Skip to main content
SpringerLink
Log in

On Invariant Measures on Intuitionistic Fuzzy Sets

  • Conference paper
  • First Online:
Advances in Fuzzy Logic and Technology 2017 (EUSFLAT 2017, IWIFSGN 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 642))

Abstract

Very well known and important is the theory of the existence and uniqueness of measures invariant under a shift on a group (so-called Haar measure) in some groups. It was studied in many spaces and transformations. Such measure m is defined on a family \(\mathcal {F}\) of sets and such that \(m(T^{-1}(A))=m(A)\) for any \(A\in \mathcal {F}.\) In the paper instead of sets intuitionistic fuzzy sets (IF-sets) are studied. As a special case the theory of invariant measures on fuzzy sets can be obtained.

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 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
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. Atanassov, K.: Intuitionistic Fuzzy Sets: Theory and Applications. Physic Verlag, Heidelberg (1999)

    Book  MATH  Google Scholar 

  2. Ciungu, L., Riečan, B.: General form of probabilities on IF-sets. In: Fuzzy Logic and Applications. Proceedings of WILF Palermo, pp. 101–107 (2009)

    Google Scholar 

  3. Ciungu, L., Riečan, B.: Representation theorem for probabilities on IFS-events. Inf. Sci. 180, 793–798 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  4. Halmos, P.R.: Measure Theory. Van Nostrand, New York (1950)

    Book  MATH  Google Scholar 

  5. Michalíková, A., Riečan, B.: On the Lebesgue IF-measure. Notes Intuitionistic Fuzzy Sets 23(2), 8–12 (2017). Academic Publishing House, Sofia. Print ISSN 1310-4926, Online ISSN 2367-8283

    Google Scholar 

  6. Riečan, B.: On a problem of Radko Mesiar: general form of IF-probabilities. Fuzzy Sets Syst. 152, 1485–1490 (2006)

    MathSciNet  MATH  Google Scholar 

  7. Riečan B.: Analysis of fuzzy logic models. In: Koleshko, V. (ed.) Intelligent Systems, INTECH, pp. 217–244 (2012)

    Google Scholar 

  8. Schwarz, Š.: On the existence of invariant measures on certain type of bicompact semigroups. Czech. Math. J. 7, 165–182 (1957). (in Russian)

    MATH  Google Scholar 

  9. Stehlíková, B., Markechová, D., Tirpáková, A.: On the existence of a Haar measure in topological IP-loops. Kybernetika (to appear)

    Google Scholar 

  10. Zadeh, L.: Fuzzy Sets. Inform. Control 8, 338–358 (1965)

    Article  MATH  Google Scholar 

  11. Zadeh, L.: Probability measures of fuzzy events. J. Math. Anal. Appl. 23, 421–427 (1968)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Natural Science, Matej Bel University, Tajovského 40, 97401, Banská Bystrica, Slovakia

    Alžbeta Michalíková & Beloslav Riečan

  2. Mathematical Institut, Slovak Academy of Sciences, Stefánikova 49, Bratislava, Slovakia

    Alžbeta Michalíková & Beloslav Riečan

Authors
  1. Alžbeta Michalíková
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Beloslav Riečan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alžbeta Michalíková .

Editor information

Editors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

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

    Eulalia Szmidt

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Slawomir Zadrożny

  4. Department of Telecommunications and Information Processing, Bulgarian Academy of Sciences, Sofia, Bulgaria

    K. T. Atanassov

  5. WIT - Warsaw School of Information Technology, Warsaw, Poland

    Maciej Krawczak

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this paper

Cite this paper

Michalíková, A., Riečan, B. (2018). On Invariant Measures on Intuitionistic Fuzzy Sets. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K., Krawczak, M. (eds) Advances in Fuzzy Logic and Technology 2017. EUSFLAT IWIFSGN 2017 2017. Advances in Intelligent Systems and Computing, vol 642. Springer, Cham. https://doi.org/10.1007/978-3-319-66824-6_46

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-66824-6_46

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66823-9

  • Online ISBN: 978-3-319-66824-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation