Representation of non-commutative, idempotent, associative functions by pair-orders

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Representation of non-commutative, idempotent, associative functions by pair-orders

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Representation of non-commutative, idempotent, associative functions by pair-orders

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Fuzzy Sets and Systems

ISSN

0165-0114

e-ISSN

—

Svazek periodika

—

Číslo periodika v rámci svazku

January 2024

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

17

Strana od-do

1-17

Kód UT WoS článku

001098533300001

EID výsledku v databázi Scopus

2-s2.0-85174579215