CC-integrals: Choquet-like Copula-based aggregation functions and its application in fuzzy rule-based classification systems

Abstract

This paper introduces the concept of Choquet-like Copula-based aggregation function (CC-integral) and its application in fuzzy rule-based classification systems. The standard Choquet integral is expanded by distributing the product operation. Then, the product operation is generalized by a copula. Unlike the generalization of the Choquet integral by t-norms using its standard form (i.e., without distributing the product operator), which results in a pre-aggregation function, the CC-integral satisfies all the conditions required for an aggregation function. We build some examples of CC-integrals considering different examples of copulas, including t-norms, overlap functions and copulas that are neither t-norms nor overlap functions. We show that the CC-integral based on the minimum t-norm, when applied in fuzzy rule-based classification systems, obtains a performance that is, with a high level of confidence, better than that which adopts the winning rule (maximum). We concluded that the behavior of CC-integral is similar to the best Choquet-like pre-aggregation function. Consequently, the CC-integrals introduced in this paper can enlarge the scope of the applications by offering new possibilities for defining fuzzy reasoning methods with a similar gain in performance.