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Fuzzy Switch Graphs (FSG) generalize the notion of Fuzzy Graphs by adding high-order arrows and aggregation functions which update the fuzzy values of arrows whenever a zero-order arrow is crossed. In this paper, we propose a more general structure called Reversal Fuzzy Switch Graph (R F S G), which promotes other actions in addition to updating the fuzzy values of the arrows, like activation and deactivation of the arrows. R F S G s are able to model dynamical aspects of some systems which generally appear in engineering, computer science and some other fields. The paper also provides the relationship between R F S G s and fuzzy graphs, a logic to verify properties of the modeled system and closes with an application. • Fuzzy logic and aggregation functions are used to specify reactive systems. • Fuzzy Reactive Switch Graphs generalize the notion of fuzzy graphs. • Bisimulation of reactive systems is threated in this system. • An example of a control system is provided for Fuzzy Reactive Switch Graphs. [ABSTRACT FROM AUTHOR]