Ordered semigroups characterized in terms of generalized fuzzy ideals

In the present paper, the notions of (k*, q)-quasi-coincident, (is an element of, is an element of boolean OR(k*, q(k)))-fuzzy left ideal, (is an element of, is an element of boolean OR(k*, q(k)))fuzzy right ideal and (is an element of, is an element of boolean OR(k*, q(k)))-fuzzy generalized bi-ideal of an ordered semigroup are introduced. The (k* k)-lower parts of an (is an element of, is an element of boolean OR(k*, q(k)))-fuzzy left ideal, (is an element of, is an element of boolean OR(k*, q(k)))-fuzzy right ideal and (is an element of, is an element of boolean OR(k*, q(k)))-fuzzy generalized bi-ideal are also defined. Then, we characterize these various fuzzy ideals. Finally, using the properties of these fuzzy ideals, we characterize regular, left regular, right regular, completely regular and left weakly regular ordered semigroups.