Bideterminants and balanced interval max-plus matrices

The study of discrete event dynamic systems with inexact (interval) data plays an important role in optimization problems such as scheduling or project management in which the objective function depends on the interval data and the maximum and plus operations. This approach is based on the formalism and characteristics of max-plus balanced matrices, balanced determinants, and Hankel matrices as their properties are key in modeling discrete event dynamic systems. This article deals with the generalization of balanced max-plus matrices and two basic versions of balanced matrices with interval entries, i.e. universally and possibly balanced matrices, and two other versions derived from them, namely EA-balanced and AE-balanced circulant-Hankel interval matrices. For each concept of circulant-Hankel interval matrices, we present polynomially checking equivalent conditions.