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arXiv · 1408.6774

Tropical linear algebra with the Lukasiewicz T-norm

Martin Gavalec·Zuzana Nemcova·Sergei Sergeev
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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.

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Martin Gavalec, Zuzana Nemcova, Sergei Sergeev. 2014-10-31. Tropical linear algebra with the Lukasiewicz T-norm. https://doi.org/10.1016/j.fss.2014.11.008

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