On Solvability Degree of Systems of Partial Fuzzy Relational Equations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F24%3AA2502NM4" target="_blank" >RIV/61988987:17610/24:A2502NM4 - isvavai.cz</a>

Výsledek na webu

<a href="https://ieeexplore.ieee.org/document/10612055" target="_blank" >https://ieeexplore.ieee.org/document/10612055</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1109/FUZZ-IEEE60900.2024.10612055" target="_blank" >10.1109/FUZZ-IEEE60900.2024.10612055</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On Solvability Degree of Systems of Partial Fuzzy Relational Equations

Popis výsledku v původním jazyce

Systems of partial fuzzy relational equations employing undefined values in the antecedents and consequents have been approached recently. The primary focus was on the issues of sufficient solvability and solvability criteria. This study introduces another perspective, investigating the behavior of solvability degrees of these systems. We employ operations from the Lower estimation and Dragonfly partial algebras developed in the partial fuzzy set theory framework. Initially, we establish a degree of solvability in an appropriate space of approximations containing potential solutions for the systems. Subsequently, we introduce the concept of the alpha-lift for a given partial fuzzy set and provide its fundamental properties. This concept is employed to modify the antecedents and consequents of a given system of partial fuzzy relational equations, resulting in a modified system. The solvability degree of this modified system is then studied, and we demonstrate that, under sufficient conditions, it significantly enhances the solvability degree of the initial system. This positive impact is observed in the G"{o}del algebra, the underlying algebraic structure of partial algebras. In conclusion, we provide illustrative examples that effectively demonstrate the theoretical results.

Název v anglickém jazyce

On Solvability Degree of Systems of Partial Fuzzy Relational Equations

Popis výsledku anglicky

Systems of partial fuzzy relational equations employing undefined values in the antecedents and consequents have been approached recently. The primary focus was on the issues of sufficient solvability and solvability criteria. This study introduces another perspective, investigating the behavior of solvability degrees of these systems. We employ operations from the Lower estimation and Dragonfly partial algebras developed in the partial fuzzy set theory framework. Initially, we establish a degree of solvability in an appropriate space of approximations containing potential solutions for the systems. Subsequently, we introduce the concept of the alpha-lift for a given partial fuzzy set and provide its fundamental properties. This concept is employed to modify the antecedents and consequents of a given system of partial fuzzy relational equations, resulting in a modified system. The solvability degree of this modified system is then studied, and we demonstrate that, under sufficient conditions, it significantly enhances the solvability degree of the initial system. This positive impact is observed in the G"{o}del algebra, the underlying algebraic structure of partial algebras. In conclusion, we provide illustrative examples that effectively demonstrate the theoretical results.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10100 - Mathematics

Projekt

<a href="/cs/project/EH22_008%2F0004583" target="_blank" >EH22_008/0004583: Excelentní výzkum v oblasti digitálních technologií a wellbeingu</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název statě ve sborníku

2024 International Conference on Fuzzy Systems (FUZZ)

ISBN

979-835031954-5

ISSN

1098-7584

e-ISSN

1558-4739

Počet stran výsledku

7

Strana od-do

—

Název nakladatele

IEEE

Místo vydání

—

Místo konání akce

Yokohama, Japan

Datum konání akce

1. 1. 2024

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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