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On Construction Methods of (Interval-Valued) General Grouping Functions

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Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2022)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1601))

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Abstract

Recently, several theoretical and applied studies on grouping functions and overlap functions appeared in the literature, mainly because of their flexibility when comparing them with the popular aggregation operators t-conorms and t-norms, respectively. Additionally, they constitute richer classes of disjunction/conjunction operations than t-norms and t-conorms. In particular, grouping functions have been applied as the disjunction operator in several problems, like decision making based on fuzzy preference relations. In this case, when performing pairwise comparisons, grouping functions allow one to evaluate the measure of the amount of evidence in favor of either of two given alternatives. However, grouping functions are not associative. Then, in order to allow them to be applied in n-dimensional problems, such as the pooling layer of neural networks, some generalizations were introduced, namely, n-dimensional grouping functions and the more flexible general grouping functions, the latter for enlarging the scope of applications. Then, in order to h andle uncertainty on the definition of the membership functions in real-life problems, n-dimensional and general interval-valued grouping functions were proposed. This paper aims at providing new constructions methods of general (interval-valued) grouping functions, also providing some examples.

Supported by CNPq (301618/2019-4, 305805/2021-5), FAPERGS (19/2551-0001660-3), Spanish Ministry Science and Tech. (TIN2016-77356-P, PID2019-108392GB I00 (MCIN/AEI/10.13039/501100011033)), Navarra Servicios y Tecnologías, S.A. (NASERTIC).

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Author information

Authors and Affiliations

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

    Graçaliz P. Dimuro, Tiago Asmus, Helida Santos, Eduardo Borges & Giancarlo Lucca

  2. Universidad Publica de Navarra, Pamplona, Spain

    Graçaliz P. Dimuro, Tiago Asmus, Helida Santos, Iosu Rodriguez-Martinez & Humberto Bustince

  3. Universidade Federal Rural do Semi-Árido, Mossoró, Brazil

    Jocivania Pinheiro

  4. Slovak University of Technology, Bratislava, Slovakia

    Radko Mesiar

Authors
  1. Graçaliz P. Dimuro
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  2. Tiago Asmus
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  4. Helida Santos
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  5. Eduardo Borges
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  9. Humberto Bustince
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Correspondence to Graçaliz P. Dimuro .

Editor information

Editors and Affiliations

  1. University of Milano-Bicocca, Milan, Italy

    Davide Ciucci

  2. University of Oviedo, Oviedo, Spain

    Inés Couso

  3. University of Cádiz, Cádiz, Spain

    Jesús Medina

  4. University of Warsaw, Warsaw, Poland

    Dominik Ślęzak

  5. University of Perugia, Perugia, Italy

    Davide Petturiti

  6. Sorbonne Université, Paris, France

    Bernadette Bouchon-Meunier

  7. Iona College, New Rochelle, NY, USA

    Ronald R. Yager

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Dimuro, G.P. et al. (2022). On Construction Methods of (Interval-Valued) General Grouping Functions. In: Ciucci, D., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2022. Communications in Computer and Information Science, vol 1601. Springer, Cham. https://doi.org/10.1007/978-3-031-08971-8_30

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  • DOI: https://doi.org/10.1007/978-3-031-08971-8_30

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