### 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 |
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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: júl. 2 2018 → júl. 5 2018 |

### Publication series

Name | Advances in Intelligent Systems and Computing |
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Volume | 945 |

ISSN (Print) | 2194-5357 |

### Conference

Conference | 3rd Conference on Information Technology, Systems Research and Computational Physics, ITSRCP 2018 |
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Country | Poland |

City | Krakow |

Period | 7/2/18 → 7/5/18 |

### Fingerprint

### ASJC Scopus subject areas

- Control and Systems Engineering
- Computer Science(all)

### Cite this

*Information Technology, Systems Research, and Computational Physics*(pp. 74-84). (Advances in Intelligent Systems and Computing; Vol. 945). Springer Verlag. https://doi.org/10.1007/978-3-030-18058-4_6

**On the convergence of fuzzy grey cognitive maps.** / Harmati, István; Kóczy, L.

Research output: Conference contribution

*Information Technology, Systems Research, and Computational Physics.*Advances in Intelligent Systems and Computing, vol. 945, Springer Verlag, pp. 74-84, 3rd Conference on Information Technology, Systems Research and Computational Physics, ITSRCP 2018, Krakow, Poland, 7/2/18. https://doi.org/10.1007/978-3-030-18058-4_6

}

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 -