Representation of non-commutative, idempotent, associative functions by pair-orders
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F24%3AA2502LNU" target="_blank" >RIV/61988987:17610/24:A2502LNU - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/abs/pii/S0165011423004049" target="_blank" >https://www.sciencedirect.com/science/article/abs/pii/S0165011423004049</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.fss.2023.108759" target="_blank" >10.1016/j.fss.2023.108759</a>
Alternative languages
Result language
angličtina
Original language name
Representation of non-commutative, idempotent, associative functions by pair-orders
Original language description
The non-commutative, idempotent, associative functions are studied. It is well known that each commutative, idempotent (internal), associative function can be represented by a partial (linear) order. In this work it is shown that each non-commutative, idempotent (internal), associative function can be represented by a (linear) pair-order. Moreover, each internal, associative function can be expressed as an ordinal sum of trivial semigroups and semigroups, where the corresponding semigroup operation is the projection to one of the coordinates. Vice versa, each linear pair-order induces a unique internal, associative function and a condition under which each (non-linear) pair-order defined on a chain induces a unique monotone, idempotent, associative function is also introduced. Several examples of non-commutative, idempotent, associative functions and related pair-orders are shown.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Fuzzy Sets and Systems
ISSN
0165-0114
e-ISSN
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Volume of the periodical
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Issue of the periodical within the volume
January 2024
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
17
Pages from-to
1-17
UT code for WoS article
001098533300001
EID of the result in the Scopus database
2-s2.0-85174579215