(K,L) eigenvectors in max-min algebra

Martin Gavalec; Zuzana Němcová; Sergey Sergeev

doi:10.1016/j.fss.2020.07.008

(K,L) eigenvectors in max-min algebra

Martin Gavalec, Zuzana Němcová, Sergey Sergeev^*

^*Corresponding author for this work

Mathematics

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Abstract

Using the concept of (K,L)-eigenvector, we investigate the structure of the max-min eigenspace associated with a given eigenvalue of a matrix in the max-min algebra (also known as fuzzy algebra). In our approach, the max-min eigenspace is split into several regions according to the order relations between the eigenvalue and the components of x. The resulting theory of (K,L)-eigenvectors, being based on the fundamental results of Gondran and Minoux, allows to describe the whole max-min eigenspace explicitly and in more detail.

Original language	English
Pages (from-to)	75-89
Number of pages	15
Journal	Fuzzy Sets and Systems
Volume	410
Early online date	17 Jul 2020
DOIs	https://doi.org/10.1016/j.fss.2020.07.008
Publication status	Published - 1 May 2021

Bibliographical note

Funding Information:
Supported by the Czech Science Foundation grant #18-01246S.Supported by EPSRC grant EP/P019676/1.

Publisher Copyright:
© 2020

Keywords

Eigenvector
Fuzzy algebra
Max-min

ASJC Scopus subject areas

Logic
Artificial Intelligence

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10.1016/j.fss.2020.07.008

GavalecM2020eigenvectorsAccepted author manuscript, 1.94 MBLicence: Creative Commons: Attribution-NonCommercial-NoDerivs (CC BY-NC-ND)

Tropical Optimisation
Sergeev, S.
Engineering & Physical Science Research Council
1/04/17 → 31/08/19
Project: Research Councils

Cite this

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abstract = "Using the concept of (K,L)-eigenvector, we investigate the structure of the max-min eigenspace associated with a given eigenvalue of a matrix in the max-min algebra (also known as fuzzy algebra). In our approach, the max-min eigenspace is split into several regions according to the order relations between the eigenvalue and the components of x. The resulting theory of (K,L)-eigenvectors, being based on the fundamental results of Gondran and Minoux, allows to describe the whole max-min eigenspace explicitly and in more detail.",

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AU - Němcová, Zuzana

AU - Sergeev, Sergey

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JO - Fuzzy Sets and Systems

JF - Fuzzy Sets and Systems

ER -

(K,L) eigenvectors in max-min algebra

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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Projects

Tropical Optimisation

Cite this