期刊
IEEE TRANSACTIONS ON FUZZY SYSTEMS
卷 29, 期 5, 页码 1252-1261出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TFUZZ.2020.2973853
关键词
Neurons; Transfer functions; Biological system modeling; Mathematical model; Numerical models; Fuzzy cognitive maps; Recurrent neural networks; Fuzzy cognitive maps; nonlinear systems; recurrent neural networks; shrinking state spaces
The article introduces definitions and theorems about the dynamic behavior of FCM, as well as analytical expressions for estimating activation values and analyzing coverage and proximity of activation spaces. The main theoretical findings suggest that the state space of FCM models equipped with transfer F-functions shrinks infinitely, with no guarantee of convergence to a fixed point but rather to its limit state space.
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.
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