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International Summer School on Aggregation Operators

AGOP 2017: Aggregation Functions in Theory and in Practice pp 83–95Cite as

CMin-Integral: A Choquet-Like Aggregation Function Based on the Minimum t-Norm for Applications to Fuzzy Rule-Based Classification Systems

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 581))

Abstract

This paper studies the concept of Choquet-like copula-based aggregation function (CC-integral), introduced by Lucca et al. [1], when one considers the Minimum t-norm, showing an application in fuzzy rule-based classification systems. The CC-integral is built from the standard Choquet integral, which is expanded by distributing the product operation, and, then, the product operation is generalized by a copula. In this paper, we study the behavior of this aggregation function in fuzzy rule-based classification systems, when one considers the Minimum t-norm as de copula of the CC-integral, which we call the CMin-integral. We show that the CMin-integral obtains a performance that is, with a high level of confidence, better than the approach that adopts the winning rule (maximum). Moreover, its behaviour is similar to the best Choquet-like pre-aggregation functions, introduced by Lucca et al. [10], with excellent performance. Consequently, the CMin-integral enlarge the scope of the applications by offering new possibilities for defining fuzzy reasoning methods with a similar gain in performance.

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Notes

  1. 1.

    http://www.keel.es.

  2. 2.

    For an increasing (decreasing) function we do not mean a strictly increasing (decreasing) function.

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Acknowledgment

This work is supported by Brazilian National Counsel of Technological and Scientific Development CNPq (under the Processes 233950/2014-1, 305882/2016-3, 307781/2016-0) and by the Spanish Ministry of Science and Technology (under project TIN2016-77356-P). G.P. Dimuro is also supported by Caixa and Fundación Caja Navarra of Spain.

Author information

Authors and Affiliations

  1. Institute of Smart Cities, Universidad Pública de Navarra, 31006, Pamplona, Spain

    Graçaliz Pereira Dimuro

  2. Centro de Ciências Computacionais, Universidade Federal do Rio Grande, Rio Grande, 96201-900, Brazil

    Graçaliz Pereira Dimuro

  3. Departamento de Automática y Computación, Universidad Pública de Navarra, 31006, Pamplona, Spain

    Giancarlo Lucca

  4. Departamento de Automática y Computación and Institute of Smart Cities, Universidad Pública de Navarra, 31006, Pamplona, Spain

    José António Sanz & Humberto Bustince

  5. Departamento de Informática e Matemática Aplicada, Universidade Federal do Rio Grande do Norte, Natal, Brazil

    Benjamín Bedregal

Authors
  1. Graçaliz Pereira Dimuro
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  2. Giancarlo Lucca
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  3. José António Sanz
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  4. Humberto Bustince
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  5. Benjamín Bedregal
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Corresponding author

Correspondence to Graçaliz Pereira Dimuro .

Editor information

Editors and Affiliations

  1. School of Informatics, University of Skövde, Skövde, Sweden

    Vicenç Torra

  2. Department of Mathematics and Descriptive Geometry, Slovak University of Technology, Bratislava, Slovakia

    Radko Mesiar

  3. KERMIT Research Unit Knowledge-based Systems, Ghent University, Ghent, Belgium

    Bernard De Baets

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Dimuro, G.P., Lucca, G., Sanz, J.A., Bustince, H., Bedregal, B. (2018). CMin-Integral: A Choquet-Like Aggregation Function Based on the Minimum t-Norm for Applications to Fuzzy Rule-Based Classification Systems. In: Torra, V., Mesiar, R., Baets, B. (eds) Aggregation Functions in Theory and in Practice. AGOP 2017. Advances in Intelligent Systems and Computing, vol 581. Springer, Cham. https://doi.org/10.1007/978-3-319-59306-7_9

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  • DOI: https://doi.org/10.1007/978-3-319-59306-7_9

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