Transfer-stable means on finite chains

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F19%3A73597072" target="_blank" >RIV/61989592:15310/19:73597072 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0165011418307851" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0165011418307851</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.fss.2018.10.009" target="_blank" >10.1016/j.fss.2018.10.009</a>

Result language
angličtina
Original language name
Transfer-stable means on finite chains
Original language description
According to [5], the arithmetic mean is a function characterized by four features: it is non-decreasing, idempotent, symmetric and additive. The first three of them can be naturally converted to the theory of posets but the last one generally can not. Due to this problem, we will replace it with another suitable property, which is called transfer-stability. However, we do not get the exact arithmetic mean but some approximation. These functions will be called transfer-stable means. The first aim of the paper is to show that transfer-stable means on a finite chain form a lattice which is isomorphic to the direct power of a finite chain. The second goal is to create a generating set of transfer-stable means, i.e., means that can generate all other transfer-stable means of the same arity by classical composition of functions. The last goal deals with question of how to generate all transfer-stable means of any arity by binary transfer-stable means only. For this problem we define special transfer-stable means composition.
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
—
OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/GA18-06915S" target="_blank" >GA18-06915S: New approaches to aggregation operators in analysis and processing of data</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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