On the Convergence of Sigmoidal Fuzzy Grey Cognitive Maps

István Harmati, László T. Kóczy

Research output: Contribution to journalArticle


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.

Original languageEnglish
Pages (from-to)453-466
Number of pages14
JournalInternational Journal of Applied Mathematics and Computer Science
Issue number3
Publication statusPublished - Sep 1 2019



  • fixed point
  • fuzzy cognitive map
  • fuzzy grey cognitive map
  • grey system theory

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Engineering (miscellaneous)
  • Applied Mathematics

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