Consider a linear system of equations with interval coefficients, and each
interval coefficient is associated with either a universal or an existential
quantifier. The AE solution set and AE solvability of the system is defined by
∀∃-quantification.
Herein, we deal with the problem what properties must the coefficient matrix
have in order that there is guaranteed an existence of an AE solution. Based on
this motivation, we introduce a concept of AE regularity, which implies that
the AE solution set is nonempty and the system is AE solvable for every
right-hand side. We discuss characterization of AE regularity, and we also
focus on various classes of matrices that are implicitly AE regular. Some of
these classes are polynomially decidable, and therefore give an efficient way
for checking AE regularity. We also state open problems related to
computational complexity and characterization
