<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></abstract>

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.

On the Convergence of Sigmoidal Fuzzy Grey Cognitive Maps

Department of Mathematics and Computational Sciences

Department of Telecommunication and Media Informatics

Budapest University of Technology and Economics

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"On the Convergence of Sigmoidal Fuzzy Grey Cognitive Maps"}

Fuzzy cognitive maps (FCMs) are recurrent neural networks applied for modelling complex systems using weighted causal relations. In FCM-based decision-making,...

On the Convergence of Sigmoidal Fuzzy Grey Cognitive Maps

Publicado en línea: 28 sept 2019

Páginas: 453 - 466

Recibido: 19 oct 2018

Aceptado: 06 abr 2019

DOI: https://doi.org/10.2478/amcs-2019-0033

Palabras clave
fuzzy cognitive map, grey system theory, fuzzy grey cognitive map, fixed point

© 2019 István Á. Harmati et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

On the Convergence of Sigmoidal Fuzzy Grey Cognitive Maps

Publicado en línea: 28 sept 2019

Páginas: 453 - 466

Recibido: 19 oct 2018

Aceptado: 06 abr 2019

DOI: https://doi.org/10.2478/amcs-2019-0033

Palabras clavefuzzy cognitive map, grey system theory, fuzzy grey cognitive map, fixed point

© 2019 István Á. Harmati et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Palabras clave
fuzzy cognitive map, grey system theory, fuzzy grey cognitive map, fixed point