On the Behavior of Fuzzy Grey Cognitive Maps

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

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review


Fuzzy Cognitive Maps (FCMs) are recurrent neural networks made up of well-defined neurons and causal relations. Fuzzy Grey Cognitive Maps (FGCMs) are an extension of FCMs, intended to surpass the intrinsic uncertainties modeling real-world problems by means of Grey theory. Despite the rising number of studies about FGCM-based models, little has been investigated with regard to the convergence of such networks. In this paper, we build a mathematical basis to uncover the behavior FGCM-based models equipped with transfer F-functions. To do so, we propose sufficient conditions for the existence and unicity of fixed-point attractors. Also, the results reported in the literature on the convergence of FGCMs, are compared with ours. Furthermore, we elucidate the reach and depth of our findings, especially and not exclusive to the prediction of FCMs' behavior.
Original languageEnglish
Title of host publicationRough Sets
EditorsRafael Bello, Duoqian Miao, Rafael Falcon, Michinori Nakata, Alejandro Rosete, Davide Ciucci
Place of PublicationCham
PublisherSpringer International Publishing
Number of pages15
ISBN (Print)9783030527051
Publication statusPublished - 2020


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