Skip to main content
Book cover

On Fuzziness pp 223–228Cite as

Local Finiteness in T-Norm Based Bimonoides

  • Chapter

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 298))

Abstract

This paper offers a short discussion of the property of local finiteness for t-norm monoids and bimonoids. Such bimonoids are of interest in the context of weighted automata. The paper shows that, perhaps unexpectedly, the situation is more complex in the bimonoidal case than it is for monoids: there there are more possibilities for local finiteness.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alsina, C., Trillas, E., Valverde, L.: On Non-distributive Logical Connectives for Fuzzy Sets Theory. Busefal 3, 18–29 (1980)

    Google Scholar 

  2. Cintula, P., Hájek, P.: Triangular Norm Based Predicate Fuzzy Logics. Fuzzy Sets and Systems 161, 311–346 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  3. Cintula, P., Hájek, P., Noguera, C. (eds.): Handbook of Mathematical Fuzzy Logic. Studies in Logic, vol. 37-38. College Publications, London (2011)

    Google Scholar 

  4. Droste, M., Stüber, T., Vogler, H.: Weighted Finite Automata Over Strong Bimonoids. Information Sciences 180, 156–166 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  5. Dubois, D.: Triangular Norms for Fuzzy Sets. In: Klement, E.P. (ed.) Proceedings of the 2nd International Seminar Fuzzy Set Theory, pp. 39–68. Johannes Kepler University, Linz (1980)

    Google Scholar 

  6. Gottwald, S.: T-Normen und ϕ-Operatoren als Wahrheitswertfunktionen Mehrwertiger Junktoren. In: Wechsung, G. (ed.) Proceedings of the International Frege Conference 1984, Schwerin, Mathematical Research, vol. 20, pp. 121–128. Akademie-Verlag, Berlin (1984)

    Google Scholar 

  7. Gottwald, S.: Fuzzy Set Theory with t-norms and ϕ-operators. In: di Nola, A., Ventre, A.G.S. (eds.) The Mathematics of Fuzzy Systems. Interdisciplinary Systems Research, vol. 88, pp. 143–195. TÜV Rheinland, Köln (1986)

    Google Scholar 

  8. Gottwald, S.: Fuzzy Sets and Fuzzy Logic. Artificial Intelligence. Verlag Vieweg, Tecnea, Wiesbaden, Toulouse (1993)

    Google Scholar 

  9. Gottwald, S.: A Treatise on Many-Valued Logics. Studies in Logic and Computation, vol. 9. Research Studies Press, Baldock (2001)

    MATH  Google Scholar 

  10. Gottwald, S., Hájek, P.: T-norm Based Mathematical Fuzzy Logics. In: Klement, E.P., Mesiar, R. (eds.) Logical, Algebraic, Analytic, and Probabilistic Aspects of Triangular Norms, pp. 275–299. Elsevier, Dordrecht (2005)

    Chapter  Google Scholar 

  11. Hájek, P.: Metamathematics of Fuzzy Logic. Trends in Logic, vol. 4. Kluwer Acad. Publ., Dordrecht (1998)

    Book  MATH  Google Scholar 

  12. Klement, E.P.: Construction of Fuzzy σ-algebras Using Triangular Norms. Journal Mathematical Analysis Applications 85, 543–565 (1982)

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  14. Prade, H.: Unions et intersections d’ensembles flous. Busefal 3, 58–62 (1980)

    MathSciNet  Google Scholar 

  15. Schweizer, B., Sklar, A.: Probabilistic Metric Spaces. North-Holland Publ. Comp., Amsterdam (1983)

    MATH  Google Scholar 

  16. Weber, S.: A General Concept of Fuzzy Connectives, Negations and Implications Based on t-norms and t-conorms. Fuzzy Sets and Systems 11, 115–134 (1983)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Gottwald, S. (2013). Local Finiteness in T-Norm Based Bimonoides. In: Seising, R., Trillas, E., Moraga, C., Termini, S. (eds) On Fuzziness. Studies in Fuzziness and Soft Computing, vol 298. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35641-4_34

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-35641-4_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35640-7

  • Online ISBN: 978-3-642-35641-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics