Skip to main content

Crisp Fuzzy Implications

  • Conference paper
  • First Online:
Fuzzy Information Processing (NAFIPS 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 831))

Included in the following conference series:

Abstract

Implications play an important role in fuzzy logics as they can be used both in practical and theoretical works. There exist many works in the literature where fuzzy implications behave in a crisp manner, i.e., implications that map to either zero or one. In this sense, we call those implications as crisp fuzzy implications and our goal is to study some their main features.

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 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

Institutional subscriptions

References

  1. Baczyński, M., Balasubramaniam, J.: Fuzzy Implications. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-69082-5

    Book  MATH  Google Scholar 

  2. Baczyński, M., Beliakov, G., Bustince, H., Pradera, A. (eds.): Advances in Fuzzy Implication Functions, Studies in Fuzziness and Soft Computing, vol. 300. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-35677-3

    Book  Google Scholar 

  3. Bedregal, B.C.: A normal form which preserves tautologies and contradictions in a class of fuzzy logics. J. Algorithms 62(3–4), 135–147 (2007)

    Article  MathSciNet  Google Scholar 

  4. Cruz, A., Bedregal, B.C., Santiago, R.H.N.: On the characterizations of fuzzy implications satisfying I(x, I(y, z)) = I(I(x, y), I(x, z)). Int. J. Approx. Reason. 93, 261–276 (2018)

    Article  MathSciNet  Google Scholar 

  5. Dimuro, G.P., Bedregal, B., Santiago, R.H.: On (G, N)-implications derived from grouping functions. Inf. Sci. 279, 1–17 (2014)

    Article  MathSciNet  Google Scholar 

  6. Dimuro, G.P., Bedregal, B.C.: On residual implications derived from overlap functions. Inf. Sci. 312, 78–88 (2015)

    Article  MathSciNet  Google Scholar 

  7. Dimuro, G.P., Bedregal, B., Bustince, H., Jurio, A., Baczyński, M., Mis, K.: QL-operations and QL-implication functions constructed from tuples (O, G, N) and the generation of fuzzy subsethood and entropy measures. Int. J. Approx. Reason. 82, 170–192 (2017)

    Article  MathSciNet  Google Scholar 

  8. Dubois, D., Prade, H.M., Bezdek, J.C.: Fuzzy Sets in Approximate Reasoning and Information Systems. Kluwer Academic Publishers, Norwell (1999)

    MATH  Google Scholar 

  9. Dubois, D., Nakata, M., Prade, H.: Extended divisions for flexible queries in relational databases. In: Pons, O., Vila, M.A., Kacprzyk, J. (eds.) Knowledge Management in Fuzzy Databases. Studies in Fuzziness and Soft Computing, vol. 39, pp. 105–121. Physica, Heidelberg (2000). https://doi.org/10.1007/978-3-7908-1865-9_6

    Chapter  MATH  Google Scholar 

  10. Godo, L., Sandri, S.: Dealing with imprecise inputs in a fuzzy rule-based system using an implication-based rule model. In: Bouchon-Meunier, B., Gutiérrez-Ríos, J., Magdalena, L., Yager, R.R. (eds.) Technologies for Constructing Intelligent Systems 1. Studies in Fuzziness and Soft Computing, vol. 89. Physica, Heidelberg (2002). https://doi.org/10.1007/978-3-7908-1797-3_4

    Chapter  Google Scholar 

  11. Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice Hall, Upper Saddle River (1995)

    MATH  Google Scholar 

  12. Mas, M., Monserrat, M., Torrens, J., Trillas, E.: A survey on fuzzy implication functions. IEEE Trans. Fuzzy Syst. 15(6), 1107–1121 (2007)

    Article  Google Scholar 

  13. Oh, K.W., Bandler, W.: Properties of fuzzy implication operators. Int. J. Approx. Reason. 1(3), 273–285 (1987)

    Article  MathSciNet  Google Scholar 

  14. Pinheiro, J., Bedregal, B., Santiago, R.H., Santos, H.: (T, N)-implications. In: 2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), pp. 1–6 (2017)

    Google Scholar 

  15. Pinheiro, J., Bedregal, B., Santiago, R.H., Santos, H.: A study of (T, N)-implications and its use to construct a new class of fuzzy subsethood measure. Int. J. Approx. Reason. 97, 1–16 (2018)

    Article  MathSciNet  Google Scholar 

  16. Sakly, A., Benrejeb, M.: On the choice of the adequate fuzzy implication operator with the center of gravity defuzzification method based on precision criterion in fuzzy control. In: Proceedings of the 2002 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2002), Honolulu, HI, pp. 482–487 (2002)

    Google Scholar 

  17. Santos, A.S., Valle, M.E.: A fast and robust max-c projection fuzzy autoassociative memory with application for face recognition. In: IEEE World Congress on Computational Intelligence (2018, submitted)

    Google Scholar 

Download references

Acknowledgments

This work was partially supported by the Brazilian funding agency CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico), under the process No. 307781/2016-0.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jocivania Pinheiro .

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

Pinheiro, J., Bedregal, B., Santiago, R., Santos, H. (2018). Crisp Fuzzy Implications. In: Barreto, G., Coelho, R. (eds) Fuzzy Information Processing. NAFIPS 2018. Communications in Computer and Information Science, vol 831. Springer, Cham. https://doi.org/10.1007/978-3-319-95312-0_30

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-95312-0_30

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-95311-3

  • Online ISBN: 978-3-319-95312-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics