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On the Generalizations of the Choquet Integral for Application in FRBCs

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Book cover Intelligent Systems (BRACIS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13073))

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Abstract

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/10.13039/501100011033)).

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Notes

  1. 1.

    A fuzzy measure \(\mathfrak {m}\) is an increasing function on \(2^{N}\) such that \(\mathfrak {m} (\emptyset ) = 0\) and \(\mathfrak {m} (N) = 1\).

  2. 2.

    Examples of special CC-integrals were studied in [19, 20].

  3. 3.

    The function \(FNA2: [0,1]^2\) is defined, for all \(x,y \in [0,1]\) by \(F(0,y)= 0\), \(F(x,y) = \frac{x+y}{2}\) if \(0 < x \le y\) and \(F(x,y) = \min (\frac{x}{2},y)\), otherwise, which satisfies the conditions of [21, Theorems 2].

  4. 4.

    The considered datasets and the fuzzy classifier are available in KEEL repository. Available at https://www.keel.es.

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Authors and Affiliations

  1. Universidade Federal do Rio Grande, Rio Grande, RS, Brazil

    Giancarlo Lucca, Eduardo N. Borges, Rafael A. Berri, Leonardo Emmendorfer, Graçaliz P. Dimuro & Tiago C. Asmus

  2. Universidad Publica de Navarra, Pamplona, Navarra, Spain

    Graçaliz P. Dimuro & Tiago C. Asmus

Authors
  1. Giancarlo Lucca
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  2. Eduardo N. Borges
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  3. Rafael A. Berri
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  4. Leonardo Emmendorfer
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  5. Graçaliz P. Dimuro
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  6. Tiago C. Asmus
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Correspondence to Giancarlo Lucca .

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Editors and Affiliations

  1. Universidade Federal de Sergipe, São Cristóvão, Brazil

    André Britto

  2. Universidade de São Paulo, São Paulo, Brazil

    Karina Valdivia Delgado

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Lucca, G., Borges, E.N., Berri, R.A., Emmendorfer, L., Dimuro, G.P., Asmus, T.C. (2021). On the Generalizations of the Choquet Integral for Application in FRBCs. In: Britto, A., Valdivia Delgado, K. (eds) Intelligent Systems. BRACIS 2021. Lecture Notes in Computer Science(), vol 13073. Springer, Cham. https://doi.org/10.1007/978-3-030-91702-9_33

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  • DOI: https://doi.org/10.1007/978-3-030-91702-9_33

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