28 June 1994 Chaos and information loss in fuzzy dynamical systems
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Proceedings Volume 10312, Neural and Fuzzy Systems: The Emerging Science of Intelligent Computing; 1031202 (1994) https://doi.org/10.1117/12.2283785
Event: SPIE Institutes for Advanced Optical Technologies 12, 1994, Bellingham, WA, United States
That dynamical systems can produce chaotic and erratic behavior is now an accepted feature of systems modeling and controller design. This behavior is not necessarily something to be avoided at all costs, but is an aspect which should be recognized and taken into account when dealing with a control system. Despite the intense interest in chaotic systems, there is no universally accepted mathematical definition of chaos. Common descriptions are in terms of positive topological entropy, Li-Yorke scrambled sets, sensitive dependence of initial conditions and positive Liapunov exponents. The precise relationships between these competing signatures is unclear and some notions are not even independent. Fuzzy dynamical systems occur in many areas of interest and it is important to understand the repertoire of possible behaviors of fuzzy systems. This review gives an overview of chaos in fuzzy dynamical systems, studying • Dynamical systems and definitions of chaos • Metric space of fuzzy sets (D", doo). • Chaotic mappings on D" and possible loss of information due to chaotic dynamics. • A general definition of fuzzification and level set, based on t- norms/conorms and their diagonal functions, and the effect of fuzzifying chaotic mappings. • A relationship between a very simple criterion, positive topological entropy and Li-Yorke chaos. • Examples of fuzzy chaos
© (1994) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Phil Diamond, Phil Diamond, } "Chaos and information loss in fuzzy dynamical systems", Proc. SPIE 10312, Neural and Fuzzy Systems: The Emerging Science of Intelligent Computing, 1031202 (28 June 1994); doi: 10.1117/12.2283785; https://doi.org/10.1117/12.2283785

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