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.