Skip to main content
Springer Nature Link
Log in

A Construction Method for t-norms on Bounded Lattices

  • Conference paper
  • First Online:
New Trends in Aggregation Theory (AGOP 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 981))

Included in the following conference series:

Abstract

In this paper, a construction method on a bounded lattice from a given t-norm on a subinterval of the bounded lattice is presented. The supremum distributivity of the constructed t-norm by the mentioned method has been proven under some special conditions. Giving an example, the constructed t-norm need not be supremum-distributive on any bounded lattice is shown. Moreover, some relationships between the mentioned construction method and the other construction methods in the literature are presented.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Aşıcı, E., Karaçal, F.: On the T-partial order and properties. Inf. Sci. 267, 323–333 (2014)

    Article  MathSciNet  Google Scholar 

  2. Birkhoff, G.: Lattice Theory. American Mathematical Society Colloquium Publishers, Providence (1967)

    MATH  Google Scholar 

  3. Çaylı, G.D.: On a new class of t-norms and t-conorms on bounded lattices. Fuzzy Sets Syst. 332, 129–143 (2018)

    Article  MathSciNet  Google Scholar 

  4. Durante, F., Sarkoci, P.: A note on the convex combinations of triangular norms. Fuzzy Sets Syst. 159, 77–80 (2008)

    Article  MathSciNet  Google Scholar 

  5. Ertuğrul, Ü., Karaçal, F., Mesiar, R.: Modified ordinal sums of triangular norms and triangular conorms on bounded lattices. Int. J. Intell. Syst. 30, 807–817 (2015)

    Article  Google Scholar 

  6. Grabisch, M., Marichal, J.-L., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge University Press, Cambridge (2009)

    Book  Google Scholar 

  7. Karaçal, F.: On the direct decomposability of strong negations and S-implication operators on product lattices. Inf. Sci. 176, 3011–3025 (2006)

    Article  MathSciNet  Google Scholar 

  8. Karaçal, F., Khadjiev, D.: \(\vee \)-Distributive and infinitely \(\vee \)-distributive t-norms on complete lattices. Fuzzy Sets Syst. 151, 341–352 (2005)

    Google Scholar 

  9. Karaçal, F., Kesicioğlu, M.N.: A T-partial order obtained from t-norms. Kybernetika 47, 300–314 (2011)

    MathSciNet  MATH  Google Scholar 

  10. İnce, M.A., Karaçal, F.: t-closure operators. Int. J. General Syst. https://doi.org/10.1080/03081079.2018.1549041

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

    Book  Google Scholar 

  12. Menger, K.: Statistical metrics. Proc. Natl. Acad. Sci. U.S.A 8, 535–537 (1942)

    Article  MathSciNet  Google Scholar 

  13. Mesiar, R., Mesiarová-Zemánková, A.: Convex combinations of continuous t-norms with the same diagonal function. Nonlinear Anal. 69(9), 2851–2856 (2008)

    Article  MathSciNet  Google Scholar 

  14. Saminger, S.: On ordinal sums of triangular norms on bounded lattices. Fuzzy Sets Syst. 157(10), 1403–1416 (2006)

    Article  MathSciNet  Google Scholar 

  15. Schweizer, B., Sklar, A: Espaces metriques aléatoires. C. R. Acad. Sci. Paris Sér. A 247 2092–2094 (1958)

    Google Scholar 

  16. Schweizer, B., Sklar, A.: Statistical metric spaces. Pacific J. Math. 10, 313–334 (1960)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Karadeniz Technical University, 61080, Trabzon, Turkey

    Funda Karaçal & Ümit Ertuğrul

  2. Department of Mathematics, Recep Tayyip Erdogan University, 53100, Rize, Turkey

    M. Nesibe Kesicioğlu

Authors
  1. Funda Karaçal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ümit Ertuğrul
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Nesibe Kesicioğlu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Funda Karaçal .

Editor information

Editors and Affiliations

  1. Faculty of Science, Palacký University, Olomouc, Czech Republic

    Radomír Halaš

  2. Systems Research Institute, Polish Academy of Science, Warsaw, Poland

    Marek Gagolewski

  3. Slovak University of Technology, Bratislava, Slovakia

    Radko Mesiar

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Karaçal, F., Ertuğrul, Ü., Kesicioğlu, M.N. (2019). A Construction Method for t-norms on Bounded Lattices. In: Halaš, R., Gagolewski, M., Mesiar, R. (eds) New Trends in Aggregation Theory. AGOP 2019. Advances in Intelligent Systems and Computing, vol 981. Springer, Cham. https://doi.org/10.1007/978-3-030-19494-9_19

Download citation

Publish with us

Policies and ethics

Search

Navigation