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

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Intelligent Systems (BRACIS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14195))

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Abstract

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.

This research was funded by FAPERGS/Brazil (Proc. 19/2551-0001660-3, 23/2551-0000126-8), CNPq/Brazil (301618/2019-4, 305805/2021-5, 150160/ 2023-2).

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Notes

  1. 1.

    A function F is said to be averaging if \(min \le F \le max\).

  2. 2.

    For more information about this approach see [19, 20, 23].

  3. 3.

    https://keel.es.

  4. 4.

    To analyze the particular cases and results per fold please check the folowing link - https://github.com/Giancarlo-Lucca/d-CC-Integrals-generalizing-CC-integrals-by-restricted-dissimilarity-functions.

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Authors and Affiliations

  1. Centro de Ciêcias Computacionais, Univ. Fed. do Rio Grande, Porto Alegre, Brazil

    Joelson Sartori, Giancarlo Lucca, Helida Santos, Eduardo Borges & Graçaliz Pereira Dimuro

  2. Instituto de Matemática, Estatística e Física, Univ. Fed. do Rio Grande, Porto Alegre, Brazil

    Tiago Asmus

  3. Departamento de Informática e Matemática Aplicada, Univ. Fed. do Rio Grande do Norte, Natal, Brazil

    Benjamin Bedregal

  4. Dept. Estadistica, Informa. y Matem., Univ. Publica de Navarra, Pamplona, Spain

    Humberto Bustince

Authors
  1. Joelson Sartori
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  2. Giancarlo Lucca
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  3. Tiago Asmus
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  4. Helida Santos
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  5. Eduardo Borges
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  6. Benjamin Bedregal
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  7. Humberto Bustince
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  8. Graçaliz Pereira Dimuro
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Corresponding author

Correspondence to Giancarlo Lucca .

Editor information

Editors and Affiliations

  1. Federal University of São Carlos, São Carlos, Brazil

    Murilo C. Naldi

  2. Centro Universitario da FEI, São Bernardo do Campo, Brazil

    Reinaldo A. C. Bianchi

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Sartori, J. et al. (2023). d-CC Integrals: Generalizing CC-Integrals by Restricted Dissimilarity Functions with Applications to Fuzzy-Rule Based Systems. In: Naldi, M.C., Bianchi, R.A.C. (eds) Intelligent Systems. BRACIS 2023. Lecture Notes in Computer Science(), vol 14195. Springer, Cham. https://doi.org/10.1007/978-3-031-45368-7_16

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  • DOI: https://doi.org/10.1007/978-3-031-45368-7_16

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  • Online ISBN: 978-3-031-45368-7

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