d-CC Integrals: Generalizing CC-Integrals by Restricted Dissimilarity Functions with Applications to Fuzzy-Rule Based Systems

Joelson Sartori; Giancarlo Lucca; Tiago Asmus; Helida Santos; Eduardo Borges; Benjamin Bedregal; Humberto Bustince; Graçaliz Pereira Dimuro

Joelson Sartori FURG https://orcid.org/0000-0001-5379-8253
Giancarlo Lucca FURG https://orcid.org/0000-0002-3776-0260
Tiago Asmus FURG https://orcid.org/0000-0002-7066-7156
Helida Santos FURG https://orcid.org/0000-0003-2994-2862
Eduardo Borges FURG https://orcid.org/0000-0003-1595-7676
Benjamin Bedregal UFRN https://orcid.org/0000-0002-6757-7934
Humberto Bustince Univ. Publica de Navarra https://orcid.org/0000-0002-1279-6195
Graçaliz Pereira Dimuro FURG https://orcid.org/0000-0001-6986-9888

Resumo

The discrete Choquet Integral (CI) and its generalizations have been successfully applied in many different fields, with particularly good results when considered in Fuzzy Rule-Based Classification Systems (FRBCSs). One of those functions is the CC-integral, where the product operations in the expanded form of the CI are generalized by copulas. Recently, some new Choquet-like operators were developed by generalizing the difference operation by a Restricted Dissimilarity Function (RDF) in either the usual or the expanded form of the original CI, also providing good results in practical applications. So, motivated by such developments, in this paper we propose the generalization of the CC-integral by means of RDFs, resulting in a function that we call d-CC-integral. We study some relevant properties of this new definition, focusing on its monotonicity-like behavior. Then, we proceed to apply d-CC-integrals in a classification problem, comparing different d-CC-integrals between them. The classification acuity of the best d-CC-integral surpasses the one achieved by the best CC-integral and is statistically equivalent to the state-of-the-art in FRBCSs.