Tropical linear algebra with the Lukasiewicz T-norm

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.

27 pages

References in corpus (3)

• The Minkowski Theorem for Max-plus Convex Sets
• Tropical linear-fractional programming and parametric mean payoff games
• Min-plus methods in eigenvalue perturbation theory and generalised Lidskii-Vishik-Ljusternik theorem

Cited by in corpus (2)

• Application of tropical optimization for solving multicriteria problems of pairwise comparisons using log-Chebyshev approximation
• (K,L)-eigenvectors in max-min algebra