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Aggregation on a Cartesian Product of Bounded Partially Ordered Sets

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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

Aggregation functions on bounded partially ordered sets have been extensively studied for more than thirty years. In this paper, we study aggregation functions on a specific type of bounded partially ordered set: a Cartesian product of several bounded partially ordered sets. In particular, we position this type of aggregation into the recently-introduced framework of aggregation on sets equipped with a betweenness relation (besets), which are a natural generalization of partially ordered sets. The main result is that, depending on the considered set of bounds for the beset associated with the Cartesian product of several bounded partially ordered sets, we obtain two alternative notions: classical aggregation functions w.r.t. the product order on the entire Cartesian product of the bounded partially ordered sets or componentwise aggregation functions acting separately on each of the bounded partially ordered sets.

R. Pérez-Fernández—This research has been partially supported by the Spanish Ministry of Science and Technology (TIN-2017-87600-P).

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Author information

Authors and Affiliations

  1. Department of Statistics and O.R. and Mathematics Didactics, University of Oviedo, Oviedo, Spain

    Raúl Pérez-Fernández

  2. KERMIT, Department of Data Analysis and Mathematical Modelling, Ghent University, Coupure Links 653, 9000, Gent, Belgium

    Bernard De Baets

Authors
  1. Raúl Pérez-Fernández
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  2. Bernard De Baets
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Corresponding author

Correspondence to Raúl Pérez-Fernández .

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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Pérez-Fernández, R., De Baets, B. (2022). Aggregation on a Cartesian Product of Bounded Partially Ordered Sets. 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_1

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  • DOI: https://doi.org/10.1007/978-3-031-08971-8_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-08970-1

  • Online ISBN: 978-3-031-08971-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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