Association Analysis on Interval-Valued Fuzzy Sets

  • Petra Murinová
  • Viktor Pavliska
  • Michal Burda
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11144)


The aim of this paper is to generalize the concept of association rules for interval-valued fuzzy sets. Interval-valued fuzzy sets allow for intervals of membership degrees to be assigned to each element of the universe. These intervals may be interpreted as partial information where the exact membership degree is not known. The paper provides a generalized definition of support and confidence, which are the most commonly known measures of quality of a rule.


Association rules Missing values Interval-valued fuzzy sets Support Confidence 



Authors acknowledge support by project “LQ1602 IT4Innovations excellence in science” and by GAČR 16-19170S.


  1. 1.
    Hájek, P.: The question of a general concept of the GUHA method. Kybernetika 4, 505–515 (1968)zbMATHGoogle Scholar
  2. 2.
    Hájek, P., Havránek, T.: Mechanizing Hypothesis Formation (Mathematical Foundations for a General Theory). Springer, Heidelberg (1978). Scholar
  3. 3.
    Agrawal, R., Srikant, R.: Fast algorithms for mining association rules. In: Proceedings of 20th International Conference on Very Large Databases, Chile, pp. 487–499. AAAI Press (1994)Google Scholar
  4. 4.
    Ralbovský, M.: Fuzzy GUHA. Ph.D. thesis, University of Economics, Prague (2009)Google Scholar
  5. 5.
    Yager, R.R.: A new approach to the summarization of data. Inf. Sci. 28(1), 69–86 (1982)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Kacprzyk, J., Yager, R.R., Zadrożny, S.: A fuzzy logic based approach to linguistic summaries of databases. Int. J. Appl. Math. Comput. Sci. 10(4), 813–834 (2000)zbMATHGoogle Scholar
  7. 7.
    Murinová, P., Burda, M., Pavliska, V.: An algorithm for intermediate quantifiers and the graded square of opposition towards linguistic description of data. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K.T., Krawczak, M. (eds.) IWIFSGN/EUSFLAT-2017. AISC, vol. 642, pp. 592–603. Springer, Cham (2018). Scholar
  8. 8.
    Gelman, A., Hill, J.: Data Analysis Using Regression and Multilevel/hierarchical Models. Analytical methods for social research. Cambridge University Press, New York (2007)Google Scholar
  9. 9.
    Liu, Y., Gopalakrishnan, V.: An overview and evaluation of recent machine learning imputation methods using cardiac imaging data. Data 2(1), 8 (2017)CrossRefGoogle Scholar
  10. 10.
    Lukasiewicz, J.: O logice trojwartosciowej. Ruch filozoficzny 5, 170–171 (1920)Google Scholar
  11. 11.
    Malinowski, G.: The Many Valued and Nonmonotonic Turn in Logic. North-Holand, Amsterdam (2007)Google Scholar
  12. 12.
    Bergmann, M.: An Introduction To Many-Valued and Fuzzy Logic: Semantics, Algebras, and Derivation Systems. Cambridge University Press, Cambridge New York (2008)CrossRefGoogle Scholar
  13. 13.
    Ciucci, D., Dubois, D., Lawry, J.: Borderline vs. unknown: comparing three-valued representations of imperfect information. Int. J. Approx. Reason. 55, 1866–1889 (2014)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Ciucci, D., Dubois, D.: Three-valued logics, uncertainty management and rough set. Int. J. Approx. Reason. 55, 1866–1889 (2014)CrossRefGoogle Scholar
  15. 15.
    Běhounek, L., Novák, V.: Towards fuzzy partial logic. In: Proceedings of the IEEE 45th International Symposium on Multiple-Valued Logics (ISMVL 2015), pp. 139–144 (2015)Google Scholar
  16. 16.
    Běhounek, L., Daňková, M.: Towards fuzzy partial set theory. In: Carvalho, J.P., Lesot, M.-J., Kaymak, U., Vieira, S., Bouchon-Meunier, B., Yager, R.R. (eds.) IPMU 2016. CCIS, vol. 611, pp. 482–494. Springer, Cham (2016). Scholar
  17. 17.
    Novák, V.: Towards fuzzy type theory with partial functions. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K.T., Krawczak, M. (eds.) IWIFSGN/EUSFLAT-2017. AISC, vol. 643, pp. 25–37. Springer, Cham (2018). Scholar
  18. 18.
    Murinová, P., Burda, M., Pavliska, V.: Undefined values in fuzzy logic. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K.T., Krawczak, M. (eds.) IWIFSGN/EUSFLAT -2017. AISC, vol. 642, pp. 604–610. Springer, Cham (2018). Scholar
  19. 19.
    Murinová, P., Pavliska, V., Burda, M.: Fuzzy association rules on data with undefined values. In: Medina, J., Ojeda-Aciego, M., Verdegay, J.L., Perfilieva, I., Bouchon-Meunier, B., Yager, R.R. (eds.) IPMU 2018. CCIS, vol. 855, pp. 165–174. Springer, Cham (2018). Scholar
  20. 20.
    Chen, Q., Kawase, S.: An approach towards consistency degrees of fuzzy theories. Fuzzy Sets Syst. 113, 237–251 (2000)CrossRefGoogle Scholar
  21. 21.
    Cornelis, C., Deschrijver, G., Kerre, E.E.: Implication in intuitionistic fuzzy and interval-valued fuzzy set theroy: construction, classification, application. Int. J. Approx. Reason. 35, 55–95 (2004)CrossRefGoogle Scholar
  22. 22.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)CrossRefGoogle Scholar
  23. 23.
    Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer, Dordrecht (2000)CrossRefGoogle Scholar
  24. 24.
    Dubois, D., Hüllermeier, E., Prade, H.: A systematic approach to the assessment of fuzzy association rules. Data Min. Knowl. Discov. 13(2), 167–192 (2006)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Kawase, S., Chen, Q., Yanagihar, N.: On interval valued fuzzy reasoning. Trans. Japan Soc. Ind. Appl. Math 6, 285–296 (1996)Google Scholar
  26. 26.
    Geng, L., Hamilton, H.J.: Interestingness measures for data mining: a survey. ACM Comput. Surv. (CSUR) 38(3), 9 (2006)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Petra Murinová
    • 1
  • Viktor Pavliska
    • 1
  • Michal Burda
    • 1
  1. 1.Institute for Research and Applications of Fuzzy ModelingCentre of Excellence IT4Innovations, Division University of OstravaOstravaCzech Republic

Personalised recommendations