Factorization of Matrices With Grades With Overcovering

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F24%3A73627222" target="_blank" >RIV/61989592:15310/24:73627222 - isvavai.cz</a>

Výsledek na webu

<a href="https://obd.upol.cz/id_publ/333207109" target="_blank" >https://obd.upol.cz/id_publ/333207109</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1109/TFUZZ.2023.3330760" target="_blank" >10.1109/TFUZZ.2023.3330760</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Factorization of Matrices With Grades With Overcovering

Popis výsledku v původním jazyce

We present a novel algorithm for factorization of matrices with grades or, equivalently, for decomposition of fuzzy relations. The algorithm is inspired by a recent factorization method for Boolean matrices and develops two ideas in the setting of ordinal attributes. First, it uses formal concepts associated with the factorized matrix, or fuzzy relation, as essential components around which factors are built. Second, it steps back when computing new factors to check whether some computed factors may be eliminated or improved given the subsequently generated factors. The new algorithm thus uses convenient properties of formal concepts utilized by previous factorization algorithms. Still, unlike the previous algorithms, our algorithm allows for more general and therefore more precise factorizations due to a possible overcovering of the input data, which our new algorithm admits. We provide an experimental evaluation of the new algorithm and compare it to some existing algorithms for factorization of data with grades. The evaluation reveals that our new algorithm outperforms the current algorithms in terms of quality of factorization. We also present observations and improvements for factorization of Boolean matrices. We conclude with a discussion regarding open research topics.

Název v anglickém jazyce

Factorization of Matrices With Grades With Overcovering

Popis výsledku anglicky

We present a novel algorithm for factorization of matrices with grades or, equivalently, for decomposition of fuzzy relations. The algorithm is inspired by a recent factorization method for Boolean matrices and develops two ideas in the setting of ordinal attributes. First, it uses formal concepts associated with the factorized matrix, or fuzzy relation, as essential components around which factors are built. Second, it steps back when computing new factors to check whether some computed factors may be eliminated or improved given the subsequently generated factors. The new algorithm thus uses convenient properties of formal concepts utilized by previous factorization algorithms. Still, unlike the previous algorithms, our algorithm allows for more general and therefore more precise factorizations due to a possible overcovering of the input data, which our new algorithm admits. We provide an experimental evaluation of the new algorithm and compare it to some existing algorithms for factorization of data with grades. The evaluation reveals that our new algorithm outperforms the current algorithms in terms of quality of factorization. We also present observations and improvements for factorization of Boolean matrices. We conclude with a discussion regarding open research topics.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

IEEE TRANSACTIONS ON FUZZY SYSTEMS

ISSN

1063-6706

e-ISSN

1941-0034

Svazek periodika

32

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

12

Strana od-do

1641-1652

Kód UT WoS článku

001196731700051

EID výsledku v databázi Scopus

2-s2.0-85177037889