States on EMV-algebras
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
States on EMV-algebras
Original language description
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.
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
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
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Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
SOFT COMPUTING
ISSN
1432-7643
e-ISSN
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Volume of the periodical
23
Issue of the periodical within the volume
17
Country of publishing house
US - UNITED STATES
Number of pages
24
Pages from-to
7513-7536
UT code for WoS article
000486914400003
EID of the result in the Scopus database
2-s2.0-85059539234