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Remarks on Sugeno Integrals on Bounded Lattices

Author

Listed:
  • Radomír Halaš

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

  • Jozef Pócs

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

  • Jana Pócsová

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

Abstract

A discrete Sugeno integral on a bounded distributive lattice L is defined as an idempotent weighted lattice polynomial. Another possibility for axiomatization of Sugeno integrals is to consider compatible aggregation functions, uniquely extending the L -valued fuzzy measures. This paper aims to study the mentioned unique extension property concerning the possible extension of a Sugeno integral to non-distributive lattices. We show that this property is equivalent to the distributivity of the underlying bounded lattice. As a byproduct, an alternative proof of Iseki’s result, stating that a lattice having prime ideal separation property for every pair of distinct elements is distributive, is provided.

Suggested Citation

  • Radomír Halaš & Jozef Pócs & Jana Pócsová, 2022. "Remarks on Sugeno Integrals on Bounded Lattices," Mathematics, MDPI, vol. 10(17), pages 1-9, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3078-:d:898228
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    Cited by:

    1. Marta Cardin, 2023. "Rights Systems and Aggregation Functions on Property Spaces," Mathematics, MDPI, vol. 11(17), pages 1-10, August.

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