On the existence and uniqueness of fixed points of fuzzy cognitive maps

István Harmati, Miklós F. Hatwágner, L. Kóczy

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Citations (Scopus)

Abstract

Fuzzy Cognitive Maps (FCMs) are decision support tools, which were introduced to model complex behavioral systems. The final conclusion (output of the system) relies on the assumption that the system reaches an equilibrium point (fixed point) after a certain number of iteration. It is not straightforward that the iteration leads to a fixed point, since limit cycles and chaotic behaviour may also occur. In this article, we give sufficient conditions for the existence and uniqueness of the fixed point for log-sigmoid and hyperbolic tangent FCMs, based on the weighted connections between the concepts and the parameter of the threshold function. Moreover, in a special case, when all of the weights are non-negative, we prove that fixed point always exists, regardless of the parameter of the threshold function.

Original languageEnglish
Title of host publicationInformation Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations - 17th International Conference, IPMU 2018, Proceedings
PublisherSpringer Verlag
Pages490-500
Number of pages11
ISBN (Print)9783319914725
DOIs
Publication statusPublished - Jan 1 2018
Event17th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2018 - Cadiz, Spain
Duration: Jun 11 2018Jun 15 2018

Publication series

NameCommunications in Computer and Information Science
Volume853
ISSN (Print)1865-0929

Other

Other17th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2018
CountrySpain
CityCadiz
Period6/11/186/15/18

Keywords

  • Fixed point
  • Fuzzy cognitive maps
  • Fuzzy modelling

ASJC Scopus subject areas

  • Computer Science(all)
  • Mathematics(all)

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  • Cite this

    Harmati, I., Hatwágner, M. F., & Kóczy, L. (2018). On the existence and uniqueness of fixed points of fuzzy cognitive maps. In Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations - 17th International Conference, IPMU 2018, Proceedings (pp. 490-500). (Communications in Computer and Information Science; Vol. 853). Springer Verlag. https://doi.org/10.1007/978-3-319-91473-2_42