Summary: A generalized \(\Omega\)-fuzzy automaton over a complete residuated lattice \(\Omega\) and a monoid \((M,\ast)\) and with a set \(S\) of states is introduced as a monoid homomorphism \(\mathbf F:(M,\ast)\to(\mathcal R,\circ )\), where \((\mathcal R,\circ)\) is a monoid of \(\Omega\)-fuzzy sets in a set \(S\times S\). An extension principle depending of proper filters \(\Phi\) in \(\Omega\) is introduced which then enables to introduce morphisms between generalized \(\Omega\)-fuzzy automata and to introduce the category \(\mathcal F_\Phi\) of these automata. It is proved that categories of classical fuzzy automata, non-deterministic automata and some other systems are equivalent to subcategories of \(\mathcal F_\Phi\) for a suitable filter \(\Phi\).