‎Fuzzy Subgroups and Digraphs Induced by Fuzzy Subgroups

Transactions on Fuzzy Sets and Systems

مقاله 9، دوره 1، شماره 1، مرداد 2022، صفحه 114-119   

نوع مقاله: Original Article

شناسه دیجیتال (DOI): 10.30495/tfss.2022.690699

نویسندگان

Paul J. Allen¹؛ Joseph Neggers¹؛ Hee Sik Kim^{* 2}

¹Department of Mathematics University of Alabama Tuscaloosa, U.S.A.

²Department of Mathematics Hanyang University Seoul, Korea.

چکیده

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 $G$‎.

کلیدواژه‌ها

Fuzzy‎ ‎subgroup‎؛ ‎$mu$-product relation‎؛ Fuzzy normal‎؛ Digraph‎؛ ‎$(mu‎؛ ‎nu)$-homomorphism‎‏

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