Fuzzy-Rough Cognitive Networks (FRCNs) are neural networks that use rough information granules with soft boundaries to perform the classification process. Unlike other neural systems, FRCNs are lazy learners in the sense that we can build the whole model when classifying a new instance. This is possible because the weight matrix connecting the neurons is prescriptively programmed. Similar to other lazy learners, the processing time of FRCNs notably increases with the number of instances in the training set, while their performance deteriorates in noisy environments. Aiming at coping with these issues, this paper presents a new FRCN-based algorithm termed Fast k-Fuzzy-Rough Cognitive Network. This variant employs a multi-thread approach for building the information granules as computed by k-fuzzy-rough sets. Numerical simulations on 35 classification datasets show a notable reduction on FRCNs' processing time, while also delivering competitive results when compared to other lazy learners in noisy environments.