Bisimulations in fuzzy social network analysis

In this paper we introduce two types of simulations and five types of bisimulations for fuzzy social networks, and we study one of them – regular bisimulations. We prove that if there exists at least one regular bisimulation between two fuzzy networks, then there exists the greatest bisimulation of this type, and we provide a procedure for testing the existence of a regular bisimulation between two fuzzy networks, and computing the greatest one, whenever it exists. We also establish a natural relationship between regular bisimulations and regular fuzzy equivalences.

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