Fuzzy-Rough Cognitive Networks (FRCNs) are recurrent neural networks intended for structured classification purposes in which the problem is described by an explicit set of features. The advantage of this granular neural system relies on its transparency and simplicity while being competitive to state-of-the-art classifiers. Despite of their relative empirical success in terms of prediction rates, there are limited studies on FRCNs’ dynamic properties and how their building blocks contribute to algorithm’s performance. In this paper, we theoretically study these issues and conclude that boundary and negative neurons always converge to a unique fixed-point attractor. Moreover, we demonstrate that negative neurons have no impact on algorithm’s performance and that the ranking of positive neurons is invariant. Moved by our theoretical findings, we propose two simpler fuzzy-rough classifiers that overcome the detected issues and maintain the competitive prediction rates of this classifier. Toward the end, we present a case study concerned with image classification in which a Convolutional Neural Network is coupled with one of the simpler models derived from the theoretical analysis of the FRCN model. The numerical simulations suggest that, once the features have been extracted, our granular neural system performs as well as other recurrent neural networks.