Preimage Problem Inspired by the F-Transform

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

Preimage Problem Inspired by the F-Transform

Original language description

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.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10102 - Applied mathematics

Project

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Continuities

S - Specificky vyzkum na vysokych skolach

Publication year

2022

Confidentiality

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

Name of the periodical

Mathematics

ISSN

2227-7390

e-ISSN

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Volume of the periodical

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Issue of the periodical within the volume

17

Country of publishing house

CH - SWITZERLAND

Number of pages

26

Pages from-to

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UT code for WoS article

000851677800001

EID of the result in the Scopus database

2-s2.0-85137771648