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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&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.

  • 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&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.

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