Skip to main content
SpringerLink
Log in

Coimplications on Finite Scales

  • Conference paper
Advances in Computational Intelligence (IPMU 2012)

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

  • 819 Accesses

Abstract

Co-implication functions are the dual connectives of fuzzy implications. In this paper co-implications defined on finite ordinal scales, called discrete co-implications, are introduced. In particular, strong co-implications derived from smooth t-norms and residual co-implications derived from smooth t-conorms are studied in detail. The structure of such co-implications is given and several properties are investigated.

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. Aguiló, I., Suñer, J., Torrens, J.: Matrix representation of discrete quasi-copulas. Fuzzy Sets and Systems 159, 1658–1672 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  2. Baczyński, M., Jayaram, B.: Fuzzy Implications. STUDFUZZ, vol. 231. Springer, Heidelberg (2008)

    MATH  Google Scholar 

  3. De Baets, B.: Model implicators and their characterization. In: Sreele, N. (ed.) Proceedings of the First ICSC International Symposium on Fuzzy logic, ICSC 1995, pp. A42–A49. Academic Press (1995)

    Google Scholar 

  4. De Baets, B.: Coimplicators: The forgotten connectives. Tatra Mountains 12, 229–240 (1997)

    MATH  Google Scholar 

  5. De Baets, B., Fodor, J., Ruiz-Aguilera, D., Torrens, J.: Idempotent uninorms on finite ordinal scales. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 17, 1–14 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  6. Fodor, J.C.: Smooth associative operations on finite ordinal scales. IEEE Trans. on Fuzzy Systems 8, 791–795 (2000)

    Article  Google Scholar 

  7. Fodor, J., Roubens, M.: Fuzzy preference modelling and multicriteria decision support. Series D: System Theory, Knowledge Engineering and Problem Solving, vol. 14. Kluwer Academic Publishers (1994)

    Google Scholar 

  8. Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Trends in Logic - Studi Logica Library, vol. 8. Kluwer Academic Publishers (2000)

    Google Scholar 

  9. Klir, G.J., Yuan, B.: Fuzzy sets and fuzzy logic (Theory and applications). Prentice-Hall (1995)

    Google Scholar 

  10. Kolesárová, A., Mayor, G., Mesiar, R.: Weighted ordinal means. Information Sciences 177, 3822–3830 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  11. Mas, M., Monserrat, M., Torrens, J., Trillas, E.: A survey on Fuzzy Implications Functions. IEEE Transactions on fuzzy systems 15, 1107–1121 (2007)

    Article  Google Scholar 

  12. Mas, M., Mayor, G., Torrens, J.: t-operators and uninorms on a finite totally ordered set. International Journal of Intelligent Systems 14, 909–922 (1999)

    Article  MATH  Google Scholar 

  13. Mas, M., Monserrat, M., Torrens, J.: S-implications and R-implications on a finite chain. Kybernetica 40, 3–20 (2004)

    MathSciNet  MATH  Google Scholar 

  14. Mas, M., Monserrat, M., Torrens, J.: On two types of discretes implications. International Journal of Approximate Resoning 40, 262–279 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  15. Mas, M., Monserrat, M., Torrens, J.: Smooth Aggregation Functions on Finite Scales. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds.) IPMU 2010. LNCS(LNAI), vol. 6178, pp. 398–407. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  16. Mayor, G., Suñer, J., Torrens, J.: Copula-like operations on finite settings. IEEE Transactions on Fuzzy Systems 13, 468–477 (2005)

    Article  Google Scholar 

  17. Mayor, G., Torrens, J.: Triangular norms on discrete settings. In: Klement, E.P., Mesiar, R. (eds.) Logical, Algebraic, Analytic, and Probabilistic Aspects of Triangular Norms, pp. 189–230. Elsevier, Netherlands (2005)

    Chapter  Google Scholar 

  18. Oh, K., Kandel, A.: Coimplication and its applications to fuzzy expert systems. Information Sciences 56, 247–260 (1991)

    Article  MathSciNet  Google Scholar 

  19. Reixer, R., Bedregal, B.: Automorphisms acting on N-dual fuzzy functions: implications and coimplications. Anais do CNMAC 3, 229–235 (2010)

    Google Scholar 

  20. Ruiz, D., Torrens, J.: Residual implications and co-implications from idempotent uninorms. Kybernetika 40, 21–38 (2004)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Balearic Islands, Palma de Mallorca, 07122, Spain

    Juan Vicente Riera & Joan Torrens

Authors
  1. Juan Vicente Riera
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Joan Torrens
    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

Riera, J.V., Torrens, J. (2012). Coimplications on Finite Scales. 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_35

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-31715-6_35

  • 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