Advertisement

(\(\in , \in \vee {\,q}\))-Fuzzy Filter Theory in FI-algebras

  • Chun-hui Liu
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 367)

Abstract

The notions of (\(\in , \in \vee {\,q}\))-fuzzy filters and (\(\in , \in \vee {\,q}\))-fuzzy implicative (positive implicative, commutative, involution) filters in FI-algebras are introduced and their properties are investigated. Equivalent characterizations of various (\(\in , \in \vee {\,q}\))-fuzzy filters are obtained. Relations among various (\(\in , \in \vee {\,q}\))-fuzzy filters are discussed and it is proved that a fuzzy set is (\(\in , \in \vee {\,q}\))-fuzzy positive implicative filter iff it is both (\(\in , \in \vee {\,q}\))-fuzzy implicative and (\(\in , \in \vee {\,q}\))-fuzzy commutative (or involution) filter.

Keywords

Fuzzy logic FI-algebra (Open image in new window)-fuzzy filter (Open image in new window)-fuzzy 

Notes

Acknowledgments

Thanks to the support by National Natural Science Foundation of China (No. 60774073 and No. 10371106).

References

  1. 1.
    Wu, W.M.: Fuzzy implication algebras. Fuzzy Syst. Math. 4(1), 56–64 (1990)Google Scholar
  2. 2.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)CrossRefMathSciNetMATHGoogle Scholar
  3. 3.
    Jun, Y.B., Xu, Y., Qin, K.Y.: Fuzzy filters redefined in lattice implication algebras. J. Fuzzy Math. 14(2), 345–353 (2006)Google Scholar
  4. 4.
    Ma, X.L., Zhan, J.M.: On \((\in , \in \vee {\, q})\)-fuzzy filters of BL-algebras. J. Syst. Sci. Complex. 21, 144–158 (2008)Google Scholar
  5. 5.
    Liu, C.H.: \((\in , \in \vee {\, q})\)-fuzzy filters of UB algebras in universal logic. Comput. Eng. Appl. 45(34), 29–31 (2009)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.College of Mathematics and StatisticsChifeng UniversityChifengChina

Personalised recommendations