an algebraic study of lb-valued general fuzzy automata: on the concept of the layers

The present study aims at introducing a new concept of layer of lb-valued general fuzzy automata (lb-valued gfa)  where b is regarded as a set of propositions about the gfa, in which its underlying structure has been a lattice-ordered  monoid. in general, it demonstrates that the layer plays a key role in the algebraic study of lb-valued gfa by  characterizing the concepts of subautomata and separated subautomata of an lb-valued gfa in terms of its layers. in  other words, it highlights that every lb-valued general fuzzy automaton has at least one strongly connected  subautomaton. in specific, the characterization of some algebraic concepts such as subautomaton, retrievability and  connectivity of an lb-valued gfa in terms of its layers is provided. in addition, it is shown that the maximal layer of a  cyclic lb-valued general fuzzy automaton and minimal layer of a directable lb-valued general fuzzy automaton are  unique. finally, we investigate the different poset structures associated with an lb-valued general fuzzy automaton,  demonstrating some of these posets as finite upper semilattice, and introducing the isotone galois connections between  some of the pairs of the posets/finite upper semilattices introduced.