States on weak pseudo EMV-algebras. I. States and states morphisms

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F22%3A73616845" target="_blank" >RIV/61989592:15310/22:73616845 - isvavai.cz</a>

Výsledek na webu

<a href="https://obd.upol.cz/id_publ/333196732" target="_blank" >https://obd.upol.cz/id_publ/333196732</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.22111/ijfs.2022.7082" target="_blank" >10.22111/ijfs.2022.7082</a>

Jazyk výsledku

angličtina

Název v původním jazyce

States on weak pseudo EMV-algebras. I. States and states morphisms

Popis výsledku v původním jazyce

Recently in [17, 18], 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&apos;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&apos;s one-point compactification. Moreover, we give an integral representation of any (finitely additive) state by a unique regular Borel s-additive probability measure.

Název v anglickém jazyce

States on weak pseudo EMV-algebras. I. States and states morphisms

Popis výsledku anglicky

Recently in [17, 18], 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&apos;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&apos;s one-point compactification. Moreover, we give an integral representation of any (finitely additive) state by a unique regular Borel s-additive probability measure.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2022

Kód důvěrnosti údajů

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

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

15

Strana od-do

1-15

Kód UT WoS článku

000835534900001

EID výsledku v databázi Scopus

2-s2.0-85135214549