Classifier learning with data-sets that suffer from imbalanced class distributions is a challenging problem in data mining community. This issue occurs when the number of examples that represent one class is much lower than the ones of the other classes. Its presence in many real-world applications has brought along a growth of attention from researchers. In machine learning, the ensemble of classifiers are known to increase the accuracy of single classifiers by combining several of them, but neither of these learning techniques alone solve the class imbalance problem, to deal with this issue the ensemble learning algorithms have to be designed specifically. In this paper, our aim is to review the state of the art on ensemble techniques in the framework of imbalanced data-sets, with focus on two-class problems. We propose a taxonomy for ensemble-based methods to address the class imbalance where each proposal can be categorized depending on the inner ensemble methodology in which it is based. In addition, we develop a thorough empirical comparison by the consideration of the most significant published approaches, within the families of the taxonomy proposed, to show whether any of them makes a difference. This comparison has shown the good behavior of the simplest approaches which combine random undersampling techniques with bagging or boosting ensembles. In addition, the positive synergy between sampling techniques and bagging has stood out. Furthermore, our results show empirically that ensemble-based algorithms are worthwhile since they outperform the mere use of preprocessing techniques before learning the classifier, therefore justifying the increase of complexity by means of a significant enhancement of the results.

The fuzzy linguistic approach has been applied successfully to many problems. However, there is a limitation of this approach imposed by its information representation model and the computation methods used when fusion processes are performed on linguistic values. This limitation is the loss of information; this loss of information implies a lack of precision in the final results from the fusion of linguistic information. In this paper, we present tools for overcoming this limitation. The linguistic information is expressed by means of 2-tuples, which are composed of a linguistic term and a numeric value assessed in (-0.5, 0.5). This model allows a continuous representation of the linguistic information on its domain, therefore, it can represent any counting of information obtained in a aggregation process. We then develop a computational technique for computing with words without any loss of information. Finally, different classical aggregation operators are extended to deal with the 2-tuple linguistic model.

Dealing with uncertainty is always a challenging problem, and different tools have been proposed to deal with it. Recently, a new model that is based on hesitant fuzzy sets has been presented to manage situations in which experts hesitate between several values to assess an indicator, alternative, variable, etc. Hesitant fuzzy sets suit the modeling of quantitative settings; however, similar situations may occur in qualitative settings so that experts think of several possible linguistic values or richer expressions than a single term for an indicator, alternative, variable, etc. In this paper, the concept of a hesitant fuzzy linguistic term set is introduced to provide a linguistic and computational basis to increase the richness of linguistic elicitation based on the fuzzy linguistic approach and the use of context-free grammars by using comparative terms. Then, a multicriteria linguistic decision-making model is presented in which experts provide their assessments by eliciting linguistic expressions. This decision model manages such linguistic expressions by means of its representation using hesitant fuzzy linguistic term sets.