In this paper, we introduce the notion of preaggregation function. Such a function satisfies the same boundary conditions as an aggregation function, but, instead of requiring monotonicity, only monotonicity along some fixed direction (directional monotonicity) is required. We present some examples of such functions. We propose three different methods to build preaggregation functions. We experimentally show that in fuzzy rule-based classification systems, when we use one of these methods, namely, the one based on the use of the Choquet integral replacing the product by other aggregation functions, if we consider the minimum or the Hamacher product t-norms for such construction, we improve the results obtained when applying the fuzzy reasoning methods obtained using two classical averaging operators such as the maximum and the Choquet integral.

There are many real-world classification problems involving multiple classes, e.g., in bioinformatics, computer vision, or medicine. These problems are generally more difficult than their binary counterparts. In this scenario, decomposition strategies usually improve the performance of classifiers. Hence, in this paper, we aim to improve the behavior of fuzzy association rule-based classification model for high-dimensional problems (FARC-HD) fuzzy classifier in multiclass classification problems using decomposition strategies, and more specifically One-versus-One (OVO) and One-versus-All (OVA) strategies. However, when these strategies are applied on FARC-HD, a problem emerges due to the low-confidence values provided by the fuzzy reasoning method. This undesirable condition comes from the application of the product t-norm when computing the matching and association degrees, obtaining low values, which are also dependent on the number of antecedents of the fuzzy rules. As a result, robust aggregation strategies in OVO, such as the weighted voting obtain poor results with this fuzzy classifier. In order to solve these problems, we propose to adapt the inference system of FARC-HD replacing the product t-norm with overlap functions. To do so, we define n-dimensional overlap functions. The usage of these new functions allows one to obtain more adequate outputs from the base classifiers for the subsequent aggregation in OVO and OVA schemes. Furthermore, we propose a new aggregation strategy for OVO to deal with the problem of the weighted voting derived from the inappropriate confidences provided by FARC-HD for this aggregation method. The quality of our new approach is analyzed using 20 datasets and the conclusions are supported by a proper statistical analysis. In order to check the usefulness of our proposal, we carry out a comparison against some of the state-of-the-art fuzzy classifiers. Experimental results show the competitiveness of our method.

The current financial crisis has stressed the need to obtain more accurate prediction models in order to decrease risk when investing money on economic opportunities. In addition, the transparency of the process followed to make the decisions in financial applications is becoming an important issue. Furthermore, there is a need to handle real-world imbalanced financial datasets without using sampling techniques that might introduce noise in the used data. In this paper, we present a compact evolutionary interval-valued fuzzy rule-based classification system, which is based on interval-valued fuzzy rule-based classification system with tuning and rule selection (IVTURS _{FA RC-HD} ) for the modeling and prediction of real-world financial applications. This proposed system allows obtaining good prediction accuracies using a small set of short fuzzy rules implying a high degree of interpretability of the generated linguistic model. Furthermore, the proposed system deals with the financial imbalanced datasets with no need for any preprocessing or sampling method and, thus, avoiding the accidental introduction of noise in the data used in the learning process. The system is also provided with a mechanism to handle examples that are not covered by any fuzzy rule in the generated rule base. To test the quality of our proposal, we will present an experimental study including 11 real-world financial datasets. We will show that the proposed system outperforms the original C4.5 decision tree, type-1, and interval-valued fuzzy counterparts that use the synthetic minority oversampling technique (SMOTE) to preprocess data and the original FURIA, which is a fuzzy approximative classifier. Furthermore, the proposed method enhances the results achieved by the cost-sensitive C4.5, and it gives competitive results when compared with FURIA using SMOTE, while our proposal avoids preprocessing techniques, and it provides interpretable models that allow obtaining more accurate results.

Objective: To develop a classifier that tackles the problem of determining the risk of a patient of suffering from a cardiovascular disease within the next ten years. The system has to provide both a diagnosis and an interpretable model explaining the decision. In this way, doctors are able to analyse the usefulness of the information given by the system. Methods: Linguistic fuzzy rule-based classification systems are used, since they provide a good classification rate and a highly interpretable model. More specifically, a new methodology to combine fuzzy rule-based classification systems with interval-valued fuzzy sets is proposed, which is composed of three steps: 1) the modelling of the linguistic labels of the classifier using interval-valued fuzzy sets; 2) the use of the Kα operator in the inference process and 3) the application of a genetic tuning to find the best ignorance degree that each interval-valued fuzzy set represents as well as the best value for the parameter α of the Kα operator in each rule. Results: The suitability of the new proposal to deal with this medical diagnosis classification problem is shown by comparing its performance with respect to the one provided by two classical fuzzy classifiers and a previous interval-valued fuzzy rule-based classification system. The performance of the new method is statistically better than the ones obtained with the methods considered in the comparison. The new proposal enhances both the total number of correctly diagnosed patients, around 3% with respect the classical fuzzy classifiers and around 1% versus the previous interval-valued fuzzy classifier, and the classifier ability to correctly differentiate patients of the different risk categories. Conclusion: The proposed methodology is a suitable tool to face the medical diagnosis of cardiovascular diseases, since it obtains a good classification rate and it also provides an interpretable model that can be easily understood by the doctors.This work was partially supported by the Spanish Ministry of Science and Technology under project TIN2010-15055 and the Research Services of the Universidad Pública de Navarra

Interval-valued fuzzy sets have been shown to be a useful tool to deal with the ignorance related to the definition of the linguistic labels. Specifically, they have been successfully applied to solve classification problems, performing simple modifications on the fuzzy reasoning method to work with this representation and making the classification based on a single number. In this paper, we present IVTURS, which is a new linguistic fuzzy rule-based classification method based on a new completely interval-valued fuzzy reasoning method. This inference process uses interval-valued restricted equivalence functions to increase the relevance of the rules in which the equivalence of the interval membership degrees of the patterns and the ideal membership degrees is greater, which is a desirable behavior. Furthermore, their parametrized construction allows the computation of the optimal function for each variable to be performed, which could involve a potential improvement in the system's behavior. Additionally, we combine this tuning of the equivalence with rule selection in order to decrease the complexity of the system. In this paper, we name our method IVTURS-FARC, since we use the FARC-HD method to accomplish the fuzzy rule learning process. The experimental study is developed in three steps in order to ascertain the quality of our new proposal. First, we determine both the essential role that interval-valued fuzzy sets play in the method and the need for the rule selection process. Next, we show the improvements achieved by IVTURS-FARC with respect to the tuning of the degree of ignorance when it is applied in both an isolated way and when combined with the tuning of the equivalence. Finally, the significance of IVTURS-FARC is further depicted by means of a comparison by which it is proved to outperform the results of FARC-HD and FURIA, which are two high performing fuzzy classification algorithms.