ślęzak, D., Wang, G., Szczuka, M., Düntsch, I., Yao, Y. (eds) Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. RSFDGrC 2005. Lecture Notes in Computer Science(), vol 3641. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11548669_5
Download citation
DOI: https://doi.org/10.1007/11548669_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28653-0
Online ISBN: 978-3-540-31825-5
eBook Packages: Computer ScienceComputer Science (R0)