Generalized eigenproblem of interval max-min (fuzzy) matrices.

In this paper we consider the generalized eigenproblem in max-min (fuzzy) algebra, i.e. given matrices A , B find a vector x and a constant λ such that A x = λ B x where the standard pair of operations, plus and times, have been replaced by the operations maximum and minimum. The entries of the vector or matrix are, in practice, usually not exact numbers and can rather be considered as values in some intervals. In this paper the properties of matrices and vectors with inexact (interval) entries are studied and complete solutions of the strong, the universal, the L-controllable and the R-controllable generalized eigenproblems in max-min (fuzzy) algebra are presented. As a consequence of the obtained results, efficient algorithms for checking all equivalent conditions are introduced. [ABSTRACT FROM AUTHOR]