Interval multi-linear systems for tensors in the max-plus algebra and their application in solving the job shop problem

Sedighe Khaleghzade; Mostafa Zangiabadi; Aljoša Peperko; Masoud Hajarian

Kybernetika (2022)

  • Volume: 58, Issue: 5, page 708-732
  • ISSN: 0023-5954

Abstract

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In this paper, we propose the notions of the max-plus algebra of the interval tensors, which can be used for the extension of interval linear systems to interval multi-linear systems in the max-plus algebra. Some properties and basic results of interval multi-linear systems in max-plus algebra are derived. An algorithm is developed for computing a solution of the multi-linear systems in the max-plus algebra. Necessary and sufficient conditions for the interval multi-linear systems for weak solvability over max-plus algebra are obtained as well. Also, some examples are given for illustrating the obtained results. Moreover, we briefly sketch how our results can be used in the max-plus algebraic system theory for synchronized discrete event systems.

How to cite

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Khaleghzade, Sedighe, et al. "Interval multi-linear systems for tensors in the max-plus algebra and their application in solving the job shop problem." Kybernetika 58.5 (2022): 708-732. <http://eudml.org/doc/299448>.

@article{Khaleghzade2022,
abstract = {In this paper, we propose the notions of the max-plus algebra of the interval tensors, which can be used for the extension of interval linear systems to interval multi-linear systems in the max-plus algebra. Some properties and basic results of interval multi-linear systems in max-plus algebra are derived. An algorithm is developed for computing a solution of the multi-linear systems in the max-plus algebra. Necessary and sufficient conditions for the interval multi-linear systems for weak solvability over max-plus algebra are obtained as well. Also, some examples are given for illustrating the obtained results. Moreover, we briefly sketch how our results can be used in the max-plus algebraic system theory for synchronized discrete event systems.},
author = {Khaleghzade, Sedighe, Zangiabadi, Mostafa, Peperko, Aljoša, Hajarian, Masoud},
journal = {Kybernetika},
keywords = {interval tensor; max-plus algebra; multi-linear systems; weak solvability; job shop problem},
language = {eng},
number = {5},
pages = {708-732},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Interval multi-linear systems for tensors in the max-plus algebra and their application in solving the job shop problem},
url = {http://eudml.org/doc/299448},
volume = {58},
year = {2022},
}

TY - JOUR
AU - Khaleghzade, Sedighe
AU - Zangiabadi, Mostafa
AU - Peperko, Aljoša
AU - Hajarian, Masoud
TI - Interval multi-linear systems for tensors in the max-plus algebra and their application in solving the job shop problem
JO - Kybernetika
PY - 2022
PB - Institute of Information Theory and Automation AS CR
VL - 58
IS - 5
SP - 708
EP - 732
AB - In this paper, we propose the notions of the max-plus algebra of the interval tensors, which can be used for the extension of interval linear systems to interval multi-linear systems in the max-plus algebra. Some properties and basic results of interval multi-linear systems in max-plus algebra are derived. An algorithm is developed for computing a solution of the multi-linear systems in the max-plus algebra. Necessary and sufficient conditions for the interval multi-linear systems for weak solvability over max-plus algebra are obtained as well. Also, some examples are given for illustrating the obtained results. Moreover, we briefly sketch how our results can be used in the max-plus algebraic system theory for synchronized discrete event systems.
LA - eng
KW - interval tensor; max-plus algebra; multi-linear systems; weak solvability; job shop problem
UR - http://eudml.org/doc/299448
ER -

References

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