On lattices with a smallest set of aggregation functions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F15%3A33155717" target="_blank" >RIV/61989592:15310/15:33155717 - isvavai.cz</a>
Result on the web
<a href="http://www.sciencedirect.com/science/article/pii/S0020025515005277" target="_blank" >http://www.sciencedirect.com/science/article/pii/S0020025515005277</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ins.2015.07.031" target="_blank" >10.1016/j.ins.2015.07.031</a>

Result language
angličtina
Original language name
On lattices with a smallest set of aggregation functions
Original language description
Given a bounded lattice L with bounds 0 and 1, it is well known that the set Pol(0,1) (L) of all 0, 1-preserving polynomials of L forms a natural subclass of the set C(L) of aggregation functions on L. The main aim of this paper is to characterize all finite lattices L for which these two classes coincide, i.e. when the set C(L) is as small as possible. These lattices are shown to be completely determined by their tolerances, also several sufficient purely lattice-theoretical conditions are presented. In particular, all simple relatively complemented lattices or simple lattices for which the join (meet) of atoms (coatoms) is 1 (0) are of this kind.
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
<a href="/en/project/GF15-34697L" target="_blank" >GF15-34697L: New perspectives on residuated posets</a><br>
Continuities
S - Specificky vyzkum na vysokych skolach

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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