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

  • Graçaliz Pereira DimuroEmail author
  • Giancarlo Lucca
  • José António Sanz
  • Humberto Bustince
  • Benjamín Bedregal
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (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.

Notes

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.

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Graçaliz Pereira Dimuro
    • 1
    • 2
    Email author
  • Giancarlo Lucca
    • 3
  • José António Sanz
    • 4
  • Humberto Bustince
    • 4
  • Benjamín Bedregal
    • 5
  1. 1.Institute of Smart CitiesUniversidad Pública de NavarraPamplonaSpain
  2. 2.Centro de Ciências Computacionais, Universidade Federal do Rio GrandeRio GrandeBrazil
  3. 3.Departamento de Automática y ComputaciónUniversidad Pública de NavarraPamplonaSpain
  4. 4.Departamento de Automática y Computación and Institute of Smart CitiesUniversidad Pública de NavarraPamplonaSpain
  5. 5.Departamento de Informática e Matemática AplicadaUniversidade Federal do Rio Grande do NorteNatalBrazil

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