Interval Eigenproblem in Max-Min Algebra

Abstract

The eigenvectors of square matrices in max-min algebra correspond to steady states in discrete events system in various application areas, such as design of switching circuits, medical diagnosis, models of organizations and information systems. Imprecise input data lead to considering interval version of the eigenproblem, in which interval eigenvectors of interval matrices in max-min algebra are investigated. Six possible types of an interval eigenvector of an interval matrix are introduced, using various combination of quantifiers in the definition. The previously known characterizations of the interval eigenvectors were restricted to the increasing eigenvectors, see [11]. In this chapter, the results are extended to the non-decreasing eigenvectors, and further to all possible interval eigenvectors of a given max-min matrix. Classification types of general interval eigenvectors are studied and characterization of all possible six types is presented.