g-States on unital weak pseudo EMV-algebras
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F23%3A73621042" target="_blank" >RIV/61989592:15310/23:73621042 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s00500-023-07850-5" target="_blank" >https://link.springer.com/article/10.1007/s00500-023-07850-5</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00500-023-07850-5" target="_blank" >10.1007/s00500-023-07850-5</a>
Alternative languages
Result language
angličtina
Original language name
g-States on unital weak pseudo EMV-algebras
Original language description
Recently in Dvurecenskij and Zahiri (J Appl Log IfCoLog J Log Appl 8:2365-2399, 2021b, J Appl Log IfCoLog J Log Appl 8:2401-2433, 2021c), new algebras, called weak pseudo EMV-algebras (wPEMV-algebras in short), were introduced. The authors do not assume the existence of a top element-they generalize MV-algebras, pseudo MV-algebras, and pseudo EMV-algebras. A g-state is defined on a unital wPEMV-algebra M as a mapping from M into the positive half-line of reals such that it preserves a partial addition +, and in a fixed strong unit, it takes the value 1. They form a Bauer simplex, and extremal points are exactly g-states whose kernel is a maximal and normal ideal. We show that extremal g-states generate all g-states, and it can happen that in some unital wPEMV-algebra, even commutative, there is no g-state. We present some conditions for existence of g-states and establish an integral representation of g-states. In addition, we give a topological characterization of the spaces of g-states and extremal g-states, respectively. Moreover, discrete g-states are investigated.
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
2023
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
1433-7479
Volume of the periodical
27
Issue of the periodical within the volume
8
Country of publishing house
US - UNITED STATES
Number of pages
16
Pages from-to
4353-4368
UT code for WoS article
000927746000002
EID of the result in the Scopus database
2-s2.0-85147554777