On a Generalization of Fuzzy Filters of Ordered Semigroups

Abstract

The aim of this paper is to generalize the results related to fuzzy filters of ordered semigroups. In this regard, the concept of fuzzy [Formula: see text]-filters of ordered semigroups is initiated, nontrivial examples are presented, and its properties are investigated. It is known that a fuzzy set of an ordered semigroup is a fuzzy filter if and only its complement is a fuzzy prime ideal. As a generalization of the latter result, it is proved that a fuzzy set of an ordered semigroup is a fuzzy [Formula: see text]-filter if and only if its complement is a prime generalized fuzzy [Formula: see text]-ideal. Furthermore, it is shown that in an [Formula: see text]-regular semigroup, fuzzy [Formula: see text]-filters and fuzzy bi-filters coincide.