The homomorphic image of a fuzzy subgroup is always a fuzzy subgroup (Q1823314)

Let L be any complete and completely distributive lattice with 0 and 1 and X a group. \(\mu\) : \(X\mapsto L\) is called L-fuzzy group on X iff (i) \(\mu\) (xy)\(\geq \mu (x)\wedge \mu (y)\) and (ii) \(\mu (x^{-1})\geq \mu (x)\) \(\forall x,y\in X\). The aim of this paper is to prove that if L is as above and X is a group then the image of a fuzzy group \(\mu\) : \(X\mapsto L\) under a morphism of groups f: \(X\mapsto Y\) is always a fuzzy group.