A new characterization of fuzzy ideals of semigroups and its applications

Abstract

In this paper, we develop a new technique for constructing fuzzy ideals of a semigroup. By using generalized Green's relations, fuzzy star ideals are constructed. It is shown that the new fuzzy ideal of a semigroup can be used to investigate the relationship between fuzzy sets and abundance and regularity for an arbitrary semigroup. Appropriate examples of such fuzzy ideals are given in order to illustrate the technique. Finally, we explain when a semigroup satisfies conditions of regularity.

Keywords

• fuzzy sets
• fuzzy star ideals
• abundant semigroups
• abundance
• regularity