Strong Tolerance and Strong Universality of Interval Eigenvectors in a Max-Lukasiewicz Algebra

Abstract

The investigation of the steady states in a discrete events system (DES) leads to the study of the eigenvectors of the transition matrix in the corresponding max-algebra. In real systems, the input values are usually taken to be in some interval. This paper is oriented to the investigation of strong, strongly tolerable, and strongly universal interval eigenvectors in a max-Łukasiewicz algebra. The main method used in this paper is based on max-Ł linear combinations of matrices and vectors. Necessary and sufficient conditions for the recognition of strongly tolerable, and strongly universal eigenvectors have been found. The theoretical results are illustrated by numerical examples.