(K,L)-eigenvectors in max-min algebra

TL;DR

This paper introduces the concept of (K,L)-eigenvectors in max-min algebra to explicitly characterize the structure of the eigenspace associated with a given eigenvalue, enhancing understanding of max-min algebraic systems.

Contribution

It develops a new theoretical framework for (K,L)-eigenvectors in max-min algebra, providing explicit descriptions of the eigenspace structure based on order relations.

Findings

Explicit description of max-min eigenspace structure

Partitioning of eigenspace into regions based on order relations

Extension of fundamental max-min algebra results

Abstract

Using the concept of (K,L)-eigenvector, we investigate the structure of the max-min eigenspace associated with a given eigenvalue of a matrix in the max-min algebra (also known as fuzzy algebra). In our approach, the max-min eigenspace is split into several regions according to the order relations between the eigenvalue and the components of x. The resulting theory of (K,L)-eigenvectors, being based on the fundamental results of Gondran and Minoux, allows to describe the whole max-min eigenspace explicitly and in more detail.