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Paper details
Number 3 - September 2019
Volume 29 - 2019
On the convergence of sigmoidal fuzzy grey cognitive maps
István Á. Harmati, László T. Kóczy
Abstract
Fuzzy cognitive maps (FCMs) are recurrent neural networks applied for modelling complex systems using weighted causal
relations. In FCM-based decision-making, the inference about the modelled system is provided by the behaviour of an
iteration. Fuzzy grey cognitive maps (FGCMs) are extensions of fuzzy cognitive maps, applying uncertain weights between
the concepts. This uncertainty is expressed by the so-called grey numbers. Similarly as in FCMs, the inference is determined
by an iteration process which may converge to an equilibrium point, but limit cycles or chaotic behaviour may also turn up.
In this paper, based on the grey connections between the concepts and the parameters of the sigmoid threshold function, we
give sufficient conditions for the existence and uniqueness of fixed points of sigmoid FGCMs.
Keywords
fuzzy cognitive map, grey system theory, fuzzy grey cognitive map, fixed point