Abstract
Formal concept analysis and rough set theory are two different methods for knowledge representation and knowledge discovery, and both have been successfully applied to various fields. The basis of rough set theory is an equivalence relation on a universe of objects, and that of formal concept analysis is an ordered hierarchical structure — concept lattice. This paper discusses the basic connection between formal concept analysis and rough set theory, and also analyzes the relationship between a concept lattice and the power set of a partition. Finally, it is proved that a concept lattice can be transformed into a partition and vice versa, and transformation algorithms and examples are given.
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References
Wille, R.: Restructuring Lattice Theory: an Approach Based on Hierarchies of Concepts. In: Rival, I. (ed.) Ordered Sets, pp. 445–470. Reidel Publishing Company, Dordrecht (1982)
Ganter, B., Wille, R.: Formal Concept Analysis, Mathematical Foundations. Springer, Heidelberg (1999)
Pawlak, Z.: Rough Sets. International Journal of Computer and Information Sciences 11, 341–356 (1982)
Pawlak, Z.: Rough Sets, Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)
Kent, R.E.: Rough Concept Analysis: a Synthesis of Rough Rets and Formal Concept Analysis. Fundamenta Informaticae 27, 169–181 (1996)
Yao, Y.Y., Chen, Y.H.: Rough Set Approximations in Formal Concept Analysis. In: Dick, S., Kurgan, L., Pedrycz, W., Reformat, M. (eds.) Proceedings of 2004 Annual Meeting of the North American Fuzzy Information Processing Society, pp. 73–78. IEEE, Los Alamitos (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)
Saquer, J., Deogun, J.S.: Concept Approximations Based on Rough Sets and Similarity Measures. Int. J. Appl. Math. Comput. Sci. 11, 655–674 (2001)
Ho, T.B.: Acquiring Concept Approximations in the Framework of Rough Concept Analysis. In: Kangassalo, H., Charrel, P.-J. (eds.) Preprint of the 7th European-Japanese Conference on Information Modelling and Knowledge Bases, Toulouse, France, pp. 186–195 (1997)
Pagliani, P.: From Concept Lattices to Approximation Spaces: Algebraic Structures of some Spaces of Partial Objects. Fundamenta Informaticae 18, 1–25 (1993)
Hu, K.Y., Lu, Y.C., Sh, C.Y.: Advances in Concept Lattice and its Application. Journal of Tsinghua University (Sci & Tech) 40, 77–81 (2000)
Zhang, W.X., Leung, Y., Wu, W.Z.: Information System and Knowledge Discovery. Science Publishing Company, Beijing (2003)
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Qi, JJ., Wei, L., Li, ZZ. (2005). A Partitional View of Concept Lattice. 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_8
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DOI: https://doi.org/10.1007/11548669_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28653-0
Online ISBN: 978-3-540-31825-5
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