States on weak pseudo EMV-algebras. II. Representations of states

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

States on weak pseudo EMV-algebras. II. Representations of states

Original language description

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&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 sigma-additive probability measure.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10101 - Pure mathematics

Project

—

Continuities

S - Specificky vyzkum na vysokych skolach

Publication year

2022

Confidentiality

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

Name of the periodical

Iranian Journal of Fuzzy Systems

ISSN

1735-0654

e-ISSN

—

Volume of the periodical

19

Issue of the periodical within the volume

4

Country of publishing house

IR - IRAN, ISLAMIC REPUBLIC OF

Number of pages

10

Pages from-to

17-26

UT code for WoS article

000835534900002

EID of the result in the Scopus database

2-s2.0-85135248447