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Uncertainty Propagation in Fuzzy Grey Cognitive Maps With Hebbian-Like Learning Algorithms
IEEE Transactions on Cybernetics
|July 11, 2018
Summary
This study introduces fuzzy grey cognitive maps (FGCMs) to manage uncertainty in small datasets. Nonlinear Hebbian learning within FGCMs demonstrated the least uncertainty in control system dynamics.
Area of Science:
- Computational intelligence
- Systems science
- Uncertainty modeling
Background:
- Fuzzy cognitive maps (FCMs) are limited in handling high uncertainty and incomplete data.
- Grey systems theory offers a framework for systems with limited data.
- Fuzzy grey cognitive maps (FGCMs) integrate FCMs and grey systems theory for enhanced uncertainty management.
Purpose of the Study:
- To investigate uncertainty propagation in fuzzy grey cognitive maps (FGCMs) dynamics.
- To apply differential Hebbian learning (DHL) and balanced DHL to FGCMs for the first time.
- To evaluate the performance of different Hebbian learning algorithms in FGCMs under uncertainty.
Main Methods:
- Extension of fuzzy cognitive maps (FCMs) with grey systems theory to create FGCMs.
- Implementation of Hebbian learning, including differential Hebbian learning (DHL) and balanced DHL, within FGCMs.
- Analysis of uncertainty propagation across eight scenarios in a chemical control problem simulation.
Main Results:
- FGCMs effectively address problems characterized by high uncertainty and limited datasets.
- Differential Hebbian learning (DHL) and balanced DHL were successfully applied to FGCMs.
- Nonlinear Hebbian learning exhibited the lowest uncertainty in the final grey states of the FGCMs.
Conclusions:
- FGCMs provide a robust framework for modeling complex systems with inherent uncertainty.
- Hebbian learning algorithms, particularly nonlinear variants, significantly impact uncertainty propagation in FGCMs.
- The study offers valuable insights into managing and reducing uncertainty in data-driven control systems.
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