On the clone of aggregation functions on bounded lattices

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F16%3A33156875" target="_blank" >RIV/61989592:15310/16:33156875 - isvavai.cz</a>
Result on the web
<a href="http://www.sciencedirect.com/science/article/pii/S0020025515006933" target="_blank" >http://www.sciencedirect.com/science/article/pii/S0020025515006933</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ins.2015.09.038" target="_blank" >10.1016/j.ins.2015.09.038</a>

Result language
angličtina
Original language name
On the clone of aggregation functions on bounded lattices
Original language description
The main aim of this paper is to study aggregation functions on lattices via clone theory approach. Observing that the aggregation functions on lattices just correspond to 0, 1-monotone clones, as the main result we show that for any finite n-element lattice L there is a set of at most 2n + 2 aggregation functions on L from which the respective clone is generated. Namely, the set of generating aggregation functions consists only of at most n unary functions, at most n binary functions, and lattice operations boolean AND, boolean OR, and all aggregation functions of L are composed of them by usual term composition. Moreover, our approach works also for infinite lattices (such as mostly considered bounded real intervals [a, b]), where in contrast to finite case infinite suprema (or, equivalently, a kind of limit process) have to be considered.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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