Intra-regular ordered semigroups play an
important role in studying the structure, especially the
decomposition of ordered semigroups. In this paper we prove that
the fuzzy ideals of an ordered semigroup *S* are weakly prime if
and only if they are idempotent and they form a chain, and that
they are prime if and only if *S* is intra-regular and the fuzzy
ideals of *S* form a chain. Moreover we show that a fuzzy ideal of
an ordered semigroup is prime if and only if it is both semiprime
and weakly prime and that in commutative ordered semigroups the
prime and weakly prime fuzzy ideals coincide. Our results extend
the corresponding results on semigroups (without order) given by
G. Szász in [11] in case of ordered semigroups using fuzzy
sets.

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