On Self-Aggregations of Min-Subgroups

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F21%3A00356044" target="_blank" >RIV/68407700:21230/21:00356044 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.3390/axioms10030201" target="_blank" >https://doi.org/10.3390/axioms10030201</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3390/axioms10030201" target="_blank" >10.3390/axioms10030201</a>

Result language
angličtina
Original language name
On Self-Aggregations of Min-Subgroups
Original language description
Preservation of structures under aggregation functions is an active area of research with applications in many fields. Among such structures, min-subgroups play an important role, for instance, in mathematical morphology, where they can be used to model translation invariance. Aggregation of min-subgroups has only been studied for binary aggregation functions. However, results concerning preservation of the min-subgroup structure under binary aggregations do not generalize to aggregation functions with arbitrary input size since they are not associative. In this article, we prove that arbitrary self-aggregation functions preserve the min-subgroup structure. Moreover, we show that whenever the aggregation function is strictly increasing on its diagonal, a min-subgroup and its self-aggregation have the same level sets.
Czech name
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Czech description
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Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/GA19-09967S" target="_blank" >GA19-09967S: Compositional Architectures for Pattern Recognition</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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