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Estimating the limit state space of quasi-nonlinear fuzzy cognitive maps
Concepción,Leonardo Nápoles,Gonzalo Jastrzebska,Agnieszka Grau,Isel Salgueiro,Yamisleydi
Concepción,Leonardo
Nápoles,Gonzalo
Jastrzebska,Agnieszka
Grau,Isel
Salgueiro,Yamisleydi
Abstract
Quasi-Nonlinear Fuzzy Cognitive Maps (q-FCMs) generalize the classic Fuzzy Cognitive Maps (FCMs) by incorporating a nonlinearity coefficient that is related to the model's convergence. While q-FCMs can be configured to avoid unique fixed-point attractors, there is still limited knowledge of their dynamic behavior. In this paper, we propose two iterative, mathematically-driven algorithms that allow estimating the limit state space of any q-FCM model. These algorithms produce accurate lower and upper bounds for the activation values of neural concepts in each iteration without using any information about the initial conditions. Asa result, we can determine which activation values will never be produced by a neural concept regardless of the initial conditions used to perform the simulations. In addition, these algorithms could help determine whether a classic FCM model will converge to a unique fixed-point attractor. As a second contribution, we demonstrate that the covering of neural concepts decreases as the nonlinearity coefficient approaches its maximal value. However, large covering values do not necessarily translate into better approximation capabilities, especially in the case of nonlinear problems. This finding points to a trade-off between the model's nonlinearity and the number of reachable states.
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Date
2025-01
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Keywords
Convergence analysis, Fuzzy Cognitive Maps, Modeling and simulation, Recurrent neural networks
Citation
Concepción, L, Nápoles, G, Jastrzebska, A, Grau, I & Salgueiro, Y 2025, 'Estimating the limit state space of quasi-nonlinear fuzzy cognitive maps', Appl. Soft Comput., vol. 169, 112604. https://doi.org/10.1016/j.asoc.2024.112604
License
info:eu-repo/semantics/openAccess