The main objective of the dissertation is to provide a detailed study of several different types of simulations and
bisimulations for Kripke models of fuzzy multimodal logics. Two types of simulations (forward and backward)
and five types of bisimulations (forward, backward, forward-backward, backward-forward and regular) are presented
hereby. For each type of simulation and bisimulation, an algorithm is created to test the existence of the simulation
or bisimulation and, if it exists, the algorithm computes the greatest one. The dissertation presents the application of
bisimulations in the state reduction of fuzzy Kripke models, while preserving their semantic properties. Next, weak simulations and bisimulations were considered and the Hennessy-Milner property was examined. Finally, an algorithm was created to compute weak simulations and bisimulations for fuzzy Kripke models over locally finite algebras
