Eigenspace structure of a max-drast fuzzy matrix

Abstract

The structure of the eigenspace of a given fuzzy matrix is considered in a specific max-t-norm algebra, called max-drast algebra, where the least t-norm (often called drastic) is used. Necessary and sufficient conditions are presented under which the monotone eigenspace (the set of all monotone eigenvectors) of a given matrix is non-empty and, in the positive case, the structure of the monotone eigenspace is described. These structural results are then extended to the whole eigenspace using permutations of rows and columns. The work is a follow up to earlier works of the authors in which the eigenspace of a max–min fuzzy matrix and/or the eigenspace of a max-Łukasiewicz fuzzy matrix has been described as a union of intervals.