Preimage Problem Inspired by the F-Transform
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F22%3AA2302G7E" target="_blank" >RIV/61988987:17610/22:A2302G7E - isvavai.cz</a>
Výsledek na webu
<a href="http://mdpi.com/2227-7390/10/17/3209" target="_blank" >http://mdpi.com/2227-7390/10/17/3209</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3390/math10173209" target="_blank" >10.3390/math10173209</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Preimage Problem Inspired by the F-Transform
Popis výsledku v původním jazyce
In this article, we focus on discrete data processing. We propose to use the concept of closeness, which is less restrictive than a metric, to describe a certain relationship between objects. We establish a fuzzy partition of a given set of objects in a way that admits a closeness space to emerge. The fuzzy (F-) transform is a tool that maps objects with common characteristics to the same discrete image—the direct F-transform. We are interested in the inverse (preimage) problem: How can we describe the class of all functions mapped onto the same direct F-transform? In this manuscript, we focus on this preimage problem, formulated accordingly. Its solution is presented from three different points of view and shows which functions belong to the same class determined by a given image (by the direct F-transform). Conditions under which a solution to the preimage problem is given by the inverse F-transform over the same fuzzy partition, or by transforming a given image using a new system of basic functions, are formulated. The developed theory contributes to a better understanding of ill-posed problems that are typical for machine learning. The appendix contains illustrative numerical examples.
Název v anglickém jazyce
Preimage Problem Inspired by the F-Transform
Popis výsledku anglicky
In this article, we focus on discrete data processing. We propose to use the concept of closeness, which is less restrictive than a metric, to describe a certain relationship between objects. We establish a fuzzy partition of a given set of objects in a way that admits a closeness space to emerge. The fuzzy (F-) transform is a tool that maps objects with common characteristics to the same discrete image—the direct F-transform. We are interested in the inverse (preimage) problem: How can we describe the class of all functions mapped onto the same direct F-transform? In this manuscript, we focus on this preimage problem, formulated accordingly. Its solution is presented from three different points of view and shows which functions belong to the same class determined by a given image (by the direct F-transform). Conditions under which a solution to the preimage problem is given by the inverse F-transform over the same fuzzy partition, or by transforming a given image using a new system of basic functions, are formulated. The developed theory contributes to a better understanding of ill-posed problems that are typical for machine learning. The appendix contains illustrative numerical examples.
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10102 - Applied 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
Mathematics
ISSN
2227-7390
e-ISSN
—
Svazek periodika
—
Číslo periodika v rámci svazku
17
Stát vydavatele periodika
CH - Švýcarská konfederace
Počet stran výsledku
26
Strana od-do
—
Kód UT WoS článku
000851677800001
EID výsledku v databázi Scopus
2-s2.0-85137771648