Fuzzy n-ary groups as a generalization of Rosenfeld's fuzzy groups

TL;DR

This paper introduces the concept of fuzzy n-ary subgroups as a generalization of fuzzy groups, exploring their properties and characterizations within n-ary group structures.

Contribution

It extends the theory of fuzzy groups to n-ary groups by defining fuzzy n-ary subgroups and analyzing their properties and characterizations.

Findings

Defined fuzzy n-ary subgroups and normal fuzzy n-ary subgroups.

Provided characterizations of fuzzy n-ary subgroups.

Explored properties related to fuzzy n-ary subgroups.

Abstract

The notion of an $n$-ary group is a natural generalization of the notion of a group and has many applications in different branches. In this paper, the notion of (normal) fuzzy $n$-ary subgroup of an $n$-ary group is introduced and some related properties are investigated. Characterizations of fuzzy $n$-ary subgroups are given.