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 · 2023
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 maxplus 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.