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We characterize the fuzzy left (resp. right) ideals, the fuzzy ideals and thefuzzy prime (resp. semiprime) ideals of an ordered $\Gamma$-groupoid $M$ interms of level subsets and we prove that the cartesian product of two fuzzyleft (resp. right) ideals of $M$ is a fuzzy left (resp. right) ideal of$M\times M$, and the cartesian product of two fuzzy prime (resp. semiprime)ideals of $M$ is a fuzzy prime (resp. semiprime) ideal of $M\times M$. As aresult, if $\mu$ and $\sigma$ are fuzzy left (resp. right) ideals, ideals,fuzzy prime or fuzzy semiprime ideals of $M$, then the nonempty level subsets$(\mu\times\sigma)_t$ are so.

On Fuzzy Ideals and Level Subsets of Ordered $\Gamma$-Groupoids