On the existence and uniqueness of fixed points of fuzzy set valued sigmoid fuzzy cognitive maps

István Harmati, L. Kóczy

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

Abstract

Fuzzy cognitive maps are decision support tools, where the complex structure is modelled by a weighted, directed graph. The nodes represent specific characteristics of the modelled system, weighted and directed edges correspond to the direction and the strength of the relationship between the factors. The system state is identified by the values of the nodes which are computed by iteration. This process may lead to a fixed point, a limit cycle or produces chaotic behaviour. The type of behaviour depends on the weights, on the topology of the graph and on the function applied for the iteration. From the practical viewpoint, it is critical to know whether the iteration converges to a fixed point or not. In this article, we discuss this problem for the case when the weights or the values of the nodes are fuzzy numbers. This scenario may occur when linguistic variables, modelled by fuzzy numbers, describe the connections.

Original languageEnglish
Title of host publication2018 IEEE International Conference on Fuzzy Systems, FUZZ 2018 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Volume2018-July
ISBN (Electronic)9781509060207
DOIs
Publication statusPublished - Oct 12 2018
Event2018 IEEE International Conference on Fuzzy Systems, FUZZ 2018 - Rio de Janeiro, Brazil
Duration: Jul 8 2018Jul 13 2018

Other

Other2018 IEEE International Conference on Fuzzy Systems, FUZZ 2018
CountryBrazil
CityRio de Janeiro
Period7/8/187/13/18

Fingerprint

Fuzzy Cognitive Maps
Directed graphs
Fuzzy sets
Linguistics
Fuzzy Sets
Existence and Uniqueness
Fixed point
Topology
Fuzzy numbers
Iteration
Vertex of a graph
Linguistic Variables
Chaotic Behavior
Decision Support
Complex Structure
Directed Graph
Limit Cycle
Converge
Scenarios
Graph in graph theory

Keywords

  • Convergence of fuzzy cognitive maps
  • Extension principle
  • Fixed point
  • Fuzzy cognitive map
  • Fuzzy valued cognitive map

ASJC Scopus subject areas

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

Cite this

Harmati, I., & Kóczy, L. (2018). On the existence and uniqueness of fixed points of fuzzy set valued sigmoid fuzzy cognitive maps. In 2018 IEEE International Conference on Fuzzy Systems, FUZZ 2018 - Proceedings (Vol. 2018-July). [8491447] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/FUZZ-IEEE.2018.8491447

On the existence and uniqueness of fixed points of fuzzy set valued sigmoid fuzzy cognitive maps. / Harmati, István; Kóczy, L.

2018 IEEE International Conference on Fuzzy Systems, FUZZ 2018 - Proceedings. Vol. 2018-July Institute of Electrical and Electronics Engineers Inc., 2018. 8491447.

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

Harmati, I & Kóczy, L 2018, On the existence and uniqueness of fixed points of fuzzy set valued sigmoid fuzzy cognitive maps. in 2018 IEEE International Conference on Fuzzy Systems, FUZZ 2018 - Proceedings. vol. 2018-July, 8491447, Institute of Electrical and Electronics Engineers Inc., 2018 IEEE International Conference on Fuzzy Systems, FUZZ 2018, Rio de Janeiro, Brazil, 7/8/18. https://doi.org/10.1109/FUZZ-IEEE.2018.8491447
Harmati I, Kóczy L. On the existence and uniqueness of fixed points of fuzzy set valued sigmoid fuzzy cognitive maps. In 2018 IEEE International Conference on Fuzzy Systems, FUZZ 2018 - Proceedings. Vol. 2018-July. Institute of Electrical and Electronics Engineers Inc. 2018. 8491447 https://doi.org/10.1109/FUZZ-IEEE.2018.8491447
Harmati, István ; Kóczy, L. / On the existence and uniqueness of fixed points of fuzzy set valued sigmoid fuzzy cognitive maps. 2018 IEEE International Conference on Fuzzy Systems, FUZZ 2018 - Proceedings. Vol. 2018-July Institute of Electrical and Electronics Engineers Inc., 2018.
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