Tropical linear algebra with the Łukasiewicz T-norm

Martin Gavalec, Zuzana Němcová, Sergey Sergeev

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8 Citations (Scopus)
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Abstract

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.
Original languageEnglish
Pages (from-to)131-148
JournalFuzzy Sets and Systems
Volume276
Early online date12 Nov 2014
DOIs
Publication statusPublished - 1 Oct 2015

Keywords

  • Matrix power
  • Tropical
  • Max-plus
  • Łukasiewicz
  • Eigenvector

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