TOLERANCE PROBLEMS FOR GENERALIZED EIGENVECTORS OF INTERVAL FUZZY MATRICES

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18450%2F22%3A50020230" target="_blank" >RIV/62690094:18450/22:50020230 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.kybernetika.cz/content/2022/5/760/paper.pdf" target="_blank" >https://www.kybernetika.cz/content/2022/5/760/paper.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.14736/kyb-2022-5-0760" target="_blank" >10.14736/kyb-2022-5-0760</a>

Jazyk výsledku

angličtina

Název v původním jazyce

TOLERANCE PROBLEMS FOR GENERALIZED EIGENVECTORS OF INTERVAL FUZZY MATRICES

Popis výsledku v původním jazyce

Fuzzy algebra is a special type of algebraic structure in which classical addition and multiplication are replaced by maximum and minimum (denoted circle plus and circle times, respectively). The eigenproblem is the search for a vector x (an eigenvector) and a constant lambda (an eigenvalue) such that A circle times x = lambda circle times x, where A is a given matrix. This paper investigates a generalization of the eigenproblem in fuzzy algebra. We solve the equation A circle times x = lambda circle times B circle times x with given matrices A;B and unknown constant lambda and vector x. Generalized eigenvectors have interesting and useful properties in the various computational tasks with inexact (interval) matrix and vector inputs. This paper studies the properties of generalized interval eigenvectors of interval matrices. Three types of generalized interval eigenvectors: strongly tolerable generalized eigenvectors, tolerable generalized eigenvectors and weakly tolerable generalized eigenvectors are proposed and polynomial procedures for testing the obtained equivalent conditions are presented.

Název v anglickém jazyce

TOLERANCE PROBLEMS FOR GENERALIZED EIGENVECTORS OF INTERVAL FUZZY MATRICES

Popis výsledku anglicky

Fuzzy algebra is a special type of algebraic structure in which classical addition and multiplication are replaced by maximum and minimum (denoted circle plus and circle times, respectively). The eigenproblem is the search for a vector x (an eigenvector) and a constant lambda (an eigenvalue) such that A circle times x = lambda circle times x, where A is a given matrix. This paper investigates a generalization of the eigenproblem in fuzzy algebra. We solve the equation A circle times x = lambda circle times B circle times x with given matrices A;B and unknown constant lambda and vector x. Generalized eigenvectors have interesting and useful properties in the various computational tasks with inexact (interval) matrix and vector inputs. This paper studies the properties of generalized interval eigenvectors of interval matrices. Three types of generalized interval eigenvectors: strongly tolerable generalized eigenvectors, tolerable generalized eigenvectors and weakly tolerable generalized eigenvectors are proposed and polynomial procedures for testing the obtained equivalent conditions are presented.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

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

Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Kybernetika

ISSN

0023-5954

e-ISSN

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Svazek periodika

58

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

19

Strana od-do

760-778

Kód UT WoS článku

000920480300007

EID výsledku v databázi Scopus

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