Fuzzy fractals, chaos, and noise
To distinguish between chaotic and noisy processes, the authors analyze one- and two-dimensional chaotic mappings, supplemented by the additive noise terms. The predictive power of a fuzzy rule-based system allows one to distinguish ergodic and chaotic time series: in an ergodic series the likelihood of finding large numbers is small compared to the likelihood of finding them in a chaotic series. In the case of two dimensions, they consider the fractal fuzzy sets whose {alpha}-cuts are fractals, arising in the context of a quadratic mapping in the extended complex plane. In an example provided by the Julia set, the concept of Hausdorff dimension enables one to decide in favor of chaotic or noisy evolution.
- Research Organization:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE Assistant Secretary for Human Resources and Administration, Washington, DC (United States)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 474949
- Report Number(s):
- LA-UR-97-778; CONF-970693-1; ON: DE97005017; TRN: AHC29711%%119
- Resource Relation:
- Conference: International fuzzy systems association conference, Prague (Czech Republic), 25-29 Jun 1997; Other Information: PBD: [1997]
- Country of Publication:
- United States
- Language:
- English
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