Residuated lattice-valued automata based on graphs

At first, by considering the notion of residuated lattice-valued zero-forcing set (L-valued Z-forcing set), we present the definition of residuated lattice-valued epidemic automata (RLEA). In addition, we study some kinds of languages recognizable by some RLEA which cannot be recognized by any zero-forcing automata. We prove that if two L-valued strong graphs are isomorphic with threshold [Formula: see text], then the RLEA of them are isomorphic with threshold [Formula: see text], where [Formula: see text]. Moreover, we present a regular residuated lattice-valued epidemic grammar. After that, we present the closure properties of RLEA. We have seen that there does not exist graph such that the language of zero-forcing automata of it recognize the word [Formula: see text], but in this paper, we present some L-valued strong graphs in which their RLEA recognize this kind of languages. We present some examples to clarify these notions.