On the generalizations of the Choquet integral for application in FRBCs

An effective way to cope with classification problems, among others, is by using Fuzzy Rule-Based Classification Systems (FRBCSs). These systems are composed by two main components, the Knowledge Base (KB) and the Fuzzy Reasoning Method (FRM). The FRM is responsible for performing the classification of new examples based on the information stored in the KB. A key point in the FRM is how the information given by the fired fuzzy rules is aggregated. Precisely, the aggregation function is the component that differs from the two most widely used FRMs in the specialized literature. In this paper we provide a revision of the literature discussing the generalizations of the Choquet integral that has been applied in the FRM of a FRBCS. To do so, we consider an analysis of different generalizations, by t-norms, copulas, and by F functions. Also, the main contributions of each generalization are discussed.Supported by PNPD/CAPES (process. 464880/2019-00), FAPERGS (19/2551-0001279-9, 19/2551-0001660), CNPq (301618/2019-4), the Spanish Ministry of Science and Technology (TIN2016-77356-P, PID2019-108392GB I00 (AEI/10.13039/501100 011033))