Simulations and bisimulations for fuzzy multimodal logics over Heyting algebras

In the present paper, we study fuzzy multimodal logics over complete Heyting algebras and Kripke models for these logics. We introduce two types of simulations (forward backward) five bisimulations (forward, backward, forward-backward, backward-forward regular) between models, as well corresponding presimulations prebisimulations, which are with relaxed conditions. For each type an efficient algorithm has been provided that works follows: it computes greatest presimulation/prebisimulation type, then checks whether meets additional condition: if does, is also simulation/ bisimulation otherwise, there not any simulation/bisimulation type. The algorithms inspired by checking existence computing automata. demonstrate application in state reduction models. show forward equivalences on model provide reduced equivalent to original concerning plus-formulas, backward minus-formulas, while regular all modal formulas.