Interval Max-drast Systems of Linear Equations

Max-drast algebra uses instead of conventional operations for addition and multiplication of vectors and matrices the operations maximum and one of the triangular norms, the drastic norm, respectively. Transition matrices in maxdrast algebra and their power sequences occur in describing complex fuzzy systems in which extreme demands are put on the reliability of the system. Many practical problems lead to solving systems of linear equations, which are given by transition matrix A and right-hand side vector b of suitable size. However, in practice we deal often with inexact input data. This leads to the requirement to replace the scalar matrices and vectors with so-called interval matrices and vectors. We can define several types of solvability of interval systems. In this paper, we shall deal with the weak, control and tolerance solvability of interval max-drast systems of linear equations. We give necessary and sufficient conditions for each of them.