Uncertainty Propagation in Fuzzy Grey Cognitive Maps With Hebbian-Like Learning Algorithms

This paper is focused on an innovative fuzzy cognitive maps extension called fuzzy grey cognitive maps (FGCMs). FGCMs are a mixture of fuzzy cognitive maps and grey systems theory. These have become a useful framework for facing problems with high uncertainty, under discrete small and incomplete datasets. This paper deals with the problem of uncertainty propagation in FGCM dynamics with Hebbian learning. In addition, this paper applies differential Hebbian learning (DHL) and balanced DHL to FGCMs for the first time. We analyze the uncertainty propagation in eight different scenarios in a classical chemical control problem. The results give insight into the propagation of the uncertainty or greyness in the iterations of the FGCMs. The results show that the nonlinear Hebbian learning is the choice with less uncertainty in steady final grey states for Hebbian learning algorithms.