isotone galois connections in lb-valued general fuzzy automata

The present study aimed at investigating the interior and closure operators which have been characterized by isotone galois connections between posets/finite upper semilattices associated with an lb-valued general fuzzy automaton (for simplicity lbvalued gfa). in addition, the existence of isotone galois connections between different pairs of posets/finite upper semlattices associated with a given lb-valued gfa was examined and explicated in detail. the properties of isotone galois connections were also discussed under some conditions imposed on lb-valued gfa. further, the decomposition of an lb-valued general fuzzy automaton was defined and a subautomaton of an lb-valued gfa was characterized in terms of its decomposition components. we have also demonstrated that the cardinality of set of all subautomata of an lb-valued general fuzzy automaton is not equal to sum of cardinalities of set of all subautomata of finite decomposition components.