On fuzzy prime and fuzzy semiprime ideals of $\le$-hypergroupoids

Abstract

We deal with an hypergroupoid endowed with a relation denoted by "$\le$", we call it $\le$--hypergroupoid. We prove that a nonempty subset $A$ of a $\le$--hypergroupoid $H$ is a prime (resp. semiprime) ideal of $H$ if and only if its characteristic function $f_A$ is a fuzzy prime (resp. fuzzy semiprime) ideal of $H$.