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.Comment: 27 page

Gavalec, Martin

Nemcova, Zuzana

Sergeev, Sergei

English

arXiv

The max-Łukasiewicz 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-Łukasiewicz 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-Łukasiewicz semiring

Němcová, Zuzana

Sergeev, Sergey

University of Birmingham Research Portal

Tropical linear algebra with the Łukasiewicz T-norm

AbstractThe max-Łukasiewicz 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-Łukasiewicz 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-Łukasiewicz semiring

Sergeev, Sergeĭ

Elsevier - Publisher Connector 

Tropical linear algebra with the Łukasiewicz T-norm 

arXiv.org e-Print Archive