Towards Higher-Degree Fuzzy Projection

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F23%3AA2402I31" target="_blank" >RIV/61988987:17610/23:A2402I31 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s40815-023-01506-0" target="_blank" >https://link.springer.com/article/10.1007/s40815-023-01506-0</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s40815-023-01506-0" target="_blank" >10.1007/s40815-023-01506-0</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Towards Higher-Degree Fuzzy Projection

Popis výsledku v původním jazyce

Fuzzy projection is a mathematical operator inspired by the inverse fuzzy transform that is used to approximate functions. The fuzzy projection is designed such that the coefficients of the linear combination of the basis functions (fuzzy sets in a fuzzy partition) are optimized to obtain the best approximation of the functions from a global perspective, as opposed to the fuzzy transform, where the approximation focuses on fitting functions locally. The aim of this paper is to extend the fuzzy projection to a higher degree, similarly to the fuzzy transform, where the coefficients of the linear combination of the basis functions are expressed by polynomials. In this way, we can significantly improve the quality of the approximation by combining the settings of the fuzzy partition and the degree of polynomnials. In this paper, we show that a higher-order fuzzy projection can be computed using matrix calculus, leading to an easy algorithmization of the method. We also give its approximation properties and its applicability to discrete functions. The usefulness of higher-order fuzzy projection is demonstrated on two tasks, namely continuous function approximation and audio signal compression and decompression, where the results are compared with other relevant methods.

Název v anglickém jazyce

Towards Higher-Degree Fuzzy Projection

Popis výsledku anglicky

Fuzzy projection is a mathematical operator inspired by the inverse fuzzy transform that is used to approximate functions. The fuzzy projection is designed such that the coefficients of the linear combination of the basis functions (fuzzy sets in a fuzzy partition) are optimized to obtain the best approximation of the functions from a global perspective, as opposed to the fuzzy transform, where the approximation focuses on fitting functions locally. The aim of this paper is to extend the fuzzy projection to a higher degree, similarly to the fuzzy transform, where the coefficients of the linear combination of the basis functions are expressed by polynomials. In this way, we can significantly improve the quality of the approximation by combining the settings of the fuzzy partition and the degree of polynomnials. In this paper, we show that a higher-order fuzzy projection can be computed using matrix calculus, leading to an easy algorithmization of the method. We also give its approximation properties and its applicability to discrete functions. The usefulness of higher-order fuzzy projection is demonstrated on two tasks, namely continuous function approximation and audio signal compression and decompression, where the results are compared with other relevant methods.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

Projekt

<a href="/cs/project/GA23-06280S" target="_blank" >GA23-06280S: Nové přístupy pro předvídání finančních časových řad v rámci fuzzy-pravděpodobnostního prostředí</a><br>

Návaznosti

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

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

International Journal of Fuzzy Systems

ISSN

1562-2479

e-ISSN

2199-3211

Svazek periodika

—

Číslo periodika v rámci svazku

30.03.2024

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

16

Strana od-do

2234-2249

Kód UT WoS článku

000960863100002

EID výsledku v databázi Scopus

2-s2.0-85151321331