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.
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