Lattice-valued fuzzy residual finite automata

In this paper, we introduce the notion of lattice-valued fuzzy residual finite automaton (LRFA) and the LRFA-regular language with membership values in a complete residu-ated lattice. Next, we define saturation operator and reduction operator on lattice-valued finite automata(Li´M), which provide a way to simplify LRFA based on their closure properties in LRFA. At last, we define the canonical LRFA based on the notion of irreducible residual language, prove that every LRFA-regular language is recognized by a unique canonical LRFA which has a minimal number of states and largest initial and transition functions.