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On Join-Dense Subsets of Certain Families of Aggregation Functions

Author

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  • Radomír Halaš

    (Department of Algebra and Geometry, Faculty of Science, Palacký University Olomouc, 17. listopadu 12, 771 46 Olomouc, Czech Republic)

  • Jozef Pócs

    (Department of Algebra and Geometry, Faculty of Science, Palacký University Olomouc, 17. listopadu 12, 771 46 Olomouc, Czech Republic
    Mathematical Institute, Slovak Academy of Science, Grešákova 6, 040 01 Košice, Slovakia)

  • Jana Pócsová

    (Faculty of BERG, Technical University of Košice, Němcovej 3, 042 00 Košice, Slovakia)

Abstract

Several important classes of aggregation functions defined on a bounded lattice form a lattice with respect to the pointwise operations of join and meet, respectively. The lattice structure of such classes is usually very complex; thus, it is very useful to characterize them by some appropriate sets of functions. In this paper, we focus on the three important classes of aggregation functions, namely the lattice of all aggregation functions, the lattice of idempotent aggregation functions, and the lattice of Sugeno integrals (defined on distributive lattices) and characterize their lattices by means of join-dense subsets. Moreover, the minimality of these sets is discussed.

Suggested Citation

  • Radomír Halaš & Jozef Pócs & Jana Pócsová, 2022. "On Join-Dense Subsets of Certain Families of Aggregation Functions," Mathematics, MDPI, vol. 11(1), pages 1-11, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2022:i:1:p:14-:d:1009344
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    References listed on IDEAS

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    1. Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2009. "Aggregation functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445120, HAL.
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