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 (m,n) -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 (m,n) -filter if and only if its complement is a prime generalized fuzzy (m,n)-ideal. Furthermore, it is shown that in an (m,n)-regular semigroup, fuzzy (m,n)-filters and fuzzy bi-filters coincide. Keywords: Ordered semigroupfuzzy (m,n), filtergeneralized fuzzy (m,n), idealfuzzy prime subset