Skip to main content

Some Results About Fuzzy Consequence Operators and Fuzzy Preorders Using Conjunctors

  • Conference paper
  • First Online:
Aggregation Functions in Theory and in Practice (AGOP 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 581))

Included in the following conference series:

  • 638 Accesses

Abstract

The purpose of this paper is to study fuzzy operators induced by fuzzy relations and fuzzy relations induced by fuzzy operators. Many results are obtained about the relationship between \(*\)-preorders and fuzzy consequences operators for a fixed t-norm \(*\). We analyse these properties by considering a semi-copula (generalization of t-norm concept) instead of a t-norm. Moreover, we show that the conditions imposed cannot be relaxed. We have been able to prove some important results about the relationships between fuzzy relations and fuzzy operators in this more general context.

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

Access this chapter

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. Bassan, B., Spizzichino, F.: Relations among univariate aging, bivariate aging and dependence for exchangeable lifetimes. J. Multivar. Anal. 93(2), 313–339 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  2. Carmona, N., Elorza, J., Recasens, J., Bragard, J.: Permutable fuzzy consequence and interior operators and their connection with fuzzy relations. Inf. Sci. 310, 36–51 (2015)

    Article  MathSciNet  Google Scholar 

  3. Castro, J.L., Delgado, M., Trillas, E.: Inducing implication relations. Int. J. Approx. Reason. 10(3), 235–250 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  4. Castro, J.L., Trillas, E.: Tarski’s fuzzy consequences. In: Proceedings of the International Fuzzy Engineering Symposium 1991, vol. 1, pp. 70–81 (1991)

    Google Scholar 

  5. Díaz, S., Montes, S., De Baets, B.: On the compositional characterization of complete fuzzy pre-orders. Fuzzy Sets Syst. 159, 2221–2239 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Díaz, S., Montes, S., De Baets, B.: General results on the decomposition of transitive fuzzy relations. Fuzzy Optim. Decis. Making 9, 129 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  7. Durante, F., Guiselli Ricci, R.: Supermigrative semi-copulas and triangular norms. Inf. Sci. 179, 2689–2694 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. Elorza, J., Fuentes-González, R., Bragard, J., Burillo, P.: On the relation between fuzzy closing morphological operators, fuzzy consequence operators induced by fuzzy preorders and fuzzy closure and co-closure systems. Fuzzy Sets Syst. 218, 73–89 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  9. Elorza, J., Burillo, P.: On the relation of fuzzy preorders and fuzzy consequence operators. Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 7(3), 219–234 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  10. Elorza, J., Burillo, P.: Connecting fuzzy preorders, fuzzy consequence operators and fuzzy closure and co-closure systems. Fuzzy Sets Syst. 139(3), 601–613 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  11. Esteva, F.: On the form of negations in posets. In: Proceedings of The Eleventh International Symposium on Multiple-Valued Logic (1981)

    Google Scholar 

  12. Esteva, F. García, P., Godo, L., Rodríguez, R.O.: Fuzzy approximation relations, modal structures and possibilistic logic. Mathware Soft Comput. V (23) pp. 151–166 (1998)

    Google Scholar 

  13. Esteva, F., García, P., Godo, L., Rodríguez, R.O.: On implicative closure operators in approximate reasoning. Int. J. Approx. Reason. 33, 159184 (2003)

    MathSciNet  MATH  Google Scholar 

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

    Book  MATH  Google Scholar 

  15. Pavelka, J.: On fuzzy logic i, Zeitschr. f. Math. Logik und Grundlagen d. Math. Bd. 25, 4552 (1979)

    Google Scholar 

  16. Recasens, J.: Indistinguishability Operators. STUDFUZZ, vol. 260. Springer, Heidelberg (2010)

    MATH  Google Scholar 

  17. Ward, M.: The closure operators of a lattice. Ann. Math. 43(2), 191–196 (1940)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors acknowledge the financial support of the Spanish Ministerio de Economía y Competitividad (Grant TIN2014-59543-P and Grant MTM 2016-79422-P) and Carlos Bejines also thanks the support of the Asociación de Amigos of the University of Navarra.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Susana Montes .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this paper

Cite this paper

Bejines, C., Chasco, M.J., Elorza, J., Montes, S. (2018). Some Results About Fuzzy Consequence Operators and Fuzzy Preorders Using Conjunctors. In: Torra, V., Mesiar, R., Baets, B. (eds) Aggregation Functions in Theory and in Practice. AGOP 2017. Advances in Intelligent Systems and Computing, vol 581. Springer, Cham. https://doi.org/10.1007/978-3-319-59306-7_26

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-59306-7_26

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59305-0

  • Online ISBN: 978-3-319-59306-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics