Abstract
Fuzzy cognitive maps are recurrent neural networks, applied for modelling and simulation of complex dynamic systems. They have been successfully applied to many engineering problems. The conclusion about the system depends on the mathematical behaviour of an iteration, namely, a first-order recursion. The first-order dynamics have some limitations since it takes into account only the previous time step. To overcome these limitations higher-order memory-based fuzzy cognitive maps have been introduced, which use a sequence of preceding states to determine the next one. In this paper, some dynamical properties of higher-order fuzzy cognitive maps are analyzed. Particularly, the existence and uniqueness of equilibrium points and the stability are discussed.
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Acknowledgements
This research was supported in part by National Research, Development and Innovation Office (NKFIH) K124055.
The research for this paper was financially supported by the EU and the Hungarian Government from the project “Intensification of the activities of HU-MATHS-IN - Hungarian Service Network of Mathematics for Industry and Innovation” under grant number EFOP-3.6.2-16-2017-00015.
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Harmati, I.Á., Kóczy, L.T. (2022). Some Dynamical Properties of Higher-Order Fuzzy Cognitive Maps. In: Harmati, I.Á., Kóczy, L.T., Medina, J., Ramírez-Poussa, E. (eds) Computational Intelligence and Mathematics for Tackling Complex Problems 3. Studies in Computational Intelligence, vol 959. Springer, Cham. https://doi.org/10.1007/978-3-030-74970-5_17
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