On approximation of lattice-valued functions using lattice integral transforms

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F25%3AA2603B0T" target="_blank" >RIV/61988987:17610/25:A2603B0T - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0888613X25001173?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0888613X25001173?via%3Dihub</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.ijar.2025.109476" target="_blank" >10.1016/j.ijar.2025.109476</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On approximation of lattice-valued functions using lattice integral transforms

Popis výsledku v původním jazyce

This paper examines the approximation capabilities of lattice integral transforms and their compositions in reconstructing lattice-valued functions. By introducing an integral kernel Q on the function domain, we define the concept of a Q-inverse integral kernel, which generalizes the traditional inverse kernel defined as a transposed integral kernel. Leveraging these Q-inverses, we establish upper and lower bounds for a transformed version of the original function induced by the integral kernel Q. The quality of approximation is analyzed using a lattice-based modulus of continuity, specifically designed for functions valued in complete residuated lattices. Additionally, under specific conditions, we demonstrate that the approximation quality for extensional functions with respect to the kernel Q can be estimated through the integral of the square of Q, and in certain cases, these extensional functions can be perfectly reconstructed. The theoretical findings, illustrated through examples, provide a strong foundation for further theoretical advancement and practical applications.

Název v anglickém jazyce

On approximation of lattice-valued functions using lattice integral transforms

Popis výsledku anglicky

This paper examines the approximation capabilities of lattice integral transforms and their compositions in reconstructing lattice-valued functions. By introducing an integral kernel Q on the function domain, we define the concept of a Q-inverse integral kernel, which generalizes the traditional inverse kernel defined as a transposed integral kernel. Leveraging these Q-inverses, we establish upper and lower bounds for a transformed version of the original function induced by the integral kernel Q. The quality of approximation is analyzed using a lattice-based modulus of continuity, specifically designed for functions valued in complete residuated lattices. Additionally, under specific conditions, we demonstrate that the approximation quality for extensional functions with respect to the kernel Q can be estimated through the integral of the square of Q, and in certain cases, these extensional functions can be perfectly reconstructed. The theoretical findings, illustrated through examples, provide a strong foundation for further theoretical advancement and practical applications.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

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

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

INTERNATIONAL JOURNAL OF APPROXIMATE REASONING

ISSN

0888-613X

e-ISSN

1873-4731

Svazek periodika

—

Číslo periodika v rámci svazku

October 2025

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

27

Strana od-do

1-27

Kód UT WoS článku

001502517900001

EID výsledku v databázi Scopus

2-s2.0-105006502575