Regularity of interval fuzzy matrices

Max-min (fuzzy) algebra is applied to various problems related to optimization, modeling of discrete dynamic systems, cluster analysis and is used for designing some graph-theoretical algorithms, also for the computations of the optimization problems such as scheduling in which the objective function depends on the matrix operations maximum and minimum.The columns of a matrix A are strongly independent if the max-min (fuzzy) linear system A circle times x = b has a unique solution for at least one vector b. A square matrix A with strongly linearly independent columns is called strongly regular. The investigation of properties of strongly regular interval matrices is important for the applications.The paper deals with the analysis of three versions of the strong regularity of interval matrices, i.e., universal strong regularity, possibly strong regularity and EA/AE strong regularity. For each concept of strong regularity we will present equivalent conditions and polynomial algorithms for their checking.(c) 2023 Elsevier B.V. All rights reserved.