On the clone of aggregation functions on bounded lattices

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

On the clone of aggregation functions on bounded lattices

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

On the clone of aggregation functions on bounded lattices

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2016

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Information Sciences

ISSN

0020-0255

e-ISSN

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Svazek periodika

329

Číslo periodika v rámci svazku

FEB

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

10

Strana od-do

381-389

Kód UT WoS článku

000367485000024

EID výsledku v databázi Scopus

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