Fuzzy right (left) ideals in hypergroupoids and fuzzy bi-ideals in hypersemigroups

Abstract

We introduce the concepts of fuzzy right and fuzzy left ideals of hypergroupoids and the concept of a fuzzy bi-ideal of an hypersemigroup and we show that a fuzzy subset $f$ of an hypergroupoid $H$ is a fuzzy right (resp. fuzzy left) ideal of $H$ if and only if $f\circ 1⪯f$ (resp. $1\circ f⪯f)$ and for an hypersemigroup $H$, a fuzzy subset $f$ of $H$ is a bi-ideal of $H$ if and only if $f\circ 1\circ f⪯f$. These characterizations are very useful for the investigation. The paper serves as an example to show the way we pass from fuzzy groupoids (semigroups) to fuzzy hypergroupoids (hypersemigroups).