Abstract
We present a method of constructing a concept lattice of a formal context with incomplete data. The lattice reduces to a classical concept lattice when the missing values are completed. The lattice also can reflect any known dependencies between the missing values. We show some experiments indicating that in most cases, when the number of missing values is not large, the size of the incomplete concept lattice is not substantially greater than the size of the concept lattice of completed data.
Supported by grant no. P103/10/1056 of the Czech Science Foundation.
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References
Belohlavek, R.: Concept lattices and order in fuzzy logic. Ann. Pure Appl. Log. 128(1-3), 277–298 (2004)
Belohlavek, R.: Fuzzy Relational Systems: Foundations and Principles. Kluwer Academic Publishers, Norwell (2002)
Bělohlávek, R., Sklenář, V., Zacpal, J.: Crisply Generated Fuzzy Concepts. In: Ganter, B., Godin, R. (eds.) ICFCA 2005. LNCS (LNAI), vol. 3403, pp. 269–284. Springer, Heidelberg (2005)
Belohlavek, R., Vychodil, V.: Reducing the size of fuzzy concept lattices by hedges. In: Proceedings of FUZZ-IEEE 2005: The 14th IEEE International Conference on Fuzzy Systems, pp. 663–668 (2005)
Burmeister, P., Holzer, R.: On the Treatment of Incomplete Knowledge in Formal Concept Analysis. In: Ganter, B., Mineau, G.W. (eds.) ICCS 2000. LNCS, vol. 1867, pp. 385–398. Springer, Heidelberg (2000)
Ganter, B., Wille, R.: Formal Concept Analysis – Mathematical Foundations. Springer (1999)
Gratzer, G.A.: General lattice theory. Academic Press, New York (1978)
Obiedkov, S.: Modal Logic for Evaluating Formulas in Incomplete Contexts. In: Priss, U., Corbett, D., Angelova, G. (eds.) ICCS 2002. LNCS (LNAI), vol. 2393, pp. 314–325. Springer, Heidelberg (2002)
Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered Sets, Boston, pp. 445–470 (1982)
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Krupka, M., Lastovicka, J. (2012). Concept Lattices of Incomplete Data. In: Domenach, F., Ignatov, D.I., Poelmans, J. (eds) Formal Concept Analysis. ICFCA 2012. Lecture Notes in Computer Science(), vol 7278. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29892-9_19
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DOI: https://doi.org/10.1007/978-3-642-29892-9_19
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