LB-valued General Fuzzy Automata and minimal Determinization

Although a variety of methods have already been developed to convert and adapt a fuzzy automaton to its related language equivalent fuzzy deterministic finite automaton, they can still be applied merely for fuzzy automata which have been characterized over particular underlying sets of truth values. Filling this gap, thus, this study attempts to focus on developing a method for computing a minimal deterministic LB-valued general fuzzy automaton for an LB-valued GFA defined over a locally finite and divisible residuated lattice. This proposed method uses the concept of a reduction graph that helps us achieve a minimal deterministic LB-valued GFA. Accordingly, the present investigation aimed at establishing the notions related to L-valued language identified by LB-valued general fuzzy automata (LBvalued GFA) and also crisp deterministic LB-valued GFA ˜ Fc equivalent to LB-valued GFA ˜ F. It then indicated the properties of ˜ Fc. The method of determinization through factorization of L-valued states and also a method concerning state reduction were proposed and studied in details. In particular, the main focus and contribution of this study was the automaton H( ˜ Fc) which is recognized as a deterministic LB-valued GFA that assures the necessary conditions intended for minimality and that its size is always equal or lesser than a minimal crisp deterministic LB-valued GFA equivalent to that. The related concepts and the results obtained in this study have also been clarified and explicated through representative examples.