Unveiling the Dynamic Behavior of Fuzzy Cognitive Maps

Leonardo Concepción, Gonzalo Nápoles, Rafael Falcon, Koen Vanhoof, Rafael Bello

Research output: Contribution to journalArticleScientificpeer-review

11 Citations (Scopus)


Fuzzy cognitive maps (FCMs) are recurrent neural networks comprised of well-defined concepts and causal relations. While the literature about real-world FCM applications is prolific, the studies devoted to understanding the foundations behind these neural networks are rather scant. In this article, we introduce several definitions and theorems that unveil the dynamic behavior of FCM-based models equipped with transfer F-functions. These analytical expressions allow estimating bounds for the activation value of each neuron and analyzing the covering and proximity of feasible activation spaces. The main theoretical findings suggest that the state space of any FCM model equipped with transfer F-functions shrinks infinitely with no guarantee for the FCM to converge to a fixed point but to its limit state space. This result in conjunction with the covering and proximity values of FCM-based models helps understand their poor performance when solving complex simulation problems.

Original languageEnglish
Article number8998575
Pages (from-to)1252-1261
Number of pages10
JournalIEEE Transactions on Fuzzy Systems
Issue number5
Publication statusPublished - May 2021


  • Fuzzy cognitive maps
  • nonlinear systems
  • recurrent neural networks
  • shrinking state spaces


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