Abstract
In this note, we focus on behavior of BL-general fuzzy automata (for simplicity BL-GFA) and we obtain the free realization for a given behavior, that is, a BL-general fuzzy automaton whose behavior is given behavior. Then we find the realization with the minimum number of states. The minimization takes two steps: at first discard all superfluous states, and then we merge all pairs of states which have the same behavior. Moreover we prove some theorems. In particular, we show that the minimal reduction of the reachable part of an BL-GFA is the minimal realization of the behavior it. Finally we give some examples to clarify these notions.
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