Fuzzy subgroups and digraphs induced by fuzzy subgroups

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.

کلیدواژه ها:

fuzzy‎ ‎subgroup‎ ، ‎mu-product relation‎ ، Fuzzy normal‎ ، Digraph‎ ، ‎(mu‎ ، ‎nu)-homomorphism‎