States on EMV-algebras
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F19%3A73597341" target="_blank" >RIV/61989592:15310/19:73597341 - isvavai.cz</a>
Výsledek na webu
<a href="https://link.springer.com/article/10.1007%2Fs00500-018-03738-x" target="_blank" >https://link.springer.com/article/10.1007%2Fs00500-018-03738-x</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00500-018-03738-x" target="_blank" >10.1007/s00500-018-03738-x</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
States on EMV-algebras
Popis výsledku v původním jazyce
We define a state as a [0,1]-valued, finitely additive function attaining the value 1 on an EMV-algebra, which is an algebraic structure close to MV-algebras, where the top element is not assumed. The state space of an EMV-algebra is a convex space that is not necessarily compact, and in such a case, the Krein-Mil'man theorem cannot be used. Nevertheless, we show that the set of extremal states generates the state space. We show that states always exist and the extremal states are exactly state-morphisms. Nevertheless, the state space is a convex space that is not necessarily compact; a variant of the Krein-Mil'man theorem, saying states are generated by extremal states, is proved. We define a weaker form of states, pre-states and strong pre-states, and also Jordan signed measures which form a Dedekind complete l-group. Finally, we show that every state can be represented by a unique regular Borel probability measure, and a variant of the Horn-Tarski theorem is proved.
Název v anglickém jazyce
States on EMV-algebras
Popis výsledku anglicky
We define a state as a [0,1]-valued, finitely additive function attaining the value 1 on an EMV-algebra, which is an algebraic structure close to MV-algebras, where the top element is not assumed. The state space of an EMV-algebra is a convex space that is not necessarily compact, and in such a case, the Krein-Mil'man theorem cannot be used. Nevertheless, we show that the set of extremal states generates the state space. We show that states always exist and the extremal states are exactly state-morphisms. Nevertheless, the state space is a convex space that is not necessarily compact; a variant of the Krein-Mil'man theorem, saying states are generated by extremal states, is proved. We define a weaker form of states, pre-states and strong pre-states, and also Jordan signed measures which form a Dedekind complete l-group. Finally, we show that every state can be represented by a unique regular Borel probability measure, and a variant of the Horn-Tarski theorem is proved.
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Návaznosti výsledku
Projekt
—
Návaznosti
S - Specificky vyzkum na vysokych skolach
Ostatní
Rok uplatnění
2019
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
SOFT COMPUTING
ISSN
1432-7643
e-ISSN
—
Svazek periodika
23
Číslo periodika v rámci svazku
17
Stát vydavatele periodika
US - Spojené státy americké
Počet stran výsledku
24
Strana od-do
7513-7536
Kód UT WoS článku
000486914400003
EID výsledku v databázi Scopus
2-s2.0-85059539234