Advertisement

Some Remarks on Generalized Hypothetical Syllogism and Yager’s Implications

  • Piotr HelbinEmail author
  • Katarzyna Miś
  • Michał Baczyński
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 981)

Abstract

In this paper we investigate some properties of generalized hypothetical syllogism (GHS). We focus on the class of Yager’s implications and give some solutions of (GHS) among this family. Furthermore, we show some relations between the class of aggregated fuzzy implications and (GHS).

Keywords

Aggregation function Fuzzy connectives Fuzzy implication T-norm Generalized hypothetical syllogism Yager’s f- and g-generated implications 

Notes

Acknowledgment

M. Baczyński and K. Miś acknowledge the support of the National Science Centre, Poland, under Grant No. 2015/19/B/ST6/03259.

References

  1. 1.
    Baczyński, M., Jayaram, B.: Fuzzy Implications, Studies in Fuzziness and Soft Computing, vol. 231. Springer, Heidelberg (2008)Google Scholar
  2. 2.
    Baczyński, M., Miś, K.: Selected properties of generalized hypothetical syllogism including the case of R-implications. In: Medina, J., Ojeda-Aciego, M., Verdegay, J.L., Pelta, D.A., Cabrera, I.P., Bouchon-Meunier, B., Yager, R.R. (eds.) Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations. IPMU 2018. Communications in Computer and Information Science, vol. 853, pp. 673–684. Springer International Publishing, Cham (2018)Google Scholar
  3. 3.
    Calvo, T., Martín, J., Mayor, G.: Aggregation of implication functions. In: Pasi, G., Montero, J., Ciucci, D. (eds.) 8th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT 2013), pp. 569–574. Atlantis Press (2013)Google Scholar
  4. 4.
    Grabisch, M., Marichal, J., Mesiar, R., Pap, E.: Aggregation Functions, Encyclopedia of Mathematics and Its Applications, vol. 127. Cambridge University Press, Cambridge (2009)Google Scholar
  5. 5.
    Klement, E., Mesiar, R., Pap, E.: Triangular Norms. Kluwer, Dordrecht (2000)Google Scholar
  6. 6.
    Klir, G., Yuan, B.: Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice Hall, Upper Saddle River (1995)zbMATHGoogle Scholar
  7. 7.
    Massanet, S., Torrens, J.: On the characterization of Yager’s implications. Inf. Sci. 201, 1–18 (2012)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Massanet, S., Torrens, J.: An overview of construction methods of fuzzy implications. In: Baczyński, M., Beliakov, G., Bustince Sola, H., Pradera, A. (eds.) Advances in Fuzzy Implication Functions, Studies in Fuzziness and Soft Computing, vol. 300, pp. 1–30. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  9. 9.
    Vemuri, N.R.: Investigations of fuzzy implications satisfying generalized hypothetical syllogism. Fuzzy Sets Syst. 323, 117–137 (2018)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Yager, R.R.: On some new classes of implication operators and their role in approximate reasoning. Inf. Sci. 167, 193–216 (2004)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Zadeh, L.: Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans. Syst. Man Cybern. 9, 28–44 (1973)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of Silesia in KatowiceKatowicePoland

Personalised recommendations