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Attribute Implications in a Fuzzy Setting

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3874))

Abstract

The paper is an overview of recent developments concerning attribute implications in a fuzzy setting. Attribute implications are formulas of the form A \(\Longrightarrow\) B, where A and B are collections of attributes, which describe dependencies between attributes. Attribute implications are studied in several areas of computer science and mathematics. We focus on two of them, namely, formal concept analysis and databases.

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.

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References

  1. Abiteboui, S., et al.: The Lowell database research self-assessment. Communications of ACM 48(5), 111–118 (2005)

    Article  Google Scholar 

  2. Armstrong, W.W.: Dependency structures in data base relationships. In: IFIP Congress, Geneva, Switzerland, pp. 580–583 (1974)

    Google Scholar 

  3. Bělohlávek, R.: Similarity relations in concept lattices. J. Logic Comput. 10(6), 823–845 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  4. Bělohlávek, R.: Fuzzy Relational Systems: Foundations and Principles. Kluwer, Academic/Plenum Publishers, New York (2002)

    MATH  Google Scholar 

  5. Bělohlávek, R.: Concept lattices and order in fuzzy logic. Ann. Pure Appl. Logic 128, 277–298 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  6. Bělohlávek, R.: Algorithms for fuzzy concept lattices. In: Proc. Fourth Int. Conf. on Recent Advances in Soft Computing, Nottingham, United Kingdom, December 12-13, pp. 200–205 (2002)

    Google Scholar 

  7. Bělohlávek, R., Chlupová, M., Vychodil, V.: Implications from data with fuzzy attributes. In: AISTA 2004 in Cooperation with the IEEE Computer Society Proceedings, 5 p. (2004) ISBN 2–9599776–8–8

    Google Scholar 

  8. Bělohlávek, R., Funioková, T., Vychodil, V.: Fuzzy closure operators with truth stressers. Logic Journal of IGPL (to appear)

    Google Scholar 

  9. Bělohlávek, R., Vychodil, V.: Implications from data with fuzzy attributes vs. scaled binary attributes. In: FUZZ-IEEE 2005, The IEEE International Conference on Fuzzy Systems, Reno (Nevada, USA), May 22-25, pp. 1050–1055 (2005); (proceedings on CD), abstract in printed proceedings, p. 53, ISBN 0–7803–9158–6

    Google Scholar 

  10. Bělohlávek, 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, pp. 663–668 (2005) (proceedings on CD), abstract in printed proceedings, p. 44, ISBN 0–7803–9158–6

    Google Scholar 

  11. Bělohlávek, 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) ISBN 7–302–11377–7

    Google Scholar 

  12. Bělohlávek, R., Vychodil, V.: Fuzzy attribute logic: syntactic entailment and completeness. In: JCIS 2005, 8th Joint Conference on Information Sciences, Salt Lake City, Utah, USA, July 21-26, pp. 78–81 (2005)

    Google Scholar 

  13. Bělohlávek, R., Vychodil, V.: Reducing attribute implications from data tables with fuzzy attributes to tables with binary attributes. In: JCIS 2005, 8th Joint Conference on Information Sciences, Salt Lake City, Utah, USA, July 21-26, pp. 82–85 (2005)

    Google Scholar 

  14. Bělohlávek, R., Vychodil, V.: What is a fuzzy concept lattice? In: Proc. CLA 2005, Olomouc, Czech Republic, September 7-9, pp. 34–45 (2005)

    Google Scholar 

  15. Bělohlávek, R., Vychodil, V.: Fuzzy attribute implications: computing non-redundant bases using maximal independent sets. In: Zhang, S., Jarvis, R.A. (eds.) AI 2005. LNCS (LNAI), vol. 3809, pp. 1126–1129. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  16. Bělohlávek, R., Vychodil, V.: Axiomatizations of fuzzy attribute logic. In: IICAI 2005, Pune, India (to appear)

    Google Scholar 

  17. Bělohlávek, R., Vychodil, V.: Functional dependencies of data tables over domains with similarity relations. In: IICAI 2005, Pune, India (2005) (to appear)

    Google Scholar 

  18. Buckles, B.P., Petry, F.E.: Fuzzy databases in the new era. In: Proceedings of the 1995 ACM symposium on Applied computing, Nashville, Tennessee, pp. 497–502 (1995) ISBN 0-89791-658-1

    Google Scholar 

  19. Cubero, J.C., Vila, M.A.: A new definition of fuzzy functional dependency in fuzzy relational datatabses. Int. J. Intelligent Systems 9(5), 441–448 (1994)

    Article  Google Scholar 

  20. Ganter, B.: Begriffe und Implikationen (1998) (manuscript)

    Google Scholar 

  21. Ganter, B.: Algorithmen zur formalen Begriffsanalyse. In: Ganter, B., Wille, R., Wolff, K.E. (Hrsg.) Beiträge zur Begriffsanalyse, pp. 241–254. B. I. Wissenschaftsverlag, Mannheim (1987)

    Google Scholar 

  22. Ganter, B., Wille, R.: Formal Concept Analysis. Mathematical Foundations. Springer, Berlin (1999)

    MATH  Google Scholar 

  23. Gerla, G.: Fuzzy Logic. Mathematical Tools for Approximate Reasoning. Kluwer, Dordrecht (2001)

    MATH  Google Scholar 

  24. Goguen, J.A.: The logic of inexact concepts. Synthese 18, 325–373 (1968)

    Google Scholar 

  25. Guigues, J.-L., Duquenne, V.: Familles minimales d’implications informatives resultant d’un tableau de données binaires. Math. Sci. Humaines 95, 5–18 (1986)

    MathSciNet  Google Scholar 

  26. Hájek, P.: Metamathematics of Fuzzy Logic. Kluwer, Dordrecht (1998)

    MATH  Google Scholar 

  27. Hájek, P.: On very true. Fuzzy Sets and Systems 124, 329–333 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  28. Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic. Theory and Applications. Prentice-Hall, Englewood Cliffs (1995)

    MATH  Google Scholar 

  29. Maier, D.: The Theory of Relational Databases. Computer Science Press, Rockville (1983)

    MATH  Google Scholar 

  30. Pavelka, J.: On fuzzy logic I, II, III. Z. Math. Logik Grundlagen Math. 25, 45–52, 119–134, 447–464 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  31. Pollandt, S.: Fuzzy Begriffe. Springer, Heidelberg (1997)

    MATH  Google Scholar 

  32. Prade, H., Testemale, C.: Generalizing database relational algebra for the treatment of incomplete or uncertain information and vague queries. Information Sciences 34, 115–143 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  33. Raju, K.V.S.V.N., Majumdar, A.K.: Fuzzy functional dependencies and lossless join decomposition of fuzzy relational database systems. ACM Trans. Database Systems 13(2), 129–166 (1988)

    Article  Google Scholar 

  34. Takeuti, G., Titani, S.: Globalization of intuitionistic set theory. Annals of Pure and Applied Logic 33, 195–211 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  35. Tyagi, B.K., Sharfuddin, A., Dutta, R.N., Tayal, D.K.: A complete axiomatization of fuzzy functional dependencies using fuzzy function. Fuzzy Sets and Systems 151(2), 363–379 (2005)

    Article  MATH  MathSciNet  Google Scholar 

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Bělohlávek, R., Vychodil, V. (2006). Attribute Implications in a Fuzzy Setting. In: Missaoui, R., Schmidt, J. (eds) Formal Concept Analysis. Lecture Notes in Computer Science(), vol 3874. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11671404_3

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  • DOI: https://doi.org/10.1007/11671404_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-32203-0

  • Online ISBN: 978-3-540-32204-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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