Fuzzy simulations and bisimulations between fuzzy automata

Simulations and bisimulations between two fuzzy automata over a complete residuated lattice were defined by Ćirić et al. (2012) [7], [8] as relations the sets of states automata. However, they act crisp relationship In particular, if there exists (forward) bisimulation automata, then languages recognized them are crisply equal. Approximate simulations introduced Stanimirović (2022) [36] aim at fuzzifying this phenomenon. only for Heyting algebra do not give exact article, we introduce study lattice. These notions novel have good properties. They any We prove that language automaton is fuzzily preserved invariant under bisimulations. also simulation Hennessy-Milner properties, which logical characterization greatest or addition, provide results showing our more general refined than approximate