Skip to main content
Springer Nature Link
Log in

On an Open Problem of U. Höhle - A Characterization of Conditionally Cancellative T-Subnorms

  • Conference paper
Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Methods (IPMU 2010)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 80))

  • 1018 Accesses

Abstract

In this work we solve an open problem of U.Höhle [Problem 11, Fuzzy Sets and Systems 145 (2004) 471–479]. We show that the solution gives a characterization of all conditionally cancellative t-subnorms. Further, we give an equivalence condition for a conditionally cancellativite t-subnorm to be a t-norm and hence show that conditionally cancellativite t-subnorms whose natural negations are strong are, in fact, t-norms.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Baczyński, M., Jayaram, B.: Fuzzy Implications. In: Studies in Fuzziness and Soft Computing, vol. 231. Springer, Heidelberg (2008)

    Google Scholar 

  2. Demirli, K., De Baets, B.: Basic properties of implicators in a residual framework. Tatra Mount. Math. Publ. 16, 31–46 (1999)

    MathSciNet  MATH  Google Scholar 

  3. Jenei, S.: Continuity of left-continuous triangular norms with strong induced negations and their boundary condition. Fuzzy Sets and Systems 124, 35–41 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  4. Jayaram, B., Mesiar, R.: I-Fuzzy Equivalence Relations and I-Fuzzy Partitions. Info. Sci. 179, 1278–1297 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. Klement, E.P., Mesiar, R., Pap, E.: Triangular norms. Kluwer, Dordrecht (2000)

    Book  MATH  Google Scholar 

  6. Klement, E.P., Mesiar, R., Pap, E.: Problems on triangular norms and related operators. Fuzzy Sets and Systems 145, 471–479 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  7. Ouyang, Y., Li, J., Fang, J.: A conditionally cancellative left-continuous t-norm is not necessarily continuous. Fuzzy Sets and Systems 157, 2328–2332 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  8. Ouyang, Y., Li, J.: An answer to an open problem on triangular norms. Info. Sci. 175, 78–84 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  9. Viceník, P.: Additive generators of associative functions. Fuzzy Sets and Systems 153, 137–160 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  10. Viceník, P.: Intersections of ranges of additive generators of associative functions. Tatra Mt. Math. Publ. 40, 117–131 (2008)

    MathSciNet  MATH  Google Scholar 

  11. Viceník, P.: Additive generators of border-continuous triangular norms. Fuzzy Sets and Systems 159, 1631–1645 (2008)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Indian Institute of Technology Hyderabad, Yeddumailaram, 502 205, India

    Balasubramaniam Jayaram

Authors
  1. Balasubramaniam Jayaram
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Marburg, Germany

    Eyke Hüllermeier

  2. Department of Knowledge Processing and Language Engineering, Otto-von-Guericke University of Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Rudolf Kruse

  3. Fakultät für Elektrotechnik und Informationstechnik, Technische Universität Dortmund, 44221, Dortmund, Germany

    Frank Hoffmann

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Jayaram, B. (2010). On an Open Problem of U. Höhle - A Characterization of Conditionally Cancellative T-Subnorms. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Methods. IPMU 2010. Communications in Computer and Information Science, vol 80. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14055-6_71

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-14055-6_71

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14054-9

  • Online ISBN: 978-3-642-14055-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics