‎Fuzzy Subgroups and Digraphs Induced by Fuzzy Subgroups

Subject Areas : Transactions on Fuzzy Sets and Systems

Paul J. Allen ¹ , Joseph Neggers ² , Hee Sik Kim ³

1 - Department of Mathematics, University of Alabama, Tuscaloosa, U.S.A..
2 - Department of Mathematics, University of Alabama, Tuscaloosa, U.S.A..
3 - Department of Mathematics, Hanyang University, Seoul, Korea.

Received: 2022-02-21 Accepted : 2022-02-23 Published : 2022-05-07

Keywords: Fuzzy‎ ‎subgroup‎, ‎$\mu$-product relation‎, ‎Fuzzy normal‎, ‎Digraph‎, ‎$(\mu‎, ‎\nu)$-homomorphism‎.,

Abstract :

Given a fuzzy subgroup $\mu$ of a group $G$‎, ‎$x\rhd_uy$ if and only if $\mu(xy) < \mu(yx)$ defines a directed relation with an associated digraph $(G‎, ‎\rhd_u)$‎. ‎We consider $(\mu‎, ‎\nu)$-homomorphisms $\varphi‎: ‎(G‎, ‎\mu)\to (H‎, ‎\nu)$ where $\mu$ and $\nu$ are fuzzy subgroups of $G$ and $H$ respectively and the preservation of properties of the digraphs $(G‎, ‎\rhd_u)$ several of which are also noted here‎, ‎e.g.‎, ‎$(G‎, ‎\rhd_u)$ is an anti-chain if and only if $\mu$ is a fuzzy normal subgroup of the group $G$‎.

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