Fuzzy sets membership functions integrated with logistic map as the chaos generator were used to create reliability bifurcations diagrams of the system with redundancy of the components. This paper shows that increasing in the number of redundant components results in a postponement of the moment of the first bifurcation which is considered as most contributing to the loss of the reliability. The increasing of redundancy also provides the shrinkage of the oscillation orbit of the level of the system’s membership to reliable state. The paper includes the problem statement of redundancy optimization under conditions of chaotic behavior of influencing parameters and genetic algorithm of this problem solving. The paper shows the possibility of chaos-tolerant systems design with the required level of reliability.
This paper presents a method of time series forecasting based on the integration of fuzzy logic and chaos theory. The proposed method has two stages. On the first stage, we consider the time series as a dynamic system and using the methods of mutual information and false nearest neighbors, as a part of applied chaos theory, we reconstruct the phase portrait corresponding to the original time series. On the second stage, we are learning the neuro fuzzy network as a model of time series forecasting using the vectors points of reconstructed phase portrait. We consider all the formalisms necessary for understanding the method and present the results of two computer experiments proving the ability of fuzzy inference accuracy increasing using the selection of optimal parameters of time delay and phase portrait dimension.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.