ISSN 2673-494X
Two-page Reports on Science

Cuban Sci. 2021, 2(2): 5–6

Published on 12 Oct 2021 PDF (333K)
Theoretical Analysis of the State Space of Fuzzy Cognitive Maps using Shrink Functions
Leonardo Concepción, Gonzalo Nápoles, Rafael Bello, Koen Vanhoof
  • Department of Computer Science, Universidad Central de Las Villas, Cuba
  • Faculty of Business Economics, Hasselt Universiteit, Belgium
  • Department of Cognitive Science & Artificial Intelligence, Tilburg University, The
  • Netherlands
“We proposed definitions and theorems regarding Fuzzy Cognitive Maps (FCMs), which 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 to understand their poor performance when solving complex simulation problems.”


  1. Kosko, B. (1986). Fuzzy Cognitive Maps, International Journal Man-Machine Studies, 24 1 65-75
  2. Boutalis, Y., Kottas, T., & Christodoulou, M. (2009). Adaptive Estimation of Fuzzy Cognitive Maps with Proven Stability and Parameter Convergence, IEEE Transactions Fuzzy Systems, 17 4 874-889
  3. Harmati, I., Hatwágner, M., & Kóczy, L. (2018). On the Existence and Uniqueness of Fixed Points of Fuzzy Cognitive Maps, Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations, 490-500
  4. Nápoles, G., Bello, R., & Vanhoof, K. (2014). How to Improve the Convergence on Sigmoid Fuzzy Cognitive Maps?, Intelligent Data Analysis, 18 6S S77-S88
  5. Nápoles, G., Papageorgiou, E., Bello, R. & Vanhoof, K. (2016). On the convergence of sigmoid Fuzzy Cognitive Maps, Information Sciences, 349-350 154-171
  6. Nápoles, G., Concepción, L., Falcon, R., Bello, R., & Vanhoof, K. (2018). On the accuracy-convergence tradeoff in sigmoid Fuzzy Cognitive Maps, IEEE Transactions on Fuzzy Systems, 26 4 2479-2484
  7. Concepción, L., Nápoles, G., Falcon, R., Vanhoof, K., & Bello, R. (2021). Unveiling the Dynamic Behavior of Fuzzy Cognitive Maps, IEEE Transactions on Fuzzy Systems, 29 5 1252-1261