Controllable and tolerable generalized eigenvectors of interval max-plus matrices

Title:

Controllable and tolerable generalized eigenvectors of interval max-plus matrices

Creator:

Gazda, Matej and Plavka, Ján

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:b64f2ff8-7db7-4bd3-aa43-ca0787a6bf41
uuid:b64f2ff8-7db7-4bd3-aa43-ca0787a6bf41
doi:10.14736/kyb-2021-6-0922

Subject:

interval generalized eigenvector and fuzzy matrix

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

By max-plus algebra we mean the set of reals R equipped with the operations a⊕b=max{a,b} and a⊗b=a+b for a,b∈R. A vector x is said to be a generalized eigenvector of max-plus matrices A,B∈R(m,n) if A⊗x=λ⊗B⊗x for some λ∈R. The investigation of properties of generalized eigenvectors is important for the applications. The values of vector or matrix inputs in practice are usually not exact numbers and they can be rather 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 controllable, the tolerable and the strong generalized eigenproblem in max-plus algebra are presented. As a consequence of the obtained results, efficient algorithms for checking equivalent conditions are introduced.

Language:

English

Rights:

http://creativecommons.org/licenses/by-nc-sa/4.0/
policy:public

Coverage:

922-938

Source:

Kybernetika | 2021 Volume:57 | Number:6

Harvested from:

CDK

Metadata only:

false