Elsevier

Fuzzy Sets and Systems

Volume 152, Issue 2, 1 June 2005, Pages 333-348
Fuzzy Sets and Systems

Fuzzy Boolean and positive implicative filters of BL-algebras

https://doi.org/10.1016/j.fss.2004.10.005Get rights and content

Abstract

The aim of this paper is to introduce the notions of fuzzy Boolean filters and fuzzy positive implicative filters in BL-algebras and to investigate their properties. Several characterizations of fuzzy Boolean filters and fuzzy positive implicative filters are derived. The extension theorems of fuzzy Boolean filters and fuzzy positive implicative filters are obtained. The relation between fuzzy Boolean filters and fuzzy positive implicative filters is investigated and it is proved that every fuzzy Boolean filter is a fuzzy positive implicative filter, but the converse may not be true. Furthermore, the conditions under which a fuzzy positive implicative filter is a fuzzy Boolean filter are established.

References (22)

  • C.S. Hoo

    Fuzzy implicative and Boolean ideals of MV-algebras

    Fuzzy Sets and Systems

    (1994)
  • Y.B. Jun

    Fuzzy positive implicative and fuzzy associative filters of lattice implication algebras

    Fuzzy Sets and Systems

    (2001)
  • L.A. Zadeh

    Fuzzy sets

    Inform. and Control

    (1965)
  • C.C. Chang

    Algebraic analysis of many valued logics

    Trans. Amer. Math. Soc.

    (1958)
  • P. Hájek

    Metamathematics of Fuzzy Logic

    (1998)
  • C.S. Hoo et al.

    Implicative and Boolean ideals of MV-algebras

    Math. Japon.

    (1994)
  • A. Iorgulescu

    Some direct ascendents of Wajsberg and MV-algebras

    Sci. Math. Japon.

    (2003)
  • K. Iséki et al.

    Ideal theory of BCK-algebras

    Math. Japon.

    (1976)
  • K. Iséki et al.

    An introduction to the theory of BCK-algebras

    Math. Japon.

    (1978)
  • Y.B. Jun et al.

    On fuzzy implicative filters of lattice implication algebras

    J. Fuzzy Math.

    (2002)
  • M. Kondo

    Fuzzy congruence on BCI-algebras

    Sci. Math. Japon.

    (2003)
  • Cited by (76)

    View all citing articles on Scopus
    View full text