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.
István Á. Harmati, Ádám Bukovics and László T. Kóczy
Fuzzy signatures were introduced as special tools to describe and handle complex systems without their detailed mathematical models. The input parameters of these systems naturally have uncertainties, due to human activities or lack of precise data. These uncertainties influence the final conclusion or decision about the system. In this paper we discuss the sensitivity of the weigthed general mean aggregation operator to the uncertainty of the input values, then we analyse the sensitivity of fuzzy signatures equipped with these aggregation operators. Finally, we apply our results to a fuzzy signature used in civil enginnering.