Fuzzy ideals of ordered semigroups with fuzzy orderings

Abstract

Abstract:The purpose of this paper is to introduce the notions of .2; 2 _q k /-fuzzy ideals of a fuzzy ordered semigroup with the ordering being a fuzzy relation. Several characterizations of .2; 2 _q k /-fuzzy left (resp. right) ideals and .2; 2 _q k /-fuzzy interior ideals are derived. The lattice structures of all .2; 2 _q k /-fuzzy (interior) ideals on such fuzzy ordered semigroup are studied and some methods are given to construct an .2; 2 _q k /-fuzzy (interior) ideals from an arbitrary fuzzy subset. Finally, the characterizations of generalized semisimple fuzzy ordered semigroups in terms of .2; 2 _q k /-fuzzy ideals (resp. .2; 2 _q k /-fuzzy interior ideals) are developed.