Abstract
We present graded extension of the algorithm LinClosure. Graded LinClosure can be used to compute degrees of semantic entailment from sets of fuzzy attribute implications. It can also be used together with graded extension of Ganter’s NextClosure algorithm to compute non-redundant bases of data tables with fuzzy attributes. We present foundations, the algorithm, and illustrative examples.
Supported by grant No. 1ET101370417 of GA AV ČR, by grant No. 201/05/0079 of the Czech Science Foundation, and by institutional support, research plan MSM 6198959214.
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
Belohlavek, R.: Fuzzy Relational Systems: Foundations and Principles. Kluwer, Academic/Plenum Publishers, New York (2002)
Belohlavek, R., Chlupova, M., Vychodil, V.: Implications from data with fuzzy attributes. In: AISTA 2004 in Cooperation with the IEEE Computer Society Proceedings, p. 5 (2004)
Belohlavek, R., Funiokova, T., Vychodil, V.: Fuzzy closure operators with truth stressers. Logic Journal of IGPL 13(5), 503–513 (2005)
Belohlavek, R., Vychodil, V.: Reducing the size of fuzzy concept lattices by hedges. In: FUZZ-IEEE 2005, The IEEE International Conference on Fuzzy Systems, Reno (Nevada, USA), May 22–25, 2005, pp. 663–668 (2005) (proceedings on CD), abstract in printed proceedings, p. 44
Belohlavek, R., Vychodil, V.: Fuzzy attribute logic: attribute implications, their validity, entailment, and non-redundant basis. In: Liu, Y., Chen, G., Ying, M. (eds.) Fuzzy Logic, Soft Computing & Computational Intelligence: Eleventh International Fuzzy Systems Association World Congress, vol. I, pp. 622–627. Tsinghua University Press and Springer (2005)
Belohlavek, R., Vychodil, V.: Fuzzy attribute implications: Computing non-redundant bases using maximal independent sets”. In: Zhang, S., Jarvis, R. (eds.) AI 2005. LNCS (LNAI), vol. 3809, pp. 1126–1129. Springer, Heidelberg (2005)
Belohlavek, R., Vychodil, V.: Attribute implications in a fuzzy setting. In: Missaoui, R., Schmidt, J. (eds.) Formal Concept Analysis. LNCS (LNAI), vol. 3874, pp. 45–60. Springer, Heidelberg (2006)
Belohlavek, R., Vychodil, V.: Functional dependencies of data tables over domains with similarity relations. In: Proc. IICAI 2005, pp. 2486–2504 (2005)
Belohlavek, R., Vychodil, V.: Data tables with similarity relations: Functional dependencies, complete rules and non-redundant bases. In: Li Lee, M., Tan, K.-L., Wuwongse, V. (eds.) DASFAA 2006. LNCS, vol. 3882, pp. 644–658. Springer, Heidelberg (2006)
Belohlavek, R., Vychodil, V.: Computing non-redundant bases of if-then rules from data tables with graded attributes. In: Zhang, Y.Q., Lin, T.Y. (eds.) Proc. IEEE-GrC 2006, pp. 205–210 (2006)
Belohlavek, R., Vychodil, V.: Properties of models of fuzzy attribute implications. In: Proc. SCIS & ISIS 2006: Joint 3rd International Conference on Soft Computing and Intelligent Systems and 7th International Symposium on advanced Intelligent Systems, Tokyo Institute of Technology, Japan Society for Fuzzy Theory and Intelligent Informatics, pp. 1880–3741 (2006)
Belohlavek, R., Vychodil, V.: Fuzzy attribute logic over complete residuated lattices. J. Exp. Theor. Artif. Intelligence 18(4), 471–480 (2006)
Carpineto, C., Romano, G.: Concept Data Analysis. Theory and Applications. J. Wiley, Chichester (2004)
Ganter, B.: Begriffe und Implikationen, manuscript (1998)
Ganter, B.: Algorithmen zur formalen Begriffsanalyse. In: Ganter, B., Wille, R., Wolff, K.E. (eds.) (Hrsg.): Beiträge zur Begriffsanalyse, pp. 241–254. B. I. Wissenschaftsverlag, Mannheim (1987)
Ganter, B., Wille, R.: Formal Concept Analysis. Mathematical Foundations. Springer, Berlin (1999)
Goguen, J.: The logic of inexact concepts. Synthese 18(9), 325–373 (1968)
Guigues, J.-L., Duquenne, V.: Familles minimales d’implications informatives resultant d’un tableau de données binaires. Math. Sci. Humaines 95, 5–18 (1986)
Hájek, P.: Metamathematics of Fuzzy Logic. Kluwer, Dordrecht (1998)
Hájek, P.: On very true. Fuzzy Sets and Systems 124, 329–333 (2001)
Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic. Theory and Applications. Prentice-Hall, Englewood Cliffs (1995)
Maier, D.: The Theory of Relational Databases. Computer Science Press, Rockville (1983)
Pavelka, J.: On fuzzy logic I, II, III. Z. Math. Logik Grundlagen Math. 25, 45–52, 119–134, 447–464 (1979)
Pollandt, S.: Fuzzy Begriffe. Springer, Berlin Heidelberg (1997)
Takeuti, G., Titani, S.: Globalization of intuitionistic set theory. Annals of Pure and Applied Logic 33, 195–211 (1987)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Belohlavek, R., Vychodil, V. (2008). Graded LinClosure and Its Role in Relational Data Analysis. In: Yahia, S.B., Nguifo, E.M., Belohlavek, R. (eds) Concept Lattices and Their Applications. CLA 2006. Lecture Notes in Computer Science(), vol 4923. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78921-5_9
Download citation
DOI: https://doi.org/10.1007/978-3-540-78921-5_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78920-8
Online ISBN: 978-3-540-78921-5
eBook Packages: Computer ScienceComputer Science (R0)