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

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.