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This study aims to develop the notion of general fuzzy automata (GFA) to a new one which is known as “ L B -valued general fuzzy automata”. Instead of the term L B -valued general fuzzy automata, for simplicity, L B -valued GFA is used where B is regarded as a set of propositions about the GFA, in which its underlying structure has been a complete infinitely distributive lattice. Further, L B -valued GFA is scrutinized via different operators and also the interrelationship among these operators is examined. Specifically, it is shown that L B -valued successor, L B -valued predecessor and L B -valued residuated operators play an important role in the algebraic study of L B -valued general fuzzy automaton and that under certain conditions these operators are interrelated. In addition, the concept of a homomorphism between L B -valued general fuzzy automata is introduced and studied. Finally, the concepts of equivalence and congruence are defined, the quotient L B -valued GFA with respect to congruence is formulated and the equivalence between L B -valued GFA and its quotient automaton is proved. To clarify the notions and the results obtained in this study, some examples are submitted as well. |
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