Tropical linear algebra with the Lukasiewicz T-norm
Combinatorics
2022-07-11 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1408.6774,
title = {Tropical linear algebra with the Lukasiewicz T-norm},
author = {Martin Gavalec and Zuzana Nemcova and Sergei Sergeev},
journal= {arXiv preprint arXiv:1408.6774},
year = {2022}
}
Comments
27 pages