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Equivalences between neural-autoregressive time series models and fuzzy systems
José Luis Aznarte1, José Manuel Benitez
1Center for Energy and Processes of MINES ParisTech, France. jlaznarte@decsai.ugr.es
IEEE Transactions on Neural Networks
|August 26, 2010
Summary
This study reveals functional equivalences between soft computing models, specifically regime-switching autoregressive models and fuzzy rule-based systems. This finding bridges artificial neural networks and fuzzy systems for time series analysis.
Area of Science:
- Computational Intelligence
- Time Series Analysis
- Statistical Modeling
Background:
- Soft computing (SC) integrates artificial neural networks, fuzzy systems, evolutionary algorithms, and probabilistic reasoning.
- A key goal in SC is understanding the relationships among its constituent techniques.
- This research focuses on two SC model families: regime-switching autoregressive models and fuzzy rule-based systems.
Purpose of the Study:
- To establish novel functional equivalences between regime-switching autoregressive models and fuzzy rule-based systems.
- To explore the interconnections between statistical time series modeling and fuzzy logic.
- To facilitate the transfer of research findings and methodologies between these two domains.
Main Methods:
- Analysis of regime-switching autoregressive models, a recent development in statistical time series.
- Investigation of fuzzy rule-based systems within the context of time series analysis.
- Mathematical derivation of functional equivalences between the two model classes.
Main Results:
- Original results demonstrating functional equivalences between regime-switching autoregressive models and fuzzy rule-based systems.
- Proof of the asymptotic stationarity for a class of fuzzy rule-based systems as a consequence of the established equivalences.
- Simulation-based evidence highlighting the impact of membership function selection on model performance.
Conclusions:
- The identified equivalences open new avenues for research, allowing techniques from one field to inform the other.
- The study contributes to a deeper understanding of the relationships within soft computing.
- Proper selection of membership functions is crucial for the effective application of fuzzy rule-based systems in time series analysis.
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