Cut systems with relational morphisms for semiring-valued fuzzy structures

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F23%3AA2402HSE" target="_blank" >RIV/61988987:17610/23:A2402HSE - isvavai.cz</a>

Výsledek na webu

<a href="https://www.mdpi.com/2075-1680/12/2/153" target="_blank" >https://www.mdpi.com/2075-1680/12/2/153</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/axioms12020153" target="_blank" >10.3390/axioms12020153</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Cut systems with relational morphisms for semiring-valued fuzzy structures

Popis výsledku v původním jazyce

Many of the new $MV$-valued fuzzy structures, including intuitionistic, neutrosophic or fuzzy soft sets can be transformed into so-called $AMV$-valued fuzzy sets, or, equivalently, $R$-valued fuzzy sets, where $R$ is a so-called dual pair of semirings. This transformation allows any construction of $AMV$-valued fuzzy sets to be retransformed into an analogous construction for these new fuzzy structures. In this way, approximation theories for $R$-fuzzy sets, rough $R$-fuzzy sets theories, or $F$-transform theories for $R$-fuzzy sets have already been created and then retransformed for these new fuzzy structures. In the paper, we continue this trend and define, on the one hand, the theory of extensional $R$-fuzzy sets defined on sets with $R$-fuzzy similarity relations and power sets functors related to this theory and, at the same time, the theory of cuts with relational morphisms of these structures. Illustratively, the reverse transformations of some of these concepts into new fuzzy structures are presented.

Název v anglickém jazyce

Cut systems with relational morphisms for semiring-valued fuzzy structures

Popis výsledku anglicky

Many of the new $MV$-valued fuzzy structures, including intuitionistic, neutrosophic or fuzzy soft sets can be transformed into so-called $AMV$-valued fuzzy sets, or, equivalently, $R$-valued fuzzy sets, where $R$ is a so-called dual pair of semirings. This transformation allows any construction of $AMV$-valued fuzzy sets to be retransformed into an analogous construction for these new fuzzy structures. In this way, approximation theories for $R$-fuzzy sets, rough $R$-fuzzy sets theories, or $F$-transform theories for $R$-fuzzy sets have already been created and then retransformed for these new fuzzy structures. In the paper, we continue this trend and define, on the one hand, the theory of extensional $R$-fuzzy sets defined on sets with $R$-fuzzy similarity relations and power sets functors related to this theory and, at the same time, the theory of cuts with relational morphisms of these structures. Illustratively, the reverse transformations of some of these concepts into new fuzzy structures are presented.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Axioms

ISSN

2075-1680

e-ISSN

2075-1680

Svazek periodika

—

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

22

Strana od-do

—

Kód UT WoS článku

000938812600001

EID výsledku v databázi Scopus

2-s2.0-85148883344