Remarks on Sugeno Integrals on Bounded Lattices

Radomír Halaš (), Jozef Pócs and Jana Pócsová
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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
Jana Pócsová: Faculty of BERG, Technical University of Košice, Němcovej 3, 042 00 Košice, Slovakia

Mathematics, 2022, vol. 10, issue 17, 1-9

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.

Keywords: Sugeno integral; compatibility; distributive lattice; uniqueness of extension (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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