Skip to main content
SpringerLink
Log in
SpringerLink
Log in

Generation of Interval-Valued Intuitionistic Fuzzy Implications from K-Operators, Fuzzy Implications and Fuzzy Coimplications

  • Conference paper
Advances in Computational Intelligence (IPMU 2012)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 298))

Abstract

The interval-valued intuitionistic fuzzy implications which are generated from interval-valued fuzzy implications and coimplications and from K-operators are introduced, extending the main properties of fuzzy implication and exploring the class of interval-valued intuitionistic S-implications.

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

Access this chapter

Log in via an institution
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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Atanassov, K.: Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems 20, 87–96 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  2. Atanassov, K.: Intuitionistic Fuzzy Sets, Theory and Applications. Physica-Verlag, Heilderberg (1999)

    MATH  Google Scholar 

  3. Baczyński, M.: Residual Implications Revisited, Notes on the Smets-Magrez Theorem. Fuzzy Sets and Systems 145(2), 267–277 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bedregal, B., Takahashi, A.: The Best Interval Representation of T-Norms and Automorphisms. Fuzzy Sets and Systems 157(24), 3220–3230 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bedregal, B., Takahashi, A.: Interval-Valued Versions of T-conorms, Fuzzy Negations and Fuzzy Implications. In: IEEE Proc. of the Int. Conf. on Fuzzy Systems, pp. 1981–1987. IEEE Press, Vancouver (2006)

    Chapter  Google Scholar 

  6. Bedregal, B., Dimuro, G., Santiago, R., Reiser, R.: On Interval Fuzzy S-implications. Inf. Sci. 180(8), 1373–1389 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  7. Bustince, H., Barrenechea, E., Pagola, M.: Generation of Interval-valued Fuzzy and Atanassov’s Intuitionistic Fuzzy Connectives from Fuzzy Connectives and from K α Operators: Law of Conjunctions and Disjunctions, Amplitude. Int. J. Intell. Syst. 23(6), 680–714 (2008)

    Article  MATH  Google Scholar 

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

    MATH  Google Scholar 

  9. Cornelis, C., Deschrijver, G., Kerre, E.: Implications in Intuitionistic Fuzzy and Interval-Valued Fuzzy Set Theory: Construction, Classification and Application. Int. J. of Approximate Reasoning 35, 55–95 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. Hickey, T., Ju, Q., Emdem, M.: Interval Arithmetic: from Principles to Implementation. J. of the ACM 48(5), 1038–1068 (2001)

    Article  Google Scholar 

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

    MATH  Google Scholar 

  12. Reiser, R.H.S., Bedregal, B.R.C.: Generation of Interval-Valued Fuzzy Implications from K α Operators. In: Fanelli, A.M., Pedrycz, W., Petrosino, A. (eds.) WILF 2011. LNCS (LNAI), vol. 6857, pp. 41–49. Springer, Heidelberg (2011)

    Google Scholar 

  13. Reiser, R., Bedregal, B., Reis, G.: Interval-Valued Fuzzy Coimplications. Journal of Computer and System Sciences, 1–32 (to be published)

    Google Scholar 

  14. Santiago, R., Bedregal, B., Acióly, B.: Formal Aspects of Correctness and Optimality in Interval Computations. Formal Asp. of Comput. 18(2), 231–243 (2006)

    Article  MATH  Google Scholar 

  15. Trillas, E., Valverde, L.: On Implication and Indistinguishability in the Setting of Fuzzy Logic. In: Kacprzyk, J., Yager, R. (eds.) Management Decision Support Systems using Fuzzy Sets and Possibility Theory, pp. 198–212. Verlag TUV Rheinland, Cologne (1985)

    Google Scholar 

  16. Yager, R.R.: On Some New Classes of Implication Operators and Their Role in Approximate Reasoning. Inf. Sci. 167(1-4), 193–216 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  17. Zadeh, L.A.: Fuzzy sets. Information and Control 8(3), 338–353 (1965)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centro de Desenvolvimento Tecnológico, Universidade Federal de Pelotas, Rua Gomes Carneiro, 1, Centro, 96010/610, Pelotas, Brazil

    Renata Reiser

  2. Depto. de Informática e Matemática Aplicada, Universidade Federal do Rio Grande do Norte, Campus Universitário s/n, 59072-970, Natal, Brazil

    Benjamín Bedregal

  3. Depto. de Automática y Computación, Universidad Pública de Navarra, Campus Arrosadia s/n, 31006, Pamplona, Spain

    Humberto Bustince & Javier Fernandez

Authors
  1. Renata Reiser
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Benjamín Bedregal
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Humberto Bustince
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Javier Fernandez
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Faculty of Economics, University of Catania, Corso Italia, 55, 95129, Catania, Italy

    Salvatore Greco  & Benedetto Matarazzo  & 

  2. Université Pierre et Marie Curie - Paris6, CNRS UMR 7606, DAPA, LIP6 8, rue du Capitaine Scott, F-75015, Paris, France

    Bernadette Bouchon-Meunier

  3. Dip. Matematica e Informatica, Università di Perugia, 06123, Perugia, Italy

    Giulianella Coletti

  4. Department of Computer and Management Science, University of Trento, Via Inama 5, 38122, Trento, Italy

    Mario Fedrizzi

  5. Machine Intelligence Institute, IONA College, 10801, New Rochelle, NY, USA

    Ronald R. Yager

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Reiser, R., Bedregal, B., Bustince, H., Fernandez, J. (2012). Generation of Interval-Valued Intuitionistic Fuzzy Implications from K-Operators, Fuzzy Implications and Fuzzy Coimplications. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances in Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 298. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31715-6_48

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-31715-6_48

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31714-9

  • Online ISBN: 978-3-642-31715-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation