Fuzzy ideals extenstions of ordered semigroups

In this paper, we introduce the concepts of the extension of fuzzy ideals , prime, semiprime and 3-prime fuzzy ideals in an ordered semigroup $S$, respectively. We discuss properties of fuzzy ideals extensions and the relationships between prime fuzzy ideals and 3-prime fuzzy ideals of $S$ in terms of the extension of fuzzy ideals of $S$, we give an example to show that 3-prime fuzzy ideal is not necessarily prime. Moreover, for commutative ordered semigroups, we obtain some properties of the extension of fuzzy ideals in commutative ordered semigroup.