Remarks on Sugeno Integrals on Bounded Lattices

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F22%3A73616095" target="_blank" >RIV/61989592:15310/22:73616095 - isvavai.cz</a>
Result on the web
<a href="https://www.mdpi.com/2227-7390/10/17/3078" target="_blank" >https://www.mdpi.com/2227-7390/10/17/3078</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3390/math.10173078" target="_blank" >10.3390/math.10173078</a>

Result language
angličtina
Original language name
Remarks on Sugeno Integrals on Bounded Lattices
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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