In this paper, at first, we define the notion of general fuzzy automaton over a field; we call this automaton vector general fuzzy automaton (VGFA). Moreover, we present the concept of max-min vector general fuzzy automaton. We show that if two max-min VGFA are similar, they constitute an isomorphism. After that, we prove that if two VGFA constitute an isomorphism with threshold α, they are equivalent with threshold α, where $\alpha \in [0,1]$. Also, some examples are given to clarify these new notions.