Skip to main content

Association Analysis on Interval-Valued Fuzzy Sets

  • Conference paper
  • First Online:
  • 624 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11144))

Abstract

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.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Hájek, P.: The question of a general concept of the GUHA method. Kybernetika 4, 505–515 (1968)

    MATH  Google Scholar 

  2. Hájek, P., Havránek, T.: Mechanizing Hypothesis Formation (Mathematical Foundations for a General Theory). Springer, Heidelberg (1978). https://doi.org/10.1007/978-3-642-66943-9

    Book  MATH  Google Scholar 

  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. Ralbovský, M.: Fuzzy GUHA. Ph.D. thesis, University of Economics, Prague (2009)

    Google Scholar 

  5. Yager, R.R.: A new approach to the summarization of data. Inf. Sci. 28(1), 69–86 (1982)

    Article  MathSciNet  Google Scholar 

  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)

    MATH  Google Scholar 

  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). https://doi.org/10.1007/978-3-319-66824-6_52

    Chapter  Google Scholar 

  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. Liu, Y., Gopalakrishnan, V.: An overview and evaluation of recent machine learning imputation methods using cardiac imaging data. Data 2(1), 8 (2017)

    Article  Google Scholar 

  10. Lukasiewicz, J.: O logice trojwartosciowej. Ruch filozoficzny 5, 170–171 (1920)

    Google Scholar 

  11. Malinowski, G.: The Many Valued and Nonmonotonic Turn in Logic. North-Holand, Amsterdam (2007)

    Google Scholar 

  12. Bergmann, M.: An Introduction To Many-Valued and Fuzzy Logic: Semantics, Algebras, and Derivation Systems. Cambridge University Press, Cambridge New York (2008)

    Book  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  14. Ciucci, D., Dubois, D.: Three-valued logics, uncertainty management and rough set. Int. J. Approx. Reason. 55, 1866–1889 (2014)

    Article  Google Scholar 

  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. 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). https://doi.org/10.1007/978-3-319-40581-0_39

    Chapter  Google Scholar 

  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). https://doi.org/10.1007/978-3-319-66827-7_3

    Chapter  Google Scholar 

  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). https://doi.org/10.1007/978-3-319-66824-6_53

    Chapter  Google Scholar 

  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). https://doi.org/10.1007/978-3-319-91479-4_14

    Chapter  Google Scholar 

  20. Chen, Q., Kawase, S.: An approach towards consistency degrees of fuzzy theories. Fuzzy Sets Syst. 113, 237–251 (2000)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  22. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  Google Scholar 

  23. Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer, Dordrecht (2000)

    Book  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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. Geng, L., Hamilton, H.J.: Interestingness measures for data mining: a survey. ACM Comput. Surv. (CSUR) 38(3), 9 (2006)

    Article  Google Scholar 

Download references

Acknowledgements

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

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Petra Murinová .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Murinová, P., Pavliska, V., Burda, M. (2018). Association Analysis on Interval-Valued Fuzzy Sets. In: Torra, V., Narukawa, Y., Aguiló, I., González-Hidalgo, M. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2018. Lecture Notes in Computer Science(), vol 11144. Springer, Cham. https://doi.org/10.1007/978-3-030-00202-2_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-00202-2_8

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-00201-5

  • Online ISBN: 978-3-030-00202-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics