Reversal fuzzy switch graphs

Abstract

We present a state-based Fuzzy model called Reversal Fuzzy Switch Graph (RF SG). This model enables the activation or deactivation of edges as well as the updating of fuzzy values from the action of aggregation functions, whenever a transition occurs between the states. The fuzzy feature of RF SGs allows you to model uncertainties, whereas the activation and deactivation of edges allow the simulation of dynamic aspects of access to system states. When more than one aggregation function is used in this process, we have the Reversal Fuzzy Reactive Graph (RF RG). In addition, we propose some operations that are based on aggregation functions (unions, intersections, Cartesian product and extension). We also present the relationship between the RF RGs and the usual fuzzy graphs together with a notion for simulation and bisimulation. We introduce the concept of homomorphism between RF SGs and a class of formal languages for verifying properties of systems that are modeled by such graphs.