Skip to main content

Abstract

The article deals with diverse types of fuzzy equivalences interpreted as fuzzy connectives. It presents some dependencies between well known fuzzy C-equivalences as well as lately examined fuzzy \(\alpha \)C-equivalences, fuzzy semi-C-equivalences, fuzzy weak C-equivalences, and a fuzzy equivalence defined by Fodor and Roubens.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.99
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

Institutional subscriptions

References

  1. Baczyński, M., Jayaram, B.: Fuzzy Implications. Springer, Berlin (2008). https://doi.org/10.1007/978-3-540-69082-5

    Book  MATH  Google Scholar 

  2. Bentkowska, U., Król, A.: Aggregation of fuzzy \(\alpha \)-\(C\)-equivalences. In: Alonso, J.M. et al. (ed.) Proceedings of the International Joint Conference IFSA-EUSFLAT 2015, pp. 1310–1317. Atlantis Press (2015). https://doi.org/10.2991/ifsa-eusflat-15.2015.185

  3. Bentkowska, U., Król, A.: Fuzzy \(\alpha \)-\(C\)-equivalences. Fuzzy Sets Syst. https://doi.org/10.1016/j.fss.2018.01.004

  4. Bodenhofer, U.: A similarity-based generalization of fuzzy orderings preserving the classical axioms. Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 8, 593–610 (2000). https://doi.org/10.1142/S0218488500000411

    Article  MathSciNet  MATH  Google Scholar 

  5. Bodenhofer, U., Küng, J.: Fuzzy orderings in flexible query answering systems. Soft Comput. 8, 512–522 (2004). https://doi.org/10.1007/s00500-003-0308-9

    Article  MATH  Google Scholar 

  6. Bustince, H., Barrenechea, E., Pagola, M.: Restricted equivalence functions. Fuzzy Sets Syst. 157, 2333–2346 (2006). https://doi.org/10.1016/j.fss.2006.03.018

    Article  MathSciNet  MATH  Google Scholar 

  7. Bustince, H., Barrenechea, E., Pagola, M.: Image thresholding using restricted equivalence functions and maximizing the measures of similarity. Fuzzy Sets Syst. 158, 496–516 (2007). https://doi.org/10.1016/j.fss.2006.09.012

    Article  MathSciNet  MATH  Google Scholar 

  8. De Baets, B., Mesiar, R.: Pseudo-metrics and \(T\)-equivalences. J. Fuzzy Math. 5, 471–481 (1997). http://hdl.handle.net/1854/LU-268970

  9. Dimuro, G.P., Bedregal, B., Bustince, H., Asiáin, M.J., Mesiar, R.: On additive generators of overlap functions. Fuzzy Sets Syst. 287, 76–96 (2016). https://doi.org/10.1016/j.fss.2015.02.008

    Article  MathSciNet  Google Scholar 

  10. Drewniak, J., Król, A.: A survey of weak connectives and the preservation of their properties by aggregations. Fuzzy Sets Syst. 161, 202–215 (2010). https://doi.org/10.1016/j.fss.2009.08.011

    Article  MathSciNet  MATH  Google Scholar 

  11. Fodor, J., Roubens, M.: Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer, Dordrecht (1994)

    Book  Google Scholar 

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

    Book  Google Scholar 

  13. Król, A.: Fuzzy (C, I)-equivalences. In: Baczyñski, M. et al. (ed.) Proceedings of the 8th International Summer School on Aggregation Operators (AGOP 2015), University of Silesia, Katowice, Poland, pp. 157–161 (2015)

    Google Scholar 

  14. Nguyen, H.T., Walker, E.: A First Course in Fuzzy Logic. CRC Press, Boca Raton (1996)

    Google Scholar 

  15. Schweizer, B., Sklar, A.: Probabilistic Metric Spaces. North-Holland, Amsterdam (1983)

    MATH  Google Scholar 

Download references

Acknowledgment

The work on this paper was partially supported by the Centre for Innovation and Transfer of Natural Sciences and Engineering Knowledge in Rzeszów, through Project Number RPPK.01.03.00-18-001/10.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Anna Król .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Bentkowska, U., Król, A. (2018). Dependencies Between Some Types of Fuzzy Equivalences. In: Medina, J., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations. IPMU 2018. Communications in Computer and Information Science, vol 853. Springer, Cham. https://doi.org/10.1007/978-3-319-91473-2_56

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-91473-2_56

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-91472-5

  • Online ISBN: 978-3-319-91473-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics