Fuzzy Cognitive Maps (FCMs) keep growing in popularity within the scientific community. However, despite substantial advances in the theory and applications of FCMs, there is a lack of an up-to-date, comprehensive presentation of the state-of-the-art in this domain. In this review study we are filling that gap. First, we present basic FCM concepts and analyze their static and dynamic properties, and next we elaborate on existing algorithms used for learning the FCM structure. Second, we provide a goal-driven overview of numerous theoretical developments recently reported in this area. Moreover, we consider the application of FCMs to time series forecasting and classification. Finally, in order to support the readers in their own research, we provide an overview of the existing software tools enabling the implementation of both existing FCM schemes as well as prospective theoretical and/or practical contributions.

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Abstract-Imbalanced classification deals with learning from data with a disproportional number of samples in its classes. Traditional classifiers exhibit poor behavior when facing this kind of data because they do not take into account the imbalanced class distribution. Four main kinds of solutions exist to solve this problem: modifying the data distribution, modifying the learning algorithm for considering the imbalance representation, including the use of costs for data samples, and ensemble methods. In this paper, we adopt the second type of solution and introduce a classification algorithm for imbalanced data that uses fuzzy rough set theory and ordered weighted average aggregation. The proposal considers different strategies to build a weight vector to take into account data imbalance. Our methods are validated by an extensive experimental study, showing statistically better results than 13 other state-of-the-art methods.Index Terms-Fuzzy rough sets, imbalanced classification, machine learning, ordered weighted average (OWA).

In this paper we propose a new model of ParticleSwarm Optimization called Two-Step PSO. The basic idea is to split the heuristic search performed by particles into two stages. We have studied the performance of this new algorithm for the Feature Selection problem by using the reduct concept of the Rough Set Theory. Experimental results obtained show that the Two-step approach improves over the PSO model in calculating reducts, with the same computational cost.

Rough Cognitive Networks (RCNs) are a kind of granular neural network that augments the reasoning rule present in Fuzzy Cognitive Maps with crisp information granules coming from Rough Set Theory. While RCNs have shown promise in solving different classification problems, this model is still very sensitive to the similarity threshold upon which the rough information granules are built. In this paper, we cast the RCN model within the framework of fuzzy rough sets in an attempt to eliminate the need for a user-specified similarity threshold while retaining the model's discriminatory power. As far as we know, this is the first study that brings fuzzy sets into the domain of rough cognitive mapping. Numerical results in the presence of 140 well-known pattern classification problems reveal that our approach, referred to as Fuzzy-Rough Cognitive Networks, is capable of outperforming most traditional classifiers used for benchmarking purposes. Furthermore, we explore the impact of using different heterogeneous distance functions and fuzzy operators over the performance of our granular neural network.