Chaos in Fuzzy and Neuro-Fuzzy Networks. Fuzzy Pattern Formation
Technical University of Iasi
Last modified: October 5, 2007
According to the Representation Theorem (better known as the Universal Approximation Theorem), any classical (crisp) system can be approximated with whatever precision by a fuzzy logic system provided with a defuzzifier. We further detail the theoretical representation of crisp systems as limit of sequences of fuzzy logic systems, thus endowing the space of generalized systems with a topological structure. Further, the space of crisp system trajectories is embedded in the space of fuzzy trajectories, thus allowing a more general representation for the dynamic evolution of such systems.
In this framework, we deal with theoretical issues of fuzzy logic chaos and with dynamic pattern formation in networks of fuzzy logic systems and in networks of crisp systems implemented with defuzzified fuzzy logic systems. Various examples of networks of fuzzy logic systems are presented and their dynamic patterns are shown and discussed. The paper concludes with a brief presentation of potential applications of fuzzy logic chaotic systems and networks. Beyond modelling applications, a few engineering applications are briefly mentioned.