Geodesic
Interval multi-linear systems for tensors in the max-plus algebra and their application in solving the job shop problem
Kybernetika, Tome 58 (2022) no. 5, pp. 708-732

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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.
DOI : 10.14736/kyb-2022-5-0708
Classification : 15A06, 15A69, 15A80, 65G30
Keywords: interval tensor; max-plus algebra; multi-linear systems; weak solvability; job shop problem 
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     title = {Interval multi-linear systems for tensors in the max-plus algebra and their application in solving the job shop problem},
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Khaleghzade, Sedighe; Zangiabadi, Mostafa; Peperko, Aljoša; Hajarian, Masoud. Interval multi-linear systems for tensors in the max-plus algebra and their application in solving the job shop problem. Kybernetika, Tome 58 (2022) no. 5, pp. 708-732. doi: 10.14736/kyb-2022-5-0708

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