States on weak pseudo EMV-algebras. II. Representations of states
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F22%3A73616846" target="_blank" >RIV/61989592:15310/22:73616846 - isvavai.cz</a>
Výsledek na webu
<a href="https://ijfs.usb.ac.ir/article_7083_caafda9029c9d7ff19aa93da1356de84.pdf" target="_blank" >https://ijfs.usb.ac.ir/article_7083_caafda9029c9d7ff19aa93da1356de84.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.22111/ijfs.2022.7083" target="_blank" >10.22111/ijfs.2022.7083</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
States on weak pseudo EMV-algebras. II. Representations of states
Popis výsledku v původním jazyce
Recently in [7, 8], new algebras, called weak pseudo EMV-algebras, wPEMV-algebras for short, were introduced generalizing pseudo MV-algebras, generalized Boolean algebras and pseudo EMV-algebras. For these algebras a top element is not assumed a priori. For this class of algebras, we define a state as a finitely additive mapping from a wPEMV-algebra into the real interval [0, 1] which preserves a partial addition of two non-interactive elements and attaining the value 1 in some element. It can happen that some commutative wPEMV-algebras are stateless, e.g. cancellative ones. The paper is divided into two parts. Part I deals with basic properties of states and state-morphisms which are wPEMV-homomorphisms from a wPEMV-algebra into the real interval [0, 1] endowed as a commutative wPEMV-algebra. We show that there is a one-to-one correspondence between the set of state-morphisms and the set of maximal and normal ideals having a special property. In Part II, we present an analogue of the Krein-Mil'man theorem applied to the set of states. We characterize the space of the state-morphisms of a wPEMV-algebra without top element as a Hausdorff locally compact space in the weak topology of states and we present its Alexandroff 's one-point compactification. Moreover, we give an integral representation of any (finitely additive) state by a unique regular Borel sigma-additive probability measure.
Název v anglickém jazyce
States on weak pseudo EMV-algebras. II. Representations of states
Popis výsledku anglicky
Recently in [7, 8], new algebras, called weak pseudo EMV-algebras, wPEMV-algebras for short, were introduced generalizing pseudo MV-algebras, generalized Boolean algebras and pseudo EMV-algebras. For these algebras a top element is not assumed a priori. For this class of algebras, we define a state as a finitely additive mapping from a wPEMV-algebra into the real interval [0, 1] which preserves a partial addition of two non-interactive elements and attaining the value 1 in some element. It can happen that some commutative wPEMV-algebras are stateless, e.g. cancellative ones. The paper is divided into two parts. Part I deals with basic properties of states and state-morphisms which are wPEMV-homomorphisms from a wPEMV-algebra into the real interval [0, 1] endowed as a commutative wPEMV-algebra. We show that there is a one-to-one correspondence between the set of state-morphisms and the set of maximal and normal ideals having a special property. In Part II, we present an analogue of the Krein-Mil'man theorem applied to the set of states. We characterize the space of the state-morphisms of a wPEMV-algebra without top element as a Hausdorff locally compact space in the weak topology of states and we present its Alexandroff 's one-point compactification. Moreover, we give an integral representation of any (finitely additive) state by a unique regular Borel sigma-additive probability measure.
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10101 - Pure mathematics
Návaznosti výsledku
Projekt
—
Návaznosti
S - Specificky vyzkum na vysokych skolach
Ostatní
Rok uplatnění
2022
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Iranian Journal of Fuzzy Systems
ISSN
1735-0654
e-ISSN
—
Svazek periodika
19
Číslo periodika v rámci svazku
4
Stát vydavatele periodika
IR - Íránská islámská republika
Počet stran výsledku
10
Strana od-do
17-26
Kód UT WoS článku
000835534900002
EID výsledku v databázi Scopus
2-s2.0-85135248447