An experimental study of the dynamics of the certainty neuron fuzzy cognitive maps

Abstract

Certainty Neurons have been introduced as a new type of artificial neurons that use a two variable transfer function that provides them with memory capabilities and decay mechanism. They are used in fuzzy cognitive maps which is an artificial neural network structure that creates models as collections of concepts – neurons and the various causal relationships – weighted arcs that exist between them. An experimental study of the certainty neuron fuzzy cognitive maps (CNFCMs) dynamical behaviour is presented as this appears through simulations. Two control parameters are used: the symmetry of the system's weight matrix and the strength of the decay mechanism. The values of these two parameters can lead the system to exhibit stable fixed point behaviour, limit cycle behaviour or to collapse. The ways that the two control parameters cause the change of the system's dynamical behaviour from fixed point to limit cycle are also presented. The areas where the systems exhibit specific dynamical behaviour are identified.