Abstract
Fuzzy Cognitive Maps are network-like decision support tools, where the final conclusion is determined by an iteration process. Although the final conclusion relies on the assumption that the iteration reaches a fixed point, it is not straightforward that the iteration will converge to anywhere, since it can produce limit cycles or chaotic behaviour also. In this paper, we briefly analyse the behaviour of the so-called rescaled algorithm for fuzzy cognitive maps with respect to the existence and uniqueness of fixed points.
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References
Papageorgiou, E.I., Salmeron, J.L.: Methods and algorithms for fuzzy cognitive map-based decision support. In: Papageorgiou, E.I (ed). Fuzzy Cognitive Maps for Applied Sciences and Engineering (2013)
Busemeyer, J.R.: Dynamic decision making. International Encyclopedia of the Social & Behavioral Sciences 39033908 (2001)
Felix, G., Nápoles, G., Falcon, R., Froelich, W., Vanhoof, K., Bello, R.: A review on methods and software for fuzzy cognitive maps. Artif. Intell. Rev. 1–31 (2017)
Stylios, C.D., Groumpos, P.P.: Modeling complex systems using fuzzy cognitive maps. IEEE Trans. Syst. Man Cybern. Part A Syst. Humans 34(1), 155–162 (2004)
Tsadiras, A.K.: Comparing the inference capabilities of binary, trivalent and sigmoid fuzzy cognitive maps. Inf. Sci.178(20), 3880–3894 (2008)
Nápoles, G., Papageorgiou, E., Bello, R., Vanhoof, K.: Learning and convergence of fuzzy cognitive maps used in pattern recognition. Neural Process. Lett. 45(2), 431–444 (2017)
Nápoles, G., Papageorgiou, E., Bello, R., Vanhoof, K.: On the convergence of sigmoid fuzzy cognitive maps. Inf. Sci. 349–350, 154–171 (2016)
Boutalis, Y., Kottas, T.L., Christodoulou, M.: Adaptive estimation of fuzzy cognitive maps with proven stability and parameter convergence. IEEE Trans. Fuzzy Syst. 17(4), 874–889 (2009)
Knight, C.J., Lloyd, D.J., Penn, A.S.: Linear and sigmoidal fuzzy cognitive maps: An analysis of fixed points. Appl. Soft Comput. 15, 193–202 (2014)
Harmati, I.A., Hatwágner, F.M., Kóczy, L.T.: On the existence and uniqueness of fixed points of fuzzy cognitive maps. In: 17th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, pp. 490–500 (2018)
Papageorgiou, E.I.: A new methodology for decisions in medical informatics using fuzzy cognitive maps based on fuzzy rule-extraction techniques. Appl. Soft Comput. 11(1), 500–513 (2011)
https://www.rdocumentation.org/packages/fcm/versions/0.1.3/topics/fcm.infer
Acknowledgements
The research presented in this paper was funded by the Higher Education Institutional Excellence Program. This work was supported by the National Research, Development and Innovation Office (NKFIH), Hungary; grant number K124055.
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Harmati, I.Á., Kóczy, L.T. (2020). Notes on the Rescaled Algorithm for Fuzzy Cognitive Maps. In: Kóczy, L., Medina-Moreno, J., Ramírez-Poussa, E., Šostak, A. (eds) Computational Intelligence and Mathematics for Tackling Complex Problems. Studies in Computational Intelligence, vol 819. Springer, Cham. https://doi.org/10.1007/978-3-030-16024-1_6
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DOI: https://doi.org/10.1007/978-3-030-16024-1_6
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