Fuzzy-Rough Cognitive Networks: Theoretical Analysis and Simpler Models

Abstract

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Dynamics of Fuzzy-Rough Cognitive Networks

“…In this subsection, we shortly summarize the main contributions of [37] regarding the dynamics of fuzzy-rough cognitive networks. For detailed explanations and proofs, see [37].…”

“…In this section, we shortly summarize the basic notions of fuzzy-rough cognitive networks and the findings about their dynamical properties reported in the literature. It is based on the works [35][36][37].…”

“…In Section 3, a summary of the mathematical background necessary for further investigation of the dynamics of FRCNs is provided, including contraction mapping and elements of bifurcation theory. Section 4 presents general result about the dynamics of positive neurons, condition for unique fixed point attractor and refinement of some findings of [37]. Section 5 introduces size-specific results for FRCNs, providing a complete description for the case of two and three decision classes and pointing out that over a specific size, oscillation behaviour will be naturally present.…”

“…They concluded that the connections between positive neurons might not necessary to maintain the performance of FRCNs. The theoretical study by Concepción et al [37] discussed the contribution of negative and boundary neurons. Moreover, they arrived at the conclusion that negative neurons have no impact on the decision, and the ranking between positive neuron remains invariant during the whole reasoning process.…”

“…Besides the results presented in [37], this paper was motivated by the fact that only a few studies are discussing the behaviour of cognitive networks from the strict mathematical point of view. Nevertheless, such studies may provide us with information about what we can or cannot achieve with these models.…”