The paper is a reflection of ``fuzzy sets'' applied to ``hyper $p$-ideals'' and their comparison with simple ``fuzzy hyper BCK-ideals''. The idea of ``fuzzy (weak, strong) hyper $p$-ideals'' is presented and characterization of these ideals is conferred using different concepts like that of ``level subsets, hyper homomorphic pre-image'' etc. The connections between ``fuzzy (weak, strong) hyper $p$-ideals'' are discussed and ``the strongest fuzzy relation'' on a ``hyper BCK-algebra'' is conferred.