Fuzzy Rules in Data Mining: From Fuzzy Associations to Gradual Dependencies

Chapter
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 271)

Abstract

Fuzzy rules, doubtlessly one of the most powerful tools of fuzzy logic, have not only been used successfully in established application areas like control engineering and approximate reasoning, but more recently also in the field of data mining. In this chapter, we provide a synthesis of different approaches to fuzzy association analysis, that is, the data-driven extraction of interesting patterns expressed in the form of fuzzy rules. In this regard, we highlight a specific advantage of a fuzzy in comparison to a conventional approach, namely an increased expressiveness that allows for representing patterns of interest in a more distinctive way. Therefore, we specifically focus on the modeling of a less common type of pattern, namely gradual dependencies between attributes in a data set.

Keywords

Data Mining Fuzzy Logic Association Rule Fuzzy Rule Association Rule Mining 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Agrawal, R., Srikant, R.: Fast algorithms for mining association rules. In: Proceedings of the 20th Conference on VLDB, Santiago, Chile, pp. 487–499 (1994)Google Scholar
  2. 2.
    Babuska, R.: Fuzzy Modeling for Control. Kluwer Academic Publishers, Boston (1998)CrossRefGoogle Scholar
  3. 3.
    Berzal, F., Cubero, J.C., Sanchez, D., Serrano, J.M., Vila, M.A.: An alternative approach to discover gradual dependencies. Int. Journal of Uncertainty, Fuzziness and Knowledge-based Systems 15(5), 559–570 (2007)CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Bodenhofer, U.: Representations and constructions of similarity-based fuzzy orderings. Fuzzy Sets and Systems 137, 113–136 (2003)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Bodenhofer, U., Demirci, M.: Strict fuzzy orderings with a given context of similarity. Int. J of Uncertainty, Fuzziness and Knowledge-Based Systems 16(2), 147–178 (2008)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Bodenhofer, U., Klawonn, F.: Robust rank correlation coefficients on the basis of fuzzy orderings: Initial steps. Mathware & Soft Computing 15, 5–20 (2008)MATHMathSciNetGoogle Scholar
  7. 7.
    Chen, G., Wei, Q., Kerre, E., Wets, G.: Overview of fuzzy associations mining. In: Proc. ISIS–2003, 4th International Symposium on Advanced Intelligent Systems, Jeju, Korea (September 2003)Google Scholar
  8. 8.
    Delgado, M., Marin, N., Sanchez, D., Vila, M.: Fuzzy association rules: general model and applications. IEEE Transactions on Fuzzy Systems 11(2), 214–225 (2003)CrossRefGoogle Scholar
  9. 9.
    Dubois, D., Hüllermeier, E., Prade, H.: A systematic approach to the assessment of fuzzy association rules. Data Mining and Knowledge Discovery 13(2), 167–192 (2006)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Dubois, D., Prade, H.: Gradual inference rules in approximate reasoning. Information Sciences 61(1,2), 103–122 (1992)CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    Dubois, D., Prade, H.: What are fuzzy rules and how to use them. Fuzzy Sets and Systems 84, 169–185 (1996)CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Fayyad, U., Piatetsky-Shapiro, G., Smyth, P.: From data mining to knowledge discovery: An overview. In: Advances in Knowledge Discovery and Data Mining, pp. 1–34. MIT Press (1996)Google Scholar
  13. 13.
    Frank, A., Asuncion, A.: UCI machine learning repository (2010)Google Scholar
  14. 14.
    Goodman, L.A., Kruskal, W.H.: Measures of Association for Cross Classifications. Springer, New York (1979)CrossRefMATHGoogle Scholar
  15. 15.
    Hüllermeier, E.: Implication-based fuzzy association rules. In: Siebes, A., De Raedt, L. (eds.) PKDD 2001. LNCS (LNAI), vol. 2168, pp. 241–252. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  16. 16.
    Hüllermeier, E.: Association rules for expressing gradual dependencies. In: Elomaa, T., Mannila, H., Toivonen, H. (eds.) PKDD 2002. LNCS (LNAI), vol. 2431, pp. 200–211. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  17. 17.
    Hüllermeier, E.: Mining implication-based fuzzy association rules in databases. In: Proceedings IPMU 2002, 9th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, Annecy, France, pp. 101–108 (July 2002)Google Scholar
  18. 18.
    Hüllermeier, E.: Fuzzy sets in machine learning and data mining: Status and prospects. Fuzzy Sets and Systems 156(3), 387–406 (2005)CrossRefMathSciNetGoogle Scholar
  19. 19.
    Hüllermeier, E., Yi, Y.: In defense of fuzzy association analysis. IEEE Transactions on Systems, Man, and Cybernetics–Part B: Cybernetics 37(4), 1039–1043 (2007)CrossRefGoogle Scholar
  20. 20.
    Koh, H.W., Hüllermeier, E.: Mining gradual dependencies based on fuzzy rank correlation. In: Proceedings SMPS 2010, 5th International Conference on Soft Methods in Probability and Statistics, Tolouse, France (2010)Google Scholar
  21. 21.
    MacVicar-Whelan, P.: Fuzzy sets, the concept of height, and the hedge very. IEEE Trans. Systems, Man and Cybernetics 8, 507–511 (1978)CrossRefGoogle Scholar
  22. 22.
    Mamdani, E., Assilian, S.: An experiment in linguistic synthesis with a fuzzy logic controller. International Journal of Man-Machine Studies 7, 1–13 (1975)CrossRefMATHGoogle Scholar
  23. 23.
    Michels, K., Klawonn, F., Kruse, R., Nrnberger, A.: Fuzzy Control. Springer, Heidelberg (2006)MATHGoogle Scholar
  24. 24.
    Prade, H.: Raisonner avec des règles d’inférence graduelle - Une approche basée sur les ensembles flous. Revue d’Intelligence Artificielle 2(2), 29–44 (1988)Google Scholar
  25. 25.
    Savasere, A., Omiecinski, E., Navathe, S.: An efficient algorithm for mining association rules in large databases. In: VLDB 1995, Proceedings of 21st International Conference on Very Large Data Bases, Zurich, pp. 432–444 (September 1995)Google Scholar
  26. 26.
    Sudkamp, T.: Examples, counterexamples, and measuring fuzzy associations. Fuzzy Sets and Systems 149(1), 57–71 (2005)CrossRefMATHMathSciNetGoogle Scholar
  27. 27.
    Zadeh, L.A.: A fuzzy-set theoretic interpretation of linguistic hedges. J. Cybernetics 2(3), 4–32 (1972)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of MarburgMarburgGermany

Personalised recommendations