Fuzzy ideals and semiprime fuzzy ideals in semigroups

KAZANCI O., YAMAK S.

INFORMATION SCIENCES, vol.179, no.20, pp.3720-3731, 2009 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 179 Issue: 20
  • Publication Date: 2009
  • Doi Number: 10.1016/j.ins.2009.06.026
  • Journal Name: INFORMATION SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.3720-3731
  • Karadeniz Technical University Affiliated: Yes

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 phi-fuzzy ideals of a fuzzy semigroup X is a complete sublattice of the lattice of all fuzzy sets in X when phi is an infinitely V-distributive weak pseudo-t-norm on L. A definition of phi-semiprime fuzzy ideal of a fuzzy semigroup is given. A description of all phi-semigroups, in which every phi-fuzzy ideal is phi-semiprime, is obtained. (C) 2009 Elsevier Inc. All rights reserved.