Interval two-sided (max, min)-linear equations

Practical problems related to scheduling optimization, modeling of fuzzy discrete dynamic systems and fuzzy analysis in which the objective function depends on the operations maximum and minimum, can be formulated and solved in max-min algebra. Systems of discrete events are obviously described by max-min linear equations. In particular, if the system is in a synchronization process, then its state is characterized by a solution of the corresponding two sided linear system. In reality, the entries of matrices and vectors are considered as intervals. The paper deals with the solvability of interval systems of two-sided (max,min)-linear equations depending on the used forall and exists quantifiers and provide the equivalent conditions for a solvability. The results are illustrated by numerical examples.