On fuzzy ordered semigroups

The main goal of this paper is to introduce and study some classes of ordered semigroups and to investigate some interesting characterizations theorems of these classes in terms of fuzzy ideals. In this respect, we characterize weakly regular ordered semigroups for example (see Theorem 3.4, Theorem 3.5 and Theorem 3.7) intra-regular and left weakly regular ordered semigroups (see Theorem 4.2 and Theorem 4.4 and semisimple ordered semigroups (see Theorem 5.5 and Theorem 5.7) in terms of fuzzy ideals. In this regard, we define semisimple ordered semigroups and characterize it in terms of fuzzy ideals. We also characterize intra-regular and weakly-regular ordered semigroups in terms of fuzzy ideals.