arXiv subjects

Martin Gavalec

Publications and source records attributed to Martin Gavalec.

2 recordsLinked to original sources

arXiv2018

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

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.

math.RA↗

arXiv2014

Tropical linear algebra with the Lukasiewicz T-norm

The max-Lukasiewicz semiring is defined as the unit interval [0,1] equipped with the arithmetics "a+b"=max(a,b) and "ab"=max(0,a+b-1). Linear algebra over this semiring can be developed in the usual way. We observe that any problem of the max-Lukasiewicz linear algebra can be equivalently formulated as a problem of the tropical (max-plus) linear algebra. Based on this equivalence, we develop a theory of the matrix powers and the eigenproblem over the max-Lukasiewicz semiring.

math.CO↗