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.
| Original language | English |
|---|---|
| Title of host publication | Information Technology, Systems Research, and Computational Physics |
| Editors | László T. Kóczy, Radko Mesiar, László T. Kóczy, Piotr Kulczycki, Piotr Kulczycki, Janusz Kacprzyk, Rafal Wisniewski |
| Publisher | Springer Verlag |
| Pages | 74-84 |
| Number of pages | 11 |
| ISBN (Print) | 9783030180577 |
| DOIs | |
| Publication status | Published - Jan 1 2020 |
| Event | 3rd Conference on Information Technology, Systems Research and Computational Physics, ITSRCP 2018 - Krakow, Poland Duration: Jul 2 2018 → Jul 5 2018 |
Publication series
| Name | Advances in Intelligent Systems and Computing |
|---|---|
| Volume | 945 |
| ISSN (Print) | 2194-5357 |
Conference
| Conference | 3rd Conference on Information Technology, Systems Research and Computational Physics, ITSRCP 2018 |
|---|---|
| Country | Poland |
| City | Krakow |
| Period | 7/2/18 → 7/5/18 |
Fingerprint
Keywords
- Fixed point
- Fuzzy cognitive map
- Fuzzy grey cognitive map
- Grey system theory
ASJC Scopus subject areas
- Control and Systems Engineering
- Computer Science(all)
Cite this
On the convergence of fuzzy grey cognitive maps. / Harmati, István; Kóczy, L.
Information Technology, Systems Research, and Computational Physics. ed. / László T. Kóczy; Radko Mesiar; László T. Kóczy; Piotr Kulczycki; Piotr Kulczycki; Janusz Kacprzyk; Rafal Wisniewski. Springer Verlag, 2020. p. 74-84 (Advances in Intelligent Systems and Computing; Vol. 945).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - On the convergence of fuzzy grey cognitive maps
AU - Harmati, István
AU - Kóczy, L.
PY - 2020/1/1
Y1 - 2020/1/1
N2 - 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.
AB - 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.
KW - Fixed point
KW - Fuzzy cognitive map
KW - Fuzzy grey cognitive map
KW - Grey system theory
UR - http://www.scopus.com/inward/record.url?scp=85065451472&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85065451472&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-18058-4_6
DO - 10.1007/978-3-030-18058-4_6
M3 - Conference contribution
AN - SCOPUS:85065451472
SN - 9783030180577
T3 - Advances in Intelligent Systems and Computing
SP - 74
EP - 84
BT - Information Technology, Systems Research, and Computational Physics
A2 - Kóczy, László T.
A2 - Mesiar, Radko
A2 - Kóczy, László T.
A2 - Kulczycki, Piotr
A2 - Kulczycki, Piotr
A2 - Kacprzyk, Janusz
A2 - Wisniewski, Rafal
PB - Springer Verlag
ER -