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Quadratic transformation of multivariate aggregation functions

Author

Listed:
  • Boonmee Prakassawat

    (Graduate Degree Program in Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, 50200, Thailand)

  • Tasena Santi

    (Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai50200, Thailand)

Abstract

In this work, we prove that quadratic transformations of aggregation functions must come from quadratic aggregation functions. We also show that this is different from quadratic transformations of (multivariate) semi-copulas and quasi-copulas. In the latter case, those two classes are actually the same and consists of convex combinations of the identity map and another fixed quadratic transformation. In other words, it is a convex set with two extreme points. This result is different from the bivariate case in which the two classes are different and both are convex with four extreme points.

Suggested Citation

  • Boonmee Prakassawat & Tasena Santi, 2020. "Quadratic transformation of multivariate aggregation functions," Dependence Modeling, De Gruyter, vol. 8(1), pages 254-261, January.
    • Handle: RePEc:vrs:demode:v:8:y:2020:i:1:p:254-261:n:5
    DOI: 10.1515/demo-2020-0015
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    References listed on IDEAS

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    1. Durante Fabrizio & Fernández-Sánchez Juan & Trutschnig Wolfgang, 2014. "Solution to an open problem about a transformation on the space of copulas," Dependence Modeling, De Gruyter, vol. 2(1), pages 1-8, November.
    2. Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2011. "Aggregation functions: construction methods, conjunctive, disjunctive and mixed classes," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00539032, HAL.
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