‎Fuzzy Subgroups and Digraphs Induced by Fuzzy Subgroups

Given a fuzzy subgroup µ of a group G, x ▷u y if and only if µ(xy) µ(yx) defines a directed relation with an associated digraph (G, ▷u). We consider (µ, ν)-homomorphisms φ : (G, µ) → (H, ν) where µ and ν are fuzzy subgroups of G and H respectively and the preservation of properties of the digraphs (G, ▷u) several of which are also noted here, e.g., (G, ▷u) is an anti-chain if and only if µ is a fuzzy normal subgroup of the group G.