Fuzzy ideals and semiprime fuzzy ideals in semigroups

  • Authors:
  • O. Kazancı;S. Yamak

  • Affiliations:
  • Department of Mathematics, Karadeniz Technical University, 61080 Trabzon, Turkey;Department of Mathematics, Karadeniz Technical University, 61080 Trabzon, Turkey

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2009

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Abstract

In this paper, we investigate relationships between different definitions of fuzzy ideals of a fuzzy semigroup. The equivalence of different definitions of fuzzy ideals of a fuzzy semigroup is obtained. We show that the lattice of all @f-fuzzy ideals of a fuzzy semigroup X is a complete sublattice of the lattice of all fuzzy sets in X when @f is an infinitely @?-distributive weak pseudo-t-norm on L. A definition of @f-semiprime fuzzy ideal of a fuzzy semigroup is given. A description of all @f-semigroups, in which every @f-fuzzy ideal is @f-semiprime, is obtained.