Boolean matrix equations for node identification in fuzzy rule based networks

This paper proposes a novel approach for modelling complex interconnected systems by means of fuzzy networks. The nodes in these networks are interconnected rule bases whereby outputs from some rule bases are fed as inputs to other rule bases. The approach allows any fuzzy network of this type to be presented as an equivalent fuzzy system by linguistic composition of its nodes. The composition process makes use of formal models for fuzzy networks and basic operations in such networks. These models and operations are used for defining several node identification cases in fuzzy networks. In this case, the unknown nodes are derived by solving Boolean matrix equations in a way that guarantees a pre-specified overall performance of the network. The main advantage of the proposed approach over other approaches is that it has better transparency and facilitates not only the analysis but also the design of complex interconnected systems.