Notes on the Dynamics of Hyperbolic Tangent Fuzzy Cognitive Maps

Istvan A. Harmati, Laszlo T. Koczy

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

Abstract

Fuzzy cognitive maps (FCMs) are recurrent neural networks applied for modelling complex systems and structures. In this method, the system is represented by a weighted, directed digraph, where the nodes of the network represent the main characteristics of the modelled system, while the weighted and directed edges correspond to the direction and strength of causal relationships between these factors. The FCM based decision making is based on the so-called activation values of the nodes, which represents the state of the system. These activation values are determined by an iteration, which may lead to an equilibrium point (fixed point), but limit cycles or chaotic behaviour may also occur. In this paper, the dynamics of fuzzy cognitive maps with hyperbolic tangent threshold function is mathematically discussed. Theoretical conditions are provided for the existence and uniqueness of fixed points. Moreover, the stability of fixed points and their basins of attractions are also analysed. The results presented here give insight into the special symmetric nature of hyperbolic FCMs.

Original languageEnglish
Title of host publication2019 IEEE International Conference on Fuzzy Systems, FUZZ 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781538617281
DOIs
Publication statusPublished - Jun 2019
Event2019 IEEE International Conference on Fuzzy Systems, FUZZ 2019 - New Orleans, United States
Duration: Jun 23 2019Jun 26 2019

Publication series

NameIEEE International Conference on Fuzzy Systems
Volume2019-June
ISSN (Print)1098-7584

Conference

Conference2019 IEEE International Conference on Fuzzy Systems, FUZZ 2019
CountryUnited States
CityNew Orleans
Period6/23/196/26/19

Fingerprint

Hyperbolic tangent
Fuzzy Cognitive Maps
Fixed point
Activation
Chemical activation
Tangent function
Threshold Function
Recurrent neural networks
Basin of Attraction
Recurrent Neural Networks
Chaotic Behavior
Vertex of a graph
Complex Structure
Equilibrium Point
Digraph
Limit Cycle
Large scale systems
Complex Systems
Existence and Uniqueness
Decision making

Keywords

  • convergence of fuzzy cognitive maps
  • fixed point
  • fuzzy cognitive map
  • hyperbolic tangent fuzzy cognitive map

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Artificial Intelligence
  • Applied Mathematics

Cite this

Harmati, I. A., & Koczy, L. T. (2019). Notes on the Dynamics of Hyperbolic Tangent Fuzzy Cognitive Maps. In 2019 IEEE International Conference on Fuzzy Systems, FUZZ 2019 [8858950] (IEEE International Conference on Fuzzy Systems; Vol. 2019-June). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/FUZZ-IEEE.2019.8858950

Notes on the Dynamics of Hyperbolic Tangent Fuzzy Cognitive Maps. / Harmati, Istvan A.; Koczy, Laszlo T.

2019 IEEE International Conference on Fuzzy Systems, FUZZ 2019. Institute of Electrical and Electronics Engineers Inc., 2019. 8858950 (IEEE International Conference on Fuzzy Systems; Vol. 2019-June).

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

Harmati, IA & Koczy, LT 2019, Notes on the Dynamics of Hyperbolic Tangent Fuzzy Cognitive Maps. in 2019 IEEE International Conference on Fuzzy Systems, FUZZ 2019., 8858950, IEEE International Conference on Fuzzy Systems, vol. 2019-June, Institute of Electrical and Electronics Engineers Inc., 2019 IEEE International Conference on Fuzzy Systems, FUZZ 2019, New Orleans, United States, 6/23/19. https://doi.org/10.1109/FUZZ-IEEE.2019.8858950
Harmati IA, Koczy LT. Notes on the Dynamics of Hyperbolic Tangent Fuzzy Cognitive Maps. In 2019 IEEE International Conference on Fuzzy Systems, FUZZ 2019. Institute of Electrical and Electronics Engineers Inc. 2019. 8858950. (IEEE International Conference on Fuzzy Systems). https://doi.org/10.1109/FUZZ-IEEE.2019.8858950
Harmati, Istvan A. ; Koczy, Laszlo T. / Notes on the Dynamics of Hyperbolic Tangent Fuzzy Cognitive Maps. 2019 IEEE International Conference on Fuzzy Systems, FUZZ 2019. Institute of Electrical and Electronics Engineers Inc., 2019. (IEEE International Conference on Fuzzy Systems).
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