Dynamics of Fuzzy-Rough Cognitive Networks

Abstract

Fuzzy-rough cognitive networks (FRCNs) are interpretable recurrent neural networks, primarily designed for solving classification problems. Their structure is simple and transparent, while the performance is comparable to the well-known black-box classifiers. Although there are many applications on fuzzy cognitive maps and recently for FRCNS, only a very limited number of studies discuss the theoretical issues of these models. In this paper, we examine the behaviour of FRCNs viewing them as discrete dynamical systems. It will be shown that their mathematical properties highly depend on the size of the network, i.e., there are structural differences between the long-term behaviour of FRCN models of different size, which may influence the performance of these modelling tools.

Keywords

• fuzzy-rough cognitive network
• fuzzy cognitive map
• granular computing
• fuzzy-rough sets
• stability
• convergence