Deterministic learning of hybrid Fuzzy Cognitive Maps and network reduction approaches

Gonzalo Nápoles*, Agnieszka Jastrzebska, Carlos Mosquera, Koen Vanhoof, Wladyslaw Homenda

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

13 Citations (Scopus)


Hybrid artificial intelligence deals with the construction of intelligent systems by relying on both human knowledge and historical data records. In this paper, we approach this problem from a neural perspective, particularly when modeling and simulating dynamic systems. Firstly, we propose a Fuzzy Cognitive Map architecture in which experts are requested to define the interaction among the input neurons. As a second contribution, we introduce a fast and deterministic learning rule to compute the weights among input and output neurons. This parameterless learning method is based on the Moore-Penrose inverse and it can be performed in a single step. In addition, we discuss a model to determine the relevance of weights, which allows us to better understand the system. Last but not least, we introduce two calibration methods to adjust the model after the removal of potentially superfluous weights. (C) 2020 Elsevier Ltd. All rights reserved.


  • Fuzzy cognitive maps
  • Hybrid models
  • Inverse learning
  • Interpretability


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