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On the Convergence of Fuzzy Grey Cognitive Maps

  • István Á. HarmatiEmail author
  • László T. Kóczy
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 945)

Abstract

Fuzzy grey cognitive maps (FGCMs) are extensions of fuzzy cognitive maps (FCMs), applying uncertain weights between the concepts. This uncertainty is expressed by so-called grey numbers. Similarly to 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 weighted connections between the concepts and the parameter of the sigmoid threshold function, we give sufficient conditions for the existence and uniqueness of fixed points for sigmoid FGCMs.

Keywords

Fuzzy cognitive map Grey system theory Fuzzy grey cognitive map Fixed point 

Notes

Acknowledgment

The primary version of this paper was presented at the 3rd Conference on Information Technology, Systems Research and Computational Physics, 2–5 July 2018, Cracow, Poland [1].

This research was supported by National Research, Development and Innovation Office (NKFIH) K124055.

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Mathematics and Computational SciencesSzéchenyi István UniversityGyőrHungary
  2. 2.Department of Information TechnologySzéchenyi István UniversityGyőrHungary
  3. 3.Department of Telecommunication and Media InformaticsBudapest University of Technology and EconomicsBudapestHungary

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