For an ordered semigroup, the authors introduce some concepts which they call \((\in,\in\vee q_k)\)-fuzzy left (right) ideals, \((\in,\in\vee q_k)\)-fuzzy ideals, \((\in,\in\vee q_k)\)-fuzzy bi-ideals, \((\in,\in\vee q_k)\)-fuzzy generalized bi-ideals and study them. They give, among others, characterizations of regular and both regular and intra-regular ordered semigroups in terms of this type of fuzzy ideals.