Fuzzy Sets and Systems, volume 410, pages 27-44
Generalized eigenproblem of interval max-min (fuzzy) matrices
1
Department of Mathematics and Theoretical Informatics, Technical University, Nemcovej 32, 04200 Košice, Slovakia
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Publication type: Journal Article
Publication date: 2021-05-01
Journal:
Fuzzy Sets and Systems
Q1
Q1
SJR: 1.009
CiteScore: 6.5
Impact factor: 3.2
ISSN: 01650114, 18726801
Artificial Intelligence
Logic
Abstract
In this paper we consider the generalized eigenproblem in max-min (fuzzy) algebra, i.e. given matrices A , B find a vector x and a constant λ such that A x = λ B x where the standard pair of operations, plus and times, have been replaced by the operations maximum and minimum. The entries of the vector or matrix are, in practice, usually not exact numbers and can rather be considered as values in some intervals. In this paper the properties of matrices and vectors with inexact (interval) entries are studied and complete solutions of the strong, the universal, the L-controllable and the R-controllable generalized eigenproblems in max-min (fuzzy) algebra are presented. As a consequence of the obtained results, efficient algorithms for checking all equivalent conditions are introduced.
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Plávka J., Gazda M. Generalized eigenproblem of interval max-min (fuzzy) matrices // Fuzzy Sets and Systems. 2021. Vol. 410. pp. 27-44.
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Plávka J., Gazda M. Generalized eigenproblem of interval max-min (fuzzy) matrices // Fuzzy Sets and Systems. 2021. Vol. 410. pp. 27-44.
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TY - JOUR
DO - 10.1016/j.fss.2020.09.006
UR - https://doi.org/10.1016/j.fss.2020.09.006
TI - Generalized eigenproblem of interval max-min (fuzzy) matrices
T2 - Fuzzy Sets and Systems
AU - Plávka, Ján
AU - Gazda, Matej
PY - 2021
DA - 2021/05/01
PB - Elsevier
SP - 27-44
VL - 410
SN - 0165-0114
SN - 1872-6801
ER -
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@article{2021_Plávka,
author = {Ján Plávka and Matej Gazda},
title = {Generalized eigenproblem of interval max-min (fuzzy) matrices},
journal = {Fuzzy Sets and Systems},
year = {2021},
volume = {410},
publisher = {Elsevier},
month = {may},
url = {https://doi.org/10.1016/j.fss.2020.09.006},
pages = {27--44},
doi = {10.1016/j.fss.2020.09.006}
}