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

TL;DR

This paper explores the relationship between prime and semiprime ideals in $$-hypergroupoids and their fuzzy counterparts, establishing an equivalence via characteristic functions.

Contribution

It proves that nonempty subsets are prime or semiprime ideals if and only if their characteristic functions are fuzzy prime or fuzzy semiprime ideals.

Findings

Characterization of prime ideals via fuzzy prime ideals

Characterization of semiprime ideals via fuzzy semiprime ideals

Equivalence between subset ideals and fuzzy ideals in $$-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 $H$.