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http://hdl.handle.net/1942/35890
Title: | Unveiling the Dynamic Behavior of Fuzzy Cognitive Maps | Authors: | Concepcion, L NAPOLES RUIZ, Gonzalo Falcon, R VANHOOF, Koen Bello, R |
Issue Date: | 2021 | Publisher: | IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC | Source: | IEEE transactions on fuzzy systems, 29 (5) , p. 1252 -1261 | Abstract: | Fuzzy cognitive maps (FCMs) are recurrent neural networks comprised of well-defined concepts and causal relations. While the literature about real-world FCM applications is prolific, the studies devoted to understanding the foundations behind these neural networks are rather scant. In this article, we introduce several definitions and theorems that unveil the dynamic behavior of FCM-based models equipped with transfer F-functions. These analytical expressions allow estimating bounds for the activation value of each neuron and analyzing the covering and proximity of feasible activation spaces. The main theoretical findings suggest that the state space of any FCM model equipped with transfer F-functions shrinks infinitely with no guarantee for the FCM to converge to a fixed point but to its limit state space. This result in conjunction with the covering and proximity values of FCM-based models helps understand their poor performance when solving complex simulation problems. | Keywords: | Neurons;Transfer functions;Biological system modeling;Mathematical model;Numerical models;Fuzzy cognitive maps;Recurrent neural networks;nonlinear systems;recurrent neural networks;shrinking state spaces | Document URI: | http://hdl.handle.net/1942/35890 | ISSN: | 1063-6706 | e-ISSN: | 1941-0034 | DOI: | 10.1109/tfuzz.2020.2973853 | ISI #: | 000648333700025 | Rights: | 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See https://www.ieee.org/publications/rights/index.html for more information. | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2022 |
Appears in Collections: | Research publications |
Files in This Item:
File | Description | Size | Format | |
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Unveiling the Dynamic Behavior of Fuzzy Cognitive Maps.pdf Restricted Access | Published version | 2.41 MB | Adobe PDF | View/Open Request a copy |
FCMStateSpace-TFS (1).pdf | Peer-reviewed author version | 4.79 MB | Adobe PDF | View/Open |
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