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

TL;DR

This paper introduces fuzzy right, left ideals in hypergroupoids and fuzzy bi-ideals in hypersemigroups, providing characterizations that facilitate the study of fuzzy algebraic structures and illustrating the transition from fuzzy semigroups to hyperstructures.

Contribution

It defines and characterizes fuzzy ideals in hypergroupoids and hypersemigroups, extending fuzzy algebra concepts from semigroups to hyperstructures.

Findings

Characterizations of fuzzy right and left ideals via composition inequalities.

Characterization of fuzzy bi-ideals in hypersemigroups.

Demonstrates the transition from fuzzy semigroups to hyperstructures.

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 $f\circ 1\preceq f$ (resp. $1\circ f\preceq f)$ and for an hypersemigroup $H$, a fuzzy subset $f$ of $H$ is a bi-ideal of $H$ if and only if $f\circ 1\circ f\preceq f$. 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).