Advertisement

The Lattice of Interval Valued Open image in new window-fuzzy Filters in a Given MTL-algebra

  • Chunhui LiuEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1074)

Abstract

In the present paper, the interval valued Open image in new window -fuzzy filter theory in MTL-algebras is further studied. Some new properties of interval valued Open image in new window -fuzzy filters are given. It is proved that the set consisting of all interval valued Open image in new window -fuzzy filters in a given MTL-algebra, under the partial order \(\sqsubseteq \), forms a complete distributive lattice.

Keywords

Many-valued logic MTL-algebra Interval-valued Open image in new window -fuzzy filter Complete distributive lattice 

References

  1. 1.
    Hájek, P.: Meta Mathematics of Fuzzy Logic. Kluwer Academic Publisher, Dordrecht (1998)CrossRefGoogle Scholar
  2. 2.
    Esteva, F., Godo, L.: Monoidal \(t\)-norm based logic: towards a logic for left-continuous \(t\)-norms. Fuzzy Sets Syst. 124, 271–288 (2001)Google Scholar
  3. 3.
    Borzooei, R.A., Shoar, S.K., Ameri, R.: Some types of filters in MTL-algebras. Fuzzy Sets Syst. 187, 92–102 (2012)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Haveshky, M.: A note on some types of filters in MTL-algebras. Fuzzy Sets Syst. 247, 135–137 (2014)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)CrossRefGoogle Scholar
  6. 6.
    Kim, K.H., Zhang, Q., Jun, Y.B.: On fuzzy filters of MTL-algebras. J. Fuzzy Math. 10(4), 981–989 (2002)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Liu, C.H.: On fuzzy filters of MTL-algebras. Fuzzy Syst. Math. 29(2), 98–108 (2015)zbMATHGoogle Scholar
  8. 8.
    Jun, Y.B., Xu, Y., Zhang, X.H.: Fuzzy filters of MTL-algebras. Inf. Sci. 175(1–2), 120–138 (2005)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Zadeh, L.A.: The concept of a lingistic variable and its application to approximate reason. Inf. Control 18, 199–249 (1975)Google Scholar
  10. 10.
    Ma, X.L., Zhan, J.M., Shum, K.P.: Interval valued \((\in , \in \!\!\vee {\,q})\)-fuzzy filters of MTL-algebras. J. Math. Res. Exposition 30(2), 265–276 (2010)Google Scholar
  11. 11.
    Belohlavek, R.: Some properties of residuated lattices. Czechoslovak Math. J. 123, 161–171 (2003)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Belohlavek, R.: Fuzzy Relational Systems: Foundations and Principles. Kluwer Academic, New York (2002)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsChifeng UniversityChifengChina

Personalised recommendations