An algebraic study of LB-valued general fuzzy automata: On the concept of the layers

Document Type : Original Article


1 Department of Math.,Faculty Member, Islamic Azad University,Shiraz,Iran

2 Behbahan Khatam Alanbia University of Technology, Khouzestan, Iran


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. 


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