The max-?ukasiewicz semiring is defined as the unit interval [0, 1] equipped with the arithmetics ââ?¬Å?a + bââ?¬Â = max(a, b) and\nââ?¬Å?abââ?¬Â = max(0, a + b ? 1). Linear algebra over this semiring can be developed in the usual way. We observe that any problem of\nthe max-?ukasiewicz linear algebra can be equivalently formulated as a problem of the tropical (max-plus) linear algebra. Based\non this equivalence, we develop a theory of the matrix powers and the eigenproblem over the max-?ukasiewicz semiring.
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