g-States on unital weak pseudo EMV-algebras

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

g-States on unital weak pseudo EMV-algebras

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

g-States on unital weak pseudo EMV-algebras

Popis výsledku anglicky

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.

Druh

J_imp - 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)

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

SOFT COMPUTING

ISSN

1432-7643

e-ISSN

1433-7479

Svazek periodika

27

Číslo periodika v rámci svazku

8

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

16

Strana od-do

4353-4368

Kód UT WoS článku

000927746000002

EID výsledku v databázi Scopus

2-s2.0-85147554777