Isomorphism between two BL-general fuzzy automata

In this note first we develop the notion of general fuzzy automata (GFA) to a new one which is called “BL-general fuzzy automata” and for simplicity, we write BL-GFA, instead of BL-general fuzzy automata. Then we focus on derivation, active state set, membership assignment, output mappings, and concept of belonging to an output label according to the entrance input strings for BL-general fuzzy automata. Therefore, we define the concepts of run map and behavior of BL-GFA. After that we present the morphism with threshold between two BL-general fuzzy automata. Moreover we give some examples, to clarify these notions. Finally, we prove some theorems. In particular, we show that the isomorphic BL-general fuzzy automata have the same behavior.